Rationalize the denominator and simplify:
√5a+√5

Rationalize The Denominator And Simplify:5a+5

Answers

Answer 1
answer: the first option


Related Questions

Find the slope of the line that passes through (54, -61) and (8, -56).

Answers

Answer:

The slope m of the line that passes through the two given points is;

[tex]m=-\frac{5}{46}[/tex]

Explanation:

We want to calculate the slope of the line that passes through the given point;

[tex](54,-61)\text{ and }(8,-56)[/tex]

Recall that the slope formula can be written as;

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

substituting the given points;

[tex]\begin{gathered} (x_1,y_1)=(54,-61) \\ (x_2,y_2)=(8,-56) \end{gathered}[/tex]

We have;

[tex]\begin{gathered} m=\frac{-56-(-61)}{8-54}=\frac{5}{-46} \\ m=-\frac{5}{46} \end{gathered}[/tex]

Therefore, the slope m of the line that passes through the two given points is;

[tex]m=-\frac{5}{46}[/tex]

5 In nahiangle Bcm. Ireos B = / 13 which function also cauals

Answers

Given data:

The given measurement of angle C is 90 degrees.

The given value of cos(B) =5/13.

The sum of all angles of triangle is,

[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]

Substitute the above value in the given expression.

[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]

Thus, the correct answer is sin(A), so the third option is correct.

Use percents to find price of each set of items.(1) You purchase one pair of jeans, 2 hoodies and 3 t-shirts. what is the Total cost with no Sale? You purchase the same items but now you receive a 40% off coupon, How much is your total including the discount?

Answers

We can multiply the number of items by the price of each item to find the total cost:

[tex]\begin{gathered} C=C_{jeans}+C_{hoodies}+C_{shirts}=1\cdot25+2\cdot30+3\cdot8 \\ C=25+60+24 \\ C=109 \end{gathered}[/tex]

The total cost is $109.

If we have a 40% discount, we have to substract it from the total cost.

The discount is equal to 40% of the total cost, so we can calculate the discount as:

[tex]D=\frac{40}{100}\cdot C=0.4\cdot109=43.60[/tex]

Then, we will pay a total cost with discount of:

[tex]C^{\prime}=C-D=109-43.60=65.40[/tex]

The total including the discount is $65.40.

NOTE: we could also have calculated it as 109*(1-0.4)=109*0.6=65.40.

In a third day of randomly selected subjects, the mean age of the 36 respondents is 40 years and the standard deviation of ages is 10 years. Use the sample results to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected. Repeat the previous problem assuming that the population standard deviation is known to be six years.

Answers

a. Given that:

- The mean age of the 36 respondents is 40 years.

- The standard deviation of ages is 10 years.

You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.

Then, you need to use this formula:

[tex]x\pm z\cdot\frac{\sigma}{\sqrt{n}}[/tex]

Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.

In this case:

[tex]\begin{gathered} x=40 \\ \sigma=10 \\ n=36 \end{gathered}[/tex]

Therefore, by substituting values into the formula:

[tex]40\pm\frac{10}{\sqrt{36}}[/tex]

You get these two values:

[tex]40+\frac{10}{\sqrt{36}}\approx41.67\text{ }[/tex][tex]40-\frac{10}{\sqrt{36}}\approx38.33[/tex]

b. If you assume that:

[tex]\sigma=6[/tex]

You get the following values by substituting them into the formula:

[tex]40+\frac{6}{\sqrt{36}}=41[/tex][tex]40-\frac{6}{\sqrt{36}}=39[/tex]

Hence, the answers are:

a.

[tex](38.33,41.67)[/tex]

b.

[tex](39,41)[/tex]

I need help answering this question, if you can thank you very much.

Answers

Answer: We have to factor out the polynomial which is:

[tex]x^2+6x-16[/tex]

The factorization is as follows:

[tex]\begin{gathered} \text{ Method:} \\ \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ \\ \\ ----------------------- \\ \text{ Solution:} \\ \\ x^2+6x-16 \\ \\ \text{ The unknowns }\rightarrow\begin{cases}ab={-16} \\ a+b={6}\end{cases} \\ \\ \\ \text{ The possible values are:} \\ \\ \\ a=8 \\ b=-2 \\ \\ \\ \text{ Because:} \\ \\ \\ (8)\times(-2)=-16 \\ (8)+(-2)=6 \\ \\ \\ \text{ Therefore the factored form is:} \\ \\ \\ (x+8)(x-2)=x^2+6x-16 \end{gathered}[/tex]

what is the slope of any line is perpendicular to the equation y=1/2x-7

Answers

Answer:

The slope = -2

Explanations:

The given equation is:

[tex]y\text{ = }\frac{1}{2}x\text{ - 7}[/tex]

This is of the form y = mx + c

where the slope, m = 1/2

The equation perpendicular to the equation y = mx + c is:

[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex][tex]\begin{gathered} \text{The slope = }\frac{-1}{m} \\ \text{The slope = }\frac{-1}{\frac{1}{2}}=\text{ -2} \end{gathered}[/tex]

The slope = -2

Determine whether the graph represents a function.

