The equation y = 2x + 4 has the following missing value: 3.
What is an equation's solution?The x and y values of an ordered pair whose values, if substituted into the equation, would make it true are the answer to the given equation.
According to the Given information
If the value of x is the missing value in the solution to the equation y = -2x + 4, and the solution is (x, -2) Hence, by adding y = -2 to the equation and solving for x, the value of x can be found:
-2 = -2x + 4
Take 4 away from both sides.
-2 - 4 = -2x + 4 - 4 (subtraction property of equality)
-6 = -2x
Add -2 to both sides.
-6/-2 = -2x/-2
3 = x
x = 3
The equation y = 2x + 4 has the following missing value: 3.
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Convert 97°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=(F-32)
9
F ==C+32
5
97 °C
= F
Answer: 97 degrees Celsius is 206.6 degrees Fahrenheit.
A crew of highway workers paved
mile in minutes. If they work at the same rate, what portion of a mile will they pave in one hour?
I don't know .............
5. a rectangular plot of land is to be enclosed by fencing. one side is along a river and so needs no fence. if the total fencing available is 600 meters, fi d the dimensions of the plot to have maximum area.
Using basic geometry and applying the fence only on 3 sides, The required dimensions of the plot to have maximum area is 200 x 200.
What do you mean by geometry?A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.
What do you mean by dimensions of a figure?In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
fence length available = 600m
We only need to fence 3 sides. So length in each side = 600/3
=200m
So, Final dimension = 200 x 200
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Question 1: Find the percent of change to the nearest tenth of a percent for Centerville
Question 2: Which town had the greatest percent of change
Question 3: What was the percent of change? (From your answer in Part B) Do Not Include 'Increase' or 'Decrease.' Round to the nearest whole percent.
Answer:
Sorry just trying to get points
describe the end behavior of the function y=-x^2+4
The end behaviour of the function [tex]y = -x^{2} + 4[/tex] is
f(x) → −∞, as x → −∞
f(x) → −∞, as x → +∞
The degree of the function is even, and the leading coefficient is negative.
End behaviour of a function:
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behaviour is determined by a polynomial function's degree and leading coefficient.
For very big or very small values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behaviour based on the sign of the leading coefficient.
To predict the end-behaviour of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
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Container A has 300 liters of water, and is being filled at a rate of 6 liters per minute. Container B has 900 liters of water, and is being drained at 2 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
It will take 150 minutes for the two containers to have the same amount of water.
To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:
m = |A - B| / (a - b)
where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.
In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:
m = |300 - 900| / (6 - 2)
m = |-600| / 4
m = 600 / 4
m = 150 minutes
Therefore, it will take 150 minutes for the two containers to have the same amount of water.
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5. At Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair. How many cars needed both repairs? How many cars needed new brakes, but not a new exhaust system.
13 cars needed both repairs and 10 cars needed new brakes, but not a new exhaust system.
In the given question, at Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair.
(a) We have to find the how many cars needed both repairs.
Total inspected cars = 50
The cars needed new brakes = 23
The cars needed new exhaust systems = 34
The cars needed neither repair = 6
So the cars that needed repair = 50-6 = 44
Total cars that needed new brakes and new exhaust systems = 23+34 = 57
So, the cars that needed both repairs = 57-44
The cars that needed both repairs = 13
Hence, 13 cars needed both repairs.
(b) Now we have to find how many cars needed new brakes, but not a new exhaust system.
The cars needed new exhaust systems = 34
The cars that needed repair = 44
So, the cars needed new brakes, but not a new exhaust system = 44-34
The cars needed new brakes, but not a new exhaust system = 10
Hence, 10 cars needed new brakes, but not a new exhaust system.
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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 27 seconds, the elevator for the miners begins to descend. What position of each elevator relative to the surface after 17 seconds? At that time, which elevator is deeper?
1. The position (distance covered) of each elevator relative to the surface after additional 17 seconds is as follows:
The equipment elevator descended 176 feet from the surface.The miners' elevator descended 255 feet from the surface.2. After 17 seconds, the miners' elevator is deeper by 79 feet than the equipment elevator.
How are the distances computed?Distance is a function of speed and time.
This implies that distance is the product of speed and time.
