Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2
3.5 x 4 + 11 x 2.2 = 14 + 24.2
3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.
Using BODMAS,
B-Bracket
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction
Multiplication comes first before addition, so
3.5×4=17
+
11×2.2=24.2
17+24.2=41.2
witch are linear and witch are not linear!?
Step-by-step explanation:
a linear relationship or function is described by
y = ax + b
that means that the difference from one y value to the next is defined by a constant ratio of y diff / x diff.
so, the first one is not linear.
because the difference ratios are not constant :
(1-0)/(1-0) = 1
(4-1)/(2-1) = 3
(9-4)/(3-2) = 5
the second one is linear.
the difference ratios are constant :
(1-0)/(1-0) = 1
(4-1)/(4-1) = 1
(9-4)/(9-4) = 1
the third one is not linear.
the difference ratios are not constant :
(3-1)/(3-2) = 2
(9-3)/(4-3) = 6
(27-9)/(5-4) = 18
the fourth one is linear.
the difference ratios are constant :
(5-1)/(4-2) = 4/2 = 2
(9-5)/(6-4) = 4/2 = 2
(13-9)/(8-6) = 4/2 = 2
The perimeter Of rectangle is 106 cm its length is 2X -1 cm and breath is X +9 cm find its length and breadth
[tex] \longmapsto \: 2(2x - 1 + x + 9) = 103 \\ \\ \longmapsto \: 2(3x + 8) = 106 \\ \\ \longmapsto \: 6x +16 = 106 \\ \\ \longmapsto \: x = \frac{90}{6} \\ \\ \longmapsto \: x = 15 [/tex]
So,
[tex]l = 2 \times 15 - 1 = 29 \\ \\ b = 2 + 15 = 17[/tex]
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the breadth (or width) of the rectangle.
In this case, we know that the perimeter is 106 cm, so we can set up the equation:
106 = 2(l + (X + 9))
106 = 2l + 2X + 18
We also know that the length of the rectangle is 2X - 1, so we can set this equal to l:
2X - 1 = l
Now we have a system of two equations with two unknowns (l and X). We can substitute the value of l from the second equation into the first equation and solve for X:
106 = 2(2X - 1 + (X + 9))
106 = 2(3X + 8)
106 = 6X + 16
90 = 6X
X = 15
Now that we know the value of X, we can substitute it back into the equation for the length of the rectangle to find the length:
l = 2X - 1 = 2(15) - 1 = 29 cm
And then we can use the value of X again to find the breadth:
w = X + 9 = 15 + 9 = 24 cm
So the length of the rectangle is 29 cm and the breadth is 24 cm.
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4. What function represents an absolute value that has a vertex at (-7,-10)?
a. |y-7|-10 3
b. |y+7|+10
c. |y+7|-10
d. -|y+7|+10
More than one applies to the slope.
How is the absolute value function calculated?The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.
The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)
The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.
m = 3
It is steeper than one.
As a result, a scale factor other than 1 has been used to dilate the graph.
The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.
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Last year, Michael was 36 inches tall and grew 0. 75 inch each month. Caroline was 39 inches tall and grew 0. 4 inch per month. How many months passed before they reached the same height?
In 8 months and 17 days Michael will reach the height of Caroline.
What is Linear Equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Ax + B = 0, where A and B are both real integers, and x is the only variable, is the standard form or general form of a linear equation in one variable. Ax + By = C is the formula used to describe linear equations with two variables, where x and y are the variables and A, B, and C are any real values.
Let in x months Michael and Caroline will be at same height so,
36 + 0.75x = 39 + 0.4x
⇒0.35x = 3
⇒x = 8.57
So, in 8 months and .57*30 = 17 days Michael will reach the height of Caroline.
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Insurance company executives surveyed 200 young adults about their first motor vehicle. The results are shown in the two-way table.
A 4-column table with 3 rows. Column 1 has entries 4, 6, 8. Column 2 is labeled car with entries 118, 16, 2. Column 3 is labeled truck with entries 6, 12, 6. Column 4 is labeled S U V with entries 18, 20, 2. The columns are titled motor vehicle and the rows are titled cylinders.
A survey participant is randomly selected. Let S be the event that the participant’s first motor vehicle had six cylinders and let T be the event that the participant’s first motor vehicle was a truck. What is the value of P(S and T)?
0.06
0.12
0.24
0.30
answer. is A 0.06
Nilda has 40 points on a game show. She answers the next question incorrectly and loses 50 points. Sketch a number line to find the new score.
The point N(-2,-3) is rotated 270° clockwise about the origin. What are the coordinates of N'?
