Write a linear equation and one variable that has infinitely many solutions. show the process of simplifying the equation to prove that it has infinitely many solutions.

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{28p^5-8p^4 + 40p^2}{4p^3}\implies \cfrac{28p^5}{4p^3}-\cfrac{8p^4 }{4p^3}+\cfrac{ 40p^2}{4p^3}\implies 7p^5 p^{-3}-2p^4 p^{-3}+10p^2p^{-3} \\\\\\ 7p^{5-3}-2p^{4-3}+10p^{2-3}\implies 7p^2-2p+10p^{-1}\implies 7p^2-2p+\cfrac{10}{p}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]Pythagoras \ theorem,\\BC^2 = AB^2 + AC^2 = 12.2^2 +8.3^2 =217.73\\\\BC =14.8mm[/tex]

Answer:

the independent quantity is "t" (time in seconds)

Step-by-step explanation:

The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.

Answer:

C. 107 + 2x - 5 + x = 180

Step-by-step explanation:

The sum of interior angles of a triangle = 180°

Therefore, to find x, we would state that all three angels indicated in the figure above equals 180°.

Thus:

107 + 2x - 5 + x = 180

We can solve and find the value of x using the equation above

Answer:

C

Step-by-step explanation:

The inequality to represent each situation is Harry > 60 inches, Sherry ≠ 4 years, and Hank ≥ $7.50.

a) Harry: This inequality states that Harry is taller than 60 inches. This is likely referring to Harry's height, as most people measure height in inches. This inequality can also be written as Harry ≥ 60 inches, emphasizing that Harry is at least 60 inches tall.

b) Sherry: This inequality states that Sherry is not equal to 4 years. This could be referring to Sherry's age, as it is common to measure age in years. This inequality can also be written as Sherry ≠ 4 years, emphasizing that Sherry is not exactly 4 years old.

c) Hank: This inequality states that Hank is greater than or equal to $7.50. This is likely referring to Hank's amount of money, as it is common to measure money in dollars. This inequality can also be written as Hank ≥ $7.50, emphasizing that Hank has at least $7.50.

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Answer:

x = 28

Step-by-step explanation:

3x - 21 = 63, I am making them equal to each other because of the vertical angle theorem.

3x - 21 = 63, add 21 to both sides

3x = 84, divide 3 to both sides to make x by itself

x = 28  

Answer:

=28

Step-by-step explanation:

Answer:

13.

Step-by-step explanation:

Let X be the number.

Given information from the question, we can formulate an equation:

Six times a number less 20 = 4 times the same number increased by 6

6X - 20 = 4X + 6

From the equation, we can solve for X.

6X - 4X = 6 + 20

2X = 26

X = 26 ÷ 2

X = 13

Therefore the number is 13.

The value of the unknown number is = 13.

Let the unknown number be expressed by the variable = x.

According to the question, the mathematical linear equation in one variable that is 'x' can be expressed as:

=> 6x - 20 = 4x + 6

=> 6x - 4x = 6 + 20

=> 2x = 26

=> x = 26/2

=> x = 13

Therefore, the value of 'x' which is the unknown number is 13.

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Answer:

Step-by-step explain

We know that the campsite is 65 miles north of her town.

There are 63,360 inches in a mile

so, if you multiply it would look like

63,360 x 65 = 4,118,400

so, your answer would be 4,118,400 inches

Answer: look at the picture

Step-by-step explanation: Hope this help :D

Answer: The Sale price is $196

Step-by-step explanation:

We can start by converting 30% to a decimal 0.3, then we will multiply the $280 by the decimal (280*0.3 = $84) This means it is marked down by $84, so to get the sale price we subtract the mark down by the original price, ($280-$84 = $196).

Answer:

The suit's sale price is $196.

Step-by-step explanation:

⭐What is "mark down"?

To find the sale price, we need to form an equation representing the given situation.

MARK DOWN:

original price - (mark down percentage)(original price) = sale price

Substitute the known values.

280 - (0.3)(280) = sale price

Compute.

280 - 84 = sale price

∴ $196 = sale price

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The speed of travel will be 4 m/s.

The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).

The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.

Total distance=10+30=40

speed=distance/time=40/10=4m/s

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Using it's concept, it is found that there is a 0.054 probability that the next customer will pay with a credit card.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 56 + 14 + 4 = 74 customers, 4 used credit cards, hence:

p = 4/74 = 0.054.

There is a 0.054 probability that the next customer will pay with a credit card.

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Find the scale:

30 miles / 5miles = 6

Multiply km by the scale:

8 km x 6 = 48 km

The answer is 48 km

Answer: 48km

Step-by-step explanations:. It's just simple cross multiplication.

