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Answer:

The arrow will take 4.19 seconds to hit the ground

The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height

Step-by-step explanation:

The quadratic function is f(t) = -5t² + 20t + 4, where

f(t) is the height in feet

t is the time in seconds

If the arrow hit the ground that means h(t) = 0

→ Substitute h(t) by 0 and use the quadratic formula to find t

∵ h(t) = 0

∴ 0 = -5t² + 20t + 4

→ Switch the two sides

∴ -5t² + 20t + 4 = 0

→ Multiply all terms by -1 to make the coefficient of t² positive

∴ 5t² - 20t - 4 = 0

→ The quadratic formula is [tex]t=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] , where

∵ a = 5, b = -20, c = -4

∴ [tex]t=\frac{-5+-\sqrt{(-20)^{2}-4(5)(-4)}}{2(5)}[/tex]

∴ [tex]t=\frac{-5+-\sqrt{400+80}}{10}[/tex]

→ Find the values of t in decimal

∴ t = 4.19 seconds OR t = -0.19 ⇒ refused because it is negative

∴ The arrow will take 4.19 seconds to hit the ground

The graph of this quadratic function is a parabola with maximum vertex (h, k), where

To find the maximum height and the time taking for this to occur find h and k where k is the maximum height and h is the time for this to occur

∵ f(t) = -5t² + 20t + 4

∵ a = -5 and b = 20

∴ h = [tex]-\frac{20}{2(-5)}=-\frac{20}{-10}=2[/tex]

∴ The time for the maximum height is 2 seconds

→ Now use it to find k

∵ k = f(h)

∴ k = f(2)

∵ f(2) = -5(2)²+ 20(2) + 4

∴ f(2) = -5(4) + 40 + 4

∴ f(2) = -20 + 40 + 4

∴ f(2) = 24

∴ k = 24

∴ The maximum height is 24 feet

The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height

Option C, a = (w - 4b )/7 is the correct answer

w = 7a + 4b

7a = w - 4b

a = (w- 4b )/7

Answer:

Step-by-step explanation:

last year won 57 games

this year won 15 games

the difference is 57 - 15 = 42,

this means it drops 42 / 57 = 0.73 (100%)  ≈ 73%

therefore,  the percentage decrease from the given choices is: J

42 =   x  

57     100

Answer:

Slope = - 5/6

Step-by-step explanation:

Step 1:

y = mx + b        Slope Intercept Form

Step 2:

6x - 5y = - 40      Equation

Step 3:

- 5y = - 6x - 40       Subtract 6x on both sides

Step 4:

y = 5/6x - 80      Divide 5 on both sides

Step 5:

m = Slope

Answer:

Slope = - 5/6

Hope This Helps :)

Answer:

y=1/2x+0.5

Step-by-step explanation:

The slope is 1/2, which you can see by looking at the change of y/x. The y intercept is 0.5, which can be seen on the y axis.

Answer:

5

Step-by-step explanation:

Question #1

first, you need to find the slope. Use the formula: m=(y₂-y₁)/(X₂-X₁). Plug in x and y values. once you have found the slope, use point-slope form;

(y-y₁)=m(x-x₁). Again, plug in x and y values. Simplify the equation. Do that with the coordinate pairs, to see which one matches y=-1/2x+4. The answer though is A, (-2,5) and (2,3).

Question #2

Do the same thing, find the slope using the formula, and then use point-slope form. After that, find the matching equation and that's the answer. I am confused though because the right equation would be [tex]y=-3x[/tex], but that's not one of the answers.

Answer:

88

Step-by-step explanation:

Answer:

1 whole and 15/100= 1.15

Step-by-step explanation:

The first box is 1 whole, in total there are 100 squares. All u need to do is count the number of squares

The equation that shows a proportional relationship is y = 7x.

Two variables have a proportional relationship if all the ratios of the variables are equivalent.

In other words, a proportional relationship is one in which two quantities vary directly with each other.

Therefore, a proportional relationship can be represented as y = kx.

where

Therefore, y varies directly as x in a proportional relationship.

Hence, the equation that shows proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.

learn more on proportional relationship here: brainly.com/question/20213987

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Answer:

y = 7x

Step-by-step explanation:

the proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.

Answer:

The values are   [tex]x =  46 miles /hr [/tex]

                            [tex]y = 4 \  miles / hr[/tex]

Step-by-step explanation:

From the question we are told that

   The distance covered is  d =  264 miles

     The time taken is [tex]t_1 =  6 hours[/tex]

     The time taken for the return trip is  [tex]t_2  =  5.5 \ hours[/tex]

Generally during the trip  toward fishing spot , the velocity is mathematically represented as

     [tex]v_t  =  \frac{d}{t_1 } = x - y[/tex]

=>  [tex]v_t  =  \frac{264}{6 } = x - y[/tex]

=>    [tex]x - y  = 44 \cdots 1 [/tex]

Generally during the  return trip  , the velocity is mathematically represented as

      [tex]v_r  =  \frac{d}{t_2}  =  x+ y[/tex]

=>   [tex]v_r  =  \frac{264}{5.5}  =  x+ y[/tex]

=>   [tex]48 =  x+ y\cdots 2[/tex]

add equation 1 and 2

       [tex]2x =  92[/tex]

=>    [tex]x =  46 miles /hr [/tex]

substituting this  into  equation 1

     [tex] 46 - y  = 44 \cdots 1 [/tex]

=>   [tex]y = 4 \  miles / hr[/tex]

Answer:

B. y=3/4x+6

Step-by-step explanation:

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Answer: B

Step-by-step explanation: the y-intercept is always the b in the equation y=mx+b. in this case it’s 6. Then you look at the rise and the run. its 3/4 because you go up 3 units, and to the right 4 units, to get to the next coordinate point.

Answer:

Kali needs 104 more tiles to completely cover the box.

Step-by-step explanation:

Length of box =  20 in

Breadth of box = 6 in

Height of box= 9 in

Total surface area of box = 2lw + 2lh + 2wh

Total surface area of box = 2(20)(6) + 2(20)(9) + 2(6)(9)

Total surface area of box = 708 sq. in.

Side of tile = 1 in

Area of 1 tile = [tex]Side^2 = 1^2 = 1 sq. in[/tex]

Area of 604 tiles = 604 sq. in.

Area remain uncovered = 708 - 604 = 104 sq.in.

So, Kali needs 104 more tiles to completely cover the box.

Answer:

B. 125

Step-by-step explanation:

square roots:

81 = 9

169 = 13

125 = 11.180..

289 = 17

Answer:

n=24

Step-by-step explanation:

add 4 to both sides

Answer:

Step-by-step explanation:

[tex]n-4=20\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\n-4+4=20+4\\\\Simplify\\\\n = 24[/tex]

Answer:

D

Step-by-step explanation:

f(-9) = 3/5(-9) + 8 = 13/5

Answer:c

Step-by-step explanation:move up 3 units on the y axis and create the graph

Answer:

x=40

Step-by-step explanation:

x/4 - x/8

LCM of 4,8=8

x/4x2/2 - x/8=5

2x/8 - x/8 =5

x/8=5

transpose

x=5x8

x=40

hope this helps

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Answer:

Corresponding angles are

1 and 3

or 5 and 7

or 2 and 4

or 6 and 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The idea hear is to find the least common multiples of 15 and 24

Given that they separated at exactly 1:00pm

the multiples are

15= 15,30,45,60,75,90,105,120

24= 24, 48,72,96,120

the multiples common is 120

Therefore they will meet in 120minute, which is 2 hours time \

hence the time will be 3:00pm

Answer: f(x)=(x+2)(4x-3)(x-5)

Step-by-step explanation:

Alg2.2.5 practice 2

Polynomial function has zeros when  x=[tex]-2, \frac{3}{4} , 5[/tex] is

[tex]4x^3-15x^2-31x+30[/tex]

Given :

polynomial function has zeros when x= -2, 3/4, 5

Lets write the zeros in factor form

If 'a' is a zero , then factor is (x-a)

The given zeros are [tex]-2, \frac{3}{4} , 5[/tex]

lets write all the three zeros in factor form

[tex](x-(-2)) (x-\frac{3}{4})(x-5)\\(x+2)(4x-3)(x-5)[/tex]

Now multiply the parenthesis to get the polynomial

[tex]\left(x+2\right)\left(4x-3\right)\left(x-5\right)\\\left(4x^2+5x-6\right)\left(x-5\right)\\4x^2x+4x^2\left(-5\right)+5xx+5x\left(-5\right)-6x-6\left(-5\right)\\combine \; like \; terms\\4x^3-15x^2-31x+30[/tex]

polynomial function has zeros when x= -2, 3/4, 5 is

[tex]4x^3-15x^2-31x+30[/tex]

Learn more : https://brainly.com/question/21970844

Answer:

A (-2,-3) B (3,-3)

Step-by-step explanation:

I took math in high school

Answer:

The coordinate numbers are A (-2,-3) B(3,-3)

Answer:

The 3 problem

Step-by-step explanation:

Answer:

The answer is C) x+y = 233, 14x + 20y = 3748

Step-by-step explanation:

x(number of t-shirts sold) + y(number of sweatshirts sold) = 233 (total number of pieces of clothing sold)

14x (14 is the cost of each t-shirt and since x = number of t-shirts sold then it is 14x or 14 multiplied by number of t-shirts sold) + 20y (20 is the cost of each sweatshirt and since y = number of sweatshirts sold then it is 20y or 20 multiplied by number of sweatshirts sold) = 3748 (total of money raised)

Answer:

The equation is linear. Standard form:

7n - 6m - 4 =0

Step-by-step explanation:

Linear Equations

The linear equations are identified because all terms form a polynomial of degree 1 or zero (no variable).

The standard form of a linear equation is:

ax+by+cz+d=0

where x, y, z are the variables, and a,b,c are constants.

The equation:

7n - 8m = 4 - 2m

Is linear, both variables have an exponent of 1 and there is an independent term. Moving all terms to the left side:

7n - 8m - 4 + 2m =0

Simplifying:

7n - 6m - 4 =0

14 + (-8) / 2 x -3

Follow order of operations: divide and multiply from left to right:

-8/2 = -4 x -3 = 12

Now you have 14 + 12

The answer is 26

Answer:

26

Step-by-step explanation:

14+(-8) ÷ 2 (-3)

14+ (-4)(-3)

14+12

26

Answer:

a^20

Step-by-step explanation:

a^21-a^1

a^20