The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by

h(t) = −16t2 + 128t, 0 ≤ t ≤ 8.

Find the average rate of change of h over the interval

[4, 8].

Answer:

A (0,3)

Step-by-step explanation:

The given trapezoid has vertices:

(0,6), (7,12), (7,9) and (0,12).

We want to choose from the given options, a point that is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2.

Note that the mapping for such a dilation is:

[tex](x,y)\to( \frac{1}{2} x, \frac{1}{2} y)[/tex]

This implies that:

[tex](0,6)\to(0,3)[/tex]

[tex](7,12)\to(3.5,6)[/tex]

[tex](7,9)\to(3.5,4.5)[/tex]

[tex](0,12)\to(0,6)[/tex]

Therefore correct choice is (0,3)

Answer:

17p:34p:17p

Step-by-step explanation:

68p/(1+2+1)=

17p(1):17p(2):17p(1)=

17p:34p:17p

Answer:

24,48,72,96

Step-by-step explanation:

Multiples of 8

8, 16,24,32,40,48,56,64,72,80,88,96

Multiples of 12

12,24,36,48,60,72,84,96

Common multiples

24,48,72,96

Answer:

See below.

Step-by-step explanation:

"List all the multiples of 8 that are less than or equal to 100."

0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

"List all the multiples of 12 that are less than or equal to 100."

0, 12, 24, 36, 48, 60, 72, 84, 96

Common multiples: 0, 24, 48, 72, 96

Answer:

-1 is the smallest according to this question

Answer:

8. D 269.6

9. A 20 +10h

Step-by-step explanation:

8.  The large rectangle is 4+6.4+4+6.4 = 20.8 width and 10.5 length.  The area is

A = l*w = 20.8* 10.5 =218.4

The top rectangle is 6.4 width and length is 4

A = l*w =6.4*4 =25.6

The same is true for the rectangle on the bottom.

Add the three rectangles together to get the total surface area

218.4+25.6+25.6 =269.6

9. The plant is 20 inches tall

It grows 2h inches a week for 4 weeks

20 +2h*4

20 +8h

It grows h inches a week after  4 weeks

At 6 weeks, that is 2 weeks of growth

The growth is h *2

Add that to the previous total

20 +8h +2h

20 +10h

Answer:144 m

Step-by-step explanation:

9x6=54/2=27

27x4=108

6x6=36

108+36=144

Answer:

quadrilateral; irregular

Step-by-step explanation:

Answer:

B) III only, it doesn't suggests relationship between x and y.

minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

Step-by-step explanation:

Here we have ,  f(x) = x² - 2x + 7 or [tex]f(x) = x^2 - 2x + 7[/tex] . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function  . Let's solve this:

[tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}[/tex]

⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2)}{dx} - \frac{d(2x)}{dx} + \frac{d(7)}{dx}[/tex]

⇒ [tex]\frac{df(x)}{dx} = 2x-2 = 0[/tex]

⇒ [tex]2x-2 = 0[/tex]

⇒ [tex]x =1[/tex]

Now, value of function at x=1 is :

[tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(1) = 1^2 - 2(1) + 7[/tex]

⇒ [tex]f(1) = 8- 2[/tex]

⇒ [tex]f(1) = 6[/tex]

Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

The minimum value of the quadratic function f(x) = x² - 2x + 7 is 6, which occurs at x = 1, as determined by finding the vertex of the parabola.

The minimum value of the quadratic function f(x) = x² - 2x + 7 can be determined by finding the vertex of the parabola represented by the function. This is because the graph of a quadratic function is a parabola, and if the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents the minimum point.

To find the vertex, use the formula -b/2a to determine the x-coordinate of the vertex. For the function f(x), the value of 'a' is 1 and 'b' is -2. Substituting these values gives us the x-coordinate of the vertex as x = -(-2)/(2*1) = 1. Substituting x = 1 back into the function f(x), we get the y-coordinate of the vertex, which is the minimum value of the function: f(1) = (1)² - 2*(1) + 7 = 6.

Therefore, the minimum value of the quadratic function f(x) is 6, occurring at x = 1.

When we say "a is at most b" we mean that "a is less than or equal to b" or "a is not greater than b". So let's solve this problem as follows:

Step 1. Twice the difference of a number and 2

Let's call that unknown number as n. Then, twice the difference of a number and 2 is:

[tex]2(n-2)[/tex]

Step 2. Twice the difference of a number and 2 is at most -27

[tex]2(n-2)\leq -27[/tex]

_________________________________________

So the mathematical form of the statement twice the difference of a number and 2 is at most -27 is:

[tex]\boxed{2(n-2)\leq -27}[/tex]

Answer:

Yes.

Step-by-step explanation:

Note that  15^2 = 122^ + 9^2  ( 225 = 144 + 81 = 225).

