write the slope intercept form of the equation of the line through the given points 4) through: (1,-5) and (4, 2)​

The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)

What is parabola?

A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.

Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.

To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:

2 = a(0 + 1)(0 - 4)

2 = -4a

Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.

To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:

0 = a(-2 - h)² + k

0 = a(3 - h)² + k

Solving for h and k, we get:

h = 1/2

k = 4

Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:

y = a(z - 1/2)² + 4

We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:

4 = a(0 - 1/2)² + 4

4 = a(1/4)

a = 16

Therefore, the equation of the parabola in factored form is:

y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.

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Step-by-step explanation:

with 2 cubes we have 12 faces to paint.

each face has 2 options (black or white).

so, we have a total of 2¹² possible outcomes.

a probability is always the ratio of

desired cases / totally possible cases

so, we need to find a way to express the desired cases of both cubes being painted the same way.

essentially that means we have a totally free choice of painting the faces of the first cube.

that is 2⁶ possible outcomes.

for the second cubes we have then only one basic choice : to repeat the choices done on the first cube.

BUT : we have 6×4 ways to orient the second cube before painting it identically.

6 ways to pick e.g. the front face, and then 4 options to rotate the cube with the same front face for the e.g. top face.

in other words, we have 2⁶ different desired patterns on the first cube and 24 options to repeat the pattern on the second cube.

that means the desired options are 2⁶×1×24

so, the probability for them to be identical is

24×2⁶ / 2¹² = 24/2⁶ = 3/2³ = 3/8 = 0.375

The probability that after they are painted, the cubes can be rotated to be identical in appearance is (a) 64/9

Probability is a branch of mathematics that deals with the study of random phenomena or events with uncertain outcomes.

Let's start by assuming that one of the cubes has the black face facing up. The other cube can be painted in any of the possible ways.

Let's list all the possible configurations for the second cube.

There are six faces, and each can be painted either black or white. Therefore, there are 2⁶ = 64 possible configurations for the second cube.

The cube with the black face facing up has been accounted for separately, so there are 63 configurations that we need to consider.

If the second cube is painted all black or all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the black or white face is facing up.

There are two such configurations. If the second cube has exactly one white face and five black faces, there are three ways to position it so that the cubes look identical. There are three such configurations

.If the second cube has two white faces and four black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.

If the second cube has three white faces and three black faces, there are eight ways to position it so that the cubes look identical. There are eight such configurations.

If the second cube has four white faces and two black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.

If the second cube has five white faces and one black face, there are three ways to position it so that the cubes look identical. There are three such configurations

.If the second cube is painted all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the white face is facing up. There are two such configurations.

In total, there are 2 + 3 + 6 + 8 + 6 + 3 + 2 = 30 ways to position the two cubes so that they look identical.

There are 63 × 64 possible configurations for the two cubes, so the probability of the cubes being able to be rotated to be identical in appearance is given by:

30/ (63×64) = 64/9

Therefore, the correct answer is (a) 64/9.

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Answer:

evaluate: −0.68171817=18.7

Step-by-step explanation:

The length AC of the triangle is 4.47 units.

The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.

To find the length AC in the triangle, we have to use distance formula as follows:

Therefore,

A = (1, 1)

C = (3, 5)

AC = √(y₂ - y₁)² + (x₂ - x₁)²

AC = √(5 - 1)² + (3 - 1)²

AC = √4² + 2²

AC = √16 + 4

AC = √20

Hence,

AC = 4.472135955

AC = 4.47 units

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If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.

Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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There are 13,800 different ways to have the first, second, and third place winners without any ties.

In a rubber duck regatta with 25 people competing and each person having only one entry, we can determine the number of ways to have the first, second, and third place winners by using permutations.
Step 1: Calculate the number of options for the first place winner.

There are 25 contestants, so there are 25 options for the first place.
Step 2: Calculate the number of options for the second place winner.

Since the first place winner has been determined, there are 24 remaining contestants to choose from for the second place.
Step 3: Calculate the number of options for the third place winner.

After determining the first and second place winners, there are 23 remaining contestants to choose from for the third place.
Step 4: Multiply the number of options for each place to get the total number of possible outcomes.
25 options (first place) × 24 options (second place) × 23 options (third place) = 13,800 possible outcomes.

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The percent increase in her pay is by 26.06% if she takes the new job.

A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.

Given that, the pat increases from $8.25 an hour to $8.25 an hour.

percent increase = [(new value - old value) / old value] x 100%

Substituting the values we have:

percent increase = [(10.40 - 8.25) / 8.25] x 100%

percent increase = 26.06%

Therefore, Lily's pay would increase by 26.06% if she takes the new job.

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Answer: D.) 2x + 22 = 50

Step-by-step explanation:

P=2(l+w)

2x+22=50 is correct because

2 times x is 2 times the unknown length

11 times 2 is 22 so, you add that to the 2x

50 is the perimeter

Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.

So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.

To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.

Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

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Answer:

92 hours

Step-by-step explanation:

7 * 12 + 8 = 92

Answer:

8

Step-by-step explanation:

To find the length of the third side, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

So, in this case, we have:

x^2 + 6^2 = 10^2

Simplifying this equation, we get:

x^2 + 36 = 100

Subtracting 36 from both sides, we get:

x^2 = 64

Taking the square root of both sides, we get:

x = 8 or x = -8

Since the length of a side of a triangle can't be negative, the length of the third side is x = 8 cm.

There are [tex]18[/tex] square units in the area of the shaded rectangle.

The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.

In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.

width [tex]= 7[/tex] units

length [tex]= 10[/tex] units

We remove the frame, each measure will lose[tex]2*2[/tex] units, or [tex]4[/tex] units

[tex]width = 7 units - 4 units = 3 units[/tex]

[tex]length = 10 units - 4 units = 6 units.[/tex]

[tex]A = (3 units)*(6 units) = 18[/tex] square units.

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The completed question is:

One rectangle is "framed" within another. Find the area of the shaded region if the

"frame" is 1 unit wide.

10

5

Using the given clues, we can fill out the table as follows:

Section     Number      Color

A                    3             Green

B                    5              Purple

C                    9              Brown

D                    8              Orange

E                    1               Yellow

F                    6                Blue

G                   4                 Pink

Using this information, we can deduce the values of each section:

The number 8 is in all shapes

So, D = 8

Number C is the largest

For the blue section, we have

F = Blue

For the triangle, we have

DEF = 48

D + E + F = 15

So, we have

EF = 6

E + F = 7

This means that

(E, F) = (1, 6) or (6, 1)

Number 1 is yellow

So, we have

Since F is not yellow, then

A = Green

A and G add up to 7, and A's number is smaller than G's.

So A and G must be (1, 6), (3, 4) because 2 and 7 are not used

Because of the values of E and F, we have

A = 3 and G = 4

Green and pink are in the rectangle only

So:

G = Pink

Purple and Orange are in the circle

So:

(B, D) = (Orange, Purple), (Purple, Orange)

The purple section is 5 and D = 8

So:

(B, D) = (Purple, Orange) = (5, 8)

The table has been completely filled

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The value of the expression 5x - 3y, is -29 obtained by elimination method by eliminating the two equations.

The equations are :

3x - 4y= -24     -----------   A

3x +2y= -6       -----------   B

On multiplying minus sign in B equation, to eliminate the x- component in the equation.

3x +2y= -6 becomes (-3x - 2y = 6)

Then, the equation becomes,

3x - 4y= -24

-3x - 2y = 6          (+ 3x - 3x are equal and opposite becomes zero.)

------------------

    -6y = -18

------------------

6y = 18          (both minus sign gets cancelled)

y = 18/6

 = 3

The value of y=3.

Substitute the value of y=3 in A equation.

Equation A is,  3x - 4y= -24

3x - 4(3) = -24

3x = -24 + 12

3x = -12

x = -12 / 3

 = -4

The value of x= -4.

Thus, the value of x= -4 and y = 3. By using this x and y values, the equation  5x - 3y, can be solved as,

= 5x - 3y

= 5(-4) - 3 (3)

= -20 -9

= -29

The value of the expressions 5x - 3y = -29.

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If a tank is shaped like an upside down square-pyramid, then the rate at which the height of water is increasing when the water is 2 m deep is 51.75 m/sec.

The tank is upside down square-pyramid, with sides as 4 meter,

Let the height of water at any time "t" be = "h",

The height of the tank is = 12 meter,

Let, the side of the base of pyramid shaped water at any time "t" be = "b",

So, b = (1/3)h   ...because height of pyramid is 12 and each side is of 4, the ratio is 1/3,

The volume of water at nay time "t" is (V) = (1/3)b²h,

⇒ V = (1/3)(1/3h)²h,

⇒ V = h³/27,

Now, dv/dt = (d/dt)(h³/27),

On simplifying further,

we get,

⇒ dv/dt = (h²/9)(dh/dt),

⇒ dh/dt = (9/h²)(dv/dt),

We know that, when the water is 2 meter deep, and if water is pumped out at rate of 23 m³/sec, it means that h = 2, and dv/dt = 23,

So, dh/dt = (9/2²)(23) = 51.75 m/sec.

Therefore, the rate of change of height is 51.75 m/sec.

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Answer:

To find the values of a and b, we need to substitute the coordinates of the given point (11,3) into both equations and solve for a and b.

Substituting (11,3) into the first equation ax-2y=5:

a(11)-2(3)=5

11a-6=5

11a=11

a=1

Substituting (11,3) into the second equation 2x-by =8:

2(11)-b(3)=8

22-3b=8

-3b=-14

b=14/3

Therefore, a=1 and b=14/3.

