Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

Dante deposited $5,000 into an account with an annual interest rate of

3.5%. He plans to deposit an additional $200 each year, just after the

interest is compounded. His balance will be $9,838.44 after 16 years.

It displays the actual percentage rate of interest owed on any outstanding debts, including credit card debt and loans.

Because it takes compounding effects into account, the effective annual interest rate is the real interest rate on an investment or loan. The rate increases as the compounding periods get more frequent. Advertisements for loans or savings accounts may include both the nominal interest rate and the effective yearly interest rate. The rate that should be used to compare loan and investment rates of return is the effective annual interest rate.

We can substitute the known values into the formula and calculate the final balance:

A = $5,000 (1 + 0.035)¹⁶

We can calculate the final balance by using a calculator, or we can use the formula of compound interest:

A = P(1 + r/n)ˣ

where, A= Amount

P= Principle($5,000 )

x= Time(16 years)

n= Rate(3.5%)

A = $5,000 (1 + 0.035/1)¹⁶

Now we can add the $200 deposit each year for 16 years:

A = $5,000 (1 + 0.035)¹⁶ + $200 × 16

A = $9,838.44

Dante's balance will be $9,838

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Answer: Mei had $21.25

Step-by-step explanation: if you add $12 to $9.25 you get $21.25

Answer:

The money she had in the beginning was $21.25

Step-by-step explanation:

Given ,

The cost of the ticket Mei spent = $12.00

Money remaining = $9.25

To Find : The Money she had in the beginning

When we add the given values we get the money she had in the beginning

which is,

Amount = Amount Spent on a Ticket + Money Remaining

Amount = [tex]$12.00 + 9.25[/tex]

Amount = [tex]21.25[/tex]

Hence ,  the amount she had in the beginning was $21.25

The area of the triangle is 42 cm².

To calculate the area of a triangle, we need to use the formula:

Area = (base x height) ÷ 2

Therefore, the area of a triangle with a base of 7 cm and a height of 12 cm is:

Area = (7 cm x 12 cm) ÷ 2

Area = 42 cm²

The area of a triangle with a base of 7 cm and a height of 12 cm is 42 cm². This can be calculated by using the formula: Area = (base x height) ÷ 2. The base and the height of the triangle are multiplied together and then divided by two to get the area. Therefore, the area of the triangle is 42 cm².

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The magic ratio for muffins in 2:2:1:1.

The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!

Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.

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Answer:

No

Step-by-step explanation:

For the passenger to be correct, the two ratios should equal each other.

[tex]\frac{156}{34}[/tex] = [tex]\frac{39}{9}[/tex]  Multiply both sides by 34 and 9

[tex]\frac{(34)(9)}{1}[/tex] x [tex]\frac{156}{34}[/tex] = [tex]\frac{(34)(9)}{1}[/tex] x [tex]\frac{39}{9}[/tex]  On the left side of the equation, the 34's cancel each other out.  On the right side of the equation, the 9's cancel out.  That leaves us with:

(9)(156) = (340)(39)

1404 = 13260

These numbers do not equal each other so the ratios are not equal.

The expression 70x-40x^4 if  factor is:-10x (4x^3-7).

Expressions  can be defined as equation that has both number that are known as well as numbers that are not known .

Example of expression is the sum of 9 and 1  will gives us 10  which is calculated as (9+1 =10).

Given data:

Expression: 70x-40x^4

Now let factor the expression using the given expression

70x-40x^4

Rearrange the expression

-40x^4 +70x

Common factor

-10(4x^4 -7x)

So the expression is:

-10x (4x^3-7)

Therefore we can conclude that the expression is -10x (4x^3-7).

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The 3 cans of peas cost 39 = $27

The 5 bags of flour cost 515 = $75

The 7 packs of milk cost 7*12.50 = $87.50

The total cost of all the items is 27+75+87.50 = $189.50

To calculate the change she received, you subtract the total cost from the amount she had:

change = 200 - 189.50 = $10.50

So Alicia received $10.50 change.

The average rate of change of f(x) over -6≤x-4 is -70.

The average rate of change of g(x) over -6≤x-4 is -140.

