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Arte-miy333 [17]

2 years ago

11

Alondra says that (12 + 31) × 5 is equivalent to 12 + 31 × 5 because of the associative property. Determine if Alondra is correc

t. Justify your answer.

1 answer:

MAXImum [283]2 years ago

7 0

Answer:

No

Step-by-step explanation:

(12 + 31) × 5 = 215

12 + 31 × 5 = 167

order of operations are the rules that state the sequence in which the multiple operations in an expression should be solved.

Order of Operations :

1. Parentheses

2. Exponents

3. Multiplication and Division

4. Addition and Subtraction

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cupoosta [38]

Answer:

n= 24

because 3*24=72

and (3^2)8 = 9*8=72

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The scale factor of S to T is 4:1

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Scale Factor - Finding Sides. L1S1. 3) Scale factor of S to T is 4 : 1. ; x = y = 4) Scale factor of G to H is 1 : 7. ; x = y = 20 yd. 10 yd. S. T.

Step-by-step explanation:

<em> A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.</em>

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What is the discriminate of the following quadratic equation?<br> 4x^2 - 2x + 6 = 0

hram777 [196]

-92

Step-by-step explanation:

If a quadratic equation has the following form:

$ax^2 + bx + c =0, \;\;\;a \neq 0$

then its discriminant D is defined as

$D = b^2 - 4ac$

In our given quadratic equation, a = 4, b = -2 and c = 6, so its discriminant is

$D = (-2)^2 - 4(4)(6) = -92$

Note: The value of the discriminant D will determine the characteristics of the roots of the quadratic equation according to the following rules:

$D > 0,\;\;$ there will be 2 real roots

$D = 0,\;\;$ there will be 1 real root

$D < 0,\;\;$ there will be 2 imaginary roots

Hence our given quadratic equation will not have any real roots but only imaginary ones.

7 0

2 years ago

What is the value of x g^x-1 -2 = 25

In-s [12.5K]

<h2>Answer: </h2>

Third choice, option C

x = 5/2

To solve for the value of x<em> </em>if <em>9^(x-1) - 2 = 25</em>, we can substitute each of the options into a simplified equation.

<h2>Simplify the equation</h2>

We <em>could </em>substitute each option into the given equation, but then we would have to simplify it four more times. It's easier to simplify once first.

$9^{x-1} -2=25$ Start with the given equation

$9^{x-1} -2+2=25+2$ Add 2 to both sides

$9^{x-1} =25+2$ –2 + 2 on the left side cancels out

$9^{x-1} =27$ Add on the right side

We found a simplified equation.

<h2>Substitute</h2>

Now, let's substitute each option choice for 'x' in the simplified equation. We only have to substitute choices until we find the choice that makes the left and right sides of the equation equal, but let's try all of the choices today.

<h3>Option A: x = 1/2</h3>

$9^{x-1} =27$ Start with the simplified equation

$\displaystyle{9^{\frac{1}{2}-1} =27}$ Substitute x = 1/2

$\displaystyle{9^{\frac{1}{2}-\frac{2}{2}} =27}$ Find a common denominator within the exponent

$\displaystyle{9^{\frac{1-2}{2}} =27}$ Combine numerators and subtract

$\displaystyle{9^{-\frac{1}{2}} =27}$

$\displaystyle{(3^{2})^{-\frac{1}{2}} =27}$ Convert 9 into a base and exponent

$\displaystyle{ 3^{ 2*-\frac{1}{2} } =27 }$ Multiply exponents

$\displaystyle{ 3^{ -\frac{2*1}{2} } =27 }$ Combine into numerator

$\displaystyle{ 3^{ -\frac{2}{2} } =27 }$ Simplify the fraction

$\displaystyle{ 3^{ -1 } =27 }$ Use negative exponent rule to simplify

$\displaystyle{ \frac{1}{3^{1}} =27 }$ Simplify the denominator

$\displaystyle{ \frac{1}{3} \neq 27 }$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 1/2.

<h3>Option B: x = 2</h3>

$9^{x-1} =27$ Start with the simplified equation

$9^{2-1} =27$ Substitute x = 2

$9^{1} =27$ Subtract within the exponent

$9 \neq 27$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 2.

<h3>Option C: x = 5/2</h3>

$9^{x-1} =27$ Start with the simplified equation

$\displaystyle{9^{\frac{5}{2}-1} =27}$ Substitute x = 5/2

$\displaystyle{9^{\frac{5}{2}-\frac{2}{2}} =27}$ Find a common denominator within the exponent

$\displaystyle{9^{\frac{5-2}{2}} =27}$ Combine numerators and subtract

$\displaystyle{9^{\frac{3}{2}} =27}$ Use fractional exponent rule to simplify

$\displaystyle{\sqrt[2]{9^{3}} =27}$

$\displaystyle{\sqrt{9^{3}} =27}$

$\displaystyle{\sqrt{9 * 9 * 9} =27}$ Solve the exponent by multiplying bases

$\displaystyle{\sqrt{729} =27}$ Solve the root

$\displaystyle{27 =27}$ Left and right sides are <u>equal</u>

So, <em>x</em> is equal to 5/2.

<h3>Option D: x = 4</h3>

$9^{x-1} =27$ Start with the simplified equation

$9^{4-1} =27$ Substitute x = 4

$9^{3} =27$ Subtract within the exponent

$9*9*9 =27$ Solve the exponent by multiplying bases

$729 \neq 27$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 4.

∴ in $9^{x-1} -2=25$ , <em>x</em> is equal to $\displatestyle{\frac{5}{2}}$ , making option C correct.

Learn more about exponent rules here:

brainly.com/question/84608

brainly.com/question/12173411

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2 years ago