Write an equation of the line in slope-intercept form.
The line passing through (0, 1) and (-4,5)

Answer:

The expression can be simplified into [tex]2\,\sqrt{5} +2\sqrt{2}[/tex]

with no square roots in the denominator

Step-by-step explanation:

We are considering the expression  [tex]\frac{6}{\sqrt{5}-\sqrt{2} }[/tex]  which I believe is what you wanted to type in your question.

The idea behind simplification of the expression, is normally associated with the rationalization of the denominator by eliminating irrational numbers from it. This means to get rid of any "irrational" number expression (like in this example, the square root of non-perfect square numbers ([tex]\sqrt{5}\,\,\,and \,\,\sqrt{2}[/tex]).

We proceed by writing this quotient in an equivalent form by multiplying its numerator and its denominator by what is called the "conjugate" of the denominator. In our case, multiply by " [tex](\sqrt{5} +\sqrt{2})[/tex] ", because such product will allow the denominator to become a rational number:

[tex]\frac{6}{\sqrt{5}-\sqrt{2} }\,*\,\frac{(\sqrt{5}+\sqrt{2} )}{(\sqrt{5}+\sqrt{2}) } =\frac{6\,(\sqrt{5}\,+\,\sqrt{2} )}{\sqrt{5}^2-\sqrt{2}^2 }=\frac{6\,(\sqrt{5}\,+\,\sqrt{2} )}{3}=2\,\sqrt{5} +2\sqrt{2}[/tex]

where we find all square roots eliminated from the denominator

Answer:

1.32

Step-by-step explanation:

3 gallon = 1

12 quarts = 4

12 quarts =1

$15.84=  1.32

Answer:

$1.32 per quart

Step-by-step explanation:

To find the price per quart, we must divide the price by the number of quarts.

price / quarts

We are told that a 3 gallon container costs $15.84. First, we must find out how many quarts are in 3 gallons.

We know that 1 gallon is equal to 4 quarts.

Let’s set up a proportion.

quarts/ gallons = quarts/ gallons

4 quarts /1 gallon = x quarts/ 3 gallons

4/1= x/3

Multiply both sides by 3

3*4/1= x/3*3

3*4/1=x

3*4=x

12=x

There are 12 quarts in 3 gallons.

Now we know how many quarts are in 3 gallons. We can find the price per quart.

price / quarts

It costs $15.84 for 12 quarts.

$15.84/12 quarts

Divide 15.84 by 12

$1.32 / quart

It costs $1.32 per quart of window cleaner.

Answer:

X=3

Step-by-step explanation:

Answer:

Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64  ---4 67x54 5xe4t4 6x

Answer:

x e [-10,-4]

Step-by-step explanation:

||x-5|+2|≤3

|x+5+2|≤3

|x+7|≤3

x+7≤3

x≤-4

x+7≥-3

x≥-10

x e [-10,-4]

Answer:

There is a zero percent chance of him giving his friends two green pens.

Step-by-step explanation:

He only has One pen.

Answer:

x = - 2

Step-by-step explanation:

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

Evaluating the numerator

9³ × 9 = [tex]9^{(3+1)}[/tex] = [tex]9^{4}[/tex] , thus

[tex]\frac{9^{4} }{9^{6} }[/tex]

= [tex]9^{(4-6)}[/tex] = [tex]9^{-2}[/tex]

and [tex]9^{-2}[/tex] = [tex]9^{x}[/tex]

Since bases on both sides are 9, then equate exponents

x = - 2

Given:

4(2 + a)= 24

Use Distributive Property:

8 + 4a = 24

Subtract 8 to both sides:

4a = 16

Divide 4 to both sides:

a = 4

Answer:

A = 4

Step-by-step explanation:

Assuming the question is asking what a is, then all you have to do is follow a few steps to get the right answer.

1) Use the distributive property to simplify the first part of the equation.

4(2+a) distribute the 4 to what is within the parenthesis, so multiply 4 to what is in the parenthesis. P.S: This also gets rid of the parenthesis.

(8 + 4a)

2) Now your equation looks like 8 + 4a = 24. Now, use inverse operations to isolate a. Inverse operations are basically using the opposite signs and processes to get some parts of an equation to another side.

2a. Subtract 8 from both sides of the equation:

8 + 4a - 8 = 24 - 8.

So now you have 4a = 16.

2b. Divide 4 from both sides of the equation.

4a/4 = 16/4

So now you have a = 4.

Final answer:

A = 4

Answer: 4.97 ft

Step-by-step explanation:

h = V / pi r^2

h = 250 / 3.14 x 4^2

Answer:

a. 2/5 and 2:3

b.  

c. 6

d. 40% and 60%

Step-by-step explanation:

a) The ratio of lemon juice to water as a fraction can be expressed as: 2/3.

b) The amount of water Sarah needs when she has 1¹/₂ cups of lemon juice,  is: 2.25 cups

c) The amount of lemon juice Sarah should add to 9 cups of water is: 6 Cups

d) 40% of the lemonade is lemon juice, and 60% is water.

e) She should increase the ratio to 3:2

f) Yes, Sarah would need more lemon juice than water to make the lemonade stronger.

a. The ratio of lemon juice to water as a fraction can be expressed as: 2/3.

b. The amount of water Sarah needs when she has 1¹/₂ cups of lemon juice,  is solved as:

1¹/₂ cups of lemon / water = 2/3

³/₂ cups of lemon / water = 2/3

Cross multiply to get:

water = 9/4

water = 2.25 cups

c. The amount of lemon juice Sarah should add to 9 cups of water is as follows:

lemon juice / 9 = 2/3

Cross multiply to get:

lemon juice = 18 / 3

lemon juice = 6 cups

d. The percentage of lemon juice and water in the lemonade if the total volume is 5 cups is:

Lemon juice: (2/5) * 100% = 40%

Water: (3/5) * 100% = 60%

e. What Sarah can do is to increase the ratio of lemon juice to water. One possible ratio could be 3 parts lemon juice to 2 parts water, or 3:2.

f. Yes, Sarah would need more lemon juice than water to make the lemonade stronger.

Read more about Ratio Problems at: https://brainly.com/question/12024093

#SPJ1

Answer:

[tex] x^{33} [/tex]

Step-by-step explanation:

[tex] \dfrac{x^8y^{-26}}{x^{14}y^{-5} \times x^{-39}y^{-21}} = [/tex]

A negative exponent in the numerator is a positive exponent in the denominator.

A negative exponent in the denominator is a positive exponent in the numerator.

[tex] = \dfrac{x^8y^{5}x^{39}y^{21}}{x^{14}y^{26}} [/tex]

[tex] = \dfrac{x^{8 + 39} y^{5 + 21}}{x^{14}y^{26}} [/tex]

[tex] = \dfrac{x^{47} y^{26}}{x^{14}y^{26}} [/tex]

[tex] = x^{47 - 14} y^{26 - 26} [/tex]

[tex] = x^{33} y^{1} [/tex]

[tex] = x^{33} [/tex]

Step-by-step explanation:

Answer:

200 miles

Explaination:

in order to fiind the point of interaction you must put the world problem into an liner equation.

y=mx+b

key:

miles : x

y= 0.70x + 120

&

y= 0.90x + 80

now you put them together

0.70x + 120 = 0.90x + 80

-0.70x. -0.70x

____________________ subtract slope from both sides

120 = 0.20x + 80. ( doesn't matter which one)

-80 - 80

____________________ subtract

40 = 0.20x

_________ Divide each # with the slope

0.20 0.20

200 = x

hope this helps!

Answer:

90in^3

Step-by-step explanation:

v=w*h*l=3×5×6=90

Answer:

Please I can't see it it clearly

Answer:

N>4

Step-by-step explanation:

Plugin numbers based on your options. Just check if any number less than four fits, if not, next option. In this case if you plug in 4, 4 * 6 = 24 which is equal to 20 more than 4 which is 24. Since our option is N>4 we can try 5 which will work and so will every number after that.

Answer:

a. the number of people at Friday's, Saturday's, and Sunday's performances combined.

Step-by-step explanation:

The reason this information is needed to solve this problem is because we are looking to find the number of people who attended Saturday's performance. Without any information on Saturday's performance, there is no way to solve the problem. We are given the number of people on Friday and Sunday's performance, but are not given a total amount of people on all performances.

Answer:

A) The number of people at Friday's, Saturday's, and Sunday's performances combined.

Step-by-step explanation:

We are looking for the amount of people who attended Saturday's performance, but only one of the answers contains anything about Saturday, which is A. All the information in the other 3 choices we already know, because we know the amount of people at both Friday and Saturday's performance, so we can do some simple math to figure it out.

Answer:

About 4 oranges I think...

