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2 years ago

What is the value of x? Enter your answer in the box. _____ units

Mathematics

2 answers:

krek1111 [17]2 years ago

6 0

Answer:

x=28

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.

x 42

---------- = ----------

x+10 42+15

Simplify

x 42

---------- = ----------

x+10 57

Using cross products

57x = 42 (x+10)

Distribute

57x = 42x+420

Subtract 42x from each side

57x-42x = 42x-42x +420

15x = 420

Divide each side by 15

15x/15 = 420/15

x=28

MariettaO [177]2 years ago

5 0

Answer: The value of x is 28 units.

Step-by-step explanation:

Since we have given that

DC ║ PA

So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.

So, it becomes,

$\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28$

Hence, the value of x is 28 units.

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3 years ago

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2 years ago

3. (05.06 MC)

AveGali [126]

Answer:

Step-by-step explanation:

y > 3x + 10

y < -3x - 1

You'd graph the given systems of linear inequalities the same way as you graph the linear equations.

To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph. Use a dashed line (because of the ">" symbol).

Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).

Pick a test point on either side of the boundary line and plug it into the original problem. This will help determine which side of the boundary line is the solution. Plug in a test point that is not on the boundary line.

Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.

y > 3x + 10

0 > 3(0) + 10

0 > 0 + 10

0 > 10 (False statement).

y < -3x - 1

0 < -3(0) - 1

0 < 0 - 1

0 < -1 (false statement).

Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.

You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.

y > 3x + 10

10 > 3(8) + 10

10 > 24 + 10

10 > 34 (False statement).

y < -3x - 1

10 < -3(8) - 1

10 < -24 - 1

10 < -25 (false statement).

Therefore, (8, 10) is not a solution to the system.

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2 years ago