Following the formula (-b+-√b^2-4ac) / 2a, working out -√b^2

7 square yards is equal to how many square meters? A. 2.58 square meters B. 3.50 square meters C. 5.85 square meters D. 14.25 sq

love history [14]

5.85289 so C.

1 square yard is equal to 0.836127 square meters.

7 0

3 years ago

Explain why the hypotenuses of the triangles below have the same slope.

andrew11 [14]

The hypotenuse of the two triangles have the same slope because they are in the same straight line and the slope of a straight line is constatn.

You can prove that in this way:

slope = rise / run = Δy / Δx

For the upper triangle: slope = (4 - 2) / (8 - 4) = 2 / 4 = 1 / 2

For the lower triangle: slope = (-1 - (-5)) / (- 2 - (-10)) = 4 / 8 = 1 / 2

So, this proves that the two slopes are the same: 1 / 2

3 0

4 years ago

Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. He realizes he doesn't have enough cash and instead takes on

Brums [2.3K]

Let x be the price of each pen and y be the price of each pencil. From the given, the equations that are described are,
6x + 8y = 8.50
4x + 4y = 5
Solving for x and y simultaneously gives an answer of x = 0.75 and y = 0.5.

Thus, each pen costs $0.75 and each pencil costs $0.50.

8 0

3 years ago

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

Convert <br>11 m^2 to yd^2

AveGali [126]

1 yd = 3 m

11/3 = 3.667 (rounded

11m^2 = 3.667yd^2

hope this helps

6 0

4 years ago

Following the formula (-b+-√b^2-4ac) / 2a, working out -√b^2 - 4ac) / 2a