So by the Inverse of Pythagoras Theorem  it is a right triangle.

The given values of side makes a proper right angle triangle.

To determine if the three given side lengths, 9, 12, and 15, form a right triangle, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check if this holds true for the given side lengths:

[tex]9^2 + 12^2 = 81 + 144 = 225\\\\15^2 = 225[/tex]

The sum of the squares of the two shorter sides, 9 and 12, is equal to the square of the longest side, 15. This satisfies the Pythagorean theorem.

Therefore, the side lengths 9, 12, and 15 do form a right triangle.

Learn more about right-angle triangle here:

https://brainly.com/question/3770177

#SPJ6

The right answer is Option B: 9/26

Step-by-step explanation:

Given equations are;

[tex]2x+\frac{4}{3}y=1[/tex]     Eqn 1

[tex]y-\frac{9}{13}x=9[/tex]     Eqn 2

For eliminating x, we will make the variables equal with opposite signs.

In Eqn 1;

We will multiply Eqn 1 by 9/26 to get +9/13x.

[tex]\frac{9}{26}(2x+\frac{4}{3}y=1)\\\\\frac{9}{13}x+\frac{6}{13}y=\frac{9}{26}[/tex]

Therefore;

We will multiply Eqn 1 by 9/26.

The right answer is Option B: 9/26

Answer:

[tex]QP=20\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Let

O ---> the center of the circle

we have that

Line segment QP is tangent to the circle

That means

OQ (radius) is perpendicular to segment QP

OQP is a right triangle

Applying Pythagorean Theorem

[tex]OP^2=OQ^2+QP^2[/tex]

we have

The radius is equal to

[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter

[tex]OP=r+NP=12+11.5=23.5\ units[/tex]

[tex]OQ=r=12\ units[/tex]

substitute

[tex]23.5^2=12^2+QP^2[/tex]

[tex]QP^2=23.5^2-12^2[/tex]

[tex]QP^2=408.25[/tex]

[tex]QP=20\ units[/tex]

Answer:20 units

Step-by-step explanation:

Answer: 200

Step-by-step explanation:

First I would do it like this.

12.5

X. 16

—————-

6 times 5 is 0, carry the 3, 6 times 2 is 12 and add 3 from the other which is 15, put the 1 from the 15 to the one next to the 12. 6 times 1 is 6 plus 1 is 7 which now you have 750. 5 times 1 is 5, 2 times 1 is 2, 1 times 1 is 1. It should look like this now.

12.5

X 16

—————

750

+ 1250

——————-

Which is 8750 but wait. Where is the decimal? Well, there is only one number behind the decimal so it is 875.0 or 875.

Slope of v: a=(9-14)/(10-1)=-5/9

Slope of w: b=-1/a=9/5=1.8

Volume of the cone is 17 cm³

Step-by-step explanation:

Volume = 1/3 × 3.14 × 2² × 4

             = 16.75 cm³ ≈ 17 cm³ (rounding off to nearest whole number)

To prove ABCD is a rhombus, showing that all sides of parallelogram ABCD are equal in length would suffice.

If ABCD is a parallelogram, to prove that it is a rhombus, a statement that would suffice is that all four sides of the parallelogram are of equal length.

This is because a rhombus is defined as a parallelogram with four congruent sides. If any one of its diagonals bisects an angle of the parallelogram, or its diagonals are perpendicular, or its diagonals are of the same length, these conditions would not exclusively prove it to be a rhombus, although they are properties of a rhombus. However, the definition of a rhombus centers on the equality of all sides.

Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.

The correct option is (B).

To prove that a parallelogram is a rhombus, you need to show that all four sides are of equal length. A parallelogram has opposite sides that are equal and parallel, but for it to be a rhombus, every side must be equal in length to every other side.

The statement options you might have in your image could be something like:

a. Diagonals are perpendicular (AC ⊥ BD)

b. Adjacent angles are equal (∠ABC ≅ ∠CDA)

c. One pair of opposite sides are equal (AB ≅ CD)

d. Diagonals are equal (AC ≅ BD)

From these options:

- Option a: If the diagonals are perpendicular, it's an indication that the parallelogram could be a rhombus, but it's not conclusive proof because a rectangle also has perpendicular diagonals.

- Option b: Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.

- Option c: Having one pair of opposite sides that are equal is already a property of a parallelogram and does not prove it's a rhombus.

- Option d: Equal diagonals would be a property of a rectangle, not necessarily a rhombus.

The conclusive proof that a parallelogram is a rhombus would be if you can show that all sides are of equal length (not provided in the typical options above), or if the diagonals are perpendicular and bisect each other into equal segments. This latter property is unique to a rhombus among parallelograms. If this were one of the choices, it would be the correct answer.