The average rate of change of g(x) is 2 times that of f(x)

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 7x², g(x) = 7x² and  x₁ = -6, x₂ = -4

For f(x) = 7x²:

average rate of change =  ([7(-4)²] - [7(-6)²]) / (-4-(-6))

                                       = (112-252)/2

                                      = -70

For g(x) = 14x²:

average rate of change =  ([14(-4)²] - [14(-6)²]) / (-4-(-6))

                                       = (224-504)/2

                                      = -140

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Answer: false

Step-by-step explanation:

False

Answer:

cubic polynomial

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 2 and 3

2 + 3 < 7

5 > 7

Now we add 2 and 7

2 + 7 > 3

9 > 3

Now we add 3 and 7

7 + 3 > 2

10 > 2

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

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Answer:

  ∠MAR = 28

Step-by-step explanation:

Given angle MAR bisected by ray AT to form angle MAT = (6x-4) and RAT = (2x+8), you want to know the measure of MAR.

An angle bisector divides an angle into two congruent parts:

  ∠MAT = ∠RAT

  6x -4 = 2x +8

  4x = 12 . . . . . . . . add 4-2x

  x = 3 . . . . . . . divide by 4

Then the measure of one of the halves is ...

  ∠RAT = 2x +8 = 2·3 +8 = 14

So, the measure of the whole is ...

  ∠MAR = 2·14

  ∠MAR = 28

Answer:

3 seconds?

Step-by-step explanation:

I mean he throws it up at x= 0 and it drops at x=3 So technically it must be 3?

This seems too simple, but see if it is correct.

The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them.

This is usually expressed as:

The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them. This means that if one expression is equal to another, then the same value can be swapped in for any of the variables within them and the equality will still hold.

For example, if we have the equation 4x + 7 = 11, then we can swap in any value for x and the equation will still be true. This is because the substitution property allows us to make a substitution for any of the variables and the equation will remain true.

This property is useful in solving equations and is a key part of algebra.

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Answer: 37-12=25

25 divided by 5 = 5 so you can figure it out

On solving the provided question, we can say that by trigonometry so sin 90 = p/h => y = 19

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures

here,

it is a right angled triangle

by trigonometry

so sin 90 = p/h

1 = 19/y

y = 19

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The Mixed number is -6 1/6, an integer is -6.16, proper fraction is -13/6

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The factoring of the polynomial x^4+4x^3+7x^2+16x+12 = 0, considering it's linear factors, is given as follows:

(x² + 5.4x + 11.29)(x + 1)(x + 3).

The polynomial for this problem is defined as follows:

x^4+4x^3+7x^2+16x+12 = 0.

We want to factor the polynomial according to it's linear factors, hence the Factor Theorem is used.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

The coefficients of the polynomial in this problem are given as follows:

a = 1, b = 4, c = 7, d = 16, e = 12.

Inserting these coefficients into a 4th degree equation solver, the roots are given as follows:

Hence the polynomial is factored as follows:

(x + 2.7 - 2i)(x + 2.7 + 2i)(x + 1)(x + 3).

Applying the subtraction of perfect squares for the first two linear factors, considering that i² = -1, we have that:

(x + 2.7 - 2i)(x + 2.7 + 2i) = (x + 2.7)² - (2i)²

(x + 2.7 - 2i)(x + 2.7 + 2i) = (x² + 5.4x + 11.29).

Hence the factored polynomial is of:

(x² + 5.4x + 11.29)(x + 1)(x + 3).

The problems asks to factor the polynomial according to it's linear factors.

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Answer：[tex]2\sqrt34+12[/tex]

Step-by-step explanation:Draw a planar Cartesian coordinate system and that's it

The distance flown by the plane East of the starting point is (60 minutes * 500 km/h * cos(120°))/60 minutes/hour = 250 * cos(120°) km.

What is the Pythagorean theorem in plain English?

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The distance flown by the plane South of the starting point is (60 minutes * 500 km/h * sin(120°))/60 minutes/hour = 250 * sin(120°) km.

To find the distance of the plane from the starting point, we need to use the Pythagorean theorem.

The distance would be √((250 * cos(120°))^2 + (250 * sin(120°))^2) = √(62,500 + 62,500) = √125,000 = approximately 111.8 km

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The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).

Estimate the level of DVD sales for movies, by using the amount of annual revenue  generated by the box office gross

We randomly selected a sample of 43 movies for the same year.

Excel  α = 0.05,  r^2 = 0.5123

=51.23%

51.23% of the DVD sales variation is explained by annual revenue.

SY.X = 12.2279.

Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.

b. The hypothesis being tested is:

Null Hypothesis, H0: β1 = 0

Alternative Hypothesis, H1: β1 ≠ 0

The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07

The F-critical value is 4.0785.

Since 43.07 > 4.0785, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.

c. y = bo + b1*x

y = 4.8445 + 0.1631*x

Put x = 100

y = 4.8445 + 0.1631*100 = 21.1545

The 95% confidence interval for the given value of x is:

= y ± t*s*[tex]\sqrt{0.026249}[/tex]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{0.026249}[/tex]

= (17.1536, 25.1554)

d.  The 95% prediction interval for the given value of x is:

= y ± t×s×[tex]\sqrt{}[/tex]1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{1 + 0.026249}[/tex]

= (-3.8623, 46.1713)

Therefore, the value is (-3.8623, 46.1713).

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Answer:

all i could do was simplify it

Step-by-step explanation:

For the shape to be a quadrilateral, then the measure of angle k must 128 degrees

For quadrilateral PQRS to be an actual quadrilateral, then:

J+M=180 implies that:

2x+9+6x-1=180

Collect like terms:

2x+6x=180-9+1

8x=172

Divide both sides by 8

x=21.5

We have:

K=M

This becomes

K=6x-1

Substitute 21.5 for x

K=6*21.5-1

K=129-1

Subtract 1 from 129

K=128

Hence, the measure of angle K must be 128 degrees

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Answer:

x = 16

Step-by-step explanation:

[tex]\frac{8+x}{24+x}=\frac{3}{5}\\ \\ 5(8+x)=3(24+x)\\\\40+5x=72+3x\\\\5x=32+3x\\\\2x=32\\\\x=16[/tex]

The domain of the modulus function is the set of all real numbers. The range of the modulus function is the set of non-negative real numbers.

The modulus function, also known as the absolute value function, is a function that takes any real number as input and returns its distance from zero on the number line.

In mathematical notation, the modulus function can be represented as |x|, where x is the input.

For example, if x = -3, then |x| = 3, and if x = 5, then |x| = 5.

In class 11, the domain of the modulus function is all real numbers, which is represented by (-∞, +∞) and the range is non-negative real numbers represented by [0, +∞)

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The number of aerobics classes that will cost the same for members and non-members is 5 classes.

The linear equation that represents the amount paid by members is:

membership fee + (amount per class x number of classes)

= $10 + ($3 x m)

= $10 + $3m

The linear equation that represents the amount paid by no-members is: (amount per class x number of classes)

$5 x m

= $5m

When the two costs are the same, the two equations would be equal:

$5m = $10 + $3m

$5 - $3m = $10

$2m = $10

m = $10 / $2

m = 5

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Answer:

Step-by-step explanation:

The solution to the following linear equation problem can be seen in the graph showing how the width and diameter of one face are linearly related.

In a linear model, one level is the maximum amount of levels that may be used. Any equation that has a theoretical extension of at least two is said to be nonlinear. There is a straight line on a map with a simple equation. A nonlinear equation's curve is depicted on the graph.

Here,

one face's perimeter and side lengths are linearly related.

line-drawing formula.

The formula y = mx + b can be used to describe a regular model.

If m is the rising rate and b is in reality the y intercept, then x and y are variables.

The graph shows a linear relationship between the length and perimeter of one face.

Therefore, the graph showing how the perimeter or edge length of one face are linearly connected is the solution to the provided linear equation problem.

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Answer: 23

Step-by-step explanation: Both triangles are the same in measurements so whatever number - 4 that equals 19 is the answer. 23-4=19

The line TU is parallel to QR and SQR is dilated version of STU by a scale factor of 4.

What is midpoint theorem?

The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Through the diagram it can be seen that T and U are midpoints of SQ and SR respectively.

And it can also be seen that TU is parallel to QR.

It is given that ST = 2, TQ = 6, SU = 3 and UR = 9

The length of side SQ -

SQ = ST + TQ

SQ = 2+6

SQ = 8

The length of side SR -

SR = SU + UR

SR = 3+9

SR = 12

The measurement of QR = SQ as seen in the diagram.

According to midpoint theorem the mid points line segment TU measures half of its parallel third side of triangle QR.

Now, to find the scale factor -

= QR - TU

= 8 - 4

= 4

Therefore, the scale factor is 2.

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