5miles----->8km

30miles---->?km

Answer is ( 30×8)÷5= 48km

Answer:

9m^8 n^2

Step-by-step explanation:

Open up the parenthesis and simplify to find your answer.

When they ask for X, you are generally supposed to look at all the points in which the line intercepts the X axis. So that would be -2, 1, and 3.

PS. even if it asked for Y, instead of X, you would do the same thing.

Answer:

x = 79

Step-by-step explanation:

This is an isosecles triangle so the bottom angles have equal measure

and since the sum of interior angles in a triangle is equal to 180

2x + 32 = 180 subtract 32 from both sides

2x = 158 divide both sides by 2

x = 79

The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.

Calculating the margin of error for a given sample from a population:

Let the level of significance be   and the standard deviation of the population be σ and the sample size be n, then we have:

MOE(Margin of Error)=  [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]

Using the above formula to calculate the margin of errors for two specified samples

For first sample:

Sample size = n(1) = 1000

MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]

For second sample:

Sample size = n(2) = 4000

MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]

(since it was given that they have same point estimates, so same standard deviation)

Their ratios are given by

MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]

MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]

MOE(2)/MOE(1) = 1/2

MOE(1) = 2*MOE(2)

Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.

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Therefore after using the Pythagorean Theorem and the properties of chords in a circle we got 626 when m+n is divided by 1000.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

Let M and N be the midpoints of chords AB and CD, respectively.

Let X and Y be the foot of the perpendicular from P to chord AB and CD respectively.

Since X,Y are on the circle and P is the midpoint of XY,

OP = PX = PY = radius = 25

Now, using the Distance Formula:

(XM)^2 + (YN)^2 = (12)^2

By the Pythagorean Theorem, on triangle PXN and PYM,

(25)^2 + (YN)^2 = (PN)^2 = (14/2)^2 and

(25)^2 + (XM)^2 = (PX)^2 = (30/2)^2

OP^2 = 625 = 25^2

thus m+n = 625 + 1 = 626

and remainder when m+n is divided by 1000 is 626 % 1000 = 626

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The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.

If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now

Using midpoint formula

[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2

Find common denominator and write the numerators above common denominator

-5+2/12 =-3/12

            =-1/4

Hence we find midpoint between numbers.

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Answer:

Your answer is wrong, H is the correct answer.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Note: This rule must be satisfied for all 3 conditions of the sides.

Answer:

8x^3

Step-by-step explanation:

(2x)^3

=(2x)^3

=2x*2x*2x

=8x^3

Answer:

80%

Step-by-step explanation:

First we find the percentage she got wrong:

[tex]\frac{18}{90}[/tex] Is the fraction she got wrong, now we convert this into a percentage by divding 18 by 90 and multiplying by 100

18÷90×100=20

so to find the remaining percent we subtract 20 from 100

100-20=80

And our answer is 80

Answer:

80%

Step-by-step explanation:

10%= 9

20%= 18

18= how many they got wrong

90=total questions

90= 100%

18= 20%

100%=20%=80%

Answer:

X= 80

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hope this helps :))

Answer:

Option C

Step-by-step explanation:

Given function is,

f(x) = 9x² - 12

Steps to find the inverse of the given function,

Step 1,

Write the function in the form of an equation,

y = 9x² - 12

Step 2,

Interchange variables 'x' and 'y' in the equation,

x = 9y² - 12

Step 3,

Solve this equation for 'y',

x = 9y² - 12

9y² = x + 12

[tex]y^2=\frac{1}{9}(x + 12)[/tex]

[tex]y=\pm\sqrt{\frac{1}{9}(x + 12)}[/tex]

[tex]y=\pm\frac{\sqrt{(x+12)}}{3}[/tex] Here, x > -12

Step 4,

Covert this equation into function,

[tex]g(x)=\pm\frac{\sqrt{(x+12)}}{3}[/tex]

Therefore, Option C will be the answer.

Answer: [tex]3\dfrac{1}{8}\ \text{cups}[/tex]

Step-by-step explanation:

Given

Yoshi need [tex]1\frac{1}{4}[/tex] cups of blueberries to make 1 batch of muffins

convert mixed fraction to fraction

[tex]\Rightarrow 1\dfrac{1}{4}=\dfrac{5}{4}[/tex]

i.e. [tex]\frac{5}{4}[/tex] cups are required for 1 batch of muffins

for [tex]2\frac{1}{2}[/tex] batch or [tex]\frac{5}{2}[/tex] batch it is given by

[tex]\Rightarrow \dfrac{5}{2}\times \dfrac{5}{4}\\\\\Rightarrow \dfrac{25}{8}=3\dfrac{1}{8}\ \text{cups}[/tex]

Answer:The found angle D is:

D = 51.7°

Step-by-step explanation: