Find the area of this prism.

Answer:

6ab + 8a² - 15b - 20a

Step-by-step explanation:

Expand by using FOIL method

4(2a-5) + 3b(2a-5)

4a(2a) + 4a × -5 + 3b × -5

Simplify terms

8a² - 20a + 6ba -15b

6ab + 8a² - 15b - 20a

Given:

The expressions are:

[tex]\sqrt[3]{24},\sqrt{48},\sqrt[3]{54},\sqrt{45}[/tex]

To find:

The simplified form of each expression.

Solution:

We have,

[tex]\sqrt[3]{24}[/tex]

It can be written as:

[tex]\sqrt[3]{24}=\sqrt[3]{2\times 2\times 2\times 3}[/tex]

[tex]\sqrt[3]{24}=2\sqrt[3]{3}[/tex]

Similarly,

[tex]\sqrt{48}=\sqrt{2\times 2\times 2\times 2\times 3}[/tex]

[tex]\sqrt{48}=(2\times 2)\sqrt{3}[/tex]

[tex]\sqrt{48}=4\sqrt{3}[/tex]

And,

[tex]\sqrt[3]{54}=\sqrt[3]{2\times 3\times 3\times 3}[/tex]

[tex]\sqrt[3]{54}=3\sqrt[3]{2}[/tex]

In the same way,

[tex]\sqrt{45}=\sqrt{3\times 3\times 5}[/tex]

[tex]\sqrt{45}=3\sqrt{5}[/tex]

Therefore, the required pairs are:

[tex]\sqrt[3]{24}\to 2\sqrt[3]{3}[/tex]

[tex]\sqrt{48}\to 4\sqrt{3}[/tex]

[tex]\sqrt[3]{54}\to 3\sqrt[3]{2}[/tex]

[tex]\sqrt{45}\to 3\sqrt{5}[/tex]

Answer:

[tex]y = \sqrt{900 - x^2[/tex]

Step-by-step explanation:

Given

From the complete question, we have:

[tex]r=30[/tex] --- radius

Required

Expression for the height of the roller coaster

We have:

[tex]x^2 + y^2 = r^2[/tex] --- equation of circle

Substitute 30 for r

[tex]x^2 + y^2 = 30^2[/tex]

[tex]x^2 + y^2 = 900[/tex]

Since the roller coaster is half of the circle, the height is defined by y.

So: make y the subject

[tex]y^2 = 900 - x^2[/tex]

Take square roots

[tex]y = \sqrt{900 - x^2[/tex]

Hence, the height is:

[tex]\sqrt{900 - x^2[/tex]

Given:

Scott can run 20 km in 85 minutes.

To find:

How long will it take Scott to run 52 km?

Solution:

Let us consider x be the number of minutes it will take him to run 52 km.

We know that,

[tex]Speed=\dfrac{Distance}{Time}[/tex]

By using this formula, we get

[tex]Speed=\dfrac{20}{85}[/tex]           ...(i)

[tex]Speed=\dfrac{52}{x}[/tex]             ...(ii)

On equating (i) and (ii), we get

[tex]\dfrac{20}{85}=\dfrac{52}{x}[/tex]

[tex]20\times x=52\times 85[/tex]

[tex]20x=4420[/tex]

On dividing both sides by 20, we get

[tex]x=\dfrac{4420}{20}[/tex]

[tex]x=221[/tex]

Hence, it will take 221 minutes to run 52 km.

Answer:

B

Step-by-step explanation:

that is a linear equation, therefore it makes a line, eliminating choices C and D.

Lines can literally Any x or y. So it would be B, a set of all the solutions to the equations.

Answer:

x = 39.59

Step-by-step explanation:

take 43 degree as reference angle

using sin rule

sin 43 = opposite / hypotenuse

0.682 = 27 / x

x = 27 / 0.682

x = 39 . 589

x = 39. 59

Answer:

thas multiple matrix bro

Step-by-step explanation:

Answer:

Mean = 7

Step-by-step explanation:

Given the following data;

Number of games = 8

Scores = 5, 11, 9, 9, 4, 5, 6, 7

We would sum all the scores together to get a total score.

Total scores = 5 + 11 + 9 + 9 + 4 + 5 + 6 + 7 = 56

Now, to find the mean;

[tex] Mean = \frac {total \; scores}{number \; of \; games} [/tex]

Mean = 56/8

Mean = 7

Answer:

7 is the mean score.

Step-by-step explanation:

Now we have to,

→ find the required mean score.

The given scores are,

→ 5, 11, 9, 9, 4, 5, 6, 7

→ Numbers = 8

Then the mean score will be,

→ (5 + 11 + 9 + 9 + 4 + 5 + 6 + 7)/8

→ 56/8 = 7

Hence, the mean score is 7.

Answer:

[tex]{ \tt{2 {x}^{2} + 10x + 8 }} \\ { \tt{ = (x + 1)(x + 4)}}[/tex]

Answer:

A. 2 ( x + 4 )( x + 1 )

Step-by-step explanation:

2x² + 10x + 8

factor out 2 from the equation

2 ( x² + 5 x + 4 )

write 5x as a sum and rewrite the expression

2 ( x² + 4x + x + 4 )

factor out x from the equation

2 ( x ( x + 4 ) + x + 4 )

factor out x + 4 from the equation

2 ( x + 4 ) ( x + 1 )

Answer:

4/10=40%

Step-by-step explanation:

Answer:

Empty square = +

Empty Circle = ÷

Step-by-step explanation:

In order to eliminate the extra numbers from the equation you have to do the opposite of the problem. So...

-6x-1=5

-6x -1+1 = 5+1 (eliminating the 1 from the -6x side and adding it to the other side)

-6x = 6

-6x ÷ -6 = 6 ÷ -6 ( eliminating the-6 so that one side just has x)

so... x= -1

Answer: Option B is your correct answer.

Step-by-step explanation:

answer is in photo above

Answer:

A = 9x² + 12x

Step-by-step explanation:

The area (A) of the rectangle is calculated as

A = height × width

  = 3(3x² + 4x) ← distribute parenthesis by 3

   = 9x² + 12x

Answer:

For the blue one:

A1=length*breadth

   =3*3x^2

   =9x^2

For pink:

A2=length*breadth

    =3*4x

    =12x

So the total area is:

A=A1+A2

  =9x^2+12x

Step-by-step explanation:

5x + 3 = x + 11

4x=8

x=2

!!!!!

[tex]5x + 3 = x + 11 \\ 5x + 3 - x = 11 \\ 4x + 3 = 11 \\ 4x = 11 - 3 \\ 4x = 8 \\ x = \frac{8}{4} \\ x = 2[/tex]

Step-by-step explanation:

the answer is in the above image

Answer:

[tex]6\sqrt{2}[/tex]

Step-by-step explanation:

let the diagonal be d

using the pythagoras theorem,

[tex]6^{2} + 6^{2} = d^{2}[/tex]

[tex]d=\sqrt{72}[/tex]

which in radical form is

[tex]6\sqrt{2}[/tex]

Answer:

In 10 hours, the population is 6050 bacteria. In 20 hours, the population is 732050 bacteria.

Step-by-step explanation:

Bacterial populations can be assumed to grow exponentially. In 5 hours, since the population will have multiplied by 11, in 10 hours it will have multiplied by 121 (11^2) and by 14641 (11^4).

50 * 11 * 11 = 6050

50 * 11 * 11 * 11 * 11 = 732050

Answer:

Step-by-step explanation:

550 = 50 [tex]x^{5}[/tex]

11 =   [tex]x^{5}[/tex]

ln(11) = 5 ln(x)

x = [tex]e^{ln(11)/5}[/tex]

x = 1.615

10 hours ....

A= 50 ([tex]1.615^{10}[/tex] )

A= 50 ([tex]1.615^{10}[/tex] )

A=6050

20 hours ....

A= 50 ([tex]1.615^{20}[/tex] )

A= 50 ([tex]1.615^{20}[/tex] )

A=732,050

Answer:

yes it is correct

Step-by-step explanation:

option 1  

Answer:

Your answer is correct! 9:1

Step-by-step explanation:

Old Area = side x side

? = 2 x 2

     4cm

New Area-

Step 1: Triple the sides

2 x 3 = ?

    6cm

Step 2: Find the area

6 x 6 = ?

  36cm

The ratio of the new area to the old area is:

                     36 : 4

But wait! You can simply it!

36 / 4 = 9

4 / 4 = 1

So the new ratio would be:

                     9 : 1

Hope this helps!

Good Luck!

:)

Answer: Choice B

x+6y = 29  and  x+3y = 24.5

==============================================

Explanation:

x is the cost of a throw blanket

On top of this cost is the cost to embroider letters on it

Your name has 6 letters so it costs you an extra 6y dollars. Overall, you pay x+6y dollars. It says that your cost is $29

So that's where x+6y = 29 comes from.

-------------

Similarly, your friend also pays x dollars for the blanket itself plus an extra 3y dollars for the 3 letters in their name. Overall, they pay x+3y dollars. We're told they spent $24.50 which is where the equation x+3y = 24.5 comes from.

Answer:

2nd one = x + 6y = 29 , x + 3y = 24.5

Step-by-step explanation:

Have a nice day!