Answer:

a = 1

b = 4.67 OR 14/3

Step-by-step explanation:

ax - 2y = 5

a(11) - 2(3) = 5

11a - 6 = 5

11a = 11

a = 1

2x - by = 8

2(11) - b(3) = 8

22 - 3b = 8

3b = 14

b = 4.67 OR 14/3

Answer:

660cm^2

Step-by-step explanation:

area of 2 triangle= 10×12

= 120cm^2

area of 3 rectangles= (13×15×2)+(10×15)

= 390+150

= 540cm^2

surface area of triangular prism

= 540+120

= 660cm^2

Step-by-step explanation:

To find Sara's semi-monthly salary, we need to divide her annual salary by the number of semi-monthly periods in a year.

Since there are 24 semi-monthly periods in a year (twice a month), we can divide her annual salary by 24 to get her semi-monthly salary:

$37,560 ÷ 24 = $1,565.00

Therefore, Sara's semi-monthly salary to the nearest cent is option C) $1,565.00.

The distance between the centers of the two wheels is approximately 11.86 feet.

The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.

Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula

C = πd

Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:

C = πd = π(0.5) = 1.57 feet (approx.)

The length of the conveyor belt is given as 15 feet. So we can write

2C + d = 15

Substituting the value of C, we get

2(1.57) + d = 15

3.14 + d = 15

d = 11.86 feet

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Step-by-step explanation:

you have to subtract them which would be -1.05

Answer:

Therefore, there are approximately 102 kilocalories in the snack bar.

Step-by-step explanation:

One gram of fat provides 9 kilocalories (kcal), while one gram of carbohydrate and protein provide 4 kcal each. So, to find the total number of kilocalories in the snack bar, we can use the following formula:

Total kcal = (grams of fat * 9) + (grams of carbohydrate * 4) + (grams of protein * 4)

Plugging in the values, we get:

Total kcal = (6 * 9) + (10 * 4) + (2 * 4)

Total kcal = 54 + 40 + 8

Total kcal = 102

Therefore, there are approximately 102 kilocalories in the snack bar.

The answer is  approximately 120 kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein.

What are kilocalories? Kilocalories, also known as calories, are a unit of energy used to calculate the amount of energy in food. The number of kilocalories in food is calculated based on the number of grams of protein, carbohydrate, and fat it contains. Kilocalories are used by the body to fuel its processes and maintain its vital functions. The energy in food is released when it is digested, absorbed, and transported to the cells where it is used to produce ATP, the body's primary source of energy. ATP is used to power cellular processes such as metabolism, respiration, and movement. How many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein? To calculate the number of kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein, we need to know the number of kilocalories per gram of each macronutrient. Protein and carbohydrates each contain 4 kilocalories per gram, while fat contains 9 kilocalories per gram. To calculate the number of kilocalories in the snack bar, we multiply the number of grams of each macronutrient by the number of kilocalories per gram and then add them together. Here is the calculation:6 grams of fat x 9 kilocalories per gram of fat = 54 kilocalories10 grams of carbohydrate x 4 kilocalories per gram of carbohydrate = 40 kilocalories2 grams of protein x 4 kilocalories per gram of protein = 8 kilocalories. Total kilocalories = 54 + 40 + 8 = 102Therefore, a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories.
A snack bar with 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories. This is calculated as follows: (6 grams fat x 9 kcal/g) + (10 grams carbohydrate x 4 kcal/g) + (2 grams protein x 4 kcal/g).

Therefore, answer is 120 kilocalories.

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Answer: C. The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

Step-by-step explanation:

Answer:

(2, 3)

Step-by-step explanation:

     9x - 7y = -3                

+   -9x + 15y = 27

             8y = 24           (Divide by 8 on both sides)

             8   =  8

y = 3

Substitute y = 3 in any of the two equations.

9x - 7(3) = -3

9x - 21 = -3

     +21 = +21         (Add 21 on both sides)

 9x     =  18               (Divide by 9 on both sides)

  9      =   9

x = 2

After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.

[tex]m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\[/tex]

[tex]y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\[/tex]

The ratio in which AB is divided by x + y = 2 is:

[tex]AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\[/tex]

As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

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According to the evidence from graph a and graph b, graph a indicates that the model for the data was a good fit because it is a random.

Hence, the correct option is B.

Based on graph a, the residual plot shows a random scattering of points around the horizontal line at y=0. This indicates that the residuals (the differences between the observed and predicted values) are distributed randomly and do not show any clear pattern. This suggests that the data points are evenly distributed around the regression line, indicating a good fit for a linear regression model.

On the other hand, graph b shows a residual plot with a clear pattern or trend. The residuals are not randomly scattered, but instead show a curved pattern or a fan-like shape. This indicates that the model used to fit the data may not be appropriate, as it is not capturing the underlying relationship between the variables accurately.

Hence, the correct option is B.

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-- The given question is incomplete, the complete question is

"The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph a and graph b which graph indicates that the model for the data was a good fit and what is the reason?

A. Graph A because it is symmetrical

B. Graph A because it is random

C. Graph B because there is a pattern

D. Graph B because it is symmetrical" --

Answer:

Function decreasing: where x is (-4; 0) and (2; 4)

Function increasing: where x is (0; 2)

Step-by-step explanation:

Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.

Answer:

dont no ok i dont konow ask an easy one

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