The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.
What is polynomials?A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.
Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).
To find the difference between
(9x² + 8x) - (2x² + 3x)
We do calculation
= 9x² + 8x - 2x² - 3x
= 9x² - 2x² + 8x - 3x
= 7x² + 5x
Thus, the difference between the polynomials is 7x² + 5x.
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GIVEN: GH (congruent JH and FH (congruent) HI
PROVE: FG (congruent) IJ
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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Charlotte has a loyalty card good for a 14% discount at her local grocery store. If the total cost, before tax and discount, of all the items she wants to buy is c, which expression represents the cost after the discount?
The expression that represents the cost after the discount is
y(c) = (7/50)c
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Charlotte has a loyalty card good for a 14% discount at her local grocery store.
Let the total cost, before tax and discount, of all the items she wants to buy is {c}. Now, let the expression that represents the cost after the discount is given by y(c). We can write -
y(c) = 14% of c
y(c) = (14/100) x c
y(c) = (7/50)c
Therefore, the expression that represents the cost after the discount is
y(c) = (7/50)c.
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Rewrite in simplest rational exponent form. Show each step of your process
The final answer is 4x, which is the simplest form of expression.
What is the rational exponent?
A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.
To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:
4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)
x^(1) = x
So, the expression in simplest rational exponent form is 4x
x * 4x = 4x
Notice that 4 and x are in the same radical which means 4 is a coefficient of x.
Therefore, 4√x * √x can be written as 4x, which is in the simplest form.
hence, the final answer is 4x, which is the simplest form of expression.
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Liliana used 444 dark power crystals to raise 141414 zombie soldiers. She wants to know how many zombie soldiers (z)(z)(, z, )she can raise with 101010 dark power crystals. How many zombie soldiers can Liliana raise with 101010 power crystals
On solving the provided question, we can say that by unitary method With ten power crystals, 35 zombie troops can be raised.
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Liliana raised 14 zombie troops with the help of four dark power stones.
Zombie troops can be increased to a total of 14 with 4 Dark power crystals. Zombies can be raised with 1 Dark power crystal, or 14/4.
Zombie soldiers can be raised using 1 Dark power crystal, or 7/2.
Zombie troops can be generated with 1 Dark power crystal by adding 10 to 7/2. You can produce 5 * 7 zombie troops with 1 Dark power crystal.
35 zombie troops can be generated with 1 dark power crystal.
With ten power crystals, 35 zombie troops can be raised.
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There are 5,280 feet in a mile. Round answers
nany miles does a car traveling at 65 mi/h.
b. How many feet does a car traveling at 65 mil
c How many feet does a car traveling at 65 mi/h
d. How many feet does a car traveling at 65 mi/h o
3. There are 5,280 feet in a mile. Round answers t o
nswers to the nearestur
5 mi/h go in one hour
+ 65 mi/h go in one hour]
65 mi/h go in one minute
+ 65 mi/h go in one second?
343200 fts distance travelled in an hour
5720 ft was travelled in 1 minute and,
95.33 ft distance was travelled in 1 second.
What is miles and foot ?The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles.
The British imperial and American customary systems of measurement both use the foot as a unit of length, denoted by the standard symbol: ft. An other sign that is frequently used is the prime symbol, ′. One foot is precisely equal to 0.3048 meters as of the International Yard and Pound Agreement of 1959.
5,280 feet per mile, sometimes known as a statute mile, is a unit of measurement (1.609 km). It derives from the mille passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.
65 miles per hour
so 65 * 5280 = 343200 ft travelled in 1 hr
in one minute distance travelled = 343200/60 = 5720 fts
and in one second distance travelled = 5720/60 = 95.33 fts.
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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When the four - digit numeral is divisible by nine is given by 3AA1 the digit A represents 7
Properties of numbers divisible by 9A number itself is divisible by 9 if its digit's sum is also divisible by 9.
In mathematics, multiples are the results of multiplying an integer by a given number. number divisible by 9 is multiple of 9
using the above property we have that
3 + A + A + 1 = 9, OR 18, OR 27
4 +2A = 9, OR 18, OR 27
assuming 18
2A = 18 - 4
2A = 14
A = 7
hence the number is 3771
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Which of the following statements is not equivalent to the others?