Answer:

[tex]Range = [24, 375][/tex]

Step-by-step explanation:

Given

[tex]f(x) = 3x^3[/tex]

[tex]Domain = [2,5][/tex]

Required

Find the Range

The range is calculated by solving for f(2) and f(5). In other words, the range is calculated when x is 2 and x is 5

When x = 2;

f(2) is as follows;

[tex]f(2) = 3*2^3[/tex]

[tex]f(2) = 3 * 8[/tex]

[tex]f(2) = 24[/tex]

When x = 5;

f(5) is as follows;

[tex]f(5) = 3*5^3[/tex]

[tex]f(5) = 3 * 125[/tex]

[tex]f(5) = 375[/tex]

Hence, the range of the function is [24, 375]

Answer:

12 sides

Step-by-step explanation:

To find the number of sides of a regular polygon with the sum of interior angles of 1800 degrees, we will follow the steps below;

first write down the formula for finding sum of the interior angle of a polygon

s= (n-2)180

where s is the sum of the interior angle and n is the number of side

from the question given, sum of the interior angle s=1800 degrees

substitute s=1800 degree into the formula and solve for n

s= (n-2)180

1800 = (n-2)180

divide both-side of the equation by 180

1800/180 = n-2

10 = n - 2

add 2 to both-side of the equation

10 + 2 = n

12 = n

n= 12

The polygon have 12 sides

Answer:

C : 414.7

Step-by-step explanation:

I do not completely know if this is right or not, but I used reasoning to figure this out. I can easily find the area of a circle just based on the radius of it, and the radius of the circle (all parts included) is 452.39. And since the percentage of the shaded circle would have to be a lot larger to have the unshaded area only be 188, then I can reason that 414.7 would be the most reasonable answer.

Answer:

Answer = decrease of 22 m/min

Answer:

180

Step-by-step explanation:

its 180 cos its the closest number to 193 that 18 can go in, your overall answer to the equation is 310 remainder 13. But I dont know if u need that..

Answer:

There are twice as many people who purchased a red car than a black car.

Answer:

1. 140 in²

2. 2.25 in²

3. 182 in²

4. 55 in²

5. 374.75 in²

Step-by-step explanation:

1. Area of each triangle: 10*7*1/2 = 35 in²

Area of the roof = 4*35 = 140 in²

2. Area of the entrance hole: 1.5*1.5 = 2.25 in²

3. Area of each trapezoid: (8+5)/2*7 = 45.5 in²

Area of the sides: 4*45.5 = 182 in²

4. Area of the square of the base: 5*5 = 25 in²

Area of each rectangle: 1.5*5 = 7.5 in²

Area of the four rectangles = 4*7.5 =  30 in²

Area of the base: 25 + 30 = 55 in²

5. The  total amount of material  needed for the entire birdhouse is: 140 - 2.25 + 182 + 55 = 374.75 in²

Answer:

46.875 %

Step-by-step explanation:

30 grams of fat out of 64 grams

30/64 =.46875

Change to percent form

46.875 %

Answer:46.875

Step-by-step explanation:

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Given:

[tex]\bold{f(x)= (\frac{3}{2})^x}\\\\\bold{g(x)= (\frac{2}{3})^x}\\[/tex]

Following are the graph attachment to this question:

The second function, that is [tex]g(x)= (\frac{2}{3})^x[/tex] is not even a function.

Remember that g(x) function is the inverted f(x) function. And when you see this pattern, a reflection on the Y-axis expects you.

Reflection in the axis.

In x-axis:

Increase the function performance by -1 to represent an exponential curve around the x-axis.

In y-axis:

Increase the input of the function by -1 to represent the exponential function around the y-axis.

We want to compare the graphs of the two given functions. We will see that the graph of g(x) is the graph of f(x) reflected across the line y = x.

The given functions are:

f(x) = (3/2)*x

g(x) = (2/3)*x

Note that each point on the line f(x) is written as:

(x, (3/2)*x)

And each point on the line g(x) is written as:

(x, (2/3)*x)

Now, if we multiply both sides of the above point by (3/2) we will get:

((3/2)*x, x)

Now, remember that for a general point (x, y), if we apply reflection across the line y = x, we get.

(y, x)

So the order of the values changes, exactly as we can see for f(x) and g(x).

Then we can conclude that g(x) is obtained by reflection f(x) across the line y = x.

Then the graph of g(x) is the graph of f(x) reflected across the line y = x.

If you want to learn more, you can read:

https://brainly.com/question/14536884

Because if you divide 1/4 by 3/8 you get 2/3.

Answer:

8 units to the right of line m

Step-by-step explanation:

when reflecting over a line, u count how many units is the pre-image away from the line in order to creat your image.

Answer:

4 units to the left of line m

Step-by-step explanation:

that's how I'm seeing it

Answer:

1. 2

2. 1

Step-by-step explanation:

All work is attached!

please mark brainliest!