read above please :D

The length of DE in centimetres is 12 .

The following proportion can be established as follow:

AB / DE = BC  / EF = AC / DF

Therefore,

let's find DE as follows;

AB  / DE = BC / EF

4 / DE = 3 / 9

cross multiply

9 × 4 = 3DE

divide both sides by 3

DE = 36 / 3

DE = 12 cm

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Answer:

  c.  3a^2b^11/2

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

__

 [tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]

Answer:

m = 3a

Step-by-step explanation:

The number of pieces of candy eaten by Alex is not important.

The only thing that matters is that Marisol eats 3 times as many pieces of candy.

If a is the number eaten by Andy, then 3 times a equals the number of pieces of candy eaten by Marisol, or m=3a

Answers:

a) See the table below

b) The equation is [tex]y = 32000(1.01125)^x[/tex]

c) $40,024.02

d) See the graph below

=========================================================

Explanations:

a)

Start with part (b) where I detail how to get the equation.

Once the equation is found, plug in x = 0 to get

[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^0\\\\y = 32000\\\\[/tex]

Repeat for x = 1

[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^1\\\\y = 32360\\\\[/tex]

Repeat for x = 2, x = 3, x = 4 and x = 20 to get the table shown below.

-----------------------

b)

The template for any exponential equation is [tex]y = a(b)^x[/tex]

a = starting amount = 32000

b = growth factor

The annual interest rate is 4.5%

We compound quarterly, so the quarterly rate is (4.5%)/4 = 1.125% which converts to the decimal form 0.01125; adding one to this leads to the growth factor of b = 1.01125

We go from [tex]y = a(b)^x[/tex] to [tex]y = 32000(1.01125)^x[/tex]

-----------------------

c)

Plug in x = 20 to represent 20 quarters have elapsed (aka 20/4 = 5 years)

[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^{20}\\\\y \approx 32000(1.25075052084381)\\\\y \approx 40024.016667002\\\\y \approx 40024.02\\\\[/tex]

The investment would be worth $40,024.02 after five years, aka twenty quarters.

-----------------------

d)

See below for the graph. I'm using GeoGebra to make the graph. Another option is Desmos. It's preferable to use technology than to graph by hand. If you wanted to graph by hand, then you'd plot each of the points found in the table. Then draw a curve through all those points.

Answer:

Compound interest formula

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

[tex]\implies y=32000(1+\frac{0.045}{4})^{4 \times 0.25x}[/tex]

[tex]\implies y=32000(1.01125)^x[/tex]

[tex]\begin{tabular}{|c | c |}\cline{1-2} \bf Quarterly & \bf \$ \\\cline{1-2} 0 & 32000.00\\\cline{1-2} 1 & 32360.00\\\cline{1-2} 2 & 32724.05\\\cline{1-2} 3 & 33092.20\\\cline{1-2} 4 & 33464.48\\\cline{1-2} --- & --- \\\cline{1-2} 20 & 40024.02\\\cline{1-2}\end{tabular}[/tex]

[tex]y=32000(1.01125)^x[/tex]  (where x is the number of quarterly periods)

$40,024.02

see attached

Answer:

Step-by-step explanation:

Point P is marked in the expanded view on the 7th mark of the 10 marks between 5×10^-3 and 6×10^-3. That means it is representing ...

  (5 +7/10)×10^-3 = 5.7×10^-3 . . . . scientific notation

__

The -3 exponent of 10 means the multiplier of the value is 1 in the 3rd place to the right of the decimal point: 0.001. So, the standard form of the number is ...

  5.7×0.001 = 0.0057 . . . . . standard form

Answer:

1. No sol.

2. One Sol. x=4

3. One Sol. w=22 1/2

Step-by-step explanation:

1.

Group like terms:

4+3p=6p-3p+5

Add similar elements (6p-3p=3p):

4+3p=3p+5

Subract 4 from both sides:

4+3p-4=3p+5-4

Simplify:

3p=3p+1

Subtract 3p from both sides:

3p-3p=3p+1-3p

Simplify:

0=1

There is no solution.

2.

One Sol. x=4

Switch sides:

3x-2=10

Add 2 to both sides:

3x-2+2=10+2

Simplify:

3x=12

Divide both sides by 3:

3x/3=12/3

Simplify:

x=4

There is a solution.

3.

One Sol. w=22 1/2

Subtract 7 from both sides:

2/3w+7-7=22-7

Simplify:

2/3w=15

Multiply both sides by 3:

3*2/3w=15*3

Simplify:

2w=45

Divide both sides by 2:

2w/2=45/2

Simplify:

w=22 1/2

There is one sol.

Answer:

The answers are:x = ±7/4x = ±3/2x = ±11/8

yww:)

Answer:

Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Step-by-step explanation:

Step 1:  Add 144 to both sides

[tex]64x^2 - 144 = -23[/tex]

[tex]64x^2 - 144 + 144 = -23 + 144[/tex]

[tex]64x^2 = 121[/tex]

Step 2:  Divide both sides by 64

[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]

[tex]x^2 = 1.890625[/tex]

Step 3:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]

[tex]x =[/tex] ± [tex]1.375[/tex]

[tex]x =[/tex] ± [tex]11/8[/tex]

Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Answer: t=2

Step-by-step explanation:

add the t's and calculate

Answer:

a) 7000 x 1.06^t

b) 11156

Step-by-step explanation:

a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.

b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.

Answer: A. Complex

Step-by-step explanation: hope this helps!

Answer:

B. 2.365

Step-by-step explanation:

Divide total distance by total people in order to get distance each person traveled.

28.375 miles / 12 = 2.36458333.......

If you round taht to nearest thousandth of a mile, the answer is: 2.365

Answer:60 pages

Step-by-step explanation:

first take away the zero then devide by 2 then add the zero the the number that your left with.

Answer:

Step-by-step explanation:

Its a linear function it goes throw the y-x Axis and is in a striaght line.

Answer:

y = [tex]\frac{5}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = [tex]\frac{5}{2}[/tex] x + 5 ← equation of line

Answer:

____________

3748 x 4 = (3000+700+40+8) x 4

(3000 x 4) + (700 x 4) + (40 x 4) + (8 x 4)

12000 + 2800 + 160 + 32

= 14992

Step-by-step explanation with answer:

3748x4 = (3000+700+40+8) x 4

= 3000x4 + 700x4 + 40x4 +8x4

=12000+2800+160+32

=14992

Answer:

- 3/2 x²y

Step-by-step explanation:

Multiply the numbers and constant separately.

constant means x any y.

( - 2/3 x ) ( 9/4 xy )

- 2/3 * 9/4 * x * xy

= ( - 2/3 * 9/4 ) * ( x * xy )

= ( - (2*9)/(3*9) ) * ( x²y )

= ( - 18/12 )* x²y

= - 3/2 x²y

Answer:

Step 1. Rewrite in the form of y=mx+b

Step 2. Find and plot 2 points (x and y-intercepts)

Step 3. Connect dots

y=mx+b

y - 5x = -2

y = 5x - 2

Find 2 points

y-intecept = (0, -2)

x-intercept = ?

0 = 5x - 2

2 = 5x

x = 2/5

x-intercept = (2/5, 0)

281.2 units³

volume of Prism: Base Area x Height

Here given:

Base Area: 38 units²

Height: 7.4 units

Solve for volume:

38 x 7.4

281.2 units³

Volume:-

Answer:

Step-by-step explanation:

For mixture problems, it is convenient to let the variable represent the quantity of the high-value contributor.

Here, we can let x represent the number of quarters. Then the number of nickels is (52-x), and the total value of the coins is ...

  0.25x +0.05(52 -x) = 6.40

  0.20x +2.60 = 6.40 . . . . . . . . simplify

  0.20x = 3.80 . . . . . . . . . . . subtract 2.60

  x = 3.80/0.20 = 19 . . . . divide by the coefficient of x

The number of quarters is 19. The number of nickels is 52-19 = 33.

Answer:

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

__

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

__

Additional comment

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

Answer:

D

Step-by-step explanation:

since Δ QRS is isosceles then the base angles are congruent , that is

∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°

the sum of the 3 angles in Δ SPQ = 180° , then

∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°

Then

∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°

Answer:

v = -3

Step-by-step explanation:

1) Expand.

3v + 4v - 8 = -29

2) Simplify 3v + 4v - 8 to 7v - 8.

7v - 8 = -29

3) Add 8 to both sides.

7v = -29 + 8

4) Simplify -29 + 8 to -21.

7v = -21

5) Divide both sides by 7.

v = -21/7

6) Simplify 21/7 to 3.

v = -3

Step-by-step explanation:

problem 10 is function

but problem 9 is not

Answer:

x=75

Step-by-step explanation:

99/66=1.5

30x1.5=45

30+45 =75

Answer:

3:2

Step-by-step explanation:

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60

using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:

0.9/0.6 = 1.5

1.5 x 2 = 3

this gives 3/2 = 1.5

so we know that the ratio is 3:2 and this is the smallest whole number that it could be

Answer:

20 m/hr

Step-by-step explanation:

distance / rate = time

24 miles / 9 miles/hr  = 2 2/3 hr

(24 + 20 miles) / 12 miles/hr = 3 2/3 hr

3 2/3  -  2 2/3 = 1 hour to ride the next 20 miles   means  20 m/hr

Answer:

Step-by-step explanation:

you can think of it backwards,

-50 = 3x - 8y

x = 6y

X x 3 = 3x

6y x 3 = 18y

3x = 18y

18y - 8y = -50

10y = -50

y = -5

6 x -5 = -30

x = -30

Step-by-step explanation:

If you were to round 398 to the nearest hundred, you would get 400. that's only 2 off of 398. when you add 400 + 257 that would equal 857 because 4 + 2= 6 and then the other two digits on 400 are zeros so 5 and 7 stay the same. with 857, you must now subtract 2 because you added 2 earlier. 857 - 2 = 855.

Answer:

(-2,1)

Step-by-step explanation:

The solution of a system of equations is wherever the two lines intersect. So, this is quite easy. We can see they intersect at (-2,1). We can tell it is (-2,1) becuase it is two units left and one units up from the origin.

That is the solution.

(-2,1)

Answer:

The answer is (-2,1). Hope this helps :)

Step-by-step explanation:

Answer:

Linear expression

Step-by-step explanation:

The greateest exponent on a variable is 1 on x, so it is a linear expression,

Answer: Linear expression