The equation of line that passes through point (-8, 1) and parallel to x - 4y = 4 is x - 4y + 12 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given equation is,
x - 4y = 4.
The slope of the given equation,
m = 1/4
The slope of the required line will be equal to given line if line is parallel.
The equation of line that passes through point (-8, 1) and parallel to line x - 4y = 4.
y - 1 = m (x - (-8))
y - 1 = 1/4.(x + 8)
4y - 4 = x + 8
x - 4y + 12 = 0
The required equation of line is x - 4y + 12 = 0.
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On a bicycle Eloy can travel 20 miles in 5 hours. Write the unit ratio for miles per hour.
Answer:
100 miles
Step-by-step explanation:
20 times 5
4 miles per hour.
or if you want ratio it's 20/5
How I did it is just divide 20 and 5 to get 4
given the following table with selected values of f(x) and g(x) evaluate f(g(1))
The value of f(g(1) from the table of functions is given as 1.
What is Functions ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
when x = 1
g(x) = 3
or f(g(1) = f(3) = 1
The value of f(g(1) from the table of functions is given as 1.
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Side XY of triangle XYZ is extended to point W, creating a linear pair with ∠WYZ and ∠XYZ.
Triangle X Y Z. Point W extends from side X Y. Angle Z is 36 degrees, angle Y is x degrees, and exterior angle W Y Z is 100 degrees.
What is the value of x?
Answer:
\(x= 80^o\)
Step-by-step explanation:
Given
\(\angle Z = 36^o\)
\(\angle WYZ = 100^o\)
Required
Find x
\(\angle WYZ\) and x are on a straight line.
So:
\(\angle WYZ + x= 180^o\)
Make x the subject
\(x= 180^o -\angle WYZ\)
Substitute known value
\(x= 180^o -100^o\)
\(x= 80^o\)
Answer:
80 is correct
Step-by-step explanation:
A local gas station waits 4 days to receive its delivery after he calls and places an order. The amount of gas that the station sells in a day is independent of other days and follows a Normal distribution with mean 1000 gallons and standard deviation of 400 gallons. Which one of the statements is true?
a. The chance of selling more than 1400 is around 15%
b. The chance of selling more than 1400 is around 5%
c. The chance of selling more than 1400 is zero
d. The chance of selling more than 1400 is around 10%
Answer:
C
Step-by-step explanation:
3y + 2 + 2y + 5 =x + y + 2y – 4 =
Answer:
This is your answer ☺️. If I'm right so,
Please mark me as brainliest. thanks!!!
4x(x + 1) − (3x − 8)(x + 4)
The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.
To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.
Expanding the first term, we get 4x^2 + 4x.
Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.
Combining like terms, we obtain -3x^2 - 4x - 32.
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A number is divided by 5 then decreased by 5. It becomes -2. Find the number
Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to triple? Round to the nearest tenth of a year.
Answer:
\( 300000= 100000 e^{0.12 t}\)
We divide both sides by 100000 and we got:
\( 3 = e^{0.12 t}\)
Now we can apply natural logs on both sides;
\( ln(3) = 0.12 t\)
And then the value of t would be:
\( t = \frac{ln(3)}{0.12}= 9.16 years\)
And rounded to the nearest tenth would be 9.2 years.
Step-by-step explanation:
For this case since we know that the interest is compounded continuously, then we can use the following formula:
\(A =P e^{rt}\)
Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.
For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means \( A= 300000\) and we want to find the value for t.
\( 300000= 100000 e^{0.12 t}\)
We divide both sides by 100000 and we got:
\( 3 = e^{0.12 t}\)
Now we can apply natural logs on both sides;
\( ln(3) = 0.12 t\)
And then the value of t would be:
\( t = \frac{ln(3)}{0.12}= 9.16 years\)
And rounded to the nearest tenth would be 9.2 years.
i have so many points help me
Divide.
(−15)÷(−45)
What is the quotient?
Enter your answer as a simplified fraction in the box.
Help woth math problems
The standard form of the quadratic functions can be analyzed, by finding the specified coordinates as follows;
1. Vertex; (2, -3)
Axis of symmetry; x = 2
Minimum value; -3
Range; y ≥ -3
2. Vertex; (1, 4)
Axis of symmetry; x = 1
Maximum value; 4
Range; y ≤ 4
3. Vertex; (-3, -1)
Axis of symmetry; x = -3
Maximum value; -1
Range; y ≤ -1
4. Vertex; (-3, 5)
Axis of symmetry; x = -3
Maximum value; 5
Range; y ≤ 5
5. Vertex; (-0.75. -6.125)
Axis of symmetry; x = -0.75
Minimum value; -6.125
Range; y ≥ -6.125
6. Vertex; (2/3, 4/3)
Axis of symmetry; x = 2/3
Maximum value; 4/3
Range; y ≤ 4/3
Please find attached the graphs for the quadratic equations in question 7, 8, 9 and 10, created with MS Excel.What is the standard form of a quadratic function?The standard form of a quadratic function is the form; f(x) = a·x² + b·x + c, a, b, and c are constants and a ≠ 0.
