A group of students are at a library.
6 of them leave. 7 students are left. Which part-part-whole
model shows how many students were at the library to start?

Answer:

∠

A

=

x

=

32

∘

∠

B

=

3

x

=

3

⋅

32

=

96

∘

∠

C

=

x

+

20

=

32

+

20

=

52

∘

Step-by-step explanation: Every triangle adds up to 180.

Answer is :

The chosen at random is 25 - 44 years old is  = 26 %.  

Probability determines how likely it is that a stated event would

occur. This event would occur. This probability lies between 0 and 1.

The probability that a person chosen at random is at least

15 years = sum of percentages of people at least 15 years old :

14 + 13 + 13 + 15 + 12 + 13 = 80%

the probability that a person chosen at random is 25 - 44 years old :

13% + 13% = 26%

Therefore The probability is 26%.

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Answer: [tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

Step-by-step explanation:

64+Ax+135x^2

135x^2+Ax+64=0

[tex]x_{1,\:2}=\frac{-A\pm \sqrt{A^2-4\cdot \:135\cdot \:64}}{2\cdot \:135}[/tex]

[tex]x_{1,\:2}=\frac{-A\pm \left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x_1=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135},\:x_2=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

Answer:

(-3,1)  & (3, -1)

Step-by-step explanation:

Solving quadratic equation and linear equation:

2x² + y² = 19 -----------------(I)

x + 3y = 0 -----------------(II)

         x = -3y --------------(III)

Substitute x = -3y in equation (I) and we can find the value of y.

2(-3y)² + y² = 19

2*9y² + y²  = 19

  18y² + y² = 19

Combine like terms,

          19y² = 19

             y² = 19 ÷ 19

              y² = 1

              y = √1

              y = ±1

Substitute y = ±1 in equation (III) and find the value of x.

When y = 1,

              x = -3*1

              x = -3

When y = -1,

               x = -3*(-1)

             x = 3

Solutions:  (-3, 1) ; (3, -1)                  

Answer:

B. 35

Step-by-step explanation:

Because lines m and n are parallel, we know that x+(4x+5)=180.

So all you have to do is simplify.

x+(4x+5)=180

5x+5=180

5x=175

x=35

So the only possible value of x is 35

The value of x by setting up equation is 16.

Given in question,

∠VZW = (2x + 32)°

∠RZY = (3x + 16)°

∠VZW = ∠RZY

2x + 32 = 3x + 16

2x - 3x = 16 - 32

        -x = -16

         x = 16

Hence, x = 16.

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Economic equilibrium is a condition or state in which economic forces are balanced. In effect, economic variables remain unchanged from their equilibrium values in the absence of external influences.

Economic equilibrium is also referred to as market equilibrium. Economic equilibrium is the combination of economic variables (usually price and quantity) toward which normal economic processes, such as supply and demand, drive the economy. The term economic equilibrium can also be applied to any number of variables such as interest rates or aggregate consumption spending. The point of equilibrium represents a theoretical state of rest where all economic transactions that “should” occur, given the initial state of all relevant economic variables, have taken place.

In a competitive market, demand for and supply of a good or service determine the equilibrium price.

MARKETS:

Equilibrium is achieved at the price at which quantities demanded and supplied are equal. We can represent a market in equilibrium in a graph by showing the combined price and quantity at which the supply and demand curves intersect.

For example, imagine that sellers of squirrel repellant are willing to sell 500 units of squirrel repellant at a price of $5 per can. If buyers are willing to buy 500units of squirrel repellent at that price, this market would be in equilibrium at the price of $5 and at the quantity of 500 cans.

Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium.

A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.

A shortage will exist at any price below equilibrium, which leads to the price of the good increasing.

For example, imagine the price of dragon repellent is currently $6 per can. People only want to buy 400 cans of dragon repellent, but the sellers are willing to sell 600 cans at that price. This creates a surplus because there are unsold units. Sellers will lower their prices to attract buyers for their unsold cans of dragon repellant.

Changes in the determinants of supply or demand result in a new equilibrium price and quantity. When there is a change in supply or demand, the old price will no longer be an equilibrium. Instead, there will be a shortage or surplus, and price will subsequently adjust until there is a new equilibrium.

For example, suppose there is a sudden invasion of aggressive unicorns. There will be more people who want to buy unicorn repellent at all possible prices, causing demand to increase. At the original price, there will be a shortage of unicorn repellant, signaling sellers to increase the price until the quantity supplied and quantity demanded are once again equal.

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Answer:

D, 3216

Step-by-step explanation:

Calculators are great. I love calculators.

