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4 years ago

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The sum of three numbers is 75. The first number is 5 more than the second. The third number is 2 times the first. What are the

numbers?

1 answer:

Dahasolnce [82]4 years ago

5 0

Answer: The numbers are: 16, 11 and 48

Step-by-step explanation:

Let 1st number is a, second number is b and third number is c

1st number is 5 more than the second so a=b+5

The third number is 2 times the first so c=3*a=3*(b+5)

The sum of three numbers, so a+b+c=b+5+b+3*(b+5)=75

b+5+b+3+3b+15=75

5b+20=75

5b=55

b=11

a=b+5=11+5=16

c=3*(b+5)=3*(11+5)=3*16=48

The numbers are: 16, 11 and 48

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Drag each tile to the correct box. Arrange the angles in increasing order of their cosines.

inna [77]

Answer:

$\frac{3\pi}{4}$

Step-by-step explanation:

we are given different angles

we can see that each angles have different denominators

so, firstly we will find common denominators

denominators are 1 , 2,3,4,6

so, LCD will be 12

now, we will make denominator of all terms 12

$\frac{3\pi}{4} =\frac{3\pi\times 3}{4\times 3}=\frac{9\pi}{12}$

$\pi =\frac{\pi\times 12}{1\times 12}=\frac{12\pi}{12}$

$\frac{7\pi}{6} =\frac{7\pi\times 2}{6\times 2}=\frac{14\pi}{12}$

$\frac{5\pi}{3} =\frac{5\pi\times 4}{3\times 4}=\frac{20\pi}{12}$

$\frac{7\pi}{4} =\frac{7\pi\times 3}{4\times 3}=\frac{21\pi}{12}$

$\frac{4\pi}{3} =\frac{4\pi\times 4}{3\times 4}=\frac{16\pi}{12}$

$\frac{3\pi}{2} =\frac{3\pi\times 6}{2\times 6}=\frac{18\pi}{12}$

$2\pi =\frac{2\pi\times 12}{1\times 12}=\frac{24\pi}{12}$

we can see that denominators are same

so, we can arrange it according to numerators as

$\frac{9\pi}{12}$

we can replace values

and we get order as

$\frac{3\pi}{4}$

8 0

3 years ago

Read 2 more answers

I need the answer ASAP! Please help me!

masha68 [24]

Answer:

Please check the explanation.

Step-by-step explanation:

<u>Determining the length of BC</u>

From the diagram, it is clear that

The point B is located at (-8, 10) and point C is located at (8, 10)

Since points A and C are located on a horizontal straight line. Thus, the length of BC can be determined by counting the x-axis units from reaching x = -8 to x = 8. i.e. 8-(-8) = 8+8 = 16

Thus, the length of BC = 16 units

<u>Determining the length of CD</u>

Given

C (8, 10)

D (2, -2)

The distance between C(8, 10) and D(2, -2)

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}$

$=\sqrt{6^2+12^2}$

$=\sqrt{36+144}$

$=\sqrt{180}$

$=\sqrt{36\times 5}$

$=6\sqrt{5}$

Thus, the length of CD $=6\sqrt{5}$ units

<u>Determining the length of ED</u>

Given

E (-8, -4)

D (2, -2)

The distance between E(-8, -4) and D(2, -2)

$ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}$

$=\sqrt{10^2+2^2}$

$=\sqrt{100+4}$

$=\sqrt{104}$

$=\sqrt{26\times \:4}$

$=2\sqrt{26}$

Thus, the length of ED $=2\sqrt{26}$ units

<u>Determining the length of EB</u>

From the diagram, it is clear that

The point E is located at (-8, -4) and the point B is located at (-8, 10)

Since points E and B are located on a vertical straight line. Thus, the length of EB can be determined by counting the y-axis units from reaching y = -4 to y = 10. i.e. 10-(-4) = 10+4 = 14

Thus, the length of EB = 14 units

4 0

3 years ago

ONLY SERIOUS ANSWERS!!!! 25 POINTS

AveGali [126]

Answer:

FD≈25.94.. rounded = 26

Step-by-step explanation:

FD²=12²+(4x+11)²

FD²=144+16x²+88x+121

FD²=265+16x²+88x

also

FD²=12²+(13x-16)²

FD²=144+169x²-416x+256

FD²=400+169x²-416x

thus

265+16x²+88x = 400+169x²-416x

16x²-169x²+88x+416x+265-400 = 0

-153x²+504x-135 = 0

we will solve this quadratic equation by suing the quadratic formula to find x

x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)

x=(-504± $\sqrt{504^{2}-4(-153)(-135) }$ )/2(-153)

x=(-504± $\sqrt{254016-82620 }$ )/-306

x=(-504± $\sqrt{171396}$ )/-306

x=(-504±414)/-306

x=(-504+414)/-306 and x=(-504-414)/-306

x=-90/-306 and x=-918/-306

x= 5/17 , 3

substituting x by the roots we found

check for 5/17:

4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..

13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..

check for 3:

4x+11 = 4×3+11 = 12+11 = 23

13x-16 = 13×3-16 = 23

thus 3 is the right root

therfore

ED=23 and CD=23

FD²=FE²+ED² or FD²=FC²+CD²

FD²=12²+23²

FD²=144+529

FD²=673

FD=√673

FD≈25.94.. rounded = 26

5 0

3 years ago

Read 2 more answers

What is the value of b?

STatiana [176]

Answer:

Step-by-step explanation:

By the polygon exterior angle sum theorem, all the exterior angles of a polygon add up to equal 360 regardless of the number of sides it has. That means that 82 + 150 + b = 360 so

b + 232 = 360 and

b = 128

6 0

3 years ago

The answer step by step

vivado [14]

Remember:

-When multiplying numbers with decimals just forget about the decimals for a second and pretend you are multiplying a 3 digit number times a 2 digit number.

-one digit at a time. Multiply going from right to left.

First:

-Multiply the 3 with the top numbers.

-Pretend you are seeing this:

5.72 (3)

- 2*3=6. 7*3=21. (carry the 2). 5*3 +2=17. (leave the 1).

Second:

-write below and move a digit to the left.

-pretend you are seeing this: 5.72(6).

- 2*6 =12. (carry the 1). 7*6 +1=43. (carry the 4) 5*6+4=34. (leave the 3).

Third: since in the problem the decimal is placed in the hundredths only once, place the decimal in the hundredths as your solution.

Your solution should be 360.36

7 0

4 years ago