Amanda and her little brother each throw a model airplane at the same time, but from different heights on the playground. The functions h(x) = -16x2 + 24x + 40 and g(x) = -16x2 + 10x + 21 represent the heights of Amanda's plane and her brother's plane, respectively, x seconds after the planes are thrown.

Which of the following statements is true?


Amanda's brother's model airplane will stay in the air for 3 seconds longer than Amanda's model airplane.

Amanda's brother's model airplane will touch ground 2 seconds earlier than Amanda's model airplane.

Amanda's model airplane will touch ground 4 seconds earlier than Amanda's brother's model airplane.

Amanda's model airplane will stay in the air for 1 second longer than Amanda's brother's model airplane.

Answer:

  70 yards wide and 135 yards long

Step-by-step explanation:

The perimeter of a rectangle will be the same if the sum of length and width is the same. The area will be smaller if the difference between lenth and width is greater.

__

The sum of length and width will be the same if the length is increased by the same amount that the width is decreased. Changing each by 10 yards is one possibility.

A lot 70 yards wide and 135 yards long will have the same perimeter and a smaller area.

_____

Check

Given perimeter: 2(80 +125) = 410 yds.

Modified perimeter: 2(70 +135) = 410 yds. (same)

Given area = 80(125) = 10000 yd².

Modified area: 70(135) = 9450 yd². (smaller)

__

Additional comment

The area is greatest when the difference between the length and width is zero. That is, the rectangle will be a square.

The distance from the tree house that the ball strike the ground is 10feet

Given the path of the ball expressed by the parabola equation:

y = -2x^2+14x +60

The point where the ball strikes the ground is the point where y = 0. Substitute into the equation to have:
-2x^2+14x +60 = 0

x^2 - 7x - 30 = 0

Factorize the result

x^2 - 10x + 3x - 30 = 0
x(x-10)+3(x-10) = 0
x - 10 =0

x = 10

Hence the distance from the tree house that the ball strike the ground is 10feet

Learn more on function here: https://brainly.com/question/25638609

Answer:

35 degrees

30 degrees

Answer: x=2

Step-by-step explanation:

9(x+7)+5=86

Step 1: Simplify both sides of the equation.

9(x+7)+5=86

(9)(x)+(9)(7)+5     (Distribute)

9x+63+5=86

(9x)+(63+5)=86      (Combine Like Terms)

9x+68=86

Step 2: Subtract 68 from both sides.

9x+68−68=86−68

9x=18

Step 3: Divide both sides by 9.

[tex]\frac{9x}{9} =\frac{18}{9}[/tex]

x=2

Answer: 1 3/4(8)= 14

Step-by-step explanation:

That is the correct answer

Answer:

y=45°

x=75°

z=60°

Step-by-step explanation:

hard to explain, but I'll try my best. on a single line, it equals 180 when both angles are added up. and the opposite side of an angle is always the same.

Answer:

x = 1

Step-by-step explanation:

Given:

2(3x - 7) + 18 = 10

Solution:

Subtract 18 from both sides

2(3x - 7) + 18 = 10

              - 18    -18

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

2 (3x-7) = -8

Now divide both sides by 2

2 (3x-7)               -8

-----------     =  ------------

  2                      2

Simplify

3x - 7 = -4

Then add 7 to both sides

3x - 7 = -4

   + 7     +7

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

3x = 3

Divide both sides by 3

3x                     3

-----------     =  ------------

  3                     3

x = 1

Thus, Solution : x =1

~Lenvy~

Answer:

[tex]x = 1[/tex]

Step-by-step explanation:

Simplify both sides of the equation

[tex]2(3x - 7) + 18 = 10[/tex]

Distribute

[tex](2)(3x) + (2)( - 7) + 18 = 10 \\ 6x + - 14 + 18 = 10[/tex]

Combine like terms

[tex](6x) + ( - 14 + 18) = 10[/tex]

