Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?

Answer:

option b

137.1 cm²

Step-by-step explanation:

The given figure consist of two shapes

1) half circle

2) rectangle

Formula to use to calculate the area of this figure

half circle + rectangle

where r = radius = diameter/2 = 8/2 = 4 cm

          h = height = 14 cm

          b = base = 8 cm

plug in values in the formula

1/2(3.14)(4)² + (8)(14)

25. 133 + 112

137.13 cm²

Answer:

Step-by-step explanation:

[tex]\dfrac{4\cdot10^5}{5\cdot10^2}=\dfrac{4}{5}\cdot\dfrac{10^5}{10^2}=0.8\cdot10^{5-2}=0.8\cdot10^3=0.8\cdot1,000=800\\\\\\\text{Used}\ \dfrac{a^m}{a^n}=a^{m-n}[/tex]

Answer:

26 cuts

Step-by-step explanation:

1. convert 42 feet into inches by multiplying by 12 (12 inches=1 foot)

    42*12 = 504 inches

2. divide the total number of inches (504) by 20 (where Chad cuts)

    504/20 = 25.2

Since Chad cannot make a partial cut (.2) round up to the next whole number - 26

Most likely I would pick B

Answer:

The answer is D. 60

Step-by-step explanation:

Step 1: 18 + 12 = 30

18 = 60% of 30, therefor with this knowledge we know that 60% of a hundred, or 60 will be the answer.

(I also have proof, as I have done this quiz before.)

I hope my answer is correct.

[Please give brainliest!]

Have a good day,

-johannelbekian

Answer: OPTION D

Step-by-step explanation:

You can apply the SUBSTITUTION method:

- Solve for x from the second equation and substitute it into the first equation.

- Solve for y:

[tex]x-8y=-57\\x=-57+8y[/tex]

[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\19y=133\\y=7[/tex]

- Substitute y=7 into any of the original equations ans solve for x. Then:

[tex]x-8(7)=-57\\x-56=-57\\x=-57+56\\x=-1[/tex]

The answer is:

D.

[tex]x=-1\\y=7[/tex]

Substitution method for solving system of equations consists in isolate one variable in terms of the other variable.

So, isolating x in terms of y from the second equation, we have:

[tex]x-8y=-57\\x=-57+8y[/tex]

Then, substituting x into the first equation, we have:

[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\20y=19+114\\19y=133\\y=\frac{133}{19}=7[/tex]

Now, substituting y into the second equation we have:

[tex]x-8(7)=-57\\x-56=-57\\x=-57+56=-1[/tex]

Have a nice day!

Answer:

C.

Step-by-step explanation:

The first two questions couldn't be correct. C. Is the only logical answer.

Answer:

75% of the original paper’s size.

Step-by-step explanation:

Let’s say that the original size was 10 inches.

You then increase it by 50%. It is now 15 inches.

Now, you decrease it by 50%. 50% of 15 is 7.5. So, the paper is now 7.5 inches.

7.5 inches is 75% of the original paper size.

I hope I helped!

Let me know if you need anything else!

~ Zoe

Answer:

Smaller than you started with.

Answer:

f(x) = log x – 1 ⇒  x-intercept = (10 , 0)

f(x) = -(log x – 2) ⇒ x-intercept = (100 , 0)

f(x) = log(-x – 2) ⇒ x-intercept = (-3 , 0)

f(x) = -log -(x – 1) ⇒ x-intercept = (0 , 0)

Step-by-step explanation:

* lets talk about the log

- If log a = b, that means the base of the log is 10

- To solve it we will change it to exponential function

∴ [tex]10^{b}=a[/tex]

* Now do that in each one of the problem

* ∵ f(x) = log x - 1

- To find the x-intercept put y = 0

∴ log x - 1 = 0 ⇒ add 1 to both sides

∴ log x = 1 ⇒ change it to exponential function

∴ [tex]10^{1}=x[/tex]

∴ x = 10

* The x-intercept = (10 , 0)

* ∵ f(x) = -(log x - 2)

- To find the x-intercept put y = 0

∴ -(log x - 2) = 0 ⇒ Multiply both sides by -1

∴ log x - 2 = 0 ⇒ add 2 to the both sides

∴ log x = 2 ⇒ change it to exponential function

∴ [tex]10^{2}=(x)[/tex]

∴ x = 100

* The x-intercept = (100 , 0)

* ∵ f(x) = log (-x - 2)

- To find the x-intercept put y = 0

∴ log (-x - 2) = 0 ⇒ change it to exponential function

∴ [tex]10^{0}=(-x-2)[/tex] ⇒ any number to the power of zero = 1 except 0

∴ -x - 2 = 1 ⇒ add 2 to the both sides

∴ -x = 3 ⇒ multiply both sides by -1

∴ x = -3

* The x-intercept = (-3 , 0)

* ∵ f(x) = -log -(x - 1)

- To find the x-intercept put y = 0

∴ -log -(x - 1) = 0 ⇒ multiply both sides by -1

∴ log -(x - 1) = 0 ⇒ change it to exponential function

∴ [tex]10^{0}=-(x-1)[/tex] ⇒ any number to the power of zero = 1 except 0

∴ -(x - 1) = 1 ⇒ multiply both sides by -1

∴ x - 1 = -1 ⇒ add 1 to both sides

∴ x = 0

* The x-intercept = (0 , 0)

Answer:

Please mark as Brainliest :)

Step-by-step explanation:

Answer:

The correct answer is:

(7s-2)+3+(s+3) = 52, or 8s+4 = 52.

