Mathematics College

Find the length of the missing side. Leave your answer in the simplest radical form.

Answers

Answer 1

The length of the missing side is √69

How to find the length of the missing side?

The triangle is a right triangle with the following parameters

Hypotenuse = 13

Leg = 10

Represent the missing side with x

By the Pythagoras theorem, we have

x = √Hypotenuse² - Leg²

This gives

x = √13² - 10²

Evaluate

x = √69

Hence, the length of the missing side is √69

Related Questions

Solve each system by substitution

Answers

x = -3, y = -6
-x - y = 9
x = -y - 9

-3(-y - 9) + y = 3
4y + 27 = 3
y = -6

x = -(-6) - 9
x = 6 - 9
x = -3

All you have two unmarked cups 6 ounces and 10 ounces respectively how can you use the two cups to obtain exactly 8 ounces of liquid in the 10 ounce cup

Answers

Answer is as follows.

I don’t know the rules but here it goes.

I would fill up the 10-oz glass with liquid and use it to fill the 6-oz glass.

Now I have 4-oz left in the 10-oz glass.

Empty the liquid from the 6-oz glass and pour the 4-oz remaining from the 10-oz glass to the 6-oz glass.

Now I have 4-oz.

Then, I would fill up the 10-oz glass again and use it to fill up the 6-oz glass that has 4-oz in it.

There are 4 oz in the glass already, so I can only add 2-oz more.

10 oz minus 2 oz = 8 oz left in the 10-oz glass.

Problem solved!!

PLEASE HELP ME WITH THIS I HAVE A TEST TMR

Answers

Answer:

Go to Khan Academy and Search "Finding Slope from graph"

Step-by-step explanation:

That video will help better instead of typing it!

An accounting machine operator wanted to divide a 65 minute job between two identical machines so that one machine would take one and a half times as long as the other. How much time was taken by the machine doing the longer job?

Answers

The slow machine did the job is 39 minutes as calculated with the help of a linear equation in one variable.

A linear equation in one variable is given by the combination of the variable with constants and coefficients such that a unique relationship is established between the terms.

Let us consider the faster machine takes x minutes the finish the job.

Hence the slower machine will take one and a half times .

∴ slower machine takes 1.5 x minutes.

Total time taken by the two machines = x + 1.5x = 2.5 x

But together the two machines will take 65 minutes to complete the job .

So now we form a linear equation with the variable x to solve for the value of x

∴ 2.5 x = 65

or, x = 65 ÷ 2.5

or, x = 26 minutes

Therefore the faster machine takes 26 minutes.

Hence the slower machine will take 1.5 x = 1.5 × 26 = 39 minutes.

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Write the number for 160,060 in expanded form and using number names

Answers

Answer is as follows:

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.

160,060 in expanded form:
100,000
+ 60,000
+ 0
+ 0
+ 60
+ 0

Number name form:

Number name form can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.

160,060 is written as

One hundred sixty thousand sixty.

A box is launched upward from the ground at a speed of 69 feet per second. Calculate the height, in feet, of the box at 2 seconds if the height is given by h(t)=−16t2+69t where t is seconds.

Answers

According to the solving the Hight in feet at 2 second is 74.

What is the link between height and time, as well as height and velocity?

This asserts that the height (h) of a projectile is equal to the combination of two products: its initial velocity and time in the air, and indeed the acceleration constant as well as half of the time squared.

What is the Max height formula?

max = h plus V02 / (4 * g) When launching from the ground, the range is maximized (h = 0). If = 0°, therefore vertical velocity becomes equal to zero (Vy = 0), indicating horizontal projectile motion.

According to the given data:

Given h(t)=−16t²+69t

t = 2 sec

substituting the value of t = 2.

h(2)=−16(2)²+69(2).

= -64 + 138

= 74

According to the solving the height and time in feet at 2 second is 74.

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Step up an inequality for this situation below. Define your variable, but do not solve.

Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?

Answers

The student can take 5 number of lessons if they pay no more than $175

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of music lessons. The student can pay no more than $175, hence:

25x + 50 ≤ 175

x ≤ 5

The student can take 5 number of lessons if they pay no more than $175

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Answer this!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Based on the distance between the park bench and the basketball court, the distance between the park bench and the pond is 57¹/₈ feet

What is the distance between the park bench and pond?

