When the mortgage is completely paid off for Mark and Lynne’s house, it will be 4 times as old as it is now. If they have 21 years left on the mortgage, how old is the house right now?

Answer:

what is the expressio

Step-by-step explanation:

3x+3n+20 is the answer

Answer:

a=13 b=13

Step-by-step explanation:

Because the triangles are congruent, their corresponding angles will be congruent, too.

So, ∠Y≅∠S  and ∠Z≅∠T.

Set the values of these angles equal to each other and solve.

∠Y≅∠S               ∠Z≅∠T

4a-4= 48                5b-3= 62

4a=52                    5b= 65

a=13                        b= 13

\(5 < \sqrt{30} < 6\)

\(Locate\ \sqrt{30}\ between\ two\ integers:\\ \downarrow\\ 5 < \sqrt{30} < 6\)

I hope this helps you

:)

The solution of x in the inequality is x > 2

The inequality is given as:

5x + one third(3x + 6) > 14

Rewrite properly as:

5x + 1/3(3x + 6) > 14

Open the brackets

5x + x + 2 > 14

Subtract 2 from both sides of the inequality

5x + x + 2 - 2> 14 - 2

Evaluate the difference

5x + x > 12

Evaluate the like terms

6x > 12

Divide both sides of the inequality by 2

x > 2

Hence, the solution of x in the inequality is x > 2

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Answer:

x > 2, like the other guy said

Step-by-step explanation:

I hope this helps

Answer:

Parallel lines m and n are 6 units apart

Step-by-step explanation:

Answer-

The slope of the line that passes through the points is

Solution-

As there is a single line passing through all these points, so taking any two points and then applying the formula for slope will give the slope of the line.

The points are,

(-14, 8), (-7, 6), (0, 4), (7, 2), (14, 0)

Taking two points as, (0, 4), (7, 2)

x₁ = 0

y₁ = 4

x₂ = 7

y₂ = 2

Putting the values,

Therefore, the slope of the line that passes through the points is

Step-by-step explanation:

The slope of the line that passes through the points in the table is -2/7.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given a table which shows the points on the line.

Slope of a line passing through two points (x, y) and (x', y') is,

Slope = (y' - y) / (x' - x)

Take any two points on the line.

(0, 4) and (7, 2).

Slope = (2 - 4) / (7 - 0) = -2/7

Hence the slope of the line is -2/7.

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Answer:

Step-by-step explanation:

The rule for dilation of a quadrilaterial is Do.0.08 (z,y) (0.08z, 0.08y). What is the Y coordinate of a new point if the new coordinate is (3-9)? Round to the nearest

hundredth if necessary

Answer:

The answer is "Option A".

Step-by-step explanation:

\(\to Base= 2 \ cm\\\\\to height=3.1 \ cm\\\\\)  

Formula:

\(\bold{Area= base \times height}\\\\\)

         \(=2 \times 3.1 \\\\= 6.2 \ cm^2\)

if the height value is 3 then area is =6

Answer: Width: 56 yards, Length: 108 yards

Step-by-step explanation:

What we know:

- Perimeter is 328 yards

- The length is 4 less than double the width

In this answer, I will use w as the variable for width.

Find the equation for the length.

The length of the field is double the width, 2w, minus 4.

We get: 2w - 4

A rectangle has four sides, two for width, two for length. So now we need to add width to width and length to length

Length: (2w - 4) + (2w - 4) = 4w - 8

Width: w + w = 2w

To find perimeter, you need to add all sides. So now we add our length and width

4w - 8 + 2w = 6w - 8

Now that we have our final equation, we need to solve for w.

6w - 8 = 328

Add 8 to both sides.

6w - 8 + 8 = 328 + 8

Combine like terms.

6w = 336

Divide 6 from both sides.

w = 56

The width is 56, now that we have solved w, we can plug it into our length equation

2(56) - 4 = 108

The length is 108.

Answer: 56 yards x 108 yards (width x length)

To check your work, you can easily add up all the sides and see if it matches the perimeter given.

108 + 108 + 56 + 56 = 328

I hope this helped!

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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Based on the given points on the graph, the equation for the line of best fit or the trend line is y = 1.874x + 3.656

Due to the fact that the points on the graph are not on a straight line, the least squares method can be used to find the line of best fit equation.

Using a linear regression calculator, you can find the equation of the trend line by inputting the values of y and x in the graph.

When run through a linear regression calculator, the result will be:

y = 1.874x + 3.656

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Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Answer:

1a. x= y+1/2  1b. y=2x-1  

2a. x= -4y-8/3  2b. y= -3x/4 -2

Step-by-step explanation:

Type in math problem solver then click the first one and then you can get all your answers there

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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

Work Shown:

Law of cosines

c^2 = a^2 + b^2 - 2*a*b*cos(C)

156.5^2 = 139.5^2 + 59.5^2 - 2*139.5*59.5*cos(C)

24492.25 = 19460.25 + 3540.25 - 16600.5*cos(C)

24492.25 = 23000.5 - 16600.5*cos(C)

24492.25 - 23000.5  = -16600.5*cos(C)

1491.75  = -16600.5*cos(C)

-16600.5*cos(C) = 1491.75

cos(C) = (1491.75)/(-16600.5)

cos(C) = -0.0898617511520737

C = arccos(-0.0898617511520737)

C = 95.1556537886261

C = 95 degrees approximately

Make sure your calculator is in degree mode.

"arccos" is short for "arccosine" which is the same as inverse cosine. Your calculator may show this as the button labeled \(\cos^{-1}\)

The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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Answer:

Steps:

Step-by-step explanation:

1: Jamie had the money

2: Jamie went to the store

3: Jamie picked out the box

4: Jamie bought the box

Hope this helped uwu

Answer: 2.29

Step-by-step explanation:

The critical z-value for \((1-\alpha)\%\) confidence level is given by :

\(z_{\alpha/2}\) i.e. the two tailed z-value .

Significance level for 97.8% confidence level = 1-0.978 = 0.022

Now, required critical value = \(z_{0.022/2}=z_{0.011}=2.29\)  [From z-table]

Hence, the critical z-value for a 97.8% confidence interval = 2.29

The critical z-value for a 97.8% confidence interval is 2.529.

"To understand the calculation, check below."

Given:

confidence interval=97.8%

Formula:

The critical z-value for confidence level =.\((1-\alpha )\)%

Significance level for 97.8% confidence level = 1-0.978

Significance level for 97.8% confidence level = 0.022

Critical value = \(z0.22/2 =z0.011\)  [From z-table]

Critical value = 2.29

Hence, the critical z-value for a 97.8% confidence interval is 2.29.

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Answer:

84

Step-by-step explanation:

I watch a total of 11 hours of TV on Fridays and Ellen watches TV for ten hours every day. 

Let's plot how long Manuel watches TV each day, with M, Harry as H, and Ellen as E.

Manuel knows that from Monday to Friday he watches TV for M hours, so the total amount of time he watches TV in his week is 5 * M = 5M.

On Friday and Saturday he watches TV for H hours a day, so the total amount of time he watches TV in a week is H*2 = 2H.

Ellen watches her E hours TV from Friday to Sunday, so the total amount of time she watches TV in a week is her E*3=3E.

In total, they watch her TV 37 hours a week.

5M + 2H + 3E = 37

I watch a total of 11 hours of TV on Fridays.

M + H + E = 11

We also know that the amount of time Ellen spends watching TV on a given day is twice as much as she does on a given day as Manuel spends watching TV.

E=2M

You can substitute the value of E for M into the second expression.

M+H+2M=11

Combining equal terms gives:

3M+H=11

Now that we have two equations, we can solve the unknowns M and H. Substitute the 3M formula for H from the second formula into the first.

5M + 2H + 3(3M + H) = 37

Expanding the right-hand side, we get:

5M + 2H + 9M + 3H = 37

Combining equal terms gives:

14M + 5H = 37

Now that we have equation 14M + 5H = 37, we can solve for H.