1. The x-value of the vertex point of the quadratic equation; y = ax² + bx + c is; x = -b/(2·a)
Therefore, the x-value of the vertex point of the equation, y = x² - 4·x + 1 is; x = 4/2 = 2
The y-value of the vertex point is; y = 2² - 4×(2) + 1 = -3
The vertex is; (2, -3)
The axis of symmetry if the x-value of the vertex point, therefore;
The axis of symmetry is; x = 2
The minimum value is the y-value of the vertex point, therefore;
The minimum value is; y = -3
The range is the set of the possible y-values
The positive leading coefficient of the function, indicates that the range of the function is the set of values larger than the minimum value.
Therefore, the range is; y ≥ -3
2. The x-value of the vertex point of the equation, y = -x² + 2·x + 3, therefore is; x = -2/(-2) = 1
The y-value at the vertex point is; y = -1² + 2×1 + 3 = 4
The vertex is; (1, 4)
The axis of symmetry is; x = 1
The maximum value is; y = 4
The range is; y ≤ 4
3. The x-value of the vertex is; x = -(-6)/(2 × (-1)) = -3
The y-value at the vertex is; y = -(-3)² × -6 × (-3) - 10 = -1
The vertex is; (-3, -1)
The axis of symmetry is; x = -3
The maximum value is; y = -1
The range is; y ≤ -1
4. The x-value of the vertex is; x = -18/(2×3) = -3
The y-value of the vertex is; y = 3 × (-3)² + 18 × (-3) + 32 = 5
The vertex is; (-3, 5)
The axis of symmetry is; x = -3
The minimum value is; y = 5
The range is; y ≥ 5
5. The x-value of the vertex is; x = -3/(2 × 2) = -3/4
The y-value of the vertex is; y = 2 × (-3/4)² + 3 × (-3/4) - 5 = -6.125
The vertex is; (-3/4, -6.125)
The axis of symmetry is; x = -3/4
The minimum value is; -6.125
The range is; y ≤ -6.125
6. The x-value of the vertex is; -4/(2 × (-3)) = 2/3
Y-value at the vertex is; y = -3 × (2/3)² + 4 × (2/3) = 4/3
The vertex point is; (2/3, 4/3)
The axis of symmetry is; x = 2/3
The maximum value is; 4/3
The range is; y ≤ 4/3
7. The graphs of the quadratic equations can be obtained by finding the coordinates of the vertex, the y-intercept and the x-intercepts and joining the points using a curve symmetrical about the vertex as follows;
The following values are obtained using an online tool.
7. The graph of the equation; y = x² + 2·x - 5, can be obtained using the following points;
The vertex is; (-1, -4)
The y-intercept is; (0, -5)
The x-intercepts are; (-1 + √6, 0), and (-1 - √6, 0)
8. The graph of the equation; y = -x² + 3·x + 1, can be obtained using the following points;
The vertex is; (3/2, 5/4)
The y-intercept is; (0, 1)
The x-intercepts are; (-0.30, 0), and (3.30, 0)
9. The graph of the equation; y = 2·x² + 4·x - 4, can be obtained using the following points;
The vertex is; (-1, -6)
The y-intercept is; (0, -4)
The x-intercepts are; (-1 + √3, 0), and (-1 - √3, 0)
10. The graph of the equation; y = (-1/2)·x² - 3·x + 3, can be obtained using the following points;
The vertex is; (-3, 7.5)
The y-intercept is; (0, 3)
The x-intercepts are; (-3 + √(15), 0), and (-1 - √(15), 0)
Please find attached the graphs of the quadratic equations created with MS Excel
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18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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if a cylinder with a 6 in. radius is spinning at 24 mph, find the angular velocity in rpm of a point on its rim ?
The angular velocity in rpm of a point on its rim is equals to the 4224 rad/min.
We have, a cylinder with Radius , R = 6 inch. Spining velocity, S = 24 miles per hour
We have to calculate the the angular velocity in rpm of a point on its rim. To calculate Angular and Linear Speed from Linear velocity :
Step 1: Identify which speed we are asked to calculate and Identify the radius and the velocity. We already identified all this in above.
Step 2: To calculate the angular speed when the linear speed and the radius of the circular object use : angular velocity = linear velocity/radius
First, we need to reconcile the unit of the radius of the wheel/rim and the unit of the speed of the car. Also, we are asked to give the answer in radians per minute. So, let's convert the speed to inches per minutes. So, the linear velocity of spining = 24 miles per hour × 5280 ft. per miles× 12 inches per ft. × 1 hour / 60 minutes
= 25,344 inches per minute
Now, the angular velocity is written as
angular velocity = linear velocity /radius
= 25,344 inches per minute / 6 inches
= 4224 /min. Hence, the angular velocity of the rim is 4224 rad/min.