The distance between the park bench and the basketball is the sum of the distance between the park bench and the pond and the pond and the basketball court.

The distance between the park bench and the pond is therefore:

= Distance between park bench and basketball court - Distance between pond and basketball court

Solving gives:

= 75³/₄ - 18⁵/₈

= 75.75 - 18.625

= 57.125

= 57¹/₈ feet

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Answer:h

el]lo you commented on a post that helped me alot

Step-by-step explanation:

if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2

Answers

The average velocity is -10 ft/s.

What is Average velocity?

Average velocity is just the average speed with a direction. If a trip starts and ends at the same point, the total displacement is zero, so the average velocity is zero.

For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).

Given:

f(t) = 20t - 10t²

Now, from t=1 to t=2

f(1)= 20*1 - 10 * 1*1

f(1)= 10

and, f(2)=20*2-10*2*2

f(2)= 40-40

f(2)=0

Now,

Average velocity:

v = ( 0-10 ) / ( 2- 1 )

= -10 ft/s

hence, the average velocity is -10 ft/s.

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532,8 g = kg? [1]
O 5,328 kg
O 5 328 kg
O 0,532 8 kg
O 53,28 kg
O None of the given answers

Answers

The answer is 0,532 8 kg

Explanation:

Convert from g to kg by dividing by 1000.

532,8/1000 = 0,532 8kg

I hope this helps!!

represent the expression please help

Answers

Answer:

10,350.98

Step-by-step explanation:

The decimal number is the sum of the terms of the expression.

Sum

(1×10,000) +(3×100) +(5×10) +(9×1/10) +(8×1/100)

= 10,000 +300 +50 +0.9 +0.08

= 10,350.98

Additional comment

If you can't do this in your head, you can input the expression to your calculator, and it will give this same result.

A taxi company charges an initial fee
of $2.80 plus $3.50 per mile traveled.
a. Does the situation represent a function? If so, identify
the independent and dependent variables.
b. You have enough money to travel at most 20 miles
in the taxi. Find the domain and range.

Answers

The situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

a. Does the situation represent a function? If so, identify the independent and dependent variables.

The given parameters are

Initial Fee = $2.80

Rate = $3.50 per mile

Let the number of miles be x and the total fee be y

So, we have

Total fee = Initial Fee + Rate * Number of miles

This gives

y = 2.8 + 3.5x

This means that the situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range.

Here, we have

Maximum number of miles = 20

This means that the domain is 0 <= x <= 20

Substitute 20 for x in y = 2.8 + 3.5x

y = 2.8 + 3.5 x 20

Evaluate

y = 72.8

This means that the range is 0 <= x <= 72.8

Answers

Answer: yes the graph and the table represents the same relationship between x and y.

Step-by-step explanation: the table "x" is going up by X1 and y is going by x2 for each number meaning it does have a relationship, and the graph also has a relationship because is going (1,2) then (2,4) then (3,8) then (4,16) just like the table so yes it does have a relationship.

Which number set is the most reasonable to describe a baby’s weight at birth?

Whole numbers

Rational numbers

Irrational numbers

Integers

Answers

Rational numbers… most babies don’t weigh exactly a whole number, so you might need to use decimals or fractions. (i.e. 3.2 kg/7 lbs 1 oz)

Alejandro's goal was to ride 36 kilometers. His app says he rode 75% of his goal. How far did he ride?

Answers

Answer:

27 kilometers

Step-by-step explanation

i big brain and u not

u can use a calculator lol

A department store advertises a sale where the customer chooses the discount. A customer may choose a flat discount of $20 off any purchase or 20% off the total purchase price. The final purchase price of an item was $175.

a. What are the possible prices of the item before each discount?

b. Which discount represents a bigger savings in cost for the customer?

Answers

The answers will be :

A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75

B. The discount of flat 20 % gives a bigger savings in cost for the customer.

What do you mean by discount ?

The discount is the difference between the purchase price and the item's par value or simply deduction from the cost price of a good.