A. (-3,-2)
B. (-3,2)
C. (3,-2)
The coordinate of N' is (2, -3)
Now, According to the question:
We have the point n (-2, -3) and we need to rotate it 270 degrees clockwise about the origin.
When rotating 270 clockwise about the origin you switch the x and y coordinate and use the opposite sign of the original y coordinate.
A(x, y) becomes A' (-y, x)
This means that point N becomes:
N (-2, -3) => N'(-(-2), (-3))
=> N'(2,- 3)
Hence, The coordinate of N' is (2, -3)
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Use 10% to find 40% of 40
Triangle abc is to triangle efg because a vertical translation of units and a horizontal translation of units maps triangle abc onto triangle efg
Triangle ABC is translated to triangle EFG because a vertical translation of 10 units and a horizontal translation of 5 units maps triangle ABC onto triangle EFG.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Triangle ABC.
A = (-9, -2)
B = (-9, -7)
C = (-7, -7)
Triangle EFG.
E = (-4, 8)
F = (-4, 3)
G = (-2, 3)
Now,
With a vertical translation of 10 units up on triangle ABC and 5 units right of the horizontal translation will give us triangle EFG.
i.e,
(-9, -2) = (-9 + 5, - 2 + 10) = (-4, 8)
(-9, -7) = (-9 + 5, -7 + 10) = (-4, 3)
(-7, -7) = (-7 + 5, -7 + 10) = (-2, 3)
Thus,
Vertical translation of 10 units up and horizontal translation of 5 units right.
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Answer:
1: Congruent
2: 10
3: 5
Step-by-step explanation:
Step 1: Finding the part-to-part and part-to-whole ratios
To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
a)What is the ratio of water to drink mix?
(b)What is the ratio of drink mix to water?
(c)What is the ratio of drink mix to mixed energy drink?
d)What is the ratio of water to mixed energy drink?
Answer: ummm B
Step-by-step explanation:
Answer: B
Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.
Do the sides 12 16 and 20 make a right triangle?
A triangle with side lengths 12,16, and 20 is a right triangle.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.
The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.
consider c=20 a=12, b=16 substitute in above formula:
20²=12²+16²
⇒400=144+256
⇒400=400
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use a table to organize your guesses
A jar is filled with 100 coins, all of which are nickels and dimes. The change in the jar is worth $6.75. How many coins are nickels, and how many are dimes?
Answer:
35 dimes and 65 nickels
Step-by-step explanation:
We will need use a system of equations to find the total number of nickels and dimes.
Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.
Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75
Substitution will be the easiest method to solve:
[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]
find the values of x and y
The value of x is 45 degree and value of y is 49 degree.We can find by using supplementary and corresponding angles.
What is supplementary angle with example?Supplementary angles are those angles that sum up to 180 degrees. To find the angle which is supplementary to another angle subtract the given angle from 180 degrees. For example if one angle is 60 degrees then another angle is 180 – 60 = 120 degrees.
What is a corresponding angle example?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles.
Now we find
according to supplementary angles
3x+45=180
3x=180-45
x=45
According to corresponding angles
y-4=45
y=45+4
y=49
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32x^6-4
how do yo factor this
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, start text, space, m, end text. how many kilometers did issa travel from school to his house
The distance Issa travelled from school to his house is 9.6 km.
What is the distance travelled?The actual length covered by the body is defined as distance travelled, whereas displacement is the straight path between the initial and final points.
Here,
Let the total distance between school and home be 'x' meters.
Issa jogged two-thirds of x = 2x/3
So the total distance between school and home is = 2x/3 + 3200
However, the total distance from school to home = x
= 2x/3 + 3200 = x
= 3200 = x/3
= 9600 = x
As a result, the total distance from school to home is 9600 meters.
We're now converting it to kilometers.
We know that 1000 meters equals one kilometer.
9600 meters = 1/1000 x 9600
= 9.6 kilometers
Therefore the distance travelled will be 9.6 km.
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This line plot shows the number of laps students ran in gym class.
Select the three true statements about the line plot.
OPTIONS:
Most of the students ran more than 3 laps.
None of the students ran more than 3 1/2 laps.
The same number of students ran 1 lap as ran 2 laps.
Most of the students ran 2 1/2 laps.
The greatest number of students ran 1 1/2 laps.
Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
From the line plot shown:
Total number of students = 3 + 4 + 2 + 2 + 8 + 4 + 6 + 9 = 38
Students who ran more than 3 laps = 2 + 8 + 4 + 6 + 9 = 29
Students who ran more than 2 1/2 laps = 2 + 2 + 8 + 4 + 6 + 9 = 31
Students who ran more than 3 1/2 laps = 2 + 8 + 4 + 6 + 9 = 29
Hence:
Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.
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At what point the graph of linear equation 2x 3y 6 cuts the Y-axis A 0 2 B 4 0 C 2 6 D 2 0?
The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).
For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.
To satisfy the second condition the points of a should satisfy the equation given
LHS= 2x+3y
RHS=6
A(0,2)
Substituting the values of x and y in 2x+3y,
2(0)+3(2)=6
Therefore LHS=RHS
Hence, at point A(0,2) the graph of the given equation cuts the Y axis.
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please help!!! write the equation of the line in fully simplified slope intercept form
Answer:
y=[tex]-\frac{1}{4}[/tex] x -6
Step-by-step explanation:
y=mx+b is the slope-intercept formula, m representing the slope and the b representing the y-intercept. Pick two points shown in the graph,
such as (4,-7) and (8,-8) and use what is called rise over run. This means you count the distance between these two points by subtracting the y values (rise) and placing the difference in a fraction over the difference between the x values (run). This is where you get the fraction [tex]\frac{1}{4}[/tex]. Because the slope is going down from left to right, it means that the slope is negative, hence the [tex]-\frac{1}{4}[/tex]. The y-intercept is the point where the line intercepts the y-axis, which in this case is -6, so if you replace the representative letters with the corresponding numbers in the slope-intercept formula, the answer is y=[tex]-\frac{1}{4}[/tex] x -6.
The point P(2k, k) i equiditant from A(-2, 4) and B (7,-5). Find the value of k.
The value of k is 3. We have to equal the distance between PA and PB and then solve the equation by squaring both side.
Given is that P(2k, k) is equidistance from A(-2, 4) and B(7, -5).
First, we try to understand what is distance formula between 2 points
let's suppose we have 2 points (x1, y1) and (x2, y2).
Find the distance between them.
The separation between two points the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is also applied to the distance formula for two points.
The length of the line segment bridging two points on a plane is known as the distance between the points. d=√(x2 - x1)^2 + (y2 - y1)^2 is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Given that PA = PB.
First, find what is PA
[tex]\sqrt{(2k+2)^2 + (k-4)^2}[/tex]
Here we will use the formula of
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 -2ab + b^2
[tex]\sqrt{4k^2+8k + 4 + k^2 -8k + 16}[/tex]
[tex]\sqrt{5k^2+20}[/tex].
Now find what is PB.
[tex]\sqrt{(2k-7)^2 + (k+5)^2}[/tex]
[tex]\sqrt{4k^2 + 49 -28k + k^2 + 25 + 10k}[/tex]
[tex]\sqrt{5k^2 - 18k + 74}[/tex]
PA = PB.
[tex]\sqrt{5k^2 + 20 } = \sqrt{5k^2 -18k + 74}[/tex]
squaring both sides.
5k^2 + 20 = 5k^2 -18k + 74
18k = 74-20
18k = 54
k = 3.
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What is the solution to the equation 9(x + 2) = 27?
A. x = 2.5
B. x = 0.5
C. x = −0.5
D. x = −3.5
Please help.. what am I missing on this?
A. 78
B. 12.75
C. 136.5
D. 12
Answer:
A. 78
Step-by-step explanation:
You want the measure of one base angle of an isosceles triangle when it is given as (6x+6)° while angle K is given as 2x°.
Angle relationsYou don't need to solve any equations to determine the correct answer choice. You just need to understand the relationship between angles in an isosceles triangle.
The two base angles in an isosceles triangle are congruent, so neither can be more than 90°. (Eliminates choice C.)
The base angle at (6x+6) is more than 3 times angle K at (2x), so the base angle cannot be as little as 12.75. (Eliminates choices B and D.)
The only viable answer choice is A. 78°.
SolutionThe sum of angles in any triangle is 180°. The two base angles in an isosceles triangle are the same measure, so we have ...
(6x +6)° +(6x +6)° +2x° = 180°
14x +12 = 180 . . . . . . . . . . . divide by °, collect terms
14x = 168 . . . . . . . . . . subtract 12
x = 12 . . . . . . . . . . divide by 14
∠D = (6x +6)° = (6·12 +6)° = 78°
__
Additional comments
We are referring to the angle marked 2x° as "angle K" because Brainly doesn't like the word a.pex to show up in an answer.
We know triangle DKT is isosceles because the sides are marked with a single hash mark. The congruent base angles are opposite the congruent sides.
An altitude from K to segment DT would divide the triangle into two congruent right triangles, each with its half of angle K being x°. Then angles K/2 and T are complementary to that, so you could write ...
6x +6 +x = 90 ⇒ 7x = 84 ⇒ x = 12 ⇒ ∠D = 90° -12° = 78°
Once again, recognition that 6x+6 is somewhat greater than x means that angle D must be somewhat more than 45°. (The larger of two things is always greater than half their sum.)
how do i solve this problem 5.50h=44
Answer:
h = 8
Step-by-step explanation:
5.50h=44
Divided both sides by 5.50
h = 8
Let's check
5.50(8) = 44
44 = 44
So, h = 8 is the correct answer!
Explain how the Quotient of Powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22
The Quotient of Powers was used to simplify this expression is By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents
We have given that,
2 to the fifth power, over 8 = 22
What is the simplified form of expression?The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form or to rewriting the same algebraic expression with no like terms and in a compact manner.
By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
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What is ideal or real solution?
Answer:
An Ideal solution follows the Raoult's law strictly
A Real solution shows deviation from the Raoult's law.
Step-by-step explanation:
help pls! Given m||n, find the value of x.
(4x-6)
(8x-6)
Answer:
To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:
4x - 6 = 8x - 6
4x = 8x
4x - 8x = 0
-4x = 0
x = 0
So, the value of x that makes (4x-6) equal to (8x-6) is x=0.
Answer:
-4x = -12 Divide each side by '-4'.
How do you decide which technique to use when solving an equation?
Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.
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I need some help on the "round to the next period" part. What exactly is the answer then? Thank you!
The time period it will take a principal of $25000 to grow int $28500 at a rate of 4% is approximately 3 years
What is Compound InterestCompound interest is the interest that is calculated on the initial principal and also on the accumulated interest of previous periods. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
In the given question, our data is;
P = 25,000r = 4% = 0.04A = 28,500n = ?x = semi-annually = 2The formula is given as
A = P(1 + r/n)^nx
The given expression is
m(n) = 25000(1 + 0.04/ 2)^2n
m(n) = 28500
28500 = 25000(1 + 0.04 / 2)^2n
Solving for n,
n = 3.3
n ≈ 3
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Find the equation of the line that goes through ( 5, 3 ) and ( − 1, 2 ). Select one: a. x + 6y + 13 = 0 b. x − 6y + 13 = 0 c. 6x + y + 13 = 0 d. 6x − y + 13 = 0
Answer:
C.
Step-by-step explanation:
To find the equation of the line that goes through the points (5, 3) and (-1, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To find the slope of the line, we can use the following formula:
m = (y2 - y1)/(x2 - x1)
Plugging in the coordinates of the two points, we get:
m = (2 - 3)/(-1 - 5) = -1/6
Substituting this value of m and the coordinates of one of the points into the point-slope form, we get:
y - 3 = -1/6(x - 5)
This simplifies to:
6x + y - 13 = 0
Therefore, the equation of the line is:
6x + y - 13 = 0
Find the area of the shaded region in the above sided figure. Take = 3.14
Step-by-step explanation:
The Radius of the larger semi circle = [tex]\frac{12}{2}[/tex] = [tex]6[/tex][tex]cm[/tex]
Area of the 2 larger semi Circles = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]
= [tex]\frac{3.14X(6)^{2} }{2} X 2[/tex]
= [tex]\frac{113.04}{2} X2[/tex]
= [tex]113.04[/tex] [tex]cm^{2}[/tex]
Radius of the smaller semi circle = [tex]\frac{5}{2} = 2.5cm[/tex]
Area of the smaller semi circle = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]
= [tex]\frac{3,14X(2.5)^{2} }{2} X 2[/tex]
= [tex]196.25[/tex][tex]cm^{2}[/tex]
Combined Area = [tex]113.04 + 196.25[/tex]
= [tex]309 . 29cm^{2}[/tex]
Does 9 12 15 make a right triangle?
The side lengths measuring 9 units , 12 units and 15 units make a Right Triangle because the sides satisfy the condition of the Pythagoras Theorem .
According to the Pythagoras Theorem , which states that square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ( perpendicular and Base) ,
The side lengths of right triangle are = 9 units , 12 units and 15 units ,
According to the condition of Pythagoras theorem , [tex]15^{2} = 12^{2} + 9^{2}[/tex]
On simplifying ;
we get ;
[tex]225 = 144 + 81[/tex] ;
[tex]225 = 225 ;[/tex]
the condition is satisfied ,
that means the sides form a right triangle .
Therefore , the side 9 units , 12 units and 15 units make a right triangle .
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