A rectangle’s length is 8 feet shorter than four times its width. The rectangle’s perimeter is 134 feet. Find the rectangle’s length and width.
The rectangle’s length is ____ feet, and its width is _____ feet.

The difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m. Then the correct option is B.

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

A frequency generator sends a 550 Hz sound wave through both water and ice.

The wavelength is given as

[tex]\lambda = \dfrac{v}{f}[/tex]

f = frequency

v = velocity

Then the wavelength in the water will be

[tex]\rm \lambda _w = \dfrac{1500}{550}\\\\\lambda _w = 2.73[/tex]

The wavelength in the ice will be

[tex]\rm \lambda _I = \dfrac{3200}{550}\\\\\lambda _I = 5.82[/tex]

Then the difference in wavelength between the wave produced in ice and the wave produced in water will be

[tex]\rightarrow \lambda _I - \lambda_w \\\\\rightarrow 5.82 - 2.73 \\\\\rightarrow 3.09 \approx 3.1[/tex]

Thus, the difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m.

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Answer:

3.1

Step-by-step explanation:

B

The solution to the problem is correct and the correct option from the given options is B.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

The given logarithmic problem can be solved in the following manner, therefore,

[tex]\rm log_210\ log_48\ log_{10}4\\\\[/tex]

Using the logarithmic properties, we can write,

[tex]=\rm \dfrac{log10}{log2}\cdot \dfrac{log8}{log4}\cdot \dfrac{log4}{log10}\\\\[/tex]

Now cancelling out the values we will get,

[tex]=\rm \dfrac{log2^3}{log2}\\\\=\rm \dfrac{3log2}{log2}\\\\= 3[/tex]

Thus, the solution to the problem is correct and the correct option from the given options is B.

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Answer:

B

Step-by-step explanation:

on edge

Answer:

2:5

Step-by-step explanation:

15 are female. 10 must be male.

Out of 25 pupils, 10 are male, so it's 10:25, or 2:5

Answer:

V = 4/3 π R^3        volume of a sphere

V = π R^2 H           volume of cylinder    area of base X height

4/3 π R^3 = π R^2 H       equal volumes

H = 4/3 R       relationship of height to radius for cylinder

H = 4/3 * 13 = 52 / 3 cm = 17 1/3 cm

Answer: No solutions

- by graphing-

         First I will simplify:

8B + 7v - 5 equals -11 + 15b​

8b + 7v - 5 = -11 + 15b​

7v = -6 + 15b​

7v = -6 + 7b​

         Let's graph this and see what happens!

-> I will graph y = 7x and y = 7x - 6

-> See attached.

-> Since there are no points of intersection (they have the same slope), there is no solutions.

Answer:

Standard Form: y = 4(x-1)(x+5)

Step-by-step explanation:

4 is the leading coefficient, so it should go in front. When making a standard quadratic equation, you must do the opposite for each of the roots (negative to positive, positive to negative.)

if you’re asking for a general form quadratic equation, then sorry, I am unable to help you with that :(

Answer:

150

Step-by-step explanation:

area of your base (bh/2) 3x8/2 = 12

2 bases = 24

3 faces ---- Face1 - 7x5= 35 ------Face2 - 7x5 = 35 ------Face3 - 8x7 = 56

24 + 35 + 35 + 56 = 150

Step-by-step explanation:

1/81 gallon for 1/4 mile.

what do I need to multiply 1/81 with to get 1 gallon ?

it is simple, right ? i need to multiply it by 81 to get 1 gallon.

in order to keep the relationship (ratio) unchanged, I need to multiply the other part (1/4 mile) with the same factor :

1/4 × 81 = 81/4 = 80/4 + 1/4 = 20 1/4 miles

so, at this rate, that car can travel 20 1/4 miles using 1 gallon of gas.

Answer:

I think the answer must be c because the length is 6\5 feet so there no chances to be the answer is more than so the base is divited and the ft should be multiplied

The formula for the circumference of a circle (or a sphere) is [tex]2\pi r\\[/tex].
The formula the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex].
Assuming 43.4 includes the pi, we can do the equation [tex]43.4=2\pi r[/tex]
Solving the equation, we get [tex]\frac{43.4}{2\pi } =r[/tex]

Substituting r into the formua for the volume of a sphere, we get [tex]\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3[/tex]
Solving the cube (probably with a calculator), we get [tex]\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}[/tex]

It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with [tex]\frac{4}{3} *\frac{81746.504}{8\pi ^2}[/tex].
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: [tex]\frac{81746.504}{6\pi ^2}[/tex]
Using a calculator, we get our final answer of (about) 1380.44cm^3

This was very messy, I apologize if I did make any mistakes.

The growth of the quantity is an illustration of an exponential function

The value of the quantity after 1.55 minutes is 76759.22

The given parameters are:

Initial value, a = 2000

Rate, r = 4%

An exponential growth function is represented as:

y = a(1 + r)^x

Substitute the value in the equation

y = 2000(1 + 4%)^x

After 1.55 minuted, x = 1.55 * 60

So, we have:

y = 2000(1 + 4%)^(1.55 * 60)

Evaluate the expression

y = 76759.22

Hence, the value of the quantity after 1.55 minutes is 76759.22

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Answer:

Step-by-step explanation:

9398.61

The volume of the solid created upon dilation bythe scale factor of 3 is 5832 units³.

An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.

Dimensions of the dilataed solid = 6 x 3 = 18

Volume = 18³ = 5832 units³

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Answer:

$8.96

Step-by-step explanation:

Since 6 hot dogs are $6.72, 1 hot dog would be that divided by 6, which is $1.12. Now we want the cost of 8 of those hot dogs, so we have to multiply by 8. Hence the answer is $1.12 * 8 = $8.96.

