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2 years ago

Solve for x: −3 |x + 7| = −12

2 answers:

4 0

$-3|x + 7|=-12\quad |:(-3)\\\\|x+7|=4\\\\\\x+7=-4\qquad\vee\qquad x+7=4\\\\x=-4-7\qquad\vee\qquad x=4-7\\\\\boxed{x=-11\qquad\vee\qquad x=-3}$

Lena [83]2 years ago

4 0

First you divide both sides by -3
then you get |x + 7| = 4
what you do now is make two separate equations
drop the absolute value signs
x + 7 = 4 OR x + 7 = -4
subtract 7 from both sides AND BOTH EQUATIONS
x = -3 OR x = -11

lets check it!

-3 |-3 + 7| = -12 -3 |-11 + 7| = -12
-3 |4| = -12 -3 |-4| = -12
-3 (4) = -12 -3 (4) = -12

yep! your answers are x = -3 OR x = -11

i hope this helps!!

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At what points on the given curve x = 4t3, y = 3 + 40t − 2t2 does the tangent line have slope 1?

dexar [7]

ANSWER

The points are:

(32,-85)

and

$( \frac{500}{27} , \frac{577}{9} )$

EXPLANATION

The given parametric equation that defines the curve is:

$x = 4 {t}^{3}$

$y = 3 + 40t - 2 {t}^{2}$

We differentiate to get,

$\frac{dx}{dt} = 12 {t}^{2}$

$\frac{dy}{dt} = 40 - 4t$

The slope of the tangent is given by;

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{12 {t}^{2} }{40 - 4t}$

For the slope to be 1, then we must solve the following equation for t.

$\frac{12 {t}^{2} }{40 - 4t} = 1$

$12 {t}^{2} = 40 - 4t$

$12 {t}^{2} + 4t - 4 0 = 0$

$3{t}^{2} + t - 10 = 0$

$(t + 2)(3t - 5) = 0$

$t = - 2 \: \: or \: \: t = \frac{5}{3}$

When t=-2, we put -2 into the expression for x and y to get

x=4(-2)³ and y=3+40(-2)-2(-2)²

This implies that,

x=32, y=-85

Hence one point is (32,-85)

Similarly, when

$t = \frac{5}{3}$

$x = \frac{500}{27} ,y = \frac{577}{9}$

Another point is

$( \frac{500}{27} , \frac{577}{9} )$

7 0

2 years ago

Christina collects stamps. She has 47 stamps in all. She has 20 stamps from europe. The number of African stamps is 2 times the

astraxan [27]

She has 47 total
20 are from Europe
some are from Africa,
and some from Asia

how many from Africa? hmm let's say "a"
how many from Asia? hmm let's say "b"

we know that, she has twice as many "a" as she has "b" stamps,
so, whatever "b" is, a = 2 * b, or a = 2b

so.. let us add them together

$\bf \begin{array}{llllllll}
20&+&a&+&b&=&47\\
\uparrow &&\uparrow &&\uparrow \\
europe&&africa&&asia\\
\downarrow &&\downarrow &&\downarrow \\
20&+&2b&+&b&=&47
\end{array}$

solve for "b", to see how many from Asia she has

what's "a"? well, a = 2b , that's how many African ones she has :)

5 0

2 years ago

0.1+0.2+0.3×0.4????

Pavel [41]

0.24 should be your answer

6 0

2 years ago

Read 2 more answers

PLEASE HELP! GIVING BRAINLIST!!

erica [24]

Answer:

When x = 1, y = 10.

Step-by-step explanation:

Well, the graph is exponential. But in terms of the question, you can say if there is 1 year increase, there are 10 snakes.

4 0

1 year ago

Which relation is a function?

Brums [2.3K]

The second relation is a function.

For a relation to be a function, each x-value can only have a singular corresponding y-value. Since all other relations feature x-values with multiple y-values, the second relation is a function.

5 0

2 years ago