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3 years ago

3 + (5 + 7) = (3 + 5) + 7 what property is shown

Mathematics

1 answer:

ira [324]3 years ago

5 0

Answer:

Properties of Real Numbers ...

Step-by-step explanation:

Commutative Property of Multiplication (Numbers) 2 • 10 = 10 • 2

Associative Property of Addition (Numbers) 5 + (6 + 7) = (5 + 6) + 7

Associative Property of Multiplication (Numbers) 6 • (3 • 2) = (6 • 3) • 2

Additive Identity (Numbers) 6 + 0 = 6

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What are the solutions to

Svetllana [295]

Answer:

B and F

Step-by-step explanation:

Given

x² + 4x + 4 = 12 ( subtract 4 from both sides )

x² + 4x = 8

Using the method of completing the square to solve for x

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 8 + 4, that is

(x + 2)² = 12 ( take the square root of both sides )

x + 2 = ± $\sqrt{12}$ ( subtract 2 from both sides )

x = ± $\sqrt{12}$ - 2

= ± 2 $\sqrt{3}$ - 2

Hence

x = 2 $\sqrt{3}$ - 2 → B

x = - 2 $\sqrt{3}$ - 2 → F

4 0

3 years ago

0.45m-9=0.9m, what is the least power of ten you could multiply by to write an equivalent equation with integer coefficients?

tia_tia [17]

Answer:

m = -20

Step-by-step explanation:

Step 1 :

Simplify ——

Equation at the end of step 1 :

45 9

((——— • m) - 9) - (—— • m) = 0

100 10

Step 2 :

Simplify ——

Equation at the end of step 2 :

9 9m

((—— • m) - 9) - —— = 0

20 10

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 20 as the denominator :

9 9 • 20

9 = — = ——————

1 20

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

9m - (9 • 20) 9m - 180

————————————— = ————————

20 20

Equation at the end of step 3 :

(9m - 180) 9m

—————————— - —— = 0

20 10

Step 4 :

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

9m - 180 = 9 • (m - 20)

Calculating the Least Common Multiple :

5.2 Find the Least Common Multiple

The left denominator is : 20

The right denominator is : 10

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 2 1 2

5 1 1 1

Product of all

Prime Factors 20 10 20

Least Common Multiple:

Calculating Multipliers :

5.3 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 1

Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

5.4 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 9 • (m-20)

—————————————————— = ——————————

L.C.M 20

R. Mult. • R. Num. 9m • 2

—————————————————— = ——————

L.C.M 20

Adding fractions that have a common denominator :

5.5 Adding up the two equivalent fractions

9 • (m-20) - (9m • 2) -9m - 180

————————————————————— = —————————

20 20

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

-9m - 180 = -9 • (m + 20)

Equation at the end of step 6 :

-9 • (m + 20)

————————————— = 0

Step 7 :

When a fraction equals zero :

7.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-9•(m+20)

————————— • 20 = 0 • 20

Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-9 • (m+20) = 0

Equations which are never true :

7.2 Solve : -9 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

7.3 Solve : m+20 = 0

Subtract 20 from both sides of the equation :

m = -20

One solution was found :

m = -20

6 0

3 years ago

The diameter and height of this cylinder are equal to the side length,S,of the cube in which the cylinder is imscribed. What is

max2010maxim [7]

$V=B\times H$
$V=\pi r^{2}h$
$V=\pi (\frac{d}{2})^{2}h$
$V=\pi (\frac{s}{2})^{2}s$
$V=\pi (\frac{s^{2}}{4})s$
$V=\frac{\pi s^{3}}{4}$

3 0

3 years ago

Someone help and please make sure it’s right :)

pashok25 [27]

Answer:

Step-by-step explanation:

$11x + 1 + 7x + 17 = 180 \: \: \: \: 18x + 18 = 180 \: \: \: \: \: \: \: 18x = 180 - 18 \: \: \: \: \: \: \: \:18x = 162 \: \: \: \: \: \: \: \: \: \: 162 \div 18 = 9$

4 0

2 years ago

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in t

Natali5045456 [20]

Answer:

a) Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

b) Rachel, because her time had the lowest z-score.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The lower the time, the better the runner is. So whoever's time has a lower z-score is a better runner. So initially, we find the z-score of each student's time.

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes.

This means that for Rachel's time, we have that $X = 8, \mu = 11, \sigma = 3$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 11}{3}$

$Z = -1$

A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.

This means that for Kenji's time, we have that $X = 8.5, \mu = 9, \sigma = 2$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.5 - 9}{2}$

$Z = -0.25$

A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.

This means that for Nedda's time, we have that $X = 8, \mu = 7, \sigma = 4$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 7}{4}$

$Z = 0.25$

(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?

Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

(b) Who is the fastest runner with respect to his or her class? Explain why

Rachel, because her time had the lowest z-score.

8 0

3 years ago