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My name is Ann [436]

3 years ago

9

In one season,Kim ran 18 races. This was four fewer races than twice the number of races Kelly ran. How many races did kelly run

?

2 answers:

Furkat [3]3 years ago

5 0

Answer:

11 races

Step-by-step explanation:

The reason being that 18 is 4 less than twice the number Kelly ran. 18+4=2x when x equals the races Kelly ran. so, 18+4=22 so 22=2x. if you divide each side by 2, you get 11=x. so, kelly ran 11 races

Svet_ta [14]3 years ago

4 0

Answer:

44

Step-by-step explanation:

18+4=22 time 2 =44

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5. (05.03 LC) What is the simplified form of the quantity of x plus 5, all over the quantity of 3x plus 4 + the quantity of x pl

earnstyle [38]

Answer:

B. $\frac{4x^{2}+24x+31}{3x^{2}+13x+12}$

Step-by-step explanation:

We have been given a rational expression $\frac{(x+5)}{(3x+4)}+\frac{(x+4)}{(x+3)}$ and we are asked to simplify our rational expression.

We can see that our denominators are not equal. Since the two denominators do not share any common factors, the common denominator is simply the product of these two denominators.

To keep the value of expression same we will multiply the same quantity with numerators and denominators.

$\frac{(x+5)(x+3)}{(3x+4)(x+3)}+\frac{(x+4)(3x+4)}{(x+3)(3x+4)}$

Now let us simplify our expression using FOIL.

$\frac{x^{2}+3x+5x+15}{3x^{2}+9x+4x+12}+\frac{3x^2+4x+12x+16}{3x^{2}+4x+9x+12}$

$\frac{x^{2}+8x+15}{3x^{2}+13x+12}+\frac{3x^2+16x+16}{3x^{2}+13x+12}$

Now we have same denominators, so we can add our numerators.

$\frac{x^{2}+8x+15+3x^2+16x+16}{3x^{2}+13x+12}$

Now let us combine like terms.

$\frac{(1+3)x^{2}+(8+16)x+15+16}{3x^{2}+13x+12}$

$\frac{4x^{2}+24x+31}{3x^{2}+13x+12}$

Therefore, the simplest form of our given rational expression will be $\frac{4x^{2}+24x+31}{3x^{2}+13x+12}$ and option B is the correct choice.

8 0

3 years ago

uhammad, a shipping and receiving clerk, uses 1 yard, 2 feet, 4 inches of twine to wrap each carton he packs. He has to pack 29

irina1246 [14]

Answer

Find out the how much twine will he needs to pack 29 cartons today .

To proof

As given

uhammad, a shipping and receiving clerk, uses 1 yard, 2 feet, 4 inches of twine to wrap each carton he packs.

As given in the question

Convert the answer to larger units .

As between yard is the largest unit between yard, feet and inches.

$1 inches = \frac{1}{36} yard$

and

$1 feet = \frac{1}{3} yard$

Convert 2 feet into yard

$=\frac{2}{3}$

Convert 4 inches into yard

$= \frac{4}{36}$

twine to wrap each carton packs

$= 1 + \frac{2}{3} + \frac{4}{36}$

L.C.M of (3 , 36) = 36

than the equation becomes

$=\frac{36 +2\times 12 + 4}{36}$

$= \frac{64}{36}$

=1.77777778 yard

Now twine to wrap pack 29 cartons = 29× 1.77777778

= 51.5555556 yard

Now twine to wrap pack 29 cartons is 51.55 yard ( approx)

Hence proved

6 0

2 years ago

Pretest: Unit 5 Question 12 of 21 Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Gala2k [10]

Answer:

(10, - 9 )

Step-by-step explanation:

Given the 2 equations

y = - 2x + 11 → (1)

y = - 3x + 21 → (2)

Substitute y = - 2x + 11 into (2)

- 2x + 11 = - 3x + 21 ( add 3x to both sides )

x + 11 = 21 ( subtract 11 from both sides )

x = 10

Substitute x = 10 into either of the 2 equations and evaluate fir y

Substituting into (1)

y = - 2(10) + 11 = - 20 + 11 = - 9

solution is (10, - 9 )

3 0

2 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Sara threw her math book off a building . The height of the book, seconds after being thrownis modeled by the equation below. Th

Vikentia [17]

Answer: 70 ft

Step-by-step explanation:

Given

height of book is measured by the function is

$h(x)=-5(x+2)(x-7)$

when the book is thrown $x=0$

$\therefore h(x=0)=-5(0+2)(0-7)\\\Rightarrow h(x=0)=70\ ft$

The height of the book is $70\ ft$

4 0

2 years ago