75°
64°
2
The measure of the exterior angle of the triangle is

The main features that can be easily seen then a quadratic function is given are parabola, axis of symmetry, a maximum OR minimum value, and an y-intercept of the graph.

A quadratic function is in the form ax²+bx+c=y where a, b and c are real integers.

How to find the features of a quadratic equation?

Every quadratic equation has the following features:

When the quadratic function is graphed, it will enable us to find the other features of the function when these are identified.

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Answer:

d = 24

Step-by-step explanation:

[tex] \rm \implies - \dfrac{2}{3} d - \dfrac{1}{4} d = - 22 \\ \\ \rm \implies - \frac{2}{3} d \times \frac{4}{4} - \frac{1}{4} d \times \frac{3}{3} = - 22 \\ \\ \rm \implies - \frac{8}{12} d - \frac{3}{12} d = - 22 \\ \\ \rm \implies \frac{ - 8d - 3d}{12} = - 22 \\ \\ \rm \implies \cancel{- } \frac{11}{12} d = \cancel{-} 22 \\ \\ \rm \implies d = 22 \times \frac{12}{11} \\ \\ \rm \implies d= 2 \times 12 \\ \\ \rm \implies d= 24[/tex]

The required solution is 0.02 to the given numerical expression [1/(9-2)]².

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings.

For example 4/2 = 2

The numerical expression is given in the question as:

⇒ [1/(9-2)]²

We have to determine the solution to the given expression

As per the question,

⇒[1/(9-2)]²

⇒[1/7]²

⇒1/49

Apply the division operation to get the solution

⇒0.02040

Rounded to the nearest hundredth

⇒0.02

Thus, the required solution is 0.02 to the given numerical expression.

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The length of the rectangle-shaped classroom is 15 meters.

We have a classroom. The shape of the classroom is rectangular. The length of the classroom is 3 meters more as compared to its width. The area of the rectangular classroom is 180 square meters. We need to find the length of the classroom.

Let the width of the rectangle be represented by the variable "x". The length of the rectangle is "x + 3". We will use the formula for the area of a rectangle. The area of a rectangle is the product of its length and width.

A = x*(x + 3)

180 = x² + 3x

x² + 3x - 180 = 0

We will use the quadratic formula to solve for the values of "x".

x = [-3 ± √(3² - 4(1)(-180))]/2(1)

x = [-3 ± √(9 + 720)]/2

x = [-3 ± √729]/2

x = [-3 ± 27]/2

The values of the variable "x" are -15 and 12. The negative value is rejected because the measure of a dimension cannot be negative. Hence, the value of "x" is 12. The length of the rectangular classroom is x + 3 = 12 + 3 = 15 meters.

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Answer:

  3, 4, 5

Step-by-step explanation:

You have parallel lines crossed by a transversal, and one obtuse angle marked as 99°. You want the angle designators of the congruent angles.

Where a transversal crosses parallel lines, corresponding angles are congruent. In this figure, angle 3 corresponds to the one marked 99°, so it is congruent.

Anywhere that lines cross, vertical angles are congruent. Angles 3 and 4 are vertical angles, as are angle 5 and the one marked 99°.

Hence angles 3, 4, 5 are all congruent to the one marked 99°.

__

Additional comment

You may have observed that the listed congruent angles are all of the obtuse angles in the figure. Similarly, all acute angles in the figure are congruent. Since the acute and obtuse angles are supplementary (form linear pairs), angles 1, 2, 6, 7 are all 81°.

Ooo this is like a riddle. Let me attempt to answer:

Let's start with one of the brothers. That's 1 child. There has to be 1 more brother for each brother to have one other brothers. Then for that brother to have two sisters, they have to have two girls. This is 4 children.

Now from a girl's perspective. You are a girl so you are already 1 child. To have one brothers, there has to be 1 boy. Then to have two sisters, there has to be two additional girls. That's 3 girls and one boy - which are still 4 children in all.

Of course two parents are two parents for all.

The fewest number of children the parents have is 4

I hope this helps!

Aria's vertical distance from the top of the valley after walking 3 km along the trail is less than 3 km.

Since Here d represents distance along the trail.

And, V(d) represents the vertical distance from the top of the valley (in kilometers) after walking d kilometers along the trail.

If the distance along the trial is 3 km.

That is, d = 3

Then the vertical distance she walked from the top of the valley = V(3)

But According to the question,

V(3) < 3

Her vertical distance from the top of the valley after walking 3 km along the trail is less than 3 km.

Hence, For going 3 km along the trail her vertical distance from the top of the valley is less than 3.

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Step-by-step explanation:

v+27°+4v+39+11v=180°

v+4v+11v+27°+39°=180°

16v+66=180°

16v=180°-66

16v=114

16v÷16=114÷16

v=7.125

The options given in the question are wrong. The correct answer should be 25

The value of x is 25

(x-7)2 = 36

x-7 = 36/2

x-7 = 18

x = 18+7

x = 25

We can solve the linear equation in one variable by moving the variables to one side of the equation, and the numeric part on the other side of the equation. For example, x - 1 = 5 - 2x can be solved by moving the numeric parts on the right-hand side of the equation which is summed up to be 6, while keeping the variables on the left side which sums up to be 3x. Hence, we get x + 2x = 5 + 1. Thus, 3x = 6. This gives x = 2.

Similarly, we got the value of x which is 25.

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Answer:

ac + ad + bc + ad

Step-by-step explanation:

We are going to be using the FOIL (First, Outer, Inner, Last) method.

If we use this, we end up with:

ac + ad + bc + ad

Answer:

she can just copy and paste by holding right click and dragging across all of document A and hit ctrl c then ctrl v at the bottom of document B

The numbers has been plotted on the number line and the order of the numbers from least to greatest is -28 < -25 < -22 < -21

The given numbers are

-22, -28, -21  and -25

The inequality is the mathematical statement that shows the relationship between one expression and another expression with inequality sign. The inequalities maybe less than, less than or equal, greater than, greater than or equal . The equal sign will not be a part of inequality

The numbers are

-22, -28, -21  and -25

Plot the numbers in the number line

The order of the numbers from least to greatest is -28 < -25 < -22 < -21

Hence, the numbers has been plotted on the number line and the order of the numbers from least to greatest is -28 < -25 < -22 < -21

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Inez had won the race.

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).

Thus, Inez had won the race.

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Answer:

2/9 of the bleachers are rooting for the home team!

Answer:

f(-2)= -2

f(-0.75)= -1

f(1)= 1

Answer:The value of cos 60 degrees can be calculated by constructing an angle of 60° with the x-axis.

Step-by-step explanation:

Then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle.
The value of cos 60° is equal to the x-coordinate (0.5).
     ∴ cos 60° = 0.5.

The value of cos 60° using trigonometric ratio  is 1/2 or 0.5 .

What is trigonometric ratios?

There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here , the given is ,

=> cos60°

Since the cosine function is a periodic function, we can represent cos 60° as, cos 60 degrees = cos(60° + n × 360°),

Then

=> Cos 60° = 1/2 = 0.5.

Hence the value of cos 60° is 1/2 or 0.5.

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The probability that the song that was picked was one she liked or one she has not heard but did not enjoy is 17/22.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Total number of songs = 22

Probability of liked song  = 10/22

The probability of she has not heard but did not enjoy =  7/22

The probability that the song that was picked was one she liked or one she has not heard but did not enjoy:

= 10/22 + 7/22

= 17/22

Thus, the probability that the song that was picked was one she liked or one she has not heard but did not enjoy is 17/22.

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The weight of each small box is 25 pounds while the weight of each large box is 45 pounds

We know that we can be able to find the mass of each type of box from the use of simultaneous equations. Al we need to do is to form two systems of equations. Let the weight of each small box be x and the weight of each large box be y then;

x + y = 70 ------ (1)

50x + 70y = 4000 ----- (2)

x = 70 - y ------ (3)

Substitute equation (3) into (2)

Then;

50(70 - y) + 70y = 4000

3500 - 50y + 70y = 4000

20y = 4000 - 3500

20 y = 500

y= 25

Then substitute y = 25 into equation (1)

x + 25 = 70

x = 70 - 25

x = 45

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The result of the expression [tex]a^2bc[/tex] when a =3, b= -14 and c = -6 is 756

The expression is

[tex]a^2bc[/tex]

The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operator are addition, subtraction, division and multiplication. The equal sign or inequality signs will not be a part of expression

The expression is

[tex]a^2bc[/tex]

The value of a = 3

The value of b = -14

The value of c = -6

Substitute the values in the expression

[tex]a^2bc[/tex] = [tex]3^2[/tex] × -14 × -6

= 9 × -14 × -6

= 756

Hence, the result of the expression [tex]a^2bc[/tex] when a =3, b= -14 and c = -6 is 756

The complete question is:

Evaluate [tex]a^2bc[/tex] if a=3, b=-14 and c=-6

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Using mathematical operations, we know that the store can sell its drinks in a total of 112 ways.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, all the possible ways in which a customer can order a drink:
We know that:

This store sells 4 drinks.

The store has 4 different sizes of drinks.

The store sells 7 flavors.

Then, the total ways will be:

4 × 4 × 7

112

Therefore, using mathematical operations, we know that the store can sell its drinks in a total of 112 ways.

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The solution to the system of linear equations u = v and 4u = 2v - 12 is (-6, -6)

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

u = v and 4u = 2v - 12

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (-6, -6)

Hence, the solution is (-6, -6)

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Answer:

y = 0.54, x = 4.51

For the image 1, the angular values are x=9⁰ and y=23⁰

For the image 2, the angular values are x=9⁰ and y=14⁰

An angle is a figure in Euclidean geometry made up of two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. Dihedral angles are what they are. A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. A geometric angle's arc is centered at the vertex and is bound by its sides.

For the first image x and y values are,

As from the given figure,

(4y-2)⁰=90⁰

4y=90+2

y=92/4

y=23⁰

3x-6=21⁰

3x=27

x=9⁰

Therefore, x=9⁰ and y=23⁰

For the second image x and y values are,

2x+27=90/2

2x+27=45

2x=18

x=9⁰

4y-19=y+23

3y=42

y=14⁰

Therefore, x=9⁰ and y=14⁰

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1) The interest that will accumulate for Marlie during the 4.5-year non-payment period is $3,629.34.

2a) The new principal when Marlie begins making loan payments will be $22,429.34.

2b) Marlie will pay an additional $9,622.19 in interest for 10 years, including the 4.5-year period interest of $3,629.34 to make a total of $13,251.53.

3. If Marlie paid interest during the 4.5-year period, the total interest she will pay, thereafter, is $8,065.20.

4. Marlie's only interest payment due on January 1 is $67.21.

5a) With a private loan at 7.8% APR, Marlie's monthly payment is $226.11.

5b) The total amount Marlie will pay back with a private loan at 7.8% APR is $27,133.67.

5c) Based on a private loan, Marlie's total interest is $8,333.67.

The interest on federal student loans is based on simple interest, unlike the interest on private loans, which is compounded.

We can compute simple interest using the simple interest formula (PRT/100) and compounded interest using an online finance calculator.

Student loan amount = $18,800

Interest rate = 4.29%

Non-payment period = 4.5 years

Loan repayment period = 10 years

Interest for the 4.5-year non-payment period = $3,629.34 ($18,800 x 4.29% x 4.5 years)

New Principal after 4.5 years = $22,429.34 ($18,800 + $3,629.34)

Additional interest on the loan after 4.5 years = $9,622.19 ($22,429.34 x 4.29% x 10 years).

Total interest = $13,251.53 ($9,622.19 + $3,629.34)

Interest for 10 years on principal = $8,065.20 ($18,800 x 4.29% x 10 years).

Only Interest monthly payment = $67.21 ($18,800 x 4.29% x 1/12)

N (# of periods) = 120 months (10 years x 12)

I/Y (Interest per year) = 7.8%

PV (Present Value) = $18,800

FV (Future Value) = $0

Results:

Monthly payments (PMT) = $226.11

Sum of all periodic payments = $27,133.67

Total Interest = $8,333.67

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The velocity of the object is 108.8 m/s and the object will take 0.45 seconds to fall 50 feet.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

The time = 3.4 seconds

There is no air resistance.

v = 32t

v = 32(3.4)

v = 108.8 m/s

T = D/S = 50/108.8 = 0.45 seconds

Thus, the velocity of the object is 108.8 m/s and the object will take 0.45 seconds to fall 50 feet.

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For the given function, f(x)=(3.25)^x+6 As x decreases without bound, f(x) increases without bound

To describe the end behaviors of the function modeled by the graph,

f(x)=(3.25)^x+6

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,

The function given is,

f(x)=(3.25)^x+6

Given function contains equality so the function has no boundaries and the function is described from negative infinity to positive infinity, But the function has inverse behavior as when x is negative the function is positive.

Thus, for the given function, f(x)=(3.25)^x+6 asAs x decreases without bound, f(x) increases without bound

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Using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.

A mathematical function known as an "operation" in mathematics is one that converts zero or more input values into a precisely specified output value.

The quantity of operands has an impact on the operation's complexity.

Exponents, PEMDAS, parenthesis, multiplication, and division.

So, to check whether Brandi's answer is correct:

1621/4 = 404

So, to check it is ts correct, multiply 404 by 4.

If the answer is correct, then the product will be 1621.

If the answer is wrong, the product will not be 1621.

Calculate as follows:

404 × 4  = 1,616

Therefore, using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.

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