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To simplify the expression you can first use this property of exponents

Then you have

Now apply this property of exponents

Therefore, you have

Consider that the slope-intercept of a line is given by,

Here, 'm' is the slope and 'c' is the y-intercept of the line.

The equation of the given line is,

Comparing the coefficients, it can be observed that the slope of the given line is -2,

It is asked to determine the equation of line perpendicular line to this given line.

Let the slope of this perpendicular line be 'k'. Then, the equation of this perpendicular line will take the form,

Theorem: The product of slopes of perpendicular lines is -1.

Now, the equation becomes,

Consider that any point lying on the line must satisfy the equation of that line.

So the point (6,2) must also satisfy the equation of the perpendicular line,

Substitute the values of 'k' and c' in the equation,

Thus, the required equation of the line is obtained as,

Explanation

Step 1

set the equation

a) let x represents the number

b) now , translate

then

finally

therefore, the equation is

3x+6=12

Step 2

now, solve the equation

The subtraction property of equality states that if the same number is subtracted from both sides of an equation, then the equality still holds, so we can subtract 6 in both sides in order to isolate the term where x is, hence

finally, apply the division property of equality and divide both sides by 3

so, the number is 2

I hope this helps you

An equation of the line containing the given point and parallel to the given line is y = 2x - 19.

In Mathematics, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Mathematically, the point-slope form of a line is given by this equation:

y - y₁ = m(x - x₁)

Where:

Given the following equation:

2x - 56 = 3     ⇒ m₁ = 2

Therefore, m₁ = m₂ = 2.

At point (8, -3), we have:

y - y₁ = m(x - x₁)

y - (-3) = 2(x - 8)

y + 3 = 2(x - 8)

y + 3 = 2x - 16

y = 2x - 16 - 3

y = 2x - 19

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The number of large cups that would contain the same amount as 10 1/2 small cups is 6.

From the information, it was stated that we should find the number of large cups that would contain the same amount as 10 1/2 small cups if a large cup holds 1 3/4 times the quantity of liquid that's in a small cup.

This simply means that we have to divide the values that are given. This will be illustrated as:

= 10 1/2 ÷ 1 3/4

= 10.5 / 1.75

= 6

There'll be 6 large cups.

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To find the horizontal tangent line, we have to conduct the first derivative test. The first derivative test sets the derivative of the function equal to 0.

Let's start out with finding the derivative of the function:

It seems like we will have to use Quotient Rule.

Now we can use basic derivative rules and properties to find the final derivative:

Setting the derivative equal to 0, we can begin the first derivative test:

We can simplify the derivative before solving (expand and combine like terms):

From here, we need to determine our values of x that will make the derivative equal to 0 or undefined. In this case, since we are not trying to find relative maxima or minima, we just need to find where the entire derivative is equal to 0. We can simply just graph the numerator and find its roots:

We can see that the values of x will be -21.0416 and 3.04159 will be the values that make the derivative equal to 0.

Also recall what the derivative is. The derivative is the slope of the tangent line. In order to find the horizontal tangent line, we know that horizontal tangent lines' slope is equal to 0.

Therefore, we can use either value of x to now find our equation.

Recall what the point-slope form of a line is:

Since we know that the derivative slope must equal 0, then we know that m = 0. We now need to find a point (x, y). Substitute one of the x values into the original equation to find an actual point on the function (remember not to round intermediate values on your calculator!):

Now we have a point (x, y) (I will put it in the actual radical form here):

Substitute our variables into point-slope form:

Simplify and rewrite to obtain our final answer:

Find the intercepts and domains

1. Intercepts

x-intercept (when y = 0)

x = 0

y-intercept (when x = 0)

y = 0

Domain

y = All real numbers

Symmetry

Yes it is symmetry

The image of the point B ( − 4 , 6 ) under 270° clockwise rotation is point (-6 , -4).

A transformation that revolves a figure around a point is called a rotation. The rotational center is where we refer to it. The shape and dimensions of a figure remain the same while facing in a different direction. You can rotate a figure either clockwise or counterclockwise.

Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) is a -

270° clockwise rotation: (x,y) becomes (-y,x)

The image of the point B ( − 4 , 6 ) under this rotation is

(x , y) = (-y , x)

i.e.  (-6 , -4)

Assuming that the rotation's center is at (0, 0). Here are the guidelines for rotation:

Therefore , The image of the point B ( 4, 6) when rotated 270 degrees clockwise is point (-6 , -4).

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[tex] \: \huge \tt{\pink{A}{\orange{N}S{\green{W}{\blue{E}{\purple{R}}}}}} : \\ \\ \: \: \rightarrow \tt \: \:B. \: Smooth \: \: muscle \: \: contractions[/tex]

Esophagus move food to the stomach with the help of Smooth muscle contractions. Thus, option B is correct.