Answer:

x = 9

Step-by-step explanation:

According to the question,

Perimeter of an isosceles triangle = 37

Length of the base = x

Length of one leg = 4x - 4

As it is an isosceles triangle so length of the other leg will also be 4x - 4.

Perimeter of triangle is equal to sum of all the lengths of the triangle.

[tex] \therefore [/tex]

[tex] \rm \implies Length \: of \: base + Length \: of \: one \: leg + Length \: of \: other \: leg = 37

\\ \\ \rm \implies x + 4x - 4 + 4x - 4 = 37

\\ \\ \rm \implies 9x - 8 = 37 \\ \\ \rm \implies 9x = 37 + 8 \\ \\ \rm \implies 9x = 45 \\ \\ \rm \implies x = \frac{45}{9} \\ \\ \rm \implies x = 5

[/tex]

Answer:

Slope:   [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept.

The expression given is already in slope intercept form. In this case [tex]m=\frac{1}{2}[/tex]

Therefore the slope is [tex]\frac{1}{2}[/tex]

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 4 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Answer:

Michael has 19 sweets

Step-by-step explanation:

19+24+32 = 75

Lilly has: 24

James has: 32

Answer:

Ima say 2017

Step-by-step explanation:

Answer:

x=35

Step-by-step explanation:

29+6=35

btw are you sure that you are in highschool???

Answer:

35

Step-by-step explanation:

29+6 is 35 u sure in high school?

The value of z is given by (b) z = 63.

According to Angle Sum Property, the sum of interior angles of a triangle is 180 degree.

So for left hand triangle, interior angles are 31, 61 and x. So,

31 + 61 + x = 180

92 + x = 180

x = 180-92

x = 88

Now x and y are the linear angles so their sum is 180 degree too.

x + y = 180

88 + y = 180

y = 180-88 = 92

Again for right hand triangle the interior angles are 25, y, z. So again by Angle Sum Property,

25 + y + z = 180

25 + 92 + z = 180

117 + z = 180

z = 180-117 = 63

Hence the value of z is 63.

So the correct option is (b).

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Answer:

Step-by-step explanation:

The answer is D.

The rule for perpendicular lines is that the slope will be the negative reciprocal. Because this equation is in slope-intercept form, the coefficient of x is the slope. -7/5 becomes 5/7. Our new equation is y=5/7x+b. Plugging in (5,3), we see that b is equal to -4/7. Our equation is then y=5/7x-4/7

5 days does it take to sell 640 cupcakes.

Given:

A bakery sells 4 dozen cupcakes every 3 hours.

If the bakery is open 8 hours each day.

4 dozen cupcakes = 4*12 cupcakes

= 48 cupcakes

48 cupcakes = 3 hours

divide by 3 on both sides

3hours/3 = 48/3 cupcakes

1 hour = 16 cupcakes

Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.

128 cupcakes sells in one day.

To sell 640 cupcakes = 640/128

= 5 days.

Therefore 5 days does it take to sell 640 cupcakes.

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The option(1) that is  g(1) is 3 is True and remaining are false.

Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.

Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.

we have,

g(x) = f(x - 3)

As graph in question,

g(1) = f(1-3) = f(-2) = 3

This option is true.

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If the common difference between every term in a sequence is the same, the sequence is arithmetic. If all of the terms in a sequence have the same common ratio, the sequence is geometric.

Take a look at the sequence 2,4,6,8, and note how each new term is created by adding a constant term, in this case 2, to the one before it.

For instance, the number 4 is created by adding 2 to the previous phrase, in this case the number 2.

Similar to how 2 + 4 = 6, another number is obtained by adding 2 to 4.

As a result, the sequence is arithmetic since there is a common difference between the sequences, which in this case is 2.

Take the numbers 3, 6, 12, etc.

Keep in mind that the ratio of the following and preceding terms is the same (6/3=2 and 12/6=2).

Such a sequence is referred to as a geometric sequence, and the constant ratio is known as the common ratio of the sequence and is typically indicated by the symbol r.

What is arithmetic sequence?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

What is geometric sequence?

Every term in a geometric series is obtained by multiplying the term before it by the same number.

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Answer:

to find the max number of guests:

25x-400 = 50

25x = 50 + 400

25x + 450

then divide

x = 450/25

x = 18

to find the min number of guests:

25x = 400 - 50

25x = 350

then divide

x = 350/25

x = 14

Minimum number of tables reserved:

is dividing the max/7 per table

x = 18/7

x = 3

Step-by-step explanation:

The system of inequalities for this situation are

Cost inequality = $4x + $6y ≤ $100

Time inequality = 30x + 60 ≤ 900

And  the retailer should make 10 single layer and 10 2-layer mask by using the available time and cost.

System of inequalities

When two or more algebraic expressions are compared using the mathematical symbols like <, > ≤, or ≥, then they form an inequality. They are the mathematical expressions in which both sides are not equal.

Given,

A retail store manager makes cotton cloth facemasks for his employees during Covid. He has enough money to buy $100 worth of fabric. Fabric costs $4 for a single layer mask and $6 for a mask with 2 layers of fabric. It takes him 30 minutes to make a single layer mask and 1 hour to make double layer mask. He only has 15 hours available to work on masks. He wants to maximize his time and resources.

Here we need to find the system of inequalities and we also need to find each type of mask should he make.

Let us consider x be the number of single layer mask and y be the number of 2 layer mask.

Then based on the given cost, the cost inequality is written as,

$4x + $6y ≤ $100.

Here we know the time taken for each mask making, so, in the inequality form, it can be written as,

We know that,

1 hour = 60 minutes

So, 15 hours = 900

Therefore, the inequality of time is written as,

30x + 60 ≤ 900

While we plot these values on the graph then we get the graph like the following,

Here the blue line represent the time inequality and the red line represents the cost inequality.

Through the given graph, we have identified that the retailer should make 10 single layer and 10 2 layer mask by using the available time and cost.

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Answer:

Step-by-step explanation:

The solution of linear system of equations is the point of intersection of the lines.

Closer view of the graph gives us the point ( - 2, 6 ). See the attached.

Add vertical and horizontal lines from the point of intersection and take the closest values to the integer numbers on the x-axis and the y-axis. The numbers are -2 on the x-axis and 6 on the y-axis, therefore the answer is (- 2, 6).

The matching choice is B.

Answer:

Step-by-step explanation:Answer: 108,000m/h (108km/h or 30m/s)

The maximum number of plants Sophie can have in each pot is 18.

Highest Common factor:

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

Here it is given that Sophie plants 36 violas, 54 sweet peas, and 72 fuchsias. She wants to plant them in pots.

So we have to find the maximum number of plants she could have in each pot.

For that, we have to find the Highest common factor of the given different-different plant she has.

HCF of 36, 54, 72 = 18

So the maximum number of plants she can pot is 18.

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The function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statementr which best describes the graph is,  the graph is streched towards the x axis by a factor of 1/3

When an object is dilated the image formed is larger or smaller, but there is a difference in the size of the shape.

the rule of function change f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8

3x = 9xk

k = 1/3

Therefore, the function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statement which best describes the graph is,  the graph is streched towards the x axis by a factor of 1/3

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The cost for using 24 HCF water is 47.98(in dollars) by using a linear function.

The term linear function in mathematics refers to two distinct but related concepts.

A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. The term affine function is frequently used to distinguish such a linear function from the other concept.

A linear function is a linear map in linear algebra, mathematical analysis, and functional analysis.

The monthly cost of water use is a linear function: y=mx +b, where x represents HCF and y represents the cost of using. For example, if the cost of using x=17 HCF of water is $y=36.43, this means

that is a point (17,36.43)

the cost for using x=28 HCF is $y=54.58, means

that is a point (28, 54.58)

By using the above points we find slope m,

m=((54.58-36.43)/28-17)

m=1.65

=>y=1.65x+b

Now, we have to find the b point by using above point,

36.43=1.65*17+b

36.43=28.05+b

34.63-28.05=b

b=8.38

y=1.65x+8.38

When x=24,

y=1.65(24)+8.38

y=47.98

The cost for using 24 HCF of water is 47.98

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The number of 20 button bags are 2.

Given that, Gassama buys some bags of buttons there are 20 buttons or 21 buttons or 22 buttons or 23 buttons in each bag.

Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.

Here,

Number of 20 buttons = 20×x=20x

Number of 21 buttons = 21×5=105

Number of 22 buttons = 22×3=66

Number of 23 buttons = 23×3=69

Total = 20x+105+66+69

20x+105+66+69=280

⇒ 20x+240=280

⇒ 20x=40

⇒ x=2

Therefore, the number of 20 button bags are 2.

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A function rule for the table:  f(x) = 2x

In this question, we have been given a table.

We need to write  a function rule for the table.

x         ƒ(x)

-3        -6

-2       -4

-1        -2

0         0

We can observe that f(x) = 2x

Therefore, a function rule for the table:  f(x) = 2x

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Answer:

x + 1

Step-by-step explanation:

75+n2+n3...+..77..+..n99++

Difference = 76-75=1

x + 1

Where x is the chosen/inital number.