Answer to this math question

Answer:

You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]

Explanation:

To rationalize any expression, you must multiply it by its conjugate. A conjugate is defined as a similar expression to the original one but with an opposite sign

This means that:

The conjugate of a + b would be a -  b

Now, the given expression is [tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]

Consider the denominator:

From the above, we can conclude that the conjugate of [tex]\sqrt{13}+\sqrt{11}[/tex] is [tex]\sqrt{13}-\sqrt{11}[/tex]

And, remember that we need to keep the value of the expression unchanged. This means that we must multiply both the numerator and the denominator by the same value

Therefore:

You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex] in order to rationalize the denominator

Hope this helps :)

Answer:

[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]

Step-by-step explanation:

We are given the following expression and we are to determine the expression that we need to multiply it with in order to rationalize the denominator:

[tex] \frac { 2 } { \sqrt { 13 } + \sqrt { 11 } } [/tex]

To rationalize its denominator, we must multiply it with its conjugate.

For the denominator of the given expression, its conjugate would be [tex] \sqrt { 13 } - \sqrt { 11 } [/tex].

So to rationalize the expression, we would multiply it with:

[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]

Answer:

You would need to order 28 pounds. (27.27...)

Step-by-step explanation:

Let x be the number of cantaloupe. Then, 0.55x-=15.

0.55x=15

55x=1500

11x=300

x=300/11

x=27.27...

To make fruit salad using cantaloupe, you would need to order 28 pounds (AP) if you only need 15 pounds (EP) and the cantaloupe has a 55% yield.

To determine how much cantaloupe (AP) you would need to order, you need to consider the yield percentage. If the cantaloupe has a 55% yield, it means that 55% of the cantaloupe will be usable. So, you need to order more than 15 pounds (EP) to account for the reduced yield.

To calculate the amount of cantaloupe (AP) to order, you can use the formula:

AP = EP / Yield Percentage

Using the given values, the calculation would be:

AP = 15 pounds / 55% = 27.27 pounds

Rounded up to the nearest whole number, you would need to order 28 pounds of cantaloupe (AP) to obtain 15 pounds (EP) with a 55% yield.

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Answer:

V≈1470.27cm³

Hope this helps :D

Answer:

There would be 7 groups of students because 56 divided by 8 students gives you 7 groups.

Step-by-step explanation:

Answer:

7 groups 56÷8=7 that is the answer

Answer:

22.5

30

37.5

Step-by-step explanation:

You have to multiply each ratio part by x to get them properly set up to add to  90.

3x + 4x + 5x = 90               Combine the left side

12x = 90                              Divide by 12

12x/12 =90/12                      Do the division

x = 7.5

3x = 3*7.5 = 22.5

4x = 4*7.5 = 30

5x = 5*7.5 = 37.5

Total             90

Final answer:

The lengths of the sides of the triangle with a perimeter of 90 cm and sides in the ratio 3:4:5 are 22.5 cm, 30 cm, and 37.5 cm. This is found by setting up an equation with variable x representing the common multiplier for the ratio, solving for x, and then calculating each side's length.

Explanation:

To solve the problem of finding the length of each side of a triangle with sides in the ratio 3:4:5 and a perimeter of 90 cm, we first set up an algebraic equation. Let the sides of the triangle be 3x, 4x, and 5x, respectively. The perimeter is the sum of these sides, so we have the equation 3x + 4x + 5x = 90 cm. Simplifying this gives us 12x = 90 cm. To find the value of x, we divide both sides of the equation by 12, resulting in x = 90 cm / 12, which simplifies to x = 7.5 cm. Subsequently, the lengths of the sides are 3x = 22.5 cm, 4x = 30 cm, and 5x = 37.5 cm.

Answer: 75% Of the original price

Step-by-step explanation:

Break it down into shapes you know. There's a triangle and a rectangle. The area of a rectangle is l*w and in this case it's 5*6 or 30 units². The area of a triangle is 1/2b*h and in this case that is 1/2 * 6 * 3 or 9 units². Add the areas together to find the total area, which is 39 units².

Answer: 5

Step-by-step explanation: The first piece of information that you need to know is that the product is the answer when two numbers are multiplied. Therefore, you need to multiply the two sets of numbers, and then subtract.

The formula will be:

(5 x 2) - (5 x 1)=

First, do what is inside the parentheses:

10 - 5=

And solve...

