All categories

3 years ago

Need helpwith these

Mathematics

1 answer:

liraira [26]3 years ago

6 0

1. 4(2+3c) = 56

c = 4

3. -29 = 5(2a-1)+2a

a = -2

5 . 7p-(3p+4) = -2(2p-1)+10

p=2

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

x=4

Step-by-step explanation:

1. 4(2+3c) = 56

$4(2+3c) = 56\\8+12c = 56$

Subtracting 8 from both sides

$8-8+12c = 56-8\\12c = 48$

Dividing both sides by 12

$\frac{12c}{12} = \frac{48}{12}\\c = 4$

Checking:

$4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56$

3. -29 = 5(2a-1)+2a

Simplifying

$-29 = 10a-5+2a\\-29 = 12a-5$

Adding 5 on both sides

$-29+5 = 12a - 5+5\\-24 = 12a$

Dividing both sides by 12

$\frac{12a}{12} = \frac{-24}{12}\\a = -2$

Checking:

$-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29$

5 . 7p-(3p+4) = -2(2p-1)+10

Simplifying

$7p-3p-4 = -4p+2+10\\4p-4 = -4p+12$

Adding 4 on both sides

$4p-4+4 = -4p+12+4\\4p = -4p+16$

Adding 4p on both sides

$4p+4p = -4p+4p+16\\8p = 16$

Dividing both sides by 8

$\frac{8p}{8} = \frac{16}{8}\\p = 2$

Checking:

$7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4$

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

Simplifying

$\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18$

Adding 6 on both sides

$-6+6+9x = 3x+18+6\\9x = 3x+24$

Subtracting 3x from both sides

$9x-3x = 3x-3x+24\\6x = 24$

Dividing both sides by 6

$\frac{6x}{6} = \frac{24}{6}\\x = 4$

Checking:

$\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15$

Keywords: Linear equations

Learn more about linear equations at:

#LearnwithBrainly

You might be interested in

Need help

kow [346]

$1)\\\\\dfrac{-45}{-5}=45:5=9$

$2)\\(-2)(4)=-8\\(2)(-4)+-8\\-16:2=-8\\-16:(-2)=8\neq-8\\\\\text{All of the following expressions have the same value except}\ -16:-2.$

$3)\\-3^2=-3\cdot3=-9$

$(-2)^4=(-2)(-2)(-2)(-2)=16\\-2^4=-(2)(2)(2)(2)=-16\neq16\\(-2)(-2)(-2)(-2)=16\\2^4=(2)(2)(2)(2)=16\\\\\text{All of the following are equivalent except}\ -2^4.$

3 0

4 years ago

HELP!!!!!!!

lesantik [10]

Answer:

Option A, Left by 4 units

Step-by-step explanation:

Step 1: Convert g(x) to a function square

We currently have g(x) in this order: $ax^2 + bx + c$

However, we want g(x) to be in this order: $(ax + c)^{2}$

The first thing we have to do is to factor it out:

$g(x)=x^{2}+8x+16$

$g(x) = (x + 4)(x + 4)$

$g(x) = (x+4)^{2}$

Step 2: Now we can see which way we need to move it

The original form is: $f(x) = (ax - b)^{2}$

Since the - has changed to a +, that means that we moved -4 spaces down the x-axis. This means that we move left by 4 units.

Answer: Option A, Left by 4 units

Look at the graphs below to make sure:

7 0

3 years ago

Read 2 more answers

Which is a graph of f(x) = (6x-2)/(x-3), with any vertical or horizontal asymptotes indicated by the dashed lines?

Margaret [11]

Answer:

to find the vertical asymptote, you have to put the rational function in the simplest form, which means to cancel any common factor between the numerator and denominator. here we don't have anything to cancel. then take the denominator and equal it to 0. x-3=0 ,x=3

to find the horizontal asymptote, in this situation, the degree of the numerator and denominator are the same which is 1. therefore, y=the coefficient of the numerator ÷ the coefficient of the denominator. y=6÷1 ,y=6

7 0

3 years ago

Read 2 more answers

If (x - 2)² = 49 , then x could be?

JulsSmile [24]

$(x-2)^2=49\iff x-2=\sqrt{49}\ or\ x-2=-\sqrt{49}\\\\x-2=7\ or\ x-2=-7\\\\x=7+2\ or\ x=-7+2\\\\x=9\ or\ x=-5\\\\Answer:x\in\{-5;\ 9\}$

4 0

3 years ago

Read 2 more answers

Write an algebraic equation to match each graph. (These graphs are not drawn to scale!) please help! i will make brainliest answ

ddd [48]

Answer:

the expression of this function is:

$f(x)=|x-1|-1$

Step-by-step explanation:

This graph corresponds to an absolute value function, which as you can see has the minimum (vertex) at the point (1, -1) on the plane, and also that goes through the origin of coordinates (0, 0)

therefore, notice that from the point (0, 0) to (1, -1) there is a slope of "-1" which is going to characterize the steepness of the x- variable that resides inside the absolute value function. since the vertex has also moved from the characteristic (0, 0) in the function:

$f(x)=|x|$

then we have to include a horizontal shift to the right in one unit (by subtracting 1 units from x), and a vertical shift downwards one unit (by subtracting 1 from the full absolute value expression) in order to shift the vertex to the position (1, -1):

$f(x)=|x-1|-1$

3 0

3 years ago

Need helpwith these​

Need helpwith these