{y,x} = {10,-5}
Step-by-step explanation:
sorry if this dont make sense
solve equation [2] for the variable y
y = 4x +30
plug this in for variable y in equation [1 ]
(4x+30) +3x= -5
solve [1] for the variable x
7x= - 35
x= - 5
by now we know this much
y= 4x+30
x= - 5
use the x value to solve for y
y=4 (-5) + 30 = 10
solution
{y,x} = {10,-5}
2. Which equation has the solution x = -1? A 2x1 = 3x - 2
B 8x + 7 = 9x - 8
C -5x -4 = 4x + 3
D 7x+8 = -6x - 5
The equation that has the solution x = -1 is D. 7x+8 = -6x - 5
To find the solution of an equation, we need to find the value of the variable that makes the equation true. In this case, we need to find the value of x that makes the equation 7x+8 = -6x - 5 true.
We can start isolating the x variable by adding or subtracting the same terms on both sides of the equation.
D. 7x+8 = -6x - 5
13x = -13
x = -1
So the solution of the equation is x = -1
We can check if this is the solution by substituting it back in the equation. If the equation is true, both sides will be equal when x is -1.
7x+8 = -6x - 5
7*-1 + 8 = -6*-1 -5
-7+8 = 6 -5
1 = 1 (true)
Therefore, D. 7x+8 = -6x - 5 has x = -1 as the solution.
The angle of elevation to a nearby tree from a point on the ground is measured to be 63 degrees. How tall is the tree if the point on the ground is 22 feet from the tree? Round to the nearest foot.
The height of the tree is 43.7 feet
How to calculate the height of the tree?Height deals with the length of the tree vertically.
The given parameters that will help us solve the problem are
The angle of elevation = 63 degrees
The distance from the foot of the tree to the point is 22 feet
Using the trigonometrical ratio
Tan ∅ = Opposite/Adjacent
Tan63 = h/22⁰
Height of the tree = 22*tan63
The height of the tree is equal = 22*1.9626
Height = 43.7 feet
Therefore the tree has a height of 43.7 feet
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The area of a square photo frame is 250cm2. Find the perimeter of the photo frame, leaving your answer correct to 1 decimal place.
Therefore ,perimeter of square photo frame = 63.2 centimeter.
What is the perimeter?The total length of boundary of a closed geometric shape is called perimeter. Different geometric shape has different formula for determining perimeter. For a square shaped object perimeter is the four times of its side length.
Here,
Area of a square photo frame = 250 square centimeter.
We know, area of a square photo frame = square of side length
if side length = s
area = s²
it is given that area of a square photo frame = 250 cm²
250 cm² = s²
s = √250 cm
s = 15.81 cm
side length = 15.81 cm
formula for perimeter = 4× side length
perimeter of frame = 4×15.81 = 63.24 cm
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There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.
You will discover through this project whether a human's arm span (measured across the body with the arms extended) is correlated to his height.
You will need to collect data from 11 people, which will give you 12 data points including your own personal data. You will turn in and answer questions regarding only one scatter plot if doing the project alone.
Part One: Measurements
Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements. Record your measurements on the "Data Record" document. Use the "Data Record" to help you complete Part Two of this project.
Measure 11 additional people, and record their arm spans and heights in inches.
Part Two: Representation of Data with Plots
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word processing document.
Part Three: The Line of Best Fit
Include your scatter plot and the answers to the following questions in your word processing document.
Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
Write the equation of the line of best fit using the slope-intercept form of the line
Part two
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word processing document.
part three
Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Use the line of best fit to help you to describe the data correlation.
Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
According to your line of best fit, what is the arm span of a 74-inch-tall person?
The diagram relating to the scatterplot for the data is attached.
How to explain the scatterplot?I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.
I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.
The slope represents the rate of change arm span based on height. The y intercept is the arm span.
Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.
Based on this data, for every inch in height, the arm span increases by 1.1 inches.
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What is equality easy answer?
Equality means being equal in all aspects such as status, rights irrespective of caste, colour, race, gender, etc.
Now, According to the question:
What is a equality in math?
Equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.
Example of Equality
Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division.
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What is the first common multiple of 4 and 10?
Answer:
20
Step-by-step explanation:
4 ans ten both have 20 in common and it jas ro be the first because the next is like 40
Which of the following is a trinomial class 8?x+y³a² + b² + c²x² + 2x15z²
The algebraic expression known as a trinomial contains three terms then the trinomials exists a^2 + b^2 + c^2
What is meant by trinomial?
Three non-zero terms make up a trinomial, which is an algebraic expression. The algebraic expression known as a trinomial contains three terms. An mathematical equation called a trinomial has three terms with on-zero coefficients, each separated by a + or - sign. It is a trinomial if three monomials are divided by addition or subtraction.
When a polynomial has three terms, it is referred to as a trinomial. Its general expression is ax² + bx + c, where a and b are coefficients and c is a constant. In order to factor trinomials, you must follow these three easy steps: Calculate the values of b (middle term) and c. (last term).
A. 8x
Not a trinomial because, it contains only one term.
B. 3y +5y² + y
A trinomial because, it contains three terms.
C. 6x²
Not a trinomial because, it contains only one term.
D. + x² +1
A trinomial because, it contains three terms.
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Select the correct answer. Which two of the functions shown here have identical graphs and why? A. f and g, because the log of a quotient is the quotient of the logs B. g and j, because the quotient of two logs is the sum of the logs C. f and h, because the log of a quotient is the difference of the logs D. g and h, because the quotient of two logs is the difference of the logs
F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.
What do logs mean?
Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.
There are three common types of logarithms such as:
Common logarithms: where the base is 10 Binary logarithms: where the base is 2 Natural logarithms: where the base is e ≈ 2.71828Therefore logarithm is the mathematical expression used to answer the question.
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graph the function f: f(x)=√x²-4 x+4 and determine its range and discuss its monotony
Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.
what is function?
A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.
What is the range of the function bellow?
given, a function f(x) = √ (x² - 4x +4)
now for every input value of x we will get an output value for f(x).
we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}
when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]
f(-3) = √25 =5
similarly, f( -2) = 4
f(-1) = 3
f(0) = 2
f(1) = 1
f(2) =0
f(3) = 1
the range of function is {5, 4, 3, 2, 1, 0,1}
The range of function indicates that it is neither increasing nor decreasing.
hence the function is a monotonous function.
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wanda wants to buy a pair of shoes that cost $48 If sales tax costs 8.25% what will be the total cost
Answer:51.96 dollars total
Step-by-step explanation:
go to a smart cauculator and add 8.25% to 48
What is the coefficient of x² in 5x²y?
5y is the coefficient of x² in the given polynomial 5x²y.
What is coefficient of polynomial?Polynomial coefficients are the integers preceding a word. Terms are often composed of a number and a variable (for example, 2 x 2 2x2 2x2, where 2 is the number and x is the variable). The coefficient is represented by the number portion. Simply put, it is the leading term's coefficient. The polynomial degree is the largest power of the variable that occurs in the polynomial. The leading phrase is the one with the greatest power of the variable: the term with the greatest degree. The leading coefficient is the leading term's coefficient.
Here,
The coefficient of x^2 in the above polynomial 5x^2y is 5y.
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Answer as quickly as you can! I will mark Brainliest:
Lincoln spends $55 of his allowance every month and saves the rest.
This month he decides to spend only $45, increasing his savings by 40%.
What is his monthly allowance?
On solving the provided question we can say that by percentage 40% of savings = 40% of 20 = 40/100 X 20 = $8 140% of savings = 140% of 20 = 140/100 X 20 = $28 his monthly allowance is = $8 + $28 = $36
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Increase in savings $20
by percentage
40% of savings = 40% of 20 = 40/100 X 20 = $8
140% of savings = 140% of 20 = 140/100 X 20 = $28
his monthly allowance is = $8 + $28 = $36
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Tasha earned $7.55 per hour and an additional $100 in tips waiting tables on Saturday night. Altogether she earned $160.40. Write an equation for this situation. Use h to represent the number of hours.
The equation that represents the situation is $160.40 = $100 + $7.55h.