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If a cylinder with a 6 in. radius is spinning at 24 mph, The angular velocity of a point on the rim of the cylinder is 672.27 rpm.
Angular velocity is a measure of the speed at which an object is rotating around a central axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm). To find the angular velocity of a point on the rim of the cylinder, we need to first convert the linear velocity (24 mph) to linear velocity in feet per second (ft/s). We can use the formula:
v = r * ωwhere v is the linear velocity, r is the radius of the cylinder, and ω is the angular velocity.
Due to the 6 in. = 0.5 feet,
ω = v χ 1 r = 24 miles hr 1 0.5 ft χ 5280 ft mile = 253,440 (rad) hr
Then, 672.27 rpm at 253,440 (rad) hr 1 2pi rev rad 1 60 hr min
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How would you solve
"if f(x) / (x - 2) = x ^ 3 + 2x - 4 + 13/(x - 2) what is f(2)"
and
"if f(x) / (x + 3) = 3x ^ 2 - 4x + 2 what is f(-3)"
The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.
To solve the given equations, we need to find the value of the function f(x) for specific values of x.
"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"
To find f(2), we can substitute x = 2 into the equation and solve for f(2).
Plugging in x = 2, we get:
f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)
Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.
"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"
To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).
Plugging in x = -3, we get:
f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2
Simplifying, we have:
f(-3) / 0 = 3(9) + 12 + 2
f(-3) / 0 = 27 + 12 + 2
f(-3) / 0 = 41
Additional information or context is needed to solve for f(-3).
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Suppose that a baseball player has been a .250 hitter for his career, which means that his probability of a hit (success) has been 0.250. Then during one winter the player genuinely improves to the point that his probability of success improves to 0.333. You will investigate how likely the player is, in a sample of at-bats, to convince the manager that he has improve
Answer:
To convince the manager that he has improved, we need to take a sample and test against the null hypothesis that states that the proportion of success of this player is not significantly higher than 0.250.
If we have a sample of size n=20 with sample proportion 0.333, at a significance level of 0.05, there is not enough evidence to support the claim that the proportion of success is greater than 0.250.
Step-by-step explanation:
In this case, to demostrate that the baseball player has improved his probability of success over 0.250, we need to know the sample size of that winter (that gives p=0.333) and then perform a hypothesis test on the proportion of at-bats.
Lets assume the sample is n=20, and the sample proportion is p=0.333.
The claim is that the proportion of success is greater than 0.250.
Then, the null and alternative hypothesis are:
\(H_0: \pi=0.25\\\\H_a:\pi>0.25\)
The significance level is 0.05.
The sample has a size n=20.
The sample proportion is p=0.333.
The standard error of the proportion is:
\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.25*0.75}{20}}\\\\\\ \sigma_p=\sqrt{0.009375}=0.097\)
Then, we can calculate the z-statistic as:
\(z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.333-0.25-0.5/20}{0.097}=\dfrac{0.058}{0.097}=0.599\)
This test is a right-tailed test, so the P-value for this test is calculated as:
\(\text{P-value}=P(z>0.599)=0.275\)
As the P-value (0.275) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of success is greater than 0.250.
The length of a rectangular garden is twice the width, if the garden has an area of 8 feet2 what is the length and width
Answer:
length = 4ft
width= 2ft
Step-by-step explanation:
The length of a rectangular garden is twice the width, then
width = w
length = 2w
Area of Rectangle = length *width
8= w*2w
8= 2w^2
w^2= 4
w= 2ft.
length =2*2= 4 ft
The diameter
of the Earth is 1.3 × 10 km.
The diameter of the Moon is 3.5 × 10 km.
The diameter of the Sun is 400 times greater
than the diameter of the Moon.
How many times smaller is the diameter of
the Earth than the diameter of the Sun
Earth's diameter is 0.0092 times less than the sun's diameter.
Ratio, in math, is a time period this is used to examine or greater numbers. It is used to indicate how large or small a sum is in comparison to another.In a ratio, portions are as compared the use of division. Here the dividend is referred to as the `antecedent' and the divisor is referred to as the 'consequent'. For example, in a collection of 30 people, 17 of them opt for to stroll within side the morning and thirteen of them favor to cycle. We use the ratio formulation whilst evaluating the connection among numbers or portions. The popular shape of representing a ratio of among portions say 'a' and 'b' is a: b, that's examine as 'a is to b'.The Diameter of Earth = 1.3 * 10⁴ km
The Diameter of Moon = 3.5 * 10³ km
Let the diameter of sun be x km
According to the question
The diameter of the sun is 400 times that of the moon.
x = 400 * 3.5 * 10³ km
= 14 * 10⁵ km
The Diameter of earth / diameter of sun
= 1.3 * 10⁴ / 14 * 10⁵
= 0.0092
Hence, The diameter of the Earth is 0.0092 times that of the Sun.
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Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 120 and a y-intercept of negative 353.
What is the equation of the regression line?
Select the correct choice below and fill in the answer boxes to complete your choice.
A) y=..+(..)^x
B) y=..+(..)^x
C) y=..+(..)^x
D) y=..+(..)^x
Answer:
y = -353 + 120xStep-by-step explanation:
First step is using a linear regression equation:
In a linear regression model y = b0 + b1x
where y be the response variable
and x be the predictor variable.
let b1 = slope
b0 = intercept of the line.
Let the variable ratings be by denoted by x and the variable price be denoted by y.
From the given information it is known that, price (y) is response variable and ratings (x) predictor variable.
Therefore, price can be predicted using ratings.
Second step is to obtain the regression equation of the variables price (y) and ratings (x):
so the slope of the regression equation is 120 and the y-intercept is -353.
then b0 = -353
therefore,
(price)y = b0 + b1x (ratings)
y = -353 + 120x
The equation of the regression line is y = -353 + 120x.
Given that,
The regression equation has a slope of 120 and a y-intercept of negative 353.Based on the above information, the equation is as follows:
y = -353 + 120x
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I 0 ×I 1× I 2 ×I 3×I 4
Answer:
the answer is twelve by multiplying them all.
Answer:
2 , 40,420
Step-by-step explanation:
10 × 11 × 12 × 13 × 14
1,320 × 182
2,40,240
solve for C using law of cosine tuned to the nearest tenth
The value of angle C is calculated by applying cosine rule as 50.67 ⁰.
What is the value of C?The value of angle C is calculated by applying cosine rule as shown below;
c² = a² + b² - 2ab cosC
The given parameters in the diagram;
length a = 22
length b = 18
c = 20
The value of angle C is calculated as;
20² = 22² + 18² - (2 x 22 x 18) cos C
792 cos C = 502
cos C = 502/792
cos C = 0.6334
C = arc cos (0.6334)
C = 50.67 ⁰
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In the currency pair USD/CAN, USD is what currency?
Select the correct answer. Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel's savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin's account, at the same time, is modeled by function k. j(x) = 25 + 3x k(x) = 15 + 2x Which function correctly represents how much more money, in dollars, is in Joel's account than in Kevin's account x weeks after the start of the year? O A. (j − k)(x) = 40 + 5x (j − k)(x) = 40 + x (j-k)(x) = 10 + 5x (j-k)(x) = 10 + x O B. C. O D. Reset dtry Next
The correct answer is (j - k)(x) = 10 + x.
To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).
(j - k)(x) = (25 + 3x) - (15 + 2x)
= 25 - 15 + 3x - 2x
= 10 + x
This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.
Therefore, the correct function is (j - k)(x) = 10 + x.
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Bill takes a loan of $9000 at a 8% simple interest rate for 6 years.
A. How much interest will he pay after 2 years?
B. How much interest will he pay in total for the loan?
a. $ 720.00; $3,600.00
b. $36,000.00; $ 12,000.00
C. $1440.00; $4,320.00
D. $ 1,408.00; $4,224.00
Answer: you have to divide
Step-by-step explanation:
Find the quotient 3/4÷1 1/10
Answer:
15/22
Step-by-step explanation:
I don’t feel like doing math
Answer:
26.14
Step-by-step explanation: Just subtract.
What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price
Answer:
The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:
$442 * 0.9 = $397.80
The selling price of the same necklace at the competitor's store after 34% and 14% discount is:
$527 * 0.66 * 0.86 = $247.08
So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:
$397.80 - $247.08 = $150.72
To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:
($150.72 / $442) * 100 = 34.11%
Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.
Step-by-step explanation:
What is another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 ?
Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer
How to write a compound inequality in another way?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: y + 3 ≥ 2 and y + 3 < 6
To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:
y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:
2 ≤ y+3 and y + 3 < 6
Combine the two:
2 ≤ y+3 < 6
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write the equation for the line that goes through point (12,5) with slope m= -2
Answer:
y=-2x+29
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-2(x-12)
y=-2x+24+5
y=-2x+29
How do I do this?
My son school just gave him this and he doesn’t know how to do it and I don’t know.
Answer:
I would just search online what are corresponding angles and then base it off of angles like angle number 4 is corresponding because corresponding angles are just angles with the same size and same line
A pole that is 3.3m tall casts a shadow that is 1.44m long. At the same time, a nearby building casts a shadow that is 47.75m long. How tall is the building? Round your answer to the nearest meter.
Answer:
20.8 would be the answer
Step-by-step explanation: