Someone invested some money at 8% and $300 more than
twice this amount at 12%. Her total annual income from
the two investments is $548. How much is invested at
each rate?
32

Answers

Answer 1

Answer:

$1600 at 8% and 3500 at 12%

Step-by-step explanation:

The rule of the interest is I = PRT, where

P is the amount of investment R is the rate in decimalT is the time

Assume that the amount of money is $x

P = x

∵ The rate is 8%

R = 8/100 = 0.08

∵ She has an annual income

T = 1

→ Substitute them in the rule to find the interest amount

∴ I = x × 0.08 × 1

I = 0.08x

∵ She invested $300 more than twice the previous amount

P = 2x + 300

∵ The rate is 12%

R = 12/100 = 0.12

T = 1

→ Substitute them in the rule to find the other interest amount

∴ I = (2x + 300) × 0.12 × 1

I = 0.24x + 36

∵ Her total annual income from both investments is $548

→ Add the two amount of interest and equate their sum by 548

0.08x + 0.24x + 36 = 548

→ Add the like terms in the left side

∴ 0.32x + 36 = 548

→ Subtract 36 from both sides

∴ 0.32x + 36 - 36 = 548 - 36

∴ 0.32x = 512

→ Divide both sides by 0.32

x = 1600

She invested $1600 at 8%

→ Substitute x by 1600 in the expression of the other amount to find it

∵ 2x + 300 = 2(1600) + 300 = 3500

She invested $3500 at 12%


Related Questions

Express each number as a single-digit integer times a power of 10.
24,755,183,009,522

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2 to the 12th power should be correct

1 3/4= x/32 solve for x

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Answer:

x = 56

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Hope this helps :)

Answer:

It is 56 if you were to solve for X . It's none of the answers on the screen.

Step-by-step explanation:

Can anybody help? I don't get what this question means

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Answer: B is the only true statement.

Step-by-step explanation:

evaluate -4 1/3 + 5 2/3 show work

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Your answer will be -4/3. I showed you how I got it. Message me if you still don’t get it. Hope this helps!

sidawidnianddinhwidnaindianwdawdawd

Answers

Answer:

yes

Step-by-step explanation:

yes

I need help in this one

Answers

Answer:

7/2pi

Step-by-step explanation:

Circumference is

[tex]2r\pi \\ 2 \times 7\pi \\ 14\pi \\ \frac{1}{4} \times 14\pi \\ \frac{7}{2} \pi[/tex]

Help please. I will give brainliest.

Answers

Answer:

if you answer my most recent question ill answer this one.

Step-by-step explanation:

The price of Stock A at 9 A.M. Was ​$15.59 Since​ then, the price has been increasing at the rate of ​$0.12 each hour. At noon the price of Stock B was ​$16.34 It begins to decrease at the rate of ​$0.11 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Answer:

Prices of the two stocks A and B become​ same in 42 hours

Step-by-step explanation:

Let t denotes number of hours in which the prices of the two stocks A and B become​ same.

Price of stock A = $15.59

Increase in price per hour = $0.12 t

Price of stock B = $16.34

Decrease in price per hour = $0.11 (t - 3)

(since price of stock A starts increasing per hour after 9 A.M. and price of stock B starts decreasing per hour after 12 noon that is 3 hours after 9 A.M.)

To find number of hours in which the prices of the two stocks A and B become​ same, solve [tex]15.59+0.12t=16.34+0.11(t-3)[/tex]

[tex]15.59+0.12t=16.34+0.11(t-3)\\15.59+0.12t=16.34+0.11t-0.33\\0.12t-0.11t=16.34-0.33-15.59\\0.01t=0.42\\t=42[/tex]

So, prices of the two stocks A and B become​ same in 42 hours

Solve This Equation
x/3 - 7(x-2)/9 = 4 - 2x-5/6

Answers

exact form: 42/55
decimal form: 0.763 (a line is above 63)

the graph of g(x) is the graph of f(x)=|x| translated 6 units to the right write the equation of g(x)

Answers

Answer:

f(x)=|x-6|

Step-by-step explanation:

Translation is a shift. Opposite how many units it moved. In with the x because that's side to side. If it was not with the x, it's up and down.

The transformation of a function may involve any change. The equation of g(x) is |x-6|.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + dDown by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)

Given that the function f(x)=|x|, this function is needed to be translated 6 units to the right. Therefore, the new function can be written as,

g(x) = f(x-6)

      = |x - 6|

Hence, the equation of g(x) is |x-6|.

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select the construction that guaranties A is a reflection of point A across line BC

Answers

Answer:

I think it's Axial Symmetry.

Step-by-step explanation:

You draw a perpendicular line to the line BC through A.You get your compass and set it to the distance between the point A and the line BC. Using that distance on your compass, put the point of your compass on the point where the perpendicular line and BC intersect. Mark the distance on the perpendicular line. The reflection is the point you mark on the perpendicular line.

Y + 2x = 5 I have to solve for Y please

Answers

Answer:

Y=5-2X

Step-by-step explanation:

Answer:

IF YOU HAVE TO SOLVE FOR Y THEN TAKE X AS ANY NUMBER YOU WANT.

SUPPOSE X=2

PUT THE VALUE IN THE EQUATION THEN U WILL GET-

Y+2(2)=5

= Y+4=5

= Y=5-4

= Y=1

THIS IS JUST ONE EXAMPLE BUT THERE CAN BE INFINITIVE NUMBER OF ANSWERS FOR THIS QUESTION.

I WILL SHOW U ONE MORE EXAMPLE.

IF X=1

THEN THE EQUATION WILL BE-

Y+2(1)=5

Y+2=5

Y=5-2

Y=3

SO HERE WE GOT Y=1&3

AND ALSO Y CAN HAVE INFINITE SOLUTIONS (THIS IS ON THE BASIS OF THE PROPERTY OF LINEAR EQUATION, I.E., A LINEAR EQUATION CAN HAVE INFINITIVE SOLUTIONS)

8 m
5 m
22 m
8 m
5 m
12 m
What is the volume of the figure? Enter the answer in the box.
cubic meters

Answers

Answer:

1,280 cubic meters

Step-by-step explanation:

Length x Width x Height = Volume

The box on the left:

8m x 5m x 22m = 800[tex]m^{3}[/tex]

Box on the right:

12m x 5m x 8m = 480[tex]m^{3}[/tex]

Add them:

800[tex]m^{3}[/tex] + 480[tex]m^{3}[/tex] = 1,280[tex]m^{3}[/tex]

The volume of the figure is 1,280 cubic meters

Four time the sum of twice a number and six is thirty-two. Find the number

Answers

Answer:

4(2x+6)=32  x= 1

Step-by-step explanation:

multiply 4 to 2x and 6=   (8x+24)=32

then subtract 24 from 32 = 8

then divide 8 from both sides

8x/8=8/8

x=1

An equation is formed of two equal expressions. The unknown number is 1.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

The given statement can be written in the form of an equation as shown below.

Twice of a number → 2xSum of twice a number and six → 2x + 6Four-time the sum of twice a number and six → 4(2x + 6)Four-time the sum of twice a number and six is thirty-two

         → 4(2x + 6) = 32

The given equation can be solved as shown below.

4(2x + 6) = 32

Open the parenthesis by multiplying 4 inside the parenthesis,

8x + 24 = 32

Subtract 24 on both sides of the equation,

8x + 24 - 24 = 32 - 24

8x = 8

Divide both sides of the equation by 8,

8x/ 8 = 8/8

x = 1

Hence, the unknown number is 1.

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How many solutions does the following equation have?
23y+50+27y=50y+50

Answers

The answer is all solutions

What is an equation of the line that passes through the point
(-6, – 7) and is perpendicular to the line 6x + 5y = 30?
HELP!!!

Answers

Answer:

(y+7)=5/6(x+6)

Step-by-step explanation:

For this problem we need to use Point-Slope Form to write an equation.

We already have the point, (-6,-7), so all we need now is the slope, which we know is perpendicular to the line 6x+5y=30.

First, let's find the slope of 6x+5y=30 by converting it into Slope-Intercept Form, which is y=mx+b. m is the slope.

6x+5y=30

5y=-6x+30

y=-6/5x+6

So the slope of this line is -6/5, but we need the slope of the line is perpendicular to this line.

When a line is perpendicular to another, their slopes are negative reciprocals to one another, or opposite reciprocals. For example, a line that is perpendicular to another line that has a slope of 3/4 will have a slope of -4/3. Flip the numerator and denominator to find the reciprocal and add a negative.

x

So the negative reciprocal of -6/5 is 5/6, so that is our slope.

Now we can assemble our equation, here is the Point-Slope Form:

[tex](y -y_{1}) =m(x-x_{1})[/tex]

again, m is our slope.

[tex]y_{1}[/tex] and [tex]x_{1}[/tex] represent the coordinates of the point that this line passes through, (-6, -7).

Let's plug in the y, x, and m values:

(y-(-7))=5/6(x-(-6))

Simplify:

(y+7)=5/6(x+6)

That is our final answer.

b(x) lx+4l
b(-10)

The l on the sides of x+4 arent supposed to be numbers

Answers

Answer:

6

Step-by-step explanation:

i believe it is 6 if the l on the side are for absoulte value, then your answer would be 6

l-10+4l =6

Find the acute angle between the lines whose slopes are 2 & 1\3.​

Answers

Answer:30 degrees

Step-by-step explanation:There are a couple of ways to do this.

This is the straightforward, “follow-your-nose” way. Find a point on each line. (Say, (1,2) on the line with slope 2 and (-1,1) on the line with slope -1. Then the angle in the triangle formed by the origin (0,0) and these other two point is the desired angle. One can find the cosine of angle in the triangle using the Law of Cosines, since the lengths of all of the sides can be found directly from the distance formula and the coordinates of the points. Finally, use arccosine to get from the cosine of the angle to the angle itself.

There is also a “slick” way, which relies on remembering the subtraction formula for tangents. tan(u-v) = [tan(u) - tan(v)] / [tan(u) + tan(v)]. Consider u as the angle between the positive x-axis and the line with slope -1, and v as the angle between the positive x-axis and the line with slope 2. Then the requested angle is u-v. We know tan(u) = -1 and tan(v) = 2, so substituting into the subtraction formula for tangents allows us to find tan(u-v). Finally, use arctangent of that value to find u-v.

Whole numbers greater than zero are

Answers

Answer:

Natural numbers, because they consist of 1, 2, 3, etc...

Answer:

integers

Step-by-step explanation:

integers is what it is called

The midpoint of AB is M(7,-5). If the coordinates of A are (6, - 7), what are the
coordinates of B?

Answers

Answer:(8,-3)

Step-by-step explanation:

X2=8 Y2=-3

If 12 lb of potatoes cost $17.00, how much would 18 lb of potatoes cost?

Answers

Answer:

25.5

Step-by-step explanation:

Answer:

The answer is $25.50 for 18 pounds of potatoes.

Hope this helps.

Please mark me as Brainliest if i am correct.

Tell me two(2) things you know about the pink line?

Answers

Answer:

it's pink in colour

it's a line

it is a linear line and it has a negative value as the line is decreasing from left to right.

An alien blob started with a mass of 12 kg and is doubling in size every day. How large will the blob be after 2 weeks? y=a(b)^x

Answers

Answer:

208

Step-by-step explanation:

hurry !!! i’m so confused!

find f(4)

Answers

Answer:

2 multiplyed  + 3.

1. Point M is on PQ, PM has a length of 7 units, and point N is the midpoint of MQ. If the length of NQ
is 4 units, how long is PQ?
PA
A 3 units
B. 11 units
C. 15 units
D. 18 units

Answers

Answer:

C. 15 units

Step-by-step explanation:

PM = 7 units

p..............M..........N............Q

   7 unit                     4 unit

NQ = 4 units

Given that

N is midpoint of MQ

it means N divides MQ into two equal parts

thus

MN = NQ = 4 units

now

we have to find length of PQ

p..............M..........N............Q

   7 unit     4 units     4 unit

PQ = PM + MN + NQ

PQ = 7 units + 4 units + 4 units = 15 units

thus, correct answer is option c 15 units

Answer:

15 units

Step-by-step explanation:

Solve for n. 3(n+5)≥3n+8

Answers

Answer:

True for all N

Step-by-step explanation:

Answer:

True for all N :)

Step-by-step explanation:

Find the value of x in each diagram.

Answers

Answer:

6) 4 , 7) 35

Step-by-step explanation:

Answer:

x = 8 and x = 7

Step-by-step explanation:

(6)

Since the triangles are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{ST}{MN}[/tex] = [tex]\frac{RS}{LM}[/tex] , substitute values

[tex]\frac{x}{4}[/tex] = [tex]\frac{4}{2}[/tex] ( cross- multiply )

2x = 16 ( divide both sides by 2 )

x = 8

(7)

Since the prisms are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{x}{35}[/tex] = [tex]\frac{2}{10}[/tex] ( cross- multiply )

10x = 70 ( divide both sides by 10 )

x = 7

Can someone help me with this please?

Answers

Answer:

X = 20 degrees

Step-by-step explanation:

so we know that a triangle equals 180 degrees.

We already have 70 degrees so there are 110 degrees left.

Y is a right angle making it a 90 degree angle

110-90 equals 20 making x a 20 degree angle.

Which number is a multiple of 9?
A:109
B:3
C:27
D:89

Answers

Answer:C

Step-by-step explanation:

9 x 3 = 27

the correct answer is c 9 times 3 equals 27

Jordan gave out a survey to some students in his school about their favorite color. Students could choose between purple and blue. 96 of those surveyed said their favorite color was purple. 76% of the students surveyed said their favorite color was blue. How many students were surveyed in total?​

Answers

Answer:

169

Step-by-step explanation:

i hope this helps

Answer:

398

Step-by-step explanation:

100%-76%= 24% which should be the 96 percent that chose purple

94÷24%= 3.91(4 because it's rounded) students per percentage

4×76%=304 that chose blue if rounded

94+304=398 total

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