In the figure shown angle 1 has a measure of 90° and angle 2 has a measure of 38° find the measure of the remaining angles

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

4 years ago

The product of 8 and b is less than or equal to 13

Ugo [173]

Answer:

1 or 0

Step-by-step explanation:

8 x b = 13

You can't divide 8 by two because that equals 16 so 8 x 1 is less than 8.

And 8 x 0 is 0

7 0

3 years ago

Based on the diagram, which is a true statement?

oksian1 [2.3K]

Answer:

top god's menu back door distract 9 call scars double knot thunderous gone away gone day SKZ ALL AROUND THE WORLD

7 0

3 years ago

At a bake sell, 3/5 of the baked goods are pies. the rest of the baked goods are the plates of cookies. there are 24 plates of c

vovangra [49]

A: 2/5

B: 24x2= 48+12= 60

C: 4

3 0

3 years ago

A new gas- and electric-powered hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally di

Doss [256]

Answer:

a) P [ Z > 70 ] = 0.1075 or 10.75 %

b) P [ Z < 60 ] = 0.1038 or 10.38 %

c) P [ 55 ≤ Z ≤ 70 ] = 0.8882 or 88.82 %

Step-by-step explanation:

Normal Distribution μ = 65 and σ = 4

a) The probability of the car travels more than 70 miles per gallon is:

P [ Z > 70 ] = (Z-μ) ÷ σ ⇒ P [ Z > 70 ] = (70-65) ÷4 P [ Z > 70 ] = 1.25

the point 1.25 corresponds at values, from left tail up to 70 so we must go and look for the area for the point 1.24 which is 0.8925. Then we have the area or probability of all cars traveling up to 70 miles therefore we have to subtract 1 -0,8925

P [ Z > 70 ] = 0.1075 or 10.75 %

b)The probability of the car travels less than 60 miles per gallon is:

P [ Z < 60 ] = ( 60 - μ ) ÷ σ ⇒ P [ Z < 60 ] = (60-65)÷ 4 P [ Z < 60 ] = -1.25

Again -1.25 corresponds to 60 miles per gallon threfore we move to the left and find for point -1.26 which area is 0.1038 so

P [ Z < 60 ] = 0.1038 10.38 %

c) P [ 55 ≤ Z ≤ 70]

For point Z = 70 or 1.25 (case a above) P [ Z ≤ 70] = (70-65)÷4

P [ Z ≤ 70] = 1.25

In this case we got the whole area from the left tail up to 1.25

P [ Z ≤ 70] = 0.8944 (includes the area of the point from the left tail up to the point assocciated to 55 miles and for that reason we have to subtract that area)

P [ Z ≥ 55 ] = (55-65) ÷ 4 P [ Z ≥ 55 ] = -2.5 and the area is 0.0062

So P [ 55 ≤ Z ≤ 70 ] = 0.8944 - 0.0062 = 0.8882

8 0

4 years ago