We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.
Explanation:The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.
Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.
So, the equation of the line is y = 1/3x + 2/3.
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Four students took a national standardized test for which the mean was 500 and the standard deviation was 100. If a student’s z-value was 1.75 on the test, what was the student’s score?
z = (x - 500) / 100
1.75 = (x - 500) / 100
175 = x - 500
675 = x
Answer:
A, 675
Step-by-step explanation:
Which type of transformation does NOT result in a figure that is congruent to the original one?
Answer:
Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent.
Step-by-step explanation:
Divide 9 by z expression
Write the integer as a product of two integers such that one of the factors is a perfect square. 27
Final answer:
The integer 27 can be written as the product of the perfect square 9 and the integer 3, expressed as 9 x 3.
Explanation:
To write the integer 27 as a product of two integers such that one of the factors is a perfect square, we can break down 27 into its prime factors. The prime factorization of 27 is 3 x 3 x 3, which can be written as 9 x 3 because 9 is a perfect square (3 x 3).
Therefore, the integer 27 can be written as the product of the perfect square 9 and the integer 3, which is 9 x 3.
A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.
(a) How fast is the radius of the balloon changing at the instant the radius is 40 centimeters?
___cm/min
(b) How fast is the radius of the balloon changing at the instant the radius is 90 centimeters? _____ cm/min
...?
The rate at which the radius of the balloon is changing can be found by differentiating the volume formula for a sphere. Substituting the given values into the formula, we can calculate the rate of change at specific radii.
Explanation:To find the rate at which the radius of the balloon is changing, we can use the relationship between the volume and the radius of a sphere. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius. Taking the derivative of both sides with respect to time, we get dV/dt = 4πr²(dr/dt). We are given that dV/dt = 900 cm³/min and we need to find dr/dt when r = 40 cm and r = 90 cm.
(a) Plug in the values into the formula: 900 = 4π(40)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(40)²) ≈ 0.178 cm/min.
(b) Repeat the same steps for r = 90 cm: 900 = 4π(90)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(90)²) ≈ 0.020 cm/min.
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how many inches are in a foot then converted into millimeters
Solve the system and explain what the results mean according to your scenario.
2x + y = 9
3x + 4y = 26
...?
two cassettes and three CDs cost $175 while four cassettes and one cd cost $125. Given that one cassette costs 5x and one cd costs 5y , write two equations in x and y to represent the information.
F(x) = 2x2 – 3x 7 for the input value 2.what is the value of the function when x = 2?
Please Help!!!!!
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
What does the value 5 represent in this situation?
Quarters were added to the bowl for 5 weeks.
Five quarters are added to the bowl every week.
There were 5 quarters in the bowl on Week 1.
The value of the quarters in the bowl on Week 1 was $5.
The function p(t) represents the population of a certain town t years after 2010.
p(t)=3476(0.97)^t
What does the value 3476 represent in this situation?
Every year after 2010, the population increases by 3476.
Every year after 2010, the population decreases by 3476.
The population of the town in 2010 is 3476.
The population t years after 2010 is 3476.
Answer:
For number 2:
Step-by-step explanation:
What is the inverse of the function f(x) = x1/4 – 12?
Darwin’s age is 6 years greater than twice fiona’s age. if darwin is 50 years old, how many years old is fiona?
What is 1/50 as a percent and decimal?
The fraction 1/50 is equivalent to 0.02 as a decimal.
To convert 1/50 to a percent, we multiply the fraction by 100:
= 1/50 x 100
= 2%
Therefore, 1/50 is equivalent to 2% as a percent.
To convert 1/50 to a decimal, we divide the numerator (1) by the denominator (50):
= 1 ÷ 50
= 0.02
Therefore, 1/50 is equivalent to 0.02 as a decimal.
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Find the point on the line 6x+y=9 that is closest to the point (-3,1).
Convert the line equation to 'y = mx + c' form. We calculate the orthogonal distance from the point to a generic point on the line using the formula 'd = |Ax1 + By1 + C| / sqrt(A^2 + B^2)'. Solve the line equation for 'y' using the computed 'd'. This yields the point closest to (-3,1) on the line.
Explanation:The subject of the question involves the algebra of straight lines, specifically finding points on lines. The given line in the question is '6x + y = 9'. We want to find the point along this line that is closest to a given point (-3,1).
First, rewrite the equation in slope-intercept form: y = -6x + 9. Now recall the formula for the shortest distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where 'A', 'B' and 'C' are the coefficients in the equation of the line, and '(x1, y1)' is the point.
In this case, A = -6, B = 1, C = -9, and the point is (-3,1). If we plug these into the formula, we can solve for 'd'. Then we solve the given equation for 'y' using the resulting 'd' value and we get the point which is closest to (-3,1) on the line '6x + y = 9'.
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Whick is the shorter distance 9/10 or 10/9
Perform the indicated operation.
5/4 + 7/9
a. 4/9
b.2 and 4/9
c.2 and 1/36
Answer:
c.
Step-by-step explanation:
[tex]\frac{5}{4}+\frac{7}{9} = \frac{5*9+7*4}{4*9} = \frac{45+28}{36} = \frac{73}{36}[/tex]
and [tex]\frac{73}{36}= 2(36) + 1 = 2\frac{1}{36}[/tex]
Zinnia and Ruby earn $58 per week for delivering pizzas. Zinnia worked for x weeks and earned an additional total bonus of $13. Ruby worked for y weeks. Which expression shows the total money, in dollars, that Zinnia and Ruby earned for delivering pizzas? (5 points)
71x + 58y
58x − 13 + 58y
58x + 71y
58x + 13 + 58y
Answer:
Total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .
Step-by-step explanation:
As given
Zinnia and Ruby earn $58 per week for delivering pizzas.
Zinnia worked for x weeks and earned an additional total bonus of $13.
Ruby worked for y weeks.
Thus
Money Zinnia earns = Money earns per week × Number of weeks + Additional total bonus .
Put all the values in the above
Money Zinnia earns = 58 × x + 13
Money Zinnia earns = 58x + 13
Thus
Money Ruby earns = Money earns per week × Number of weeks
Put all the values in the above
Money Ruby earns = 58 × y
Money Ruby earns = = 58y
Thus
Total Zinnia and Ruby earned for delivering pizzas = Money Zinnia earns + Money Ruby earns
Total Zinnia and Ruby earned for delivering pizzas = 58x + 13 + 58y
Therefore the total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .
30 : 48 as a ratio in simplest form
Solve for x: 3 2x=5x-9
Answer:
Step-by-step explanation:
2x=5x-9First, add 9 to each side
2x+9=5xThen subtract 2x from each side
9=3xDivide each side by 3
3=xSorry my answer may be a bit late
What is ��1.95 x 6thanks?
264 shared in ratio 2:3:1
corresponding reference angle to 17pi/7
The corresponding reference angle to 17π/7 radians is π/7.
Explanation:The corresponding reference angle to 17π/7 radians is found by determining the smallest positive angle such that when added to 17π/7 radians, the resulting angle lies between 0 and 2π radians.
To find the reference angle, we can subtract 2π radians repeatedly until we obtain an angle between 0 and 2π radians.
In this case, we have:
17π/7 - 2π = π/7
Therefore, the corresponding reference angle to 17π/7 is π/7 radians.
7 × (–3) × (–2)2 =
a. 84b. –84c. 48d. –48
1.The table shows climate data for Death Valley, California, as recorded at the Cow Creek Station. The temperatures are rounded to the nearest integer. Climate data for Death Valley, CaliforniaTemperature Record high52 Record low Daily mean25 (a)Plot and label these values on a number line. (b)For each pair of temperatures found in the table, calculate the difference. Organize your work using a table.
Climate data for Death Valley, CaliforniaTemperature
Record high52
Record low
Daily mean25
how do you solve ky-bf=fy/m?
Final answer:
To solve the equation ky - bf = fy/m, you need to isolate the variable y. The steps are to distribute the k, add kf to both sides, and factor out y. The solution is y = (fy/m + kf)/k.
Explanation:
To solve the equation ky - bf = fy/m, we first want to isolate the variable y. Here are the steps:
Distribute the k to both terms in the equation: ky - bf = fy/m becomes ky - kf = fy/m.
Add kf to both sides of the equation: ky - kf + kf = fy/m + kf simplifies to ky = fy/m + kf.
Factor out y on the left side of the equation: y(k) = fy/m + kf becomes y = (fy/m + kf)/k.
So, the solution is y = (fy/m + kf)/k.
What are the domain, range, and asymptote of h(x) = (0.5)x – 9?
domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9
domain: {x | x > –9}; range: {y | y is a real number}; asymptote: y = –9
domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9
domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Answer:
Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Step-by-step explanation:
Given : [tex]h(x)=(0.5)^x-9[/tex]
To find : What are the domain, range, and asymptote of h(x) ?
Solution :
Domain of the function is where the function is defined
The given function [tex]h(x)=(0.5)^x-9[/tex] is an exponential function
So, the domain of the function is,
[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]
i.e, The set of all real numbers.
Range is the set of value that corresponds to the domain.
Let [tex]y=(0.5)^x-9[/tex]
If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]
If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]
So, The range of the function is
[tex]R=(-9,\infty) , y|y>-9[/tex]
The asymptote of the function,
Exponential functions have a horizontal asymptote.
The equation of the horizontal asymptote is when
[tex]x\rightarrow \infty[/tex]
[tex]y=(0.5)^\infty-9[/tex]
[tex]y=-9[/tex]
Therefore, Option 4 is correct.
Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Write an equation of the line that passes through (−5, −2)(−5, −2) and is parallel to y=23x+1y=23x+1.
The equation of a line parallel to y=23x+1 that passes through the point (-5, -2) is y = 23x + 113.
Explanation:The subject of this question is geometry, specifically, the formulation of a linear equation. You're asked to write an equation of a line that passes through point (-5,-2) and is parallel to the line defined by the equation y=23x+1.
Parallel lines have the same slope, so since the given line has a slope of 23, our line will also have a slope of 23. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here, 'm' is already known as 23. So, our equation currently is y = 23x + b.
We can determine 'b' using the given point (-5,-2). Substituting these coordinates into our equation gives -2 = 23*(-5) + b. Solving for 'b' renders b = -2 - (23*-5) = 113.
Therefore, the equation of the line that passes through (-5, -2) and is parallel to y=23x+1 is y = 23x + 113.
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1. Write the statement in parentheses as a converse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
2. Write the statement in parentheses as an inverse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
3. Write the statement in parentheses as a contrapositive and provide the truth value (2 points). "An angle that measures 90° is a right angle."
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What are the factors of 16x^4 ? Select all that apply.
5
16
7
x^3
What forms of measurement of length, width, height, and distance are forms of what measurement?
The measurement of length and distance in mathematics, including the SI unit meter, different units, and measurement systems.
Measurement of Length, Width, Height, and Distance
Length is the measurement of the extent along the greatest dimension. The SI unit of length is the meter (m). Units of length include kilometers (km), millimeters, and micrometers.
Distance is a quantity arrived at by measurements with material or optical apparatus. It is commonly measured in meters, kilometers, feet, yards, etc. in various systems of measurement.
Customary and Metric Systems are two different systems used for measuring length and distance.