consider the circle. geometry

Answer:

width = 8 ft & length = 32 ft.

Step-by-step explanation:

let the width be x and length be 4x.

we know, Perimeter = 2(l+b)

now,

2(4x + x) = 80

10x = 80

x = 80/10 = 8

x = 8

therefore,

width = x = 8 ft

length = 4x = 4 × 8 = 32 ft.

hope this helps you !

Answer:

what? I don't understand what your trying to say

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 is the greatest common factor of 7, 4 and 39

Answer:

12 cupcakes were sold

11 brownies were sold

Step-by-step explanation:

Let c = number of cupcakes sold

Let b = number of brownies sold

Total number of items sold = 23

⇒ b + c = 23

cupcake = $1.50 each

brownie = $1.25 each

Total money made = $31.75

⇒ 1.5c + 1.25b = 31.75

Rewrite  b + c = 23  to make b the subject, substitute into 1.5c + 1.25b = 31.75 and solve for c:

⇒ b = 23 - c

⇒ 1.5c + 1.25(23 - c) = 31.75

⇒ 1.5c + 28.75 - 1.25c = 31.75

⇒ 0.25c + 28.75 = 31.75

⇒ 0.25c = 3

⇒ c = 12

So 12 cupcakes were sold

Substitute found value for c into  b + c = 23  and solve for b:

⇒ b + 12 = 23

⇒ b = 11

So 11 brownies were sold

Answer:

A

Step-by-step explanation:

Let x = speed of the faster car, y = speed of the slower car

after t = 5 hours, distance of slower car = 275 = 5 * y, so y = 275/5 = 55 mph

distance of faster car = 275 + 40 = 315 miles

then x = 315/5 = 63 mph

Answer: A

The radius of the circle is a line from the center of the circle to its circumference

The radius of the circle with the same vertex as a center is 10.16 units

From the question, we understand that:

Start by calculating the area of the triangle using:

[tex]Area = 0.5ab\sin C[/tex]

So, we have:

[tex]Area = 0.5 * 12 * 12\sqrt 3 *\sin (60)[/tex]

This gives

[tex]Area = 0.5 * 12 * 12\sqrt 3 * \frac{\sqrt 3}{2}[/tex]

[tex]Area = 108[/tex]

The arc divides the triangle into two equal regions.

So, the area of the arc is:

[tex]Arc = 0.5 * Area = 0.5 * 108[/tex]

[tex]Arc = 54[/tex]

Also, the area of the arc is:

[tex]Arc = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]Arc = \frac{60}{360} *3.14 * r^2[/tex]

Simplify

[tex]Arc = 0.523 * r^2[/tex]

This gives

[tex]0.523 * r^2 = 54[/tex]

Divide both sides by 0.523

[tex]r^2 = 103.25[/tex]

Take the square roots of  both sides

[tex]r = 10.16[/tex]

Hence, the radius of the circle with the same vertex as a center is 10.16 units

Read more about circumcised triangles at:

https://brainly.com/question/4268382

Answer:

90$

Step-by-step explanation:

You multiply the number by 0.10 for your answer.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (900)(0.10)(1)\implies I=90[/tex]

Answer:

ahem...

the answer you are looking for is.....

91! :)

Answer:

  sin(8w)/1024 -sin(4w)/128 +3w/128

Step-by-step explanation:

No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...

  [tex]\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}[/tex]

After some only slightly messy algebra, we find ...

  [tex]\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}[/tex]

Then the integral becomes straightforward:

  [tex]\displaystyle \int{\cos^4(w)\sin^4(w)}\,dw=\int{\dfrac{\cos(8w)}{128}}\,dw-\int{\dfrac{\cos(4w)}{32}}\,dw+\dfrac{3}{128}\int{}\,dw\\\\=\boxed{\dfrac{\sin(8w)}{1024}-\dfrac{\sin(4w)}{128}+\dfrac{3w}{128}}[/tex]

__

Additional comment

The slightly messy algebra involves the identities ...

  (a+b)(a-b) = a² -b²

  (a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

This means the given integrand is equivalent to

cos⁴(w) sin⁴(w) = (cos(w) sin(w))⁴ = (1/2 sin(2w))⁴ = 1/16 sin⁴(2w)

Also recall the half-angle identities for sine and cosine:

cos²(x) = 1/2 (1 + cos(2x))

sin²(x) = 1/2 (1 - cos(2x))

Then we can rewrite further as

1/16 sin⁴(2w) = 1/16 (sin²(2w))²

… = 1/16 (1/2 (1 - cos(4w)))²

… = 1/16 (1/4 (1 - 2 cos(4w) + cos²(4w))

… = 1/64 (1 - 2 cos(4w) + 1/2 (1 + cos(8w)))

… = 1/128 (3 - 4 cos(4w) + cos(8w))

You'll end up with the same solution as in the other answer:

[tex]\displaystyle \int \cos^4(w)\sin^4(w) \, dw = \frac1{128} \int (3 - 4\cos(4w) + \cos(8w)) \, dw \\\\ = \frac{3w-\sin(4w)+\frac18\sin(8w)}{128} + C \\\\ = \boxed{\frac{24w-8\sin(4w)+\sin(8w)}{1024} + C}[/tex]

The monthly rent of the apartment in the 10th year is  $1041.67.

The first step is to determine the yearly rent in the first year of living in the apartment.

Yearly rent = $900 x 12 = $10,800

The second step is to determine the yearly rent in the 10th year

$10,800 + (170 x 10) = $12,500

The third step is to determine the monthly rent

Monthly rent = $12500 / 12 = $1041.67

To learn more about division, please check: https://brainly.com/question/13281206

Answer:

243

Step-by-step explanation:

Answer:

(x , y)=(0 , -2)

Step-by-step explanation:

By using the graph and the definition of inverse functions, we will see that:

g⁻¹(1) = 4.

We say that two functions f(x) and g(x) are inverse if:

Now, we know that graph of g(x) and we want to find the value of:

g⁻¹(1)

In the graph, we can see that:

g(4) = 1

Then we can replace it:

g⁻¹(1) = g⁻¹( g(4) ) = 4.

So we can conclude that:

g⁻¹(1) = 4.

If you want to learn more about inverse functions, you can read:

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Answer:

-4

Step-by-step explanation:

Khan Academy

[tex]5x+40 = 5(x+8)[/tex]

Answer:

s²+2s-80

Step-by-step explanation:

First (first in each parentheses)

Outside (the two terms on the outside of the expression)

Inside (the two terms in the inside of the expression)

Last (last in each parentheses)

An example:

(a+b)(c+d)=ac+ad+bc+bd

Therefore...

(s+10)(s-8)=(s)(s)+(s)(-8)+(10)(s)+(10)(-8)=s²-8s+10s-80=s²+2s-80

Answer:

$25

Step-by-step explanation:

$20 = 80%

100% to 80% = x 0.8 ( you have to do inverse)

$20/ 0.8 = $25

Perimeter

[tex]\\ \tt\hookrightarrow 2(L+B)[/tex]

[tex]\\ \tt\hookrightarrow 2(6+4)[/tex]

[tex]\\ \tt\hookrightarrow 2(10)[/tex]

[tex]\\ \tt\hookrightarrow 20cm[/tex]

Scale 1cm=3m

Answer:

60 m

Step-by-step explanation:

Perimeter of a rectangle = 2 x width + 2 x length

From inspection of the diagram, the width of the villa is 4 cm and the length is 6 cm

Therefore, perimeter of the villa = (2 x 4) + (2 x 6) = 20 cm

We are told that there is a scale 1 cm : 3 m

This means that 1 cm = 3 m

Therefore, to convert the perimeter found in cm into meters, we need to multiply it by 3:

Perimeter = 20 x 3 = 60 m

Answer:

8t - 5 ≤ 91

8t ≤ 96

t ≤ 12

Christine can spend up to 12 hours in the boat.

Answer:

The area of the trapezoid is 40 ft

Step-by-step explanation:

11ft + 14ft + 15ft = 40 ft

*please help with my 1st question *

#a

#b

#c

#d

#e

#f

Same like f(2)

#g

The only option for which the limit exist is option f, while for the other options the DNE.

"If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist. If the graph has a hole at the x value c, then the two-sided limit does exist and will be the y-coordinate of the hole."

Let's check the values of the given quantity exist or not. Therefore, we can write,

(a) f(-2) = DNE

(b) [tex]\lim_{x \to \--2} f(x)[/tex] = DNE

(c) f(0) = DNE because hole are exist

(d) [tex]\lim_{x \to \-0} f(x)[/tex] = DNE

(e) f(2) = DNE

(f) [tex]\lim_{x \to \-2} f(x)[/tex] = 0.5 (exist)

(g) f(4) = DNE

(h) [tex]\lim_{X \to \-4} f(x)[/tex] = DNE

Hence, the only option for which the limit exist is option f.

Learn more about Limit Existence here:

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Answer:

100 heavy on the way the calculations and the way solution of equipment and the questions

V(t)=100-4t so at the beginning of the experiment t=0

so you substitute to the given formula

V(0)=100-4(0)

=100litres .

Answer:

70

Step-by-step explanation:

The angle at the bottom right of the triangle is linear with the 105, so it is 180 - 105 = 75

The top angle of the triangle is an alternate interior angle with the 35 degrees, so it is also 35.

75 + 35 = 110

x = 180 - 110 = 70

The angle above x is 35° as alternate interior angles are equal.

Angle aside right to x

Measure of x

Answer: 153.86 cm²

Ok done. Thank to me :>

Answer:

D

lmk if im wrong :)

The expression 8√y/x is equivalent to the given radical expression. The correct answer would be an option (D).

Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.

The radical expression is given as:

√(128x⁵y⁶/2x⁷y⁵)      (Assume x > 0 and y> 0)

Reduce the likewise variables,

√(64y/x²)

8√y/x

Thus, the expression 8√y/x is equivalent to the given radical expression.

Hence, the correct answer would be an option (D) 8√y/x.

Learn more about radical expressions here:

https://brainly.com/question/3796764

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The complete question is attached below.

Answer:

x=3 and x=2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

big brain question :)

Step-by-step explanation:

That depends on the tension on the tape.

As defined, the tape, due to gravity would form a catenary, a curve, so the measurement would be less than 30 m. The tension on the tape would affect the degree to which the measurement would be less. A tension well within the limits of the steel used to make the tape would be would be well within the accuracy of the tape. Over 30 m, the tape is likely +/- 2 mm, the recorded value could be 30m, +1mm/-3mm. If you need more than that degree of accuracy, you don’t use a tape.

Answer:

-see link below for graph

-slope- 6/270

Step-by-step explanation:

link in comments

Answer:

[tex]G=(2,\frac{5}{3} ).[/tex]

Step-by-step explanation:

Let the given vertices of a triangle be [tex]A(-2,3)[/tex]and [tex]B (4,-3)[/tex] let the third vertex be[tex]C (4,5)[/tex].

Let Centroid be G = [tex][\frac{x_{1} +x_{2}+x_{3} }{3} , \frac{y_{1}+y_{2}+y_{3} }{3} ][/tex]

⇒ [tex]G=(\frac{-2+4+4}{3} ,\frac{3-3+5}{3})[/tex]

⇒ [tex]G=(\frac{6}{3} ,\frac{5}{3} )\\[/tex]

⇒ [tex]G=(2,\frac{5}{3} ).[/tex]