Given the following functions: f(x) = x2 – 5 and g(x) = x - 3.
Find f(g(x))

The simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

Area of rectangle = Length × Width

Perimeter of rectangle = 2(Length + Width)

13). Area of the rectangle = 5x × (x + 8)

Area of the rectangle = 5x² + 40

Perimeter of the rectangle = 2[5x + (x + 8)]

Perimeter of the rectangle = 2(6x + 8)

Perimeter of the rectangle = 12x + 16

12). Area of the rectangle = (x + 3)(x + 7)

Area of the rectangle = x² + 7x + 3x + 21

Area of the rectangle = x² + 10x + 21

Perimeter of the rectangle = 2[(x + 3) + (x + 7)]

Perimeter of the rectangle = 2(2x + 10)

Perimeter of the rectangle = 4x + 20.

Therefore, the simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

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The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

What in mathematics is a quadrilateral?

A quadrilateral, a two-dimensional shape, is made up of four sides, four vertices, and four angles. The most prevalent shapes are concave and convex. Also included in the list of convex quadrilateral subgroups are trapezoids, parallelograms, rectangles, rhombuses, and squares.

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

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IT HAS TO BE X=0 BECAUSE YOU ADD 8 TO X-8 THAT REMOVES THAT 8 THEN THE ADD 8 TO THE OTHERSIDE OF THE EQUAL SIGN

Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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Answer:

  y -3 = -3(x +1)

Step-by-step explanation:

You want an equation for the line parallel to y=-3x+2 through the point (-1, 3).

The given line is written in slope-intercept form:

  y = mx +b . . . . . . . where m is the slope and b is the y-intercept

Matching your equation to this form, we see that ...

The parallel line will have the same slope: m = -3.

Another form of the equation for a line is "point-slope form." That is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

Perhaps you can see this would be useful for writing the equation of a line with slope -3 through the point (-1, 3).

  y -3 = -3(x +1) . . . . . . . line with slope -3 through point (-1, 3)

The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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Answer:

The answer is d because it's the answer pls mark me brainlest

Answer:

To use the exponential growth model to estimate the number of people who would have died from AIDS in 2003, we need to know the initial value (the starting point) and the growth factor.

Step-by-step explanation: From the problem statement, we know that the growth factor in the early days of AIDS was around 2.2. This means that the number of AIDS deaths would roughly double every year.

In 1983, about 1600 people in the U.S. died of AIDS. This is our initial value.

To estimate the number of people who would have died from AIDS in 2003, we need to know how many years have passed since 1983.

2003 - 1983 = 20 years

So we need to apply the growth factor 20 times to the initial value of 1600.

Using the formula for exponential growth:

y = a * r^t

where y is the final value, a is the initial value, r is the growth factor, and t is the number of periods (in this case, years).

y = 1600 * (2.2)^20

y = 1600 * 47516.45

y = 76,026,320

Therefore, if the trend of AIDS deaths had continued unchecked with a growth factor of 2.2, it is estimated that about 76 million people in the U.S. would have died from AIDS by 2003. It's important to note that this is a theoretical estimate based on the assumption of exponential growth, and many factors could have affected the actual number of AIDS deaths over time.

total area =A1+A2+A3

A1=1/2b*h

A1=1/2*8mm*6mm

A1=24mmsquare

A2=1/2b*h

A2=1/2*8mm*6mm

A2=24mmsquare

A3=b*h

A3=8mm*6mm

A3=48mmsquare

Atotal=24mmsquare+24mmsquare+48mmsquare

Atotal=96mmsquare

Answer:

Step-by-step explanation: true

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Answer:

Circle, angle, and line segment.

Step-by-step explanation:

there is something severely wrong with the problem definition.

when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.

and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.

it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...

what ?

so, all I can do here is to show you why I said what I said :

30-60-90 triangle with Hypotenuse = 9

then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...

the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5

a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg

9² = 6² + leg²

81 = 36 + leg²

45 = leg²

leg = sqrt(45) = 6.708203932...

so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.

and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.

therefore, there is everything wrong with the problem definition.

Answer:  x= -36

Step-by-step explanation:

-36/-4=9

It's called the "y intercept" and it's the y value of the point where the line intersects the y- axis. For this line, the y-intercept is "negative 1." You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.

Answer:

40 miles

Step-by-step explanation:

She wants to run x miles.

She already ran 24 miles, and that is 60% of x.

60% of x = 24

0.6x = 24

x = 24/0.6

x = 40

Answer: 40 miles

The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.

To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.

The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.

In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.

Using the formula, we have:

P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)

C(5, 2) = 5! / (2! * (5-2)!) = 10

P(2) = 10 * (3/8)^2 * (5/8)^3

P(2) ≈ 0.164 (rounded to three decimal places)

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Answer: 2.63

Step-by-step explanation:

Using the formula \(A=\frac{1}{2} ab \sin C\),

\(6\sqrt{2}=\frac{1}{2}(2x-1)(x+3) \sin 45^{\circ}\\\\6\sqrt{2}=\frac{(2x-1)(x+3)}{2} \cdot \frac{\sqrt{2}}{2}\\\\6=\frac{(2x-1)(x+3)}{4}\\\\24=(2x-1)(x+3)\\\\24=2x^2 +5x-3\\\\2x^2 +5x-27=0\\\\x=\frac{-5 +\sqrt{5^2 -4(2)(27)}}{2(2)} \text{ } (x > 0)\\\\x=\frac{\sqrt{241}-5}{4} \approx 2.63\)

The probability of rolling a number greater than 3 is 1/2 or 0.5.

When rolling a standard cube, there are six possible outcomes, corresponding to the six faces of the cube. Each face has a number from 1 to 6.

To find the probability of rolling a number greater than 3, we need to determine the number of favorable outcomes (rolling a number greater than 3) and divide it by the total number of possible outcomes (rolling any number from 1 to 6).

The favorable outcomes for rolling a number greater than 3 are: 4, 5, and 6. So, there are three favorable outcomes.

The total number of possible outcomes is six since there are six faces of the cube.

Therefore, the probability of rolling a number greater than 3 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 3 / 6

Probability = 1/2

Hence, the probability of rolling a number greater than 3 is 1/2 or 0.5.

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Nikki swam 375 yards on Thursday.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

Given

Nikki swam 375 yards on Thursday.

425+450+350= 1,225

1,600- 1,225= 375

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Answer:

4 and 17

Step-by-step explanation:

4 because 4^2 is 16 + 1 = 17 and the other # is 17 because 21-4 is 17

Answer:

0

Step-by-step explanation:

0 to the second power:

0x0= 0

Answer:

x = 18

Step-by-step explanation:

I the given triangle, it appears that M and N are the midpoints of the segments BG and BD respectively. If it so, then let us solve it.

By mid segment theorem:

2MN = GD

2(6x - 51) = 114

12x - 102 = 114

12x = 114 + 102

12x = 216

x = 216/12

x = 18

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

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

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

1/15 kg

Step-by-step explanation:

Divide by 5 can be written as multiply by 1/5

1/3 * 1/5 = 1/15

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Answer:

A

Step-by-step explanation:

Answer:

\(B(x_2,y_2)= (20,12)\)

Step-by-step explanation:

Given

\(A = (0,0)\)

\(Ratio; m : n = 1 : 3\)

\(Point\ at\ 1 : 3 = (5,3)\)

Required

Coordinates of B

This question will be answered using line ratio formula;

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

In this case:

\((x,y) = (5,3)\)

\((x_1,y_1) = (0,0)\)

\(m : n = 1 : 3\)

Solving for \((x_2,y_2)\)

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\) becomes

\((5,3) = (\frac{1 * x_2 + 3 * 0}{1 + 3},\frac{1 * y_2 + 3 * 0}{1 + 3})\)

\((5,3) = (\frac{x_2 + 0}{4},\frac{y_2 + 0}{4})\)

\((5,3) = (\frac{x_2}{4},\frac{y_2}{4})\)

Comparing the right hand side to the left;

\(\frac{x_2}{4} = 5\) -- (1)

\(\frac{y_2}{4} = 3\) -- (2)

Solving (1)

\(x_2 = 5 * 4\)

\(x_2 = 20\)

Solving (2)

\(y_2 = 3 * 4\)

\(y_2 = 12\)

Hence;

\(B(x_2,y_2)= (20,12)\)