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3 years ago

Part B Find the total number of pounds of cheese ordered. A. 11 pounds B. 13 pounds C. 15 pounds D. 17 pounds

1 answer:

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The equation of line AB is y = 2x + 4. What is the equation of a line parallel to line AB in slope-intercept form that contains

hodyreva [135]

Answer:

Step-by-step explanation:

eq. of line parallel to AB is y=2x+a

if it passes through (3,-2) then

-2=2×3+a

a=-2-6=-8

y=2x-8

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3 years ago

Read 2 more answers

16. Let W be the set of all vectors in R3 of the form a+2b b -3a Find a basis for Wand state the dimension of W.

Yuki888 [10]

Answer:

$W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}$

Observe that if the vector $x=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ is in W then it satisfies:

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]$

This means that each vector in W can be expressed as a linear combination of the vectors $\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]$

Also we can see that those vectors are linear independent. Then the set

$\{\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]\}$ is a basis for W and the dimension of W is 2.

7 0

3 years ago

A water tank is leaking at a rate of 6 gallons per hour.

Vanyuwa [196]

The tank is leaking at the rate of 6 gallons per hour.

If you do nothing but sit there and watch it all afternoon,
here's what you'll see:

First hour . . . . 6 gallons leaks out
Second hour . another 6 gallons leaks out
Third hour . . . another 6 gallons leaks out

Total gone after 3 hours: (6 + 6 + 6) = 18 gallons .

7 0

3 years ago

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Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m2, and the area of circle

taurus [48]

Solution:

we are given that

Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m^2, and the area of circle R's sector is 49π m^2.

we have been asked to find the ratio of the radius of circle Q to the radius of circle R?

As we know that

Area of the sector is directly proportional to square of radius. So we can write

$Area \ \ \alpha \ \ r^2\\ \\ \Rightarrow A=kr^2\\ \\ \text{where k is some proportionality constant }\\ \\ \Rightarrow \frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}\\ \\ \Rightarrow \frac{r_1^2}{r_2^2}=\frac{A_1}{A_2}\\ \\ \Rightarrow \frac{r_1^2}{r_2^2}=\frac{25 \pi}{49 \pi}\\ \\ \Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{25 \pi}{49 \pi}} \\ \\ \Rightarrow \frac{r_1}{r_2}=\frac{5}{7} \\$

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3 years ago

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the sum of the digits of a two digit number is 10. if the digits are reversed, the new number will be 18 more than the original

bearhunter [10]

<span>t+u = 10
10u+t= 10t+u-54
Rearrange:
t+u=10
9t-9u=54
Simplify:

1st; t+u=10
2nd: t-u=6
Add 1st and 2nd and solve for t,as follows:
2t = 16
t = 8
Substitute in t+u=10 to solve for u:
8+u=10
u = 2
Original Number = 82</span>

3 0

3 years ago