Answers

A, the relation is not a function

in order for something to be a function, x (the input) can't repeat itself more than once

Please help me i have been struggling for two days

Answers

we have the equation

[tex]\log _5(x+1)-\log _2(x-2)=1[/tex]

using a graphing tool

see the attached figure

The solution is x=2.90

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA. 3x2−5x+1=0 Enter the exact answers.

Answers

The given quadratic equation is,

[tex]3x^2-5x+1=0[/tex]

let us use the formula,

[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

where,

[tex]\begin{gathered} a=3 \\ b=-5 \\ c=1 \end{gathered}[/tex]

subistute the values in the formula,

[tex]\begin{gathered} =\frac{-(-5)\pm\sqrt[]{(-5)^2-4\times3\times1}}{2\times3} \\ =\frac{5\pm\sqrt[]{25-12}}{6} \\ =\frac{5\pm\sqrt[]{13}}{6} \\ x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6} \end{gathered}[/tex]

The roots of the quadratic equation are ,

[tex]x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6}[/tex]

write a linear equation to: slope=2 and goes through point (4, 11)

Answers

When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:

1. Use the standard form of a linear equation:

[tex]y=mx+b[/tex]

You know the value of:

m= 2

y= 11

x= 4

You make a substitution:

[tex]11=(2)(4)+b[/tex]

You can find then the value of b:

[tex]11=8+b[/tex][tex]b=11-8=3[/tex]

Then you have now the data to form the final linear equation:

[tex]y=2x+3[/tex]

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth

Answers

Solution

To find the values of t for which the ball's height is 2 meters

we set h = 2

=> 2 = 1 + 7t - 5t^2

=>5t^2 - 7t + 1 = 0

Using the quadratic formula,

[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \Rightarrow t=\frac{7\pm\sqrt{\left(-7\right)^2-4\left(5\right)\left(1\right)}}{2\cdot5} \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}[/tex]

Therefore, t = 1.23s or 0.16s

7. 4×= 3yy=-4x + 39. y+2=0x+ 2 = 011.x-5y=45x + y = 4Determine if the graphs will show parallel or perpendicular lines, or neither.

Answers

Given:

[tex]\begin{gathered} 4x=3y \\ y=-4x+3 \end{gathered}[/tex]

Sol:.

If the both line are perpendicular then multipilcation of slope is -1 then:

[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=4x \\ y=\frac{4}{3}x \\ m_1=\frac{4}{3} \end{gathered}[/tex][tex]\begin{gathered} y=-4x+3 \\ m_2=-4 \end{gathered}[/tex][tex]\begin{gathered} =m_1m_2 \\ =\frac{4}{3}\times-4 \\ m_1m_2\ne-1 \\ \text{That mean its not perpendicular } \end{gathered}[/tex]

For parallel line slope are same then its not a parallel line

So line neither perpendicular or parallel.

Kindly help with these questions.

Answers

the answer to the first question is the third one
because the constant relationship between the x and y coordinates makes the point go through the origin and makes a straight line.
The answer of the second question is k
X is the x coordinate
Y is the y coordinate
so, K is the constant of proportionality.

You want to purchase an automobile for 28,711. The dealer offers you 0% financing for 60 months or a 3,972 rebate. You obtain 5.7% financing for 60 months at the local bank. Which option should you choose

Answers

Answer:

option 1

Step-by-step explanation:

the dealer one ok.......

Domingo had 250 baseball cards, andJennifer had 82 baseball cards. At thefirst meeting of the Card Club and atevery meeting thereafter, Domingo sold12 cards to Jennifer. After which meetingdid the two have the same numberof cards?

Answers

Data:

Domingo: D

Jennifer: J

Initial number of cards:

D=250

J=82

After each meeting(m):

D=250-12m

J=82+12m

After the first meeting: m=1

[tex]D=250-12(1)=238[/tex][tex]J=82+12(1)=94[/tex]

You increase in 1 the m after each meeting and get the next table:

Then, they have the same number of cards after 7th meeting

What is the domain of the function graphed below?
x<7
x_<7
-2_< X_<3
all real numbers

Answers

The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function so option (A) is correct.

What is the range and domain of a function?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given graph of the function,

The value of the function at x = -1 is -2.

In another place, the graph is not breaking before x = 7.

So, at x > 7 the function is not defined.

The domain of the function will be (-∞ ,7).

Hence "The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function".

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The given question is incomplete, the complete question follows with the graph below;

How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.

Answers

To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:

[tex]6+6+8.5=20.5[/tex]

Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:

[tex]21\cdot0.59=12.39[/tex]

Therefore the cost will be $12.39

Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?

does anyone know this??

Answers

Answer:

E = 2,2     F = 5,-9

Step-by-step explanation:

First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)

This results in E = 2,-2    and F = -5,-9

Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)

Hope this helped!

Differentiate. f(x) = (x3 - 3)2/3 2x f'(x) 3 x 8 х f'(x) 3 | 23-8 2x2 f'(x) 3 S x2 f'(x) 3 8

Answers

1) Let's calculate the derivative of f(x) = (x³-8) ^(2/3)

Let's start applying the power rule :

[tex]undefined[/tex]

Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards

Answers

We would section the figure into two shapes as shown below

We can see a trapezium and a rectangle. We would find the area of each figure and add them.

For the trapezium,

Area = 1/2 * (a + b)h

a nd b are the opposite sides of the trapezium while h represents the height.

Thus,

a = 20, b = 24 and h = 9es of the trapezium while h represents the height.

Thu sid

Eliminate the y in the following system of equations. What is the result when you add the two equations? [tex]x + y = 8 \\ 5x - 3y = 24[/tex]A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48

Answers

EXPLANATION

x + y = 8 ----------------------------------------(1)

5x - 3y = 24 ------------------------------------------(2)

If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.

3x + 3y = 24 ----------------------------------------(3)

Add equation (2) and equation (3).

If we add equation(1) and equation(3) together, -3y will cancel-out 3y.

(5x + 3x) = (24 + 24)

8x = 48

Therefore, the correct option is D. 8x = 48

The number of cities in a region over time is represented by the function

Answers

For this question, in order to find T(x), we need to multiply the two given functions.

[tex]T(x)=(C\cdot P)(x)[/tex][tex]T(x)=C(x)\cdot P(x)[/tex][tex]=(2.9)(1.05)^x\cdot(1.05)^{3x+5}[/tex][tex]=(2.9)(1.05)^{x+3x+5}[/tex][tex]T(x)=2.9(1.05)^{4x+5}[/tex]

Therefore, the answer must be option A.

Geo help please The price of an item has been reduced by 5% the original price was $60 what is the price of the item now

Answers

To answer this question, we can proceed as follows:

1. The original price of the item was $60.

2. If the price of this item has been reduced by 5%, we need to find the 5% of the original price as follows:

[tex]5\%=\frac{5}{100}\Rightarrow5\%(\$60)\Rightarrow\frac{5}{100}\cdot\$60=\frac{\$300}{100}=\$3[/tex]

3. Therefore, the price of the item now is:

[tex]P_{\text{item}}=\$60-\$3=\$57[/tex]

In summary, the price of the item now is $57.

[From the question, we have that the words "reduced by" imply a subtraction.]

if a certain number is added to the numerator and denominator of 9/13 the result is 9/11. find the number

Answers

We have the following:

When they tell us a certain number, we will assume a value x.

This number is added to the numerator and denominator of the fractional number 9/13 and gives us the result 9/11.

it is as follows

[tex]\frac{x+9}{x+13}=\frac{9}{11}[/tex]

solving for x:

[tex]\begin{gathered} \frac{x+9}{x+13}=\frac{9}{11} \\ 11\cdot(x+9)=9\cdot(x+13) \\ 11x+99=9x+117 \\ 11x-9x=117-99 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]

Therefore, the certain number is 9

Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.

Answers

Given that:

• There are a total number of 22 students in the classroom.

,

• 10 of them are transfer students.

,

• 7 are nursing students.

,

• 4 are AAS students.

,

• 1 student is undecided.

,

• Three students are chosen randomly.

Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:

[tex]P(A)[/tex]

Where Event A is that one of the students is a nursing student.

Therefore, the probability that three of the chosen students are nursing students can be set up as:

[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]

Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:

[tex]P(A)=\frac{7}{22}[/tex]

Therefore:

[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]

Hence, the answer is:

[tex]P=0.0322[/tex]

The one-to-one function f is defined below.

Answers

The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively

How to determine the inverse function?

The definition of the function is given as

f(x) = 6x/7x - 5

Rewrite the function as

y = 6x/7x - 5

Next, we swap or switch the variables x and y

So, we have the following equation

x = 6y/7y - 5

Cross multiply in the above equation

This gives

x(7y - 5) = 6y

Open the brackets

7xy - 5x = 6y

Collect the like terms

7xy -6y = 5x

Factor out y

y(7x -6) = 5x

So, we have

y = 5x/(7x -6)

Express as inverse function

f-1(x) = 5x/(7x -6)

Using a graphing calculator, we have

Domain: x < 6/7 or x > 6/7

Range: f(x) < 5/7 or f(x) > 5/7

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In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.3 and a standard deviation of 19.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

Answers

1) The 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is 5.3 ± 5.6.

2) Regarding the effectiveness of garlic in reducing LDL cholesterol, the confidence interval suggests A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

What is the confidence interval estimate?

The confidence interval estimate shows us the mean estimate plus or minus the margin of error (or variation in the estimate).

On the other hand, the margin of error is the difference between the actual and projected results in a random sample.

The number of subjects treated with garlic, n = 48

The mean changes in LDL cholesterol level = 5.3

The standard deviation = 19.6

The 95% confidence interval gives a Z-score of 1.96

The margin of error = Z-score x standard deviation/√n

= 1.96 x 19.6/√48

= 1.96 x 19.6/6.9

= 1.96 x 2.84

= 5.6

Lower Limit = Mean - Margin of Error

= 5.3 - 5.6

= -0.3

Upper Limit = Mean + Margin of Error

= 5.3 + 5.6

= 10.9

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Question Completion with Answer Options:

2. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

A.The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

B.The confidence interval limits do not contain0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

C.The confidence interval limits do not contain​0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

D.The confidence interval limits contain ​0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

roblems in Construction Mathematics me Frandy Ive the following problems. Show your work. Write your answers in the spaces provided. 1. A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?

Answers

A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?

Remember that

1 ft =12 inches

Convert all the measure to inches

so

15' 7 "=15(12)+7=187 in

20' 4"=20(12)+4=244 in

26' 2"=26(12)+2=314 in

Right Triangle ABC is pictured below.Which equation gives the correct value for BC?Option 1: sin(32) = BC/8.2Option 2: cos(32) = BC/10.6Option 3: tan(58) = 8.2/BCOption 4: sin(58) = BC/10.6

Answers

Given the image, we are asked which equation gives the correct value for BC?

Explanation

From the image;

[tex]\begin{gathered} A+B+C=180 \\ 32+B+90=180 \\ B=180-90-32 \\ B=58^0 \end{gathered}[/tex]

Therefore,

[tex]tan58^0=\frac{opposite}{Adjacent}=\frac{8.2}{BC}[/tex]

Answer: Option three

Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.

Answers

The equation can be written as d=30g

What is an equation?

An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.

Tyrone's car can travel about 30 miles for each gallon

So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.

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After that, replace y & solve with function notation f(x). Once you solve that, find f(4).y+3x^2=4f(x)=____f(4)=____ Rule for Input/output table Input values: 1, 2, 3, 4, n Output values: -4,-2,0,2 what is the momentum of an 7.2- kg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units. Which two sentences in the excerpt suggest that Policles loved quality music?The Contestby Arthur Conan Doyle (adapted excerpt)The blue-clad player struck several chords upon his lyre, and then burst suddenly out into the "Ode of Niobe," and Policles sat straight up on his bench and gazed at the stage in amazement. The tune demanded a rapid transition from a low note to a high, and had been purposely chosen for this reason. The low note was a grunting, a rumble, the deep discordant growling of an ill-conditioned dog. Then suddenly the singer threw up his face, straightened his figure, rose upon his tiptoes, and with wagging head and scarlet cheeks emitted a howl. All the while the lyre twanged and thrummed, sometimes in front of and sometimes behind the voice of the singer. But what amazed Policles most of all was the effect of this performance upon the audience. Every Greek was a trained critic, and as unsparing in his hisses as he was lavish in his applause. Many a singer far better than this absurd fop had been driven from the platform, but now, as the man stopped and wiped the abundant sweat from his face, the whole assembly burst into a delirium of appreciation. The shepherd held his hands to his bursting head and felt that his reason must be leaving him, for it was surely a dreadful musical nightmare, and he would wake soon and laugh at the remembrance. But no, the figures were real, the faces were those of his neighbours, and the cheers which resounded in his ears were indeed from an audience which filled the theatre of Olympia. The whole chorus was in full blast, the hummers humming, the shouters bellowing, the tappers hard at work upon the benches, while every now and then came a musical cyclone of "Incomparable! Divine!" from the trained phalanx who intoned their applause, their united voices sweeping over the tumult as the drone of the wind dominates the roar of the sea. It was madnessinsufferable madness! If this were allowed to pass, there was an end of all musical justice in Greece. Policles' conscience would not permit him to be still. Standing upon his bench with waving hands and up-raised voice, he protested with all the strength of his lungs against the mad judgment of the audience. Evaluate each expression using the values given in the table.