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2 years ago

Solve the following equation for x

Mathematics

2 answers:

OlgaM077 [116]2 years ago

8 0

X-5/2 =-6 multiply both sides
x-5=-12 move the constant to the right
x = -12+5 calcúlate
x=-7

grigory [225]2 years ago

6 0

Answer:

I have no ide- the correct answer -7 pls brainliest

Step-by-step explanation:

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The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to

Olegator [25]

Answer:

$(1,\, 10)$ .

Step-by-step explanation:

Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to $x$ . Make use of the power rule to find the following:

$g^\prime(x) = 3\, x^2 - 2\, a\, x$ .

$h^\prime(x) = 2\, (2\, x) + b = 4\, x + b$ .

The question states that the graphs of $g(x)$ and $h(x)$ touch at $x = 1$ , such that $g^\prime(1) = h^\prime(1)$ . Therefore:

$3 - 2\, a = 4 + b$ .

On the other hand, since the graph of $g(x)$ and $h(x)$ coincide at $x = 1$ , $g(1) = h(1)$ (otherwise, the two graphs would not even touch at that point.) Therefore:

$1 - a + 6 = 2 + b + 3$ .

Solve this system of two equations for $a$ and $b$ :

$\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}$ .

Therefore, $a = -3$ whereas $b = 5$ .

Substitute these two values back into the expression for $g(x)$ and $h(x)$ :

$g(x) = x^3 + 3\, x^2 + 6$ .

$h(x) = 2\, x^2 + 5\, x + 3$ .

Evaluate either expression at $x = 1$ to find the $y$ -coordinate of the intersection. For example, $g(1) = 1 + 3 + 6 = 10$ . Similarly, $h(1) = 2 + 5 + 3 = 10$ .

Therefore, the intersection of these two graphs would be at $(1,\, 10)$ .

6 0

2 years ago

Express 5/7 as a decimal.

nignag [31]

Answer:

0.71428571428

Step-by-step explanation:

Do it the old fashioned way, get out your calculator, or google it.

3 0

2 years ago

Read 2 more answers

a shopkeeper purchased a TV at ₹15,000 and gives a discount of 20% on its marked prize and still got a profit of 8% . find the m

Setler79 [48]

$\huge\sf\underline{Answer}$

$\sf\longrightarrow selling \: prize \: = \frac{100 + profit\%}{100} \times cp$

$\sf\longrightarrow \frac{108}{100} \times 15000 = 16200$

Let the marked prize of the TV be x .

$\sf\longrightarrow discount = 20\% \: of \: x \: = \frac{20}{100}x = \frac{x}{5}$

We have SP = MP - Discount

$\sf\longrightarrow 16200 \: = \: x - \frac{x}{5}$

$\sf\longrightarrow 16200 \: = \frac{4x}{5}$

$\sf\longrightarrow x \: = \: 20250$

Hence , The marked prize of the TV is ₹20,250 .

Hope it helps ~

7 0

1 year ago

Find the slope of (0,1) and (2,-3) with this equation (Y2-Y1)/(X2-X1)

aalyn [17]

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}}\implies \cfrac{-4}{2}\implies -2$

7 0

2 years ago

Find domain and range -√x-5+10

inysia [295]

When finding the domain of a square root, you have to know that it is impossible to get the square root of 0 or any negative number. since domain is possible x values this means that x cannot be 0 or any number less than 0. However, you can find the square root of the smallest most infinitely small number greater than 0. since an infinitely small number close to zero can not be written out, we must must say that the domain starts at 0 exclusive. exclusive is represented by an open or close parenthesis so in this case the domain starts with:
(0,
we can get the square root of any number larger than 0 up to infinity but infinity can never be reached so it is also exclusive. So so the ending of our domain would be:
,infinity)
So the answer if the square root is only over the x the answer is
(0, infinity)

But if the square root is over the x- 5 then this would brIng a smaller amount of possible x values. since anything under the square root sign has to be greater than 0, you can say that:
(x - 5) > 0
x > 5
Therefore the domain would start at 5 and the answer would be:
(5, infinity)

8 0

2 years ago