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Step-by-step explanation:

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Pre-Algebra Examples

Popular Problems Pre-Algebra Solve for x 12+2x-x=9x+6

12

+2

x−x=

9x

+6Subtract

x from

2x

12+x

=9x+6

Move all terms containing

x

to the left side of the equation.

Tap for more steps...

12−8x=6

to the right side of the equation.

-8x=−6

Divide each term in

−8x=−6 by −8

and simplify.

The result can be shown in multiple forms.

Exact Form:

x=3/4

Decimal Form:0.75

The function f(x+3) in terms of x is 4x+14.

It is given that -

f(x) = 4x + 2

We have to find out f(x+3) in terms of x.

Now, f(x) = 4x + 2

=> f(x+3) = 4(x+3) + 2 [Substituting (x+3) in place of x]

=> f(x+3) = 4x + 12 + 2

=> f(x+3) = 4x + 14

Thus, the function f(x+3) in terms of x is 4x+14.

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Using the Side Angle Side Theorem, ∆KWL ≅ ∆ALW.

In the given question we have to

Prove: ∆KWL ≅ ∆ALW

Given: ∠KWL ≅ ∠WLK, ∠AWL ≅ ∠WLK

As given that

∠KWL ≅ ∠WLK

∠AWL ≅ ∠WLK

WL = WL (Diagonal)

Equal Parallel Sides

WK = AL

WA = KL

From Corresponding Angle Theorem

∠KWL=∠WLK and ∠AWL = ∠WLK

So ∠W=∠L

So from the Side Angle Side(SAS) Theorem

∆KWL ≅ ∆ALW.

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Answer: the larger number is 59 and the smaller number is 17.

Step-by-step explanation:

The expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .

Given:

The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches.

The length of ribbon :

= 4([tex]2x^{2} +1[/tex]) + 4(4x - 7)

= 4(2[tex]x^{2} +1[/tex]+4x - 7)

= 4([tex]2x^{2} +4x-6[/tex])

The length at x = 3.5 is,

= 4(2([tex]3.5^{2}[/tex])+4(3.5) - 6)

= 4(24.5+14-6)

= 4(24.5+8)

= 130 inches.

Therefore the expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .

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Answer:

Step-by-step explanation:2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What

expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?

Answer:

Step-by-step explanation:

Unit conversion is the conversion of one unit to another unit with its standard conversion.

1 kg = 2.2 lb

The weight of the cat food in pounds is 33 lb.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seconds

1 km = 1000 m

We have,

Number of bags of cat food = 3

Weight of each bag = 5 kg

1 kg = 2.2 lb ______(1)

Weight of 3 bag = 3 x 5 = 15 kg _______(2)

From (1) and (2) we get,

1 kg = 2.2 lb

Multiplying 15 on both sides.

15 x 1 kg = 15 x 2.2 lb

15 kg = 33 lb

Thus,

The weight of the cat food in pounds is 33 lb.

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Answer:

yes

Step-by-step explanation:

as long as one input does not have two different outputs it is a function

After changing the smaller exponent (-3) to the larger exponent (-1), its coefficient change to?l A. 0.23.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, it should be noted that the value was illustrated as:

= 2.3 × 10^-1

= 2.3 × 0.1

= 0.23

Therefore, the correct option is A.

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Answer:

No, x=-5 is the answer

Step-by-step explanation:

Did this before, trust me

The relationship between pressure and temperature for a consisting of vapour and condensed phases is   [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex].

The Clausius-Clapeyron equation is a differential equation which specifies the temperature dependence of pressure and vapour pressure. The Clausis-Clapeyron equation is named after Rudolf Clausius and Benoit Paul Emile Clapeyron.

The Clausius-Clapeyron equation at saturation temperature and pressure is

[tex]dP/dT[/tex]= [tex]h_{g} - h_{f}/T(v_{g}-v_{f} )[/tex]     →  1

Assuming that [tex]v_{g} > > > v_{f}[/tex] , we write

[tex]v _{g}[/tex] = RT/P   →   2  ( for both liquid and solid phases)

⇒     dP/dT   =   P([tex]h_{g} - h_{f}[/tex])/R[tex]T^{2}[/tex]

⇒     dP/P   =   dT/[tex]T^{2}[/tex]([tex]h_{g} - h_{f}[/tex]/R)   →  2

By integrating 2 , we get

                        [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex]    →    3

Therefore, the equation to represent the relationship between pressure and temperature for a system consisting of vapour and condensed phases is equation 3  i.e.    [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex]

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Answer: 4

Step-by-step explanation:

6 * 2/3 First simplify the expression.

Then you would get 2 * 2/1 = 2*2

The answer is 4

This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.

A)  1: proportion of gas-guzzlers manufactured by American firms.

p2: proportion of gas-guzzlers manufactured by international firms.

In this way, the boundary of interest is p1 - p2.

B) H_0: p_1-p_2=0

H_1: p_1-p_2\neq0

C) The following requirements must be satisfied: n (1 p) 10 and np 10.

American Guzzlers do not meet this requirement because np = 7.

D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)

E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.

F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269

g. H0 should be rejected because the p-value is less than the 0.05 significance level.

There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.

Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.

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Answer:

√78,9,10

Step-by-step explanation:

we know [tex]9^{2}[/tex] is 81

so √78 is less than √81(9) and 10 is obviously more than 9

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Answer

-117/640

Step-by-step explanation:

ba + cd

b= -7/16

a= 7/8

c= 08.(4/5)

d= 1/4

Hence it can be calculated as follows

-7/16×7/8 + 4/5×1/4

-49/128 + 1/5

-246+128/640

= -117/640

The trigonometric function with its right triangle definition is matched as below:

(a) sine

opposite/hypotenuse

(b) cosine

adjacent/hypotenuse

(c) tangent

opposite/adjacent

(d) cosecant

hypotenuse/opposite

(e) secant

hypotenuse/adjacent

(f) cotangent

adjacent/opposite

We Know That,

i) sine =opposite side of the triangle /hypotenuse side of the triangle

ii) cosine=adjacent side of the triangle/hypotenuse side of the triangle

iii) tangent=opposite side of the triangle/adjacent side of the triangle

iv) cosecant=hypotenuse side of the triangle/opposite side of the triangle

v) secant=hypotenuse side of the triangle/adjacent side of the triangle

vi) cotangent=adjacent side of the triangle/opposite side of the triangle.

Therefore, each trigonometric function is matched with its right triangle definition

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Answer:

5

Step-by-step explanation:

to multiply fractions we multiply numerator with numerator and denominator with denominator

[tex]\frac{3}{36}x\frac{60}{1}[/tex]

[tex]\frac{3x60}{36x1}[/tex]

[tex]\frac{180}{36}[/tex]

5

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Expression which are equivalent to the given expression 3⁴ ×  3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.

As given in the question,

Given expression is equal to :

3⁴ ×  3ˣ

Using law of indices for multiplication we have ,

mᵃ × mᵇ = mᵃ⁺ᵇ

Here in the given expression m = 3 , a= 4 and b = x

Equivalent expression for the given expression is given by,

3⁴ ×  3ˣ

=  (3⁴⁺ˣ )

Also,

Now simplify the given expression we get,

 3⁴ ×  3ˣ

= ( 3 × 3 × 3 × 3) × 3ˣ

= 81 × 3ˣ

Therefore, expression which are equivalent to the given expression 3⁴ ×  3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.

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Answer:

8

Step-by-step explanation:

You can solve this a few different ways.

Firstly I did 102 - 97 = 5

Then I took 5 and added 3 to it

5 + 3 ---> which gets us 8 as our final answer.

Hope I helped!

Have a great day!

the slope of the given point is m=−3/4

Answer:-3/4

Step-by-step explanation:

to find slope using 2 points the equation is ...

y2-y1

x2-x1

Answer:

x = 14   y = 37

Step-by-step explanation:

180 - (9x + 12) = 3x

180 - 9x - 12 = 3x

168 = 12x

x = 14

4y - 10 + 3(14) = 180

4y - 10 + 42 = 180

4y + 32 = 180

4y = 148

y = 37

The weight of meteorite A is 207 tons and meteorite B is 23 tons.

Let the weight of B = w

Let the weight of A = 9 × w = 9w

Since the weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons. This will be illustrated as:

9w + w = 230

10w = 230

Divide

w = 230/10

w = 23

meteorite B = 23 tons

meteorite A will be:

= 9w

= 9 × 23

= 207 tons

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Answer:

61.2

Step-by-step explanation:

(36x2.9)-(24x1.8)

The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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Answer: j = 9

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

-1 = (3-(-5)) / (1-j)

-1 = (3+5) / (1-j)

-1 = 8 / (1-j)

Multiply both sides by 1 -j

= (1-j) = 8

= 1 - j = -8

= -j = -8 -1

j = 9

Given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement  "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.

As given in the question,

Given statement is equal to:

" If the measure of an angle is not 180, then it is not a straight angle"

And its conditional statement is given by:

"If an angle is a straight angle, then its measure is 180."

Explanation of the given options:

a. Counterexample : Concluding statement is against the given statement .

Here it is false.

b. Converse:  If it is not a straight angle then the measure of an angle is not 180.

Here it is false.

c. Inverse : If the measure of an angle is 180, then it is a straight angle.

False.

d. Contrapositive : "If an angle is a straight angle, then its measure is 180."

Here it is true.

Therefore,  for the given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement  "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.

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The median of the given data set is, 40.

What is median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Let, a data set contains 5 numbers: 21, 32, x, 99, 40.

x is the unknown number.

The average is to be 50.

Since,

Average = Sum of numbers / total numbers

       50   = (21 + 32 + x + 99 + 40) / 5

   50 x 5 = 192 + x

      250  = 192 + x

           x = 250 - 192

           x = 58

Hence, the unknown number is 58.

Now to find the median,

Since median is the middle number of a data set.

So, write the numbers in ascending order.

21, 32, 40, 58, 99.

In this data set the middle number is, 40.

Therefore, the median is 40.

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A guitar manufacturer sells 532,475 warranties and has to honor 12% of them. The profit the manufacturer gains from the warranties is $66,772,365 (option b)

Profit is calculated as:

Profit = revenues - total cost

While,

Revenues = number of goods sold x price per unit

In the given problem,

Revenues = number of warranty sold x price per warranty

                 = 532,475 x 225

                 = 119,806,875

Cost of honored warranty = number of honored warranty x guitar cost

                                           = 12% x 532,475 x 830

                                           = 53,034,510

Hence,

profit from warranty = 119,806,875 - 53,034,510

                                  = 66,772,365

The profit from warranty is $66,772,365 (option b)

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Answer:

its b

Step-by-step explanation: