If AC=82 and AE=2x+11 find the value of x

The initial amount of stickers given to each of the volunteers was 4 stickers while the final amount given to each of them was 6 stickers.

We are told that Mai gave each of the five volunteers the same number of stickers. Thereafter, she gave each of them 2 stickers each and the total was 30 stickers.

If the initial amount given to them each was y, then we have;

5(y + 2) = 30

y + 2 = 6

y = 6 - 2

y = 4

Thus, we can say that the amount of stickers she gave each of them initially was 4 stickers while the amount she gave them in total after the extra ones was 6 each

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The equation of the line is y = -4x - 15.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line y = m(1)x + c is perpendicular to y = x/4 - 2.

This means,

y = (1/4)x - 2 is in the form of y = m(2)x + c

So,

m(1) x m(2) = -1

m(1) = -1 / (1/4)

m(1) = -4

Now,

The line intersects (4, -1).

So,

y = -4x + c

-1 = -4(4) + c

-1 = -16 + c

c = - + 16

c = -15

Thus,

The equation of the line perpendicular to y = x/4 - 2 is y = -4x - 15.

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Answer:

Step-by-step explanation:

87.92*3.14/4=504.3

Answer:

The answer would be part C

Step-by-step explanation:

First we find the gradient by y2-y1/x2-x1

So it would be;

3-1/4-8

2/-4

-1/2

Now we put in the gradient and the points (4,3) in the equation y=mx+c;

3=-1/2(4)+c

3=-2+c

3+2=c

5=c

Finally we put c in the equation;

y=mx+c

y=-1/2x + 5

Gwen's total sales and costs would be; 50 dollars.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that x represent the number of pounds of soap that she makes and eventually sells.

we are given that Gwen intially spent $96 to purchase soap-making equipment, and the materials for each pound of soap cost $9. This means that the total cost of making x pounds of soap would be;

9x + 96

thus her revenue for x pounds of soap would be

25 × x = 25x

If she eventually sells enough soap to cover the cost of the equipment, then we get;

9x + 96 = 25x

25x - 9x = 96

x = 96/16

x = 6

she would need to sell make and sell 6 soaps.

The cost would be 9x + 96 = 150

The total sales would be;

25 x 6 = 150

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Answer: 316 ounces

Step-by-step explanation:

5 + 3 = 8 (This tells us that there are a total of 8 "parts" in the ratio)

16/8 = 2 (Each part has a total of 2 balls)

2*5 = 10 basketballs

2*3 = 6 footballs

10 basketballs * 22 ounces = 220 ounces

6 footballs * 16 ounces = 96 ounces

Total = 220 + 96 = 316 ounces

Hoped this helped! Leave a comment if you have any other questions.

Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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The future value in 13 years when compounded continuously is; $18183.25

Continuous compounding is defined as the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

The formula for continuous compounding is;

V = Pe^(rt)

where;

V is the value of the account in t years

P is the principal initially invested

e is the base of a natural logarithm.

r is the rate of interest

We are given;

P = $6770

r = 7.6% = 0.076

t = 13

Thus;

V = 6770 * e^(0.076 * 13)

V = $18183.25

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Down payment = $198, total monthly payment = $2088, installment price = $2286, finance charge = $1782

Down payment is the amount of money that a purchaser needs to pay at the early stage of purchasing an expensive goods.

Given, purchasing price = $1980, 18 monthly payments of $116 each.

down payment = 10%

amount of down payment = $1980 × 10/100

                                          = $198

Total amount of monthly payment = $116 × 18 = $2088

Total paid for the snow thrower on the installment plan = Down payment + all monthly payment = $198 + $2088

Total installment price = $2286

total finance charge = Stated purchased price - down payment

                                = $1980 - $198

                                 = $1782

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If Sal saves $55 per month, the expression for his total savings for x years is 55x.