What is the equation ?An equation is a statement that consists of numbers or letters and an equal to sign. The amount earned is a function of the tip, hours worked and the pay per hour.
The form of the equation is:
Total amount earned =tip + (amount earned peer hour)
$160.40 = $100 + ($7.55 x h)
$160.40 = $100 + $7.55h
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Can someone help me answer this question
Given E(-6, y), F(6, 5), G(14, 11), and
H(8,-13), find the value of y so that
EF is perpendicular to GH.
the answer is y = 16.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
here, we have,
E(-6, y), F(6, 5), G(14, 11), and H(8,-13),
& EF is perpendicular to GH.
now, we get,
The slope of GH is ...
G -H = (14, 11) -(8, -13) = (6, 24) = (Δx, Δy)
slope = Δy/Δx = 24/6 = 4
The perpendicular line through F will have a slope of the negative reciprocal of this, or -1/4.
The point-slope form of the equation can be written as ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
The perpendicular line through F is then ...
y -13 = (-1/4)(x -6)
For an x-value of -6, the value of y will be ...
y = (-1/4)(-6 -6) +13 = 12/4 +13 = 16
hence, The value of y so that EF is perpendicular to GH is 16.
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Kevin conducted a survey of a random sample of registered voters in his town to determine their preferred candidate for mayor in the next election. The results of the survey are shown in the table below.
Survey Results
Candidate Likely Voter Preference
A 240
B 210
C 50
There are 18,000 registered voters in Kevin’s town. Based on the data in the table, what is the best estimate of the number of people who will vote for Candidate A if all the registered voters cast a ballot?
Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: The survey results from the sample as
A -240
B-210
C-50
The total number of people surveyed is 500
Now as per the given survey results the voters likely to vote for candidate A is P(A)=240/500
=12/25
Similarly, the probability that the voters vote for Candidate A and B are
P(A)=210/500
=21/50
P(B)=1/10
∴ If 18000 voters vote the voters likely to vote for A are
=12/25 ×18000
=8640 voters
Hence, Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.
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10 POINTS FOR ANY ONE HOW CAN ANSWER THIS
:)
Answer: A=16 B=14 C=34
Step-by-step explanation:
Answer for points + 5 star + thank + brainliest (Screenshot included)
Stella bought 6 packages of balloons. Each package has 15 balloons in it.
Which TWO number sentences could be used to find the total number of balloons Stella bought?
Answers:
(6×10)+(6×5)
6×10+56
(3×10)+(6×5)
(15×3)+(15×3)
6+15
Answer:
"Choices A & D": (6 x 10) + (6 x 5). & (15 x 3) + (15 x 3) are the correct number sentences.
Step-by-step explanation:
1. How many balloons are there in total?The total amount of balloons can be found via cross-multiplication. To cross-multiply fractions, we multiply the numerator of the first fraction with the denominator of the second fraction and the numerator of the second fraction with the denominator of the first fraction.If one package has 15 balloons, how many balloons do 6 packages have?:[tex]\frac{1 package}{6 packages} = \frac{15 balloons}{X balloons}[/tex][tex]\frac{1 package xX balloons}{1 package} = \frac{6 packages x 15 balloons}{1 package}[/tex][tex]6 x 15 balloons = 90 balloons.[/tex]So now we know there are 90 balloons in 6 packages. 2. PEMDASPEMDAS states to complete the operations on numbers in the order that the letters appear.1. Parentheses, ie. (6 + 10) - (11 x 5).
2. Exponents, ie. [tex]a^{c}[/tex].
3. Division, ie. 11÷5.
4. Addition, ie. 12+1.
5. Subtraction, ie. 10-5.
3. Find the TWO NUMBER SENTENCES that can be evaluated to 90.Number Sentences:
a. (6 x 10) + (6 x 5).
According to PEMDAS. We multiply the numbers inside the parentheses first.ii. 6 x 10 = 60.
iii. 6 x 5 = 30.
iv. Then we add the products.
v. 60 + 30 = 90.
vi. So this choice IS CORRECT.
b. 6 x 10 + 5.
