Mathematics College

What is the length of the hypotenuse of the triangle?
sides 7cm and 3cm

A. sqrt 20cm
B. sqrt 23cm
C. sqrt 40cm
D. sqrt 58cm

Answers

Answer 1
So use the Pythagorean theorem formula - a² + b² = c²

7² + 3² = c²
49 + 9 = c²
49 + 9 = 58
58 = c²
Sqrt of 58 = 7.6 cm

So the answer is D) Sqrt 58 cm.

Hope this Helps!!
Answer 2

The length of the hypotenuse of the triangle is √58 cm (Option D).

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle:

Side a = 7 cm (one of the legs)

Side b = 3 cm (the other leg)

Side c = ? (the hypotenuse)

The Pythagorean theorem is:

[tex]c^2 = a^2 + b^2[/tex]

Substitute the given values:

[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]

Now, we can find the square root of both sides to solve for c:

c = √58 cm

So, the length of the hypotenuse of the triangle is √58 cm.

The correct answer is: D. √58 cm

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Related Questions

Which absolute value statement describes a 40 yard gain in football? A. |40| = 40, B. |-40| = 49, C. -|40| = 40, D. -|40| = 40,

Answers

The answer is A.) |40|=40

Answer:

d

Step-by-step explanation:

The digits of a certain three-digit number are consecutive odd numbers. If the sum of the digits is 15, find the number.

Answers

The answer is 5 because it is consecutive 3 times and it is an odd number

Let the digits of the 3 digit number be [tex] x-2,x,x+2 [/tex]. where [tex] x [/tex] is an integer greater than 1. It is given that the sum of the 3 digits is 15. Hence,

[tex] x-2+x+x+2=15\\
3x=15\\
x=5 [/tex]

Thus the digits are [tex] 3,5,7 [/tex].

Therefore, the number is [tex] 357 [/tex].

We assume that the digits of the number is increasing from the 100th place.

how to get arc length when central angle is 139

Answers

So, this is a really good video to help you. I hope you get the answer, if you still don’t- I’ll answer your question in the comments. https://youtu.be/lBOy62v-9Uk
Final answer:

To find the arc length when the central angle is 139 degrees, multiply the fraction of the circle that the angle represents (139/360) by the circle's circumference formula (2πr), where r is the radius.

Explanation:

Calculating Arc Length with a Known Central Angle

To calculate the arc length when the central angle is 139 degrees, you need to know the radius of the circle. The arc length, As, is the distance traveled along the circumference of a circle as the radius is rotated through a given angle. Since there are 360 degrees in a full revolution, a central angle of 139 degrees represents a fraction 139/360 of the full circle.



The circumference of the entire circle is given by the formula 2πr, where r is the radius. Therefore, the arc length can be calculated by multiplying the fraction of the circle represented by the angle (in this case, 139/360) by the total circumference. The formula to determine the arc length As is:



As = (139/360) × 2πr



By knowing the radius and the central angle, you can substitute these values into the formula to find the arc length for any circular path.

Two numbers rolled can be added to get a sum. Find P(sum is even.)

Answers

When you roll two numbers you have four kinds of outcomes: EE, EO, OE, OO (where E = even, O = odd).

You get an even sum only if you sum two numbers that are both even or both odd, therefore the outcomes wanted are two: EE and OO.

Therefore:
P(sum is even) = 2 / 4 = 0.5

Hence, there is a 50% probability that, when you roll two numbers, their sum will be even.

Help see photo attached

Answers

The first pair of statements is the best option. h(0) based on the given equation would be the square root of -3, which is an imaginary number. Also, w(0) should be 0, since if nobody is working on making wrenches, none can be made. This is despite the graph having a value at x = 0.

The second statement in the second pair is false, since 0 is not an imaginary number.

Write out the first four terms of the maclaurin series of f(x) if f(0)=−13,f′(0)=−6,f″(0)=5,f‴(0)=6 f(x) = +⋯

Answers


[tex] -13 - 6x + \frac{5}{2} {x}^{2} + {x}^{3} [/tex]

If the triangle on the grid below is translated by using the (x,y) -> (x+5, y-2) rule, what will be the coordinates of B'?
(–2, 0)
(0, –2)
(5, –7)
(5, –2)

Answers

we know that
the coordinates of point B ( -5,0)

the translation has the following rule
(x,y)--------> (x+5, y-2)
so
(-5,0)-----> (-5+5,0-2)-----> (0,-2)

the answer is
(0, –2) 

Answer:

[tex]B(-5,0)\rightarrow B'(0,-2)[/tex]

Step-by-step explanation:

From the diagram, B has coordinates [tex](-5,0)[/tex].


We want to find the coordinates of B' after a translation by the rule;

[tex](x,y)\rightarrow(x+5,y-2)[/tex],

We apply the rule to obtain;


[tex]B(-5,0)\rightarrow B'(-5+5,0-2)[/tex],


This implies that;


[tex]B(-5,0)\rightarrow B'(0,-2)[/tex]


Therefore the correct answer is B





a local club is arranging a charter flight to hawaii. the cost of the trip is $574 each for 81 passengers, with a refund of $5 per passenger for each passenger in excess of 81.
find the number of passengers that will maximize the revenue recieved from the flight
also find the maximum revenue.

Answers

Let x be the number of passengers.
The discounted cost is given by,

Cost = 574-5(x-81) = 574-5x + 405 = 979 -5x

Total revenue, R(x) = x(979 - 5x) = 979x - 5x^2

At maximum revenue, dR/dx = 0 => dR/dx = 979 - 10x = 0 =>10x = 979 => x =979/10 = 97.9 ≈ 98 passengers

Therefore,
Revenues, R(97) = 98[574 -5(98-81)] = 98[574-85] = $47,922

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%. If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?

Answers

The population Pa of insect A after t years is given by the equation 
     Pa = 1.3(1-0.038)^t 
while the population Pb of insect B after t years is 
     Pb = 2.1(1-0.046)^t

We equate the above expressions to find the number of years t it will take the two populations to be equal: 
     Pa = Pb
     1.3(1-0.038)^t  = 2.1(1-0.046)^t
     1.3(0.962)^t  = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.

We can now solve for t:
     (0.962)^t / (0.954)^t = 2.1/1.3
     (0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
     t = log (2.1/1.3) / log (0.962/0.954)
     t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
For these types of problems, the equations of the form should be considered:
 y = A * (B) ^ t
 Where:
 A: initial population.
 B: annual exchange rate.
 T: Time in years.
 Then the equations of the system that must be used to find the time in which both are equal are:
 1, 3,00,000 * (1-0,038) ^ t for the type of insect A
 2, 1 00 000 * (1-0,046) ^ t for the type of insect B.

Nina wants to put color tiles on a square. 3 color tiles fit across the top of the square. How many rows and columns of square will Nina need? How many color tiles will she use in all?

Answers

The area is a square. If she uses 3 tiles to fit length-wise, she will need 3 tiles to fit width-wise.

Total tiles needed = 3 x 3 = 9 tiles.

Answer: 3 rows of 3 tiles. Total of 9 tiles needed.

Nina will need 3 rows and 3 columns of square tiles. She will use 9 color tiles in total to cover the square.

To determine how many rows and columns of square tiles Nina needs, and how many color tiles in total she will use, let's break down the problem step by step:

1. Width and Height of the Square:

Nina can fit 3 color tiles across the top of the square. This implies the width of the square is 3 color tiles.

2. Rows and Columns Calculation:

  Since the square has 3 tiles across the top, and assuming the square is symmetric (same number of tiles in width and height):

Number of columns(width) = 3 tiles Number of rows (height) = 3 tiles So, Nina will need 3 columns and 3 rows of square tiles.

3. Total Number of Color Tiles:

To find out how many color tiles Nina will use in total, calculate the area of the square:

Area of the square = [tex]\( \text{Number of rows} \times \text{Number of columns} \)[/tex]

Area = [tex]\( 3 \times 3 = 9 \)[/tex] color tiles

Therefore:

Nina will need 3 rows and 3 columns of square tiles.

She will use 9 color tiles in total to cover the square.

find the lateral area of the prism 3m 6m 3m 6m 15m

Answers

To find the lateral area of a prism, we calculate the combined area of its vertical rectangular faces, excluding the top and bottom faces. This prism has dimensions of 3m x 6m x 15m. It has two pairs of congruent rectangular faces: one pair with dimensions 3m x 15m and the other with dimensions 6m x 15m. The area of each face is determined by multiplying its length by its height. For the first pair of faces, the area is 3m * 15m = 45 square meters each. Similarly, for the second pair, the area is 6m * 15m = 90 square meters each. Adding these areas together (2 * 45 + 2 * 90), we get a lateral area of 270 square meters.

Complete answer;

find the lateral area of the prism 3m 6m 3m 6m 15m

hey can you please help me posted picture of question

Answers

Points of intersection are solution set. Answer is 2.
Answer:
Two 

Explanation:
The solution of a system of equations is defined as the values which satisfies both equations.

Graphically, the solutions are represented by the points of intersection between the two equtaions.

In the given graph, we have a circle and a line, we can note that these two intersect in two points.

This means that the system has two solutions

Hope this helps :)

PLZ HELP ASAP LAST CIRCLES

Answers

AC and AB are tangents to circle O, meaning that the angles C and B are right angles of 90 degrees. Since a quadrilateral's internal angles must sum up to 360 degrees, this means that A + B + C + O = 360
70 + 90 + 90 + O = 360
O = 110 degrees.

Isabella works at Baker's Book company. If she earned a commission of $63.75 on her sales of $850, what was Isabella's rate of commission?

Answers

Rate = 63.75/850=.075*100%= 7.5%

7.5% is Isabella's rate of commission.

Is -6.175 is an irrational number?

Answers

No.

Any number you can write completely is a rational number.
Any number with a repeating decimal fraction is also a rational number.
___
Any number that goes on forever without repeating is an irrational number. These are usually represented symbolically (because they cannot be written "exactly" any other way). These include such numbers as √2, π, e, ∛(-4), and an infinite number of others.

Solve this system of equations: y = x2 – 3x + 12 y = –2x + 14 1.Isolate one variable in the system of equations, if needed. y = x2 – 3x + 12 y = –2x + 14 2.Use substitution to create a one-variable equation. –2x + 14 = x2 – 3x + 12 3.Solve to determine the unknown variable in the equation. What are the values of x?

Answers

-2x+14=x²-3x+12
add 2x on both side:
14=x²-x+12
subtract 14 on both side:
x²-x-2=0
factor: (x-2)(x+1)=0
x=2 or x=-1
HOPE THIS HELPS AND PLEASE MARK ME AS BRAINIEST AND ADD ME AS A FRIEND
The resulting equation will be

x^2 - x - 2 =0
x^2 -2x +x -2 = 0
(x-2)(x+1) = 0
x= 2 and x = -1

Hope this will help☺☺


5n+5=45 what does n =

Answers

5n+5=45
Subtract 5 from both sides
5n=40
Divide both sides by 5
n=8

I hope this helps

You collect old coins. today, you have two coins each of which is valued at $100. one coin is expected to increase in value by 5.2 percent annually while the other coin is expected to increase in value by 5 percent annually. what will be the difference in the value of the two coins 25 years from now?

Answers

The coin increasing in value by 5.2% will be valued at $230, and the coin increasing by 5% will be valued at $225. They will have a $5 difference 

0.5 log3 x=2 x = what

Answers

[tex]0.5\log_3x=2[/tex]

[tex]Domain:x\in\mathbb{R^+}[/tex]

[tex]0.5\log_3x=2\ \ \ |\cdot2\\\\\log_3x=4[/tex]

[tex]Use\ the\ de finition\ of\ the\ logarithm:\\\\\log_ab=c\iff a^c=b[/tex]

[tex]Therefore\ we\ have:\\\\\log_3x=4\iff3^4=x\to x=81[/tex]

Answer: C. 81.
Here is another method:
[tex]0.5 log_3 (x) = 2[/tex]

Multiply both sides by 10 to get rid of the decimal:
[tex]10 * 0.5 log_3 (x) = 10 * 2[/tex]
[tex]5 log_3 (x) = 20[/tex]

Divide 5 out
[tex]\frac{5 log_3 x}{5} = \frac{20}{5}[/tex]
[tex]log_3 x = 4[/tex]

Now use the log rule [tex]a = log_b b^a[/tex]
[tex]4 = log_3 (3^4) = log_3 (81)[/tex]

Since we have the same base
[tex]log_3 (x) = log_3 (81)[/tex]
x = 81


When you agree to pay a car dealer for the use of a new car during a set period of time for a set amount of money and you have to return it at the end of that period of time, you are _____

Answers

When you agree to pay a car dealer for the use of a new car during a set period of time for a set amount of money and you have to return it at the end of that period of time, you are leasing a car.

Vehicle leasing is the leasing (or the use) of a motor vehicle for a fixed period of time at an agreed amount of money for the lease. It is commonly offered by dealers as an alternative to vehicle purchase but is widely used by businesses as a method of acquiring (or having the use of) vehicles for business, without the usually needed cash outlay. The key difference in a lease is that after the primary term (usually 2, 3 or 4 years) the vehicle has to either be returned to the leasing company or purchased for the residual value.

PLZ HELP ASAP TANGENTS OF A CIRCLES PROBLEMS

Answers

The radius of circle is 5.

AO = AB + OB

AB = 8
OB = Radius of circle = 5

So, 

AO = 8 +5 = 13

The tangent of the circle is at 90 degrees to its radius. So we can say that triangle ACO is a right angled triangle, with side AO the hypotenuse.

Using the Pythagorean theorem we can find the length of tangent AC.

13² = AC² + 5²
AC² =  169 - 25 = 144
AC = 12

So, the length of side AC is 12

Nico dropped the brand new bottle of dog shampoo and 3 ounces spilled out. He measures 1 1/4 ounces each time he shampoos his dog and the bottle of shampoo originally contained 30 1/2 ounces. Which is the correct equation and value of x, the number of times Nico can bathe his dog using this one bottle?

Answers

Amount of shampoo in a bottle = [tex]30 \frac{1}{2} [/tex] ounces
Amount of shampoo Nico uses in one bathe for his dog  = [tex]1 \frac{1}{4} [/tex]

Since 3 ounces of shampoo is spilled out, the amount of shampoo left in the bottle will be =  [tex]27 \frac{1}{2} [/tex]

If Nico can Bathe his dog x times using this bottle, the value of x can be written as:

[tex]x= \frac{27 \frac{1}{2} }{ 1\frac{1}{4} } [/tex]

Using this equation we can find the number of times Nico can use the shampoo to Bathe . The value of x comes out to be 22.

Thus, Nico can Bathe his dog 22 times using the bottle
Final answer:

Nico can bathe his dog 22 times using the one bottle of shampoo.

Explanation:

To find the number of times Nico can bathe his dog using the one bottle of shampoo, we need to determine how many times 1 1/4 ounces can fit into the remaining shampoo in the bottle after 3 ounces have spilled out.

First, subtract the spilled amount of 3 ounces from the original amount of shampoo in the bottle, which is 30 1/2 ounces. This gives us 27 1/2 ounces remaining.

Next, divide the remaining amount of shampoo by the amount used per bath (1 1/4 ounces each time).

27 1/2 ounces ÷ 1 1/4 ounces = 22 baths

Therefore, Nico can bathe his dog 22 times using the one bottle of shampoo.

Learn more about Bathing a dog here:

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Multiply 3i(−1 + 2i). What is the simplified version written in standard form, a + bi, where a and b are real numbers?

Answers

3i (- 1 + 2i)     Remove the brackets.
3i (-1) + (2i)(3i) Look at the first set of brackets around the -1
-3i + 6i^2     But i^2 = - 1[ I hope that's the way you are using it]
-3i - 6 or -6 - 3i or -3(2 - i) <<<<< answer

If you need to see up direct deposit which information from your check would you likely need A. Check number B. Memo line C. Numerical amount D. Routing number

Answers

You'd need D. Routing Number
Hello there, and thank you for asking your question here on brainly.

Answer: If you need to see up direct deposit, the information you'd most likely need is your routing number.

Hope this helped you! ♥

15 points!!! GEOMETRY help please!!
Questions attached!

Answers

9.
[tex]\text{If QR is tangent to circle then m}\angle PQR=90^o[/tex]

[tex]\text{We can use the converse of Pythagorean theorem}[/tex]

[tex]8\ and\ 4\sqrt3\\\\check:\ 4^2+(4\sqrt3)^2=8^2\\16+16\cdot3=64\\16+48=64\\64=64\ -O.K.\\\\2\ and\ 4\sqrt2\\\\check:\ 4^2+2^2=(4\sqrt2)^2\\16+4=16\cdot2\\20=32\ -FALSE\\\\3\ and\ 5\\\\check:\ 3^2+4^2=5^2\\9+16=25\\25=25\ -O.K.\\\\2\ and\ 2\sqrt5\\\\check:\ 4^2+2^2=(2\sqrt5)^2\\16+4=4\cdot5\\20=20\ -O.K.\\\\6\ and\ 10\\check:\ 4^2+6^2=10^2\\16+36=100\\52=100\ -FALSE[/tex]

[tex]\text{Answer:}\boxed{8\ and\ 4\sqrt3;\ 3\ and\ 5;\ 2\ and\ 2\sqrt5}[/tex]


10.
[tex]\text{Look at the pictures}[/tex]

[tex]\text{Therefore}\\\\C=2\cdot8+2\cdot16+2\cdot9+2\cdot6=16+32+18+12=78cm[/tex]

