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2 years ago

If 2x – 3 + 3x = – 28, what is the value of x?

Mathematics

1 answer:

julsineya [31]2 years ago

5 0

Answer:

x= -14

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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Manuel is putting money into a savings account. He starts with

olga55 [171]

S=350 your starting amount + 30w which is 30× the number of weeks (19) which comes out to give you s=920 if I did it correctly

4 0

2 years ago

A 10-foot board is cut into two pieces. If one piece is x feet long, express the other length in terms of x

OleMash [197]

Answer:

10-x ft long

Step-by-step explanation:

If it starts out 10ft long, and xft is taken away, then the remaining board would be 10-x ft long.

In terms of x, I believe it would just be 10-x ft long

7 0

3 years ago

Solve quadratic formulax^2-4x+3=0

bekas [8.4K]

The general formula for a equation of the form:

$ax^2+bx+c=0$

is:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

In this case we notice that a=1, b=-4 and c=3. Plugging this values in the general formula we get:

$\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(3)}}{2(1)} \\ =\frac{4\pm\sqrt[]{16-12}}{2} \\ =\frac{4\pm\sqrt[]{4}}{2} \\ =\frac{4\pm2}{2} \end{gathered}$

then:

$x_1=\frac{4+2}{2}=\frac{6}{2}=3$

and

$x_2=\frac{4-2}{2}=\frac{2}{2}=1$

Therefore, x=3 or x=1.

8 0

6 months ago

At 6:00 the outside air temperature was 15°F. By 8:00 the temperature had dropped 9°F, and by 11:00 I had dropped another 12°. W

laila [671]

Answer:

- 6°F

Step-by-step explanation:

Given :

Temperature at 6:00 = 15°F

Temperature dropped by 9°F by 8:00

Temperature by 8:00 = 15°F - 9°F = 6°F

Temperature dropped another 12°F by 11:00

Hence, Temperature at 11:00 will be :

6°F - 12°F = - 6°F

Temperature at 11:00 = - 6°F

8 0

2 years ago

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes

ArbitrLikvidat [17]

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for $x = 3$ and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?

Answer:

The generally expression for the slope of $y = 2x^2 + 4x$ is $y' = 4x +4$

The graph is shown on the first uploaded image

The generally expression for the slope of $y=2x^2+4$ is $y' = 4x$

Step-by-step explanation:

From the question we are told that

The equation of the curve is $y = 2x^2 + 4x$

First we differentiate the equation

$y' = 4x +4$

Therefore the generally expression for the slope tangent to the curve $y=2x^2+4x$ is $y' = 4x +4$

The next step is to substitute for x = 3 and x = 0.5

So for $x_1 = 3$

$y' = 4(3) +4$

$y' =m_1= 16$

And for $x_2 = 0.5$

$y' = 4(0.5) +4$

$y' =m_2= 6$

Here m_1 and m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So at $x_1 = 3$

$y_1 = 2(3)^2 + 4(3)$

$y_1 = 21$

So the coordinate for the first tangent line is

$(x_1 , y_1 ) = (3 , 21)$

At $x_2 = 0.5$

$y_2 = 2(0.5)^2 + 4(0.5)$

=> $y_2 = 2.5$

So the coordinate for the second tangent line is

$(x_2 , y_2 ) = (0.5 , 2.5)$

Next we obtain the equation for the tangent lines

So generally the slope is mathematically represented as

$m = \frac{y - y_1 }{x-x_1}$

For $(x_1 , y_1 ) = (-3 , 21)$ and $y' =m_1= 16$

$16 = \frac{y -21 }{x-3)}$

=> $y = 16x - 27$

For $(x_2 , y_2 ) = (0.5 , 2.5)$ and $y' =m_2= 6$

$6 = \frac{y -2.5 }{x-0.5}$

$y = 6x -0.5$

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows

$y' = 4x$

7 0

2 years ago