A rectangle has a height of 2 and a width of 5x^2-2x+3x

Express the area of the entire rectangle.
Expression should be expanded.

how would I do this?^^ if you can break down the steps for me that'd be amazing!​

Answer:

Step-by-step explanation:

A = {2,8,10,14}

B= {6,8,20}

C={8,18,20,24}

A ∩ B --> intersection means elements that  are in both sets A & B

A ∩ B = {8}

A∩ C =  {8}

B ∩ C = {8 , 20}

A∩B ∩ C = {8}

First blue box = { 2,10, 14}

Second blue box = {18, 24}

First green box = { 8}

Second green box = { 20}

b) A ∩ B = {8}

n [ A ∩ B] = 1

Probability of the number to be a member of A∩B =  1 / 25

Answer:

The answer is 2.5

Step-by-step explanation:

Formula Used is is ½ x x+y

so it is ½ x 2 + 3

½ x 5 = 2.5

Answer:

2=2/1

3=3/1

multiplying both fractions by 10.

2*10/1*10

3*10/1*10

20/10 and 30/10

so nos are 21/10.......29/10

Answer:

[tex]c. \: \sqrt{9} . \sqrt{4} [/tex]

[tex] \\ [/tex]

Step-by-step explanation:

[tex] \sqrt{9.4} \\ = \sqrt{9} \times \sqrt{4} [/tex]

Answer:

x = -8

Step-by-step explanation:

6x - 3 = -51

Add 3 to each side

6x - 3+3 = -51+3

6x = -48

Divide each side by 6

6x/6 = -48/6

x = -8

Answer:

900

Step-by-step explanation:

15 TIMES 60 IS 900

Hi there! Hopefully this helps!

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Answer: There are 900 minutes in 15 hours.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:

15 x 60 = 900.

Answer: The annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.

Step-by-step explanation:

Given: Volume of Atlantic Ocean= [tex]3.1\times10^{17}[/tex] cubic meters

Annual flow of Mississippi river = [tex]6.3\times10^{11}[/tex] cubic meters.

then, the number of times the annual flow of the Mississippi river would fit in the Atlantic ocean = [tex]\dfrac{\text{ Volume of Atlantic Ocean}}{\text{Annual flow of Mississippi river}}[/tex]

[tex]=\dfrac{3.1\times10^{17}}{6.3\times10^{11}}\ \ \=0.492063492063\times10^{17-11}\ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=0.492063492063\times10^6\approx4.92\times10^5[/tex]

Hence,  the annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.

Answer:

Option C.

Step-by-step explanation:

It is given that,

[tex]\overline{AB}\cong \overline {DE}[/tex]

[tex]\overline{AC}\cong \overline {DF}[/tex]

According to SAS congruence property, two triangles are congruent if they have two congruent corresponding sides and their included angles are congruent.

Angle between [tex]\overline{AB}\text{ and }\overline {AC}[/tex] is [tex]\angle A[/tex].

Angle between [tex]\overline{DE}\text{ and }\overline {DF}[/tex] is [tex]\angle D[/tex].

So, [tex]\Delta ABC\cong \Delta DE F[/tex] by SAS, if

[tex]\angle A\cong \angle D[/tex]

Therefore, the correct option is C.

Answer:

it's about 106.71ft

Step-by-step explanation:

make this problem a triangle. the ramp length is 312ft, and it is the hypotenuse of the triangle. 20 is the angle between the ramp and the floor. so what I did was take the sine of 20 and get: sin(20)=x/312 then you multiply both sides by 312 to isolate the variable. multiplying sin(20) by 312 gave me 106.71 + some change idk if you're supposed to round it or not haha.

Answer:

x = 26, 16

Step-by-step explanation:

( x-21) ^2 = 25

Take the square root of each side

sqrt(( x-21) ^2) = ±sqrt(25)

x-21 = ±5

Add 21 to each side

x-21+21 = 21±5

x = 21±5

x = 21+5  and x = 21-5

x = 26, 16

Answer:

90000 km

Step-by-step explanation:

1 hour = 3600 sec

distance = speed x time

              = 25 km/s x 3600 s

               = 90000 km

standard form = 9 x 10⁴

Answer:

A.  6 and 30

B.  8 and 28

Step-by-step explanation:

we know that the area of the three squares must satisfy the Pythagorean Theorem so c² = a² + b²

where

c²  is the area of the largest square

a² and b² are the areas of the smaller squares

now.. 36² = a² + b2

The sum of the areas of the smaller squares must be equal to 36

therefore

6 and 30 >>>> could be the areas of the smaller squares (6 + 30 = 36)

8 and 28 >>>> could be the areas of the smaller squares (8 + 28 = 36)

hope it clears your mind.

Please mark as the brainliest

Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.

With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.

Answer:

total rotation = 90 clockwise.

Step-by-step explanation:

Rotation from B to negative y-axis = 45 degrees because B(-3,-3)

Rotation from negative y-axis to B' = 45 degrees because B(-3,3)

Therefore total rotation = 45+45 = 90 clockwise.

Answer:

m∠CDE = 60°

Step-by-step explanation:

Given that the arc at the center = 2 times the arc at the circumference, we have;

Angle at the center = arc CE = 120°

Whereby the angle at the circumference is given as m∠CDE and it is opposite the circle arc CE

We note that m∠CDE is the acute angle between chord DC and DE

Therefore, we have;

Angle at the center = 120° = 2 times the arc at the circumference = 2 × m∠CDE

120° = 2 × m∠CDE

m∠CDE = 120/2 = 60°

Therefore the angle of m∠CDE is equal to 60°.

Answer:

D(-4, -3), E(-7, 4), and F(-7, -3).

Step-by-step explanation:

The current coordinates are A(4, 2), B(7, 9), and C(7, 2).

If you reflect the coordinates over the y-axis, the y-values will not be changing, but the signs of the x-values will flip. So, you will have A'(-4, 2), B'(-7, 9), and C'(-7, 2).

When you translate the resulting triangle down 5 units, the y-values will decrease by 5 units. So, the coordinates of triangle DEF will be D(-4, -3), E(-7, 4), and F(-7, -3).

Hope this helps!

Answer:

D (-4, -3)

E (-7, 4)

F (-7,-3)

Step-by-step explanation:

Well triangle ABC reflected over the y-axis to make triangle DEF looks like the image below. ↓

Then we have to translate triangle DEF 5 units down.

With the coordinates D, E, F,

D (-4,2)

E (-7,9)

F (-7,2)

To translate it 5 units down we just subtract the y coordinates by 5.

D (-4, -3)

E (-7, 4)

F (-7,-3)

Thus,

the coordinates for triangle DEF are (-4, -3) , (-7, 4) , (-7,-3).

Hope this helps :)

Answer:

mMN + 150 = 180

Step-by-step explanation:

Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.

Given that:

NO is the radius and ∠NOP = 150°.

The angle addition postulate which states that a larger angle is formed when two smaller angles are placed side by side. If two angle x and y are small angles placed side by side, a big angle Z formed is given as:

z = x + y.

Therefore in circle O, using angle addition postulate:

mMN + ∠NOP = mMP

But mMP = 180° (angle on a straight line)

mMN +   ∠NOP = 180°

mMN + 150 = 180

Answer:

A : quadratic trinomial

Step-by-step explanation:

Given

(3x² - 11x - 4) - (2x² - x - 6)

Distribute both parenthesis, noting the second is distributed by - 1

= 3x² - 11x - 4 - 2x² + x + 6 ← collect like terms

= x² - 10x + 2 ←  this is a quadratic with 3 terms, thus quadratic trinomial → A

Hope helped.. Mark BRAINLIEST

Thanks!!

Answer:

A. quadratic trinomial

Step-by-step explanation:

[tex](3x^2-11x-4)-(2x^2-x-6)[/tex]

Remember that polynomials are closed to subtraction, therefore, linear binomial and linear monomial can't be an option.

[tex]3x^2-11x-4-2x^2+x+6[/tex]

[tex]x^2-10x+2[/tex]

We got a quadratic equation. Once it has the c term, it is a quadratic trinomial.

Answer:

18

Step-by-step explanation:

You have 25 when you are done, but you made 7, so subtract that from 27.

25-7 equals 18.

Answer:

13.33 cm

Step-by-step explanation:

Given, ratio of volumes v ÷ V = 8 ÷ 27

This ratio is applicable to heights of same containers, as the volume is directly proportional with height (V=Ah, A- base, h- height)

So we have:

and

Then,

Answer:

13.33 cm

Step-by-step explanation:

Down here.

Answer: A. [tex]9x^2 - 16y^2[/tex] .

Step-by-step explanation:

From all the options only option A has both terms square and they minus sign between them.

Also, [tex]9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)[/tex]

Here a= 3x and b= 4

Hence, the correct answer is A. [tex]9x^2 - 16y^2[/tex] .

Answer:

A

Step-by-step explanation:

Answer: 27061

Step-by-step explanation:

given that Р = 0.5

so

1 - P = 1 - 0.5  = 0.5

ERROR OF MARGIN E = 0.01

SIGNIFICANCE LEVEL α = 1 - confidence level

α = [(1 - (99.9/100)] = 0.0010

α / 2 = 0.001 / 2 = 0.0005

Zα/2 = Z0.0005 = 3.29  (using the Z table )

therefore

Sample size n = ((Zα/2) / E)² * P * (1 - P )

Sample size  n = (3.29 / 0.01)² * 0.5 * 0.5

Sample size n = 108,241 * 0.5 * 0.5

Sample size n = 27,060.25 ≈ 27,061

Answer:

sample size should be atleast n= 27069

Step-by-step explanation:

Given that,

confident level(CI) = 99%= 0.999

desired marginal error=1%= 0.01

note: marginal error = length of CL/2

significant level α = 1 - confident level = 1 - 0.999= 0.001

critical value = Zα/2 = Z(0.001/2) = Z0.0005( value of from z table) = 3.2905267

since we don't have preliminary estimate, p' = 0.5, which is require for maximum value

n = p' × (1 - p')(critical value/desired marginal)²

n= 0.5 × 0.5(3.2905267/0.01)²

n = 27068.91

the value of n has to be an integer = 27069

Answer:

the second one.its a parallelogram

Answer:

in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]

Now, to simplify this expression:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]

Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.

Answer:

Option C. 3077.2 mm³

Step-by-step explanation:

Data obtained from the question include the following:

Diameter (d) = 17 mm

Height (h) = 60 mm

Pi (π) = 3.14

Volume =?

Next, we shall determine the radius of the cone. This is illustrated below:

Diameter (d) = 17 mm

Radius (r) =.?

Radius (r) = diameter (d)/2

r = d/2

r = 14/2

r = 7 mm.

The radius therefore, is 7 mm.

To know how much frozen water

is in the icicle, we shall calculate the volume of the icicle using the formula for calculating the volume of a cone. This is illustrated below:

Height (h) = 60 mm

Pi (π) = 3.14

Radius (r) = 7 mm

Volume =..?

V = ⅓πr²h

V = ⅓ × 3.14 × 7² × 60

V = 3.14 × 49 × 20

V = 3077.2 mm³

Therefore, the amount of frozen water in the icicle is 3077.2 mm³

Answer:

C 3,077.2 mm

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

8+5+15+12+10= 50 / 5 = 10

Answer:

see explanation

Step-by-step explanation:

Using the translation rule (x, y ) → (x - 2, y + 4 )

Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus

A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )

B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )

C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )

Answer:

22 units.

Step-by-step explanation:

In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.

In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.

Hope this helps!

Answer:  1) c     2) d

Step-by-step explanation:

Use Pythagorean Theorem to find the hypotenuse (r):  x² + y² = r²

Given: x = 2, y = 6

                2² + 6² = r²

                4 + 36 = r²

                      40 = r²

                      [tex]\sqrt{40}=r[/tex]

[tex]\sin \theta=\dfrac{y}{r}\quad =\large\boxed{\dfrac{6}{\sqrt{40}}}\quad \rightarrow \dfrac{6}{2\sqrt{10}}\quad \rightarrow \dfrac{3}{\sqrt{10}}[/tex]

*******************************************************************************************

[tex]\sin \theta = \dfrac{opposite(y)}{hypotenuse(r)}\quad =\dfrac{12}{20}\quad \rightarrow \dfrac{3}{5}\quad \rightarrow \large\boxed{0.6}\\\\\\\cos \theta = \dfrac{adjacent(x)}{hypotenuse(r)}\quad =\dfrac{16}{20}\quad \rightarrow \dfrac{4}{5}\quad \rightarrow \large\boxed{0.8}[/tex]

Answer:

4

Step-by-step explanation:

The coordinates are: A(0,0), B(1,4), C(2,8), D(3,12), E(4,16)

Using coordinates B and D, slope = (12 - 4)/(3 - 1) = 8/2

        ∴ slope = 4

Answer:

4

Step-by-step explanation: