Use identities to solve each of the following. Rationalize denominators when acceptable.

The perimeter of the right triangle is 30 units.

The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.

Let's break the information into smaller chunk.

The shorter leg of a right triangle is 8 less than the hypotenuse.

The longer leg is one less than the hypotenuse.

The hypotenuse is the longest side of a right triangle.

Therefore,

let

the hypotenuse = x

short leg = x - 8

long leg = x - 1

Applying Pythagorean theorem in the given right triangle.

c² = a² + b²

where

(x - 1)² + (x - 8)² = x²

(x - 1)(x - 1) + (x - 8)(x - 8) = x²

x² - x - x + 1 + x² - 8x - 8x + 64 = x²

2x² - 18x + 65 = x²

x² - 18x + 65 = 0

(x - 13)(x - 5) = 0

Therefore,

x = 5 and x = 13

13² - 5² = a²

169 - 25 = a²

a = √144

a = 12

So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.

perimeter of the right triangle = 13 + 5 + 12 = 30

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The parametric equations are line through (0,0,0) in the direction of the vector v=uxw=(1,2,1).

The line through (0,0,0) and perpendicular to both U=(-2,1,0) and

w=(-1,0,1)

Therefore the line through (0,0,0) and parallel to (-2,1,0)

[tex]*10919-1-2, î+1=3618 = (1) ņ - (-2)5+ (1)a • Î +21 + û[/tex]

=(1,2,1)

Therefore direction ratio of the line through (0,0,0) is (1,2,1) Therefore for equation of the line through (0,0,0) and perpendicular to both (-2,1,0) and [tex]w=(-1,0,17 is (0,, z) = (0,0,0) + x (1,2,1),[/tex] & is constant.

[tex].: X (1,4,2)= (0, 1, 0)+ [1,2,1][/tex]

Therefore parametric of the line through (0,0,0) in the direction of the vector v=uxw=(1,2,1)

Equivalent Equation of a Plane in Vector Form

The equation for a plane in the real number system R, where r is the position vector of any point on the plane and n is either a normal vector perpendicular to the plane or a parallel vector.

The normal vector must be perpendicular to both as the vectors are both parallel to the plane. Recall that a vector that is perpendicular to both vectors is created by taking the cross product of two vectors. This cross product's characteristic can be used to compute a normal vector to the plane, which results in the normal vector.

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Answer:

191+192

Step-by-step explanation:

Answer:

[tex]x = 61[/tex]

Step-by-step explanation:

See the attached image for explanation

Check the picture below.

Answer:

f(x) = 2

Step-by-step explanation:

What is the value of the function f(x) = 8x when x = 0.25?

substitute in 0.25 for x to get:

f(x) = 8(0.25)

f(x) = 2

cluster sampling is the type of sampling is used.

In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters. Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique. Typically, clusters used by researchers are already-existing groups like cities or schools. Clusters are frequently more homogeneous than the population as a whole since they are typically naturally occurring groups, such as schools, cities, or houses. When conducting your study, you should be aware of this as it might compromise the validity of your findings.

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A function assigns the value of each element of one set to the other specific element of another set. The person can see upto 9.996 meters.

A function assigns the value of each element of one set to the other specific element of another set.

Given that  a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57√(h).

Now, using the same given function we can find the distance up to which the person will be able to see to the horizon. Therefore, we can write,

d=3.57√(h)

d = 3.57 √(7.84)

d = 3.57 × 2.8

d = 9.996

Hence, the person can see upto 9.996 meters.

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Answer:

C is greater than or equal to -23

Step-by-step explanation:

- 28 + 5 = -23

According to the given statement this is a type of stratified sampling.

Stratified random sampling is often when researchers want to know about different subgroups or based on the entire population being studied. For instance, if one is interested in differences between groups based on race, gender, or gender.

she measures her blood sugar level at 3 randomly selected times during each part of the day.

So,

This is a type of stratified sampling.

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I understand that the question you are looking for is :

To determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day.

What type of sampling is used?

The angle x will be 98 ⁰  

What are alternate interior angle ?

An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.

Alternate angles between a transverse and parallel lines are equal .

Let the lines are AB and CD and let us draw a transverse line HI parallel to AB and CD, then the angle FEI will be 62 degree as alternate interior angle are equal. and also angle EPC will be supplementary angle of 144 degree that is 36 degree thus forming angle GEI to be 36 degree also as shown in figure below :

Now calculating angle x :

x = 62+ 36

x = 98 ⁰

Therefore, the angle x will be 98 ⁰  

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Answer:

0.11 yards

Step-by-step explanation:

To convert centimeters to yards, find the needed unit conversions:

[tex]cm(\frac{in}{cm})(\frac{ft}{in})(\frac{yd}{ft})[/tex]

Convert centimeters to inches, inches to feet, then feet to yards!

Now replace the values with the correct quantities:

[tex]10cm(\frac{1in}{2.54cm})(\frac{1 ft}{12 in})(\frac{1 yd}{3 ft})[/tex]

Finally, simplify and cross-cancel the units:

[tex]0.10936... yd[/tex]

Round to the nearest hundredth:

[tex]0.11 yd[/tex]

The area of the shaded region of the circle is 10.972 square inches.

The formula for area of a circle sector is;

A = (θ/360) * πr²

We are given;

Radius of circle = 92 inches

Central angle = 7π/15

Thus;

Area of given sector = (7π/15)/360 * π * 92²

Area of given sector = 7π/15 * 1/360 * π * 92²

Area of given sector = 10.972 square inches

Thus, we can conclude that the area of the shaded region of the circle is 10.972 square inches.

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Answer:

3

Step-by-step explanation:

[tex]\sqrt[3]{27}[/tex]

= [tex]\sqrt[3]{3^3}[/tex]

= 3

a-/ |-5-10| = 15 ; |-2√2-√12|=2√3+√12 ; |-π-4π|=5π

The expression that represents five less than the sum of mark's and hatch's ages is ( h + m ) - 5

Given,

Mark's age is represented by m

Hatch's age is represented by h

To find an expression that shows the required relation, that is, five less than the sum of mark's and hatch's ages, we need to establish a relation between the given variables.

Sum of mark's and hatch's ages can be represented as ( m + h )

Five less than the sum of mark's and hatch's ages can be represented as ( m + h ) - 5.

Therefore, by establishing a relation between the given variables, we get the expression that represents five less than the sum of mark's and hatch's ages as ( h + m ) - 5.

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Answer: 0.16666

Step-by-step explanation:

You need to move the decimal point over

[tex]\frac{5.9}{35.4} \\ \\ \frac{59}{354}=\frac{59.0}{354} =\frac{0.16666}{554}[/tex]

Answer:

450 eggs

Step-by-step explanation:

if an egg box can hold 10 eggs

then 45x10=450

Answer: V = 75.4

Step-by-step explanation: Assuming this is a cylinder we can use the formula πr^2*h. All we have to do is plug in the numbers for the equation. Since we know radius is half of the diameter we can set radius to 2. h represents height.

So since the formula is saying we need to square the radius. We multiply 2*2=4

We can then plug this in for r squared.

Making our equation=  π*4*6 = 75.4

Answer: a=-0.75

Step-by-step explanation:

14a - (2a +9)=2/3 (12a-18)​

14a - 2a -9=2/3 * 6(2a-3)​

12a-9=2*6/3 (2a-3)​

12a-9=2*2(2a-3)​

12a-9=4(2a-3)​

12a-9=8a-12

4a-9=-12

4a=-3

a=-3/4

a=-0.75

Answer:

  11

Step-by-step explanation:

You want to simplify (2x+7) - (2x - 4).

The distributive property tells you the factor outside parentheses applies to every term inside parentheses. It is used for the purpose of removing parentheses.

