The lengths of the legs of a right angle triangle 12 cm and 35 cm. What is the length of the hypotenuse?

Answers

Answer 1

We can use the pythagorean theorem.

Allow x to be the hypotenuse.

12^2+35^2=x^2
144+1225=x^2
1369=x^2
x=37

Answer 2

we know that in a right triangle
c^2=a^2+b^2, where c is the hypotenuse
c^2=12^2+25^2=144+625=769
c=sqrt769= aprox 27.73

Related Questions

What is the value of log0.5^16? a.–4.00 b.–0.25 c.1.51 d.2.41

Answers

the answer for your question is a. -4

Answer:

The correct option is a.

Step-by-step explanation:

The given expression is,

[tex]log(0.5)^{16}[/tex]

Use property of logarithm

[tex]loga^b=bloga[/tex]

[tex]log(0.5)^{16}=16\times log(0.5)[/tex]

The value of log(0.5) is -0.30103.

[tex]log(0.5)^{16}=16\times -0.30103[/tex]

[tex]log(0.5)^{16}=-4.81648[/tex]

The value of given expression is -4.81648.

If the final answer appromatted to preceding integer, then the correct option is -4.00.

Which of the following describes the roots of the polynomial function f(x)=(x-3)^4(x-6)^2? –3 with multiplicity 2 and 6 with multiplicity 4 –3 with multiplicity 4 and 6 with multiplicity 2 3 with multiplicity 2 and –6 with multiplicity 4 3 with multiplicity 4 and –6 with multiplicity 2

Answers

In mathematics, the multiplicity of a member of a multi-set is the number of belongings it has in the multi-set.
For example, this term is used to refer to the number of times a certain polynomial has a root at a certain point.
For this polynomial we have:
f (x) = (x-3) ^ 4 (x-6) ^ 2
3 with multiplicity 4 and 6 with multiplicity 2
Answer:
3 with multiplicity 4 and 6 with multiplicity 2

Answer:

3 with multiplicity 4 and -6 with multiplicity 2

An electronics shop offers a small ic chip for $1.50 per unit and $4.00 for large ic chip. on a certain day, 2200 chips were sold and $5050 is collected. how many small ic chips and how many large ic chips were sold?

Answers

Let s and l represent the numbers of small and large ICs sold that day. The problem statement gives rise to two equations.
.. s + l = 2200
.. 1.50s +4.00l = 5050

Solving these by your favorite method gives
.. s = 1500
.. l = 700

1500 small ICs and 700 large ICs were sold.

To determine the number of small and large IC chips sold, we set up a system of linear equations with the given total number of chips (2200) and total earnings ($5050). Solving the system, we found that 1500 small IC chips and 700 large IC chips were sold.

To solve the problem, we can set up a system of linear equations to represent the sales for small and large IC chips. We have two unknowns: the number of small IC chips (let's call it x) and the number of large IC chips (let's call it y). We have two pieces of information to create our equations:

The total number of chips sold is 2200, so x + y = 2200.

The total amount collected is $5050, so 1.50x + 4.00y = 5050.

Solving this system of equations, we multiply the first equation by 1.50 to align it with the second equation:

1.50x + 1.50y = 3300 (Multiply the first equation)

1.50x + 4.00y = 5050 (Second equation)

Subtracting the first new equation from the second gives us:

2.50y = 1750

Dividing both sides by 2.50 to find y gives us y = 700. That means 700 large IC chips were sold. Now, we can substitute y in the first equation to find x:

x + 700 = 2200

x = 2200 - 700

x = 1500

Hence, 1500 small IC chips and 700 large IC chips were sold.

the average adult human has approximately 2.5 x 10 ^ 13 red blood cells + 7 x 10 ^ 9 white blood cells about how many times as great is the number of red blood cells than the number of white blood cells

Answers

To solve this problem, what we must do is use the following equation:
N = (red blood cells) / (white blood cells)
Substituting values we have:
N = (2.5 * 10 ^ 13) / (7 * 10 ^ 9)
N = 3571.428571
Nearest whole number:
N = 3571
Answer:
The number of red blood cells is 3571 as great as the number of white blood cells

Trigonometric Help Plz?

Answers

1)

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ cos(\theta )=\sqrt{1-sin^2(\theta )}\\\\ -------------------------------\\\\ sin(x)=cos(x)-1\implies sin(x)=\sqrt{1-sin^2(x)}-1[/tex]

[tex]\bf sin(x)+1=\sqrt{1-sin^2(x)}\implies [sin(x)+1]^2=1-sin^2(x) \\\\\\ sin^2(x)+2sin(x)+1=1-sin^2(x)\implies 2sin^2(x)+2sin(x)=0 \\\\\\ 2sin(x)[sin(x)+1]=0\implies \begin{cases} 2sin(x)=0\\ sin(x)=0\\ \measuredangle x=0~,~\pi ~,~2\pi \\ -------\\ sin(x)+1=0\\ sin(x)=-1\\ \measuredangle x=\frac{3\pi }{2} \end{cases}[/tex]

2)

[tex]\bf 3sin(x)+cos^2(x)=2 \\\\\\ 3sin(x)+[1-sin^2(x)]=2 \\\\\\ 3sin(x)-sin^2(x)+1=2 \\\\\\ 3sin(x)-sin^2(x)-1=0 \\\\\\ sin^2(x)-3sin(x)+1=0 \\\\\\ \boxed{[sin(x)-3][sin(x)+1]=0}\impliedby \textit{check closely this }FOIL[/tex]

Find the area under the curve y = 5/x3 from x = 1 to x = t. evaluate the area under the curve for t = 10, t = 100, and t = 1000. t = 10 t = 100 t = 1000 find the total area under this curve for x ≥ 1.

Answers

The area under the curve from x = 1 to x = t is [tex]-\frac{5}{2} (\frac{1}{t^2} -1)[/tex].

For, t = 10, 100, and 1000, the areas are 2.475, 2.49975, and 2.4999975 respectively.

The total area is 2.5.

Given that:

[tex]y=\frac{5}{x^3}[/tex]

In order to find the area integrate it with limits from x = 1 to x = t.

[tex]A=\int\limits^t_1 {\frac{5}{x^3} } \, dx[/tex]

This can be written as:

[tex]A=\int\limits^t_1 {5x^{-3} } \, dx[/tex]

[tex]=5[\frac{x^{-2}}{-2} ]_1^t[/tex]

[tex]=-\frac{5}{2} (t^{-2}-1^{-2})[/tex]

So, the area is [tex]A=-\frac{5}{2} (\frac{1}{t^2} -1)[/tex].

When t = 10,

[tex]A=-\frac{5}{2} (\frac{1}{10^2} -1)[/tex]

[tex]=2.475[/tex]

When t = 100,

[tex]A=-\frac{5}{2} (\frac{1}{100^2} -1)[/tex]

[tex]=2.49975[/tex]

When t = 1000,

[tex]A=-\frac{5}{2} (\frac{1}{1000^2} -1)[/tex]

[tex]=-2.4999975[/tex]

To find the total area, the value of t = ∞.

Now, ∞⁻² is always 0, since any negative number to the power of infinity is 0.

So, the area is:

[tex]A=-\frac{5}{2} (0-1)[/tex]

[tex]A=2.5[/tex]

Hence, the total area is 2.5.

Learn more about Area using Integrals here :

https://brainly.com/question/34160198

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2/3 of the product of 3/8 and 16

Answers

Hi there!

To solve this problem, we should first find the product of 3/8 and 16 and multiply the solution by 2/3.

Let's find the product first.

3/8 × 16 = 48/8

Simplify.

48/8 = 48 ÷ 8 = 6

Now, we find 2/3 of 6.

6 ÷ 3 × 2 = 2 × 2 = 4

So, your answer is 4.

Hope this helps!

What is greater than 1 kg

Answers

2kg is greater than 1kg if thats what you're asking

Surface area of right cone radius of 8 and 14 height
A. 896
B. 224
C. 176
D. 167

Answers

[tex]\bf \textit{total surface area of a cone}\\\\ S=\pi r\sqrt{h^2+r^2}+\pi r^2\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=14 \end{cases} \\\\\\ S=\pi (8)\sqrt{14^2+8^2}+\pi (8)^2\implies S=8\pi \sqrt{260}+64\pi \\\\\\ S\approx 405.25+201.06\implies S\approx 606.31[/tex]

The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of cone = 8

And, Height = 14

We know that;

Surface area of right cone is,

SA = πr (r + √h² + r²)

SA = 3.14 × 8 (8 + √14² + 8²)

SA = 606.31

Thus, The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

Learn more about the multiplication visit:

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1.
Find the Compound Amount.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5

2.
Find the Interest Earned.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5

Answers

1)
Principal Amount = P = $980
Interest rate = r = 8% = 0.08
Compounding periods = n = 4
Time = t = 5 years

Formula to be used for finding compounding amount:

[tex]A=P (1+ \frac{r}{n} )^{nt} [/tex]

Using the values in the formula, we get:

[tex]A=980 (1+ \frac{0.08}{4} )^{5*4} =1456.23[/tex]

Therefore, the amount compounded over a period of 5 years will be $1456.23

2)
Principal Amount = $980
Compounded Amount = $1456.23
Interest Earned = Compounded Amount - Principal Amount
Interest Earned = 1456.23 - 980 = $ 476.23

Therefore, $476.23 interest will be earned over a period of 5 years.

Estimate by division ..70/9.24

Answers

the answer is 7.58

hope this helped :)
alisa202

Here we have to divide 70 by 9.24.

we can first covert the decimal 9.24 into fraction, shifting the decimal two units to the right and dividing by 100, we have

9.24 = 924/100

Now let us divide 70 by 924/100

in division of fraction we take reciprocal of second fraction and multiply it with first.

reciprocal of 924/100 is 100/924.

multiplying 70* 100/924, we have

[tex] 70 * \frac{100}{924} [/tex]

[tex] = \frac{7000}{924} [/tex]

converting into decimal we have

[tex] \frac{7000}{924} = 7.5757..... [/tex]

mrs. west is 14 years younger than her aunt. if mrs. west’s age in years is as much below 60 as her aunt’s age is over 40, how old is each?

Answers

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

Let's represent Mrs. West's age as W and her aunt's age as A.

Given that Mrs. West is [tex]14[/tex] years younger than her aunt, we can write the equation:

[tex]W=A-14[/tex]

Also, it's given that Mrs. West's age is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex] . This can be represented as:

[tex]W=60-(A-40)[/tex]

Simplify the equation:

[tex]W=60-A+40\\W=100-A[/tex]

Now, we have two equations for [tex]W[/tex]:

[tex]W=A-14\\W=100-A[/tex]

Since both equations equal [tex]W[/tex], we can set them equal to each other:

[tex]A-14=100-A[/tex]

Now, solve for A:

[tex]A+A=100+14\\2A=114\\A=57[/tex]

Now, plug the value of [tex]A[/tex] into either equation to find [tex]W[/tex]:

[tex]W=57-14\\W=43[/tex]

So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

COMPLETE QUESTION:

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], how old is each?

A jar of crunchy peanut butter contains 1.35 kg of peanut butter. if you use 8.0 % of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container?

Answers

1. You have that:

-The jar of crunchy peanut butter contains 1.35 kilograms of peanut butter.

-You use 8.0 % of the peanut butter.

2. You must convert 1.35 kilograms to ounces, as below:

1 kilogram=35.2739 ounces

=(1.35 kilogram)(35.2739 ounces/1 kilogram)
=1.35x35.2739 ounces
=47.61 ounces

3. Then, you have:

47.61 ounces-----100%
x-----8%

8%/100=0.08
100%/100=1

x=(0.08x47.61 ounces)/1
x=3.80 ounces

How many ounces of peanut butter did you take out of the container?