Answer:

m^4 - 225c^10 = (m^2 - 15c^5 )(15c^5 + m^2)

4.8xy + 36y^2 + 0.16x^2 = (6y + 0.4x)^2

Answer:

hi, I'm glad to help! 185

Step-by-step explanation:

11*7=77

11*6=66

6*7=42

77+66+42=185

Answer:

1.4

Step-by-step explanation:

Answer:

1 = 3/2

2 = -1/14

Step-by-step explanation:

The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.

For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.

For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.

You can plug all 4 numbers in to get (2-1)/(-17- -3)

2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.

Answer:

1) 14.137 2)10

Step-by-step explanation:

area of sector is central angle / 360 times (pi)(r^2)

45/360 x pi (6^2)

1/8 x 36pi

14.137

3-4-5- right triangle. Or Pythagorean Theorem.

6^2 + 8^2 = c^2

c= 10

Answer:

Rate is 8.5%

Step-by-step explanation:

Step 1: Write the given terms

Principal (p)=Rs8800

Rate(r)=?

Time(t)=3.5 years

Interest=Rs2618

Step 2: Write the formula for calculating Simple interest

[tex]i = \frac{prt}{100} [/tex]

Step 3: Make r the subject of the equation

[tex]by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} [/tex]

Step 4: Find the value of r by substituting the values in step 1

[tex]r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5[/tex]

Hence, the rate is 8.5%

Answer:

[tex] 1 \frac{2}{3}\: liters [/tex]

Step-by-step explanation:

[tex]V_{soda}[/tex] in one bottle = 5/9 liters

No of bottles = 3

Total volume of soda

[tex] = \frac{5}{9} \times 3 \\ \\ = \frac{5}{3} \\ \\ = 1 \frac{2}{3} \: liters[/tex]

The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]

The second integral using limits a and b

[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Integration is defined as adding small parts to form a new significant part.

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

The limits of the integral

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2\pi\int_0^1\int_b^axydx[/tex]

The second integral using limits a and b

[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]

[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]

[tex]16\pi\int_0^1[r-r^5]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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Answer:

hee-hee!

Step-by-step explanation:

Marcy charges $3 to walk a small dog and $5 for a big dog.

She walks 15 small dogs and 6 big dogs.

We can use an expression that would show the problem:

3s + 5b

(s = small dogs & b = big dogs)

s = 15 | b = 6

3(15) + 5(6)

45 + 30 = 75

Marcy earns $75 of profit.

Answer: 1. [tex]x=-2[/tex]; 2. [tex]x=\frac{11}{9}[/tex]

Step-by-step explanation :

1.

[tex]6-5x=16\\6-5x-6=16-6\\-5x=10\\\frac{-5x}{-5}=\frac{10}{-5}\\x=-2[/tex]

2.

[tex]4-9x=-7\\4-9x-4=-7-4\\-9x=-11\\\frac{-9x}{-9}=\frac{-11}{-9}\\x=\frac{11}{9}[/tex]

Answer:

Q1)   x =2         Q2)     x = 11/9

Step-by-step explanation:

Q1)   6 - 5x = 16                  check : -5(2) = -10

-6         -6                     6 -- 10 =  6+ 10 = 16

-5x = 10                         Q2)   4 - 9x = -7

-x = -2                                    -4           -4  

x = 2                                      -9x = - 11

--------------                               -x = -11 /9    ----->  x = 11/9

a. answer:_77

2_ (7 * 9) _ 16

2_ (63) _16

_61_16

_77

Answer:

20. 2x+y

21. 4

22. x+y

Step-by-step explanation:

20. 9x+2y - x-2y find your LCM

4 4

=(9x+2y)-(x-2y) clear bracket

4

=9x+2y-x+2y collect terms

4

=9x-x+2y+2y

4

=8x+4y factorize

4

=4(2x+y)

4

=2x+y

with this, you will understand the following

21. 4x + 8y

x+2y x+2y

=4x+8y

x+2y

=4(x+2y)

x+2y

=4

22. 2x-y + 2x+5y

4 4

=2x-y+2x+5y

4

=4x+4y

4

=4(x+y)

4

=x+y

Answer:

3.19 millimeter round of nearest hundred

The amount of change Lucy receives if she paid with few $20 bills is $12.84

Total cost of pants = $21.79 × 4

= $87.16

If the total cost of the pants exceeds $80, then she paid with 5 $20 bills

5 $20 bills = $100

Her change = $100 - $87.16

= $12.84

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Answer:

117

Step-by-step explanation:

This is an example of a supplementary angle, so in total it is 180 degrees. Subtract what we know angle 2 is, 63, and we are left with what angle 1 equals, which is 117.

Hope this helps! pls mark brainliest

Thee intersection point of the terminal side which measure the angle pi/6 radians  is (0.886, 0.5).

A circle is a special type of ellipse in which the eccentricity is zero and the two foci are coincident.

The distance from the center to the circumference is called the radius of the circle.

Given that  the terminal side of an angle measuring π/6 radians.

The coordinate point on the circle has to be find out It is known that, the formula for the coordinate is given by

x = r cos∅   and y = r sin∅

Let the r be unity.

Then, x will be

[tex]x=\frac{\pi }{6} \\x=cos(\frac{\pi }{6}) \\\x=0.866[/tex]

The variable y will be

[tex]y=sin\frac{\pi }{6}[/tex]

y=0.5

Thus, the intersection point is (0.886, 0.5).

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