The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2+4x-60. The cost, in dollars, of producing the toy cars can be modeled by 3X2-x+ 200. The number of toy cars sold is represented by X

Step-by-step explanation:

x = earnings from the store

y = earnings from the college

x + y = 67,250

x = 3y + 1,250

now we use the identity of the second equation in the first equation :

(3y + 1,250) + y = 67,250

4y = 66,000

y = $16,500

x = 3y + 1,250 = 3×16,500 + 1,250 = 49,500 + 1,250 =

= $50,750

Answer:

20%

Step-by-step explanation:

the units of measure must be the same, so

2m = 2 × 100 cm = 200 cm

then

[tex]\frac{40}{200}[/tex] × 100%

= 0.2 × 100%

= 20%

Answer:

20%

Step-by-step explanation:

Answer:

Convert from a fraction to a decimal 1/4. 0.25

Answer:

0.25 is the correct answer of the question

Answer:

here man that's the answer

Answer:

a-3

Step-by-step explanation:

[tex]2a-(a+3)\\= 2a - a - 3\\= a - 3[/tex]

Answer:

a-3

Step-by-step explanation:

2a - (a+3)

removing bracket

2a -a-3

a-3

final answer

Answer:

3-x is the inverse of f(x)=x-3

Answer:

162.5

Step-by-step explanation:

25=height

13=base

to find the area of a triangle you do (h(b)b)/2

The cardinality of a set refers to the number of elements in the set. It is found by counting  the elements in the set.

The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.

a) There are 6 elements in this set hence the cardinality is 6.

b) There is only one element in the set hence its cardinality is 1.

c) There are two elements in the set hence the cardinality is 2.

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Answer:

8.92 * 10^10

Step-by-step explanation:

1. Convert to decimal notation

[tex]8.92*10^6[/tex]

The exponent is 6, making it 10 to the power of 6. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 6 time(s):

8.92 -> [tex]8920000[/tex]

2. Final result

[tex]8920000[/tex]

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.  If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

8.92 * 10^10

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Scientific notation, or standard form, makes things easier when working with very small or very big numbers, both of which come up frequently in the fields of science and engineering. It is used in science, for example, to convey the mass of the heavenly bodies: Jupiter’s mass is [tex]1.898*10^{27}[/tex]kg, which is easier to comprehend than writing the number 1,898 followed by 24 zeroes. Scientific notation also makes solving problems that use such high or low numbers more straightforward.

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

Scientific notation is also referred to as scientific form or standard index form, or in the UK, standard form.

Sum of two interiors=Exterior

[tex]\\ \rm\Rrightarrow 39+6x+11=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 6x+50=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 60=5x[/tex]

[tex]\\ \rm\Rrightarrow x=12[/tex]

Answer:

The answer is B. 13.7 inches

i hope this can help you! :)

Answer:

1.9 m

Step-by-step explanation:

1 ft = 30 cm (approximately)

12 in. = 1 ft

100 cm = 1 m

Find the height in ft:

4 in. / 12 in/ft = 1/3 ft

6 ft 4 in. = 6 ft + 1/3 ft = 6 1/3 ft

Convert ft to cm:

6 1/3 ft × 30 cm/ft = 190 cm

Convert cm to m:

190 cm × 1 m / 100 cm = 1.9 m

answer: 195cm

the photo should explain

Answer:

  1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

__

The partial sums, taken 3 terms at a time, are

  1+2-3 = 0

  4+5-6 = 3

  7+8-9 = 6

...

  97+98-99 = 96

So the original series is equivalent to ...

  0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

__

The sum of integers 1..n is given by the equation ...

  s(n) = n(n+1)/2

__

Using this to find the sum of our series, we find it to be ...

  series sum = 3 × (32)(33)/2 = 1584

_____

Alternate solution

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

  1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

  (99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

Answer:

25 = b

26 = c

Step-by-step explanation:

The exterior angles in the given triangle are angles 4 and 5.

The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.

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The graph that could represent the motion of the apple is graph B.

A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct

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The volume of the given cone.

[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]

[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]

Therefore, the volume of the given cone is 75.36 cubic yards.

Answer:

6 m²

Step-by-step explanation:

Original area :

12 × 14 = 168 m²

New area :

(12-3) × (14+4) =  

9 × 18 = 162 m²

168 - 162 = 6

Area would change by 6 m²

[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]

Answer:

f(-3) = -6

Step-by-step explanation:

f(x) = x^2 + 4x - 3

f(-3) means to put -3 in place of x and then do the calculation.

f(-3)

= (-3)^2 + 4(-3) - 3

= 9 - 12 - 3

= -3 - 3

= -6

First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.

f(-3) = -6

Answer:

Step-by-step explanation:

-8p^2 + 6p + 28p - 21

-8p^2 + 34p - 21

Answer:

-8p² + 34p - 21

Step-by-step explanation:

(-2p + 7)(4p-3)

= -2p*4p -2p*-3 + 7*4p + 7*-3

= -8p² + 6p + 28p - 21

= -8p² + 34p - 21

The approximate base area of the resulting figure is 79 in²

An equation is an expression that shows the relationship between two or more numbers and variables.

The resulting figure formed from the rotation is a cylinder with a radius of 5 inches and height of 4 inches

Area of base = π * radius² = π * 5² = 79 in²

The approximate base area of the resulting figure is 79 in²

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The amount of the interest with simple interest of 6.9% will be $ 10.35.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Miguel Rodriguez borrowed ​$300 from his brother Julio to pay for books and tuition.

He agreed to pay Julio in 6 months with simple annual interest at ​6.9%

Then the amount of the interest will be

Amount = P x R x T / 100

We have

P = $ 300

R = 6.9%

T = 6 months = 0.5 years

Then we have

P = (300 x 6.9 x 0.5) / 100

P = $ 10.35

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Answer:

[tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]

Step-by-step explanation:

Given :

[tex]2\frac{1}{3} -\frac{1}{2} \div \frac{3}{4} + 3\frac{2}{3}[/tex]

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

Rewrite in improper fraction form :

[tex](\frac{6}{3} +\frac{1}{3}) -\frac{1}{2} \div \frac{3}{4} + (\frac{9}{3} +\frac{2}{3})[/tex]

[tex]\frac{7}{3} - \frac{1}{2} \div \frac{3}{4} + \frac{11}{3}[/tex]

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

Finding the common denominator :

⇒ 3 × 4

⇒ LCM = 12

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

Solving with 12 as LCM :

⇒ [tex]\frac{7\times 4}{3 \times4} - \frac{1\times6}{2\times6} \div \frac{3\times3}{4\times3} + \frac{11\times4}{3\times4}[/tex]

⇒ [tex]\frac{28}{12} - \frac{6}{12} \div \frac{9}{12} + \frac{44}{12}[/tex]

⇒ [tex]\frac{28}{12} - \frac{2}{3} + \frac{44}{12}[/tex] [Division takes place first]

⇒ [tex]\frac{28}{12} - \frac{8}{12} + \frac{44}{12}[/tex]

⇒ [tex]\frac{28}{12} + \frac{36}{12}[/tex]

⇒ [tex]\frac{64}{12}[/tex]

⇒ [tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]

Answer:

1600

Step-by-step explanation:

[tex]\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600[/tex]