One angle measures 160°, and another angle measures (3k + 61)°. If the angles are vertical angles, determine the value of k.


k = 14

k = 33

k = 74

k = 160

She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

From given question :

-5x-3.5>6.5

-5x > 10

X > -50

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

- 5x - 3.5 + 3.5 > 6.5 + 3.5

- 5x > 10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

- 5x / -5 < - 50 / -5

we get

x < 10

so,

She should divide both sides by -5 while she multiplied by -5 on other side

and she also did not change the > symbol to a < symbol

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[tex]x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9[/tex]

Using these points, the correct graph is shown in option C.

Answer:

Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.

Step-by-step explanation:

What was the tax rate in 1913?

The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.

The graph that shows the straight line → x - 5y = 27 is plotted and attached.

The general equation of a straight line is -

y = mx + c

where -

[m] is slope of the line.

[c] is the y - intercept of the line.

Given is the equation of the line as -

x - 5y = 27

The given equation of the line is -

x - 5y = 27

Rearranging the equation, we get -

5y = x - 27

y = (1/5)x - (27/5)

y = 0.2x - 5.4

Now, refer to the graph attached. The slope [m] of the equation will be -

m = 0.2 and the [y] - intercept will be y = - 5.4.

Therefore, the graph that shows the linear relation → y = 0.2x - 5.4 is plotted and attached.

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Answer:

y = (2 + √2)/4   ;   y = (2 - √2)/4

Step-by-step explanation:

-8y² + 8y - 1 = 0

8y² - 8y + 1 = 0

discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2

y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16

(8 + 2²√2)/16

(8 + 4 √2) / 16

4(2+√2)/16

(2+√2)/4

y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16

(8 - 4√2) / 16

4(2-√2)/16

(2-√2)/4

The linear functions in this problem are given as follows:

1. y = 1/3x + 3.

2. y = 2.

3. y = 3x - 1.

4. x = 1.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

For item 1, the points are given as follows:

(-6, 1) and (-3,2).

When x increases by 3, increases by 1, hence the slope is given as follows:

m = 1/3.

Then:

y = 1/3x + b.

When x = -3, y = 2, then the intercept b is calculated as follows:

2 = 1/3(-3) + b

b = 3.

Thus the function is:

y = 1/3x + 3.

Then items 2 and 4 are given as follows:

For item 3, we have an intercept of -1, hence:

y = mx - 1.

When x = 3, y = 8, hence the slope m is calculated as follows:

8 = 3m - 1

3m = 9

m = 3.

Hence the function is:

y = 3x - 1.

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The months when the temperature will be 0 °C are May and August.

A trigonometric function is a function that has the trigonometric ratios.

Temperature is the degree of hotness or coldess of a body.

Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.

To find the number of months in which the temperature would be 0°C. This means T(m) = 0.

So,  T(m) = 10cos(πm/6) + 5

0 = 10cos(πm/6) + 5

-10cos(πm/6) = 5

cos(πm/6) = 5/10

cos(πm/6) = -0.5

cos⁻¹cos(πm/6) = cos⁻¹(-0.5)

(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)

πm/6 = 5π/6 or πm/6 = 8π/6

⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π

⇒ m = 5 or m = 8

Since m = 5 is May and m = 8 is August,

The months when the temperature will be 0 °C are May and August.

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5.3

80/15=5.3

which means each person completed 5.3 puzzles

Answer:

See below   ( you have it correct !)

Step-by-step explanation:

See image below....sometimes it is easier to see these things if you extend some lines a bit:

Answer:

B

Step-by-step explanation:

5x + 30 - 18x - 18 = 10

-13x + 12 = 10

The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.

A mathematical statement that expresses the inequality between two inequalities combinedly.

from the graph, we have two inequalities, x>5 and x<6

it can be written as 5<x<6

A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.

The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}

The graph also refers the inequalities of x>5 And x<6

compound inequalities of domain 5<x<6

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The Area of the shaded part is 3.44 cm²

The formula used to find the Area of a circle is given by

Where r is the radius of the circle

The formula used to find the Area of a Square is given by

Here we know

The radius of the circle = 2m

As we know Area of a Circle = 2πr

=> Area of given circle = 2(3.14)2 = 12.56 cm²

Area of circle = 12.56 cm²

As we can see the circle is inscribed in a square

Then the Length of the side square = diameter of the circle

=> Length of side = 2 × Radius of circle = 2 × 2 cm = 4 cm

Length of side = 4 cm

As we know Area of the square = side²

=> Area of given square = 4 × 4 = 16 cm²

Now using the above value we will friend the area of the shaded part

Area of shaded part = Area of the square - Area of the circle

= 16 cm² - 12.56 cm² = 3.44 cm²

Therefore,

The Area of the shaded part is 3.44 cm²

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In the octagon, the measurement of the largest exterior angle is 90°.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly, which means numerous and gon, means sides.

The given exterior angles of the octagon are,

x°, 2x°, 3x°, 4x°, 5x°, 7x°, 8x°, and 10x°.

The sum of the exterior angle of the octagon is 360°.

Implies that,

x + 2x + 3x + 4x + 5x + 7x + 8x + 10x = 360

40x = 360

x = 9

The largest exterior angle = 10 x  = 10 × 9 = 90°.

The required largest exterior angle is 90°.

