The length of the rectangle is three times its width. If the perimeter of the rectangle is one hundred and sixty meters, find the length and width of the rectangle. Enter two integers

If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.

In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.

Given: AB = 6y - 14, BC = 10 - 2y

Since B is the midpoint of AC, AB = BC then

6y - 14 = 10 - 2y

Add 14 on both sides of the equation, and we get

6y - 14 + 14 = 10 - 2y + 14

6y = - 2y + 24

Add 2y on both sides of the equation

6y + 2y = - 2y + 24 + 2y

simplifying the above equation, we get

8y = 24

y = 24/8

y = 3

Substitute the value of y in AC then we get

AC = 2(6(3) - 14)

= 2(4)

AC = 8

Therefore, the value of AC = 8.

To learn more about midpoint refer to:

https://brainly.com/question/5566419

#SPJ4

a) The square that does not touch one of the perimeter squares is the square 3C.

b) The area is 10 units.

The perimeter squares are the outer squares of the image. So, the only square that does not touch one of the perimeter squares is the central one. To identify it, you need to first see in which row it is, and you can see that it is row 3.

Then you need to identify the column, the central square is in column C.

Then the square that does not touch one of the perimeter squares is the square 3C.

What is the combined area of rows 4 and 5?

Let's say that each square has an area of one unit. Now, we have 5 columns, then each row has 5 squares, then the area of each row is 5 units.

So, if we have two rows, the area will be: 2*5  units = 10 units.

The area is 10 units.

If you want to learn more about area:

https://brainly.com/question/24487155

#SPJ1

Answer:

1.)

[tex]\frac{3a}{4} =\frac{1}{4} \\[/tex]

cross multiply

[tex]12a=4\\\frac{12a}{12} =\frac{4}{12} \\a=\frac{1}{3}[/tex]

2.)[tex]\frac{7}{2} =\frac{c}{\frac{8}{7} }[/tex]

cross multiply

[tex]c=\frac{7}{2} *\frac{8}{7} \\c=\frac{56}{14} \\c=4[/tex]

3.)[tex]\frac{6}{5} =\frac{h}{\frac{3}{8} } \\[/tex]

cross multiply

[tex]\frac{6}{5} *\frac{3}{8} =h\\h=\frac{18}{40} \\h=\frac{9}{20}[/tex]

4.)[tex]\frac{-2}{9} =\frac{-3m}{2} \\[/tex]

cross multiply

[tex]-2(2)=9(-3m)\\-4=-27m\\\frac{-4}{-27}=\frac{-27m}{-27} \\m=\frac{4}{27}[/tex]

5.)[tex]\frac{7}{6} =\frac{7p}{3} \\42p=21\\ \frac{42p}{42} =\frac{21}{42} \\p=\frac{1}{2}[/tex]

6.)[tex]\frac{x}{\frac{1}{7} } =-\frac{4}{7} \\x=\frac{1}{7} *\frac{-4}{7} \\x=\frac{-4}{49}[/tex]

7.)[tex]\frac{n}{\frac{4}{9} } =\frac{10}{9} \\n=\frac{10}{9} *\frac{4}{9} \\n=\frac{40}{81}[/tex]

8.)[tex]\frac{5}{3} g=-\frac{8}{3}\\ g=-\frac{8}{3} /\frac{5}{3} \\g=\frac{-8}{3}*\frac{3}{5} \\ g=\frac{-24}{15} \\g=\frac{-8}{5}[/tex]

The equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

Part A

24x+32-2.1x = 20.9x+30+x+2

Add like terms

24x-2.1x-20.9x-x = 30+2-32

0x = 0

Infinitely many solutions

Part B

24x+32-2.1x = 20.9x+30+x-2

Add like terms

24x-2.1x-20.9x-x = 30-2-32

0x = -4

There is no solution

Part C

24x+32-2x = 20.9x+30+x-2

Add like terms

24x-2x-20.9x-x = 30-2-32

0.1x = -4

x = (-4)/0.1

x = -40

It has only one solution

Part D

24x+32 = 20.9x+30

Add like terms

24x-20.9x = 30-32

3.1x = -2

x= (-2)/3.1

x = -0.64

It has only one solution

Hence, the equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

Learn more about solutions here

brainly.com/question/7198769

#SPJ1

Answer: 146 cm

Step-by-step explanation:

A simple way to find the perimeter of a rectangle is to double both sides and add them.

(49.5 * 2) + (23.5)

= 99 + 47

= 146

If Jim is running a race against his best friend Ryan and Jim runs at a rate of 18 miles in 3 hours while Ryan runs at a rate of 11 miles in 2 hours, then Jim can run 0.5 miles further compared to his friend Ryan.

If Jim runs at a speed of 18 miles in 3 hours, it can be represented as,

Speed = distance / time = 18 miles / 3 hours = 6 miles per hour

As Ryan runs at a rate of 11 miles in 2 hours, it can be given as,

Speed = distance / time = 11 miles / 2 hours = 5.5 miles per hour

To determine how much further Jim can run in an hour compared to his friend Ryan,

Distance ( Jim ) = speed x time = 6 x 1 = 6 miles

Distance ( Ryan) = speed x time = 5.5 x 1 = 5.5 miles

The distance that Jim can run further in an hour can be calculated by subtraction.

Distance ( Jim ) - Distance ( Ryan) = 6 - 5.5 = 0.5 miles

Thus, Jim can run 0.5 miles further in an hour compared to his friend Ryan.

To learn more about subtraction, click here:

https://brainly.com/question/13378503

#SPJ4

Answer: Option (4)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.

Of the options, the only one that satisfies this is choice 4.

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

for our rectangle here that means

2×(5x) + 2×(x - 3) = 42

10x + 2x - 6 = 42

12x - 6 = 42

12x = 48

x = 4

length = 5x = 5×4 = 20 in.

width = x - 3 = 4 - 3 = 1 in.

13.5 cm²   is the surface area of the cube  .

What is surface area of cuboid?

If the edge of a cube have a length =  a unit

then, the surface area of the cube = 6a² unit

here, the edge of a cube have length  a = 1.5 cm

Therefore , the surface area of the cube 6a² = 6 × 1.5²

                                                                          = 13.5 cm²

The area of each face = ( the length of the edges)²

The surface area of whole cube = 6 × the area of one face

Learn more about surface area of cuboid

brainly.com/question/26403859

#SPJ4

Check the picture below.

The statement, m∠A ≅ m∠B, represents the congruence property.

The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.

Given that:

The measure of angle A = 29 degrees

The measure of angle B = 29 degrees.

Since both angles have the same measure, then both angles are congruent to each other.

Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.

Learn more about congruence property on:

https://brainly.com/question/2437149

#SPJ1

The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.

The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,

[tex]x^{2}[/tex] - 20 = 8 x

[tex]x^{2}[/tex] - 8x -20 =0

on breaking -8x in two parts as -10x + 2x , we will get

[tex]x^{2}[/tex] -10x + 2x -20 = 0

x (x - 10) + 2 (x - 10) = 0

On taking (x-10) as common, we get

(x-10) (x+2) = 0

x = -2 , 10

The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.

To know more about Quadratic Equations refer to the link:

https://brainly.com/question/1214333

#SPJ4

Variable - These are the unknown quantities that expected to estimate it as an output.

Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.

Constraints - the restrictions on the variable open linear programming problem are called constraints.

The conditions x ≥ 0, y ≥ 0 called non negative restrictions.

Objective equation - the objective equation should be specified in a quantitative way.

It is of the form Z = ax + by

where x and y are decision variable.

Z is to be maximized or minimized to find the solution.

To know more about variable, constraints

https://brainly.com/question/15457305

#SPJ1

According to the solving the slope of the ramp = 0.175.

shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:

find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

The given values are indeed the heights of a two beams and indeed the distance between them, which are:

Y₁ = 3.5ft

Y₂ = 10.5 ft

ΔX = 40 ft

To get the slope of both the ramp, enter the following values into the slope formula:

m = (Y₂ - Y₁)/ΔX

  = (10.5 - 3.5)/40

  = 7/40

= 0.175

According to the solving the slope of the ramp = 0.175

To know more  about slope visit:

https://brainly.com/question/3605446

#SPJ9

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

The centroid method is an agglomerative clustering method in which the similarities (or dissimilarities) between clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the clustering variables.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The triangle has a balance point at the centroid.

Find the centroid of the triangular coffee table.

Use the centroid formula [tex](x_1+x_2+x_3/3, y_1+y_2+y_3/3)[/tex]

The centroid of the triangle is (3 + 5 + 7/3, 6 + 2 + 10/3) or(5, 6).

Let the points be A(3, 6), B(5, 2), and C(7, 10). The midpoint D of BC is  (5 + 7/2, 2 +10/2) OR (6, 6).

Note that AD is a line that connects the vertex A and D, the midpoint of BC. The distance from D(6, 6) to A(3, 6) is 6 – 3 or 3 units.

If P is the centroid of the triangle ABC, then So, the centroid is 2/3(3) or 2 units to the right of A.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

To learn more about centroid theorem refer to:

https://brainly.com/question/25845737

#SPJ4

Answer:

what

Step-by-step explanation:

Answer:

the square root rounded up is around 8

Step-by-step explanation:

because if the 5 is not beside the number it rounds down and the number was 3 so its 8

The value of top angle x will be 104° for the given isosceles triangle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Given the roof as an isosceles triangle with a base angle of 38°.

Since in an isosceles triangle two sides and two angles are equal.

Since the sum of all angles of a triangle is 180 degrees.

So,

x + 38 + 38 = 180

x + 76 = 180

x = 104°.

Hence "The value of top angle x will be 104° for the given isosceles triangle".

For more information about the triangle,

https://brainly.com/question/2773823

#SPJ4

Answer:

[tex]x=-\frac{42}{31}[/tex]

Step-by-step explanation:

2 ( 5 - 10x ) + 8x = 19x + 52

→ Expand brackets

10 - 20x + 8x = 19x + 52

→ Simplify

10 - 12x = 19x + 52

→ Minus 19x from both sides

10 - 31x = 52

→ Minus 10 from both sides

-31x = 42

→ Divide both sides by -31

[tex]x=-\frac{42}{31}[/tex]

Using it's formula, the average rates of change are given as follows:

a) 30 meters per second.

b) -10 meters per second.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the following equation:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (138 - 0)/(4.6 - 0) = 30 meters per second.

For item b, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.

More can be learned about the average rate of change of a function at https://brainly.com/question/11627203

#SPJ1

Answer:

m1 = 122°

m2= 58°

Step-by-step explanation:

M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.

The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.

180-122= 58

Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

The closest 1000 to 598 is 1000.

The standard equation for the given slope is y - 2 = 0

These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b.

We just solved using the m given in the problem and the b. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.

Putting (0,2) for (x1, y1) and m=0, we get

y-2=0(x-0)

(y-2) =

y-2=

+y-2=0

More problems related to the line equation are given in the link below.

brainly.com/question/16180119?referrer=searchResults

#SPJ4

The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137

An equation is an expression that shows the relationship between two or more numbers and variables.

Let s represent the number of shirts that Lisa buys. Lisa only has $137 to spend, therefore:

15x + 35 ≤ 137

The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

Now,

Given:

Let 'x' be the value that gives the value of grades.

The absolute value equation to find the grades will be given by: | x - 82 | = 12

=> x - 82 = ± 12

For maximum value of the grades, x - 82 = 12

=> x = 82 + 12

=> x = 94.

For minimum value of the grades, x - 82 = -12

=> x = 82 - 12

=> x = 70.

Hence, The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

To learn more about absolute value equation, refer to the link: https://brainly.com/question/5012769

#SPJ4

Answer:

18

Step-by-step explanation:

Substitute x with 8 :

6(8-5) =

8-5 = 3

6(3) = 6 × 3 = 18

Therefore 18 is our final answer

Hope this helped and have a good day

Hey there!

6(x - 5)

= 6(8 - 5)

= 6(8) + 6(-5)

= 48 - 30

= 18

OR EVEN:

6(x - 5)

= 6(8 - 5)

= 6(3)

= 18

18 = 18

Therefore, your answer should be:

18

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

   The equation of the parabola that has vertex at (0,0 ) and focus (-1, 0) is

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

  This will depend on its aperture

  Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = -1

p = 0 - 1

p= -1

(y - 0)² = 4*-1(x - 0)

(Y)² = -1(X)

x = -y²

Learn more about parabolas in:

https://brainly.com/question/28586996

#SPJ4

The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …

Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.

So the first term of the sequence is f(1) since n ≥ 1.

Given options for the sequences are:

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

We compare the first term of each sequence with the given recursive formula.

a.  2.5, 6.25, 15.625, 39.0625, …

In this sequence, the first term, f(1) = 2.5

Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.

But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.

b.2.5, 5, 10, 20

Here, f(1) = 2.5

By the recursive formula, f(2) = f(1) + 2.5 = 5

f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.

c. -10, -7.5, -5, -2.5, …

Here, f(1) = -10

Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5

f(3) = f(2) + 2.5 = -7.5 +2.5 = -5

f(4) = f(3) +2.5 = -5 +2.5 = -2.5

So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …

d.  -10, -25, 62.5, 156.25

Here the first term is, f(1) = -10.

But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.

The question is incomplete. Find out the complete question below:

Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

Learn more about sequences at https://brainly.com/question/1275192

#SPJ4