Amount is a term used to describe the total sum of money, quantity, or value of something. It is usually used to refer to a specific figure or a set of figures, such as the amount of money in a bank account, the number of items in a store, or the total cost of a purchase. Amount can also be used to describe the amount of time, energy, or effort put into something.

a. The down payment is 10% of $1,980, which is $198.

b. The total amount of the monthly payments is 18 x $116, which is $2,088.

c. Jean paid a total of $1,980 + $198 = $2,178 for the snow thrower on the installment plan.

d. The total finance charge is $2,088 - $2,178 = $90.

If Sal saves $55 per month, the expression for his total savings for x years is 55x.

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Answer: This question is asking for the range of the graph, which is the set of all possible values of the dependent variable (y-coordinate) in the graph.

Based on the options given, the correct range is:

D x:-2,-1,0,2,5 Y: 0,2,1,0,2

The range of this graph is {0, 1, 2}.

Step-by-step explanation:

Answer:

50 children tickets; 60 adult tickets

Step-by-step explanation:

Let a = number of adult tickets.

Let c = number of children tickets.

a + c = 110

5a + 3c = 450

  -3a - 3c = -330

  5a + 3c = 450

------------------------

   2a        = 120

a = 60

a + c = 110

c = 50

Answer: 50 children tickets; 60 adult tickets

Particular attention should be paid to the y=x3+x graph, which lacks any stationary points of inflexion or turning points. This illustration demonstrates that a cubic graph could contain zero stationary points. One, two, or three x-intercepts can be found on the graph of a cubic polynomial.

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In a parallelogram, the opposite angles have equal measures. Therefore, 2n + 32 = 4n - 2

32 = 2n - 2

34 = 2n

17 = n

A. Mean = 71

B. Median = 75

C. Mode = 0

D. Mean is used to represent data, because mean measures central tendency.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

We have the Data set: 35, 42, 43, 51, 55, 57, 62, 66, 68, 69, 74, 75, 76, 77, 78, 79 , 82, 84, 86, 88, 93, 94, 101

So, Mean = average

                = sum of all numbers / total number of values .

                 = 1635 / 23

                 = 71.08

                 = 71

and, Median = middle term = 12th term = 75

lastly, Mode = Most repeated term or term that has high frequency.

Here no terms are repeating so mode = 0

A comparison of the mean, median, and mode

Data are represented using the mean.

Because it averages all of the values in the data set, the mean is the most widely used measure of central tendency.

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The sentence that describes the next step in the construction is; D: draw a line through points C and D

The steps that are used to bisect a line segment are;

1) Place the compass at one end of line segment.

2) Adjust the compass to slightly longer than half the line segment length

3) Draw arcs above and below the line.

4) Keeping the same compass width, draw arcs from other end of line.

5) Place ruler where the arcs cross, and draw the line segment.

From the given procedure and looking at the image, we can say that the next logical step would be to draw a line through points C and D

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The area of the figure is 39 feet square.

A composite figure contains two or more shapes. The figure above is a composite figure. The area of the figure can be calculated as follows:

area of the figure = area of rectangle 1 + area of rectangle 2

Therefore,

area of rectangle 1  = lw

where

Therefore,

area of rectangle 1  = 2(3)

area of rectangle 1  = 6 ft²

area of rectangle 2  = 11 × 3

area of rectangle 2  = 33 ft²

Therefore,

area of the figure = 6 + 33

area of the figure = 39 ft²

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Answer: The given expression is:

m² +........+ 1/m²

We can notice that the expression has an even number of terms, and the first and last term are perfect squares, which suggests that it might be possible to write the expression as the square of a binomial.

Let's try to write the expression in the form of (a + b)²:

(a + b)² = a² + 2ab + b²

If we set a = m and b = 1/m, we get:

(a + b)² = m² + 2(m)(1/m) + (1/m)² = m² + 2 + 1/m²

Comparing this with the given expression, we see that it is the same as the given expression with 2 added to it.

Therefore, to make the given expression a perfect square, we need to add 2 to it.

So, the term to be inserted is 2.

The expression m² +........+ 1/m² can be written as (m + 1/m)² - 2.

Step-by-step explanation:

If a shopkeeper gives you a 15% discount on shirt of having total price 50, the price you will give after the 15% discount is 42.5 dollars.

If the original price of the shirt is 50 dollars, and the shopkeeper gives a discount of 15%, then the discount amount is calculated by:

Discount = Original price x Discount rate

Discount = 50 x 0.15

Discount = 7.5 dollars

The discounted price is calculated by subtracting the discount from the original price:

Discounted price = Original price - Discount

Discounted price = 50 - 7.5

Discounted price = 42.5 dollars

The discount rate of 15% means that you will save 15% of the original price, which is 7.5 dollars in this case. The discounted price is the price after subtracting the discount amount from the original price.

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The population after 5 years will be approximately 8.45 billion.

The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)^t, where P(t) is the population in billions and t is the number of years after 2022.

To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.

We can use the formula for exponential growth, P(t) = P0(1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the number of years.

Substituting the values for P0 and r into the equation, we get:

P(t) = 8(1.011)^t

This equation can be used to find the population after t years.

For example, to find the population after 5 years, we can substitute t = 5 into the equation and get:

P(5) = 8(1.011)^5 ≈ 8.45 billion

Therefore, the population after 5 years will be approximately 8.45 billion.

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The value of x is 2√13 units.

The correct option is D.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

A right-angled triangle.

The value of the base is 12 units.

And the length of the perpendicular is 8 units.

Therefore,

x = √{(8)² + (12)²}

x = √(64 + 144)

x = √208

x = 2√13

Therefore, x = 2√13.

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Answer:

x-17/2

Step-by-step explanation:

here, we can set the number to x

the question is asking for 2(x-7)=3

let's solve this by distributing

2x-14=3

2x=17

x=17/2

Answer: 2 (x - 7) = 3

Use the distributive property: 2x - 14 = 3

2x - 14 = 3 + 14

2x = 17

2x/2 = 17/2

x = 8.5

The bag that contains​ pennies, nickels,​ dimes, and quarters have the total amount of 5.26 dollars.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A bag contains 50 coins

Now, Number of pennies = 14% of 50

                               = 0.14 × 50

                               = 7 pennies

and, Number of dimes  = 40% of 50

                             = 0.40 × 50

                             = 20 dimes

Number of nickels = 6 more than pennies

                              = 6 + 7

                             = 13 nickles

Number of quarters = Rest of the coins

                               = 50 - (7 + 20 + 13)

                               = 50 - 40

                              = 10 quarters

As we know,

1 penny = 0.01 dollar

7 pennies = 0.01 ×7  = 0.07 dollar

1 dime = 0.10 dollar

20 dimes = 0.10 × 20 = 2.00 dollar

1 nickel = 0.05 dollar

13 nickel = 0.05 × 13 = 0.65 dollar

1 quarter = 0.25 dollar

10 quarter = 0.25 × 10 = 2.50 dollars

Total value of the coins in the bag = 0.07 + 2.00 + 0.65 + 2.50

                                                           = 5.22 dollars

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Answer:

78° + B = 180°

B = 102°

Step-by-step explanation:

"Supplementary" means angle A and B added together are 180°.

We know A is 78, but we don't know B

Write an equation:

A + B = 180°

Fill in what we know.

78° + B = 180° this is the equation the question is asking for.

To solve, subtract 78 from both sides of the equation.

B = 102°

The measure of ∠AOC of the circle is ∠AOC = 140°

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the measure of ∠ABC of the circle = 70°

Now , the sides AO and BO are the radius of the circle

where x + y = 70°

So , the measure of ∠AOB = 180 - 2x

And , the measure of ∠COB = 180 - 2y

Now , the measure of ∠AOC = 2 ( x + y )

On simplifying , we get

Central Angle = 2 x Angle in other segment

The measure of angle ∠AOC of the circle is = 2 ( 70 )°

The measure of angle ∠AOC of the circle is = 140°

Hence , the measure of ∠AOC of circle = 140°

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The value of x is 77.5. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is 180°.

Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.

In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:

180° = angle BAC = (x + 7) + (x + 18)

We can solve this equation by combining like terms and isolating the variable x.

180° = 2x + 25

2x = 155

x = 77.5

Therefore, the value of x is 77.5.

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Volume of cone =  100.48 cubic units.     and  The Volume of cylinder= 301.44 cubic units.

One of the fundamental three-dimensional forms in geometry is the cylinder, which has two distant, parallel circular bases. At a certain distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The distance between the two circular bases is used to define the cylinder's height. An LPG gas cylinder is one of the genuine examples of a cylinder. The cylinder is a three-dimensional object with two essential properties: surface area and volume. The whole surface area of the cylinder is composed of the combined curved surface area of the cylinder plus the areas of the two circular bases.

A cone has a radius of 4 units and a height of 6 units.

Volume of cone =  [tex]V=\frac{1}{3}\pi r^2h[/tex]

Where, r=4 and h=6

Volume of cone =  [tex]V=\frac{1}{3}\pi 4^2\times 6[/tex]

Volume of cone =  100.48 cubic units.                

If a cylinder has the same radius and the same height as the cone.

Volume of cylinder [tex]V=\pi r^2h[/tex]

Where, r=4 and h=6

[tex]V=\pi \times 4^2\times 6[/tex]

Volume of cylinder= 301.44 cubic units.

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The total number of beings surveyed is given by the equation A = 20

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the total number of beings surveyed be represented as A

Now , the percentage of beings preferred pisquet juice = 30 %

The number of beings who preferred pisquet juice = 6

Substituting the values in the equation , we get

( 30 ) % of A = 6   be equation (1)

On simplifying the equation , we get

( 30/100 )A = 6

Multiply by 100 on both sides of the equation , we get

30A = 600

Divide by 30 on both sides of the equation , we get

A = 600/30

A = 20

Therefore , the value of A is 20

Hence , the number of beings is 20

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Answer:

4 US liquid gallons = 16 US liquid quarts

( Multiply the volume value by 4 )

Have a wonderful day! :-)

Answer:

16 quarts in 4 gallons

Step-by-step explanation:

1 gallon equals 4 quarts

Answer:

9

Step-by-step explanation:

If c = -4 d = 10, we can re-write the expression:

Simplifying what is in the parenthesis:

Therefore when c = -4 d = 10,  [tex]\frac{1}{4} (-4^{3}+10^{2} ) = 9[/tex].

Answer: B. 9

Step-by-step explanation:

Let's learn some BIDMAS rules!

BIDMAS is an order of operation.

Multiply first or the indices? We can solve it with order of operations.

Here we go ↓↓

B = Brackets

I = Indices (³ ²)

D = Division

M = Multiplication

A = Addition

S = Subtraction

NOTE = Multiply or divide first? We do it from left to right

NOTE = Addition or Subtraction? We also do it from left to write in an equation.

Step 1 :

We replace all the letters with the given value, this make it :

[tex]1/4 (-4^{3} + 10^{2} )[/tex]=?

Step 2 :

Now, according to the rules, we do the numbers in the brackets first, now, in the brackets, there are indices, so we do those.

Which makes it :

1/4(-64+100)= ?

Step 3 :

Now we add the integers inside the brackets, remember, whenever the equation is like this, it is telling us it is a multiplication, here, it will be 1/4 x (-64+100) . In algebra, we don't use the × sign as it can be misinterpreted as [tex]x[/tex] .

1/4 (-64+100 = 36)

1/4 (36)

     =

   1/4 x 36

So we have = 1/4 x 36 at last.

Step 4 =

Do the multiplication!

1/4 x 36 = 9

So the answer is 9

The triangular area abc, from the graph on the market for gasoline represents, D. the deadweight loss (or excess burden) created by the tax.

The cost of market inefficiency, which happens when supply and demand are out of balance, is known as a deadweight loss. When supply and demand are out of equilibrium, a deadweight loss arises, which impairs the efficiency of the market.

Deadweight losses may result from price floors, such as minimum wage and living wage regulations, price ceilings like price controls and rent restrictions, and taxation. A society's resource distribution may also become inefficient with a decline in commerce.

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