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3 years ago

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A line passes through (2,-7)and (-3,3).Find the slope-intercept form of the equation of the line. Then fill in the value of the

slope, m, and the value of the y-intercept, b, below.

1 answer:

juin [17]3 years ago

6 0

Answer:

m = -2

b = 16.5

Step-by-step explanation:

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Jada Elena and Lin walked a total of 37 miles last week. jada walked 4 more miles that elena, and Lin walked 2 more miles than j

MA_775_DIABLO [31]

Answer:

Jada walked $13\ miles$

Elena walked $9\ miles$

Lin walked $15\ miles$

Step-by-step explanation:

Let

x----> total miles walked by Jada

y----> total miles walked by Elena

z----> total miles walked by Lin

we know that

$x+y+z=37$ -----> equation A

$x=y+4$ -----> $y=x-4$ ------> equation B

$z=x+2$ ------> equation C

Substitute equation C and equation B in equation A and solve for x

$x+(x-4)+(x+2)=37$

$3x=37+2$

$3x=39$

$x=13\ mi$

Find the value of y

$y=13-4=9\ mi$

Find the value of z

$z=13+2=15\ mi$

therefore

Jada walked $13\ miles$

Elena walked $9\ miles$

Lin walked $15\ miles$

3 0

3 years ago

Rectangle, Square, or Rhombus?

saveliy_v [14]

Answer:

maybe rhombus

Step-by-step explanation:

don't take my word for it

4 0

2 years ago

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A backpack that normally sells for $40 is on sale for $30. Find the percent decrease

pochemuha

It would be 40•.25=10 which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

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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 $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

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3 years ago

Which is greater -0.25 or 0.8

GrogVix [38]

0.8 is greater because it is a positive number..

5 0

3 years ago

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