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On solving the given equation  y=(x-2)(x-4) the point on the graph are as follows:

(4,0), (2,0), (5,3), (3,-1) &(0,8)

What is a graph?

A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.

It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.

It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.

1)

let   y=0

0=(x-2)(x-4)

i.e. x = 4 and 2

2)

Let x =0

y=(0-2)(0-4)

y=8

3)

Let x = 3

y=(3-2)(3-4)

y=-1

4)

Let x = 5

y=(5-2)(5-4)

y=3

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Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:

1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:

Lemons = 10

Cups of water = 4

Tablespoons of honey = 4

2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:

Lemons = 2.5

Cups of water = 1

Tablespoons of honey = 1

3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:

Lemons = 4

Cups of water 1

Tablespoons of honey

4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:

Lemons = 6

Cups of water 3

Tablespoons of honey = 3

Lemons = 5

Cups of water = 2

Tablespoons of honey = 2

1) Using the multiplication operation to make more lemonade taste the same as the original:

Lemons = 10 (5 x 2)

Cups of water = 4 (2 x 2)

Tablespoons of honey = 4 (2 x 2)

2) Using the division operation to make less lemonade taste the same as the original recipe:

Lemons = 2.5 (5 ÷ 2)

Cups of water = 1 (2 ÷ 2)

Tablespoons of honey = 1 (2 ÷ 2)

3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:

Lemons = 4 (5 - 1)

Cups of water 1 (2 - 1)

Tablespoons of honey = 1 (2 - 1)

4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:

Lemons = 6 (5 + 1)

Cups of water 3 (2 + 1)

Tablespoons of honey = 3 (2 + 1)

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Answer:no

Step-by-step explanation:

There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.

Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.

So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.

Answer: 28 inches

Hope this helps!!! :)

Answer:

A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.

There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:

Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).

The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.

The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.

The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.

Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.

The equivalent equations of y - 4 = 2/3(x - 1) are y - 4 = 2/3x - 2/3 and y  = 2/3x + 10/3

From the question, we have the following parameters that can be used in our computation:

y - 4 = 2/3(x - 1)

We start by expanding the bracket

So, we have the following representation

y - 4 = 2/3x - 2/3

Next, we add 4 to both sides of the equation

This gives

y - 4 + 4 = 2/3x - 2/3 + 4

Evaluate the like terms

So, we have the following representation

y  = 2/3x + 10/3

Hence, the equivalent equation is y  = 2/3x + 10/3

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3x³ + 5x² - 17x - 15

1. Distribute

(x + 3)(3x² - 4x - 5)

x(3x² - 4x - 5) + 3(3x² - 4x - 5)

2. Distribute

x(3x² - 4x - 5) + 3 (3x² - 4x - 5)

3x³ - 4x² - 5x + 3 (3x² -4x - 5)

3. Distribute

3x³ - 4x² - 5x + 3 (3x² -4x - 5)

3x³ - 4x² -5x + 9x² - 12x - 15

4. Combine like terms

3x³ - 4x² -5x + 9x² - 12x - 15

3x³ + 5x² - 5x - 12x - 15

5. Combine like terms

3x³ + 5x² - 5x - 12x - 15

3x³ + 5x² - 17x - 15

3x³ + 5x² - 17x - 15

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Reciprocal of a = [tex]\frac{1}{a}[/tex]

What is Reciprocal ?

In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.

What are real numbers ?

In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .

According to the given information

a ≠ 0

a is a real number

By the definition of reciprocal

Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]

Reciprocal of a = [tex]\frac{1}{a}[/tex]

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It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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Answer:

$0.48/pound

Step-by-step explanation:

$5.76 divided by 12

The given statement:

"the sum of a number and 10.7 is at most −3.2"

Is equivalent to the following inequality:

x + 10.7 ≤ -3.2

Here we have the following statement:

"the sum of a number and 10.7 is at most −3.2"

So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2

In that case, the symbol we need to use is: ≤

Then the inequality is:

sum ≤ -3.2

x + 10.7 ≤ -3.2

That is the statement written as an inequality.

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The only option that is not an equivalent of the product of both polynomials is; C: 6x³ + 11x² − 13x + 2

Equations can be classified as either identities or conditioned equations. For each quantity of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equals sign ("="), which separates two expressions, is a symbol for an equation.

Here,

We are given the expression;

(3x - 2)(2x² + 5x - 1)

The result of expanding the polynomial is;

6x³ + 11x² − 13x + 2

Looking at the given options as seen online, the only one that is not an equivalent of the given product is;

Option C) : 6x³ + 11x² − 13x + 2 is correct

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Answer:

18.6

Step-by-step explanation:

The graph's representation of the inequality system is

y≤3x-2 and y≥-4x+2. So, option a is correct.

One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:

A less than sign, such as a, denotes that an is greater than b.

Therefore, The  system of inequalities that is represented by the graph is

y≤3x-2 and y≥-4x+2. So, option a is correct.

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Answer: 246.7

Step-by-step explanation:

(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.

(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

Let, Songs Downloaded be x

Total Charges of Company A = 15 + 0.75*x

Total Charges of Company B = 0.9*x

(i) Total Charges by Company A = Total Charges by Company B

15 + 0.75*x = 0.9*x

15 = 0.15*x

x = 100 songs

(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150

= 15 + 112.5 = $127.5

Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135

I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

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