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3 years ago

Is x = -7, the solution to -11 + 2x = -26? Justify your answer in complete sentences.

1 answer:

4 0

First of all, you can move the +2x to the other side:
-11 = -26 - 2x

Then you can move the -26 to the other side and then simplify:
-11+26 = -2x
15 = -2x

Then you can divide both sides by 2:
7.5 = -x

Then you can flip the sides and the signs around:
x = -7.5

No, The answer is not -7, it is -7.5
Hope this helps! :)

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Which of the following is not a theorem taught from this lesson?

MariettaO [177]

Answer:

The altitude to the base of an isosceles triangle bisects the vertex angle of the triangle.

Step-by-step explanation:

7 0

2 years ago

How do you find the value of c that satisfy the equation:

victus00 [196]

Answer:

The value of c = -0.5∈ (-1,0)

Step-by-step explanation:

Step(i):-

Given function f(x) = 4x² +4x -3 on the interval [-1 ,0]

Mean Value theorem

Let 'f' be continuous on [a ,b] and differentiable on (a ,b). The there exists a Point 'c' in (a ,b) such that

$f^{l} (c) = \frac{f(b) -f(a)}{b-a}$

Step(ii):-

Given f(x) = 4x² +4x -3 …(i)

Differentiating equation (i) with respective to 'x'

f¹(x) = 4(2x) +4(1) = 8x+4

Step(iii):-

By using mean value theorem

$f^{l} (c) = \frac{f(0) -f(-1)}{0-(-1)}$

$8c+4 = \frac{-3-(4(-1)^2+4(-1)-3)}{0-(-1)}$

8c+4 = -3-(-3)

8c+4 = 0

8c = -4

$c = \frac{-4}{8} = \frac{-1}{2} = -0.5$

c ∈ (-1,0)

Conclusion:-

The value of c = -0.5∈ (-1,0)

8 0

3 years ago

A soccer ball is kicked from 3 feet above the ground. the height,h, in feet of the ball after t seconds is given by the function

dexar [7]

Here's our equation.

$h=-16t+64t+3$

We want to find out when it returns to ground level (h = 0)

To find this out, we can plug in 0 and solve for t.

$0 = -16t+64t+3 \\ 16t-64t-3=0 \\ use\ the\ quadratic\ formula\ \frac{-b\±\sqrt{b^2-4ac}}{2a} \\ \frac{-(-64)\±\sqrt{(-64)^2-4(16)(-3)}}{2*16} = \frac{64\±\sqrt{4096+192}}{32}$

$= \frac{64\±\sqrt{4288}}{32} = \frac{64\±8\sqrt{67}}{32} = \frac{8\±\sqrt{67}}{4} = \boxed{\frac{8+\sqrt{67}}{4}\ or\ 2-\frac{\sqrt{67}}{4}}$

So the ball will return to the ground at the positive value of $\boxed{\frac{8+\sqrt{67}}{4}}$ seconds.

What about the vertex? Simple! Since all parabolas are symmetrical, we can just take the average between our two answers from above to find t at the vertex and then plug it in to find h!

$\frac{1}2(\frac{8+\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(2+\frac{\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(4) = 2$

$h=-16t^2+64t+3 \\ h=-16(2)^2+64(2)+3 \\ \boxed{h=67}$

8 0

3 years ago

4 (-3x - 1) = 13x + 6

GarryVolchara [31]

Answer:

x=-2/5

Step-by-step explanation:

4(-3x-1)=13x+6 ~ Distribute the 4 into the parenthesis

-12x-4 = 13x+6 ~ add 12x to both sides

-4= 25x + 6 ~ subtract 6 from both sides

-10 =25x ~ divide by 25

-10/25 = x ~ simplify the fraction by dividing the num. and den by 5

-2/5 =x

4 0

2 years ago

Read 2 more answers

Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$