Is this a right triangle?Use the Pythagorean Theorem to find out!20 cm12 cm16 cmYesNo

Is This A Right Triangle?Use The Pythagorean Theorem To Find Out!20 Cm12 Cm16 CmYesNo

Answers

Answer 1

If this is a right triangle, then the Pythagorean theorem has to be valid.

This means that the sum of the squares of the legs has to be equal to the square of the hypotenuse (NOTE: we can identify the potential hypotenuse by finding the side with the most length).

Then, we calculate:

[tex]\begin{gathered} 12^2+16^2=20^2 \\ 144+256=400 \\ 400=400\longrightarrow\text{True} \end{gathered}[/tex]

As the Pythagorean theorem is valid for this side's lengths, we know that this triangle is a right triangle.

Answer: Yes.


Related Questions

The linear regressionequation andcorrelation coefficientfrom the above datawas calculated to be:Predicted y = 16.2+2.45(x) with r = 0.98What is the coefficientof determination?Answer Choices:A. Coefficient of determination = 0.98B. Coefficient of determination = 0.96C. Coefficient of determination = 0.99D. Coefficient of determination cannot be determined with only the given information.

Answers

Given:

[tex]\text{ coefficient of correlation \lparen r\rparen = 0.98}[/tex]

To find:

Coefficient of determination

Explanation:

The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.

If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.

So, here the required coefficient of determination is:

[tex]r^2=(0.98)^2=0.9604\approx0.96[/tex]

Final answer:

Hence, the required coefficient of determination is (B) 0.96.

Given two functions f(x) and g(x):f(x) = 8x - 5,8(x) = 2x2 + 8Step 1 of 2 Form the composition f(g(x)).Answer 2 PointsKeypadKeyboard Shortcutsf(g(x)) =>Next

Answers

we have the functions

[tex]\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}[/tex]

Find out f(g(x))

Substitute the variable x in the function f(x) by the function g(x)

so

[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=8(2x^2+8)-5 \\ f(g(x))=16x^2+64-5 \\ f(g(x))=16x^2+59 \end{gathered}[/tex]

Can someone help out with a math prob?
pic of question below

Answers

The polar equation of the curve with the given Cartesian equation is r = √7

How to convert polar equation to cartesian equation

Given the Cartesian equation: x² + y² = 7

The relationships between polar and cartesian equation :

x = r cosθ

y = r sinθ

Where r is the radius and θ is the angle

Put the values of x and y into the given cartesian equation:

(r cosθ)² + (r sinθ)² = 7

r²cos²θ + r²sin²θ = 7

r²(cos²θ + sin²θ) = 7

Since the trigonometric identity cos²θ + sin²θ = 1

r²(1) = 7

r² = 7

r = √7

Therefore, the polar equation for the represented curve is r = √7

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Are the graphs of the equations parallel, perpendicular, or neither?x -3y = 6 and x - 3y = 9

Answers

The equation of a line in Slope-Intercept form, is:

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

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

By definition:

- The slopes of parallel lines are equal and the y-intercepts are different.

- The slopes of perpendicular lines are opposite reciprocals.

For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".

- Line #1:

[tex]\begin{gathered} x-3y=6 \\ -3y=-x+6 \\ y=\frac{-x}{-3}+(\frac{6}{-3}) \\ \\ y=\frac{x}{3}-2 \end{gathered}[/tex]

You can identify that:

[tex]\begin{gathered} m_1=\frac{1}{3} \\ \\ b_1=-2 \end{gathered}[/tex]

- Line #2:

[tex]\begin{gathered} x-3y=9​ \\ -3y=-x+9 \\ y=\frac{-x}{-3}+(\frac{9}{-3}) \\ \\ y=\frac{x}{3}-3 \end{gathered}[/tex]

You can identify that:

[tex]\begin{gathered} m_2=\frac{1}{3} \\ \\ b_2=-3_{}_{} \end{gathered}[/tex]

Therefore, since:

[tex]\begin{gathered} m_1=m_2 \\ b_1\ne b_2 \end{gathered}[/tex]

You can conclude that: The graphs of the equation are parallel.

Find an equation of the line. Write the equation using function notation.
Through (4, -1); perpendicular to 4y=x-8
The equation of the line is f(x) =

Answers

The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:

[tex]y = -4x+15[/tex].

What is a equation of line?

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

Given equation of line is:

4y=x-8

We have to convert the given line in slope-intercept form to find the slope of the line

Dividing both sides by 4.

[tex]y = \frac{1}{4}x-2[/tex]

Let [tex]m_{1}[/tex] be the slope of given line

Then,

[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]

Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line

As we know that product of slopes of two perpendicular lines is -1.

[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]

The slope intercept form of line is given by

[tex]y = m_{2}x+c[/tex]

[tex]y = -4x+c[/tex]

to find the value of c, putting (4,-1) in equation

[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]

Putting the value of c in the equation

  [tex]y=-4x+15[/tex]

Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is  [tex]y = -4x+15[/tex].