According to PEMDAS. We multiply first.ii. 6 x 10 = 60.
iii. Then we add the product to 5.
iv. 60 + 5 = 65.
v. 65 DOES NOT equal 90 so this is one of the incorrect number sentences.
c. (3 x 10) + (6 x 5).
According to PEMDAS. We multiply the numbers inside the parentheses first.ii. 3 x 10 = 30.
iii. 6 x 5 = 30.
iv. Then we add the products.
v. 30 + 30 = 60.
vi. 60 DOES NOT equal 90 so this is one of the incorrect number sentences.
d. (15 x 3) + (15 x 3).
According to PEMDAS. We multiply the numbers inside the parentheses first.ii. 15 x 3 = 45.
iii. 15 x 3 = 45.
iv. Then we add the products.
v. 45 + 45 = 90.
vi. So this choice IS CORRECT.
e. 6 + 15.
i. 6 + 15 = 21.
ii.21 DOES NOT equal 90 so this is one of the incorrect number sentences.
4. (6 x 10) + (6 x 5). & (15 x 3) + (15 x 3). These are the correct number sentences.Please let me know if this helped (photo also attached)!!!
please solve this
it would mean so much to me please
How do you simplify the base of an exponent?
The base of an exponent can be simplified by multiplying it by itself as many times as the exponent indicates. If you want to simplify the base of an exponent in an expression, it would be done by raising the base to the power of the exponent using the notation aᵇ = aa...*a (b times)
THE BASE OF AN EXPONENTThe base of an exponent is the number that is being multiplied by itself a certain number of times. The exponent is the number indicating how many times the base is being multiplied by itself.
For example, in the expression 2³, the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times, or 2 * 2 * 2. The simplified form of this expression is 8.
In general, if the base is 'a' and the exponent is 'b' then the simplified form of the expression is 'a' raised to the power 'b' or aᵇ = aa*...*a (b times)
It's also important to note that when the exponent is 1, the expression can't be simplified anymore. For example, 2¹ = 2, where 2 is the base and 1 is the exponent.
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is it easier to describe the solution of a system of linear inequalities in words or to show it using a graph?
It depends on the context and the audience. Both describing the solution of a system of linear inequalities in words and showing it using a graph have their own advantages.
An explanation graph is what?
A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.
Describing the solution of a system of linear inequalities in words is often useful when the system is simple and the inequalities are easy to understand. It can be a more straightforward way to explain the solution, especially when the audience is not familiar with reading graphs.
On the other hand, using a graph to show the solution of a system of linear inequalities can be more efficient and effective when the system is more complex and the inequalities are harder to understand. Graphs can provide a visual representation of the solution, which can make it easier for the audience to understand the solution and see how it relates to the original problem. Additionally, it can be easier to find the exact point of intersection between the inequalities by looking at the graph.
Both methods can be useful depending on the situation, so it's best to consider your audience, the complexity of the system, and the goal of your explanation when deciding which method to use.
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House sales at Home Realty increased by 18% this year. Last year Billy sold 50 houses. How many houses were sold this year.
a: 9 houses
b: 59 houses
c: 68 houses
d: 900 houses
Answer:
b: 59 houses
Step-by-step explanation:
50 + 18% of 50 =
= 50 + 0.18 × 50
= 50 + 9
= 59
Answer:
b
Step-by-step explanation:
Can someone please help me with this math problem, ASAP? The problem is in the picture, THANKS!
Answer:
Length = Width = 55
Step-by-step explanation:
Perimeter of rectangle = 2(length + width)
Let x = length; let y = width.
perimeter = 2(x + y)
The perimeter must be 220.
2(x + y) = 220
x + y = 110
y = 110 - x
length = x
width = 110 - x
area = length × width
area = x(110 - x)
area = 110x - x²
A = 110x - x²
Take the first derivative of the area function and set equal to zero. Then solve for x.
