Lydia has four straws of different lengths, and she is trying to form a right triangle. The lengths are 8, 9, 15, and 17 units. Which three lengths should she use? Justify your answer.

Answers

Answer 1

The set of 3 lengths that make a right triangle is {8, 15, 17}

Which three lengths should she use?

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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Related Questions

find the slope of this line

Answers

Answer is -1/5
Step by step
Using the slope formula change in y over change in x
(y2-y1) over (x2-x1)
Using points (1,3) and (6,2)
(2-3) over (6-1)
(-1) over (5)
-1/5

You can also find slope on the graph
From point to point
You go down -1 and over +5
So -1/5
Problem solved

Solve for d
d+13 = 40

Answers

Answer:

d=27

Step-by-step explanation:

d+13=40

  -13  -13    Subtract 13 from both sides to leave by itself

d=27

Hope it helps:)

d=27 hope that helps

To convert grams to kilograms, you can use the ratio
OA. True
B. False
1,000 grams
1 kilogrami

Answers

Answer:

A. True

Step-by-step explanation:

The ratio 1000 grams=1kilogram is correct.

need help with this!

Answers

Answer:

1.The slope intercept- form of the function is:

y = x -2

2.The predicted length of the vine after 53 days is 51 cm.

Step-by-step explanation:

The slope is the [tex]\frac{change in length}{change in days}[/tex]  

In the table, every time that the length increased by 5, the days also increased by 5.  5/5 = 1

Now we have to find the y-intercept, we can use the slope and one of the points that we know to do this.  Let's use the first point (5,3). This is in the form (x,y).

y = mx + b

3 = (1)(5) + b

3 = 5 + b   Subtract both sides by 5

-2 = b  Now we can write the equation

y = mx + b

y = x -2.  Plug 53 in for x and you will find your second answer.

y = 53 - 2

y = 51

1. The function's slope intercept form is y = x -2.

2. The vine should be 51 cm long in length after 53 days.

Determining the Slope Intercept Form:

The slope is given as,

m = (Change in length) / (Change in days)

In the table, it can be seen that,

The days climbed by 5 for every 5 that the length did as well [10-5 = 8-3 = 5].

Slope, m =5/5 = 1

We may use the slope and one of the points we are familiar with to help us find the y-intercept. Utilizing the first point (5,3), this is how it looks for the point (x, y),

y = mx + c ..... (1)

3 = (1)(5) + c

3 = 5 + c

Subtract 5 from both sides to get c.

c = -2

Hence, from (1), the slope intercept form is given as,

y = x - 2 ...... (2)

Predicting the Vine Length:

Since x represents the number of days, put x = 53 in equation (2) to predict the vine length after 53 days.

y = (53) -2

y = 51 cm

Thus, the length of vine after 53 days would be 51 cm.

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f(x) =4x2 + 8x -5 factor completely

Answers

The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)

Adult tickets to the fall play cost $8
and student tickets cost $4. The drama class
sold 20 more adult tickets than student tickets
to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is

Answers

Solving a system of equations we will see that they sold 80 adult tickets.

how many adult tickets were sold?

To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:

x = adult tickets sold.y = student tickets sold.

They sold 20 more adult tickets than student tickets, then:

x = y + 20

And they collected a total of $880, then:

x*$8 + y*$4 = $880

The the system of equations is:

x = y + 20

x*$8 + y*$4 = $880

Isolating y on the first equation we get:

y = x - 20

Replacing that on the other equation we get:

x*$8 + (x - 20)*$4 = $880

Now let's solve that for x.

x*$12 - $80 = $880

x*$12 = $880 + $80 = $960

x = $960/$12 = 80

They sold 80 adult tickets.

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Please help me with this problem. Seriously desperate again !!

Answers

Answer: 17 inches by 7 inches

Step-by-step explanation:

119 = 1 x 119 & 7 x 17

7 x 17 is the more likely answer, so let's test it

7 x 2 + 3 = 17

Therefore, the dimensions are 17 by 7.

What are the exact values of a and b?
Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.

Answers

Answer:

a = 5b = 5√3

Step-by-step explanation:

A right triangle with one acute angle measuring 30° is the 30°-60°-90° "special" triangle. The ratios of its side lengths are well known to be ...

  1 : √3 : 2

Side lengths

In the given triangle, the longest side is labeled 10, so is 5 times the measure of the longest side in the ratios given above. Multiplying those ratio values by 5, we have side lengths ...

  a : b : c = 5 : 5√3 : 10

That is ...

  a = 5

  b = 5√3

__

Additional comment

If you want to figure the side lengths using trigonometry, you have ...

  a = c·sin(30°) = 10·(1/2) = 5

  b = c·cos(30°) = 10·(√3/2) = 5√3

find the y intercept of 2x - 5y + 7 = 0

Answers

The answer is in the picture below have a good day :)

Which choice is equivalent to the quotient shown here for acceptable
values of X?
√25(x-1) + √5(x-1)²
OA. √25(x-1)-5(x-1)²
OB.
5
1(x-1)
OC. √125(x-1)3³
OD. √5(x-1)

Answers

The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).

