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2 years ago

Part A: What is the value of 2x if 4x + 6 = 2x – 12?

Mathematics

1 answer:

xeze [42]2 years ago

8 0

Answer:

Step-by-step explanation:

A) 4x + 6 = 2x - 12

Subtract 6 from both sides

4x + 6 - 6 = 2x - 12 -6

4x = 2x - 18

Subtract 2x form both sides

4x - 2x = 2x - 18 - 2x

2x = -18

B) 24 = 6x - 18

6x - 18 = 24

6x - 6*3 = 24

6(x - 3) = 24

Divide both sides by 6

$\frac{6(x - 3)}{6}=\frac{24}{6}\\\\$

x - 3 = 4

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Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are

tankabanditka [31]

The coordinates of point B' are (-3, 6).

<h2>Given that</h2>

Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1).

The triangle is translated as 3 units to the left and 1 unit up.

<h3>We have to determine</h3>

What are the coordinates of B' after the translation?

<h3>According to the question</h3>

Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1).

The triangle is translated as 3 units to the left and 1 unit up.

To find the coordinates of B', we will shift the x-coordinate of point B to left by 3 units and the y-coordinate of point B to 1 unit up.

After the given transformation the coordinates of point B' would be:

$\rm B(0, \ 5) = B (0-3, \ 5+1) = B(-3, \ 6)$

Therefore, the coordinates of point B' are (-3, 6).

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brainly.com/question/26297555

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2 years ago

Joshua is going to mow lawns during his summer break. The graph in the figure shows a linear relationship between the number of

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Answer:

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Solve the for the inequality

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Answer:

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Step-by-step explanation:

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If y-3x=9, 7x+y=25, what is the value of x and y?

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$\bold{\rm{Given}}\text{ : If y - 3x = 9, 7x + y = 25, what is the value of x and y}?$

$\bold{\rm{Solution}} \text{: We'll solve this by substitution method}$

$\dashrightarrow y - 3x = 9 \\ \\ \dashrightarrow \boxed{y = 9 + 3x } \qquad .. \sf eq(1)$

$\text{we got the value of y now getting the value of x}$

$\looparrowright 7x + y = 25 \\ \\ \looparrowright 7x = 25 - y \\ \\ \looparrowright \boxed{x = \frac{25 - y}{7}} \qquad .. \sf eq(2)$

$\text{Now, putting y = 9 + 3x in eq(2)}$

$\hookrightarrow x = \frac{25 - y}{7} \\ \\ \hookrightarrow x = \frac{25 - 9 + 3x}{7} \\ \\ \hookrightarrow 7x = 25 - 9 + 3x \\ \\ \hookrightarrow 7x - 3x = 16 \\ \\ \hookrightarrow 4x = 16 \\ \\ \hookrightarrow x = \frac{16}{4} \\ \\ \star \quad \boxed{ \green{ \frak{ x = 4}}}$

$\text{Now we know the value of x, for getting y we need to put x in eq(1)}$

$: \implies y = 9 + 3x \\ \\ : \implies y = 9 + 3(4) \\ \\ : \implies y = 9 + 12 \\ \\ \star \quad \boxed{\frak{ \green{y = 21}}}$

$\text{Hence, values of x and y are} \: \frak{ \green{4}} \: \text{and} \: \frak{ \green{21}} \: \text{respectively}.$

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2 years ago

In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a tota

joja [24]

The amount spent by Seedevi is $66

<h3>How to determine the amount spent by Seedevi?</h3>

From the question, the given parameters are:

Seedevi = half as much money as Georgia,

Seedevi = $6 more than Amy

The three of them = $258

To solve this question, we use the following representations

x = Seedevi

y = Georgia

z = Amy

So, we have the following equations

x = 0.5y

x = 6 + z

x + y + z = 258

Make y and z the subjects

y = 2x

z = x - 6

Substitute y = 2x and z = x - 6 in x + y + z = 258

x + 2x + x - 6 = 258

Evaluate the like terms

4x = 264

Divide by 4

x = 66

Hence, the amount spent by Seedevi is $66