What is the length of the diagonal of the rectangle?

a) 2.5 units
b) 4.5 units
c) 5 units
d) 7 units

a) 2338 ≡ 42 • 55 + 28 ≡ 28 (mod 55)

b) We want to find a such that

23a ≡ 1 (mod 55)

Use the Euclidean algorithm:

55 = 2 • 23 + 9

23 = 2 • 9 + 4

9 = 2 • 4 + 1

⇒   1 = 9 - 2 • 4

⇒   1 = 9 - 2 • (23 - 2 • 9) = 5 • 9 - 2 • 23

⇒   1 = 5 • (55 - 2 • 23) - 2 • 23 = 5 • 55 - 12 • 23

Solve for a :

5 • 55 - 12 • 23 ≡ 1 (mod 55)

⇒   -12 • 23 ≡ 1 (mod 55)

⇒   a ≡ -12 ≡ 43 (mod 55)

Answer:

C

Step-by-step explanation:

[tex] \frac{ {5}^{8} }{ {5}^{3} } \\ [/tex]

Now you may reduce the fraction

[tex] = {5}^{5} [/tex]

Answer:   The fifth number is 5

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

The radius of the cone is 7 feet

The given parameters are:

Surface Area, A = 216π

h = 8/3r

The surface area of a cone is:

[tex]A = \pi r(r + \sqrt{h^2 + r^2})[/tex]

So, we have:

[tex]216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})[/tex]

Factor out r

[tex]216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})[/tex]

Evaluate the exponent

[tex]216\pi = \pi r(r + r * 2.85)[/tex]

Evaluate the sum

[tex]216\pi = \pi r(3.85r)[/tex]

Divide both sides by pi

[tex]216 = 3.85r^2[/tex]

Divide both sides by 3.85

[tex]56.10 = r^2[/tex]

Take the square roots of both sides

r = 7 (approximately)

Hence, the radius of the cone is 7 feet

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Answer:

The radius is about 9 feet.

Hope this helps!

Step-by-step explanation:

Answer:

no i cannot help you

Step-by-step explanation:

thats good

Answer:

see below

Step-by-step explanation:

Find the magnitude   (-1)^2  + (sqrt3)^2 = m^2   m = 2

find the angle    arctan (sqrt3/-1) = 120 degrees

the cube root would then be

[tex]\sqrt[3]{2}[/tex](cos 40 + isin 40)

Answer:

18480 feet

Step-by-step explanation:

5280 feet are in a mile 3.5 ×5280=18480

Answer:

14.375 Or 115/8

Step-by-step explanation:

since 8 7/8 = 71/8 and 7 5/6 = 47/6 and 2 1/3 = 7/3

then 71/8 + ( 47/6 - 7/3) = 115/8

Answer:

s = 3, j = 14

Step-by-step explanation:

The full perimeter is 35.

The given sides we have are 7, 2, 4, 5, and the two missing ones.  We will call the two missing ones j and s. (according to your drawing.)

-

The side with the number 7 on it is equal to the side with the number 4 and s.

Can you see that?  Even if it's not a direct side, it is under it. (if you can't see that comment below.)

-

Now since we know that we can make an equation:

7=4+s

Subtract 4 on both sides.

3=s.

We now have the length of s, which is 3.

-

Since we now know what s is, we can add them all up once more.

3+5+7+2+4=21

You said the full perimeter is 35.  This means j has to be 35-21, which is 14.

-

This drawing is not drawn to scale, I assume you are drawing this for practice.

-

Good luck on your test!

Answer:

he purchased 12 pencils

Step-by-step explanation:

1.24x12=14.88

14.88-20= 5.12

also this kid i knew has the same pfp

please

that is the solution

Answer:8 miles

Step-by-step explanation:

---Divide by 1565

9390 chairs / 1565 tables

6 chairs / table

Hope this helps!

Answer:

y= 40 degree

Step-by-step explanation:

ACD+CDA+DAC= 180 degree

y+ 90+30+20= 180 degree

y+140 = 180

y= 180- 140 degree

y= 40 degree

Hope it helps you :)))))

have a good day

Answer:

y= ⅓x +2

Step-by-step explanation:

Since the graph is a linear graph, let's use the slope-intercept form to find its equation.

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

The y-intercept is the point at which the graph cuts through the y-axis. In this case, the y-intercept is 2.

Thus, y= mx +2.

Let's find the slope of the graph.

First, identify 2 pairs of coordinates from the graph:

(0, 2) and (3, 3)

Next, substitute these coordinates into the slope formula below:

[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

slope

[tex] = \frac{3 - 2}{3 - 0} [/tex]

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

Thus, the equation of the graph is y= ⅓x +2.

Answer:

60th percentile = 23.5

Step-by-step explanation:

Put numbers in order from lowest to highest:

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

Formula:

60th percentile = 60% x Total number of elements

We have 20 scores,

60th percentile = 60% x 20

                          = 0.60 x 20

                          = 12

the 60th percentile is the 12th number on the list

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

The 60th percentile is between 23 and 24

23 + 24 / 2 = 23.5

Answer:

a. 94.444 m/s

b. 0.001 s

Step-by-step explanation:

#a

#b

By finding common factors, we conclude that we can divide the trees in 6 or in 9 parts, but not in 8.

