You cast a fishing lure from 4 feet above the water. Its travel is given by the function h = -16t^2 + 24t + 4, where t = time in seconds. After how many seconds will it reach a height of 12 feet?

Answer:

The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers

Step-by-step explanation:

Notice that the length "L" of the driveway can be written in terms of its width as:

L = 2 w + 5

based on the given information.

Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:

1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway

and the other one:

2) w + 3 times 3

Therefore the total area of the brick walkway is given by the formula:

(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet

Now we can solve for "w" in the above equation:

6 w + 15 + 3 w + 9 = 213

9 w + 24 = 213

9 w = 213 - 24

9 w = 189

w = 189/9

w = 21 feet

We can now solve for the L of the driveway, using the first formula we created:

L = 2 w + 5

L = 2 (21) + 5

L = 42 + 5

L = 47 feet

Therefore the driveway's width is w = 21 feet

and its length is L = 47 feet

Answer:

W

Step-by-step explanation:

The input is the x-axis.

The output is the y-axis.

Make them coordinates. Hope this helped!

Answer:

See explaination:

Graphs are on the right, equations are on the left, and they are color coded.

Step-by-step explanation:

Answer:

[tex]2a^2 + 3x - 2a[/tex]

Step-by-step explanation:

[tex] (6a^2 + 3x) - (4a^2 + 2a) = [/tex]

The first set of parentheses is unnecessary and can be removed.

[tex] = 6a^2 + 3x - (4a^2 + 2a) [/tex]

To remove the second set of parentheses, you must distribute the negative sign to its left as if it were a -1 multiplying the quantity inside the parentheses.

[tex] = 6a^2 + 3x - 1(4a^2 + 2a) [/tex]

[tex] = 6a^2 + 3x - 4a^2 - 2a [/tex]

Now combine like terms. Like terms are terms with the same variable part.

[tex] = 2a^2 + 3x - 2a [/tex]

Answer:

The total number of students in the college is 3,000.

Step-by-step explanation:

[tex]\frac{48}{100}=\frac{1,440}{x}[/tex]               Set up a proportion.

[tex]48x=144,000[/tex]         Cross-multiply.

[tex]x=3,000[/tex]                 Divide both sides by 48.

Answer:

Step-by-step explanation:

rectangle + semicircle

= 8*6 + pi r^2/2

=48 + 22/7 * 3/2 * 3/2

then simplyn..

Answer:

The figure is a rectangle and a semicircle

Step-by-step explanation:

Answer:

k(-7) = = -89

Step-by-step explanation:

k(t) = 10t -19

Let t = -7

k(-7) = 10*-7 -19

      = -70-19

      = -89

Answer:

-89

Step-by-step explanation:

K(t) = K(-7)

10 is being multiplied by t. t = -7

so:

10(-7) = -70

-70 - 19 = -89

Hope this helps!

Answer:

3.2 ft

Step-by-step explanation:

The initial distance from the base of the ladder to the wall is:

[tex]20^2=16^2+d^2\\d=12\ ft[/tex]

After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:

[tex]20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft[/tex]

Therefore, the top of the ladder is  3.2 ft higher now.

Answer:

3.2ft higher

Step-by-step explanation:

Answer:

The answer is 7.

Step-by-step explanation:

If you want to find what FE is, you have subtract GF from GE (GE - GF = FE).

Since GE = 13 and GF = 6, you have to subtract 6 from 13 which equals 7.

(13 - 6 = 7)

Answer:

Step-by-step explanation:

Before we begin this, there are a few things that need to be said and a few formulas you need to know. First is that we need to use the work form of a parabola, which is

[tex]y=a(x-h)^2+k[/tex]

All of the parabolas listed in blue highlight open either up or down, and this work form represents those 2 options. The only thing we need to know is that if there is a negative sign in front of the a, the parabola opens upside down like a mountain instead of up like a cup.

Another thing we need to know is how to find the focus of the parabola. The formula to find the focus for an "up" parabola is (h, k + p) and the formula to find the focus for an upside down parabola is (h, k - p). Then of course is the issue on how to find the p. p is found from the a in the above work form parabola, where

[tex]p=\frac{1}{4|a|}[/tex] .

In order to accomplish what we need to accomplish, we need to put each of those parabolas into work form (as previously stated) by completing the square. I'm hoping that since you are in pre-calculus you have already learned how to complete the square on a polynomial in order to factor it.  Starting with the first one, we will complete the square. I'll go through each step one at a time, but will provide no explanation as to how I got there (again, assuming you know how to complete the square).

[tex]y=-x^2+4x+8[/tex] and, completing the square one step at a time:

[tex]-x^2+4x=-8[/tex] and

[tex]-(x^2-4x+4)=-8-4[/tex] and

[tex]-(x-2)^2=-12[/tex] and

[tex]-(x-2)^2+12=y[/tex]

From this we can see that the h and k values for the vertex are h = 2 and k = 12. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct focus formula (h, k - p), we get that the focus is

[tex](2, 12-\frac{1}{4})[/tex] which simplifies to (2, 11.75) which is choice 2 in your options.

Now for the second one (yes, this takes forever...)

[tex]y=2x^2+16x+18[/tex] and completing the square one step at a time:

[tex]2x^2+16x=-18[/tex] and

[tex]2(x^2+8x+16)=-18+32[/tex] and

[tex]2(x+4)^2=14[/tex] and

[tex]2(x+4)^2-14=y[/tex]

From this we can see that the vertex is h = -4 and k = -14. Now to find p from a.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex] .

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-4, -14+\frac{1}{8})[/tex] which simplifies down to (-4, -13.875) which is choice 3 in your options.

Now for the third one...

[tex]y=-2x^2+5x+14[/tex] and completing the square step by step:

[tex]-2x^2+5x=-14[/tex] and

[tex]-2(x^2-\frac{5}{2}x+\frac{25}{16})=-14-\frac{50}{16}[/tex] and

[tex]-2(x-\frac{5}{4})^2=-\frac{137}{8}[/tex] and

[tex]-2(x-\frac{5}{4})^2+\frac{137}{8}=y[/tex]

From that we can see the vertex values h and k. h = 1.25 and k = 17.125. Now to find p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upside down parabola (h, k - p),

[tex](1.25, 17.125-\frac{1}{8})[/tex] which simplifies down to (1.25, 17) which is choice 4 in your options.

Now for the fourth one...

[tex]y=-x^2+17x+7[/tex] and completing the square step by step:

[tex]-x^2+17x=-7[/tex] and

[tex]-(x^2-17x)=-7[/tex] and

[tex]-(x^2-17x+72.25)=-7-72.25[/tex] and

[tex]-(x-8.5)^2=-79.25[/tex] and

[tex]-(x-8.5)^2+79.25=y[/tex]

From that we see that the vertex is h = 8.5 and k = 79.25. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct formula for an upside down parabola (h, k - p),

[tex](8.5, 79.25-\frac{1}{4})[/tex] which simplifies down to (8.5, 79) and I don't see a choice from your available options there.

On to the fifth one...

[tex]y=2x^2+11x+5[/tex] and again step by step:

[tex]2x^2+11x=-5[/tex] and

[tex]2(x^2+\frac{11}{2}x+\frac{121}{16})=-5+\frac{242}{16}[/tex] and

[tex]2(x+\frac{11}{4})^2=\frac{81}{8}[/tex] and

[tex]2(x+\frac{11}{4})^2-\frac{81}{8}=y[/tex]

from which we see that h = -2.75 and k = -10.125. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-2.75, -10.125+\frac{1}{8})[/tex] which simplifies down to (-2.75, -10) which is choice 1 from your options.

Now for the last one (almost there!):

[tex]y=-2x^2+6x+5[/tex] and

[tex]-2x^2+6x=-5[/tex] and

[tex]-2(x^2-3x+2.25)=-5-4.5[/tex] and

[tex]-2(x-1.5)^2=-9.5[/tex] and

[tex]-2(x-1.5)^2+9.5=y[/tex]

from which we see that h = 1.5 and k = 9.5. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the formula for the focus of an upside down parabola (h, k - p),

[tex](1.5, 9.5-\frac{1}{8})[/tex] which simplifies down to (1.5, 9.375) which is another one I do not see in your choices.

Good luck with your conic sections!!!

Answer:

9 cubic feet

Step-by-step explanation:

Assuming that the garden box is a rectangular prism, its volume is:

[tex]4\dfrac{1}{2} \cdot 4 \cdot \dfrac{1}{2}=9 \text{ ft}^3[/tex]

Hope this helps!

Solution,

Length(L)=4 1/2 ft

Breadth(b)= 4 ft

Height(H)=1/2 ft

Now,

Volume=L*B*H

= 4 1/2*4*1/2

=9/2*4*1/2

= 9 cubic feet

Hope it helps

Good luck on your assignment

Answer:

The equation of the relationship is y = 1.25x + 6.5

Step-by-step explanation:

I graphed the ordered pairs on the graph below and found the slope and y-intercept of the line.

The price per game is $7.75. (If needed)

Answer:

x = 1/2

Step-by-step explanation:

9x=4.5

Divide each side by 9

9x/9 = 4.5/9

x = 45/90

x = 1/2

Answer:

x = 1/2 or x = 0.5

Step-by-step explanation:

9x = 4.5/9

= 45/90

= 1/2 or 0.5

Hope this helps, and please mark me brainliest if it does!

Answer:

Step-by-step explanation:

The area for a trapezoid is

[tex]A=\frac{1}{2}h(b_{1}+b_{2})[/tex]

h is the length of ST, one of the bases is the length of MK, and the other base is the length of AS.  First we'll find h:

The coordinates for S are (0, -2) and T are (1, 2). Using the distance formula:

[tex]d=\sqrt{(1-0)^2+(2-(-2))^2[/tex] and

[tex]d=\sqrt{17}[/tex].  So h = √17

Now for the length of MK. The coordinates for M are (-7, 4) and for K (5, 1). Using the distance formula again:

[tex]d=\sqrt{(-7-5)^2+(4-1)^2}[/tex] and

[tex]d=\sqrt{(-12)^2+(3)^2}[/tex] so

[tex]d=\sqrt{153}[/tex] which simplifies to

[tex]d=3\sqrt{17}[/tex]. So MK = 3√17.