The answer is: 3.80 ounces

eva estimates that 475 songs will fit on her mp3 player the actual that fit is 380 findc the percent error

Answers

20% is the percent error
https://studysoup.com/questions/math/100256/eva-estimates-the-475-songs-will-fit-on-mp3-player

20 percent is the percent error. Hope I helped! :)

Experts/ace/geniuses

Answers

the answer would be D. 3/15

The answer is D. I hope this helped

tossing a number cube numbered from 1 to 6 and getting an odd number that is less than or equal to 3

Answers

1/3 bc only 1 and 3 are odd and less than/equal to 3, and there’s 6 total outcomes.

2/6=1/3

Since 3 is half of 6 and it is basically 50% or 1/2

In which graph does y vary directly as x? It’s not C, I got it wrong.

Answers

The answer is A. X increases Y increases.

Which of the following functions is graphed below?

Answers

we have that

observing the graph of the problem, it is evident that the solution is option D, since the graph of the parabola presents a domain for x <4 and the line presents a domain for x> = 4 and the only option with these two conditions is option D

using a graph tool
I proceed to verify
see the attached figure

the answer is the option D

The graph consists of two parts: left part (with sign < or ≤) - parabola and right part (with sign > or ≥) - straight line.

Determine signs:

From the diagram you can see that the right endpoint (4,19) of parabola is not included. This means that x cannot be equal to 4 at this part of graph and the sign should be <.

Also you can see that the left endpoint (4,8) of line is included. This means that x=4 belongs to the right part and the sign should be ≥.

Using previous conclusions, you can state that correct choice is D.

0.698 to the bestest hundreth

Answers

I.7
Is the answer ok.

0.698
The 9 is in the hundredths place
Since 9 is greater than 5 we will round up.
0.70 is your answer

what are the slope and why intercept shown on the graph below

Answers

Hello!

Let's start by finding the slope of the line. You can calculate the slope by dividing the change in y-values by the change in x-values using the following formula:

[tex] \frac{ y_{1}- y_{2} }{ x_{1} - x_{2} } [/tex]

The plotted coordinates are (0, 5) and (4, -5); let's plug those into the formula:

[tex] \frac{5(-5)}{0-4} [/tex]

Simplify:

[tex] \frac{5+5}{-4} [/tex]

[tex] \frac{10}{-4} [/tex]

[tex] \frac{-5}{2} [/tex]

The slope is [tex] \frac{-5}{2} [/tex].

Now, the y-intercept is where the line intersects the y-axis, or when x equals 0. x equals 0 when y equals 5, so the y-intercept is 5.

I hope this helps!

Hi there! The formula for finding the slope is y2 - y1/ x2 - x1, where the first x and y-coordinates are subtracted from the second x and y-coordinates. We have the two points on the graph marked. We will use (0, 5) and (4, -5) in this case. Here are the numbers that represent each:

y2 = -5
y1 = 5
x2 = 4
x1 = 0

Let's subtract. -5 - 5 is -10. 4 - 0 is 4. -10/4 is -2 1/2 in simplest form or -5/2 as a mixed number. We found the slope. The y-intercept is where the line crosses, where the x-axis is 0. In this case, we can see by the point given out that the slope intercept is 5. There. The slope is -5/2 and the slope-intercept is 5. The answer is B.

Find all integer solutions to the pair of congruences (if any) x ≡ 17 (mod 23) 70x ≡ 3 (mod 93).

Answers

First, note that [tex]93=3\times31[/tex], which gives

[tex]70x\equiv3\pmod{93}\implies\begin{cases}70x\equiv3\equiv0\pmod3\\70x\equiv3\pmod{31}\end{cases}[/tex]

so in fact we're dealing with the system

[tex]\begin{cases}x\equiv17\pmod{23}\\70x\equiv0\pmod3\\70x\equiv3\pmod{31}\end{cases}[/tex]

Now, 3, 23, and 31 are relatively prime, so we can use the Chinese remainder theorem. But before we do that, we need to rework and ultimately eliminate the coefficients of [tex]x[/tex].

From the second equivalence, it follows immediately [tex]x[/tex] is some multiple of 3; this is because [tex]70x[/tex] is divisible by 3, but 3 doesn't divide 70, so it must divide [tex]x[/tex].

For the third equivalence, we can write [tex]70x=62x+8[/tex]. Then modulo 31, we have that [tex]62x\equiv0[/tex], which leaves us with [tex]8x\equiv3\pmod{31}[/tex]. We want a congruence of the form [tex]x\equiv\cdots[/tex], and to get that we can multiply [tex]8x[/tex] and 3 by the inverse of 8 modulo 31.

To find this inverse, we solve for [tex]y[/tex] in the relation

[tex]8y\equiv1\pmod{31}[/tex]

by using the Euclidean algorithm, or making just making the observation that [tex]8\times4\equiv32\equiv1\pmod{31}[/tex], so [tex]8^{-1}\equiv4\pmod{31}[/tex]. Distributing 4 across the third equivalence in our system gives [tex]x\equiv4\pmod{31}[/tex].

So to recap, we now have

[tex]\begin{cases}x\equiv17\pmod{23}\\x\equiv0\pmod3\\x\equiv12\pmod{31}\end{cases}[/tex]

and we're ready to use the CRT.

As a starting point, let's take

[tex]x=(17)+(23)+(23)=63[/tex]

It's clear that taken modulo 23, the latter two terms vanish and we have a remainder of 17, as desired. 63 is already a multiple of 3, but just to avoid doing more work later, let's multiply each term by 3 anyway to keep getting a remainder of 0:

[tex]x=(17\times3)+(23\times3)+(23\times3)=146[/tex]

Now multiply the first two terms by 31 to make sure they vanish when taken modulo 31. Meanwhile, [tex]23\times3\equiv69\equiv7\pmod{31}[/tex], but we want to get 12, so we would multiply this term by the inverse of 7 mod 31, and again by 12.

We can make a quick observation that [tex]7\times9=63=31\times2+1[/tex], so [tex]7^{-1}\equiv9\pmod{31}[/tex]. Alternatively, you can use the Euclidean algorithm to find this inverse. Either way, we get

[tex]x=(17\times3\times31)+(23\times3\times31)+(23\times3\times9\times12)=11,172[/tex]

So we're told that

[tex]x=11,172+(23\times3\times31)k=11,172+2139k[/tex]

is our solution set, where [tex]k\in\mathbb Z[/tex]. We can "simplify" this slightly by finding the least positive residue modulo the product of our moduli, which would be

[tex]11,172\equiv477\pmod{2139}[/tex]

so we end up with

[tex]x=477+2139k[/tex]

for integers [tex]k[/tex].

Indicate whether each of the following fractions is proper or improper. a. 4⁄16 b. 75⁄70 c. 2⁄15 d. 6⁄6

Answers

75/70 is an Improper Fraction

An proper fraction is a fraction where the denominator is larger than the numerator.
An improper fraction is a fraction where the numerator is larger than or equal to the denominator.

a. 4/16
The denominator is 16. The numerator is 4. The denominator is larger than the numerator; thus, this is a proper fraction.

b. 75/70
The denominator is 70. The numerator is 75. The numerator is larger than the denominator; thus, this is an improper fraction.

c. 2/15
The denominator is 15. The numerator is 2. The denominator is larger than the numerator; thus, this is a proper fraction.

d. 6/6
The denominator is 6. The numerator is 6. The numerator is equal to the denominator; thus, this is an improper fraction.

Does anyone know how to prove that OAC and OBC are Congruent.

Answers

Hello,

The first step is to see that sides OA, OC, OB are all equal because they are the radii of the circle. Knowing that those sides are equal means that we have isosceles triangles. That gives us that the base angles are the same.

In OAC, we can subtract 118 from 180 to give us 62 degrees for the 2 bases angles. This would make each angle 31 degrees.

In OBC, the base angles are already 31, leaving the other angle 118.

There we have all the angles the same and 2 sides the same.

You could use SAS or ASA to prove that the triangles are congruent.

I hope this helps!
Good luck,
MrEquation

Answer:

You could use SAS or ASA to prove that the triangles are congruent.

Step-by-step explanation:

The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle? 5, 10, or 25?

Answers

You know the hypotenuse of a right triangle with sides 3 and 4 has length 5, so the radius of this circle will be 5. The diameter is twice that.

The diameter of the circle is 10.

Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest. Let’s help him out. Matt has already jotted down the formula he needs to use: I = P × r × t First, help him substitute the correct values in this formula. Write down the appropriate numbers for principal, rate of interest, and time

Answers

From Matt's formula:
I=P×r×t
P=principle amount (amount invested)
r=rate
t=time
From the information given:
P=$550
r=0.03
t=1
therefore
I=550*0.03*1
I=$16.5

Answer:I = 550 × 0.03 × 1

Step-by-step explanation: from plato

What is the sum of 4.2 × 105 and 5.3 × 10^5?

A.)95 × 10^5

B.)95 × 10^10

C.)9.5 × 10^5

D.)9.5 × 10^10

Answers

(4.2*105)+(5.3*10^5)
441 + 530000
530441

-----------

If your problem is (4.2*10^5)+(5.3*10^5), it would be
420000 + 530000
950000

Answer:

Option C.

Step-by-step explanation:

The two expressions are [tex]4.2\times 10^{5}[/tex] and [tex]5.3\times 10^{5}[/tex]

We have to find the total of these two terms.

[tex](4.2\times 10^{5}[/tex] + [tex]5.3\times 10^{5})[/tex]

Now we take out [tex]10^{5}[/tex] as a common term.

[tex]10^{5}(4.2+5.3)[/tex]

= [tex]9.5\times 10^{5}[/tex]

Therefore, Option C. will be the answer.

What is the y-intercept of the line that has a slope of -1/2 and passes through the point (2, 3)?

Answers

y - 3 = -1/2(x - 2)
y - 3 = -1/2(x) + 1
y = -1/2(x) + 4

y intercept is 4

answer
y intercept (0,4)

a coin is tossed twice what is the probability of the coin landing heads up both times

Answers

You have 2 choices on each toss. The total number of ways you can get a result is 2*2
The successful result is 1/2 * 1/2 = 1/4.
You can make a table to show this.

H H
T H
H T
T T

1/4 ways gives 2 heads. <<<< answer

Experts/ace/geniuses

Answers

An irrational number for a radical is one that will not have a perfect answer like [tex] \sqrt{49} [/tex] or [tex] \sqrt{16} [/tex] that means the only one is [tex] \sqrt{84} [/tex]

G let z be a random variable with a standard normal distribution. find the indicated probability. p(z ≤ −0.27)

Answers

The probability P(Z <= -0.27) in a standard normal distribution is determined by finding the corresponding right-tail probability of Z = 0.27 and subtracting it from 1, reflecting the distribution's symmetry.

To find the probability P(Z \<= -0.27), we use the properties of the standard normal distribution, which is symmetric about zero. The probability of Z scoring below -0.27 is equal to the probability of Z scoring above 0.27 due to this symmetry. Looking up the corresponding value for Z = 0.27 in a standard normal table, or using a calculator, we would find the right-tail probability. To get our desired left-tail probability for Z = -0.27, we subtract this from 1. For example, if the right-tail probability for Z = 0.27 was 0.3936, then P(Z \<= -0.27) would be 1 - 0.3936 = 0.6064.

Other Questions

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