What is the average rate of change for h(x)=x^2+x-6

Make two equations representing the position of each animal, p and k, for the puppy and kitten respectively.

p=25t and k=180+20t  

The puppy will catch the kitten when p=k so we can say:

25t=180+20t  subtract 20t from both sides

5t=180  divide both sides by 5

t=36

So the puppy will catch the kitten after 36 seconds.

Answer:

36

Step-by-step explanation:

let the points of G be (a,b)

mid point of GH =(-6,-3)

point of H =(-4,4)

now,

for x coordinate,

-6=(a-4)/2

or, a-4 =-12

or, a=-8

for y coordinate,

-3=(b+4)/2

or, -6=b+4

or, b=-10

therefore, the coordinate of G is (-8,-10)

To solve the question, we use the midpoint formula, which is derived from the concept of averages. Given the midpoint and one endpoint, we can find the other endpoint by setting up and solving simple equations. The coordinates of the other endpoint are G(-4, -14).

To find the coordinates of the other endpoint of a line segment given the coordinates of the midpoint and one endpoint, we use the midpoint formula which states that the midpoint, M, of a line segment GH is given by M = [(x1 + x2)/2 , (y1 + y2)/2], where (x1,y1) and (x2,y2) are the coordinates of H and G respectively.

Given that M (-6,-3) and H (-4,4), we can write the equations: -6 = [(-4 + x2)/2] and -3 = [(4 + y2)/2]

Solving these equations gives us: x2 = -2*(-6 + 4) = -4 and y2 = -2*(-3 - 4) = -14. Therefore, the coordinates of endpoint G are G (-4, -14).

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Answer:

"4" represents that there are 4 rabbit in the beginning.

Step-by-step explanation:

Given that the population of a species of rabbit triples every year. This

can be modeled by function [tex]f\left(x\right)=4\left(3\right)^x[/tex] and [tex]f(5) = 972[/tex].

Now we need to find about what does the 4 represent in the given function.

We know that exponential function is given by [tex]f\left(x\right)=a\left(b\right)^x[/tex]. Where "a" represents the initial amount.

we have a=4 in given function [tex]f\left(x\right)=4\left(3\right)^x[/tex].

So that means "4" represents that there are 4 rabbit in the beginning.

Answer:

162.24 ft

Step-by-step explanation:

So you first find the area of one side.

5.2 x 5.2 = 27.4

Then you times it by 6, because a cube has 6 sides.

27.4 x 6 = 162.24 ft

A steel cargo container is shaped like a cube measuring 5.2 ft on each edge. we will need 162.24 ft sq. steel to make this container.

A cube has all sides congruent, so all sides have the same area.

Supposing that the considered cube has a side length (also called edge length) of L units.

Then, its one side's area equals  L^2 sq. units (as each side is a square, so we used the formula for the area of a square).

Since there are 6 such sides in a closed cube, thus, its surface area evaluates to

[tex]S = L^2 + L^2 + ... + L^2 \text{\: (six times)} = 6L^2 \: \rm unit^2[/tex]

A steel cargo container is shaped like a cube measuring 5.2 ft on each edge.

So first we need to find the area of one side.

The area of a square = 5.2 x 5.2

                                   = 27.4

For 6 sides of cube

27.4 x 6 = 162.24 ft sq.

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Answer:

D. [tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]

Step-by-step explanation:

The given function is:

[tex]y=-3\sin(\frac{2}{3}x-2\pi)+2[/tex]

This function is of the form:

[tex]y=A\sin(Bx-C)+D[/tex], where [tex]B=\frac{2}{3}[/tex]

The period is given by:

[tex]T=\frac{2\pi}{B}[/tex]

[tex]T=\frac{2\pi}{\frac{2}{3}}=3\pi[/tex]

Half of this period is [tex]\frac{3\pi}{2}[/tex].

The function that has a period of [tex]\frac{3\pi}{2}[/tex] is

[tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]

Answer:

d.y = 3cos(4/3x - 2π) + 2

Step-by-step explanation:

For this case we must simplify the following expression:

[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]

We have that by definition of properties of powers that is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]

Answer:

[tex](x^{\frac{3}{2}})^6=x^9[/tex]

Final answer:

To simplify the expression [tex](x^{3/2)6[/tex], use the power rule of exponents to get x to the power of 9, which is the simplified form of the expression.

Explanation:

To simplify the expression [tex](x^{3/2)6[/tex], we need to apply the power of a power property, which states that when you raise a power to another power, you multiply the exponents.

So, we have:

[tex](x^{3/2)6[/tex] = [tex]x^{(3/2)\times 6[/tex]

= [tex]x^{3\times 3[/tex]

= x⁹

Therefore, [tex](x^{3/2)6[/tex] simplifies to x⁹.

This means that the expression is equivalent to x raised to the power of 9.

In summary, when you raise x to the power of 3/2 and then raise that result to the power of 6, you end up with x raised to the power of 9.

Answer:

Step-by-step explanation:

A quadratic equation is an expression that has an x^2 term. Quadratic equations are most commonly expressed as ax^2+bx+c, where a, b and c are coefficients. Coefficients are numerical values. For example, in the expression 2x^2+3x-5, 2 is the coefficient of the x^2 term. Once you have identified the coefficients, you can use a formula to find the x-coordinate and the y-coordinate for the minimum or maximum value of the quadratic equation.

Determine whether the function will have a minimum or a maximum depending on the coefficient of the x^2 term. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum. For example, if you have the function 2x^2+3x-5, the function has a minimum because the x^2 coefficient, 2, is positive.

Divide the coefficient of the x term by twice the coefficient of the x^2 term. In 2x^2+3x-5, you would divide 3, the x coefficient, by 4, twice the x^2 coefficient, to get 0.75.Multiply the Step 2 result by -1 to find the x-coordinate of the minimum or maximum. In 2x^2+3x-5, you would multiply 0.75 by -1 to get -0.75 as the x-coordinate.

Plug in the x-coordinate into the expression to find the y-coordinate of the minimum or maximum. You would plug -0.75 into 2x^2+3x-5 to get 2_(-0.75)^2+3_-0.75-5, which simplifies to -6.125. This means the minimum of this equation would be x=-0.75 and y=-6.125.

If there is not a number before a variable, the coefficient is 1. For example, if your expression is x^2+5x+1, the x^2 coefficient is 1.

Answer:

hcch6z0d7gpxufufuguftrfue6oo7

ANSWER

The preimage is (-5,-3)

EXPLANATION

If the point (x,y) is rotated 90° clockwise, then the image point is (y,-x)

This implies that, the rule for 90° clockwise rotation is :

[tex](x,y)\to (y, - x)[/tex]

To find the image of the point (3,-5), we substitute it into the rule:

[tex](3, - 5)\to ( -5, -3)[/tex]

Therefore the preimage is (-5,-3)

Answer:

Step-by-step explanation:

To rotate figures, there are several rules.

Specifically, when we want to rotate a figure 90° clockwise, the transformation is

[tex](x,y) \implies (y,-x)[/tex].

If the pre-image point has coordinates (3,-5), then its 90° rotation clockwise is (-5,-3), because it must follow the rule above.

Therefore, the right answer is (-5,-3).

Answer: 3 1/4 as an improper fraction could be 13/4. Written as a fraction would be 3 1/4.

Answer:

21

Step-by-step explanation:

There are 144 M&M's in the bag.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Number of red candies = 16

Also it is given that One-ninth of the candies in a bag of M&M's are red

1/9 of the candies in a bag of M&M's are red

Let x be the M&M's candies

So, we can write,

1/9 x = 16

⇒  x = 144

Thus, there are 144 M&M's in the bag.

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Answer:

1620

Step-by-step explanation:

180(n)-360=interior angle sum

180(11)-360=1620

n = number of sides

You also can divide it by 11 to know each interior angle.

1620/11=~147.27

Answer:

x=m-a/12

the m-a should be over 12 as the numerator but it's hard to type it like that

Step-by-step explanation:

a+12x=m

12x=m-a

x=m-a/12

Answer:

[tex]x = \frac m{12a}[/tex]

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The value of x is [tex]x = \frac m{12a}[/tex].

Answer:

Step-by-step explanation:

I'm not quite sure about my answers though, sorry :(

Hope I helped :)

Final Answer:

The proposed new cereal box design has dimensions of 6 inches in length, 2 inches in width, and 8 inches in height. This design maintains the original cereal volume of 96 cubic inches while reducing the surface area to 104 square inches.

Explanation:

The formula for the surface area [tex](\(A\))[/tex] of a rectangular prism is given by:

[tex]\[ A = 2lw + 2lh + 2wh \][/tex]

For the original box with dimensions 8 inches in length [tex](\(l\)),[/tex] 1 inch in width [tex](\(w\)),[/tex] and 12 inches in height [tex](\(h\))[/tex]:

[tex]\[ A_{\text{original}} = 2(8 \times 1) + 2(8 \times 12) + 2(1 \times 12) = 232 \][/tex]

For the proposed new design with dimensions 6 inches in length, 2 inches in width, and 8 inches in height:

[tex]\[ A_{\text{new}} = 2(6 \times 2) + 2(6 \times 8) + 2(2 \times 8) = 104 \][/tex]

Comparing the surface areas, the new design significantly reduces it from 232 square inches to 104 square inches. This reduction in surface area indicates that the proposed design will require less material for manufacturing.

By maintaining the original cereal volume of 96 cubic inches while decreasing the surface area, the proposed cereal box design is more cost-effective to manufacture. The optimization of dimensions ensures that the same cereal quantity can be accommodated with a reduction in manufacturing costs.

Answer:

B

Step-by-step explanation:

We know 2.2 pounds = 1 kg, hence,

44 pounds / 2.2 = 20 kg (weight of child in kg)

Now, since 40 mg is administered per kg, the child would need 40 * 20 = 800 mg PER DAY

Since this is going to be taken per 4 dose, each dose would need to be 800/4 = 200 mg

Answer choice B is right.

Answer:

113.0 inches squared

Step-by-step explanation:

The area of a circle with radius r is given as;

[tex]Area=pi*r*r[/tex]

We plug in the radius given and solve for the area;

[tex]Area=3.14*6*6\\Area=113.04[/tex]

Answer:

c = 14

Step-by-step explanation:

For this triangle we have to

[tex]a=18.2\\B=62\°\\C=48\°[/tex]

We want to find the length of b

We know that the sum of the internal angles of a triangle is 180 °

then

[tex]A + 62 +48=180\\\\A=180-62-48\\\\A=70\°[/tex]

Now we use the sine theorem to find the length of c:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Therefore:

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}\\\\c=\frac{sin(C)}{\frac{sin(A)}{a}}\\\\c=a*\frac{sin(C)}{sin(A)}\\\\c=(18.2)\frac{sin(48)}{sin(70)}\\\\c=14[/tex]

Answer:

c= 14

Step-by-step explanation:

First, let's find the angle A, because it's easy and because we'll need it.

We know that the sum of the interior angles of a triangle is 180, and we have 2 angles... so we can easily find A:

A = 180 - 62 - 48 = 70 degrees

Now, we can use the law of Sines to find c:

[tex]\frac{c}{sin(C)} = \frac{a}{sin(A)}[/tex]

so...

[tex]c = \frac{a * sin(C)}{sin(A)} = \frac{18.2 * sin(48)}{sin(70)} = 14.39[/tex]

The precise answer is 14.39, but you are asked to round up to the closest whole number... so 14.

Answer:

The answer is 84cm^2.

Step-by-step explanation:

To find the area, you need to find the length x width. here is an equation to help:

A=L X W

Lets plug the numbers into the equation:

A=6cm X 14cm

Now, mulitply:

A=84cm^2

hope this helps

84, you multiply 14x6 for the area

Answer:482.7972

Step-by-step explanation:

can you tell me what the points are because the graph is somewhat blurry

Answer:

if the scale is 1, then the slope is 1/3

Step-by-step explanation:

Answer:

2 the answer is 2/1 but just write 2

Step-by-step explanation:

Dilation of a polygon by a factor of 8 enlarges the polygon without changing the slope of the line. Therefore, the slope of AB and A'B' are the same. Further information is needed to provide a numerical value.

Since the polygon is dilated by a scale factor of 8, the new image A′B′C′D′ is an enlargement of the original polygon ABCD by a factor of 8. The slope of a line in a dilation remains the same, even if the length of the line is changed. Essentially, the steepness of a line isn't affected by dilations. Therefore, the slope of AB and A'B' are same. Since the slope of AB is not given in the question, it's necessary to have that information to answer your question completely.

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Answer: 4(5j+7) = 20j+28

Step-by-step explanation:

Answer:

continous

Step-by-step explanation:

Answer:

Continuous

Step-by-step explanation:

Since the problem has decimals for your t values it will most likely be continuous.

Answer:

25

Step-by-step explanation:

A box contains 100 colored chips

Some are yellow and,

Some are green.

John has recorded 57 yellow chips and 19 green chips.

The ratio of yellow chips to green chips is 57:19 simplified becomes; 3:1

The number of green chis is [tex]\frac{1}{3 + 1}[/tex] × 100 = [tex]\frac{1}{4}[/tex] × 100 = 25

Answer:

6.13

Step-by-step explanation:

Using Sine Law we know that

[tex]\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}[/tex]

Using your figure let's assign sides and angles:

A=? B = 60° C = 70°

a = 5 b = ? c = x

If we put that into our formula:

[tex]\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}[/tex]

Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?

Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°

∠A + ∠B + ∠C= 180°

∠A + 60° + 70° = 180°

∠A + 130° = 180°

∠A = 180° - 130°

∠A = 50°

Now we can use this to solve for x.

[tex]\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x[/tex]

So the closest answer would be 6.13

Answer:

The correct answer option is 6.13.

Step-by-step explanation:

We are given a scalene triangle which has no equal side and we are to find the unknown side length x.

Since the total measure of angles of a triangle is 180°, so we can find the measure of the unknown angle.

180° - 70° + 60° = 50°

Now we can use the sine formula to find the value of x.

[tex]\frac{x}{sin70} =\frac{5}{sin50}[/tex]

[tex]x=\frac{5}{sin50} \times sin70[/tex]

[tex]x=6.13[/tex]

Answer:

At the beginning

16 men and 24 women

In the end

16 men and 20 women

Step-by-step explanation:

Call x the number of men on the bus and call y the number of women on the bus.

We know that the initial ratio between men and women is 2: 3

And the final ratio is 4: 5

So

[tex]\frac{x}{y}=\frac{2}{3}\\\\y = \frac{3}{2}x[/tex]   (1)

After the 4 women are down, the proportion is:

[tex]\frac{x}{y-4}=\frac{4}{5}\\\\y-4 = \frac{5}{4}x\\\\y= \frac{5}{4}x +4[/tex]   (2)

Substitute the value of y in the first equation and solve for x

[tex]\frac{5}{4}x +4=\frac{3}{2}x\\\\-\frac{1}{4}x=-4\\\\x=16\ men[/tex]

Now solve for y.

[tex]y = \frac{3}{2}(16)\\\\y=24\ women[/tex]

Then at the end there were 20 women  (because 4 women got off the bus)

Answer:

$17.35/h

Step-by-step explanation:

In order to get the amount per hour he made, you first need to calculate the global amount of money he made.

He was paid $2,900 then he had costs of $1,200, that leaves him a net income of $1,700 ($2,900 - $1,200)

Then he worked a total of 98 hours for that money.

A salary is an amount of money expressed by a period of time.  In this case, we'll use hours.

So, Jonah earned $1,700 after 98 hours of work:

S = $1,700 / 98 hours = $17.35/h

Answer:

$60

Step-by-step explanation:

I got this bc 12*30=360 and 360-300=60

Answer: 60 dollars

Step-by-step explanation: For every 5 dollars Tom loans he has to pay 1 dollar plus the amount he loaned. If 30 times 12 is 360 and the original cost is 300 then he payed 60 dollars for the finance charge.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-3}\cdot x^3\cdot y^{-4}\implies \cfrac{1}{\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot ~~\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{1}{y^4}\implies \cfrac{1}{y^4}[/tex]

Answer:

$0.90

Step-by-step explanation:

1 quart = 2 pints

Write a proportion:

$1.80 / 4 pint = x / 2 pint

Cross multiply:

4x = 3.60

Divide:

x = 0.90

The price per quart is $0.90.

To find the price per quart of a 4-pint carton costing $1.80, divide the total cost by the number of quarts (2), resulting in $0.90 per quart.

The question asked is: A 4-pint carton of fruit punch costs $1.80. What is the price per quart? To answer this, we first need to understand that there are 2 pints in a quart. Therefore, a 4-pint carton is equivalent to 2 quarts of fruit punch. Now, we simply divide the total cost of the carton by the number of quarts to find the price per quart.

The calculation would be $1.80 ÷ 2 quarts = $0.90 per quart.

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