Step-by-step explanation:

Since s is the son's age, "two less than seven times" the son's age would be represented by 7s-2. To represent this in 3 years, we would add 3: (7s-2)+3. In 3 years, the son's age, s, would be represented by s+3. We are told that the sum of these ages will be 52; this gives us (7s-2)+3+(s+3) = 52.

To simplify this, combine like terms. 7s+s = 8s; -2+3+3 = 4. This gives us 8s+4=52.

Answer:

0

3

9

Step-by-step explanation:

0 has no opposite

-3 = 3

-9 = 9

Answer:

34°

Step-by-step explanation:

Let θ = the angle of elevation from the ground to the top of the tree. Then

tanθ = 100/150 = 0.6667

     θ = arctan0.6667

     θ = 34°

The sin's rays hit the ground at an angle of 34°.

First of all, we can find the angle B by using the fact that the interior angles of a triangle sum up to 180:

[tex]32.5+26.8+B=180 \iff B = 180-32.5-26.8=120.7

[/tex]

Now use the law of sines, which states that the ratio between a side and the sine of its opposite angle is constant. In particular, we have

[tex]\dfrac{\overwrite{BC}}{\sin(A)}=\dfrac{b}{\sin(B)}[/tex]

Plug in the known values and solve for b:

[tex]\dfrac{25}{\sin(32.5)}=\dfrac{b}{\sin(120.7)}\iff b=\dfrac{25\sin(120.7)}{\sin(32.5)}=40.01[/tex]

Final answer:

The ordered pair (10, -52) is not a solution to the equation y = -5x - 4 because when x is substituted with 10, the equation yields -54, not -52.

Explanation:

To determine which ordered pair is not a solution of the equation y = -5x - 4, you need to plug the x-value from each ordered pair into the equation and see if the y-value matches the result.

The ordered pair that is not a solution is thus (10, -52).

your answer is A 458.90.

The answer would be A)$458.90

Answer:

32.50 is the total cost, so you need to find the cost of each separate ticket.

First, you take the total, 32.50, and you divide it by the number of tickets, 5.

32.50/5

The answer is A.

Step-by-step explanation:

Final answer:

The correct equation that represents the cost of each ticket is A: x equals 32.50/5, which is obtained by dividing both sides of the original equation 5x = 32.50 by 5.

Explanation:

To determine the cost of each ticket that Nadia bought, we can use the given equation 5x = 32.50, where x represents the cost of each ticket. To solve for x, we need to isolate the variable on one side of the equation. This can be done by dividing both sides of the equation by 5, which leads us to x = 32.50 / 5. Therefore, the correct equation that represents the cost of each ticket is A: x equals 32.50/5.

Answer:

9 3/8

Step-by-step explanation:

You have to turn them both into mixed numbers so:

15/4 x 5/2

Then you just multiply across:

15 x 5/4 x 2

That should equal

75/8

Simplify! You should end up with 9 3/8

Check the picture below.

18+2n. For sure hope it helps

18+2n. Hope this helps!

Answer:

Circumference: 64π

Ratio:      1 : 4

Measure of ∠xoy:  π/2    

Step-by-step explanation:

We are given an arc length of 16π.  Since it's in terms of pi, we use the formula

S = rФ    where r is the radius, and Ф is the measure of the angle in radians (in terms of pi)

We are given S = 16π and r = 32, plug those in and find Ф

16π = 32Ф

  16π/32 = Ф

       π/2 = Ф

This is the measure of the central angle.  

The angle is π/2 radians.  There are 2π radians in the circumference, so the circumference is 4 times the arc length created by the central angle.  (There are 4 halves in 2)  so the ratio of the arc length tothe circumference is 1 : 4

The formula for circumference is C = 2πr, where r is the radius, so we hace

C = 2π(32) = 64π

The answer is

64

1/4

90

Hope this helps.

The answer is [tex]\frac{4y}{y+3}[/tex]

See the attached figure

Answer:

[tex] \frac { 4y } { y + 3 } [/tex]

Step-by-step explanation:

We are given the following terms and we are to find their product:

[tex] \frac { 2y } { y - 3 } \times \frac { 4y - 12 } { 2y + 6 } [/tex]

[tex] \frac { 8y^2 - 24y } { 2y^2 - 6y + 6y - 18 } [/tex]

Taking the common terms out and cancelling them to get:

[tex] \frac { 2 (4y^2 - 12y ) } { 2 (y^2 - 9 ) } [/tex]

[tex] \frac { 4y ( y - 3 ) } { ( y + 3 ) ( y - 3 ) } [/tex]

[tex] \frac { 4y } { y + 3 } [/tex]

Answer:

C

Step-by-step explanation:

Since the figures are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{3}{15}[/tex] = [tex]\frac{1}{x}[/tex] ( cross- multiply )

3x = 15 ( divide both sides by 3 )

x = 5 → C

Answer:

[tex]\large\boxed{V=75\ in^3}[/tex]

Step-by-step explanation:

The formula ogf a volume of  a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - area of a base

H - height

We have a base length a = 5 in and a height H = 9 in.

In the base we have a square. The formula of an area of a square is:

[tex]B=a^2[/tex]

Substitute:

[tex]B=5^2=25\ in^2[/tex]

Calculate the volume:

[tex]V=\dfrac{1}{3}(25)(9)=(25)(3)=75\ in^3[/tex]

its 8 inches, because 2 inches is to short, and a yard is too long for the width of a book

Answer:

8 inches

Step-by-step explanation:

2 feet is too long, 1 yard is way too long, and 2 inches is too short

This trigonometric function can be written as:

[tex]tan (3 cos^{-1} (\frac{3}{4}))[/tex]   (1)

Firstly, we have to solve the inner parenthesis:

[tex]cos^{-1} (\frac{3}{4})= 41.409[/tex]   (2)

Substituting (2) in (1):

[tex]tan (3(41.409))=tan(124.228)[/tex]   (4)

Finally we obtain the value:

[tex]tan(124.228)=-1.469[/tex]  

Answer:

[tex]tan(3 \times arc \ cos(\frac{3}{4} ))=\frac{\sqrt{7} }{3}[/tex]

Step-by-step explanation:

The given expression is

[tex]tan(3 \times arc \ cos(\frac{3}{4} ))[/tex]

Where

[tex]cos^{-1}(\frac{3}{4} )=x\\[/tex], which means that, [tex]cosx=\frac{3}{4}[/tex]

If we analyse this trigonometric reason in a right triangle, we would find the hypothenuses is 4 and the adjacent leg is 3. Then, using pythagorean theorem, we find the other leg

[tex]y^{2}=4^{2} -3^{2}\\ y=\sqrt{16-9}=\sqrt{7}[/tex]

Which means the opposite leg of our right triangle is the square root of seven.

Finally, using such right triangle, we find the tangent reason, which is the quotient between the opposite leg and the adjacent leg

[tex]tan(radian \ value)=\frac{\sqrt{7} }{3}[/tex]

Therefore, the answer is [tex]\frac{\sqrt{7} }{3}[/tex]

➷ The last number : n

The second number : n - 1

The third number : n - 2

n + n - 1 + n - 2

Simplify this:

3n - 3

Substitute 5 into it:

n = 5

n - 1 = (5) - 1 = 4

n - 2 = (5) - 2 = 3

3(5) - 3 = 12

Their sum is 12

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer: i dont know

Step-by-step explanation: hello im only here to complete a task, im receiving 50 points. I hope someone else can help you, cause I cant ;-;

Answer: option a.

Step-by-step explanation:

To factor a polynomial of degree 2, with the form [tex]ax^{2}+bx+c[/tex], you must find two number whose sum is a and  whose product is c. Then:

a) [tex]x^2+3x+2\\(x+1)(x+2)[/tex]

(it can be factored into two binomials)

b) [tex]x^2+4x+5[/tex] cannot be factored into two binomials.

c) [tex]x^2+5x+7[/tex]  cannot be factored into two binomials.

d) [tex]x^2+6x+10[/tex] cannot be factored into two binomials.

Therefore, the answer is the option a.

Answer:

A, cus he has other markers in the box, we dont know how many, or how many blue markeys he has so it cant be A

Step-by-step explanation:

Answer:

6x^4y^4

Step-by-step explanation:

(3xy^3)(2x^3y)

= (3*2) x^(1+3) y^(3+1)

= 6x^4y^4

Answer:

he drove 282 miles

Step-by-step explanation:

you add 136 and 146 to get 282

The volume of an average stone in the outer circle of Stonehenge is calculated by multiplying the base area, 19.5 square feet, by the height, 13 feet, resulting in a volume of 253.5 cubic feet.

To calculate the volume of a stone from Stonehenge, which is shaped like a rectangular prism, we need to multiply the height of the stone by the base area. The height is given as 13 feet, and the base area is 19.5 square feet. The formula for volume V of a rectangular prism is

V = base area × height.

So, the volume V of one of the average stones in the outer circle of Stonehenge would be:

V = 19.5 sq ft  × 13 ft

V = 253.5 cubic feet

Therefore, the volume of the stone is 253.5 cubic feet.