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3 years ago

Solve for a.

1 answer:

8 0

The correct answer is: [C]: " a = ± $\sqrt{25 - b^2}$ " .
<span>___________________________________________________________
Explanation:
_________________________________________________________
We are given:
_________________________________________________________
   </span>→ " 25 = a² + b² " ; Solve for "a" ;
_________________________________________________________

→ To solve for "a" ; we want to isolate "a" on one side of the equation.
_________________________________________________________
We can rewrite: " 25 = a² + b² " ;

as: " a² + b² = 25 " .

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Then, we can subtract " b² " from each side of the equation; as follows:
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→ " a² + b² − b² = 25 − b² " ;

to get:
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→ " a² = 25 − b² " ;
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→ Now, take the square root of EACH SIDE of the equation ;
to isolate "a" on one side of the equation; & to solve for the value(s) of "a" ;
_________________________________________________________

→ √(a²) = $\sqrt{25 - b^2}$ ;

to get:
_____________________________________________________
  → a = | $\sqrt{25 - b^2}$ | ;

→ a = ± $\sqrt{25 - b^2}$ ;

  → which is: Answer choice: [C]: " a =  ± $\sqrt{25 - b^2}$ " .
______________________________________________________

You might be interested in

What is the area of the shaded region <br> 1cm is in the middle

Archy [21]

Answer:

Area of the shaded region= $128.86\,cm^2$

Step-by-step explanation:

Area of the shaded region=Area of the rectangle-Area of the circle

Area of rectangle= $Length\times Width$

$Length=11\,cm\\Width=12\,cm$

Area is:

$=11\times 12\\\\=132\,cm^2$

Area of the circle = $\pi \times r^2$

$r=1\,cm$

As, $\pi =\dfrac{22}{7} =3.14$

Area of the Circle is :

$=3.14\times 1 \times 1\\\\=3.14\times 1\\\\=3.14\,cm^2$

Area of the Shaded region:

Area of the shaded region $=132-3.14\\\\=128.86\,cm^2$

5 0

3 years ago

A linear regression model is fitted to the data x y 37.0 65.0 36.4 67.2 35.8 70.3 34.3 71.9 33.7 73.8 32.1 75.7 31.5 77.9 with x

andrey2020 [161]

Answer:

b0= 144.59

b= -2.12

Se²= 1.02

99%CI E(Y/X=35): [68.78; 71.99]

Step-by-step explanation:

Hello!

I've arranged the given data:

X: 37.0, 36.4, 35.8, 34.3, 33.7, 32.1, 31.5

Y: 65.0, 67.2, 70.3, 71.9, 73.8, 75.7, 77.9

The equation of the linear regression model is:

Yi= β₀ + βXi + εi

Where

Yi is the dependent variable

Xi is the independent variable

εi represents the errors or residues

β₀ is the intercept of the line

β is the slope

The conditions to make a linear regression analysis are:

For each given value of X, there is a population of Y~N(μy;σy²)

Each value of Y is independent of the others.

The population variances of each population of Y are equal.

From these conditions the following characteristic is deduced:

εi~N(0;σ²)

The parameters of the regression are:

β₀, β, and σ²

If the conditions are met then you can estimate the regression line:

Yi= bo * bXi + ei.

And the point estimation of the parameters can be calculated using the formulas:

β₀ ⇒ b0= (∑y/n)-b(∑x/n)

β ⇒ b= [∑xy- ((∑x)(∑y))/n]/(∑x²-((∑x)²/n))

σ²⇒ Se²= 1/(n-2)*[∑y²-(∑y)²/n - b²(∑x²-(∑x)²/n)]

n= 7

∑y= 501.80

∑y²= 36097.88

∑x= 240.80

∑x²= 8310.44

∑xy= 17204.87

b0= 144.59

b= -2.12

Se²= 1.02

The estimated regression line is:

Yi= 144.59 -2.12Xi

You need to calculate a 99%CI E(Y/X=35), the formula is:

(b0 + bX0) ± $t_{n-2;1-\alpha /2}$ * $\sqrt{S_e^2(\frac{1}{n}+\frac{(X_0-X[bar])^2}{sumX^2-(\frac{(sumX)^2}{n} )} )}$

(144.59 + (-2.12*35)) ± 4.032* $\sqrt{1.02(\frac{1}{7}+\frac{(35-34.4)^2}{8310.44-(\frac{(240.80)^2}{7} )} )}$

[68.78; 71.99]

With a 99% confidence level youd expect that the interval [68.78; 71.99] contains the true value of the average of Y when X= 35.

I hope it helps!

6 0

3 years ago

In triangle ABC, if an exterior angle drawn at vertex C

Lorico [155]

Answer:

Part 1) Option D. must be an acute angle

Part 2) m∠A=70°

Step-by-step explanation:

Part 1) In triangle ABC, if an exterior angle drawn at vertex C measures 45, then angle B...

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

The measure of an exterior angle at C is equal to the sum of the interior angles at A and B

we have that

45°=m∠A+m∠B

therefore

m∠B < 90°

Angle B must be an acute angle

Part 2)

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

The measure of an exterior angle at B is equal to the sum of the interior angles at A and C

m∠A+m∠C=2m∠C+5

m∠C=m∠A-5 ----> equation A

m∠C=65° ----> equation B

substitute equation B in equation A

65°=m∠A-5

m∠A=(65+5)°=70°

3 0

3 years ago

The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs,

alexira [117]

Answer: 36 shirts and costs $432
step by step:
first make an equation with the amount of sold shirts being equal to cost of making them -
12x=10x+72 where x is the number of shirts
then, subtract 10x from 12x to get the variable on the same side -
2x=72
finally, divide by 2 to isolate x
x=36 shirts
to figure out the cost, substitute 36 for x in 10x+72
10(36)+72= 360+72= $432

6 0

3 years ago

What is the simplest form of the expression (14.2a + 9.8b) – (13.1b – 0.2a) – (3.7a + 4.8b)?

Sindrei [870]

Answer:

A) 10.7a - 8.1b

Step-by-step explanation:

(14.2a + 9.8b) - (13.1b - 0.2a) - (3.7a + 4.8b)

Combine like terms.

(14.2a + 0.2a - 3.7a) = 10.7a

(9.8b - 13.1b - 4.8b) = -8.1b

4 0

3 years ago

Read 2 more answers