Now for the length of AS. The coordinates for A: (-4, -1) and for S: (0, -2). Using the distance formula one more time:

[tex]d=\sqrt{(-4-0)^2+(-1-(-2))^2}[/tex] and

[tex]d=\sqrt{(-4)^2+(1)^2}[/tex] and

[tex]d=\sqrt{17}[/tex]. So AS = √17.

Now we can fill in our area formula:

[tex]A=\frac{1}{2}(\sqrt{17})(3\sqrt{17}+\sqrt{17})[/tex]

Simplifying a bit:

[tex]A=\frac{1}{2}(\sqrt{17})(4\sqrt{17})[/tex] and simplifying a bit more:

[tex]A=\frac{4*17}{2}[/tex] and

A = 34

Answer:

D

Step-by-step explanation:

a = 2 ;  b = -6 ;  c = 5

[-b±√b²-4ac]/2a=[-(-6)±√6²-4*2*5]/2*2

=[6±√√36-40]/4

=[6±√-4]/4

=[6±√i²*2²]/4

=[6±2i]/4

=2[3±i]/4

=3±i/2

= 3+i/2  or 3-i/2

Answer:

192 cubes.

Step-by-step explanation:

The volume of each cube  = (side)³  = (1/4)³  = 1/64 units ³

Next is to find how many cubes are needed to fill the prism.

The number of cubes  that will fill the prism  :

Vol. of prism / Vol. of cube = 3 / [tex]\frac{1}{64}[/tex]

                                            =192 cubes.

Therefore, it takes 192 cubes to fill the prism.

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

hope I could help

Answer:

400

Step-by-step explanation:

Answer: (15th street, 14th Avenue)

Step-by-step explanation:

Given the following :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location = 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari = (18th , 12th )

Gym distance = 2/3 of distance between ping and Ari

Gym distance = 2/3 × (18), 2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

Answer:

d) 15th Street and 14th Avenue

Answer:

easy just find the total of how many people work there then put that no. as a denominator and put 12 on the numerator then times it by 100 and the answer should be 52.2% or 52.17%

Answer:

52.2% or 52.17%

12 men

Total = 23

12 / 23 =

Answer:

65 = <JKL

Step-by-step explanation:

There are two expressions that represent the same thing.

The diagram shows that <JKL = 45 + x

The question states that JKL = 3x + 5

The two expressions must be equal since they represent the same thing.

3x + 5 = x + 45

Subtract 5 from both sides

3x + 5 -  5 = x + 45 - 5

3x = x + 40                     Subtract x from both sides

3x - x = x - x + 40

2x = 40                          Divide by 2

2x/2 = 40/2

x = 20

So x + 45 = 20 + 45 = 65

or

3x + 5 = 3*20 + 5 = 60 + 5 = 65

Answer:

The sum of all of the terms would be 255

Step-by-step explanation:You would continue to multiply all of the answers by 2 until you hit 128. Then you would add all of them together 128+64+32+16+8+4+2+1=255

Answer:

[tex]131.95[/tex] [tex]cm[/tex]

Step-by-step explanation:

[tex]C=2 \pi r[/tex]

[tex]C=2 \pi \times 21[/tex]

[tex]C=42\pi[/tex]

[tex]C \approx 131.946891451[/tex]

Answer:

(x + 2) (3x + 1)

Step-by-step explanation:

3x² + 7x + 2

3x² + 6x + x + 2

3x(x + 2) + 1(x + 2)

(x + 2) (3x + 1)

Answer:

Felipe's answer is 8.

6 divided by 3/4

= 6 * 4/3

= 24/3

= 8

Answer:

8

Step-by-step explanation:

6÷3/4=6×4/3=8

Answer:

[tex]sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Step-by-step explanation:

It is given that:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

And we have to find the value of [tex]sin\theta_1 = ?[/tex]

As per trigonometric identities, the relation between [tex]sin\theta\ and \ cos\theta[/tex] can represented as:

[tex]sin^2\theta + cos^2\theta = 1[/tex]

Putting [tex]\theta_1[/tex] in place of [tex]\theta[/tex] Because we are given

[tex]sin^2\theta_1 + cos^2\theta_1 = 1[/tex]

Putting value of cosine:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

[tex]sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}[/tex]

It is given that [tex]\theta_1[/tex] is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

[tex]\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Answer:

−  square root 15/4

Step-by-step explanation:

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

4 : 5

300 : ?

Divide 300 by 4 to find out what '1 part' would count as:

300/4 = 75

Multiply this by 5

75 x 5 = 375

Add the two values together

375 + 300 = 675

There are 675 students

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Step-by-step explanation:

Number of boys=300

Ratio of boys to girls=4:5

let the number of girls=y

300/y=4/5

Cross multiply

300×5=4×y

1500=4y

Divide through both sides by 4

1500/4=4y/4

374=y

Number of girls is 375

Total number of students=Number of boys+Number of girls

Total number of students=300+375

Total number of students=375

Answer:

i think its c idk if im wrong im sorry

Step-by-step explanation: