Name the relationship: complementary, linear pair, vertical, alternate interior, corresponding, or
alternate exterior.

Answer:

2

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer:

Rotation it almost has Rotate in the word, Reflection is a mirror of itself, Translation is when the Object stays the same, But is moved

Step-by-step explanation:

Answer:

y = 2/3 x - 2

Step-by-step explanation:

The standard form of writing equation of a line is y = mx+b

m is the slope

b is the y-intercept

Given the following:

m = 2/3

b = -2

Substitute into the formula

y = mx+b

y = 2/3 x + (-2)

y = 2/3 x - 2

Hence the required equation is y = 2/3 x - 2

Answer:

Step-by-step explanation:

Hello,

\((1+1/3)^2-\dfrac{2}{9}=\left( \dfrac{3+1}{3}\right)^2-\dfrac{2}{9}\\\\=\dfrac{16}{9}-\dfrac{2}{9}\\\\=\dfrac{16-2}{9}\\\\=\boxed{\dfrac{14}{9}\\\\}\)

Thanks

Answer:

At this distance, Jupiter takes 11.8618 Earth years to complete a single orbit of the Sun. In other words, a single Jovian year lasts the equivalent of 4,332.59 Earth days.

Step-by-step explanation:

that the best i can do !!!!

Answer:

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

where r is the radius

From the question V = 1436 cm³

\(1436 = \frac{4}{3} \pi {r}^{3} \)

Multiply through by 3

We have

\(4308 = 4\pi {r}^{3} \)

Divide both sides by 4π

\( {r}^{3} = \frac{4308}{4\pi} \)

\( {r}^{ 3} = \frac{1077}{\pi} \)

Find the cube root of both sides

\(r = \sqrt[3]{ \frac{1077}{\pi} } \)

r = 6.99

We have the final answer as

Hope this helps

========================================

Explanation:

First factor out the GCF 7

7x^2 + 7x - 42

7*x^2 + 7*x + 7*(-6)

7(x^2 + x - 6)

Now focus on factoring x^2+x-6

We need to find two numbers that multiply to -6 and add to 1. Those values are 3 and -2. That means x^2+x-6 factors to (x+3)(x-2).

The 7(x^2 + x - 6) then turns into 7(x+3)(x-2)

The factor out front, the "7", is the integer factor. The other factors (x+3) and (x-2) are binomial factors.

7, (x + 3), and (x - 2) are the three factors of the given expression.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

We can factor out the common factor of 7 from the given expression to get:

\(7(x^2 + x - 6)\)

Now, we need to factor the quadratic expression x^2 + x - 6. We can do this by finding two numbers that multiply to -6 and add to 1 (the coefficient of x).

The two numbers are 3 and -2, since 3 x -2 = -6 and 3 + (-2) = 1.

So we can write \(x^2 + x - 6\) as (x + 3)(x - 2).

Substituting this back into the expression we have:

\(7(x + 3)(x - 2)\)

Therefore, the three factors are 7, (x + 3), and (x - 2).

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The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.

A system of linear equations consists of two or more equations and looks for common answers.

1. Let us suppose small prints = x

Large prints = y

Total prints sold can be written as follows:

x + y = 52

The total cost of the prints can be written as follows:

50x + 75y = 2975

The system of equations is:

x + y = 52   . . . equation 1

50x + 75y = 2975 . . .equation 2

Using equation 1 we have:

x = 52 - y

Substituting the value of x in equation 2 we have:

50(52 - y) + 75y = 2975

2600 - 50y + 75y = 2975

25y = 2975 - 2600

25y = 375

y = 15

Now, substituting the value of y in equation 1 we have:

x + 15 = 52

x = 52 - 15

x = 37

Hence, the solution of the system of equations is y = 15 and x = 37.

2. Let us suppose the altitude = x.

The rising balloon can be thus written as:

40 +10x

The descending balloon can be written as:

165 - 15x

Solving the system of equations by substituting the value of x we get x= 5.

Hence, the altitude at which both the balloons are at the same height is 5m.

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Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

what is inequality ?

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."

So, the inequality would be:

Temperature < 8 degrees Fahrenheit

Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

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Answer:

Step-by-step explanation:

1. From the given diagram,

AB = CD and AB||CD

So that,

<APE + <BPE = 180 (sum of angles on a straight line)

But, <BPE = 60

<APE + 60 = 180

<APE = 180 - 60

         = 120

<APE = \(120^{o}\)

⇒\(\frac{1}{2}\)<APE = \(\frac{1}{2}\) x \(120^{o}\)

              = \(60^{o}\)

Thus,

\(\frac{1}{2}\)<APE = \(60^{o}\)

2. <CQF ≅ <APQ (transversal property)

and

<CQF ≅ <BPE (vertically opposite angles)

Thus,

<CQF = \(60^{o}\) (vertically opposite angle property)

Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.

However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.

Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.

In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.

Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.

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Answer:

73 and 15

Step-by-step explanation:

I made two variables for this:

x = larger number

y = smaller number

Write an equation for "the sum of two number is 88" and you get:

x + y = 88

Write an equation for "four times the smaller number is subtracted from the larger number" and you get:

x - 4y = 13

I do not want an equation with both x and y in it, so I will rewrite the first one and use substitution in the second one:

x + y = 88   -- move the x to the other side

y = 88 - x

x - 4y = 13 -- substitute for y

x - 4(88 - x) = 13 -- multiply by 4

x - 352 + 4x = 13 -- move -352 to the other side, combine x's

5x = 365 -- divide by 5

x = 73

Now that I know x is 73, I go back to my first equation (x + y = 88) and I get:

73 + y = 88 -- subtract 73 from both sides

y = 88 - 73

y = 15

The conclusion is that there is insufficient proof that the new training method increases training time at the 0.02 level of significance.

Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀

The average amount of time required to obtain an advanced driving license using conventional techniques is μ=90 hours.

According to the researcher, the new method can result in a longer training period.

A researcher tests the hypothesis with 190 pupils.

At the significance threshold of α=0.02, the researcher fails to reject the null hypothesis.

To put to the test

H₀:The average amount of time required for the new method to obtain an advanced driving license is 90 hours, or μ=90

Hₐ: The new method often requires more than 90 hours, or μ>90, to obtain an advanced driving license.

Failure to reject the null hypothesis indicates that there was insufficient data in our sample to draw a conclusion on the existence of the effect. The absence of data, however, does not demonstrate that the effect is unreal.

The new method takes fewer than 90 hours on average to get an advanced driving license as a result.

Therefore, the researcher's assumption that the new method would increase training time was unfounded.

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Answer:

Scott invested $ 3,000 at 12% annually, and $ 2,400 at 8% annually.

Step-by-step explanation:

Since Scott invested a total of $ 5400 at two separate banks, and one bank pays simple interest of 12% per year while the other pays simple interest at a rate of 8% per year, if Scott earned $ 552.00 in interest during a single year, to determine how much did he deposit in each bank, the following calculation must be performed:

5400 x 0.12 + 0 x 0.08 = 648

4400 x 0.12 + 1000 x 0.08 = 608

3000 x 0.12 + 2400 x 0.08 = 552

Therefore, Scott invested $ 3,000 at 12% annually, and $ 2,400 at 8% annually.

Answer:

Ben expected to earn $27,675 this year.

Step-by-step explanation:

First, to be able to determine the difference between this year and last year, you would multiply $22,500 by 0.23 (or, 23% in decimal form).

When you do that, the answer comes out to 5,175.

So then, you add $22,500 and $5,175 in order to get the value that he expected to earn this year. That comes out to $27,675, which is your final answer.

Answer:

Step-by-step explanation:

The number of months is our unknown, which we will call x. y is the amount she saves. Representing the fact that she puts $10 away per month is 10x. If she puts $300 down initially and then adds 10 per month to that, the first equation is

y = 10x + 300

The same goes for the second option. Putting $30 away every month is represented as 30x, and if she is starting with 100 and adding 30 a month to it, the second equation is

y = 30x + 100

We are being asked to find the number of months where the amount Tina saves is equal. Since y is the amount Tina has saved and we want to know when these amounts are equal, we will set the equations equal to each other and solve for x, the number of months.