Answer:

[tex]\text{d. }106,250\:\mathrm{cm^2},\\\text{e. }38.5\:\mathrm{cm^2},\\\text{a. }85\:\mathrm{ft^2},\\\text{b. }7.89676\:\mathrm{m^2}[/tex]

Step-by-step explanation:

Part D:

The figure shows a parallelogram with base 425 cm and height 250 cm. Its area can be found by [tex]A=bh[/tex] and therefore the area of this shape is [tex]A=425\cdot 250=\boxed{106,250\:\mathrm{cm^2}}[/tex]

Part E:

The figure shows a trapezoid. The area of a trapezoid is equal to the average of its bases multiplied by the height. Since one base is 2 cm and the other base is 9 cm, the average of these bases is [tex]\frac{2+9}{2}=\frac{11}{2}=5.5\:\mathrm{cm}[/tex]. The height is given as 7 cm, therefore the area of the trapezoid is [tex]7\cdot 5.5=\boxed{38.5\:\mathrm{cm^2}}[/tex]

Part A:

The composite figure consists of two rectangles. The area of a rectangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=bh[/tex]. The total area of the figure is equal to the sum of the areas of these two rectangles.

Area of first rectangle (rectangle on bottom): [tex]5\cdot 13=65\:\mathrm{ft^2}[/tex]

Area of second rectangle (rectangle on top):

*Since we don't know the dimensions, we must find them. Start by converting 108 inches to feet:

[tex]108\:\mathrm{in}=9\:\mathrm{ft}[/tex]. Therefore, the dimensions of this rectangle are (10-5) ft by (13-9) ft [tex]\implies5\text{ by } 4[/tex] and this rectangle's area is [tex]5\cdot 4=20\:\mathrm{ft^2}[/tex]

Thus, the area of the figure is equal to [tex]65+20=\boxed{85\:\mathrm{ft^2}}[/tex]

Part B:

We've already found the area of the figure in the previous part in square feet. To find the area in square meters, use the conversion [tex]1\text{ square foot}=0.092903\text{ square meter}[/tex].

Therefore, the area of the figure, in square meters, is [tex]85\cdot 0.092903=\boxed{7.89676\:\mathrm{m^2}}[/tex]

√129 is less than [tex] \frac{95}{8} [/tex].

[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]

Let us first solve for √129.

➝[tex] \:\sqrt{129} [/tex]

➝[tex]\:11.3578[/tex]

Now,

➝[tex]\: \frac{95}{8} [/tex]

➝[tex]\:11.875[/tex]

Clearly,

➵[tex]\:11.3578 < 11.875[/tex]

➵[tex]\: \sqrt{129} < \frac{95}{8} [/tex]

Hence, √129 is less than [tex] \frac{95}{8}[/tex].

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]

Jeevan is not correct, the answer could be 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that Jessica's teacher asks a class to find the largest number that is smaller than 4.5.

Since Jessica's friend Jeevan gives the answer 4.4.

Therefore, we can see that 4.4 is not a whole number thus, it isn’t the largest number that is also less than 4.5.

The correct answer could be 4.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

Answer:

a) is the correct answer.

Answer:

x=20, y=17, and z=6 or (20,17,6)

Step-by-step explanation:

Hi there!

We're given the system of equations:

2x+z=46

3z=18

2y+z=40

and we need to solve for x, y, and z

first, let's find the value of z, as we have z by itself (no other variables) in 3z=18

divide both sides by z

z=6

the value of z is found :)

now we can use z=6 to find the value of the other variables; for example, plug z as 6 into 2x+z=46 to solve for x

2x+6=46

subtract 6 from both sides

2x=40

divide by 2

x=20

Finally, let's find y

once again, we can substitute z as 6 in the equation 2y+z=40 to find y

2y+6=40

subtract 6 from both sides

2y=34

divide by 2

y=17

so the answer is: x=20, y=17, and z=6; if you need it in a point it's (20,17,6)

Hope this helps! :)

Answer:

48 years old

Step-by-step explanation:

a + w = 62

a+3 = 3(w+3) =>a+3=3w+9

=> a-3w = 6

a+ w = 62

a- 3w= 6

________-

4w = 56

w = 14

so, the Aini's age now is 62-14 = 48 years old

semoga membantu

Answer:

Approximately 0.0121 will be left after 15 days.

Step-by-step explanation:

We can write an exponential function to model the situation. The standard exponential function is given by:

[tex]y=a(b)^x[/tex]

Let x represent the amount of days. Since the initial amount is 3,820 pounds, a = 3820. It decays at a rate of 57% per day. So, after one day, it will only have 100% - 57% = 43% or 0.43 of its previous amount. So, b = 0.43.

Hence, our function is:

[tex]y=3820(0.43)^x[/tex]

After 15 days, x = 15. Substitute and evaluate:

[tex]y(15)=3820(0.43)^{15}\approx 0.0121\text{ pounds}[/tex]

$50.00÷7hours=×$

$50.00÷7hours= 7.25

7.25 he charges per hour

Answer:

perpendicular

Step-by-step explanation:

start but putting each line into the standard line format

2x-y=-5

-y=-2x-5

y=2x+5

x+2y=-6

2y=-x-6

y=-(1/2)x-3

if lines are parallel the slopes would be the same. 2 is not equal to -1/2

if lines are perpendicular the slope of one would be the opposite inverse of the other.

negative inverse of 2 = - (1/2)

so the lines are perpendicular