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4 years ago

. Are the triangles similar and if so why? What is the value of x? Show your work. Answer:

Mathematics

1 answer:

alexdok [17]4 years ago

5 0

Answer:

yes; x=7

Step-by-step explanation:

When two corresponding angles are congruent, all angles are congruent, so the triangles are similar. The sides of the triangle on the right are 30/25 = 6/5 times the length of the sides of the left triangle, so side MP will be 6/5 times the length of JL, or (6/5)·20 = 24.

Then the expression for that length lets us find the value of x:

24 = 4x -4

6 = x -1 . . . . . divide by 4

7 = x . . . . . . . add 1

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Evaluate. 9.75 + 4.625 + (-9.75) + 2.6=?

marusya05 [52]

The answer would be 7.225.

4 0

3 years ago

Read 2 more answers

Find the following integral

ololo11 [35]

There's nothing preventing us from computing one integral at a time:

$\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2$

$\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2$

$\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx$

Expand the integrand completely:

$x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x$

Then

$\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}$

4 0

3 years ago

Compare the functions shown below:

emmasim [6.3K]

The intersection with the y axis occurs when x = 0.
We have then:

For f (x):
$f (0) = -3 (0) - 5

f (0) = 0 - 5

f (0) = - 5$

For g (x):
We can observe in the graph that when x = 0, the value of the function cuts to the y axis in y = -3

For h (x):
$h (0) = 2cos (2 (0) -\pi) +4

h (0) = 2cos (0-\pi) +4

h (0) = 2cos (-\pi) +4$
$h (0) = 2 (-1) +4

h (0) = -2 + 4

h (0) = 2$

Therefore, the graph with the intersection with the largest y axis is h (x)

Answer:
the greatest y-intercept is for:
C. h(x)

6 0

3 years ago

The volume of the shape below is 6 square units. Determine the volume of the shape in two different ways.

REY [17]

The volume of the shape is 6 cubic units

<h3>How to determine the volume of the shape?</h3>

<u>Method 1</u>

From the figure, we can see that:

There are 6 cubes in the figure
The dimensions of the cubes are equal
The volume of each cube is 1 cubic unit

So, the volume of the shape is

Volume = Number of cubes * Volume of each cube

Substitute the known values in the above equation

Volume = 6 * 1

Evaluate

Volume = 6

<u>Method 2</u>

From the figure, we can see that:

There are 6 cubes in the figure
2 cubes at the top and 4 at the bottom
The dimensions of the cubes are equal
The volume of each cube is 1 cubic unit

So, the volume of the shape is

Volume = Top cubes + Bottom cubes

This gives

Volume = 2 * Volume of each cube + 4 * Volume of each cube

Substitute the known values in the above equation

Volume = 2 * 1 + 4 * 1

Evaluate

Volume = 6

Hence, the volume of the shape is 6 cubic units