[tex]6x + 4 = 10[/tex]

Subtract 4 from both sides

[tex]6x + 4 - 4 = 10 - 4[/tex]

[tex]6x = 6[/tex]

Divide both sides by 6

[tex] \frac{6x}{6} = \frac{6}{6} [/tex]

[tex]x = 1[/tex]

Answer:

A. x = -9

Step-by-step explanation:

6x + 8 = 3x - 19 <== subtract 3x from both sides

-3x       -3x

3x + 8 = -19 <== subtract 8 from both sides

    - 8     - 8

3x = -27 <== divide both sides by 3

/3     /3

x = -9

Hope this helps!

Answer:

[tex]\tt x=-9[/tex]

Step-by-step explanation:

[tex]\tt 6x + 8 = 3x - 19[/tex]

Subtract 8 from both sides:-

[tex]\tt 6x+8-8=3x-19-8[/tex]

[tex]\tt 6x=3x-27[/tex]

Subtract 3x from both sides:-

[tex]\tt 6x-3x=3x-27-3x[/tex]

[tex]\tt 3x=-27[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}=\cfrac{-27}{3}[/tex]

[tex]\tt x=-9[/tex]

The vaule of x that makes the equation true is A) x= -9.

Answer:

C. 309 cm2

Step-by-step explanation:

A=2(1+sqr2)a^2

A=2(1+sqr2)8^2

≈309.01934

Answer: 309 cm2

Step-by-step explanation:

plato

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \:4x - 16 = 64[/tex]

[tex]\qquad \sf  \dashrightarrow \:4(x - 4) = 64[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 4) = 64 \div 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x - 4 = 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 16 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x =20[/tex]

[tex] \boxed{ \bf \huge \: Answer \: }[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x - 16 = 64[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x = 64 + 16[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x = 40[/tex]

[tex] \: [/tex]

[tex] \sf \large \: x = \cancel \frac{80}{4} [/tex]

[tex] \: \: [/tex]

[tex] \sf \large x = 20[/tex]

[tex] \: \: [/tex]

Hope It's Helps uh Miss<3"

Answer:

3+15=18 i guess

Step-by-step explanation:

dont judge me im only in 2 grade

Answer:

what??? I can't understand you sorry

Answer:

The answer is 28 Units

It's number 3.

Answer:

See below ↓↓

Step-by-step explanation:

1) 3a - 6

2) 1/2zfy10

Answer:

Letters as in the attached image.
Triangles ABC and ADC are congruent by SSS. From that, corresponding angles are congruent, in parcicualre B and D, both measuring 94°.
Final angle is obtained by difference. The internal angles of a quadrilater add to 360, so the remaining is 360-90-94-94 =82°

Step-by-step explanation:

Length = 94 cm

breadth = ?

Perimeter = 298 cm

Now..............

Perimeter = 2 ( l + b )

298cm = 2 ( 94 cm + b )

298 / 2 = 94 + b

149 cm = 94 + b

b = 149 - 94 cm

b = 55 cm

Answer:

Step-by-step explanation:

In the question we have given perimeter of rectangular painting that is 298 cm , length of the painting is 94 cm , and we have asked to find the width of the rectangular painting . So perimeter of rectangle is ,

[tex] \purple{ \boxed{Perimeter \: of \: rectangle = 2 ( l + w ) }}[/tex]

Where ,

Now , we are substituting value of length and equating it with given perimeter :

[tex] \longrightarrow \: 2(94 + w) = 298[/tex]

Now, our last step is of calculations . So from here we are calculating ,

[tex] \longrightarrow \: 94 + w = \frac{298}{2} [/tex]

[tex] \longrightarrow \: 94 + w= 149[/tex]

[tex] \longrightarrow \: w = 149 - 94[/tex]

[tex] \longrightarrow \: \blue{\boxed{ \bold{w = 55 \:cm}}}[/tex]

Answer:

25[tex]\pi[/tex]

Step-by-step explanation:

[tex]\pi[/tex]r^2 is the formula for a circle (in this case, a circular rug)
and we would set it equal to 84 (since we are trying to get the biggest size possible).
We would isolate r so that r^2 = 84/[tex]\pi[/tex], and r would be around 5.17219.
If we were going by rounding 5 would be the largest radius possible and the radius would be 25[tex]\pi[/tex] or about 78.5398 units.