What is the equivalent of the quotient?

It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).

It therefore follows from the the laws of indices that the evaluation is thus;

= √{(25/5) ×(x-1)/(x-1)²}.

Ultimately, upon evaluation we have;

= √(5/(x-1))

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Pls hellp

A small bowl of candy has a piece of chocolate, cinnamon, and butterscotch candy. Over the course of a few days, the three candies were eaten. Determine the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order.


Please show work.

Answers

Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:

[tex]\frac{1}{6}[/tex].

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, there are 3 candies, hence the number of ways they can be eaten is:

[tex]A_3 = 3! = 6[/tex]

The desired order is only one, hence the probability is:

[tex]\frac{1}{6}[/tex].

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find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29

Answers

Answer:

x = 15, UV = 12, SV = 31

Step-by-step explanation:

13 + 6 + (2x - 18) = 4x - 29

2x + 1 = 4x - 29

2x = 30

x = 15

UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12

SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31

Find a Cartesian equation for the curve.
r = 3 sec(θ)

Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle

Answers

[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]

[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]

[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]

To what power must 10 be raised to give 10

Answers

The answer is 1

10¹ = 10

i hope it was helpful

Select all the correct answers.
Exponential function fis represented by the table.
2
X
0
0
-12
B
-4
Function gis represented by the equation.
9 (2) = -12 (3)
Which statements are true about the two functions?
0
3
2
4
3
Both functions are increasing on all intervals of x.
Both functions approach the same value as x approaches ...
The functions have the same x-intercept.
Both functions approach - as x approaches -...
The functions have the same y-intercept.

Answers

The true statements are

(d) they have the same y-intercept(e) they approach negative infinity as x approaches negative infinity

How to determine true statements?

The function g(x) is given as:

[tex]g(x) = -12(\frac 13)^x[/tex]

Set x = 0, to determine the y-intercept

[tex]g(0) = -12(\frac 13)^0[/tex]

g(0) = -12

From the table, we y-intercept of f(x) is

f(0) = -12

This means that they have the same y-intercept

Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity

Hence, the true statements are (d) and (e)


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An 8ft length of 4 inch wide crown molding cost $13. How much it cost to buy 88ft of crow molding

Answers

The amount it costs to buy 88ft of crow molding is; $143.

How much does it cost to buy 88ft if crow molding?

It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.

On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;

88 × ($13/8)

= $143.

Therefore, the cost of 88ft of crow molding is; $143.

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An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.

Answers

Answer:

19.50

Step-by-step explanation:

32m = 624

m = 19.50

need more words

Dan & Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?

A. Alex is 50% taller than Dan.
B. Dan is 60% taller than Alex.
C. Dan is 40% taller than Alex.
D. Alex is 40% taller than Dan.

Answers

The true statement is that Alex is 50% taller than Dan.

How to solve percentage questions?

They both measured themselves against a tree in their backyard.

Therefore, the tree is 80% taller than Dan and 20% taller than Alex.

Hence,

let

Dan height = x

Tree's height = x + 0.8x

Tree's height = 1.8x

let

Alex height = y

Tree's height = y + 0.2y

Tree's height = 1.2y

Therefore, if we use Dan height as 100, the height of the tree will be 180.

Then,

180 = 1.2y

y = 150

This means Alex is 50 percent taller than Dan.

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You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?



Answers

Answer:

10.4403 or the square root of 109

Step-by-step explanation:

We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value

what is 3495 x 30595

Answers

Multiplication of 3495 by 30595 is: 106,929,525.

Multiplication

Multiplication can be defined as the way of multiplying a number by another name.

Using  a calculator to multiply  3495 by 30595.

Hence:

Multiplication= 3495×30595

Multiplication= 106,929,525

Therefore Multiplication of 3495 by 30595 is: 106,929,525.

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How to solve for X in the triangle

Answers

Answer:

22.6

Step-by-step explanation:

a^2+b^2=c^2

8^2+b^2=24^2

b^2=512

b=22.6

Answer:

[tex]x = 16\sqrt{2}[/tex]

Step-by-step explanation:

we are given a right triangle.

then

In order to determine x we need to use

the Pythagorean theorem:

[tex]x^{2}+8^{2}=24^{2}[/tex]

⇔ x² + 64 = 576

⇔ x² = 576 - 64

⇔ x² = 512

⇔ x² = 2⁹

⇔ x² = 2 × 2⁸

[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]

[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]

[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]

Triangle PQR is rotated, translated, and dilated to obtain triangle P'Q'R' as shown. An Image of triangle PQR and PQR prime are displayed. The Triangle PQR intersects P at (minus 2, 0.5), R at (minus 2, minus 2.5) and Q at (0, minus 1.5). Similarly P, R, Q prime at (1.5,minus 1.5), (1.5,3), and (minus 1.5,1.5). Which statement about the two figures is correct? A. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. B. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. C. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent. D. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.

Answers

The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.

How to determine the true statements?

The transformations are given as:

RotationTranslationDilation

Rotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.

Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.

The above means that the angles of triangle PQR and triangle P'Q'R' are congruent

Hence, the true statement is (d)

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How do i convert the follwing Powers Of Ten into standard numbers?
i need help w/ this fast!


[tex]10^{7}[/tex]

[tex]10^{5}[/tex]


[tex]10^{8}[/tex]

[tex]10^{12}[/tex]

[tex]10^{6}[/tex]

Answers

The given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

Standard form of a number

From the question, we are to write the given numbers in standard form

To write the given numbers in standard form,

Multiply each of the numbers by 1.0

Then,

10⁷ in standard form is 1.0 × 10⁷

10⁵ in standard form is 1.0 × 10⁵

10⁸ in standard form is 1.0 × 10⁸

10¹² in standard form is 1.0 × 10¹²

10⁶ in standard form is 1.0 × 10⁶

Hence, the given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

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give at least five problems solving about area of a sector of a circle.
five example of arc length
fixe example or arc of a circle

Answers

See below for the examples of sectors and arcs of a circle

Area of sector of a circle

The area of a sector is calculated as:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees

[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degrees

Using the above formulas, the sector areas are:

1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]

2.  [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]

3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]

4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]

5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]

Examples of arc length

The length of an arc is calculated as:

[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees

[tex]L = r\theta[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degrees

Using the above formulas, the arc lengths are:

1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]

2.  [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]

3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]

4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]

5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]

Examples of the arcs of a circle

The examples include:

A parabolic pathDistance in a curveCurved bridgesPizzaBows

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Find the standard deviation for the set of data. (17,26,28,9,30, 29,6,21,23}​

Answers

Using it's concept, the standard deviation for the given data-set is of 8.22.

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean for this problem is:

M = (17 + 26 + 28 + 9 + 30 + 29 + 6 + 21 + 23)/9 = 21

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(17-21)^2 + (26-21)^2 + (28-21)^2 + \cdots + (21-21)^2 + (23-21)^2}{9}} = 8.22[/tex]

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suppose that you borrowed 2000 from a friend and promise to pay back 3600 in 4 years. What simple interest rate will you pay?

Answers

The simple interest rate that the money would be paid is 20%

Simple interest

From the question, we are to determine the interest rate that the money would be paid

Using the formula for simple interest,

S.I = PRT/100

Where S.I is the simple interest

P is the principal

R is the rate

and T is the time

From the given information,

P = 2000

S.I = Amount - Principal = 3600 - 2000 = 1600

R = ?

T = 4

Putting the parameters into the equation, we get

1600 = (2000 ×R × 4) / 100

1600 = 20 × R × 4

1600 = 80R

R = 20%

Hence, the simple interest rate that the money would be paid is 20%

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Please help ASAP
What is the measure of YZ?
A.142
B.52
C.128
D.38

Answers

Answer:  142 degrees  (choice A)

Work Shown:

(arc YZ + arc XU)/2 = angle YVZ

(arc YZ + 38)/2 = 90

arc YZ + 38 = 90*2

arc YZ + 38 = 180

arc YZ = 180 - 38

arc YZ = 142

A committee of 6 members is to be selected from 8 senior and 10 junior. find how many ways can this be done if there is no restriction​

Answers

Answer:

18564 ways

Step-by-step explanation:

The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :

then

This can be done in [tex]C^{6}_{18}[/tex]  ways.

[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]

Find the indicated real nth root(s) of a.
n=3, a = - 216

Answers

Answer:

  -6

Step-by-step explanation:

A suitable calculator can find this for you directly.

Odd root of a negative number

-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:

  ∛(-216) = -∛216 = -6

__

Additional comment

Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.

The second attachment shows a calculator capable of finding the complex roots as well as the real one.

Evaluate each expression:
I-3|=

Answers

The value of the modulus function |-3| is 3.

What is the value of modulus?

'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.

The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.

For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.

Therefore, the value of the modulus function |-3| is 3.

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