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3 years ago

Solve the equation with special factors. (Please show all steps) 16q^2 - 81 = 0

Mathematics

2 answers:

steposvetlana [31]3 years ago

6 0

Answer:

q = ± $\frac{9}{4}$

Step-by-step explanation:

16q² - 81 = 0 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16q² - 81 = 0

(4q)² - 9² = 0

(4q - 9)(4q + 9) = 0

Equate each factor to zero and solve for q

4q - 9 = 0 ⇒ 4q = 9 ⇒ q = $\frac{9}{4}$

4q + 9 = 0 ⇒ 4q = - 9 ⇒ q = - $\frac{9}{4}$

guapka [62]3 years ago

5 0

Answer: $q=\frac{\sqrt{81}}{16}$

Step-by-step explanation:

$16q^2-81=0\\16q^2=0+81=81\\16q=\sqrt{81} \\q=\frac{\sqrt{81}}{16}$

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64% of 25 students in the class have a phone. How many students have a phone?

Damm [24]

Answer: 16

Step-by-step explanation: looked it up on Google

6 0

3 years ago

Read 2 more answers

I need help with # 14 and 15 ASAP... It is due tomorrow ..can some one please help me with it

Angelina_Jolie [31]

Answer:

See explanation

Step-by-step explanation:

A. Gasoline fill-up fee = $4.50

Cost per hour = $40

Average cost = C

Number of hours the scootcar is rented = h

Cost per h hours = $40h

Total cost = $40h + $4.50

Hence,

C = 40h+4.5

B. To plot the graph of the function, find h- and C- intercepts.

When h = 0, then C = 4.5, and we have point (0,4.5)

When C = 0, then 0 = 40h + 4.5, h = -45/400 = -0.1125, and we have point (-0.1125,0)

Plot these two points and connect them with a straight line.

Graph is attached, but you should take only that part of the graph that corresponds to points with h > 0, because the number of hours cannot be negative

8 0

4 years ago

While on a road trip, Steve drove 300 miles in 5 hours. After stopping for gas, he drove an additional 120 miles in 2 hours. Doe

lawyer [7]

Answer:

B. Yes, this is direct variation. Time is the independent variable, and miles driven is the dependent variable.

Step-by-step explanation:

In a direct variation, when the independent variable increase the dependent variable also increases. In this case, the independent variable is the time (time is always independent) and the miles driven by Steve is the dependent variable. This means, the miles driven increase as time pass.

3 0

3 years ago

What equation is graphed in this figure?

topjm [15]

Answer:

The third equation: $y+2=-3(x-1)$

Step-by-step explanation:

The two points on the line are $(-1,4)$ and $(1,-2)$ .

Slope of the line passing through two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$m=(y_{2} -y_{1})/ (x_{2} -x_{1})$

Here, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are $(-1,4)$ and $(1,-2)$ .

Therefore, slope is equal to, $m=(-2-4 )/ (1-(-1)$

$m=-6/2$

$m=-3$

Now, equation of a straight line with slope m and points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$y-y_{1}=m(x-x_{1})\\y-y_{2}=m(x-x_{2})$

Now, if we use the 2nd form, then $x_{2}=1,y_{2}=-2$ .

So, the equation is given as :

$y-(-2)=-3(x-1)\\y+2=-3(x-1)$

8 0

3 years ago

ASAP Please help. Thank You!!! :)

liraira [26]

#25.
Convert the fractional numbers into decimals for easier comparison.
3 2/3 is approximately 3.66
-4 2/5 is approximately -4.4
We now have: 3, 3.66, -4.2, -4.4
In order: -4 2/5, -4.2, 3, 3 2/3

#26.
All positive numbers are greater than negative numbers.
When comparing two negative numbers, the one with the larger absolute value, will be less.
So (G) is correct

#27.
25 = m + 6.3
25 - 6.3 = m + 6.3 - 6.3
m = 18.7

#28.
h = 3.2-1.6 = 1.6

#29.
x = 15.6 - 9.8 = 5.8

#30
p = 17 - 4.5 = 12.5

6 0

4 years ago