5

The expression for the calculation the difference of the products 5 and 2 and 5 and 1 is (5 x 2) - (5 x 1).

Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×' ) Division (Finding the quotient; '÷')

The first thing you should be aware of is that the result of multiplying two integers is the product.

The two sets of numbers must therefore be multiplied before being subtracted.

The Expression will be:

(5 x 2) - (5 x 1)

First, work on the brackets separately

(5 x 2) = 10

(5 x 1)= 5

So, (5 x 2) - (5 x 1)

= 10 - 5

=5

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Answer:

The area would be 170 cubic inches.

Step-by-step explanation:

To find the area, use the area of a trapezoid formula.

A = (a + b)/2*h

Now input the values

A = (18 + 22)/2 * 8.5

A = 40/2 * 8.5

A = 20 * 8.5

A = 170

Answer:8

Step-by-step explanation:

Move all terms not containing  x  to the right side of the equation.Raise each side of the equation to the  2 /3  power to eliminate the fractional exponent on the left side.

Solve the equation for  x .

Answer:

[tex] x = 8 [/tex]

Step-by-step explanation:

[tex] (x + 1)^\frac{3}{2} - 2 = 25 [/tex]

[tex] (x + 1)^\frac{3}{2} = 27 [/tex]

[tex] \left((x + 1)^\frac{3}{2} \right)^\frac{2}{3} = 27^\frac{2}{3} [/tex]

[tex] x + 1 = 3^2 [/tex]

[tex] x + 1 = 9 [/tex]

[tex] x = 8 [/tex]

Answer:

The answer C. y=60x+120

Step-by-step explanation:

By using desmos, you can see the plotted points and what goes correctly into the line.

Answer: n=16

Step-by-step explanation:

The solution to the equation is n = 16.

The equation 1/2 * n = 8 can be solved by multiplying both sides by 2 to find n = 16.

To solve the equation 1/2 * n = 8:

Multiply both sides by 2 to isolate n: n = 8 * 2 = 16.

Therefore, the solution to the equation is n = 16.

I believe that the answer is there is 1 thirds in 1/3 I hope this helps

Answer:

one

Step-by-step explanation:

There is only one third is 1/3.

If you enjoy baking, think of it in the sense of a recipe calling for 4/3 cups of sugar. You grab a 1/3 cup and you would scoop four times in order to have 4/3 cups of sugar.

however since your recipe only calls for 1/3, you will only need one scoop.

Answer: 5h + d

Step-by-step explanation: The equation that Sara could use to determine her pay check is 5h + d = amount she will earn.

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❖ The correct answer choice is A. 34 min.

Find the difference (subtraction):

20 - -14 = 34

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I think it’s D. But I’m not 100 sure

the answer is D. Multiply by 2 to get the next term

Answer:

It is D, multiply by 2 to get the next term.

Step-by-step explanation:

1 x 2 = 2

2 x 2 = 4

4 x 2 = 8

and so on.....

Answer:

a

Step-by-step explanation:

Based on the slope and y-intercept, the graph most closely models the linear equation 3x + 5y = 10.

Out of the three choices you provided, the graph most closely resembles the equation 3x + 5y = 10. Here's why:

        So, the equation 3x + 5y = 10 also has a y-intercept of 2.

The other two equations do not match the graph as well:

Final answer:

To calculate the Boeing 747's average speed, you subtract the one hour it departs after the small plane from the total travel time of the small plane and divide the same distance of 750 miles by this new time. The 747's average speed is found to be 500 mph.

Explanation:

The question asks for the average speed of a Boeing 747 that departs one hour after a small airplane and arrives at the same time. The small airplane travels 750 miles at an average speed of 300 miles per hour (mph). To find the average speed of the 747, we first calculate the time it takes for the small airplane to reach the destination:

Time = Distance ÷ Speed = 750 miles ÷ 300 mph = 2.5 hours

The 747 leaves an hour later, so its travel time is 2.5 hours - 1 hour = 1.5 hours. The 747 covers the same 750 miles in this shorter time frame:

Average speed of 747 = Distance ÷ Time = 750 miles ÷ 1.5 hours = 500 mph

The computed result is that the 747's average speed is 500 mph to cover the same distance and arrive simultaneously with the small airplane.

Answer:

False

Step-by-step explanation:

To form a triangle, the sum of any two sides must be LARGER than the length of the third side.  

This question says the sum of two sides are equal to the length of the third side.  This wouldn't form a triangle.

Final answer:

Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.

Explanation:

Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.

In an isosceles triangle, two sides have the same length (congruent sides) and the remaining side is different (non-congruent side).

For example, if we have a triangle ABC where AB = BC (congruent sides) and AC is a different length (non-congruent side), then the triangle ABC is isosceles.

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]

[tex]120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing tool -----> solve the quadratic equation

see the attached figure

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5[/tex] ----> [tex]x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

47 cm

Step-by-step explanation:

its really simple just put them in from least to greatest then cross one off from each side until you get your middle number.

The number 6 is 75 percent of 8

Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.

We need to find the number that is state 25% of number is 1.

Let the unknown number is represneted by b.

It can be written by;

x% x 8 = 6

6/8 = 0.75

0.75 x 100

x= 75%

Therefore, the percent would be 75%

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Answer:

circumference so with all the diameters and stuff it would be 4[tex]\pi[/tex] or 12.56

[tex] \frac{12}{n} - 12[/tex]

Final answer:

An algebraic expression for '12 less than the quotient of 12 and a number z' is represented by the mathematical expression (12/z) - 12.

Explanation:

To write an algebraic expression for "12 less than the quotient of 12 and a number z," you need to understand how to translate the words into a mathematical expression. The quotient of 12 and a number z is written as 12/z. To represent 12 less than this quotient, you simply subtract 12 from it, thus the expression becomes (12/z) - 12.

Answer:

A

Step-by-step explanation:

The volume of a prism can be found by multiplying the area of the base by the height. It is the formula V = B*h. Here B = 108. Substitute and solve.

V = 108*8 = 864

This is answer A.

Answer:

152,587,890,625

Step-by-step explanation:

5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5=[tex]5^{16}[/tex]

[tex]5^{16}[/tex]=152,587,890,625

Answer:

152,587,890,625

Step-by-step explanation:

I don't know if your joking nor not but this is the answer if your weren't <#3

Answer:

Step-by-step explanation:

The is neither geometric nor arithmetic. The differences have to be the same.

99 - 89.9 = 9.1

89.9 - 78.8 = 11.1

78.8 - 68.7 = 10.1

==========

Answer:

-76.204

37.673

Step-by-step explanation:

ur welcome :0

Final answer:

To find an equation of the form y = a + b ln(x) to model the data, follow these steps: Enter the data into a calculator and make a scatter plot, use the calculator's regression function to find the equation of the least-squares regression line, and add the equation of the regression line to the scatter plot.

Explanation:

Logarithmic Regression

To find an equation of the form y = a + b ln(x) to model the data, follow these steps:

By doing this, you will obtain the equation that models the data using logarithmic regression.

Answer:

The answer is ⇒ x = 0.73244

Step-by-step explanation:

∵ 90^x = 27 ⇒ insert log in both sides

∴ [tex]log(90)^{x}=log(27)[/tex]

∵ 90 = 9 × 10 , 27 = 3³

∵ log(a)^b = b log(a)

∴ log(9 × 10)^x = x log(9 × 10)

∴ [tex]xlog(9*10)=log(3^{3})[/tex]

∵ log(a × b) = log(a) + log(b)⇒log(9 × 10) = log(9) + log(10)

∴ [tex]x[log(9)+log(10)]=3log(3)[/tex]

∵ log(10) = 1 , 9 = 3²

∴ [tex]x[log(3)^{2}+1]=3log(3)[/tex]

∴ [tex]x[2log(3)+1] = 3log(3)[/tex]

∴ x = (3log3)/[2log(3)+1]

∴ x = 0.73244

ANSWER

[tex]x \approx0.732[/tex]

EXPLANATION

The given exponential equation is

[tex] {90}^{x} = 27[/tex]

We take natural log of both sides

[tex] ln( {90}^{x} ) = ln(27) [/tex]

Recall and the following property of logarithms.

[tex] ln( {a}^{n} ) = n \: ln(a) [/tex]

This implies that;

[tex]x ln(90) = ln(27) [/tex]

Solve for x.

[tex]x = \frac{ ln(27) }{ ln(90) } [/tex]

[tex]x \approx0.732[/tex]