It is given that the final purchase price of the item is $175.

Let's try to find out the possible price of item before each discount.

So , price before discount can be calculated by using formula which is :

Price before discount = Discount + Final purchase price

As in first case the flat discount is of $20 , so :

Price before discount = $20 + $ 175

Price before discount = $195

Now as per the question , there is a flat discount of 20% off the total purchase price .

So , let's assume if price before discount is P then :

[ P - ( 20P / 100) ] = 175

P - 0.2 P = 175

0.8 P = 175

P = $ 218.75

From the above calculations which we have done , we can conclude that the discount of 20 % represents a bigger savings in cost for the customer because customer is saving an amount of $218.75 which is greater than $195.

Therefore , the answers will be :

A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75

B. The discount of flat 20 % gives a bigger savings in cost for the customer.

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The florist makes the greatest number of identical arrangements with the carnations and asters. She has 72 carnations and 42 asters. How can she decide how many carnations to place in each arrangement?

Answers

The carnations to place in each arrangement is 6.

How to calculate the value?

It should be noted that from the information, the florist makes the greatest number of identical arrangements with the carnations and asters and she has 72 carnations and 42 asters.

In order to know the carnations to place in each arrangement, this can be done by finding the common factor. This will be illustrated that the numbers have a highest common factor of 6.

Therefore, the number of carnation is 6.

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Which is a true statement? Question 3 options:

–4 > 0
–12 < –3
–15 > –5
2 < –5

Answers

Answer:

-12<-3

Step-by-step explanation:

-3 is bigger than -12 and is closer to 0

An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.

Answers

Hills region has the advantage for sheep production because when a farmer raised 2 bushels of grain, then gaze 4 sheep.

The most popular animal fiber is sheep's wool, which is often gathered by shearing. In Commonwealth nations, ovine meat is referred to as lamb when it comes from younger animals and mutton when it comes from older ones; in the United States, meat from both older and younger animals is often referred to as a lamb.

Today, sheep are still farmed for their meat and wool, as well as on occasion for their pelts, as dairy animals, or as scientific model organisms. Most of the world's populated areas engage in sheep farming, which has been a foundational activity for several civilizations.

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Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
equation:
x=

Answers

Answer:

13 players

Step-by-step explanation:

1353 - 943.50 = 409.50

$31.50 per player for meals

31.50*x = 409.50

x = 13

13 players

What is the slope of a line graphed below?

Answers

Answer:

Undefined

Step-by-step explanation:

The slope of a horizontal line is zero. The slope of a vertical line is undefined.

need to find the value of x

Answers

Answer:

(6x+10)+(10x+10)=180

16x+20=180

16x=160

x=10

Step-by-step explanation: Due it being a supplementary angle which means 180 degrees in total.

6. Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at 4.25%
interest rate. What should the length of the loan be? Round your answer to the nearest year.

Answers

Answer: 4 years

====================================================

Work Shown:

L = 20,000 = loan amountP = 475 = monthly paymenti = 0.0425/12 = 0.0035417 approximately is the decimal form of the monthly interest raten = unknown number of months

Let A = P/i = 475/0.0035417 = 134116.384787 approximately

Then,

[tex]n = \frac{\text{Ln}(A) - \text{Ln}(A-L)}{\text{Ln}(1+i)}\\\\n \approx \frac{\text{Ln}(134116.384787) - \text{Ln}(134116.384787-20000)}{\text{Ln}(1+0.00354)}\\\\n \approx \frac{11.80646 - 11.64497}{0.00353}\\\\n \approx \frac{0.16149}{0.00353}\\\\n \approx 45.74788\\\\n \approx 46[/tex]

It will take about 46 months to pay off the loan.

Divide by 12 to convert from months to years.

46 months = 46/12 = 3.83333 years approximately

That rounds to 4 years

please help
maths geometry

Answers

Step-by-step explanation:

ABCD is a rectangle.

so, it has 2 pairs of equal and parallel sides.

all 4 angles are 90°.

both diagonals are equally long and intersect each other at their midpoint. so, all 4 half-diagonal segments are equally long.

(1)

2x + 4y = 4x - y = 36/2 = 18 cm

we can split this into 2 equations

2x + 4y = 4x - y

5y = 2x

x = 5y/2

and e.g.

4x - y = 18

now we use the first equation in the second

4(5y/2) - y = 18

20y/2 - y = 18

10y - y = 18

9y = 18

y = 2

x = 5y/2 = 5×2/2 = 5

(2)

I cannot draw here, but the shortest distance between a point and a line is always a height (a line segment from the point meeting it intersecting the line at a right angle, 90°).

(3)

e.g.

AE, AD/2 and the drawn height from E to AD create a right-angled triangle.

we know AD/2 = 15 cm

from (1) we know AE = 4x - y = 4×5 - 2 = 20 - 2 = 18 cm.

the height E to AD we get via Pythagoras

AE² = (AD/2)² + height²

height² = AE² - (AD/2)² = 18² - 15² = 324 - 225 = 99

height = sqrt(99) = sqrt(9×11) = 3×sqrt(11)

remember trigonometry ?

this height = sin(theta) × AE

sin(theta) = height / AE = 3×sqrt(11) / 18 = sqrt(11)/6 =

= 0.552770798...

theta = 33.55730976...° ≈ 34°

(4)

the diagonals of a square bisect the angles of the square, so that theta would become 90/2 = 45°.

Evaluate. Write your answer as a fraction in simplest form. 3/8 - 1/6 + 5/12

Answers

Answer:

5/8

Step-by-step explanation:

Get LCD of 24 and do the math

9/24 - 4/24 - 10/24

15/24

Divide top and bottom by 3

5/8

Answer is 5/8 that is what I got

the circle below centred at O has a radius of 12cm

Answers

Answer:

x = 9.7 cm

Step-by-step explanation:

OB is perpendicular bisector of AC (since AB = BC) so triangle OBC is right triangle.

We have:

OB = x,OC = 12 cm,BC = 7 cm

Use Pythagorean to find the missing value:

x² + BC² = OC²x² = OC² - BC²x² = 12² - 7²x² = 144 - 49x² = 95x = √95x = 9.7 cm (rounded)

Shreya is training for a marathon. The graph shows the miles she ran each day of her training. Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. How far did Shreya run on day 5 of her training? Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.

Answers

She ran the distance on the day of 5 is 2miles.

Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.

⇒ (8-6-3-7)/5

⇒ (-8)/5

⇒ 1.8

⇒ 2 miles

The fraction whose numerator is 8 minus 6 minus 3 minus 7, whose denominator is 5 which is equal to the fraction of 2 miles.

Hence, Shreya ran on the day of 5 in her training is 2 miles.

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Name all segments on the line that contain point c

Answers

The name of all segments on the line that contain point c are AD, BD, AE, BE

How to name all segments on the line that contain point c?

The points on the number line are given as:

A, B, C, D and E

On this number line, the point either sides of point C are

A and B & D and E

This means that the point C is on the lines AD, BD, AE, BE

Hence. the name of all segments on the line that contain point c are AD, BD, AE, BE

Answers

Answer:

1.If you are to check the figure you will find that it is a rectangles. You should know the properties of a rectangle.

we are goin to use the property: Each vertex of a rectangle has angle equal to 90 degreesmeaning since m∠SUT and m∠ RUS form the vertex when added they give 90°

3x+6+(5x-4)=90°

3x+5x+6°-4°=90°

8x+2°=90°

8x=90°-2°

8x=8°

[tex]\frac{8x}{8} =\frac{88}{8} \\x=11[/tex]

2.m ∠SUT is donated by 3x+6

and now we know the value of x=11°

m∠SUT=3(11°)+6

m∠SUT=33°+6°

m∠SUT=39°

Lucie works out 25 x 12.2 without a calculator.
Here is her working.
10 × 12.2 = 12.20
20 × 12.2 = 24.40
5 x 12.2 = 61
25 x 12.2 = 24.40 +61 = 85.40
Lucie's working is incorrect.
Identify and (only) correct the lines containing a mistake
to work out the correct answer.
122
244

Answers

Answer:

[tex]25 \times 12.2 = 305.00[/tex]

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