1) f(x) = 3x - 4 g(x) – x2 + 3x Find f(g(x))

Find the value of c that completes the square for x2−15x+c

meriva

Answer:

The value of c is $\frac{225}{4}$ .

Step-by-step explanation:

The perfect square of the difference between two numbers is:

$(x-y)^{2}=x^{2}-2xy+y^{2}$

The expression provided is:

$x^{2}-15x+c$

The expression is a perfect square of the difference between two numbers.

One of the number is x and the other is √c.

Use the above relation to compute the value of c as follows:

$x^{2}-15x+c=(x-\sqrt{c})^{2}\\\\x^{2}-15x+c=x^{2}-2\cdot x\cdot\sqrt{c}+c\\\\15x=2\cdot x\cdot\sqrt{c}\\\\15=2\cdot\sqrt{c}\\\\\sqrt{c}=\frac{15}{2}\\\\c=[\frac{15}{2}]^{2}\\\\c=\frac{225}{4}$

Thus, the value of c is $\frac{225}{4}$ .

5 0

3 years ago

Request edit access 2. 7x + 4 = -3 How to solve

Gre4nikov [31]

Answer:

x= -1

Step-by-step explanation:

7x+4= -3 take -4 off both sides> 7x= -7 now divide 7x/-7> x= -1

7 0

3 years ago

the performance score of 10 adults is recorded, and the results are 83 87 90 92 93 100 104 111 115 121 find the standard deviati

luda_lava [24]

Answer:

The standard deviation of the data set is $\sigma = 12.7906$ .

Step-by-step explanation:

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)

To find the standard deviation of the following data set

$\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}$

we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }$

Step 1: Find the mean $\left( \overline{X} \right)$ .

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}$

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6$

Step 2: Create the below table.

Step 3: Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 1472.4$

Step 4: Calculate σ using the above formula.

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906$

3 0

3 years ago

What is the distance between the two points (5,-2) and (-3,8)

bearhunter [10]

You need to use the distance formula
$d = \sqrt{ {(x - x)}^{2} + {(y - y)}^{2} }$

$\sqrt{ {(5 + 3)}^{2} + {( - 2 - 8)}^{2} }$
so the distance between points (5,-2) and (-3,8) is
$2 \sqrt{41}$
which won't simplify so it stays as is

4 0

3 years ago

Solve for each equation

IrinaK [193]

w divided by 7 1/2
Substitute variable for numbers
5 5/6 divided by 7 1/2
Convert the mixed numbers into improper fractions
35/6 divided by 15/2
Convert the division sign to multiplication while flipping the fraction 15/2 to 2/15
35/6*2/15
Multiply
Final Answer: 70/90

7 0

3 years ago

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