Shona cycles at an average speed of 8km/h. How far has she travelled if she cycles for 4 hours

Write an equivalent expression for 7(2x - 3y + 6) by modeling and by using the distributive property.

alexandr402 [8]

14x-21y+42 is the answer to this question.

3 0

3 years ago

What is the value of x in the equation 25x2 = 16. A. 5/4. B. 4. C. 4/5. D. 16/25

Sergeeva-Olga [200]

Answer:

x = ⅘

Step-by-step explanation:

For clarity, exponents should be marked with a ^. 25x² can be written as 25x^2.

25x² = 16

divide both sides by the 25

x² = 16/25

take the square root of both sides

x = √(16/25) = √16/√25 = 4/5

6 0

3 years ago

The temperature at a ski resort was 12°F at 5:00 A.M. If the temperature increased by 1.5°F each hour, what would be the tempera

Mariana [72]

The <em><u>correct answer</u></em> is:

22.5° F.

Explanation:

The temperature increases 1.5° per hour. From 5:00 AM to 12:00 PM is 12-5 = 7 hours. This makes an increase of 1.5(7) = 10.5°.

The temperature started at 12°F; increasing by 10.5° gives us

12+10.5 = 22.5°F.

3 0

3 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .