Which prism has an volume of 6 cubic units? 1 3 1 1 2 1 12 2

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has

Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0), Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0

3 years ago

What is the answer ?

kifflom [539]

The system of inequalities is the following:

i) <span>y ≤ –0.75x
ii)</span><span>y ≤ 3x – 2

since </span> $0.75= \frac{75}{100}= \frac{3}{4}$ , we can write the system again as

$i) y \leq - \frac{3}{4}x$
$ii) y \leq 3x-2$

Whenever we are asked to sketch the solution of a system of linear inequalities, we:

1. Draw the lines
2. Color the regions of the inequalities.
3. The solution is the region colored twice.

A.

to draw the line $y =- \frac{3}{4}x$

consider the points: (-4, 1) and (0, 0), or any 2 other points (x,y) for which $y =- \frac{3}{4}x$ hold.

since we have an "smaller or equal to" inequality, the line is a solid line (not dashed, or dotted).

In order to find out which region of the line to color, consider a point not on the line, for example P(1, 1), which is clearly in the upper region of the line.

For (x, y)=(1, 1) the inequality $y \leq - \frac{3}{4}x$ , does not hold because

$1 \leq - \frac{3}{4}*1= -\frac{3}{4}$ is not true,

this means that the solution is the region of the line not containing (1, 1), as shown in picture 1.

B.
similarly, to draw the solution of inequality ii) y ≤ 3x – 2,

we first draw the line y=3x-2, using the points (0, -2) and (2, 4), or any other 2 points (x,y) for which y=3x-2 holds.

after we draw the line, we can check the point P(1, 7) which clearly is above the line y=3x-2.

for (x, y) = (1, 7), the inequality y ≤ 3x – 2 does not hold

because 7 is not ≤ 3*1-2=1, so the region we color is the one not containing P(1, 7), as shown in picture 2.

The solution of the system is the region colored with both colors, the solid lines included. Check picture 3.

the lines intersect at (0.533, -0.4) because:

–0.75x=3x-2
-0.75x-3x=-2
-3.75x=-2, that is x= -2/(-3.75)=0.533

for x=0.533, y=3x-2=3(0.533)-2=-0.4

Answer: Picture 3, the half-lines included. So the graph is in the 3rd and 4th Quadrants

8 0

3 years ago

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

kipiarov [429]

Answer:

The relationship between the circumference of a circle and its diameter represent a direct variation and the constant of proportionality is equal to the constant $\pi$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

$C=\pi D$

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant $\pi$

3 0

4 years ago

Help me please brainly

3241004551 [841]

Step-by-step explanation:

1)

3x+3

2)

10+2x

3)

8x+24

4)

8a+8b+8c

6 0

3 years ago

The following dataset represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80

neonofarm [45]

Answer:

yes

Step-by-step explanation:

The mode is the measure of the central tendency for the given data set. The mode represents the highest frequency of the number

Since in the given data set as we can see that the 100 would be appeared 6 times

So this represent that the mode is 100

So here the mode would be the good measure

3 0

3 years ago

Which prism has an volume of 6 cubic units? 1 3 1 1 2 1 12 2​

Which prism has an volume of 6 cubic units? 1 3 1 1 2 1 12 2