The esophagus is the tubular structure that transports food from your mouth to your stomach. Esophagitis can cause uncomfortable swallowing and chest discomfort. Esophagitis can be caused by a number of factors. Some typical causes comprise stomach acids backing up into the esophagus, illness, oral medications, and allergies.

As food enters the stomach, the esophagus contracts. The lower esophageal sphincter (LES) is a "valve" placed directly before the stomach entrance. This valve opens to allow food to travel from the esophagus into the stomach and closes to prevent food from moving back up into the esophagus from the stomach. Hence, option B is correct.

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Solution:

iven :

To solve,

step 1: Convert the mixed fractions into improper fractions.

Thus,

step 2: Perform the operation of multiplication between both fractions.

Thus,

step 3: Convert the resulting improper fraction into a mixed fraction.

Thus,

Hence, the solution is

Hello! So....

We are given the following:

[tex]\frac{4250}{204}= \frac{y}{528}[/tex]

_______________________

1. Switch sides.

[tex]\frac{y}{528} =\frac{4250}{204}[/tex]

_______________________

2. Cancel the common factor (34).

[tex]\frac{y}{528}= \frac{125}{6}[/tex]

_______________________

3. Multiply both sides by 528.

[tex]\frac{528y}{528} =\frac{125*528}{6}[/tex]

_______________________

4. Simplify.

[tex]y=11,000[/tex]

^Hence, our solution.

____________________________________

Hope this helps! If so, please lmk! Thanks and good luck!

4,250/204 = y/528

Multiply both sides of the equation by 8976, the lowest common denominator of 204,528.

44×4250 = 17y

Multiply 44 and 4,250 to get 187,000.

187000 = 17y

Swap the sides so that all the terms of the variables are on the left side.

17y = 187000

Divide both sides by 17.

y = 187000/17

Divide 187,000 by 17 to get 11,000.

y=11000

The amount in Roxy's table listing of expenses gives the ratio of the items in the pie chart as follows;

Emergency fund; 3.89%

Cell phone; 6.93%

Internet; 4.28%

Rent payment; 76.79%

Transportation; 2.34%

Insurance; 1.17%

Gym membership; 1.97%

Entertainment; 2.73%

The pie chart can then be constructed using those percentage as a proportion of 100

Please see the attached pie chart of the expenses created with Sheets

A pie chart illustrates the numerical proportion of items in a dataset by using a circular graphic that is divided into sector slices

The given values in the question are;

Emergency fund = $50

Cell phone = $89

Internet = $55

Rent payment = $986

Transportation = $30

Insurance = $15

Gym membership = $24

Entertainment = $35

The total cost of the fixed expense is therefore;

$50+$89+$55+$986+$30+$15+$24+$35 = $1284

The proportion of each component in the pie chart is found as follows;

[tex] \displaystyle{Emergency \: fund = \frac{50}{1284} \times 100 \approx 3.89 \%}[/tex]

[tex] \displaystyle{Cell \: phone = \frac{89}{1284} \times 100 \approx 6.93 \%}[/tex]

[tex] \displaystyle{Internet = \frac{89}{1284} \times 100 \approx 4.28 \%}[/tex]

[tex] \displaystyle{Rent \: payment = \frac{986}{1284} \times 100 \approx 76.79 \%}[/tex]

[tex] \displaystyle{Transportation = \frac{30}{1284} \times 100 \approx 2.34 \%}[/tex]

[tex] \displaystyle{Insurance = \frac{15}{1284} \times 100 \approx 1.17 \%}[/tex]

[tex] \displaystyle{Gym \: membership = \frac{24}{1284} \times 100 \approx 1.87 \%}[/tex]

[tex] \displaystyle{Entertainment = \frac{35}{1284} \times 100 \approx 2.73 \%}[/tex]

Using the above percentages, the pie chart can be constructed

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Anime Girl, this is the solution:

We have a total of 70 students (male and female), in consequence:

• Students that got an A = 18

• Students that got a B = 28

• Stiudents that got a C = 24

• P(A or B) = A + B / Total students

• P(A or B) = 18 + 28/70

• P(A or B )= 46/70

• P(A or B) = 23/35 (Simplifying) or 0.66

It should be noted that the purchase price of the home will be $160865.

Based on the information, the following can be illustrated:

Purchasing price = $150000

Purchase price fee = 5% × $150000 = $7500

Title search = $300

Love cost = 1/2 × 4% × $150000 = $3000

Taxes = $65

Total amount = $150000 + $7500 + $300 + $3000 + $65

= $160865

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The parametric equations for this problem are given as follows:

31. [tex]x = t, y = \sqrt[3]{t} + 1[/tex].

35. x(t) = -1 + 3t, y(t) = 5 - 2t.

For item 31, the parent function is the cube root function, defined as follows:

[tex]y = \sqrt[3]{x}[/tex]

From the graph of the function, it was translated two units up, hence it is defined as follows:

[tex]y = \sqrt[3]{x} + 2[/tex]

We want to parametrize the equation as a function of t, hence:

A linear function is parameterized as follows:

The initial point of the function, at t = 0, is (-1, 5), hence:

x(0) = -1, y(0) = 5.

After 1 second, they moved to point (2,3), hence the coefficients are given as follows:

Thus the parameterized equations are given as follows:

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The percentage that 7.64% gain experienced you if sold your shares, your account showed $4680 for a total gain of $357.50.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

Given that when you sold your shares, your account showed $4680.00 ($72.00 × 65 shares)

For a total gain of $357.50 ($4680.00 – $4322.50).

Let the percentage gain you experienced be x %

As per the given data, the solution would be as:

⇒ x% of 357.50 = 4680.00

x%  is expressed as x/100 in fractional form

⇒ (x/100)(357.50) = 4680.00

⇒ x = 357.50/4680.00 × 100

⇒ x = 7.64%

Therefore, the percentage that 7.64% gain experienced you.

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She has 3838 shells in her collection after 66 months of gathering. The equation using this data is 33x+33y=1919.

Given that,

Giana has begun to gather seashells. She grows her collection by 66 new shells each month. She has 3838 shells in her collection after 66 months of gathering.

We have to create an equation using this data that models the number of shells y Giana's collection will include after x months in point-slope form.

We can write as

The total number of shells she collected =(The amount of shells she collect each month)×y+(The month of collecting the shells)×x

3838=66y+66x

66x+66y=3838

33x+33y=1919

Therefore, the equation using this data that models the number of shells Giana's collection will include after x months in point-slope form is 33x+33y=1919.

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Answer: give correct answers only or people on here will do the same thing u did to them bozo

Step-by-step explanation:EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answer:

D. Organ systems

Step-by-step explanation:

Homeostasis is maintained by the nervous and endocrine systems.

The warmest recorded temperature is 214°F higher than the coldest temperature.

Since the sign of the two numbers are same, their final values will be added and the result will have the same signs as the two numbers (or the one with the greater absolute value). This is called the multiplicative property.

Expression for difference between the two temperatures is,

= 134−(−80)

By applying the multiplicative property of negative sign, we get

=134+80

= 214°F

Therefore, we conclude that the warmest recorded temperature is 214°F  higher than the coldest temperature.

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The number of cups of broccoli that would be needed for a pound of beef is C. 1 1/2 cup of broccoli per beef.

From the information, it was stated that Tyler was making a meal for his family and that for every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli.

Therefore, the cups of broccoli that would be needed for a pound of beef will be:

3/4/1 = 9/8/x.

where x = cups of broccoli

Cross multiply

3/4x = 9/8

x = 9/8 ÷ 3/4

x = 9/8 × 4/3

x = 3/2

x = 1 1/2cups

Therefore, the correct option is C.

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Answer:

[tex]\textsf{c) \quad $1 \frac{1}{2}$ cups of broccoli per 1 lb of beef}.[/tex]

Step-by-step explanation:

Given information:

Create a ratio of pounds of beef to cups of broccoli, where x is the number of cups of broccoli to one pound of beef:

[tex]\implies \dfrac{3}{4}: \dfrac{9}{8}=1:x[/tex]

[tex]\implies \dfrac{\frac{3}{4}}{\frac{9}{8}}=\dfrac{1}{x}[/tex]

Cross multiply:

[tex]\implies \dfrac{3}{4}x=\dfrac{9}{8}[/tex]

[tex]\implies x=\dfrac{9}{8} \div \dfrac{3}{4}[/tex]

To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

[tex]\implies x=\dfrac{9}{8} \times \dfrac{4}{3}[/tex]

[tex]\implies x=\dfrac{9 \times 4}{8 \times 3}[/tex]

[tex]\implies x=\dfrac{36}{24}[/tex]

[tex]\implies x=\dfrac{3 \cdot \diagup\!\!\!\!\!\!12}{2 \cdot \diagup\!\!\!\!\!\!12}[/tex]

[tex]\implies x=\dfrac{3}{2}[/tex]

[tex]\implies x=1 \frac{1}{2}[/tex]

Therefore, 1¹/₂ cups of broccoli would be needed to one pound of beef.

For this problem, we are given the dimensions of a right triangle, we need to apply the trigonometric relation to determine which one results in 3/5.

We have three possible options sin, cos, and tan. The sine is the division between the opposite cathetus and the hypothenuse, which for this case is equal to 3/5, therefore it is the correct option.

The answer is A. sin.

The solution for the given inequalities are as follows

(17)k≥1     ,(18)c > 14      ,(20)y ≥ 2      ,(21)z < 9     ,(23)x < 1    ,(24)v ≤ -1  .

In the question ,

it is given that

(17) the inequality

3(k-5)+9k≥-3

3k-15+9k ≥ -3

12k -15 ≥ -3

12k ≥ 15-3

12k ≥ 12

k≥1

(18) the inequality

-(7c-18)-2c > 0

-7c+126-2c>0

-9c+126>0

-9c > -126

c > 126/9

c > 14

(20)given the inequality

-4 ≤ 4(6y-12)-2y

-4 ≤ 24y - 48 -2y

-4 ≤ 22y - 48

48-4 ≤ 22y

44/22 ≤ y

y ≥ 2

(21) given the inequality

30 > -(5z+15)+10z

30 > -5z -15 +10z

30 > 5z-15

45 > 5z

45/5 > z

z < 9

(23) given the inequality

4x+3 < 3x+6

4x-3x < 6-3

3x < 3

x < 1

(24) given the inequality

4v+8 ≥ 6v+10

-10+8 ≥ 6v-4v

-2 ≥ 2v

-2/2 ≥ v

-1 ≥ v

v ≤ -1

Therefore , the solution for the given inequalities are (17)k≥1     ,(18)c > 14      ,(20)y ≥ 2      ,(21)z < 9     ,(23)x < 1    ,(24)v ≤ -1  .

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Answer:0.07142857142

Step-by-step explanation:

0.07142857142 because 1/2/7= or .5/7=0.07142857142

.5= how much paint

7= how many tables that are needed to be filled

0.07142857142= how much paint

each table will receive

b) No, it is not

c) x + 1 is a factor

To determine if 10 is a function, we substitute x with 10 in the function:

No, it isn't a . This is because f(10) is not equal to zero, it is not a zero o. It has a remanider of 396.

c) Using synthetic division:

for x + 1: to be a factor, x = -1

+1 1 0

The last number is equal to zero. This indicates the remainder is zero.

Hence, x + 1 is a factor of the function f(x)

Answer: A.

Step-by-step explanation:

D is not less than c because c is a negative number.

Answer:

2. Speed of the car.

Step-by-step explanation:

Given equation:

[tex]D=280-59t[/tex]

where:

The car begins its journey at Albany.  

Therefore, the car is at Albany when t = 0:

[tex]t=0 \implies D=280-59(0)=280[/tex]

Therefore, 280 represents the distance between Buffalo and Albany.

After 1 hour of driving:

[tex]t=1 \implies D=280-59(1)=221[/tex]

Therefore, after 1 hour of driving, the car is 59 miles closer to Buffalo and therefore 59 miles from Albany.

After 2 hours of driving:

[tex]t=2 \implies D=280-59(2)=162[/tex]

Therefore, after 2 hours of driving, the car is 158 miles closer to Buffalo and therefore 158 miles from Albany.

Therefore, the 59 represents the speed of the car as the car travels 59 miles per hour.

Answer:$11.05

Step-by-step explanation:

Answer:

$11.05 each

Step-by-step explanation:

To find x, the cost between Aisha and her two friends you must divide the total amount by the number of people.

There are three people, her and two friends and the total cost for the pizza is $33.15

$33.15 ÷ 3 = $11.05

The function is  f(x) = [tex]x^3[/tex]  + 2x is an odd function.

Given the function is :

f(x)=x^3-2x

To determine the function is Even , Odd , or Neither.

Let's Know :

What is  an Odd function?

A function f is said to be an odd function if -f(x) = f(-x), for all value of x. In Mathematics, the functions even and odd are those that satisfy specific symmetry relations, with respect to considering additive inverses.

Now, Come to the question:

According to the question;

f(x) = [tex]x^{3}[/tex] - 2x

f(-x) = (-[tex]x^3[/tex])  - 2(-x)

f(-x) = -[tex]x^3[/tex]  + 2x

Identify the relation between f(x) and f(-x)

f(x) ≠ f(-x)

Find -f(-x)

-f(-x) = -( -[tex]x^3[/tex]  + 2x)

Remove the parentheses:

-f(-x) =  [tex]x^3[/tex]  + 2x

Identify the relation:

f(x) = -f(-x)

Hence, The function is  f(x) = [tex]x^3[/tex]  + 2x is an odd function.

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We will investigate how to use the mileage meter of a car to determine the amount of distance a car can travel per given fuel.

Mileage is a economic performance parameter of a car that gives the fuel economy. It is usually expressed as a ratio of:

The mileage of a car is given as follows:

We can say that this car can travel 29.7 miles per gallon on highway.

We now stop at the petrol station for re-fueling. We fuel up the car to:

We need to determine the distance that this car can travel for the amount of re-fueling. This is where we can use the mileage to determine the distance the car can travel as follows:

Plug in the respective quantitites and solve for the distance that the car can travel as follows:

For the amount of re-fueling the distance travelled is 310.365 miles