We know that each of these parts needs to have the same number of each type of trees.

So we need to see if 6, 8, or 9, are common factors between 36 and 54.

First:

6*6 = 36

9*4 = 36

So 9 and 6 are factors of 36.

And 9*6 = 54

So 9 and 6 are factors of 54.

(8 is not a factor of neither)

So 9 and 6 are common factors between 36 and 54.

Then we can divide the trees in 6 or in 9 parts, but not in 8.

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Answer:

x = -2

Step-by-step explanation:

Given: [tex]\textsf{$\dfrac{x+3}{x+4}=\dfrac{x+5}{x+8}$}[/tex]

1. Cross-multiply

(x + 3)(x + 8) = (x + 5)(x + 4)

2. Distribute

⟹ (x + 3)(x + 8) = (x + 5)(x + 4)

⟹ x(x) + x(8) + 3(x) + 3(8) = x(x) + x(4) + 5(x) + 5(4)

⟹ x² + 8x + 3x + 24 = x² + 4x + 5x + 20

3. Combine like terms

⟹ x² + 8x + 3x + 24 = x² + 4x + 5x + 20

⟹ x² + 11x + 24 = x² + 9x + 20

4. Subtract x² from both sides

⟹ x² - x² + 11x + 24 = x² - x²  + 9x + 20

⟹ 11x + 24 = 9x + 20

5. Subtract 24 from both sides

⟹ 11x + 24 - 24 = 9x + 20 - 24

⟹ 11x = 9x - 4

6. Subtract 9x from both sides

⟹ 11x = 9x - 4

⟹ 11x - 9x = 9x - 9x - 4

⟹ 2x = -4

7. Divide both sides by 2 to isolate the variable

⟹ 2x ÷ 2 = -4 ÷ 2

⟹ x = -2

Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Thus, the probability of milk then white is given by:

[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]

0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.

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The functions in ascending orders are:

1. 3x

2. 3x + 8

3. x^2

4. x^2 + 6

5. 4^x

6. 4^x + 3

A function is known to be that relation that is said to exist between a set of numbers that is known to be having one output each.

Note that in the above such as 3x, 3x + 8, the  functions in ascending orders as it start with the function that has it least value.

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Answer:

-3y^2+5xy

Step-by-step explanation: Just cancel out all of the numbers with the variable "y"

Binomial [tex]-3y^{2}+5xy[/tex] when added to polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex]  gives  polynomial  that does not contain the variable y .

A mathematical expression consisting of two terms connected by a plus sign or minus sign .

Example: x + 2 is a binomial, where x and 2 are two separate terms.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer

According to the question

polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex]

when added with  [tex]-3y^{2}+5xy[/tex]  

= [tex]2x^{2}+1[/tex]   (as [tex]3y^{2} -5xy[/tex] got cancelled )

that does not contain the variable y

Hence, Binomial [tex]-3y^{2}+5xy[/tex] when added to polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex]  gives that does not contain the variable y .

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Answer:

centre = (- 3, 2 )

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 )

(x + 3)² + (y - 2)² = 64 ← is in standard form

with centre (- 3, 2 )

Answer:

Approximately 6 cups

Step-by-step explanation:

One pint is equal to 2.402 cups. Multiplied by 2.5, that gives you 6.00475. The final answer (6 cups) is rounded.

Length be x

width be x-5

So

Area=Length×Breadth

Or

If x turned y

Option C

Option A can be true as per commutatI've property

Option B is true

Answer:

y² - 5y = 750

750 - y(y - 5) = 0

(y + 25)(y - 30) = 0

Step-by-step explanation:

Formula

Area of a rectangle = length × width

Given:

Substituting the given values into the formula and rearranging in different way:

Equation 1

⇒ 750 = y(y - 5)

⇒ y(y - 5) = 750

⇒ y² - 5y = 750

Equation 2

⇒ 750 = y(y - 5)

⇒ 750 - y(y - 5) = 0

Equation 3

⇒ 750 = y(y - 5)

⇒ y(y - 5) - 750 = 0

⇒ y² - 5y - 750 = 0

⇒ y² - 30y + 25y - 750 = 0

⇒ y(y - 30) + 25(y - 30) = 0

⇒ (y + 25)(y - 30) = 0

Answer: I think it might be 10y

2

+39y+35

Step-by-step explanation: Apply the distributive property by multiplying each term of 2y+5 by each term of 5y+7. Then, Combine 14y and 25y to get 39y.

hope this helps!

♥ Chen was here

Answer:

10y^2 + 39y +35

Step-by-step explanation:

First distribute (2y+5)(5y+7)-

2y(5y + 7 )+ 5(5y + 7) This turns into:

10y^2 + 14y + 25y +35

Now combine the like terms (14y+25y)

You should get 10y^2 + 39y + 35 which is your final answer. :)