Solve the equation by factoring. 2x^2 = 28 – x

x = –3.5 or x = 4
x = 2 or x = –7
x = –2 or x = 7
x = –4 or x = 3.5

The value of t  at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

Given that the height of the ball at time t is given by the function,

[tex]h(t) = 3+ 28t -16t^2[/tex]

where t is in seconds and h is in feet.

Now, the height of the ball is given to be 11 feet, therefore, substituting the value of h in the function as 11,

[tex]h(t) = 3+ 28t -16t^2\\\\11 = 3+ 28t -16t^2\\\\-16t^2 + 28t +3 -11 = 0\\\\-16t^2 + 28t -8 = 0[/tex]

Now, solving the given quadratic equation, we will get,

[tex]x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-(28)\pm \sqrt{(28)^2-4(-16)(-8)}}{2(-16)}\\\\t= 0.36\ or\ 1.39[/tex]

Hence, the value of t  at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.

Learn more about Quadratic Equations:

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#SPJ1

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]12^3~~ = ~~x^4 y^3 z^6\implies \log_{12}(x^4 y^3 z^6)=3 \\\\\\ \log_{12}(x^4)~~ + ~~\log_{12}(y^3)~~ + ~~\log_{12}(z^6)~~ = ~~3 \\\\\\ 4\log_{12}(x)~~ + ~~3\log_{12}(y)~~ + ~~6\log_{12}(z)~~ = ~~3[/tex]

Answer:

46.8 cm

Step-by-step explanation:

A hexagon has six sides. If it is a regular hexagon, then it is equilateral, meaning that each side is the same length. If one side is 7.8cm, then all sides will be 7.8cm. You can find the perimeter by adding 7.8 six times, or multiplying 7.8 by six.

7.8 · 6 = 46.8

hope this helps!

Answer:

0.5n

Step-by-step explanation:

n/2 is equal to n * 1/2. 1/2 is equal to 0.5, so n * 1/2 = n * 0.5 = 0.5n.

Answer:

13 inches

Step-by-step explanation:

Answer:

The base must be 13 inches

Step-by-step explanation:

Step 1:  Determine the length of the base

[tex]A = 1/2 * b * h[/tex]

[tex]117\ in^2 = 1/2 * b * 18\ in[/tex]

[tex]117\ in^2 = 9\ in * b[/tex]

[tex]\frac{117\ in^2}{9\ in} = \frac{9\ in * b}{9\ in}[/tex]

[tex]13\ in = b[/tex]

Answer:  The base must be 13 inches

Answer:

y = 40, x = 9

Step-by-step explanation:

2(3y)+2(2y-20)=360

y = 40

2x=18

x = 9

Answer:

20 burgers

Step-by-step explanation:

4/6×30 = 2/3 ×30 = 60/3 = 20

Answer:

1/3

Step-by-step explanation:

Multiply left to right, so you start with -1/6*4/7=-2/21

Then you apply the fraction rule so -1/6*4

and 4 can be expressed by 4/1 so -1/6*4/1=-2/3

Then after solving you will get -4/6

then you factor 4=2*2 what will be -2*2/6

Then you cancel the common factors what are 2

so you bring back the 7 so -2/3/7 and 7 can be expressed as 7/1 and then you apply the fraction rule and flip it to 1/7 what will be solved as -2/21

so then it will be -2/21+1/2-1/14-3/7*1/6

Then you will have to solve -3/7*1/6 what is 1/14

so -2/21+1/2-1/14=1/3 final equation

Answer:

Step-by-step explanation:

Answer:

5/2 or 2 1/2 hours

Step-by-step explanation:

Multiply 5/8 by 4, which is 20/8, then you simply from there so 5/2=2 1/2

Answer:

The answer is B.

[tex]t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a}[/tex]

Step-by-step explanation:

[tex]d=3+at^2\\\\d-3=at^2\\\\\frac{d-3}{a}=t^2\\\\ t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a} }[/tex]

Answer: 1 1/20

Step-by-step explanation:

1/2 / 5/8 + 1/4

=8/10 +1/4

=21/20

=1 1/20

Answer:

C= 34.56 cm

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving for C

C= πd = π·11 ≈ 34.55752cm

27

using bodmas rule:

[tex]\sf b - bracket, o - order, d - division, m - multiplication, a - addtion, s - subtraction[/tex]

=================

Solve:

11 x 12 - 7 x 15        (carry out multiplication first)

132 - 105                (subtract)

27                           (final answer)

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{11}{12}-\dfrac{7}{15}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{11(5)-7(4)}{60}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{55-28}{60}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{27}{60}[/tex]

The amount of money Ben had to begin with after spending 1/6 and 1/2 of it is 57 dollars.

let

x = amount he had to begin with

He  spent 1/6 of his money on a burger, fries, and a drink. Therefore,

amount spent on burger, fries, and a drink = 1  / 6 x

Hence,

amount he had left = x - 1 / 6 x =6x - x /6 = 5 / 6 x

Then he spent half of the money he had left.

1  / 2(5  /6 x) = 5 + 8.25 + 10.50

5 / 12 x = 23.75

cross multiply

5x = 23.75 × 12

5x = 285

divide both sides by 5

x = 285 / 5

x = 57

Therefore, the amount of money he have to begin with is $57.

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Answer:

$57

Step-by-step explanation:

10.50 - 7.50 = 3

3 x 19 =57

$57

Answer:

65

Step-by-step explanation:

t = 10

e = 11

10 + (11*5)

65

Answer:

Hi there!

As we know that the sum of all three angles of a triangle is 180°.

If ∆ABC is right angled at C

C = 90°

=> [tex]\:\mathsf\red{∠A\: +\:∠B\: +\: ∠C\:=\:180°}[/tex]

=> [tex]\:\sf{∠A\: +\:∠B\: +\: 90°\:=\:180°}[/tex]

=> [tex]\:\sf{∠A\: +\:∠B\: =\:180°\:-\:90°}[/tex]

=> [tex]\:\sf{∠A\: +\:∠B\: =\:90°}[/tex]

Multiplying cos both sides. We get,

=> [tex]\:\sf{cos\:(∠A\: +\:∠B)\: =\:cos\:90°}[/tex]

We know cos 90° = 0, by trigonometric ratio.

=> [tex]\:\sf{cos\:90°\:=\:0}[/tex]

So,

[tex]\:\mathsf{cos(∠A\: +\:∠B)=\:cos\:90°\:=\:0}[/tex]

=> [tex]\:\sf\purple{cos\:(∠A\:+\:∠B)\:=\:0}[/tex]

[tex]\:\mathsf\blue{Hope\:this\:helps\:you!\:}[/tex]

Answer:

120 degrees

Step-by-step explanation:

30 * 4 = 120

Answer:

Step-by-step explanation:

30 + 30 + 30 + 30 = 30 x 4 = 120 degrees

Step-by-step explanation:

z = 0 -7i ....................

For the  Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players :  the median is 26, the range is 12 and the IQR is 12.

The median is regarded as the middle number among a series of  sorted numbers  that are placed in ascending or descending order.

Note that from the image attached, the northside ages are 22, 25, 28, 29, 29, 36, 36, 41, 49, 49, 54.

The median northside ages therefore is 36

For Range = Highest number - Lowest number

54-22 = 32

IQR = Q₃ - Q₁

Note that first quartile Q1 is said to be the median of the n lowest values and third quartile Q3 is the median of the n highest values.

Lowest value is 22 + 25/2 = 28.5.

Highest value is 49 + 44/ 2=  46.5.

Therefore,  IQR = Q₃ - Q₁

46.5 - 28.5 =

IQR = 36

Note, for Southside Players;

If the Ages of Actors is the Southside Players are 20 22 24 26 28 30 32 34.

Then the median is =  26

Range is = 34-22 = 12

IQR = Q₃ - Q₁

Lowest = 20 + 22/ 2 = 21

Highest is 32 + 34 / 2 = 33

33 - 21

IQR  = 12

Therefore, for the  Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players :  the median is 26, the range is 12 and the IQR is 12.

Learn more about Range from

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Based on the annual income, the payment period, and the amount deducted for the 403(b), the amount deposited into Sandy's 403(b) is $220.

First find the biweekly income:

= 51,350 / (52 weeks / 2 )

= 51,350 / 21 weeks

= $2,445.24

5% is deducted from her wages and the employer matches 4% of the salary. The amount deposited is:

= (5% + 4%) x 2,445.24

= $220

Find out more on 403(b) at https://brainly.com/question/2908111.

Answer:

She received $5 back

Step-by-step explanation:

Answer:

170

Step-by-step

Add 5 27 times count by 5s and you will get the answer.

Answer:

[C] 75/100

Step-by-step explanation:

0.75 as a fraction is 75/100.

Steps:

0.75 over 1

0.75/1

Multiply both the numerator and denominator by 100

75/100

Hence, the answer is [C] 75/100

[RevyBreeze]

Answer:

[C] 75/100

Step-by-step explanation:

Given:

What is 0.75 written as a fraction?

Solution:

0.75 = Decimal

Rewriting the decimal number as a fraction with 1 in the denominator

[tex]0.75=\frac{0.75}1[/tex]

Now, multiply to remove the 2 decimal places. So, you multiply top and bottom by 10²  = 100

10²  is the same thing as 100 because 10²  = 10 × 10 and 10 × 10 = 100

[tex]\frac{0.75}{1}\times\frac{100}{100}=\frac{75}{100}[/tex]

Thus, the answer is [C] 75/100

Kavinsky

Answer:

540 cubic inches.

Step-by-step explanation:

Answer:

y = 9x

Step-by-step explanation:

We can make the x-values represent how many hours Jessica babysat, and the y-values represent how much money she earned each day.

We have these points:

The days of the week she worked do not matter in this problem. We are just trying to find the association between hours worked and money earned.

We can start by finding the slope of the line by using two of the points. I will be using (3, 27) and (6, 54).

The slope formula is [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex].

Substitute these two points into the formula:

The slope of the line is m = 9.

Now, we can use the point-slope equation to find the equation of the line that represents Jessica's earnings.

Point-slope equation: [tex]y-y_1=m(x-x_1)[/tex].

Substitute the slope m = 9 and the point (3, 27) into the equation.

The equation y = 9x  represents Jessica's earnings, where x represents hours and y represents earnings.

Answer:

Step-by-step explanation:

Answer:

57064

Step-by-step explanation:

Answer:

B. F(0) = 4

Step-by-step explanation:

Im unsure about the C tho.