Since I can't see the options, please review them and look for the one that indicates all four sides are of equal length or that the diagonals bisect each other into equal segments and are perpendicular. That would be the correct choice to prove the parallelogram is a rhombus.

Answer:

00.300

Step-by-step explanation:

What value does the 3 represent in the number 16.344

The 3 in the number 16.344 represents 0.003, since it's located on the third decimal place. It contributes three-thousandths to the total value. The position of the number changes the value it represents.

The value of 3 in the number 16.344 is represented as 0.003 in decimal place value. This is because it is situated in the third digit after the decimal point, signifying that it contributes the amount equal to three thousandths (0.003) to the total value of the number. For example, in using the concept of Six significant figures, we can say the number 16.344 has five significant figures, that is, the digits that give us precise information about the magnitude of the number - these digits being 1, 6, 3, 4 and 4.

It's also worthwhile to note that the placement of the digit 3 in the number 16.344 is different from a 3 that is located at other decimal places. For instance, if we look at the number 16.3443, the second 3 after the decimal point represents three ten-thousandths (0.0003) contribution to the total value of the number.

https://brainly.com/question/29687080

#SPJ3

Answer:

1. [tex](b+8)^{2}[/tex]

2. [tex]-3k(k^{2} -5k+2)[/tex]

3. [tex](3x-1)(x-5)[/tex]

Step-by-step explanation:

1. Both [tex]x^{2}[/tex] and 64 are perfect squares, meaning [tex]16b[/tex] is twice the product of x and 8. Since all signs are positive, the equation would be: [tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]. Let [tex]a=x[/tex] and [tex]b=8[/tex]. Answer: [tex](b+8)^{2}[/tex] or [tex](b+8)(b+8)[/tex].

2. Since -3 is a factor of all 3 terms, factor out the -3 which makes,  [tex]-3(k^{2} +5k^{2} -2k)[/tex] . K is also a common factor, so you would factor that out too, [tex]-3k(k^{2} -5k-2)[/tex]. Then simply, find the two factors whose product is -2 and whose sum is -5. Answer: [tex]-3k(k^{2} -5k+2)[/tex].

3. By factoring [tex]3x^{2} -16x+5[/tex], you would break the expressions in the group=[tex](3x^{2} -x)+(-15x+5)[/tex]. Then, factor out "x" from [tex]3x^{2} -x: x(3x-1)[/tex]. Factor out "5" from [tex]-15x+5:-5(3x-1)[/tex] = [tex]x(3x-1)-5(3x-1)[/tex]. Finally, factor out the common term "3x-1" = [tex](3x-1)(x-5)[/tex]

The area of the triangle is 90 m²

Explanation:

Given that the base of the triangle is 15 m

The altitude of the triangle is 12 m

Area of the triangle:

The area of the triangle can be determined using the formula,

[tex]Area=\frac{1}{2}bh[/tex]

where b is the base and h is the altitude

Thus, we have,

[tex]b=15[/tex] and [tex]h=12[/tex]

Substituting the values in the above formula, we get,

[tex]Area=\frac{1}{2}(15)(12)[/tex]

Multiplying the terms, we get,

[tex]Area=\frac{180}{2}[/tex]

Dividing, we get,

[tex]Area=90 \ m^2[/tex]

Therefore, the area of the triangle is 90 m²

Answer: x=7

Step-by-step explanation:

×+4=4×-17

×-4×=-17-4

-3×=-21

×=-21/-3

×=7

Answer:

Equation for total number of balls = 8x+6x+5x =19x where x represent a single tennis ball.

Step-by-step explanation:

Given that Kayla has;

8 red tennis balls

6 green tennis balls

5 blue tennis balls

Let;

red tennis ball be r

green tennis balls be g

blue tennis balls be b

The total number of tennis balls is 8+5+6=19 balls

Multiplication is a repeated form of addition where ;

5*5*5 = 3*5= 5+5+5= 15

In this case, r+g+b=19 but r ,g and b are not repeated thus applying multiplication equation will not give the sum of the balls

However if you let a single ball to be represented by x then a single ball x will be multiplied by the number of balls in that category to get the total number of balls per color

For red balls= 8x

For green balls=6x

For blue balls=5x.

Total number of balls = 8x+6x+5x =19x where x represent a single tennis ball.

To find the total number of tennis balls Kayla has, she needs to add the number of each color of balls together, not multiply. When she adds 8 red, 6 green, and 5 blue balls, she gets 19 tennis balls in total.

In this case, Kayla doesn't need to use a multiplication equation to find out the total number of tennis balls she has. Rather, she just needs to add the numbers together. Kayla has 8 red tennis balls, 6 green tennis balls, and 5 blue tennis balls. So, to figure out how many tennis balls she has in total, she simply adds these numbers together: 8 + 6 + 5 = 19 tennis balls in total.

https://brainly.com/question/35006189

#SPJ3

The value of [tex](f+g)(18500)[/tex] is [tex]\Dollar 16675[/tex] dollars.

The interest he earns on x dollars invested in the first account is given by,

                     [tex]f(x)=0.05x[/tex]

The interest he earns from the second account,

                   [tex]g(x)=0.075(x+2500)[/tex]

[tex]f(x)+g(x)=0.05x+0.75(x+2500)\\\\f(x)+g(x)=0.05x+0.75x+1875\\\\f(x)+g(x)==0.8x+1875\\\\(f+g)(18500)=(0.8*18500)+1875\\\\f(x)+g(x)=14800+1875\\\\f(x)+g(x)=16675[/tex]

Learn more about the interest rate here:

https://brainly.com/question/25545513

Correct option B)[tex]63.4km^2[/tex] .

Step-by-step explanation:

We have the following figure attached as shown below.

Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:

2 similar right angled surfaces

We know that area of triangle = [tex]\frac{1}{2} b(h)[/tex]

⇒ [tex]area = \frac{1}{2} b(h)[/tex]

⇒ [tex]area = \frac{1}{2} (3.6)(7.7)[/tex]

⇒ [tex]area = 13.86km^{2}[/tex]

But there 2 such surfaces so , [tex]area = 2(13.86) = 27.72km^2[/tex]

3 rectangular surfaces

Area of rectangle = [tex]length(breadth)[/tex]

⇒ [tex]area_1 = 3.6(1.8)[/tex]

⇒ [tex]area_1 = 6.48km^2[/tex]

⇒ [tex]area_2= 7.7(1.8)[/tex]

⇒ [tex]area_2 = 13.86km^2[/tex]

⇒ [tex]area_3 = 8.5(1.8)[/tex]

⇒ [tex]area_2 = 15.3km^2[/tex]

Total area =[tex]6.48 + 13.86 + 15.3 = 35.64km^2[/tex]

Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:

[tex]Area = 27.72+35.64 = 63.36km^2[/tex] = [tex]63.4km^2[/tex]

Correct option B)[tex]63.4km^2[/tex] .

Answer:

It is B.

Step-by-step explanation:

Trust me it's B

Answer:

y = 9

Step-by-step explanation:

Calculate the slope m of line k using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 8) and (x₂, y₂ ) = (2, y)

m = [tex]\frac{y-8}{2-5}[/tex] = [tex]\frac{y-8}{-3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

The slope of line l is m = 3, thus slope of line k is

m = - [tex]\frac{1}{3}[/tex]

Equating the 2 slopes for line k

[tex]\frac{y-8}{-3}[/tex] = - [tex]\frac{1}{3}[/tex] ( multiply both sides by - 3 )

y - 8 = 1 ( add 8 to both sides )

y = 9

To find the value of y, we can use the fact that the slopes of Perpendicular lines are negative reciprocals of each other. Using the given information and equations, we can solve for y.

To determine the value of y, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since line l has a slope of 3, the slope of line k would be -1/3. We can use the slope-intercept form, y = mx + b, to find the equation of line k.

Substituting the coordinates (5, 8) and the slope -1/3 into the equation, we can solve for y.

Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point (2, y). We can rearrange this equation to get y = mx + b form, substitute the values, and solve for y to find the value of y.

https://brainly.com/question/18271653

#SPJ2

Answer:

They paid $4.00 per ticket

Step-by-step explanation:

Step 1:  Convert words into an inequality

A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.

6t + 3 = 27

Step 2:  Solve for t/tickets

6t + 3 = 27

6t + 3 - 3 = 27 - 3

6t / 6 = 24 / 6

t = 4

Answer:  They paid $4.00 per ticket

Answer:

4

Step-by-step explanation:

3 - 27 = 24

24 ÷ 6 = 4

4 · 6 = 24

3 + 24 = 27

A = $27

Answer:

Yes

Step-by-step explanation:

2/5 + 3/4 = [2(4) + 3(5)]/20

= 23/20 = 1 3/20

1 3/20 = 1 9/60

1 1/6 = 1 10/60

1 1/6 > 1 3/20

Answer:

23/4

Step-by-step explanation:

multiply the whole number (5) by the denominator (4) and add your numerator (3), which for you is 23, then put that over your denominator (4). so it would be 23/4 :)

Well I'm a bit confused since 5 3/4 is a mixed number. Please elaborate!

Answer:

490

Step-by-step explanation:

oh lord here we go again

get the area of all signs again

5 x 5 = 25

theres 2 of those squares so make that 50

8 x 5 = 40

theres 4 of those sides so 40 x 4 = 160

10 x 10 = 100

theres two of those so its 200

2 x 10 = 20

4 of these so 80

add all the final ones

50 + 160 + 200 + 80 = 490

Answer:

its near 1 mile or half a mile