16-34
|34 -16|
34-16
|16 -34
Answer:
the one that is not equivalent to the others would be 116-34
Step-by-step explanation:
because its 116 and the others dont have anything to do with 116 :)
Answer: The statement that is not equivalent should be D. |16-34
Before sending track and field athletes to the Olympics, the U. S. Holds a qualifying meet. The upper box plot shows the top 12 men's long jumpers at the U. S. Qualifying meet. The lower box plot shows the distances (in meters) achieved in the men's long jump at the 2012 Olympic games. Which pieces of information can be gathered from these box plots?
We require median, interquartile range, outliers, minimum and maximum value.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:
The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.
From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:
The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.
The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.
Hence, we require median, interquartile range, outliers, and minimum and maximum values.
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We require median, interquartile range, outliers, and minimum and maximum values.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:
The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.
From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:
The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.
The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.
Hence, we require median, interquartile range, outliers, and minimum and maximum values.
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Solve this problem
Step by step
Answer:
√259 or 16.09
Step-by-step explanation:
Hello!
I'll be labeling the vertices so that it is easier to understand the sides.
These are both right triangles, and we can find the measures of right triangles (given two other sides) by using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenuse (leg opposite to 90°)In Triangle BCD, we have the measures of the hypotenuse and a leg. We can use that to find the missing side: CB
Since DB is the hypotenuse, it would be side c, and we can say that CD can be side a.
Solve for CB:[tex]a^2 + b^2 = c^2[/tex][tex]10^2 + b^2 = 25^2[/tex][tex]100 + b^2 = 625[/tex][tex]b^2 = 525[/tex][tex]b = 5\sqrt21[/tex]CB in simplest radical form is 5√21.
We can now solve for x, because now in triangle ABC, we have the measures of two sides: hypotenuse AC and leg CB.
Solve for AB:[tex]a^2 + b^2 = c^2[/tex][tex](5\sqrt{21})^2 + b^2 = 28^2[/tex][tex]525 + b^2 = 784[/tex][tex]b^2 = 259[/tex][tex]b = \sqrt{259}[/tex]AB in simplest radical form is √259, which is approximately 16.09.
The solution for x is √259 or 16.09.
plsss answer for brainliest
Answer:
answer is below
Step-by-step explanation:
1.
Two lines from right angles.
The lines are perpendicular
2.
x + 20 = 32
x =12
3.
You are a third year high school student.
You are a junior high school student.
4.
An angle measures 20°.
The angle is acute.
5.
A figure is square.
The figure is quadrilateral.
Saad yearly income is rs 236000.How much income tax he paid
Saad's income tax will be N.I.L.
Here, saad's yearly income is Rs 2,36,000.
The rate of income tax on his income will be nil because,
INCOME TAX RATE
0-2,50,000 NIL
2,50,000-5,00,000 5%
5,00,001-10,00,000 20%
More than 10,00,000 30%
Computation of tax liability of Saad
Tax on 1st 2,36,000 = N.I.L
As his income is less than 2,50,000 no income tax shall be charged to saad's income.
Therefore, the tax liability of saad would be 0.
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If AnB= {2,4}
AnB'= {0,1}
AUB= {0,1,2,3,4,5}, Then what is B\A?
Answer:
I don't know I'm just a grade 6 girl
Select the correct answer.
What is the reaction quotient for the following reaction; AB + 2C?
Q = [B][C], ²
[A].
OA.
OB.
O C. Q=
Q = BIC
[A].
OD. Q=
[A]
[B].[C].2
[A],
[B]. [C].
Slope Sales will be $-159.474 at 0 degrees Celsius, which is nonsensical to understand.
what is slope?A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
given information,
Temperature=20 egression equation,
[tex]sales= 442.284\\ Slope=$ 30.0879[/tex]
temperature increases by 1 degree
$30.0879, on average.
[tex]y-intercept= -159.474[/tex]
At 0 degree celsius of temperature, Sales will be [tex]$-159.474[/tex]which is meaningless to interpret.
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For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8. 25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0. 8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
The school is 24.63 meters tall.
