write the equation of the line in slope intercept form that passes through (10,21) and (15,36)

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Answer:

2.5 cm

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

c

Step-by-step explanation:

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

So, 7x³ + 21x² - 63x = 0:

Now, solve for x as follows:

Zero factor principal, if ab = 0, then a = 0 and b = 0.

Now, x² + 3x - 9 = 0:

Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

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The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Answer:

The answer is 28.8, When finding the Volume of a shape, you multiply all numbers.

Answer:

A) P(chooses a blue pencil and then a red pencil) = 5/27

B) P(chooses yellow then blue) = 5/81

Step-by-step explanation:

She has 3 red pencils, 5 blue pencils, and 1 yellow pencil in her backpack

Thus;

total number of pencils = 3 + 5 + 1 = 9 pencils

A) probability that she chooses a blue pencil and then a red pencil;

P(blue) = 5/9

Now she puts it bag after choosing which means the sum is back to 8 pencils.

Thus, if she now chooses a red pencil, then P(red) = 3/9 = 1/3

Thus;

P(chooses a blue pencil and then a red pencil) = 5/9 × 1/3

P(chooses a blue pencil and then a red pencil) = 5/27

B) probability that Chloe chooses the yellow pencil and then a blue pencil;

Similar to A above;

P(yellow) = 1/9

P(blue) = 5/9

P(chooses yellow then blue) = 1/9 × 5/9

P(chooses yellow then blue) = 5/81

Answer:

The answer is b..

Step-by-step explanation:

hope its helpful

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

Part A: the drone would need to fly up 1.3 miles  Part B:  the drone would need to fly up 1.8 miles. Part C:  the value of zero represents the top of the waterfall . Part D: the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.

It can be measured in various units such as meters, kilometers, feet, miles, etc. In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them

Part A: The distance from the top of the waterfall to the place where you eat lunch is 1.3 miles, so the drone would need to fly up 1.3 miles

Part B: The distance from the top of the waterfall to the place where you go swimming is 1.8 miles, so the drone would need to fly up 1.8 miles

Part C: In this problem, the value of zero represents the top of the waterfall where you and your friend are currently located.

Part D: Let x be the distance you hiked to go swimming, and let y be the distance you hiked to go back to the top to meet your friend. Then, the total distance you hiked is the sum of the absolute values of x and y, which can be written as |x| + |y|. Since you hiked down 1.8 miles to go swimming and then hiked back up 1.8 miles to the top, x = -1.8 and y = 1.8. Substituting these values, we get |(-1.8)| + |1.8| = 1.8 + 1.8 = 3.6. Since the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.

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The complete question is :

Answer= yes because we are solving for a and 3 divided 1/3=6

Step-by-step explanation:

Substituting a=-12 into the original equation yields a true statement, so their solutions are correct.

Answers vary. There are at least two solution paths to this equation: you can divide each side by 5 first, then collect like terms, or you can distribute and collect like terms, then continue to solve.

Answers vary. There are still two solution paths to this equation, but one is much simpler than the other. Since not all the terms are multiples of 4, dividing first by 4 will give a fractional coefficient of x on one side. Therefore, distributing first and then collecting like terms and solving is the simpler solution path.

Applying a translation of 5 units left and 2 units up to LM yields the transformed figure L'M' and choice A.

A graph can be moved either laterally or vertically parallel to the -axis, and this movement is called a translation.

LM can be converted to L'M' by carefully following the steps below:

The coordinates (10, -8) are translated 5 units left and 2 units up, which means that the location is obtained by deducting 5 from the x-coordinate and adding 2 to the y-coordinate. (5, -6).

Due to its location on the y-axis, the point (10%, 8) does not shift.

The translation of the point (8, 6M) is 5 units left and 2 units up, which indicates Consequently, we need to add 2 to the y-coordinate and remove 5 from the x-coordinate to get the point. (3, 8M).

The coordinates of the point (2, 6) are moved 5 units to the left and 2 units to the up, giving us the coordinates of the point. (-3, 8).

The translation of the point (6, -8) is 5 units left and 2 units up, so we deduct 5 from the x-coordinate and add 2 to the y-coordinate to get the point. (1, -6).

The point (-8, M) is translated 5 units to the left and 2 units to the right, so we take 5 off the x-coordinate and add 2 to the y-coordinate to get the point. (-13, M).

The key argument (4, 6) is translated as 5 units to the left and 2 units to the up, which means we take 5 away from the x-coordinate and add 2 to the y-coordinate to get the location. (-1, 8).

The coordinates (6, 8) are moved 5 units left and 2 units up, which means we need to deduct 5 from the x-coordinate and add 2 to the y-coordinate to get the new coordinates. (1, 10).

As a consequence, option A is produced by applying a translation of 5 units to the left and 2 units to the up to LM, yielding the transformed figure L'M'.

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The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

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Answer: the probability that a child is within the normal range of long growth is 0.8664

Step-by-step explanation:

Given that;

A child is considered to have a normal long growth if his or her standardized FVC is within 1.5 standard deviation of the mean.

he probability that a child is within the normal range of long growth = ?

so we need to find

P( -1.5 < z < 1.5)  

which can also be represented as;

⇒2 × ( 0 < z < 1.5)

so we have

⇒ 2 × 0.4332

= 0.8664

Therefore the probability that a child is within the normal range of long growth is 0.8664

We have the following:

The first thing is to determine when it is bigger.

In this case x are 4 parts and y are 5 parts, therefore, y is larger, therefore

Therefore, the answer is the option 2 y = 1.25*x

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

2/3x-4

Step-by-step explanation:

2/3*x=2/3x

2/3*6=4

-12a is  a cubic function in exercises when Relative minimum (4,2).

What in mathematics is a relative maximum?

A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .

  f'(x) = 3ax² + 2bx + c

(3,3) and (5,1 ) are print of  relative maximum

   so,    f'(3) = f'(5) = 0

  3a(3)² + 2b(3) + c = 0

or   27a + 6b + c = 0

and   3a(5)² + 2b(5) + c = 0

       75a + 10b + c = 0   ...................... 2

the  Inflection point occurs at point where f''(x) = 0

     d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0

       because (4,2) is point of  Inflection .

           6a(4) + 2b = 0

          24a + 2b = 0

          b = -12a

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Answer:82

Step-by-step explanation:

Hi there!

\(\large\boxed{x = \frac{3}{4}, y = \frac{9}{4}}}\)

8x + 4y = 15

x + y = 3

Use the second equation to solve for a particular variable since it is easier to isolate. We can begin by solving for y:

x + y = 3

Subtract y from both sides:

x = -y + 3

Substitute in this expression for x into the other equation:

8(-y + 3) + 4y = 15

Distribute and simplify:

-8y + 24 + 4y = 15

-4y + 24 = 15

-4y = -9

y = 9/4

Substitute in this value of y to solve for x:

8x + 4(9/4) = 15

8x + 9 = 15

8x = 6

x = 6/8 = 3/4

The values respectively are:

x = 3/4, y = 9/4

Considering the given linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

His payment for x copies bought is:

y = 120x + 2400.

Hence:

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The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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Answer:

it would be 7 dollars per football

Step-by-step explanation:

\(42 \div 6\)

Answer:

-29>(5*x)-10

Step-by-step explanation:

Answer:

-29 >  5x - 10

Step-by-step explanation:

Since it says PRODUCT in there it means its times

so 5x

x = a number

ten subtracted from that would be

5x - 10

and since its going to be less than -29 that would be <-29

-29 > 5x - 10

sorry if Im wrong

\(-4.46(j + 19)= -8.92\)

Distribute:

\((-4.46)(j)+(-4.46)(19)=-8.92\)

\(-4.46j-84.74=-8.92\)

Add 84.74 to both sides:

\(-4.46j-84.74+84.74=-8.92+84.74\)

\(-4.46j=75.82\)

Divide both sides by -4.46:

\(\dfrac{-4.46j}{-4.46} =\dfrac{75.82}{-4.46}\)

\(=\fbox{j = -17}\)

The dimensions of the rectangular field are given as follows:

The perimeter of a rectangle is given by twice the sum of the length and the width of the rectangle, as follows:

P = 2(l + w).

For this problem, the perimeter is of 582 yards, hence:

2(l + w) = 582

l + w = 291.

The length of the field is 4 yards less than quadruple the width, hence:

l = 4w - 4.

Then the width is obtained as follows:

4w - 4 + w = 295

5w = 295

w = 295/5

w = 59.

The length is obtained as follows:

l = 4 x 59 - 4

l = 232 yards.

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if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is

One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.

A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows

assuming the number of laps is L

1 lap = 1/4 mile

L laps = 7/8 miles

cross multiplying

1 * 7/8 = L * 1/4

multiplying by 4 for each side

1 * 7/8 * 4 = L * 1/4 * 4

1 * 7/8 * 4 = L * 1

7/8 * 4 = L

hence option C is correct

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