### 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?

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.

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???

-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?

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 ?

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

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.

-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

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.

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!!!!

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**

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

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

### Need help with this problem

(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?

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.** ,

**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.**

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

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

### Need help with this problem

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

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 ?

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

0.9/10 =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

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

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** =

**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** =

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

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 someone help me for 25? Thx

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 ?

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

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?

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.

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

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

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?

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

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