Answer:

Rounded to one decimal place, the maximum area circular rug that can fit in the dining room is 38.5 square feet.

Please See the attached screenshot for the exact solutions and answer for this question

Answer: B and C

Step-by-step explanation:

404 + 50 + 50 = 504

you are buying  144 magazines total

504/144 = cost of one magazine

cost of one = 3.50

you are paying $60 a year for 12 years

60 x 12 = 720

720/144 = 5

5 - 3.50 = 1.50

2.

120x + 180x = 1080

300x = 1080

x = 1080/300

x = 3.6

3.6 x 60 = 216

Answer:

Adolescence

Step-by-step explanation:

We are constantly changing and developing in adolescence, it is the bridge between childhood and adulthood, mixed with youth (taking risks more frequently, less worries) and responsibilities and coming-of-age.

Answer:

  17

Step-by-step explanation:

The expression of interest is the difference of the two given expressions.

  (-4x +6y) -(-2x -7y) = (9) -(-8)

  -2x +13y = 17

The value is 17.

_____

Additional comment

You could go to the trouble to solve the two equations for x and y, then compute the value of the expression you want. As we saw above, that is not necessary.

The first step in problem solving is always "look at the given information and how it relates to what you are asked." A little time spent doing that can save a lot of effort in the actual problem solving process.

Answer:

15 shrimps

Step-by-step explanation:

We already know that a small shrimp taco has 5 shrimps.

⇒ [tex]\text{1st equation: small shrimp taco = 5 shrimps}[/tex]

We also know that a large taco has 3 times more shrimps than a small taco.

⇒ [tex]\text{2nd equation: shrimps in a large taco = 3(Shrimps in a small taco)}[/tex]

Finding the number of shrimps in a large taco:

Now, simply substitute the number of shrimps in a small shrimp taco in the second equation to find the number of shrimps in a large taco.

Answer:

15 shrimp

Step-by-step explanation:

5 shrimp * 3 = 15shrimp

Answer:

468 ft²

Step-by-step explanation:

Area = (37+15)/2 × 18

37 + 15 is 52

Divide 52 by 2 which is 26

26 × 18 is 468

We know,

[tex] \text{Area of trapezoid =} \frac{a + b}{2} h[/tex]

Here, a and b are base and h is height

[tex] = \frac{37 + 15}{2} \times 18 \\ \\ = \frac{52}{2} \times 18 \\ \\ = \cancel\frac {52}{2} \times 18 \\ \\ = 26 \times 18 \\ = 468 \: \text{ft²}[/tex]

Answer:

1

Depends on the cross section axis

place a cylinder can on a table , circular and side down .Look down at it and you see the other end so the cross section is circle

Turn it on its side and the cross section is rectangle

Answer:

2

Step-by-step explanation:

so if you take away 14 by 2 =12 and 12 divided by 6= 2

Answer:

each candy bar cost 2 dollars

Step-by-step explanation:

Answer:

The answer is 15

Step-by-step explanation:

f(x) = -4x + 3, f(-3)

f(-3) = -4x + 3

f(-3) = -4(-3) + 3

f(-3) = 12 + 3

f(-3) = 15

Thus, The answer is 15

Answer:

f(-3)=-4(-3)+3

=12+3=15

Step-by-step explanation:replace x with -3

Answer:

60 degree is the value of m

Answer:

6 - 6r

Step-by-step explanation:

we just plug in 3r - 1 instead of x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= 6 - 6r