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3 years ago

6

12 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will eac

h pot hold? as a mixed number as a mixed

1 answer:

Oksanka [162]3 years ago

4 0

Answer:

2.4 or 12/5 or 2 2/5

Step-by-step explanation:

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Write the equation of the line from the given information. slope 1/2, through (4,-3)

wariber [46]

Answer:

y+3 = 1/2 (x-4)

Step-by-step explanation:

We can write the equation in point slope form

y-y1 = m(x-x1)

The slope is m and the point is (x1,y1)

y - -3 = 1/2(x -4)

y+3 = 1/2 (x-4)

5 0

3 years ago

2. What is the approximate value of b in the triangle below?

s344n2d4d5 [400]

Answer:

d) 17.6

Step-by-step explanation:

Use the law of Sines

SinA/a=SinB/b=SinC/c

6 0

3 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

Write an algebraic expression for " the minimum value of 2x + 1 is 13"

bezimeni [28]

2x+1=13 x=6 so an ok answer would be: 2x+10=40 x=15

6 0

4 years ago

Find the common ratio of the sequence. –172, –86, –43, –21.5, . . .

seropon [69]

If you divide each number by the previous one, you get:

-86 / -172 = 1/2
-43 / -86 = 1/2
-21.5 / -43 = 1/2

The common ratio is 1/2 = 0.5

4 0

4 years ago

Read 2 more answers