10x + 300 = 30x + 100 and

200 = 20x so

x = 10. After 10 months, Tina will have saved the same amount of money regardless of which option she has chosen. This is only true for 10 months though. After that, one will show more of a savings than the other.

If a value of 80.2° is added to the data, the range stays at 48º.

The mean of the data-set would change the most, and it would assume a value of 84º.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations. The range of a data-set is given by the difference between the highest value of the data-set by the smallest value of the data-set.

here, we have,

The highest and smallest high temperatures for the city are given as follows:

Smallest: 57º.

Highest: 105º.

Hence the range is obtained as follows:

105 - 57 = 48º.

80.2º would be neither the highest nor the smallest value in the data-set, which would then remain constant.

As it involves all values, it would be changed the most by changing the value of 58º to 101º, and would then assume a value of 84º.

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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The vertex and axis of symmetry of the parabola is (-2,-3) and x = -2 respectively.(optionA).

An axis of symmetry is a line about which a figure is symmetrical.

A vertex is the maximum or minimum point of a parabola.

The vertex of the parabola can be found from the graph.

The y coordinate of the vertex is -3 and the x coordinate of the vertex is -2

Therefore the vertex of the parabola is (-2,-3).

The axis of symmetry is can also be found from the graph,

The point where the parabola can be divided into two is the axis of symmetry.

The axis of symmetry is x = -2

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

\( x+y = 30\)   (1)

\( 1.95x+ 2.85y = 78.30\)   (2)

From equation (1) we can solve for x and we got:

\( x = 30-y\) (3)

Replacing (3) into (2) we got:

\( 1.95(30-y) +2.85 y = 78.30\)

And solving for y we got:

\( 58.5 -1.95 y +2.85 y = 78.30\)

\( 0.9 y = 19.8\)

\( y = 22\)

And then solving for x we got:

\( x = 30-22 = 8\)

So then we have 8 donuts and 22 cupcakes

Step-by-step explanation:

Let x the number of donuts and y the number of cupcakes, from the info given we can set up the following equations:

\( x+y = 30\)   (1)

\( 1.95x+ 2.85y = 78.30\)   (2)

From equation (1) we can solve for x and we got:

\( x = 30-y\) (3)

Replacing (3) into (2) we got:

\( 1.95(30-y) +2.85 y = 78.30\)

And solving for y we got:

\( 58.5 -1.95 y +2.85 y = 78.30\)

\( 0.9 y = 19.8\)

\( y = 22\)

And then solving for x we got:

\( x = 30-22 = 8\)

So then we have 8 donuts and 22 cupcakes

Answer:

4^8

Step-by-step explanation:

4^3 * 4^5

We know a^b * a^c = a^(b+c)

4^(3+5)

4^(8)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(4^8\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Simplifying the answer...}}\\\\4^3 * 4 ^ 5\\-----------------\\\text{Recall the exponent rule:}\\\\a^x * a^y = a^{x+y}\\\\\rightarrow 4^3 + 4^5\\\\\rightarrow 4^{3+5}\\\\\rightarrow \boxed{4^8}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

\(y1 = 4 \\ x1 = 3\)

\(y - y1 = m(x - x1)\)

\(y - 4 = 0(x - 3)\)

\(y - 4 = 0\)

\(y = 4\)

Answer:

394,898

Step-by-step explanation:

9.8% = 0.098

0.098x = 38700

Divide both sides by 0.098

x = 38700/0.098

x = 394,897.9591836735

Rounding

x = 394,898

The additional gas it will take to fill the tank is 16 gallons

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

Capacity = 24 gallons

Current volume = 1/3 full

This means that

Remaning volume = 1 - 1/3

Evaluate

Remaning volume = 2/3

The additional gas it will take to fill the tank is

Additional = 2/3 * 24

Evaluate

Additional = 16

Hence, the additional gas it will take to fill the tank is 16 gallons

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Answer: 12

Step-by-step explanation: