Which of the following graphs shows a pair of lines that represents the equations with the solution (4, −1)?

A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the right and 4 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the right and 1 unit down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the left and 1 unit up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the left and 4 units up.

Nolan wrote an incorrect value as the y-intercept, the actual linear equation is:

y = -5x + 25

Remember that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we know that Nolan starts with $25, and then he loses $5 per day, so after x days, he will have:

$25 - $5*x

That is the linear equation he should have written, instead of:

y = -5x + 5

So you can see that the y-intercept is wrong, because Nolan used 5 instead of 25.

Then:

The mistake is that he wrote the y-intercept wrong.

The actual linear equation is:

y = -5x + 25

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Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Answer:

Since this is a right triangle with one angle and hypotenuse given and opposite side unknown, we can use the definition of sine to find the unknown side.

sin 17 = x/hypotenuse = x/19

x = 19sin17 = 5.6

Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.

To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:

Help Center to Water Slide #1:

Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)

Toddler area to Concessions:

Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)

Gift Shop to Restrooms:

Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)

Security desk to Water Slide #2:

Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)

Lazy River to Large Whirlpool:

Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5

Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)

Presently, let's calculate the linear equations for each case:

Help Center to Water Slide #1:

The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.

Toddler area to Concessions:

The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:

-7.5 = (-1/3)(1.5) + b

-7.5 = -0.5 + b

b = -7

Gift Shop to Restrooms:

The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.

Security desk to Water Slide #2:

The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.

Lazy River to Large Whirlpool:

The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:

12 = (2/5)(-2) + b

12 = -4/5 + b

b = 61/5

The Linear equations for each case are as follows:

Help Center to Water Slide #1: y = 3

Toddler area to Concessions: y = (-1/3)x - 7

Gift Shop to Restrooms: y = -9

Security desk to Water Slide #2: y = 4

Lazy River to Large Whirlpool: y = (2/5)x + 61/5

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Answer: 13.10

Is power

Answer:

Step-by-step explanation:

its not to hard

  1  1

  2.35

+0.75

~~~~~~

   3.1 0  

+10

~~~~~~~  

 13.10

The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.

Given the quadratic equation in the question:

6x² = -3x + 1

To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:

6x² + 3x - 1 = 0

Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)

Here; a = 6, b = 3, and c = -1.

Let's substitute these values into the quadratic formula:

\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)

Therefore, the values of x are -0.73 and 0.23.

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Answer:

Its the first one

Step-by-step explanation:

It is a statistical question because the data may vary for each player. :)

Answer:

C: EAF Is the correct answer

Answer:

67

6+7=13

76-67=9

Done!

Answer:

-9

Step-by-step explanation:

\(z^{-1}(-2)=k \implies z(k)=-2 \\ \\ k=-9 \implies z^{-1}(-2)=-9\)

Answer:

If you need to find s when t is 9, its simple.

Step-by-step explanation:

All ypu need to do is see what t is

t equals 2

you want to find what s is when t is 9

when t is 2, s is 294

when t is 9, all you have to do is find what times 2 equals 9, then times that number by 294

Answer:

it is -1.5.

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

hope this helps

Answer:

20

Step-by-step explanation:

20 but by 10 and the eay it sees

Answer: x=-2

Step-by-step explanation:

they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem

Considering the polynomial f(x) = x^4  - 16x³ + 70x² + 48x - 219, we have that:

a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).

c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

The given zero of the polynomial is:

8 + 3i

Hence it's conjugate is also a zero, that is:

8 - 3i.

Thus the first two factors are given as follows:

(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.

Then the polynomial can be written as follows:

x^4  - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).

As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:

x^4  - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.

Then the coefficients are given as follows:

Hence the other two factors are given as follows:

x² - 3.98 = 0

x = ± sqrt(3.98)

x = ± 1.995.

The linear factors are:

(x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots.

The solutions to f(x) = 0 are the roots.

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The sample variance is approximately 44.79 and the sample standard deviation is approximately 6.692.

To find the sample variance and standard deviation, follow these steps:

1. Calculate the mean of the data set:

  Mean (μ) = (22 + 11 + 4 + 9 + 10) / 5 = 56 / 5 = 11.2

2. Calculate the difference between each data point and the mean, and square each difference:

  \((22 - 11.2)^2 = 121.00 \\(11 - 11.2)^2 = 0.04 \\(4 - 11.2)^2 = 51.84 \\(9 - 11.2)^2 = 4.84 \\(10 - 11.2)^2 = 1.44\)

3. Calculate the sum of all the squared differences:

  121.00 + 0.04 + 51.84 + 4.84 + 1.44 = 179.16

4. Calculate the sample variance:

  Variance \((s^2)\) = sum of squared differences / (n - 1)

                 = 179.16 / (5 - 1)

                 = 179.16 / 4

                 = 44.79

5. Calculate the sample standard deviation:

  Standard Deviation (s) = square root of the variance

                         = √44.79

                         ≈ 6.692

Therefore, the sample standard deviation is about 6.692, while the sample variance is about 44.79.

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Answer:

0.05

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

helping you bud just gotta borrow 50 points

Step-by-step explanation:

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  0 ft

Step-by-step explanation:

The line hangs down 15 feet from the top of each pole, so the distance between them must be zero if the total line length is 30 feet.

Answer:

of what?

Step-by-step explanation:

umm probably like 3% if there's a lot of other colors and theres on one red. but if there in only like 15 other colors and theres on one red it would probably be like 25% that you gonna get the red one.

Answer:

d. Several means when there are two independent variables, and the same entities have been used in all conditions.

Step-by-step explanation:

ANOVA is an abbreviation for analysis of variance and it was developed by the notable statistician Ronald Fisher. It is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors. In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.

Two-way repeated-measures ANOVA compares several means when there are two independent variables, and the same entities have been used in all conditions.

Hence, the aim of a two-way analysis of variance (ANOVA) is to give the relationship or identify if there is an interaction between the two independent variables on the dependent variable.

-2/3

\(s = \frac{y2 - y1}{x2 - x1} \)

1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

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Answer:

Step-by-step explanation:

Slope intercept form of a line is

y=mx+b, where m=slope and b=y intercept

m=(y2-y1)/(x2-x1) I chose points (0,3) and (4,4) from graph so

m=(4-3)/(4-0)=1/4 so now the line is

y=x/4+b, using point (4,4) we can solve for b

4=4/4+b

4=1+b

b=3 so the line is

y=x/4+3 or more neatly

y=(x+12)/4