  (2x+7) - (2x - 4) = 2x +7 -(2x) -(-4) = 2x +7 -2x +4

Terms that have the same variable (or product of variables) are "like terms." Their coefficients can be combined. (This is another use of the distributive property.)

  2x +7 -2x +4 = 2x -2x +7 +4 = (2 -2)x +(7 +4) = 0x +11

  = 11 . . . . simplified form of the given expression

The amount borrowed by the print shop: $5700

Time for which loan is taken: 193 days

Rate of interest: 12%

Day in terms of year is given by: 1/365

The formula for simple interest:

Simple interest = P*R*T/100

where P = principal amount invested

R = rate of interest

T = time in years

Solving the question using the formula we have:

Simple interest = (5700*12*193)/(100*365)

= 13201200/36500

= 361.67 or $362

Interest that will be owed after 193 days will be $362

Amount owed after 193 days will be $5700 + $362 = $6062

Although a part of your question is missing, you might refer to this full question: A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day of a year. Find the interest that will be owed after 193 days. If no payments are made on the loan find the amount owed after 193 days.

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Answer:  $41.50  41 dollars and 50 cents in profit

Step-by-step explanation:

First, 1.25x48=60

Second, 60-18.50=41.50

Answer:

$41.50

Step-by-step explanation:

So we know that Gavin bought 48 water bottles before the game for $18.50. We also know that he sold the water bottles for $1.25 each.

If we want to know how much profit he made, we first have to find the amount of money he received.

To find this, we need to multiply the number of water bottles by the price for each bottle;

48 × $1.25

This gives us a total of $60.

Now to find the profit, we have to subtract the amount he paid for the water bottles by the total he made;

$60 - $18.50

This means he made a profit of $41.50.

hope this makes sense! <3

A=9, B=5 and D=7 are the correct options.

In the *Geometry*, a *triangle* is a closed 2-dimensional figure with 3 angles, 3 sides and 3 vertices. Triangles are considered as a *polygon* with the least number of sides.

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

AAAAAA. 9 it is true

B.5   it is true

C.17   This is clearly false, since it doesn't satisfies inequality third.

D.7   it is true

EE. 3  it is not true since it doesn't satisfies second inequality.

F.11 This is clearly false, since it doesn't satisfies inequality third

Hence, The correct answer of the given question is A,B and D.

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The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.

It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.

Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.

It follows that all sides of the room are equal and the length of each side can be determined as;

s = √Area; since Area = s².

s = √775

s = 27.839 ft.

Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.

However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;

= 27.839 - 3 -3 = 21.839 ft on all sides.

Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.

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The x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

X Intercept is defined as the point where the line crosses the X axis .

For Example : if the line x+y=2 crosses the x axis at 2 ,  then it's x intercept will be (2,0).

Y Intercept is defined as the point where the line crosses the Y axis.

For Example ; if the line x+y=2 crosses the y axis at 2 , then it's Y intercept will be (0,2) .

In the given question

7x-9y=35

To find the x intercept we substitute the value of y=0,

On substituting  y=0 we get

7x=35

x=5

The x intercept is (5,0).

To find the y intercept we substitute the value of x=0,

On substituting x=0 we get ,

-9y=35

y=-35/9

The y intercept is (0,-35/9) .

Therefore , the x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

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By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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The simplified form of the given expression is x raise to the power of one-thirty.

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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Answer:

number of fish caught between 60 and 75 cm =40

Step-by-step explanation:

The mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

We use the rotation of 90 degree to find the mapping of 270 degrees.

The rotation of 270 degree clockwise is same as the anticlockwise rotation of 90 degrees about the origin.

So the mapping of 270 degree clockwise rotation is exactly the mapping of 90 degree anti clockwise rotation.

Now the mapping of 90 degree anti clockwise rotation is  (x, y) -----> (-y, x).

So the mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

This implies that a point (x, y) on the co-ordinate plane becomes (-y, x) after a clockwise 270 degree rotation.

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