A' = 110 - 2x
110 - 2x = 0
2x = 110
x = 55
y = 110 - x = 110 - 55 = 55
Answer: Length = Width = 55
Sam and harry are family. Sam is currently five times harry's age. Sam's age is also 10 more than three times harry's age. The following system of equations models this scenario: x = 5y x = 10 + 3y what are their current ages? sam is 25 years old, and harry is 5 years old. Sam is 30 years old, and harry is 6 years old. Sam is 35 years old, and harry is 7 years old. Sam is 40 years old, and harry is 8 years old.
Sam is 25 years old, and Harry is 5 years old.
If we multiply the age of Harry (5) five times, it will give us 25:
5×5= 25
and if we multiply Harry's age three times and then add up ten, it will give us 25:
(5×3) +10 = 25
15 + 10 = 25
25 = 25
Which of the following is a rational number?
A. 66
B.π
C. 36
D. 40
Answer:
36
Step-by-step explanation:
16. Coach Murphy has an end of the season celebration for his basketball team. He provided a pizza lunch and
distributed a homemade DVD of the season's highlights to each player. It cost him $5 per player for the pizza
lunch and $2 per player for the DVD. If there were 8 players on the team, use the Distributive Property to find
the total cost for the celebration.
Answer:
$56.00
Step-by-step explanation:
8(5 + 2) Distribute the 8
8(5) + 8(2)
40 + 16
56
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue
How to determine which statement about probability is true?Probability is the likelihood of a desired event happening.
Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.
Thus, we can write the probabilities as follow:
probability of orange = 1/8
probability of purple = 2/8 = 1/4
probability of yellow = 2/8 = 1/4
probability of blue = 3/8
Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement
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Help frrr thankkk you
Answer:
14
Step-by-step explanation:
What is the approximate side length of the square?
3.0 units
3.5 units
4.2 units
4.9 units
The approximate side length of the square is 4.2 units. Hence option B is the correct option.
What is a square?
A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
Given that the length of half of the diagonal is 3 units.
The diagonals of the square cut each other at a right angle.
The length of OB is 3 units and OC is 3 units.
The △BOC is a right triangle at O.
The hypotenuse of △BOC is BC. The legs of △BOC are OB and OC.
According to the Pythagorean theorem,
OB² + OC² = BC²
3² + 3² = BC²
BC² = 9 + 9
BC² = 18
BC = 3√2
BC ≈ 4.2
The approximate side length of the square is 4.2 units.
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Find the measure of the missing angles. 34° b . c b = ° c = °
The sum of all the internal angle is [tex]$180^{\circ}$[/tex].
What is Internal angles?The internal angle formed by a closed polygon's sides inside of itself. A shape's interior can contain angles. The closed, side-and-vertex-containing shapes are known as polygons. All of the internal angles of a regular polygon are equal. For instance, the inner angles of a square are all exactly 90 degrees, or the right angle. Triangles always have three inner angles that add up to 180 degrees. Because the other two angles (180°+0°+0°) would not be present, a triangle cannot have an individual angle of 180°.The sum of all the internal angle is [tex]$180^{\circ}$[/tex].
[tex]$$\angle A+\angle B+\angle C=180^{\circ}$$[/tex]
1. 34 and 88
[tex]34+88+\angle C=180 \\[/tex]
[tex]122+\angle C=180 \\[/tex]
[tex]\angle C=180-122 \\[/tex]
[tex]\angle C=58^{\circ}[/tex]
2. 45 and 90
[tex]45+90+\angle C=180 \\[/tex]
[tex]135+\angle C=180 \\[/tex]
[tex]\angle C=180-135 \\[/tex]
[tex]\angle C=45^{\circ}[/tex]
3. 10 and 102
[tex]10+102+\angle C=180 \\[/tex]
[tex]112+\angle C=180[/tex]
[tex]\angle C=180-112 \\[/tex]
[tex]\angle C=68^{\circ}[/tex]
4. [tex]$\boldsymbol{x}$[/tex]and 50
[tex]x+50+\angle C=180 \\[/tex]
[tex]\angle C=180-50-x \\[/tex]
[tex]\angle C=(130-x)^{\circ}[/tex]
The complete question is,
Find the measure of the third angle of a triangle given the measures of two angles.
1. 34 and 88
2. 45 and 90
3. 10 and 102
4. x and 50
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