H = (37 - 14 eyes) / 5

Then you can substitute the formula for H with respect to M into the formula for H.

H = (37 - 14 eyes) / 5

Finally, we can solve for M using the value of H.

M = (37 - 5H) / 14

We know that H = (37 - 14M) / 5, so we can substitute this formula into the formula for M.

M = (37 - 5((37 - 14M) / 5)) / 14

Expanding and simplifying the right-hand side, we get:

M = (37 - 37 + 70M) / 14

Solving for M gives:

M=5

So Manuel watches TV for 5 hours every day and Harry watches TV for (37 - 5 * 5) / 5 = 2 hours every day.

Finally, we can use the equation E = 2M to find out how many hours Ellen watches TV each day.

E = 2 * 5 = 10

So Ellen watches TV for ten hours every day. 

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The temperature drops each hour will be 3.968°. Then the correct option is B.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The meteorologist made a forecast that a cold front was coming through and the temperature would steadily drop 24.8 degrees over the next six and one-fourth hours.

The number of hours will be

6 1/4 = 6.25 hours

Then the temperature drop each hour will be

⇒ 24.8 / 6.25

⇒ 3.968°

The temperature drops each hour will be 3.968°.

Then the correct option is B.

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Answer:

B

Step-by-step explanation:

trust me its correct. this is not sus

The interest rate that Ellie needs to look for will be: 11.1%.

The formula with which the interest required by Ellie will be determined is this: A = P (1 + rt)

where:

A = Doubled value after investment

P = Principal

r = rate

t = time

Therefore, we will insert the figures accordingly in the provided equation;

$10,000 = $5000 (1 + 9r)

$10,000 = $5000 + $45000r

$10,000 - $5000 = $45000r

$5000 = $45,000r

r = $5,000\45,000

r = 1/9

r = 0.111

Now we convert this to a percentage

= 0.111 × 100

= 11.1%

Therefore, the interest rate Ellie needs to look out for while trying to double her investment will be 11.1%.

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Answer:

Solving Absolute Value Inequalities. As we know, the absolute value of a quantity is a positive number or zero. From the origin, a point located at [latex]\left(-x,0\right)[/latex] has an absolute value of [latex]x[/latex] as it is x units away. Consider absolute value as the distance from one point to another point.

Step-by-step explanation:

Answer:

Well you see an absolute value means that it will be absolute value, and inequality means not equal. (I had to make the answer more advanced ;)

Step-by-step explanation:

But thanks for the points ;)))

Answer:

C

Step-by-step explanation:

It is C because 64 to 1/4 power is just 64 divided by 4.

This is a probability question. Let's take note first of the important parts that we will be needing to write the probability for the problem.

Mr. Griese only chooses the sophomore class. The sophomore class has 17 males and 17 females, which means that he has a total of 34 students in the sophomore class.

To compute for the probability, we have:

For this problem, the total sample space is the total number of students of Mr. Griese in the sophomore class, which is 34 students. The number of objects is the number of female students that he has since we are looking for the probability that a female will be picked up to collect yesterday's work. He has 17 females in his class. We now substitute these numbers on the probability equation, having:

Therefore, the probability of choosing a female to collect yesterday's work in sophomore class will be P = 1/2 or 0.50.

Answer: P = 1/2 or 0.50

The average number of hours that adults spend working each day is 8 hours and Ryan is correct because he got the average of 8 right.

We know that,

The sample mean is a statistic that is computed by taking the arithmetic mean of the values of a variable in a sample. If the sample is taken from probability distributions with a shared expected value, the sample mean is an estimator of that value.

The mean is gotten from the formula;

x' = ∑x/n

Number of hours of work per day are; 6, 7, 8, 9 and 10

Thus; sum up all of it

∑x = 6 + 7 + 8 + 9 + 10

∑x = 40

Mean is; x' = 40/5

x' = 8

Since Ryan concluded that the average is 8 hours,

Therefore,

We can say that Ryan is correct.

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Answer:

30

Step-by-step explanation:

3kg=45pounds

2kg=?

2kg×45/3

=30 pounds.