[tex]Other\ method:\\C=2\cdot(8+16+6+9)=2\cdot39=78cm[/tex]

Answer:

\text{If QR is tangent to circle then m}\angle PQR=90^o

\text{We can use the converse of Pythagorean theorem}

8\ and\ 4\sqrt3\\\\check:\ 4^2+(4\sqrt3)^2=8^2\\16+16\cdot3=64\\16+48=64\\64=64\ -O.K.\\\\2\ and\ 4\sqrt2\\\\check:\ 4^2+2^2=(4\sqrt2)^2\\16+4=16\cdot2\\20=32\ -FALSE\\\\3\ and\ 5\\\\check:\ 3^2+4^2=5^2\\9+16=25\\25=25\ -O.K.\\\\2\ and\ 2\sqrt5\\\\check:\ 4^2+2^2=(2\sqrt5)^2\\16+4=4\cdot5\\20=20\ -O.K.\\\\6\ and\ 10\\check:\ 4^2+6^2=10^2\\16+36=100\\52=100\ -FALSE

\text{Answer:}\boxed{8\ and\ 4\sqrt3;\ 3\ and\ 5;\ 2\ and\ 2\sqrt5}

10.

\text{Look at the pictures}

\text{Therefore}\\\\C=2\cdot8+2\cdot16+2\cdot9+2\cdot6=16+32+18+12=78cm

Other\ method:\\C=2\cdot(8+16+6+9)=2\cdot39=78cm

Step-by-step explanation:


hey can you please help me posted picture of question

Answers

To find if the pairs are inverse of each other, find their composition. The composition of the inverse function will always be equal to x.

For first option, the composition will be:

[tex]f(g(x))=2+ \sqrt[3]{2- x^{3} } [/tex]

For second option, the composition will be:

[tex]f(g(x))= \frac{6x-8}{6}+8= \frac{6x-8+48}{6} = \frac{6x-40}{6} [/tex]

For third option, the composition will be:

[tex]f(g(x))= \frac{49}{x+9}-9 [/tex]

For Fourth option, the composition will be:

[tex]f(g(x))=5( \frac{x+11}{5})-11=x+11-11=x [/tex]

So the pair of function given in Fourth option are inverse of each other

Stefano calculated the mean absolute deviation for the data set 32, 4, 12, 40, 20, and 24. His work is shown below. Step 1: Find the mean. mc006-1.jpg Step 2: Find each absolute deviation. 10, 18, 10, 18, 2, 2 Step 3: Find the mean absolute deviation. mc006-2.jpg What is Stefano’s error? Stefano should have divided by 5 when finding the mean. Stefano found the absolute deviation of 20 incorrectly. Stefano should have divided by 6 when finding the mean absolute deviation. Stefano did not find the correct value for the mean.

Answers

Here is the correct work. The picture is not showing up, but you can compare this work to what is given.

To find the mean, you will find the sum of all the numbers and divide by how many numbers there are.

Mean: 4 + 12 + 20  + 24 + 32 + 40 = 132
          132/6 = 22
Mean: 22

To find the mean absolute deviation, you find how far away each of the numbers are from the mean.  Find the sum of these and divide by the same number of numbers.

(22 - 4) + (22-12) + (22-20) +(24 - 22) + (32-22) + (40-22)
18 + 10 + 2 + 2 + 10 + 18 = 60
60/6 = 10

The MAD is 10.

I think the correct answer is that Stefano should have divided by 6 when finding the mean absolute deviation.

Answer:

Stefano should have divided by 6 when finding the mean absolute deviation. ed quiz correct

Step-by-step explanation:

what is -1/2x+1=9 with work shown.

Answers

[tex]-1/2x+1=9 (-1/2x+1=9)2 -x+2 = 18 -x = 16 x = -16[/tex]

Hank delivers packages in his office building. On Tuesday he delivered four more packages than on Monday, and on Wednesday he delivered 6 more packages than on Monday. If he delivered 28 packages all together, how many did he deliver on Monday?
A) 6
B) 10
C) 18
D) 22

Answers

The answer is A because if X represents the # of packages sold on Monday, then Tuesday can be represented by x+4 and Wednesday by x+6. Add the three expressions to get 3x+10=28, subtract 10 from both sides. 3x=28, divide by 3 and get x=6

Answer:

a

Step-by-step explanation:

x-5 is less than or equal to 1/3 (9x-6)

Answers

x-5 is less than 1/3 (9x-6) so that problem is correct
Other Questions
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