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Pepsi [2]
3 years ago
10

What are the roots of the equation? x^2+24=−11x Enter your answers in the boxes.

Mathematics
2 answers:
docker41 [41]3 years ago
8 0
<span>The <u>correct answers</u> are:

x=-3 and x=-8.

Explanation<span>:

We can first write this in standard form, ax</span></span>²<span><span>+bx+c=0. To do this, we will add 11x to both sides:
x</span></span>²<span><span>+24+11x=-11x+11x
x</span></span>²<span><span>+11x+24=0.

Now we can factor this. Look for factors of c, 24, that sum to b, 11. Factors of 24 are:
1 and 24 (sum 25)
2 and 12 (sum 14)
3 and 8 (sum 11)
4 and 6 (sum 10).

The factors we need are 3 and 8, since they sum to 11. This gives us factored form:
(x+3)(x+8)=0.

Using the zero product property, we know that in order to have a product of 0, one or both of the factors must be 0. This means we have:
x+3=0 or x+8=0.

Solving the first equation:
x+3-3=0-3
x=-3.

Solving the second equation:
x+8-8=0-8
x=-8.</span></span>
kotegsom [21]3 years ago
4 0

Answer:

x_1 = -8

x_2 = -3

Step-by-step explanation:

Given the equation:

x^2+24 = -11x

Add 11x to both sides we have;

x^2+11x+24 = 0

Split the middle terms we have;

⇒x^2+8x+3x+24 = 0

⇒x(x+8)+3(x+8)= 0

⇒(x+8)(x+3)= 0

By zero product property we have;

x+8 = 0 and x+3= 0

⇒x = -8 and x = -3

Therefore, the roots of the given equations are:

x_1 = -8

x_2 = -3

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During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the rem
liraira [26]

Answer:

 3.825 kg apples.

Step-by-step explanation:

Let x kg be the amount of apples stand owner had initially.

We have been given that during the first hour of operation the farm stand owner sold 15% of the apples he had. Then the amount of sold apples will be:

\text{The amount of sold apples during 1st hour}=\frac{15}{100}x=0.15x

\text{The amount of remaining apples after 1st hour}=x-0.15x

\text{The amount of remaining apples after 1st hour}=0.85x

On the second hour he sold 20% of the remaining apples. So the amount of sold apples on the second hour will be 20% of 0.85x.

\text{The amount of sold apples during 2nd hour}=0.85x*\frac{20}{100}  

\text{The amount of sold apples during 2nd hour}=0.85x\times 0.20  

\text{The amount of sold apples during 2nd hour}=0.17x

During the second hour 25.5 kg of apples were sold, so we can set up an equation as:

25.5=0.17x

\frac{25.5}{0.17}=\frac{0.17x}{0.17}

150=x

So, stand owner had initially 150 kg of apples.

\text{The amount of remaining apples after 2nd hour}=0.85x-0.17x

\text{The amount of remaining apples after 2nd hour}=0.68x

On the third hour he sold 25% of the remaining apples. So the amount of sold apples on the 3rd hour will be 25% of 0.68x

\text{The amount of sold apples during 3rd hour}=0.68x*\frac{25}{100}

\text{The amount of sold apples during 3rd hour}=0.68x*0.25

\text{The amount of sold apples during 3rd hour}=0.17x  

\text{The amount of remaining apples after 3rd hour}=0.68x-0.17x

\text{The amount of remaining apples after 3rd hour}=0.51x

As remaining apples were sold 5% more each following hour.

\text{The amount of sold apples during 4th hour}=0.51x*\frac{5}{100}

\text{The amount of sold apples during 4th hour}=0.51x*0.05

\text{The amount of sold apples during 4th hour}=0.0255x

Let us substitute x=150 into above equation we will get,

\text{The amount of sold apples during 4th hour}=0.0255*150

\text{The amount of sold apples during 4th hour}=3.825

Therefore, 3.825 kg of apples were sold during the 4th hour.

7 0
3 years ago
Help i only have 2 more questions and im done with this quiz
kvv77 [185]

{d}^{2}  \div (4c) - b + 5a \\  =  {(8)}^{2}  \div( 4 \times 2) - 3 + 5 \times  \frac{1}{5}  \\  = 64  \div 8 - 3 + 1 \\  = 8 - 3 + 1 \\  = 9- 3 \\  = 6

<u>Answer</u><u>:</u>

6

Hope you could understand.

If you have any query, feel free to ask.

6 0
3 years ago
Can you help me with numbers 1,2,3 I will mark you Brainiest please I need your help
Ket [755]

Answer:

3 is b

Step-by-step explanation:

6 0
3 years ago
A random sample of 121 students from the University of Oklahoma had a sample mean ACT score of 23.4 with a sample standard devia
Grace [21]

Answer:

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 121

Sample mean = 23.4

Sample standard deviation = 3.65

Level of significance = 0.05

Degree of freedom

= n - 1 = 120

95% Confidence interval:  

\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

Calculation of critical value:

t_{critical}\text{ at degree of freedom 120 and}~\alpha_{0.05} = \pm 1.9799  

Putting the values, we get,  

23.4\pm 1.9799(\dfrac{3.65}{\sqrt{121}} )\\\\ = 23.4 \pm 0.6569\\\\ = (22.7431 ,24.0569)\approx (22.74,24.06)  

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.

5 0
3 years ago
Shanti is taking a cube-shaped gift to a friend's birthday party. She wants to wrap it but she doesn't have very much paper, so
Marrrta [24]

Answer:

It will take Shanti 150 square inches of paper to wrap the gifts

Step-by-step explanation:

Shanti wraps the gift she is taking to a friend's birthday party. She doesn't have very much paper, so she does not overlap any of the edges. The side lengths of the cube are all 5in.

How much paper did it take to cover the gift?

Solution

To solve this, you will find the surface area of a cube

Surface area of a cube = 6a^2

Where,

a=side length of the cube

a= 5 in

a^2=a × a

=5 × 5

=25 in^2

a^2=25 in^2

Surface area of a cube = 6a^2

=6 × 25 in^2

=150 in^2

It will take Shanti 150 square inches of paper to wrap the gifts

7 0
3 years ago
Read 2 more answers
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