A rectangle has a perimeter of 25 meters. If the lengths of the sides of the rectangle are multiplied by 7 to make a new rectangle, what is the perimeter of the new rectangle?

To find the length of the rectangle, use the given information about the width and perimeter. Solve the equations to find the values of the variables and determine the length of the rectangle.

To find the length of the rectangle, we can use the information given in the problem. Let's let the width be represented by W and the length be represented by L. We are told that the length is 26 feet more than the width, so we can write the equation L = W + 26. We are also given that the perimeter of the rectangle is 60 feet, so we can write the equation 60 = 2(W + L). We can substitute the value of L from the first equation into the second equation to solve for W. After finding the value of W, we can substitute it back into the first equation to find the value of L.

Let's start with the first equation: L = W + 26. Since we have an equation with two variables, we'll need to use the second equation to solve for the variables. Let's substitute the value of L in the second equation: 60 = 2(W + (W + 26)). We can simplify this equation by combining like terms: 60 = 2(2W + 26). We can distribute the 2 to the terms inside the parentheses: 60 = 4W + 52. We can then subtract 52 from both sides of the equation: 8 = 4W. Finally, we can divide both sides of the equation by 4 to solve for W: W = 2.

Now that we have the value of W, we can substitute it back into the first equation L = W + 26. This gives us: L = 2 + 26. We can simplify this equation to find that L = 28.

Answer:

It is a prime number which is either 2 less or 2 more than another prime number

Step-by-step explanation:

Final answer:

The twin prime conjecture posits the existence of an infinite number of twin prime pairs, which are pairs of prime numbers that are two units apart.

Explanation:

The twin prime conjecture is an unsolved question in mathematics that relates to the distribution of prime numbers. It specifically addresses the existence of pairs of primes that are only two numbers apart, such as (11, 13), (17, 19), and (41, 43), which are known as twin primes. The conjecture proposes that there are an infinite number of these twin prime pairs, even though prime numbers themselves become less frequent as numbers increase. Despite many efforts, a definitive proof of this conjecture has not yet been found.

Final answer:

To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.

Explanation:

To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.

Final answer:

To find the ratio of red to yellow marbles, given the ratios of red to blue and blue to yellow, we equalize the blue part of both ratios and combine them, resulting in a red to yellow ratio of 2:5.

Explanation:

The question concerns finding the ratio of red marbles to yellow marbles given the ratios of red to blue marbles and blue to yellow marbles. To solve this, we use the given ratios: the ratio of red marbles to blue marbles is 1 : 4, and the ratio of blue marbles to yellow marbles is 2 : 5. Firstly, we make the number of blue marbles consistent in both ratios by finding a common value. Multiplying the first ratio by 2 gives us red to blue as 2 : 8, and keeping the second ratio as is (blue to yellow as 2 : 5), we can now combine these to find the ratio of red marbles to yellow marbles. The red to yellow ratio, through the intermediary blue, becomes 2 : 5.

Answer:

B.)

87.92 feet

Step-by-step explanation:

Given:

Area of the circular garden [tex]= 615.44 ft^2[/tex]

      [tex]\pi =3.14[/tex]

 Finding the radius of the circle.

Area of the circle= [tex]\pi r^2[/tex]

          [tex]615.44=\pi *r^2[/tex]

             [tex]r^2=\frac{615.44}{\pi } \\\\r^2=\frac{615.44}{3.14} \\r^2=196\\r=14 ft.[/tex]

Circumference of the garden:

                                           [tex]=2\pi r\\=2*3.14*14\\=87.92ft.[/tex]

Answer:

The novel has 180 pages.

Step-by-step explanation:

108 pages is 60% of the novel.

108 / 3 = 36.

20% of the novel is 36 pages.

36 * 5 = 180 pages

Answer:

For x = 0, the value of y will be 10 miles.

Step-by-step explanation:

Mark is in training for a marathon race. Each day he runs 10 miles for this training purpose. He will  be increasing his running by this weekly formula: [tex]y = 10(1.1)^{x}[/tex], where y is the number of miles he  will run each day, x represents the number of weeks from now.

Now, for x = 0, the value of y will be [tex]y = 10(1.1)^{0} = 10[/tex] miles. (Answer)

Answer:

The Value of y is 10

Step-by-step explanation:

Answer:

(x + 4)² + (y + 5)² = 73

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 4, - 5), thus

(x - (- 4))² + (y - (- 5))² = r², that is

(x + 4)² + (y + 5)² = r²

The radius is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)

r = [tex]\sqrt{(4+4)^2+(-2+5)^2}[/tex]

  = [tex]\sqrt{8^2+3^2}[/tex]

 = [tex]\sqrt{64+9}[/tex] = [tex]\sqrt{73}[/tex] ⇒ r² = 73, thus

(x + 4)² + (y + 5)² = 73 ← equation of circle

Answer: [tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

Step-by-step explanation:

the formula for finding equation of circle is given as :

[tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex]

where ( a,b) is the coordinate of the center and r is the radius

The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :

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

d = [tex]\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}[/tex]

[tex]d = \sqrt{(4+4)^{2}+(-2+5)^{2}}[/tex]

[tex]d = \sqrt{8^{2}+3^{2}}[/tex]

[tex]d = \sqrt{73}[/tex]

since "r" is the distance , then

[tex]r = \sqrt{73}[/tex]

The the equation of the circle , using the formula [tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex] , will be

[tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

Yo sup??

by angle sum property we know that the sum of all angles in a triangle is 180

let the unknown angle be x

then,

x+60+90=180

x=180-150

x=30

Hope this helps

The sum of the angles of a triangle is 180°.

The angle measures you know are 60° and 90° (because the box in the top right corner of the triangle means that it is a right angle, which equals 90°). So you can do this to find the missing angle:

60° + 90° + ? = 180°    Add 60 and 90

150° + ? = 180°     Subtract 150 on both sides

? = 30°  The missing angle is 30°

Answer:

Step-by-step explanation:

x + 3y = - 28

y = -5x

x + 3(-5x) = -28

x -15x = -28

-14x=-28

x=2

y = -5(2)

y=-10

Answer:

the answer is B

Step-by-step explanation:

give me brainly

Answer:

Your answer is 9

Step-by-step explanation:

the answer is nine because if you look at the pattern, every number to the left is times 3 to the right. For example, 4 to 12 is times 3. this would work for n because 9x3 equals 27. the rule is times three.

Step-by-step explanation:

[tex](6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1} [/tex]

Answer:

There are 12 students in Miss Jacobs class.

Step-by-step explanation:

Divided 10.2 and 0.85

If you check your answer. 0.85 multiplied by 12 is 10.2

Answer: C: 0 < x < 31

Step-by-step explanation: Because the < sign shows the line is going up towards the top. It starts from 0 and travels to the top-right to 31

A reasonable domain for this function to have would be 0 ≤ x ≤ 31.

We have f(x) as the number of fishes that are present in this water. The month is October and October has 31 days.

The x values is the maximum of the number of days in October. The minimum value is given as 0 because it is the population in the beginning of the month.

Hence we have 0 ≤ x ≤ 31

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 100

0 ≤ x ≤ 31

All positive integers greater than 100

All positive integers less than 100

Read more on domains of a function here:

https://brainly.com/question/1942755

#SPJ6

No if you simplify 27/8 it equals 3 3/8.

Step-by-step explanation: To graph x < 6 on a number line, we start with an open dot at +6. The reason we use an open dot at +6 is that x is less than +6 but it is not equal to +6. Next we drawn an arrow going to the left to show that all numbers less than +6 are solutions to this inequality.

Image is attached below.

Elsa's rate of typing = 1.25 words per sec

Time is taken for typing each word = 0.8 a

It is a method of solving by finding the value of one unit and the calculating the value of given unit by multiplying with the single value.

Numbers of words Elsa can type in 1 minute(the 60s)  = 75

Numbers of words Elsa can type in one second = 75/60

∴ Rate of typing = 1.25 words per sec

Time is taken to type one word = 60/75

                                                = 0.8 sec

Learn more about ut unitary method here: https://brainly.com/question/15300456

#SPJ2

Answer:

d

Step-by-step explanation:

[tex]-\frac{6}{5}[/tex] is rational

3.5 is rational

0.5 repeating is rational

[tex]\sqrt{4}[/tex] is rational

[tex]\sqrt{5}[/tex] is NOT rational

The answer correct answer is D.

Answer:

The monthly payment, PMT = $450.71

Therefore the correct option is C.) $450.71

Step-by-step explanation:

i) Value of Loan, or Present value, PV = 24000

ii) Annual percentage rate , APR = 0.048

iii) number of periods, n = 12

iv) periodic interest, R = APR / n  = 0.048 / 12 = 0.004

v) number of years, t = 5

v) Monthly Payment, PMT =  [tex]\frac{PV\times R}{1 - (1 + R)^{(-1\times n \times t})} = \frac{24000 \times 0.004}{1 - ( 1 + 0.004)^{-60}}[/tex] = $450.71

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

Answer:

$1575

Step-by-step explanation:

70 % of his salary is 0.7 X 450 = 315

He gets it for 20 weeks

presuming the salary is monthly.

You do 315 X 5 = 1575   20 /4 = 5 months

Step-by-step explanation:

[tex]area \: of \: sector = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times {(16)}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times 256 \\ \\ = \frac{88,422.4}{360} \\ \\ = 245.617778 \\ \\ \approx245.62 \: {in}^{2} [/tex]

Two nontrivial functions f(x) and g(x) that satisfy the equation f(g(x)) = (-6-3x)^6 are f(x) = x^6 and g(x) = -6 - 3x. These functions were found by assigning the inner function to g(x) and the outer function to f(x).

Looking at the expression [tex]f(g(x)) = (-6-3x)^6[/tex], we can see that it is a composition of two functions. A possible way to choose the functions f(x) and g(x) is to let g(x) be the inner function and f(x) be the outer function.

Let's choose g(x) = -6 - 3x. This function linearly transforms the input x. Now, let's choose the function [tex]f(x) = x^6[/tex]. This function takes any input (including results from the g(x) function) and raises it to the power of 6.

So, when we apply g to x (g(x)) and then f to the result (f(g(x))), we get the original equation[tex]f(g(x)) = (-6-3x)^6[/tex]. Therefore, the two nontrivial functions f(x) and g(x) that satisfy the equation are f(x) = x^6 and g(x) = -6 - 3x.

https://brainly.com/question/17348508

#SPJ3

Solve by elimination.

 2x-3y=-19

+(4x+3y=7)

-----------------

6x=-12

x=-2

2(-2)-3y=-19

-3y=-15

y=5

Intersection Point: (-2,5)

Answer:

132

Step-by-step explanation:

65+67=132 || 180-132=48 || 180-48=132

Answer:

132 Degrees.

Step-by-step explanation:

The interior of any triangle is 180 degrees.

Solve for angle DBC

65 + 67 = 132

180 - 132 = 48 degrees

Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.

None of the given points are solutions to the inequality.

To determine which of the given points is a solution to the inequality y > 1/2x + 2, you need to substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's start with point (1, 4):

4 > 1/2 * 1 + 2

4 > 1/2 + 2

4 > 2.5 + 2

4 > 4.5

The inequality does not hold, so point (1, 4) is not a solution to the inequality.

Now, let's try point (-1, 1):

1 > 1/2 * -1 + 2

1 > -1/2 + 2

1 > 1.5

The inequality does not hold, so point (-1, 1) is not a solution to the inequality.

Similarly, checking for points (2, 3) and (0, 2), we find that neither of them satisfy the inequality.

Therefore, none of the given points, (1, 4), (-1, 1), (2, 3), or (0, 2), are solutions to the inequality y > 1/2x + 2.

https://brainly.com/question/22010462

#SPJ12

Answer:

Step-by-step explanation:

Answer:

28)  B

33)  D

Step-by-step explanation:

28)   Numbers on the dice

1, 2, 3, 4, 5, 6

Numbers greater than 4

5, 6

There are 2 possibilities of rolling a number greater than 4 on the cube

2 numbers greater than 4 / Total amount of numbers

2/6 = 1/3

There is a 1/3 chance of rolling a number greater than 4

If the cube is tossed 120 times, about 1/3 of the time the number will be greater than 4

120 (1/3) = 120/1 * 1/3  = 120/3 = 40

The best estimate is 40 times, B

33)

These are all of the possibilities:

W - shaded

W - unshaded

X - shaded

X - unshaded

Y - shaded

Y - unshaded

Z - shaded

Z - unshaded

The answer that corresponds with all of these possibilities is D

Hope this helps :)

Answer:

  1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

  B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

  V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

Comment on the geometry

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.