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2 years ago

70. Georgia has only dimes and quarters in her bag. She has a total of 18 coins

Mathematics

1 answer:

____ [38]2 years ago

3 0

Georgia has two more dimes than quarters.
Quarters: 8
Dimes: 10
(WORK SHOWN BELOW)

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Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 + 2x + 3 y2 = 2x + 12F

Svet_ta [14]

Answer:

$A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36$

Step-by-step explanation:

The equations are:

$y = x^{2} + 2x + 3$

$y = 2x + 12$

The two graphs intersect when:

$x^{2} + 2x + 3 = 2x + 12$

$x^{2} = 0$

$x_{1} = 3\\x_{2} = -3$

To find the area under the curve for the first equation:

$A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

To find the area under the curve for the second equation:

$A_{2} = \int\limits^3__-3}{2x + 12} \, dx$

To find the total area:

$A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

Simplifying the equation:

$A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx$

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).

3 0

3 years ago

a set contains the numbers 0,6,12, and 15 Two different numbers are selected randomly from this set. What is the probability tha

steposvetlana [31]

Answer:

the probability is 5 i think

Step-by-step explanation:

4 0

3 years ago

3. Find the midpoint between the following points. (-2,-5) and (-3,1)

Vadim26 [7]

Answer:

Step-by-step explanation:

(x₁, y₁) = (-2 , -5) & (x₂ , y₂) = (-3 , 1)

Midpoint = $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

$=(\frac{-2 + [-3]}{2} ,\frac{-5 + 1}{2})\\\\\\=(\frac{-5}{2} , \frac{-4}{2})\\\\=(-2.5, -2)$

7 0

3 years ago

Phred has already graded 40 papers and he still needs to grade more. Write an equation for how many papers he is grading if he c

vladimir2022 [97]

y=4x+40

x represents the number of minutes

y is the total

40 because he already graded 40 papers, and 4x because that's how many phred grades times the number of minutes

5 0

3 years ago

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor sho

RoseWind [281]

Answer:

325,452 more meteors fell during the Perseid meteor shower

Step-by-step explanation:

An year has 365 days.

Each day has 24 hours.

Each hour has 60 minutes.

Minutes in an year:

365*24*60 = 525600

Persoid:

$1 + \frac{1}{5} = 1 + 0.2 = 1.2$

One each 1.2 minutes. How many during an year?

1 meteor - 1.2 minutes.

x meteors - 525600 minutes.

$1.2x = 525600$

$x = \frac{525600}{1.2}$

$x = 438000$

438,000 meteors fell during the Persoid shower.

Leonid:

$4 + \frac{2}{3} = 4.67$

One each 4.67 minutes. How many during an year.

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

$4.67x = 525600$

$x = \frac{525600}{4.67}$

$x = 112548$

112,548 meteors fell during the Leonid Shower.

How many more meteors fell during the Perseid meteor shower?

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

5 0

3 years ago