To calculate the height of the school, Elijah can use the concept of similar triangles. Since the mirror is on the ground and parallel to it, the angle between the ground and the line from his eyes to the mirror is 90 degrees. The angle between the ground and the line from his eyes to the top of the school is also 90 degrees. The triangle formed by these lines and the line from his eyes to the top of the school is similar to the triangle formed by these lines and the line from his eyes to the mirror.
Using the similar triangles, the ratio of the height of the school to the distance from Elijah's eyes to the mirror is equal to the ratio of the distance from Elijah's eyes to the ground to the distance from the mirror to the school.
Therefore
(Height of school) / (Distance from eyes to mirror) = (Distance from eyes to ground) / (Distance from mirror to school)
Plug in the given values:
(Height of school) / 0.8 = 1.45 / (8.25 - 0.8)
Solving for the height of the school:
Height of school = (0.8 * 1.45) / (8.25 - 0.8)
= 1.16 / 7.45
= 0.1562
= 24.63 meters
The school is 24.63 meters tall.
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Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn
$21 (3 x 7 = 21).
If she works 5 hours, she would earn
$35 (5 x 7 = 35).
If she works 8 hours, she would earn
$56 (8 x 7 = 56).
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Operation with parenthee ,5 number , two different operation and ha a value of 20
The equation is (5 x 2) - (5 + 5) = 20
The given equation can be solved by performing the operations within the parentheses first.
First, 5 x 2 = 10, then 5 + 5 = 10.
Then, the next step is to subtract the second set of parentheses from the first set, 10 - 10 = 0.
Finally, we can see that 0 + 20 = 20.
In this equation, the operation of multiplication and addition are used and the final value is 20.
The equation is (5 x 2) - (5 + 5) = 20
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Complete Question is -
solve the following mathematical operation that involves parentheses, five numbers, two different operations and has a value of 20?
Solve the following system of equations graphically on the set of axes below.
y= x-2
y=x−2
y= -3x-6
y=−3x−6
The solution of the equation is x = -1 and y = -3.
And the intersection point is (-1, -3).
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.
And simultaneous equation is the system of equation.
Given system of equations:
y = x-2 ...... equation 1
y = −3x−6 ...... equation 2
To solve the system of equations:
Substitute the value of y from the equation 1 to equation 2,
we get,
x - 2 = -3x - 6
x + 3x = -6 + 2
4x = -4
x = -1
Then y = -1 -2 = -3.
By graphically:
1). Draw the linear equation on the graph.
2). And the intersection point of the lines is a solution of the equation.
3). The solution is x = -1 and y = -3.
The complete graph is given in the attached image.
Therefore, the solution is x = -1 and y = -3.
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What is the value of tan θ?
The value of tan 1 is 45 degree.
tangent is the trigonometric ratio.
we can find out the value of tangent by taking opposite side of the theta angle divided by the adjacent side of the theta angle.
tan Q = perpendicular of triangle /base of triangle.
sine theta divided by cos theta gives the value of tan theta.
tan Q = sin Q/ cos Q.
some formula of the tan Q are as follows,
1- tan Q = sin Q/cos Q
2- tan Q= 1 /cot Q
3-tan^2 Q =sec^2 Q -1
4- tan(90 - Q)=cot Q
5- tan (Q+π)=tan Q
6- tan (π-Q)=-tan Q
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Quadrilateral ABCD below is reflected about line m. After the reflection, how is the perimeter of A'B'C'D' related to the perimeter of ABCD?
Quadrilateral ABCD below is rotated 180°. After the rotation, how is the area of A'B'C'D' related to the area of ABCD?
Reflection and rotation will not alter the perimeter of the quadrilateral
What is transformation?
Transformation is a term used in mathematics to refer to the movements made by objects.
Transformations has basically classifications
non rigid transformationRigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation
In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are
rotationreflectiontranslationBecause the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved
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If you deposit $8,000 into an account paying 6% simple interest, how long until there is $13,000 in the account? Round to the nearest
tenth
• The balance of the account will be $13,000, in
years.
After 10 years the balance of the account will be $13000.
What is simple interest?
A simple interest is one that does not compound anyway. In this system, a creditor only pay interest on the initial amount and the rate of interest is not changed during the time period.
How many years needed to reach the required amount?
given, initial deposit money = initial principal amount = $8000
initial money is denoted by P
interest rate (annually), r = 6%
generally, simple interest is annual.
expected amount after t years = final amount = $13000
final amount is denoted by A.
t is the time in years.
According to the formula for simple interest, A = P (1 + rt)
$13000 = $8000(1 + 6/100×t)
$13000/ $8000 = (1 + 0.06t)
(1 + 0.06t) = 1.625
0.06t = 0.625
t = 10.417 years or t = 10 years
Therefore, after 10 years the balance of the account will be $13000.
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why is the product of the circumradius and the area of the triangle equal to the product of the sides of the triangle
Answer:
It isn't.
The correct relation is 4r·Area = abc.
Step-by-step explanation:
You want to show the relation between the product of triangle side lengths and the product of the triangle area and the radius of the circumcircle.
Triangle areaThe area of the triangle in the attached diagram can be found by ...
Area = 1/2(bc)sin(α)
Side lengthThe inscribed angle theorem tells you the measure of the arc subtended by an inscribed angle is twice the measure of the inscribed angle. That means the opposite chord will be twice the length of the product of the radius and the inscribed angle value:
a = 2r·sin(α)
Circumradius productThe product of the circumradius and the area of the triangle is ...
r·Area = r·(1/2)(bc)sin(α) = 1/4(bc)(2r·sin(α)) = 1/4abc
Without the fractions, the relation is ...
4r·Area = abc
__
Additional comment
As a simple example, consider a 3-4-5 right triangle. The area of the triangle is ...
A = 1/2(3)(4) = 6
The circumradius is half the length of the hypotenuse, r = 5/2.
The relation of interest is ...
4r·Area = abc
4(5/2)(6) = 3·4·5
60 = 60 . . . . . . . . . . as expected
This could be a very simple way to find the circumradius of a triangle.
Answer the following questions:
1. a. 126 ÷ 12
b. 217 ÷ 4
c. 75 ÷ 6
d. 11 ÷ 9
e. 200 ÷ 35
2. a. Determine whether the quotient of 7 ÷ 2.2 is a terminating or nonterminating, repeating decimal.
b. Find out if the quotient of 0.5 ÷ 0.12 is a terminating or nonterminating, repeating decimal.
c. Which of these has a quotient that is a nonterminating, repeating decimal:
3 ÷ 0.8, 9 ÷ 0.16 or 2 ÷ 2.7?
d. Mr. Pelaez wants to divide his 1.3 hectares of land among his three children. How much land will each child get?
3. Identify if each resulting quotient is a terminating or nonterminating, repeating
decimal.
a. 2 ÷ 3
b. 5 ÷ 1.2
c. 0.3 ÷ 0.9
d. 2.4 ÷ 1.8
4. In a feeding activity, the teacher used 1.25 kilograms of ground pork to make 30 pieces of hamburger patties. How much meat was there in one piece of hamburger?
1. The quotients of the following division operations are as follows:
a) 126 ÷ 12 is 10.5.
b) 217 ÷ 4 is 54.25.
c) 75 ÷ 6 is 12.5.
d) 11 ÷ 9 is 1.2222.
e) 200 ÷ 35 is 5.7143.
2a) The quotient of 7 ÷ 2.2 is a nonterminating or repeating decimal.
2b) The quotient of 0.5 ÷ 0.12 is a nonterminating or repeating decimal.
2c) The division operation with a quotient that is nonterminating or repeating decimal is 2 ÷ 2.7.
3) The identification of each resulting quotient as a terminating or nonterminating, repeating decimal is as follows:
a. 2 ÷ 3 Nonterminating quotientb. 5 ÷ 1.2 Nonterminating quotientc. 0.3 ÷ 0.9 Nonterminating quotientd. 2.4 ÷ 1.8 Nonterminating quotient.4) The quantity of meat in one piece of hamburger, if they are evenly shared or divided, is 41.67 g.
What is the quotient?The quotient is the result of the division operation.
Every division operation involves the dividend (the numerator), the divisor (the denominator), the division operand (÷), and the equal sign (=).
2)
a) 7 ÷ 2.2 = 3.181818
b) 0.5 ÷ 0.12 = 4.16667
c) 3 ÷ 0.8 = 3.75
9 ÷ 0.16 = 56.25
2 ÷ 2.7 = 0.740740
3)
a. 2 ÷ 3 = 0.6667
b. 5 ÷ 1.2 = 4.16667
c. 0.3 ÷ 0.9 = 0.3333
d. 2.4 ÷ 1.8 = 1.3333
4) Total weight of ground pork = 1.25 kilograms
1 kg = 1,000 g
1.25 kg = 1,250 g
The pieces of patties = 30
The weight of each piece = 41.67 g (1,250/30)
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e:f =2:5 f:g=3:4 work out e:g in simpliest form
After a work out, the simplest form of e:g is 3:10.
What is a ratio?Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.
To work out the simplest form of e:g as required in the question,
e/ f = 2/ 5
2f = 5e ........... 1
f/g = 3/ 4
3g = 4f ........... 2
From equation 1,
f = 5e/2
substitute the value of f in equation 2
3g = 4(5e/2)
3g = 10e
Therefore, e:g is given as;
3/ 10 = e/ g
3:10 = e: g
Thus in its simplest form, e:g = 3:10
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0.5- 2 2/5 = 1/2y +2.4 Please help! Find the value of y! Thanks!
The value of y, given the equation, can be found to be - 8 .6
How to find the value of y ?To find the value of y, first convert the mixed fraction to a decimal for easier calculation :
2 ² / ₅ = 2 + 2 / 5
= 2 + 0. 4
= 2. 4
The equation then becomes :
0. 5 - 2.4 = 1 / 2 y + 2. 4
This can be rewritten as :
0. 5 - 2.4 = 1 / 2 y + 2. 4
0. 5 - 2 . 4 - 2. 4 = 1 / 2 y
1 / 2 y = - 4. 3
y = - 4. 3 / 1 / 2
y = - 8 .6
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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
Therefore , the solution of the given problem of equation comes out to bem² + p² =z².
Equation: What is it?The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.
Here,
Given : a triangle of m,p,z of length of right triangle :
By using Pythagoras theorem :
The relationship comes out to be :
=> m² + p² =z²
Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.
Therefore , the solution of the given problem of equation comes out to be m² + p² =z².
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how do i do this question
Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.
Step-by-step explanation:
The tip of a minute-hand travels 103. 62mm in one hour. Find the length of the minute
hand
Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.
What is circumference of a circle?
The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.
Circumference of circle(C) = 2πR
where,
R represents the radius of the circle
π is a constant with an approximate value of 3.14
Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.
This means that C= 103.62
So, using the concept of circumference of a circle,
C= 2πR
103.62= 2*3.14*R
So, R= 103.62/6.28
R=16.5mm
Hence, the length of the minute hand is 16.5mm.
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Is (1,-2) a solution to this system of equations?
20x+20y=-2
2x+5y=-8
YES OR NO
The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)
What is a system of equations?A system of equations are two (or more) equations that have common variables.
The system of equation is presented as follows;
20·x + 20·y = -2
2·x + 5·y = -8
The specified possible solution of the equation is; (1, -2)
Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;
20·x + 20·y = -2
20·y = -2 - 20·x
y = (-2 - 20·x)/20
Therefore; y = (-2 - 20 × 1)/20 = -1.1
When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2
Evaluating the second equation, we get;
2·x + 5·y = -8
5·y = -8 - 2·x
y = (-8 - 2·x)/5
Plugging in x = 1, we get;
y = (-8 - 2 × 1)/5 = -2
When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation
The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;
y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5
Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5
-10 - 100·x = -160 - 40·x
60·x = 150
x = 150 ÷ 60 = 2.5
x = 2.5
y = (-2 - 20 × 2.5)/20 = -2.6
y = -2.6
The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)Learn more about systems of linear equations here: https://brainly.com/question/11867840
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What is the first step in a 2 step equation?
Answer:Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
Step-by-step explanation:
What is 648 rounded to the nearest ten
Answer: 640
Step-by-step explanation:
1. To help identify what place value to round write out the numbers with their place
the hundreds value in this question is 600
the tens value in this question is 40
and the ones value is 8
Since the questions asks to round to the nearest 10, you would look at the number after 4 and see if it is equal or greater than 5, if so, you would round it up to the next number, which would be 5 and write it like 640.