Taylor is older than Julian. Their ages are consecutive even integers. Find Taylor's age if the sum of Taylor's age and 4 times Julian's age is 132.

Answer: twenty eight-twelfths (or seven-thirds in the simplest form)

Step-by-step explanation:

The distance travelled by the car in 34 minutes is 22.667 miles.

We are given a car. The car is travelling at a steady speed. It travels 1.5 miles in 2.25 minutes. We need to find the distance travelled by the car in 34 minutes. First of all, we need to find the speed of the car. The speed of the car is the ratio of the distance travelled and the corresponding time taken.

v = s/t

v = 1.5/2.25

v = 0.667

Hence, the speed of the car is 0.667 miles per minute. The speed of the car remains constant throughout its journey. Let the distance travelled by the car be denoted by "d" . The distance travelled in 34 minutes is calculated below.

d = v*t

d = 0.667*34

d = 22.667

Hence, the distance travelled by the car in 34 minutes is 22.667 miles.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-2y=6\implies -2y=-x+6\implies y=\cfrac{-x+6}{-2} \\\\\\ y-\cfrac{-x}{-2}+\cfrac{6}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so we're really looking for the equation of a line whose slope is -2 and that it passes through (-3 , -1)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-3)}) \implies y +1= -2 (x +3) \\\\\\ y+1=-2x-6\implies {\Large \begin{array}{llll} y=-2x-7 \end{array}}[/tex]

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

What is the Distribution Property?

The distribution property in math is a process that allows an equation to be simplified to help easily solve problems. Expressions that qualify to use the distributive property are usually written in the format: a(b +c)

a is then distributed to both b and c, rewriting the equation as ab +ac, where a has been multiplied to both values.

In this problem, you can distribute -15 to both 5x and 6y.

This will leave you with and equation that resembles this:

(-15×5x) + (-15×6y)

Multiply -15 to the coefficient attached to the variable to get your answer.

Your answer is -75x + -90y or -75x-90y

Answer:

[tex]-18x+20[/tex]

Step-by-step explanation:

We can simplify to find an equivalent expression

Take a look at the attachment...

Hope this helps! :)

Answer:

W = 35/4 aka 8 3/4 or 8.75

Step-by-step explanation:

Answer: w = 35/4

Step-by-step explanation: w−

2

1

​

=8

4

1

​

Multiply both sides of the equation by 4, the least common multiple of 2,4.

4w−2=8×4+1

Multiply 8 and 4 to get 32.

4w−2=32+1

Add 32 and 1 to get 33.

4w−2=33

Add 2 to both sides.

4w=33+2

Add 33 and 2 to get 35.

4w=35

Divide both sides by 4.

w= 35/4

​

The equation that gives the value of k in terms of x and y is  k = y*x  .

In the question ,

it is given that ,

the variation is an inverse variation .

So , equation representing the inverse proportionality is

y ∝ 1/x ,

to remove the proportionality sign (∝) , we introduce

the constant k which is called as Constant of Proportionality .

So , the equation becomes

y = k * 1/x

y = k/x

Simplifying further , we get

k = y*x

Therefore , The equation that gives the value of k in terms of x and y is  k = y*x  .

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Answer:

Let r be the rate at which he travels and t be the time.

Then, rt = 60

If he travels 8 mph faster, he arrives 10 hours sooner, so

(r+8)(t - 10) = 60

Multiplying, rt - 10r + 8t - 80 = 60

Substituting rt = 60, we get

60 - 10r + 8t - 80 = 60

Then, 8t = 10r + 80

t = 5/4r + 10

Substitute this into rt = 60

r(5/4r + 10) = 60

5/4r^2 + 10r - 60 = 0

Multipling by 4/5

r^2 + 8r - 48 = 0

(r + 12)(r - 4) = 0

r = -12, 4

A negative solution does not make sense

Thus, r = 4 4 mph is the solution.

Checking, rt = 60, so 4t = 60, and t = 15

Showing that this meets the other condition,

(r+8)(t - 10) = (4+8)(15-10) = 12 * 5 = 60

It checks.

Answer:

what is ur questions we cant see them

Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies then,

Here, given data as the first batch was 120 gingerbread cookies and the second batch consist of 150 shortbread cookies.

And, the same fractions of cookies from each batch were saved.

Let x parts of each of cookies were saved.

Then, the number of the saved gingerbread cookies = 120 x

While, the number of the saved shortbread cookies = 150 x

And, Again according to the question, the number of the saved shortbread cookies is 20 more than the number of the saved shortbread cookies.

That is equal to 150 x - 120 x = 20

⇒ 30 x = 20

⇒ x = 2/3

Hence the answer is, Mrs. Nicholas saved 2/3 part of each cookies.

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The product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

What is a matrix?

A rectangular matrix is a set of numbers arranged into a predetermined number of rows and columns. The rows of a matrix are formed when the elements are placed in a horizontal matrix. The columns of a matrix are formed by the elements when they are stacked in the matrix vertically.

Here, we have given a matrix that is

A = [tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex]       B = [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

We have to find the product of this matrix

[tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

First, we multiply the first row of matrix A with the first column of matrix B then continue in this manner, we get

[tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

Hence, the product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

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Answer:

1/6

Step-by-step explanation:

[tex]36^{-1/2}=\frac{1}{36^{1/2}}=\frac{1}{\sqrt{36}}=\frac{1}{6}[/tex]

Answer:

350 seconds to jog 5 laps.

Step-by-step explanation:

One lap of a running track is 350m Kyle jogs 5 complete laps at an average speed of 5 m/s. How long does it take him in seconds?

First, to run one lap:

350m / 5 meters per second = 70 seconds

Now, solve for five laps:

70 seconds * 5 laps = 350 seconds to jog 5 laps.

Answer:

HCE or ECH

Explanation:

Supplementary is angle that add up to 180° (A line)

Answer: HCE

Step-by-step explanation:

A supplementary angle is an angle that when added to another angle, equals 180 degrees, or a straight line.

Angles HCE and ECF add up to 180 degrees.

The monthly payment To pay off $170,000 in 9 years at 8.5%

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula of monthly payment is given as

M = PJ / 1- (1 + J)^-n

M = $2257.49

The monthly payment on this loan is $2257.49

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The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Given:

A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.

x be the number of small animals and y be the number of large animals

The number of small animals = 10x

Number of large animals = 6y

The equation:

= 10x + 6y = 12.

Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

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well, the population before the increase was "x", which oddly enough is the 100%, now if it increased by 16% that means 100% + 16% = 116%, and we happen to know that's 667

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 667& 116 \end{array} \implies \cfrac{x}{667}~~=~~\cfrac{100}{116} \\\\\\ \cfrac{x}{667}=\cfrac{25}{29}\implies 29x=(25)(667)\implies x=\cfrac{(25)(667)}{29}\implies x=575[/tex]

The statement which correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' is "Trapezoid ABCD ≅ trapezoid A'B'C'D'.

The correct answer option is option C

The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1).

The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

Given trapezoid ABCD:

Parent coordinates of ABCD = A (2,6), B (5,6), C (7,1), and D (-1,1)

Translated coordinates of A'B'C'D' = A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

Based on the reflection rule:

Reflection across x axis (x , y) -> ( x , -y) and rotating it 90°clockwise (x , y) -> ( -y, x).

Therefore, if trapezoid ABCD is reflected across the x-axis and then rotating it 90°clockwise

ABCD ≅ trapezoid A'B'C'D'

Complete question:

The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?

A. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then across the y-axis.

B. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.

C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

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The probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].

= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]

= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]

= [tex](1-e^{-2} )^2[2e^-2+1][/tex]

Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

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Answer: Error

Step-by-step explanation: Its impossible to divide by zero.

Answer:

0

Explanation Anything divided by zero is zero

Answer:

m<M = 76°

m<N = 76°

LN = 18 in

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

triangle LMN is an isosceles triangle and the measure of M is equal to N and LM = LN.

Now the measure of missing angle:

m<M + m<N + 28 = 180 subtract 28 from both sides

m<M + m<N = 152 since the measure of M is equal to N divide 152 by 2

152 ÷ 2 = 76 each angle is 76°

The function (f-g)(x) = x²+3x+5

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable

Given: f(x) = √16x⁴ = 4x² and g(x) = 3x²-3x-5

To evaluate (f-g)(x) such g(x) from f(x). Thus:

(f-g)(x) = 4x²-(3x²-3x-5)

          = 4x²-3x²+3x+5

          = x²+3x+5

Therefore, (f-g)(x) is x²+3x+5. The 4th option is the answer

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The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

The coordinates of the point = (9,1)

The equation of the line is

y = 2x + 3

Here the slope of the line is 2

The shortest distance between the point and the second line will be the perpendicular distance between the point and line

The perpendicular line slope will be -(1/m)

= -(1/2)

This perpendicular line will pass through the point (9, 1)

The point slope form is

y - 1 = -(1/2)(x - 9)

y - 1 = -(1/2x) + 9/2

y = -(1/2)x + 9/2 + 1

y = -(1/2)x + 11/2

Solve the equation

y = 2x + 3

y = -(1/2)x + 11/2

0 = (2 + 1/2)x -5/2

5/2 x = -5/2

x = -5/2 / 5/2

x = -1

Then

y = 2(-1) + 3

y = -2 + 3

y = 1

The distance between the point (9,1) and (-1, 1)

= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

= [tex]\sqrt{(-1-9)^2+(1-1)^2}[/tex]

= [tex]\sqrt{100}[/tex]

= 10 units

Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

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The sub contractor pays $0.94 per hour for the work .

In the question ,

it is given that ,

the amount paid by the contractor for 25 hours of work = $23.50

We need to find the amount paid by the contractor for 1 hour .

The per hour pay can be calculated using the formula ,

amount paid per hour = (amount paid for 25 hours)/( number of hours)

substituting the values ,we get

So , the amount paid by the contractor for 1 hour of work = 23.50/25

= $0.94

Therefore , The sub contractor pays $0.94  per hour for the work .

The given question is incomplete , the complete question is

A sub-contracted job pay $23. 50 for 25 hour of work. How much money does it pay per hour ?

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Answer:

Absolute value is to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Hope this helped, good luck on your homework!

Answer:  how far a number is from zero

Step-by-step explanation: Cannot be a negative. The absolute value of -12 is 12.

Answer:

45

Step-by-step explanation:

At this point, b) is basically asking for how many two digits numbers have a greater digit on the right from 0-9, because we already know the other two digits in the four-digit pin.

01-09 has 9 poissibilites.

12-19 has 8 possibilites.

23-29 has 7 possibilites.

34-35 has 6 possibilites.

45-49 has 5 possibilites.

56-59 has 4 possibilities.

67-69 has 3 possibilities.

78-79 has 2 possibilities.

89 has 1 possibility.

90-99 has 0 possibilities.

9+8+7+6+5+4+3+2+1+0=45 possibilities.

Answer:

Step-by-step explanation:

Each of the digits 3 and 4 can get numbers 0 through 9, in total 10 options per each digit:

The two- digit combinations with the last digit being larger has the following cases:

Total number of possibilities:

An equation for the curve that passes through the point (1,0) and whose slope at (x,y) is xe^y is y = -1/x -1.

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches. The slope is nothing more than the tangent to the angle formed with the x-axis measured. As a result, it is simply an angle's measurement.

Given,

The curve that passes through the point (1,0) and whose slope at (x,y) is xe^y.

Since x-2 is equal to the slope of the function f(x), we can express that as

dy/dx = x^-2

dx multiplication and integration of both sides:

y = -1/x + C

Connecting the provided point:

0 = -1/1 + C

C = -1

Consequently, the curve's equation is

y = -1/x -1

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Answer:

its A

Step-by-step explanation:

At least 10 people or guests could go to a party and the second caterer is $250 cheaper to hire.

In the question we can use the equation :

  Y = mx + b ,  which is the slope-intercept form of the equation of a straight line. Here, m is the slope of the line and b is the intercept, x and y represent the distance of the line from the x-axis and y-axis, respectively.

For caterer A, the cost per guest is $15. This is the m value. The b value is the additional fee for setting up the tables, $100.

Here, the equation will be  y = 15x + 100     -------------------------(1)

For Caterer B, the cost per guest is $20. The b value is the additional fee for setting up the tables $50.

For this the equation will be : Y = 20X + 50.  --------------------- (2)

To find the number of guests that will result in an equal cost, set the equations equal to one another. Solve for x.

                    15x + 100 = 20x + 50        ---------------------- (3)

solving the equation (3),

   15x - 20x = 50 - 100

⇒ -5x = - 50

⇒ x = 10

Putting x = 10 in equation (1),

   15 × 10 + $100 = $250

Therefore, the cost of 10 people or guest will attend the party and the second caterer is $250 cheaper then the first caterer.  

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