1. Given: Angle 2 is 65 degrees.

(a) What is the angle measurement of Angle 4. Explain the angle relationship used and show your work.
(b) What is the angle measurement of Angle 7. Explain the angle relationship used and show your work.
(c) What is the angle measurement of Angle 3. Explain the angle relationship used and show your work.

Answer:

4 pencils.

Step-by-step explanation:

The ratio of pencils to pens in the original package is 10:4, which means that for every 4 pens, there are 10 pencils. To find the number of pencils in the larger package, we can use this same ratio.

If the large package has 10 pens, we can set up the proportion:

x/10 = 10/4

Where x is the number of pencils in the large package. To solve for x, we can cross-multiply:

10 * 4 = x * 10

40 = x*10

x = 40/10

x = 4

So the large package contains 4 pencils.

Question: Darby has a $50 gift card to spend at a coffee shop. Each cup of coffee is $2.40. Write and solve an inequality to determine how many cups of coffee she can buy so she has at least $8 left to purchase an insulated mug.

To make an equation we need to do $50-$8 to see how much money we have left to spend on coffee after buying the mug which is $42

42 divided by 2.4 = 17.5 but since you cant buy half a coffee you’d get 17 with $1.2o left over

A way to write this equation is 2.4C + 8 = 50

C acts as a variable to represent the number of cups of coffee you can get while 8 just stands for the one insulated mug you want

hope this helps :D

Answer: 2.4C + 8 = 50

This year 71, 274 ounce cream used.

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 French restaurant used 203,640 ounces of cream last year.

This, year 65% less cream used.

So, this year the amount of cream used

= 203640 - 203640 x 65%

= 203640 - 203640 x 0.65

= 203640 - 132366

= 71274 ounce

Hence, 71274 ounce cream used this year.

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The original cost for each concert ticket is given as follows:

$34.

The original cost for each concert ticket is obtained applying the proportions in the context of this problem.

The fee for a single ticket is divided as follows:

Hence the proportional relationship that models the cost of purchasing x tickets is given as follows:

y = (5 + n)x.

Alex purchased 3 concert tickets, meaning that x = 3, for a total of $117, meaning that y = 117, hence the original cost n is obtained as follows:

117 = (5 + n) x 3

Dividing by 3 on both sides, we have that:

5 + n = 39

n = 39 - 5

n = $34.

Which is the original cost for each concert ticket.

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The solution of this equation is given by x = -10 ( option A)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The equation is

2x - 10 = 3x

⇒ x = -10

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Equation   that represents Chris's total income = ($5.75+$17.5) X, where X is the number of hours he works in a day.

Equation is a mathematical statement that expresses the equality between two or more expressions.

Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.

Assume, Chris works X hours in a day.

He earns $5.75 per hour.

during his work time he serves two groups.

The average tip per group = $8.75

tips earned from two groups = $8.75 × 2 = $17.5

Outputs of Chris total income if he works total X hours in a day

= ($5.75+$17.5) X

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There are 24 red peppers and 8 yellow peppers.

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

Casey has 48 red peppers and 16 yellow peppers.

Now, Divide it into equal part.

Hence, Number of red peppers in two parts = 48/2

                                                                     = 24

And, Number of yellow peppers in two parts = 16/2

                                                                     = 8

Thus, After divide into parts, we get;

There are 24 red peppers and 8 yellow peppers.

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Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.

given

m∠V + m∠W + m∠X + m∠Y = 360

10x -27 + 2x + 19 = 180

12x - 8 = 180

188 = 12x

x = 15.66

m∠V + m∠X = 180

2x = 180

x = 90

Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

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Answer:

From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.

Step-by-step explanation:

From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.

Therefore, the linear function that relates y to x, using this table, is:

y = -7

It's a constant function, no matter what the x value is, the y value is always -7.

Answer:

A) x= -4

Step-by-step explanation:

-7x+3x=7+9

-4x= 16

x= 16÷ -4 = -4

Answer: 2nd picture

Step-by-step explanation: its rotating 90 degrees

Answer:20

Step-by-step explanation:

Answer:

the percent of 40 is 50

the answer to this is 10

The total income tax imposed on $47,000 is $12,800

The term "income tax" describes a class of taxes that governments impose on income generated by people and businesses within their territorial jurisdiction.

Taxpayers are required by law to submit an income tax return each year in order to determine their tax obligations.

Income taxes are the main source of funding for governments. They are employed to fund public services, provide residents with goods, and settle debts owing to the government.

A number of states and municipal governments, in addition to the federal government, also require payment of income tax. The Internal Revenue Service is responsible for collecting taxes and enforcing the tax laws in the United States (IRS).

Regarding credits, deductions, and other forms of taxable and reportable income.

Firstly let us break the income tax as per the given condition

Income = 47,000 = 30,000 + 17,000

hence 20% tax is imposed on $30,000 and 40% on $17,000

Total income tax = 20% of 30000 + 40% of 17000

Total income tax = 6000 + 6800 = 12800

hence,  The total income tax imposed on $47,000 is $12,800.

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The correct solution of the expression 3/4 ( 6x - 4) = 1/2 (x + 4) with the property that justify each step is shown below.

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

Given that;

The expression is,

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

Now, Solve the expression as;

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

⇒ 9/2x - 3 = 1/2x + 2                        By Distributive property

⇒ 9/2x - 3 - 1/2x = 1/2x + 2 - 1/2x     Subtraction property of equality

⇒ (9/2 - 1/2)x - 3 = 2                        Combine like terms

⇒ 4x - 3 = 2                                     Subtraction property

⇒ 4x - 3 + 3 = 2 + 3                         Addition property of equality

⇒ 4x = 5

⇒ 1/4 × 4x = 1/4 × 5                          Multiplication property of equality

⇒ x = 5/4

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Answer:

45c-20c²

Step-by-step explanation:

You just multiply the number outside the bracets with the numbers inside.

5c×9= 45c

5c×-4c= -20c²

So the answer is 45c-20c²

Which is option 'B'

Option A is appropriate since the table's function is linear.

The equals sign is used in equations to indicate the equality of two expressions in a formula. The expressions relate two or more variables with each other.

Given that:

x = 2 and y =4

x= 4 and y= 8 and so on.

In all the values given, the value of y is two times the value of x.

Also, these values satisfy the condition of linear expression:

y=mx

where, m =2 for the represented value.

This means that the function is linearly dependent on x.

The function shown in the table is linear.

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Answer:

13

Step-by-step explanation:

the using the Pythagorean Theorem A^2+b^2=c^2

5^2 is 25

12^2 is 144

add 144+25=169 then you square root this and it should be 13

Answer:

a. the 2% commission he receives

b. $138

c. He must make $47,500 in sales

Step-by-step explanation:

a. No work needed

b. E= 0.02 (4,400) +50, which simplifies to E= 88+50 which continues to 138 dollars

c. To find this you already know E, so you can work backwards

1,000= 0.02 (x) + 50

then subtract 50 from each side

950 = 0.02 (x)

then divide both sides by the 0.02 to get X alone

47,500 = X

From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.

Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate.

Let x and y be proportional relation

=> x ∝ y

=> x = ky    

=> x/y = k    [ where 'k' proportionality constant ]

Here we have

Table 1

x   2   3   4    5  

y   7   9   11   13    

=>  [tex]\frac{x}{y} = \frac{3}{7} = \frac{3}{9}[/tex]    [ which is not true ]

Hence,

Table 1 not shows any proportional relationship between x and y

Table 2

x  3   7.5  15  25

y  1    2.5  4    6    

=>  [tex]\frac{x}{y} = \frac{3}{1} = \frac{7.5}{2.5} = 3[/tex]  [ which is true ]

Hence, Table 2, shows a proportional relationship between x and y

Table 3

x   1      2     7     8

y  0.5    1    3.5   4    

=> [tex]\frac{x}{y} = \frac{1}{0.5} = \frac{2}{1} = 2[/tex]  [ Which is true ]

Hence, Table 3 shows a proportional relationship between x and y

Table 4

x    3    6    8   10  

y    12   15  18  20  

=> [tex]\frac{x}{y} = \frac{3}{12} = \frac{6}{15}[/tex]   [ Which is not true ]  

Hence, Table 4 not shows a proportional relationship between x and y

Therefore,

From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.

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Answer: The graph represents the solution to the following sentence is the option number 3:

-3 -2 -1 0 1 2 3 4 5

This is because the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2. The graph shows all the values of x that are greater than 4 and all values of x that are less than -2. The graph also includes the values of x between -3 and 5, it encompasses all the values that are greater than 4 and all values that are less than -2.

The graph represents the solution to the following sentence is (C).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

{x | x >4 } ∪ {x | x < -2}

Here the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2.

The graph displays all instances of x larger than 4 and all instances of x less than -2.

The graph covers all x values higher than or equal to 4, as well as all x values less than or equal to -2.

It also includes x values between -3 and 5.

Thus, the number line is C.

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The interval over which h(t) has a negative rate of change is given as follows:

(-∞, -3).

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

The equation for this problem is given as follows:

h(t) = (t + 3)² + 5.

The leading coefficient is positive, hence the function is concave up.

Considering the t-coordinate of t = -3 at the vertex, the decreasing and increasing intervals are given as follows:

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Of those who were not happy with their purchase, about 20% purchased model A, and about 36% purchased model B.

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Answer:

We can start solving this problem by using a system of linear equations. Let x be the number of gallons of the 20% pure slime mixture and y be the number of gallons of the 80% pure slime mixture. We know the following:

The total amount of slime mixture is 1000 gallons. This means that x + y = 1000.

The final mixture is 65% pure slime, which means that 0.65 = (0.20)x + (0.80)y. This is because we are mixing 20% pure slime and 80% pure slime to get the final mixture.

We can use these two equations to solve for x, which is the number of gallons of the 20% pure slime mixture needed.

First, we'll use the first equation to solve for y in terms of x:

y = 1000 - x

Then we'll substitute this expression into the second equation:

0.65 = (0.20)x + (0.80)(1000 - x)

Simplifying we get:

0.65 = 0.20x + 800 - 0.80x

0.45x = 200

x = 200/0.45

x = 444.44 gallons

So, you would need 444.44 gallons of the 20% pure slime mixture to make 1000 gallons of a 65% pure slime mixture.

Step-by-step explanation:

For expression 4x=8x-1, x will be 1/4.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

As given expression is 4x=8x-1

8x-4x=1

4x=1

x=1/4

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On solving the provided question, we can say that from the given graph, it is shown that it is a starlight line so the equation that represents is x = y => x-y = 0

Mathematicians use graphs to logically convey facts or values using the visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here, from the given graph

it is shown that it is a starlight line

so the equation that represents is x = y

x-y = 0

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Since this system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w, the three statements which must be true about their heights include all of the following:

A. Darius is at least 36 inches tall.

C. William’s height is less than 68 inches.

F. Darius is no more than 4 inches taller than twice William’s height.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the possible heights, in inches, for Darius and Williams, and then translate the word problem into algebraic equation as follows:

Next, we would interpret the given system of linear inequalities as follows;

d ≥ 36 ⇒ "Darius is at least 36 inches tall." because of the greater than or equal to (≥) inequality symbol.

w < 68 ⇒ "William’s height is less than 68 inches." because of the less than (<) to inequality symbol.

Additionally, d ≤ 4 + 2w ⇒ "Darius is no more than 4 inches taller than twice William’s height." because of the less than or equal to (≤) inequality symbol.

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Answer :-77. ✅

Step-by-step explanation:

To find the quotient of -231 and 3, we divide -231 by 3.

-231 ÷ 3 = -77

The quotient of -231 and 3 is ✅

In the circle the area of the shaded region and the length of arc ADB is 23/4 π and 23/6 π respectively.

What is length of arc?

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Given that the circle has a center O.

The radius of the circle is 3 yd.

The measure of ∠AOB is 130°.

First find the measure of ∠ADB -

∠ADB = 360° - ∠AOB

Substituting the values in the equation -

∠ADB = 360° - 130°

∠ADB = 230°

Now find the area of the shaded region.

The area of the shaded region can be determined using the formula -

A = (θ/360)πr²

Substituting the values in the equation -

A = (230/360) π(3)²

A = (230/360) π 9

A = 23/4 π or 5.75 π

Therefore, the area of the shaded region is 5.75 π yd².

Now, find the length of the arc ADB.

The length of arc ADB can be determined using the formula -

Arc Length = (θ/360)2πr

Arc Length = (230/360)2π3

Arc Length = 23/6 π or 3.83 π

Therefore, the length of arc is 3.83 π yd.

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The number of elements in [tex]A^c[/tex] is zero.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, and the complement of sets.

We have,

U = universal set

This includes all values.

[tex]A^c[/tex] = complement of set A.

This means,

All the elements of U except the elements of A.

[tex]A^c[/tex] = U - A

Now,

If A = U,

[tex]A^c[/tex] = U - U = 0

Thus,

There are no elements in [tex]A^c[/tex].

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