The descent speed of the equipment elevator = 4 feet per second
The total time in seconds the equipment elevator descended = 44 seconds (27 + 17)
The descent distance covered in 44 seconds = 176 feet (44 x 4)
The descent speed of the miners' elevator = 15 feet per second
The total time in seconds the miners' elevator descended = 17 seconds
The descent distance covered in 17 seconds = 255 feet (17 x 15)
Thus, the difference in the descent distance between the equipment elevator and the miners' is 79 feet (255 - 176).
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This is due tomorrow please help
The two solutions are (0, 1) and (-4, 0)
Increasing graphx-intercept= -4 and y-intercept = 1The slope of the graph is 0.25Two solutions on the lineFrom the question, we have the following parameters that can be used in our computation:
Graph of a linear relationship
From the graph of the linear relationship, we have the following points on the line
(0, 1) and (-4, 0)
Hence, the solutions are (0, 1) and (-4, 0)
Increasing or decreasingOn the graph, we can see that as x increases, the y value increases
This means that the graph is an increasing graph
The interceptsIn (a), we have
(0, 1) and (-4, 0)
These points represent the intercepts
So, we have
x-intercept= -4
y-intercept = 1
The slope of the lineThe slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 1) and (-4, 0)
Substitute the known values in the above equation
So, we have the following equation
Slope = (0 - 1)/(-4 - 0)
Evaluate
Slope = 0.25
Hence, the slope of the line is 0.25
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Sandy wants to graph the equation y=2x^2+4x-6. What set of key points can she use to graph the equation?
The key points of option (B) are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
What are graphs?Write the equation in the form y = MX + b to determine the slope m and the y-intercept.
This will allow you to graph the equation using the slope and y-intercept (0, b). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
y=2x^2+4x-6
Now, plot this equation in the graph as follows:
(Refer to the image attached below)
x-axis: (1, 0)
y-axis: (-3, 0)
Vertex: (-1, -8)
Therefore, the key points of option (B) which are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
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4) Find 14.56 ÷ 2.8.
First, find an equivalent expression with a
whole number divisor.
1.456 = 28
14.56 28
145.628
1,456 ÷ 28
The value of the expression is 5.2.
The equivalent expression with a whole number divisor is 145.6/28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
14.56 ÷ 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
= 145.6 / 28
= 5.2
Thus,
The value of the 14.56÷ 2.8 is 5.2.
The equivalent expression is 145.6/28.
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Answer:
The expression answer is 5.2.
145.6/28 is the equivalent expression using a whole number divisor.
Explanation:
For the time being, we have:
14.56 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
For the time being, we have:
As a result, the value of 14.56 2.8 is 5.2.
145.6/28 is an equivalent expression.
Find x in this equation
Answer:
5
Step-by-step explanation:
[tex]\triangle HBK \cong \triangle NBK[/tex] by SAS. Using CPCTC, [tex]3x=x+10 \implies 2x=10 \implies x=5[/tex].
If random samples are drawn from two independent populations where we draw samples of size 51 from population A which has mean 20.1 and standard deviation 5.49, and samples of size 76 are drawn from population B with mean 27.3 and standard deviation 5.06, what is the standard error for the sampling distribution? Round to four decimal places.
the required standard error is 6.9 for the sampling distribution.
The standard error of the sampling distribution is given by the formula SE = sqrt( (SD1² / n1) + (SD2² / n2) )
As per the question, we are given that samples of size 51 are drawn from population A with a standard deviation of 5.49, and samples of size 76 are drawn from population B with a standard deviation of 5.06.
Substituting these values into the formula, we get:
SE = √( (5.49² / 51) + (5.06² / 76) )
SE = √( (30.11) + (17.93) )
SE = √(48.04)
SE = 6.9
Therefore, the required standard error is 6.9 for the sampling distribution.
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Regina ran 31 miles last week. This week, she ran 42.5 miles. What is her percent increase to the nearest tenth?
Answer:
36.8%
Step-by-step explanation:
PLEASE MARK BRAINLIEST
42.5-31=11.4
11.4/31 is approx 0.367741935 , or 36.7741935 %.
Rounding it to the nearest tenth gives you 36.8%.
Question 1 of 10
What is the value of x?
35⁰
70⁰
⇒Sum of interior angles of a triangle is 180°
⇒ The above statement means that
[tex]70+35+x=180[/tex]
⇒Solving for x :
[tex]105+x=180\\x=180-105\\x=75[/tex]
∴ x=75°
Option D is the answer.
Please help I need it please hrlpppp
The composition of the two functions g of x and f of x is:
(g o f)(x) = 3x² - 15x + 1
How to find the composition of functions?Here we have three known functions, these are:
f(x) = x² - 5xg(x) = 3x + 1h(x)= (x - 1)/xAnd we want to find the composition of functions:
(g o f)(x)
That means that we need to evaluate the function g(x) on f(x), so we will get:
(g o f)(x) = g( f(x))
Then we will get:
g( f(x)) = 3*f(x) + 1
Now we can replace the actual function f(x) there, so we will get:
g( f(x)) = 3*f(x) + 1
g( f(x)) = 3*(x² - 5x) + 1
Now we can simplify that:
g( f(x)) = 3*(x² - 5x) + 1
g( f(x)) = 3*x² - 3*5x + 1
g( f(x)) = 3x² - 15x + 1
Then the composition of functions is:
(g o f)(x) = 3x² - 15x + 1
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My new dog! Wanted to show him off cause he’s adorable
Answer: So Cute!
Step-by-step explanation:
Answer:
Yes. I also think he is adorable.
Find the slope for the answer
The Equation for the given line in the graph is x+ y = 3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
From the Graph take two points (0, 3) and ( 3, 0)
So, slope for the line
= ( 0-3 ) ( 3-0)
= -3/3
= -1
So, the Equation of line is
y[tex]- y_1[/tex] = m(x[tex]-x_1[/tex])
y- 3 = (-1)(x- 0)
y- 3 = -x
y+ x = 3
x+ y = 3
Hence, the Equation line is x+ y= 3.
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6. Rachel has a $10,000, three-year loan with an APR of 7.25%.
a. What is the monthly payment?
b. What is the total amount of the monthly payments?
c. What is the finance charge?
a) Rachel's monthly payment for the $10,000 three-year loan with an APR of 7.25% is $309.92.
b) The total amount of the monthly payments is $11,157.12.
c) Rachel's finance charge for the loan is $1,157.12.
What is the finance charge?The finance charge is the interest and other fees paid for a loan or credit.
The finance charge is based on the annual percentage rate (APR).
The monthly payments, total monthly payments, and the finance charge can be determined using an online finance calculator as follows:
N (# of periods) = 36 months (3 years x 12)
I/Y (Interest per year) = 7.25%
PV (Present Value) = $10,000
FV (Future Value) = $0
Results:
Monthly Payment (PMT) = $309.92
Sum of all periodic payments = $11,157.12 ($309.92 x 36)
Total Interest (finance charge) = $1,157.12
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Rosa is planting bulbs in her garden. She can plant 3 bulbs every 2 minutes. How long will it take her to plant 57 bulbs?
Answer: It would take her 38 minutes to plant 57 bulbs.
Step-by-step explanation:
write an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1
An equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
What is a slope-intercept form?When the line to be examined slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula. In order to make it simple to identify the slope and y-intercept of a line, its equation can be written in the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is referred to as the slope.
Perpendicular line slopes are reciprocals with a negative sign. In the slope-intercept form, y = mx + b, where m is the slope, the supplied line, y = 3x+1, is already in the slope-intercept form.
The line in the example has a slope of 3.
The negative reciprocal of three, or -1/3, is the slope of the perpendicular.
Y = -1/3x + b is the equation for the line that we are looking for.
We must track down b. We solve for b by using the x and y coordinates of the provided location as x and y in the equation above.
y = -1/3x + b
5 = (1/3)(2) + b
5 = (2/3) + b
b = -5-(2/3)
b= -17/3
B is now substituted for in the equation
y = -1/3x-17/3 as we know that b =-17/3.
Therefore, an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
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Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in slope intercept form is y = 1 / 5 x + 7.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's find the slope of the line as follows:
using (0, 7) and (5, 8)
m = 8 - 7 / 5 - 0
m = 1 / 5
m = 1 / 5
Therefore, let's find the y-intercept using (0, 7).
Hence,
y = 1 / 5 x + b
7 = 1 / 5 (0) + b
b = 7
Therefore, the equation of the line is y = 1 / 5 x + 7
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Using the slope formula, find the slope of the line through the points (0,0) and (5,10). Use pencil and paper. Explain how you can use mental math to find the slope of the line.
Two friends take a 4000-mile cross-country trip together, but they drive their own cars. Car A has a 10-gallon gas tank
and averages 30 miles per gallon, while car B has a 20-gallon gas tank and averages 20 miles per gallon. Assume
both drivers pay an average of $2.65 per gallon of gas.
a. What is the cost of one full tank of gas for car A? For car B?
b. How many tanks of gas do cars A and B each use for the trip?
c. About how much do the drivers of cars A and B each pay for gas for the trip
Answer:
a.
Car A: $26.50
Car B: $53.00
b.
Car A: 13 1/3
Car B: 10
c.
Car A: $353
Car B: $530
Step-by-step explanation:
Car A: 10 gal, 30 mpg
Car B: 20 gal, 20 mpg
a.
Car A: 10 gal × $2.65/gal = $26.50
Car B: 20 gal × $2.65/gal = $53.00
b.
Car A: 1 full tank will drive 10 gal × 30 mpg = 300 miles
4000 miles / 300 miles = 13 1/3
Car B: 1 full tank will drive 20 gal × 20 mpg = 400 miles
4000 miles / 400 miles = 10
c.
Car A: 13 1/3 × 10 gal × $2.65/gal = $353
Car B: 10 × 20 gal × $2.65/gal = $530
Approximate -12+√32 to the nearest tenth.
-6.3
-5.7
5.7
6.3
The approximate value of -12 + [tex]\sqrt{32}[/tex] is option (A) -6.3
The given expression is
-12 + [tex]\sqrt{32}[/tex]
First find the value of [tex]\sqrt{32}[/tex]
Prime factorization of 32
Prime factorization is defined as the method of expressing a number as a product of its prime factors
32 = 2 × 2 × 2 × 2 × 2
Therefore,
[tex]\sqrt{32}[/tex] = 2 × 2[tex]\sqrt{2}[/tex]
Multiply the numbers
[tex]\sqrt{32}[/tex] = 4[tex]\sqrt{2}[/tex]
The value of [tex]\sqrt{2}[/tex] = 1.414
The the value of 4[tex]\sqrt{2}[/tex] = 4 × 1.414
Multiply the numbers
= 5.656
The value of the expression
-12 + [tex]\sqrt{32}[/tex] = -12 + 5.656
Add the numbers
= -6.344
Approximate value will be
≈ -6.3
Therefore, the result of the expression -12 + [tex]\sqrt{32}[/tex] is -6.3
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how do i simplify 3(8x-4)-6x+6?
Answer:
18x−6
Step-by-step explanation:
Distribute
A psychologist is studying the self image as measured by the self image score for a personality
The minimum sample size needed for the desired margin of error of the confidence interval is given as follows:
44.
How to obtain the sample size needed?The sample size needed is obtained using the z-distribution, as the standard deviation for the population is known.
The equation that gives the margin of error for a z-distribution confidence interval is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given as follows:
z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The known measures in this problem are given as follows:
[tex]M = 20, \sigma = 80, z = 1.645[/tex]
Then the desired sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.645\frac{80}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.645 \times 80[/tex]
Simplifying by 4, we have that:
[tex]\sqrt{n} = 1.645 \times 4[/tex]
[tex](\sqrt{n})^2 = (1.645 \times 4)^2[/tex]
n = 43.3.
Rounding up, as a sample size of 43 would have a margin of error slightly above 20, the sample size needed is of 44.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Is 70/100 equal to 7/10?
Answer:
Yes
Step-by-step explanation:
A simple way to know is by simplifying them.
70/100 divided by 10 is 7/10
First divide 70 by 10: you get 7
Then divide 100 by ten: you get 10
please perform the following division !!
Answer:
[tex]\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{3}{a}+\frac{2}{b}}{\frac{5}{a^2}-\frac{2}{b^2}} \\ \\ =\frac{a^2 b^2 \left(\frac{3}{a}+\frac{2}{b} \right)}{a^2 b^2 \left(\frac{5}{a^2}-\frac{2}{b^2} \right)} \\ \\ =\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]
Suppose that 18 inches of wire costs 72 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
Answer:
39 inches of wire would cost 156 cents
Step-by-step explanation:
1) Make an Equation
18x = 72
2) Solve for x to determine cost per inch of wire
x = 72/18
x = 4
3. Multiply x value by 39 to get the cost for 32 inches of wire (c)
39x = c
39 (4) = c
156 = c