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Find the future value using the future value formula and a calculator in order to achieve $420,000 in 30 years at 6% interest compounded monthly

Answers

The present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60

The future value = $420000

The time period = 30 years

The interest percentage = 6%

The interest is compounded monthly

A = [tex]P(1+\frac{i}{f})^{fn}[/tex]

Where A is the final value

P is principal amount

i is the interest rate

f frequency where compound interest is added

n is the time period

Substitute the values in the equation

420000 = P × [tex](1+\frac{0.06}{12} )^{(12)(30)[/tex]

420000 = P × 6.02

P = 420000 / 6.02

P = $69737.60

Hence, the present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60

The complete question is:

Find the present value using the future value formula  in order to achieve $420,000 in 30 years at 6% interest compounded monthly

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The graph of function f is shown. The graph of an exponential function passes through (minus 0.25, 10), (0, 6), (5, minus 2) also intercepts the x-axis at 1 unit. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 - 3 4 - 15 16 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept but different end behavior as x approaches ∞. C. They have the same x- and y-intercepts. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.

Answers

The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;

B. They have the same x–intercept but different end behaviours as x approaches ∞

What is the end behaviour of a graph?

The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.

The given points on the exponential function, f, are;

(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)

The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;

(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)

The coordinates of the x–intercept is given by the point where the y–value is zero.

The x–intercept for the exponential function, f, is therefore (1, 0)

Similarly, the x–intercept for the function, g, is (1, 0)

Therefore, both functions have the same x–intercept

However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.

The correct option is therefore;

B. They have the same x–intercept but different end behaviour as x approaches ∞

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An equation that can be used to determine the total

Answers

The equation that we have to build has the following form:

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

• The fixed cost of the phone is $88, which will be represented by ,b,.

,

• The variable cost per month is $116.43, which will be represented by ,m,.

,

• y ,is the dependent variable that we want to know (, C(t) ,)

,

• x ,is the independent variable, in our case, ,t,.

Replacing the values given in the problem we get:

[tex]C(t)=116.93t+88[/tex]

The cost for 22 months will be:

[tex]C(22)=116.93\cdot22+88[/tex][tex]C(22)=2660.46[/tex]

Answer:

• Equation

[tex]C(t)=116.93t+88[/tex]

• Cost in 22 months: $2660.46

Alexa claims that the product of 2.3 and 10^2 is 0.23. Do you agree or disagree? Explain why or why not?

Answers

Answer:

disagree

Step-by-step explanation:

product = 2.3 * 10²

             = 2.3 * 100

             = 230

thus, the answer is different from the one acclaimed by Alexa.

A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 3.8 seconds.

Answers

Given

The data can be modeled using a quadratic regression equation.

Using the general form of a quadratic equation:

[tex]y=ax^2\text{ + bx + c}[/tex]

We should use a regression calculator to obtain the required coefficients. The graph of the equation is shown below:

The coefficients of the equation is:

[tex]\begin{gathered} a\text{ = -17.5 (nearest tenth)} \\ b\text{ = }249.0\text{ (nearest tenth)} \\ c\text{ = }-0.5 \end{gathered}[/tex]

Hence, the regression equation is:

[tex]y=-17.5x^2\text{ + 249.0x -0.5}[/tex]

We can find the height (y) at a time of 3.8 seconds by substitution:

[tex]\begin{gathered} y=-17.5(3.8)^2\text{ + 249}(3.8)\text{ - 0.5} \\ =\text{ }693 \end{gathered}[/tex]

Hence, the height at time 3.8 seconds is 693 ft

In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4

Answers

The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1

How to calculate the value?

From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.

In this case, the entire score will be:

= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)

= -13 - 13.75 + 6 + 22

= 11.25

Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.

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What is the measure of the base of the rectangle if the area of the triangle is 32 ft2 ?A) 8 ftB) 16 ft C) 32 ftD) 64 ft

Answers

Answer:

B) 16 ft

Explanation:

The area of a triangle is equal to

[tex]Area\text{ =}\frac{Base\times Height}{2}[/tex]

We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get

[tex]32=\frac{\text{Base}\times4}{2}[/tex]

Now, we can solve for the base. So multiply both sides by 2

[tex]\begin{gathered} 32\times2=\frac{\text{Base }\times4}{2}\times2 \\ 64=\text{Base }\times4 \end{gathered}[/tex]

Then divide both sides by 4

[tex]\begin{gathered} \frac{64}{4}=\frac{Base\times4}{4} \\ 16=\text{Base} \end{gathered}[/tex]

Therefore, the measure of the base is 16 ft

1. The equations y = x2 + 6x + 8 and y = (x + 2)(x+4) both define thesame quadratic function.Without graphing, identify the x-intercepts and y-intercept of the graph.Explain how you know

Answers

Given the quadratic equation

[tex]y=x^2\text{ +6x + 8}[/tex]

(1) x-intercepts are -2 and -4 is the points that pass through the x-axis

when y = 0

[tex]\begin{gathered} y\text{ = 0 } \\ x^2\text{ + 6x + 8 = 0} \\ x^2+2x\text{ +4x +8 = 0} \\ (x\text{ + 2)(x +4)=0} \\ x\text{ +2 = 0 or x +4 =0} \\ x\text{ = -2 or x = -4} \end{gathered}[/tex]

(11) y-intercepts = 8 is the points that pass through the y axis when x = 0

[tex]\begin{gathered} y=x^2\text{ +6x +8} \\ \text{when x = 0} \\ y=0^2\text{ +6(0) +8} \\ \text{y = 8} \end{gathered}[/tex]

HELP PLEASE!

Dave has a piggy bank which consists of dimes, nickels, and pennies. Dave has seven
more dimes than nickels and ten more pennies than nickels. If Dave has $3.52 in his piggy bank, how many of each coin does he have?

Answers

Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.

According to the question,

We have the following information:

Dave has 7 more dimes than nickels and 10 more pennies than nickels.

Now, let's take the number of nickels to be x.

So,

Dimes = (x+7)

Pennies = (x+10)

Now, Dave has $3.52 in his piggy bank.

We will convert nickels, dimes and pennies into dollars.

We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.

Now, we will convert the given numbers of nickel, dime and pennies into dollars.

x Nickels in dollars = $0.05x

(x+7) dimes in dollars = $0.1(x+7)

(x+10) pennies in dollars = $0.01(x+10)

Now, we will them.

0.05x + 0.1(x+7) + 0.01(x+10) = 3.52

0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52

0.16x + 0.8 = 3.52

0.16x = 3.52-0.8

0.16x = 2.72

x = 2.72/0.16

x = 17

Now, we have:

Number of nickels = 17

Number of dimes = (17+7)

Number of dimes = 24

Number of pennies = (17+10)

Number of pennies = 27

Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.

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Find the area and the perimeter of the following rhombus. round to the nearest whole number if needed.

Answers

ANSWER

[tex]\begin{gathered} A=572 \\ P=96 \end{gathered}[/tex]

EXPLANATION

To find the area of the rhombus, we have to first find the length of the other diagonal.

We are given half one diagonal and the side length.

They form a right angle triangle with half the other diagonal. That is:

We can find x using Pythagoras theorem:

[tex]\begin{gathered} 24^2=x^2+16^2 \\ x^2=24^2-16^2=576-256 \\ x^2=320 \\ x=\sqrt[]{320} \\ x=17.89 \end{gathered}[/tex]

This means that the length of the two diagonals is:

[tex]\begin{gathered} \Rightarrow2\cdot16=32 \\ \Rightarrow2\cdot17.89=35.78 \end{gathered}[/tex]

The area of a rhombus is given as:

[tex]A=\frac{p\cdot q}{2}[/tex]

where p and q are the lengths of the diagonal.

Therefore, the area of the rhombus is:

[tex]\begin{gathered} A=\frac{32\cdot35.78}{2} \\ A=572.48\approx572 \end{gathered}[/tex]

The perimeter of a rhombus is given as:

[tex]P=4L[/tex]

where L = length of side of the rhombus

Therefore, the perimeter of the rhombus is:

[tex]\begin{gathered} P=4\cdot24 \\ P=96 \end{gathered}[/tex]

The product two consequences positive even numbers is 728. Find the smaller of the two numbers. The smaller number is

Answers

Let the first number = n

So second number = n+2

the product of number is 728.

That mean:

[tex]n(n+2)=728[/tex]

Solve the equation:

[tex]\begin{gathered} n(n+2)=728 \\ n^2+2n=728 \\ n^2+2n-728=0 \end{gathered}[/tex][tex]\begin{gathered} n^2+2n-728=0 \\ n^2+28n-26n-728=0 \\ n(n+28)-26(n+28)=0 \\ (n+28)(n-26)=0 \\ n=-28;n=26 \end{gathered}[/tex]

For positive number is n=26.

scond number is:

[tex]\begin{gathered} =n+2 \\ =26+2 \\ =28 \end{gathered}[/tex]

So smaller number is 26.

3 * 10 ^ - 6 = 4.86 * 10 ^ - 4 in scientific way

Answers

Answer:

3*10=30

10^-6=1^-6. (10 raised to the power of-6)

therefore 3*1^-6=3

is equal to

4.86*10=48.6

10^-4=1^-4

therefore 48.6*1^-4=48.6

Determine the angle relationship. Drag the correct answer to the blank. what is the angle relationship of < 3 & <7

Answers

we have that

between m<3 and m<7 -----> no relationship (because q and p are not parallel)

Part 2

the relationship between m<12 and m<10

is

vertical angles

m<12=m<10 ------> by vertical angles

A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth

Answers

Given:

[tex]h(t)=-16t^2+600t+225[/tex]

To find the time interval when the height is about more than 4000 feet:

Let us substitute,

[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]

Using the quadratic formula,

Here, a= -16, b=600, and c= -3775

[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]

So, the interval is,

[tex]8.00\le\: t\le\: 29.50[/tex]

help meeeeeeeeee pleaseee !!!!!

Answers

Because x is continuous, we should use interval notation, the domain is:

D: [1, ∞)

How to find the domain?

For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).

To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.

There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:

D: x ≥ 1

We know that the value x =1 belongs because there is a closed dot there.

The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:

D: [1, ∞)

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C) 1) if Z1 and 22 are complementary angles, and mZ1 = 74°; find m22.

Answers

Answer:

16

Explanation:

The angles ∠1 and ∠2 are complementary, meaning

[tex]\angle1+\angle2=90^o[/tex]

Visually,

Now, ∠1 = 74; therefore,

[tex]74^o+\angle2=90^o[/tex]

subtracting 74 from both sides gives

[tex]\angle2=90^o-74^o[/tex][tex]\angle2=16^o[/tex]

which is our answer!

I need a math tutor asap .

Answers

For this exercise you need to remember that a Cube is a solid whose volume can be calculated using the following formula:

[tex]V=s^3[/tex]

Where "V" is the volume of the cube and "s" is the length of any edge of the cube (because all the edges of a cube have the same length).

For example, if you have a cube and you know that:

[tex]s=5\operatorname{cm}[/tex]

You can substitute this value into the formula and then evaluate, in order to find the volume of the cube. This would be:

[tex]\begin{gathered} V=(5\operatorname{cm})^3 \\ V=125\operatorname{cm}^3 \end{gathered}[/tex]

The answer is:

You can find it using the formula

[tex]V=s^3[/tex]

Where "s" is the length of any edge of the cube

Which values are solutions to the inequality below? Check all that applySqrt x>=9Choices are:-2, 82, 32, 180, 99, 63

Answers

We notice the following:

[tex]\begin{gathered} \sqrt[]{x}\ge9\ge0 \\ \Rightarrow \\ x\ge81 \end{gathered}[/tex]

Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:

[tex]82,\text{ 180 and 99}[/tex]

Find x.special 10A. 3B. 23√3- this is in fractionC. 6√3D. 3√3

Answers

First, we need to remember the cosine formula which is: cosine(theta)= adjacent/hypotenuse, now let's apply the formula to the triangle we have:

By using the formula we find that x=3√3 .

The answer is D.

Plot Points & Graph Function (Table Given)

Answers

We have the next function

[tex]y=-\sqrt[]{x}+3[/tex]

We need to calculate some points

x y

0 3

1 2

4 1

9 0

Let's plot the points and then we connect them in order to obtain the graph

Find the 5th term of the arithmetic sequence -5x – 5, -123 – 8,- 19x – 11, ...Answer:Submit Answer

Answers

5x – 5, -123x – 8,

- 19x – 11, ...

Difference is =

there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation

Answers

According to the given data we have the following:

total households in the US=1.2*10^8. hence:

[tex]1.2*10^8=120000000[/tex]

average household uses 400 gallons of water each day

let x=total number of gallons of water used by households in the US each day

Therefore x=total households in the US*average gallons of water households uses each day

x=120,000,000*400

x=48,000,000,000

The total number of gallons of water used by households in the US each day is 48,000,000,000

what is the slope for the following points?(-1,1) and(3,3)

Answers

To find the slope for a line that connects the given points, use the following formula:

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

where (x1,y1) and (x2,y2) are the given points.

Use:

(x1,y1) = (-1,1)

(x2,y2) = (3,3)

replace the values of the previous parameters in the formula for m:

[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]

Hence, the slope is 1/2

Which 3 pairs of side lengths are possible measurements for the triangle?

Answers

SOLUTION

From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC

And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)

So this means

[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]

So from the first option

[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]

Hence the 1st option is correct, so its possible

The second option

[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]

Hence the 2nd option is wrong, hence not possible

The 3rd option

[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]

Hence the 3rd option is wrong, not possible

The 4th option

[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]

Hence the 4th option is correct, it is possible

The 5th option

AB = BC

This is correct, and its possible

The last option

[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]

This is wrong and not possible because AB should be equal to BC

Hence the correct options are the options bolded, which are

1st, 4th and 5th

Find decimal notation for 100%

Answers

The decimal notation of percentage is the quotient of the percentage divided by 100.

So it follows that :

[tex]\frac{100\%}{100}=1[/tex]

The answer is 1

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