How to rationalize the denominator of sqrt(a)/sqrt(a)-2

so namely how many times does 1¼ go into 15⅓?

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{15\frac{1}{3}}\implies \cfrac{15\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{46}{3}\div\cfrac{5}{4}\implies \cfrac{46}{3}\cdot \cfrac{4}{5}\implies \cfrac{184}{15}\implies 12\frac{4}{15}[/tex]

Answer:

x = 11.2

Step-by-step explanation:

-5x - 12y = -8  

5x + 2y = 48

you can combine all like terms from both equations together:

0x-10y=40

simplified:

-10y=40

y=-4

now you plug in the value of y into either equation:

5x+2(-4)=48

simplify

5x-8=48

add 8

5x=56

divide by 5

x=56/5=11.2

In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.

[tex]692,119[/tex]

[tex]2,119[/tex]

[tex]1<5[/tex]

[tex]= 2000[/tex]

[tex]= 692,000[/tex]

Which means your answer is "692,000."

Hope this helps.

The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.

The given number is 692,119

The digit in the thousands place of the given number is 2.

The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.

Therefore, the rounded number is 692,000.

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Check the picture below.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]

[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]

Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.

To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.

Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.

Answer:

Obtuse and Scalene

Step-by-step explanation:

Obtuse means that it is over 90 degrees, in which there is an angle of 102 degrees.

Scalene means that all three side lengths are different.

Answer:

A. Obtuse

C. Scalene

Answer:

False

Step-by-step explanation:

2 = x - 8

Add 8 to each side

2+8 = x-8+8

10 = x

x=4 is not a solution

For this case we have the following equation:

[tex]2 = x-8[/tex]

If we add 8 to both sides of the equation, we have:

[tex]2 + 8 = x-8 + 8\\10 = x[/tex]

Thus, the solution of the equation is [tex]x = 10,[/tex] therefore[tex]x = 4[/tex]is not a solution of the given equation.

Answer:

[tex]x = 4[/tex] is not a solution to the given equation.

False

Answer:

$24,000

Step-by-step explanation:

After putting in trust they have left:

48000 - 9600 = $38,400

If Tori gets 3/8, Akira will get the remaining (1 - 3/8 = 5/8). So Akira will get:

[tex]\frac{5}{8}*38,400=24,000[/tex]

Hence akira will get $24,000

Step-by-step explanation:

[tex]for\ 2<x\leq4-\text{the horizontal segment}\ y=2\\\\for\ 4<x<8\to y=x+3\\\\\text{put}\ x=4,\ \text{and}\ x=8\ \text{to the equation}\\\\y=4+3=7\to(4,\ 7)\\y=8+3=11\to(8,\ 11)\\\\for\ x\geq8\to y=2x\\\\\text{put}\ x=8,\ and\ x=9\ \text{to the equation}\\\\y=2(8)=16\to(8,\ 16)\\y=2(9)=18\to(9,\ 18)\\\\==========================[/tex]

[tex]<,\ >\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}[/tex]

Answer:

tan(90 - A) = 1/tan(A) ⇒ last answer

Step-by-step explanation:

* Lets revise some important information for the right triangle

- In any right triangle

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

∵ The sum of the interior angles of any triangle is 180°

∵ m∠B = 90°

∴ m∠A + m∠C = 180° - 90° = 90°

- If the measure of angle A is x°

∴ The measure of angle C = 90° - x°

- tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB  ⇒(1)

- tan(C) = opposite/adjacent

∵ The opposite to ∠C is AB

∵ The adjacent to ∠C is BC

∴ tan(C) = AB/BC ⇒  (2)

- From (1) and (2)

∴ tan(A) = 1/tan(C)

∵ m∠A = A , m∠C = (90 - A)

∴ tan(A) = 1/tan(90 - A)

OR

∴ tan(90 - A) = 1/tan(A)

Answer:

LAST OPTION.

Step-by-step explanation:

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

[tex]\frac{cos(x)}{sin(x)}=cot(x)=\frac{1}{tan(x)}[/tex]

[tex]sin(x\±y) = sin(x)cos(y)\±cos(x)sin(y)\\\\cos(x\±y) =cos(x)cos(y)\± sin(x)sin (y) [/tex]

[tex]sin(90\°)=1\\cos(90\°)=0[/tex]

Then, you need to rewrite [tex]tan(90-A)[/tex]:

[tex]tan(90-A)=\frac{sin(90-A)}{cos(90-A)}[/tex]

Applying the identities, you get:

[tex]tan(90\°-A)=\frac{sin(90\°)cos(A)-cos(90\°)sin(A)}{cos(90\°)cos(A)-sin(90\°)sin(A))}[/tex]

Finally, you must simplify. Then:

[tex]tan(90\°-A)=\frac{(1)cos(A)-(0)sin(A)}{(0)cos(A)-(1)sin(A))}\\\\tan(90\°-A)=\frac{cos(A)}{sin(A)}\\\\tan(90\°-A)=\frac{1}{tan(A)}[/tex]

Answer:

1/3 - 1/x=1/5

Step-by-step explanation:

Let the total work be "1"

                        Brody          Hudson              Brody+Hudson

  Time              3 mins            x min                       5 min

  Efficiency        1/3                   -1/x                          1/5

The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,

1/3 - 1/x = 1/5....

To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.

The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).

First, substitute g(x) into f(x) to get f(g(x)):

f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.

The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.

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Answer:

[tex]24\sqrt{5}\ yards[/tex]

Step-by-step explanation:

Let A1 be the area of one square and A2 be the area of second square

So,

A1 = s^2

where s is side of square

[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]

So side of one square is [tex]5\sqrt{5}[/tex]

To calculate the length of fence we need to find the perimeter of the square

So,

P1 = 4 * s

[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]

For second square:

[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]

The perimeter will be:

[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]

So the total fence will be: P1+P2

[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]

For this case we have a function of the form [tex]y = g (x)[/tex]

Where:

[tex]g (x) = x ^ 2 + 2[/tex]

We must find the value of the function when x = 3. Then we substitute:

[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]

Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]

Answer:

[tex]g (3) = 11[/tex]

Option C

Answer: Third Option

[tex]g(3) = 11[/tex]

Step-by-step explanation:

We have the function  [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).

To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function

Then

[tex]g(x) = x^2 + 2[/tex]

[tex]g(3) = (3)^2 + 2[/tex]

[tex]g(3) = 9 + 2[/tex]

[tex]g(3) = 11[/tex]

Finally the correct answer is the third option

Answer:

The answer is C

Step-by-step explanation:

Answer: D. The interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.

Step-by-step explanation:

The interquartile range is most suitable term to compare the spread of two different data displayed by box-whisker plot.

The formula for interquartile range :-

 [tex]IQR=Q_3-Q_1[/tex]

For Town A , First quartile : [tex]Q_1=15[/tex]

Second quartile : [tex]Q_2=30[/tex]

[tex]IQR=30-15=15[/tex]

For Town B , First quartile : [tex]Q_1=20[/tex]

Second quartile : [tex]Q_2=40[/tex]

[tex]IQR=40-20=20[/tex]

Clearly , the interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.

Answer:

-59/17 =x

Step-by-step explanation:

53=-6-17x​

Add 6 to each side

53+6=-6+6-17x​

59 = -17x

Divide each side by -17

59/-17 = -17x/-17

59/-17 = x

-59/17 =x

Answer:

The radius of the circle is already there, 11cm, and the diameter is 2 times the radius, which is 22

Step-by-step explanation:

First, you look at the radius (which is half of the circle) which is 11, then you multiply that times two to get the diameter. :)

Answer:

The answer is 192

Step-by-step explanation:

2^8 = 256

8^2 = 64

256 - 64 = 192

Remember:

2^8 is really 2*2*2*2*2*2*2*2

Remember:

8^2 is really 8*8

To find the difference, you must subtract the smaller product from the larger product.

<Hope this helps!>

Answer:

192

Step-by-step explanation:

Method 1:

2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192

Method 2:

2^8 - 8^2 = 256 - 64 = 192

Answer:

C. AB/XY = AC/XZ

Step-by-step explanation:

Dilation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.

In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.

So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:

AB/XY = AC/XZ = BC/YZ = 5

Answer with explanation:

When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.

Pre-Image = ΔABC

Image = ΔX Y Z

When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.

⇒Similar triangles has Corresponding sides proportional as well as Corresponding  Angles are congruent.

≡Corresponding congruent Angles are

→∠A=∠X

→∠B=∠Y

→∠C=∠Z

≡Corresponding congruent Sides are

     [tex]\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}[/tex]

The Proportionality statement which proves two triangles are Similar

Option B

 [tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]

Answer:

(x,y)  (2,-1)

Step-by-step explanation:

Answer:

the first one is 2 the second one is 3

Step-by-step explanation:

The true statements about the result of the coin toss experiment described are :

Number of heads :__0 __ 1 __ 2 __ 3

Frequency _____ :_ 2___7___9___2

Therefore, expected Number of 3 and 0 heads are the same. And the expected number of 1 and 2 heads are almost the same.

The experiment cannot be used to model the events in the options as it only gives the number of occurence of a single event.

Hence, only statements 1 and 2 are true.

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The frequency of 0, 1, 2, and 3 heads in the experiment is 2, 7, 10, and 1 respectively. Statement 2 is the most accurate regarding long-term expectations, while statement 4 can be considered conditionally true. Statements 1 and 3 are not related to the probability outcomes of the experiment.

To complete the frequency table based on the given results, we will count the occurrences of each number of heads (0, 1, 2, or 3) in the 20 trials. The frequencies are:

Based on these results, we can discuss the truthfulness of the provided statements:

Answer:

parallel

Step-by-step explanation:

we have

2x=-3-y

isolate the variable y

y=-2x-3 ----> equation A

4+y=-2x-2

isolate the variable y

y=-2x-2-4

y=-2x-6 -----> equation B

Remember that

If two lines are parallel, then their slopes are the same

Line A and Line B have the same slope m=-2 and different y-intercept

therefore

The lines are parallel

Answer:

Second option: Parallel.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

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

Equation 2

[tex]4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=-2[/tex]

And the slope of the Equation 2 is:

[tex]m_2=-2[/tex]

Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are: Parallel.

Answer:

No, Lorena cannot make the inference about all the seniors going to college.

Step-by-step explanation:

We are given that Lorena took a survey of students in her science class to determine how many of them were going to college.

From the survey results, she found that 85% of the students from her science class were going to the college but with these results she cannot infer that 85% of all the seniors at her school were going to college.

This is because the survey was biased as it was not taken from the entire school but only Lorena's science class.

Answer:

No, Lorena’s sample was biased because it was taken only from an honors class.

No, Lorena’s sample was not a random sample of the entire school.

those are the two correct answers, i took the test!

Answer:

Step-by-step explanation:

that would be written as  1.2^10, and the end result would be the same as you'd get if you use 1.2 as a factor 10 times:  1.2*1.2*1.2* .......1.2

You could use a calculator to evaluate 1.2^10:  

Typing in 1.2^10, you'll get  6.191736422.

This is not an exact answer; there are more digits following the ones shown.

Another way in which you could do this problem would be to use logs:

Let y = 1.2^10.  Then log y = 10*log 1.2, or log y = 10(0.07918) = 0.791812.

Finding the antilog, we get y = 6.19174

Answer:

The 17th term in arithmetic sequence is 68

Step-by-step explanation:

The general formula of arithmetic sequence is:

aₙ = a₁ + (n – 1)d.

We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇

To find the term a₁₇ we should know a₁ and d. So we would find both

a₆ = a₁ +(6-1)d

101 = a₁ +(5)d

101 = a₁ +5d     eq(1)

and

a₉ = a₁ +(9-1)d    

83 = a₁ + 8d       eq(2)

Subtracting eq(2) from eq(1)

101 = a₁ +5d

83 = a₁ + 8d

-       -     -

__________

18 = -3d

=> d = 18/-3

=> d = -6

Putting value of d in eq(1)

101 = a₁ + 5d

101 = a₁ + 5(-3)

101 = a₁ -15

=> a₁ = 101+15

=> a₁ = 116

Now finding a₁₇:

aₙ = a₁ + (n – 1)d.

a₁₇ = 116 +(17-1)(-3)

a₁₇ = 116+(16)(-3)

a₁₇ = 116 - 48

a₁₇ = 68

So, the 17th term in arithmetic sequence is 68

Answer:

$22.68

Step-by-step explanation:

21×.08= 1.68

21+1.68=22.68

Total cost =$22.68

Answer:

22.68

Step-by-step explanation:

The first step is to find the amount of tax

tax = original cost * tax rate

       = 21 * 8%

       = 21 * .08

      =1.68

Then we add the tax to the original cost to find the total cost

total cost = original cost + tax

               = 21 + 1.68

               =22.68

Answer:

250, -1250

Step-by-step explanation:

Geometric Sequence is a hint to think multiplication:

What can you multiply to -2 to get 10

or what is 10/-2

I hope you said -5.

So just multiply -5 to a term to get the term right after!

So

-50(-5)=250

250(-5)=-1250

Answer:

A

Step-by-step explanation:

Just try to label the data in a table for every choice. It is clearly A. If you tried to solve it you will find that =

(-2)² = 4

(-1)² = 1

1² = 1

2² = 4

Answer:

∠C = 143°

Step-by-step explanation:

For the quadrilateral to be a parallelogram

Then ∠C = ∠A

Given ∠B = ∠D then consecutive angles are supplementary, that is

∠C + ∠D = 180

∠C + 37 = 180 ( subtract 37 from both sides )

∠C = 143°

Answer:

A:  x-axis

I did a quiz and got it wrong when I choose B: y-axis.

Final answer:

The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.

Explanation:

A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.

Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.

Answer:

A. 24 square units

Step-by-step explanation:

length is 8 and height is 6

gets you 48 but you need to divide by 2 because its a triangle so you get 24

Answer:

a

Step-by-step explanation: