Questions posted in Mathematics

She invested "a" at 5% and "b" at 6%.

now, we know whatever amounts "a" and "b" are, they add up to 8000, thus a + b = 8000.

how much is 5% of a? well, (5/100) * a, or 0.05a.
how much is 6% of b? well, (6/100) * b, or 0.06b.

After a year, their combined interest, their yield, was 455, thus, we also know that 0.05a + 0.06b = 455.



how much was invested at 6%?  well, b = 8000 - a.

So I used a percent proportion to solve this question. On the left I have 65 over 100 since that is equivalent to 65%. I put that equal to x, our unknown, over 45. 45 goes on the bottom because 45 is the "whole". We are trying to find a part of that 45. An easy way to identify this is the is, of rule. If the question asks "40 is 40% of what number?" Then you are trying to identify the whole. You can identify that by noticing that the unknown comes after the word of. In your case, the unknown comes before is, showing us that we need to find the part. The part goes on the top and the whole goes in the bottom(refer to picture above). This method doesn't always work in word problems, however, because it may be worded in a tricky way. Anyways, after everything is set up, you multiply across as shown by the arrows. So 65•45 and 100•x resulting in my second step. You have 100x=2925. This has now become a one step equation. You simply need to isolate the variable, so divide both sides by 100 to get an answer of x=29.25. Hope this helped!!!

-Liananna

This means the tallest man was 204 cm taller than the shortest. You add 204 to 68.

68 + 204 = 272

The tallest man was 272 cm tall.

Good question


Let his hourly rate is x

then:

31x + (35-31)*1.3x = 448.88

solve for x:

31 x + 5.2x = 448.88

36.2 x =448.88

x = 12.4$

not fair hourly rate by the way ;)

For the revenue to be greater than the cost, that means that 0.07b > 200+0.03b   Subtract 0.03b from both sides to get 0.04b > 200, and remake that into b/25 >200. Multiply by 25 on both sides to get b >5000

Since x is our unknown number, on one side of our equation we will have the "Subtracting two times a number from 10", and on the other will be -3. So,
-3=10-2x

The answer is x=90, y=43. For any and all triangles, their angles must add up to 189 degrees. Since we know that C's degree is 47, we just have to then look at our choices and see which would equal 180. Also x is clearly a 90 degree angle because it is a right angle. That's one way to narrow down the choices quick.

2x - 8 = 10. 
Twice a number is 2x.
8 less than that number is minus 8.
Is ten is =10.                  

In a triangle the midline joining the midpoints of two sides is parallel to the third side and half as long ⇒

AE = BD*2 = 10*2 = 20
also AE = 2x (given) ⇒
2x = 20
x = 20/2
x = 10

CD = 3x = 3*10 = 30

BD is the midsegment of ΔACE ⇒ ΔBCD ∼ ΔACE therefore:



Answer: 60

According to PEMDAS you have to work inside each set of parenthesis first, then exponents, then multiply so
(12-9)^3 simplified is 3^3 which = 9
now onto
[8^2/(1+7)]
1+7=8
8^2=64
now you have left

9 x (64/8)

64 divided by 8 is 8 so now you just have
9 x 8
which is 72
soooo the answer is 72

X2+3 = 5x if you mean simplify by estimate

Answer:

A. ,

Step-by-step explanation:

We have been given an image and we are asked to find the values of x and y that will make our given triangles congruent by HL.

Hypotenuse-leg theorem states that if any leg and hypotenuse of one triangle is equal to leg and hypotenuse of another triangle, then both triangles are congruent.

We can see that hypotenuse and one leg of triangle ABC are AC and BC respectively. The hypotenuse and one leg of triangle AED are AD and ED respectively.

To make these our triangles congruent by HL theorem, we can set two equations as:

Substituting equation (2) in equation (1) we will get,

Therefore, the value of y is 6.

Upon substituting in equation (2) we will get,

Therefore, the value of x is 5.

Upon looking at our given choices we can see that option A is the correct choice.

A represents 1/9 and B represent 8/9

Answer: HL Theorem

Step-by-step explanation:

In the given picture, there are two right triangles .

Here one side of both triangles are equal.

Also they both have one side as common.

So they are congruent by HL Theorem.

• HL theorem or hypotenuse leg theorem tells that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

7.75 x 10⁻¹

Note that 10⁻¹ = 1/10 = 0.1

7.75 x 0.1 = 0.775

The equation will be written as $236=$16x+$124, where $236 is what she wants to save, $124 is what she already saved, and x is the number of weeks where she adds $16. 

So,
$236=$16x+$124
$236-$124=$16x
$112=$16x
$112/$16=x
x=7

She needs exactly 7 weeks to be able to have enough money to get her bike.

0.9×1/10
0.9/10 =0.09
when a number has a 0 power then u have to flip over the number and change the power to positive

Sum and difference problem.

Larger number  = (sum+difference)/2=(96+50)/2=73
Smaller number= (sum-difference)/2=(96-50)/2=23

I find it easier to write it instead of typing so look at the picture above

Answer:

Coordinates of point Q =

Step-by-step explanation:

Given points are M(-3,-4) and T(5,0). Point Q divides the line segment  in m:n that is 2:3. Now, we have to find the coordinates of point Q.

The coordinates of point Q is

         

 m=2, n=3

⇒m+n=2+3=5

= 2(5)+3(-3) = 1

= 2(0)+3(-4) = -12

Therefore, coordinates of point Q =

For the big block cubes, with 6 sides, one hundred squares on each side, it's 600 for each big block cube. 600 x 3 = 1800. The two sticks equals 20 because there is 10 on each. And there are 7 cubes. Add together.
1,800 + 20 + 7 = 1,827

Answer: 600 + 600 + 600 + 10 + 10 + 7 = 1,827
I hope this helps :)

Let's see together

The perimeter is the sum of all sides' length of a shape

so for the rectangle:
x+ x+4 + x + x+4 = 4x + 8

and for the square:
4(x+2) = 4x + 8

So they have the same perimeter

So the student was correct

Hi, Globabypatricia! :)

All the time worked past 31 hours gets paid 1.3 times.
He worked 4 hours at such a rate.

31+4(1.3)
31+5.2
=36.2
Paid as if he worked 36.2 at a normal rate. 

To find his normal wage, divide 448.88 by 36.2
448.88/36.2
=12.40

His normal wage is $12.40.

To check:
12.40*31=384.40
12.40*1.3=16.12
16.12*4=64.48

384.40+64.48
=$448.88

Hope this helps.
-Benjamin

No because the perimeter of a rectangle is L×W or (2L+2W) , but the perimeter of a square is S×S×S×S so there is a difference between the two.

E=240T

For the lower limit of energy:
E=12,000 cal

so 12000 = 240 T            >>>      T = 50 degrees Celsius

For the upper limit of energy:
E=18,000 cal

so 18000 = 240 T            >>>      T = 75 degrees Celsius

The difference in temperature = 75 - 50 = 25 degrees Celsius

I hope I helped you.

Yes, it is possible!
Look at this picture!
 Due to copyright issues, i have to say! I don't own this picture, all credit goes to it's owners. 
Source:https://google.com

The Table image link: http://bestpickr.com/wp-content/uploads/3485-750x750.jpg

Plz don't ban me, as I have noted, I don't own this, I'm just providing an example.

His current age now = x

and after 10 years, it will be triple of now >>    x+10 = 3x

solve for x


x+10 = 3x
x-x+10 = 3x-x
10 = 2x
5=x

so he is 5 years old now

The answer to this question would be A. 4.5