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3 years ago

7

Solve inequalities for x : |5x -3|< 12.

1 answer:

goldenfox [79]3 years ago

6 0

Hello!

→ To answer the question we need to know about inequations, then...

$\huge {\text {$ \blue{ \sf \mid 5x - 3 \mid < 12 } $}}$

$\swarrow$

$\huge {\text {$ \red {\sf \mid 5x \mid < 12+3 }$}}$

$\searrow$

$\huge {\text {$ \purple { \sf \mid 5x \mid < 15} $}}$

$\swarrow$

$\huge {\text {$ \bf \mid x \mid < 15 \div 5 $}}$

$\large {\text {$ \downarrow $}}$

$\huge {\boxed { \bf \mid x \mid < 3 }}$

<em>Good studies!</em>

<em />

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One-half of a number added to itself equals twice the difference of the number and four.

dybincka [34]

Answer:One-half of a number added to itself equals twice the difference of the number and four.

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

PLEASE HELP ASAP

Crank

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts $(-2,0)$ and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points $(-2,0)$ , $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$ , we get,

$4a -2b+c=0$ -----------(1)

$16a +4b+c=0$ ----------(2)

$a-b+c=10$ -----------(3)

Subtracting (1) and (2), we get,

$\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \ \ -12a-6b=0$ -----------(4)

Subtracting (2) and (3), we get,

$16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10$ ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

$-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2$

Thus, the value of a is $a=-2$

Substituting $a=-2$ in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is $b=4$

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is $c=16$

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$ , we get,

$y=-2x^{2} +4x+16$

Taking out the common term as -2 we get,

$y=-2(x^{2} -2x-8)$

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

7 0

3 years ago

Which lines are perpendicular to 7x-3y=18

inna [77]

The answer is going to be 3y=7x-15. hope that helped

8 0

3 years ago

Let u =<-4,-3> . Find the unit vector in the direction of u, and write your answer in component form.

vova2212 [387]

Can someone answer this for me too

4 0

3 years ago

Please help it will be brainlist please make sure you are 100% the awnser is right

Dominik [7]

Answer:

Step-by-step explanation:

Step 1: Sum of angles on a straight line is 180

Step 2:

2x + 25 + y = 180

2x + y = 180 - 25

2x + y = 155 (1)

Step 3:

3x - 10 + y = 180

3x + y = 180 + 10

3x + y = 190 (2)

Step 4: Substract equation 1 from 2

3x + y - 2x - y = 190 - 155

x = 35

Step 5:

Substitute x in equation 1 to find y

2x + y = 55

2(35) + y = 155

70 + y = 155

y = 155 - 70

y = 85

4 0

3 years ago