Questions posted in Mathematics

Katie invested a total of ​$8000​, part at 5% simple interest and part at 6% simple interest. At the end of 1​ year, the investments had earned ​$455 interest. How much was invested at each​ rate?

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.

\bf \begin{cases}
a+b=8000\implies \boxed{b}=8000-a\\
0.05a+0.06b=455\\
----------\\
0.05a+0.06\left( \boxed{8000-a} \right)=455
\end{cases}
\\\\\\
0.05a-0.06a+480=455\implies -0.01a=-25\implies a=\cfrac{-25}{-0.01}
\\\\\\
\boxed{a=2500}

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

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

What is 65% of 45 Do not round the answer???

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

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

The height of the shortest man in history was 68 cm. This is 204 less than the height of the tallest man. how tall was the tallest man?

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.

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?

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 ;)

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

I need help with this problem

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

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

Write an equation. Let x be the unknown number. Subtracting two times a number from 10 is -3.

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

ANSWERED AT 22/11/2019 - 02:46 PM


QUESTION POSTED AT 22/11/2019 - 02:46 PM

Can someone help me with this!!ASAP and can you show me how you got the answer

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.

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Write an equation. Let x be the unknown number. Eight less than twice a number is 10.

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Can someone please help me with this!!!!

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:

 \frac{BD}{CD}= \frac{AE}{CE} \ \ \ \to \ \ \  CE= \frac{CD*AE}{BD}= \frac{30*20}{10}=60

Answer: 60

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Need help with this problem

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

When I solve for variables but there is no answer how do I solve/estimate?

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Find the values of x and y that make these triangles congruent by HL. I need help please

Answer:

A. x=5,y=6

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:

3x-2=2y+1...(1)

x=y-1...(2)

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

3(y-1)-2=2y+1

3y-3-2=2y+1

3y-5=2y+1

3y-2y-5+5=2y-2y+5+1

y=6

Therefore, the value of y is 6.

Upon substituting y=6 in equation (2) we will get,

x=6-1

x=5

Therefore, the value of x is 5.

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Need help with this problem

A represents 1/9 and B represent 8/9

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Name the postulate or theorem you can use to prove the triangles congruent. ASA Postulate AAS Theorem HL Theorem SAS Postulate

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.

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

What is 7.75×10-1 in standard notation

7.75 x 10⁻¹

Note that 10⁻¹ = 1/10 = 0.1

7.75 x 0.1 = 0.775

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Jennifer is saving money to buy a bike. The bike costs $236. She has $124 saved, and each week she adds $16 to her savings. How long will it take her to save enough money to buy the bike ?

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.

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

0.9×10-1 in Standard notation

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

The sum of two numbers is 96 the difference is 50, what are the two numbers

Sum and difference problem.

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


ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Square root of 4 plus 45 over 4 plus 125 over 25

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

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Given the points M(-3,-4) and T(5,0).Find the coordinates of the point Q on directed line segment MT that partitions MT in the ratio 2:3

Answer:

Coordinates of point Q = (\frac{1}{5},\frac{-12}{5} )

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

         (\frac{(mx_{2}+nx_{1})}{m+n},\frac{(my_{2}+ny_{1})}{m+n})

 m=2, n=3

⇒m+n=2+3=5

mx_{2} + nx_{1} = 2(5)+3(-3) = 1

my_{2} + ny_{1} = 2(0)+3(-4) = -12

Therefore, coordinates of point Q = (\frac{1}{5},\frac{-12}{5} )


ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

What does it mean and how to do it

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 :)

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Can't figure it out!!

\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)= \cfrac{1}{x}  \qquad 
\begin{cases}
x_1=2\\
x_2=b
\end{cases}\implies \cfrac{f(b)-f(2)}{b-2}=-\cfrac{1}{10}
\\\\\\
\cfrac{\frac{1}{b}-\frac{1}{2}}{b-2}=-\cfrac{1}{10}\implies 
\cfrac{\frac{2-b}{2b}}{b-2}=-\cfrac{1}{10}\implies \cfrac{2-b}{2b}=-\cfrac{b-2}{10}
\\\\\\


\bf \cfrac{2-b}{2b}=\cfrac{2-b}{10}\implies 20-10b=4b-2b^2\impliedby cross-multiplying
\\\\\\
2b^2-4b-10b+20=0\implies 2b^2-14b+20=0
\\\\\\
b^2-7b+10=0\implies 
(b-2)(b-5)=0\implies b=
\begin{cases}
\boxed{5}\\
2
\end{cases}

ANSWERED AT 22/11/2019 - 02:45 PM


QUESTION POSTED AT 22/11/2019 - 02:45 PM

Can someone help me for 25? Thx

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


ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?

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

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

A student is given the rectangle and the square shown below the student states that the two figures have the same perimeter is the student correct explain reasoning

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.

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

The amount of energy, E, required to raise the temperature, T, of a container of water is E=240T, where E is measured in calories and T is the change in Temperature in degrees Celsius. A fuel source will provide between 12,000 and 18,000 calories of heat. What is the expected change in temperature of the container of water if the entire fuel source is used to heat the water?

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.



ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

Is it possible to design a table where no two legs have the same length? Assume that the endpoints of the legs must all lie in the same plane. Include a diagram as part of your answer.

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.

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

In 10 years mike will be 3. Times his current age. What is his current age

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

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

Select the best answer for the question. .45÷10? A. 4.5. B. .45. C. 45. D. .045

The answer to this question would be A. 4.5

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM

Are the functions f(x) = (x^2-1)/(x-1) and g(x)= x+1 equal for all x?

\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\

\bf f(x)=\cfrac{x^2-1}{x-1}\implies f(x)=\cfrac{x^2-1^2}{x-1}\implies f(x)=\cfrac{(\underline{x-1})(x+1)}{\underline{x-1}}
\\\\\\
f(x)=x+1\qquad \qquad \qquad  \qquad  \qquad  g(x)=x+1\\\\
-------------------------------\\\\
\textit{they're, kinda, except that, when x = 1}
\\\\\\
g(x)=(1)+1\implies g(x)=2
\\\\\\
f(x)=\cfrac{(1)^2-1}{(1)-1}\implies f(x)=\cfrac{0}{0}\impliedby und efined

ANSWERED AT 22/11/2019 - 02:44 PM


QUESTION POSTED AT 22/11/2019 - 02:44 PM