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3 years ago

For what values of a are the following expressions true? a+5=5+a

Mathematics

1 answer:

kenny6666 [7]3 years ago

6 0

Answer:

a ∈ ℝ

Step-by-step explanation:

The statement is true for any value of a

since both members are identical

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3) Solve each equation using the quadratic formula. Show<br> a. x2 – 3x – 10 = 0

Naya [18.7K]

Answer:

Step-by-step explanation:

The quadratic formula of a quadratic equation

$ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}$

$\text{If}\ b^2-4ac$

We have:

$x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5$

5 0

3 years ago

Choose the arithmetic series that is associated with this summation.

Verizon [17]

Plug n = 1 into the expression 20-9n and we get
20-9n = 20-9*1 = 20-9 = 11

So 11 is the first term of the series that we add up. Therefore the answer must be choice C, which has 11 listed as the first term added

7 0

4 years ago

In January, the depth of a lake was 1,014 feet. In August, the depth of the lake was 659.1 feet. What is the percentage decrease

Colt1911 [192]

Answer:

35% decrease

Step-by-step explanation:

To find the percent decrease, divide the difference in price by the original price:

(1014 - 659.1) / 1014

354.9 / 1014

= 0.35

So, the percent decrease was 35%

7 0

3 years ago

5. Rounded to three decimal places, what is the value of r for this data set?

IrinaVladis [17]

The value of correlation coefficient (r) for the dataset is 0.981

<h3>What is correlation coefficient (r)?</h3>

The correlation coefficient (r) is used to determine the closeness and association of a scatter plot points.

The dataset is given as:

x: 8 15 3 7 2 14
y: 15 21 6 12 3 20

Using a graphing calculator, we have the following parameters:

<h3>X Values </h3>

∑x = 49
Mean = 8.167
∑(X - Mx)2 = SSx = 146.833

<h3>Y Values </h3>

∑y = 77
Mean = 12.833
∑(Y - My)2 = SSy = 266.833

<h3>X and Y Combined </h3>

N = 6
∑(X - Mx)(Y - My) = 194.167

The correlation coefficient (r) is then calculated as:

$r = \frac{\sum{((x - My)(Y - Mx)) }}{ \sqrt{((SSx)(SSy))}}$

This gives

$r = \frac{194.167 }{ \sqrt{((146.833)(266.833))}}\\$

$r = 0.9809$

Approximate

$r = 0.981$

Hence, the value of correlation coefficient (r) for the dataset is 0.981

Read more about correlation coefficient at:

brainly.com/question/4219149

3 0

2 years ago

What is this and how do i solve

Troyanec [42]

Answer:

Step-by-step explanation:

The angles 7x° and (x + 20)° are supplementary angles.

Supplementary angles add up to 180°.

Therefore we have the equation:

7x + (x + 20) = 180

7x + x + 20 = 180 <em>subtract 20 from both sides</em>

8x = 160 <em>divide both sides by 8</em>

x = 20

8 0

4 years ago