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Degger [83]
3 years ago
8

What is the slope of the line through A(2, 6) and B(8, -1)

Mathematics
1 answer:
zimovet [89]3 years ago
5 0
A. -6/7

Because:
(2,6) (8,-1)

(x1,y1) (x2,y2)

x1 = 2. Y1=6. X2=8. Y2= -1.

Equation for slope is m = y2-y1
x2-x1
-1-6 = -7
8-2=6
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A negative number plus a positive number is a negative number.
ipn [44]

Answer:

Sometimes

Step-by-step explanation:

Examples:

-5 + 10 = 5   FALSE

-10 + 5 = -5  TRUE

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3 years ago
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Abbot is paid weekly for every hour he works. He worked 6 hours each day for 5 days last week. He earned $408, before taxes. Wri
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Answer:

p=13.6h

Step-by-step explanation:

if he works 6 hours a day for five days that's 30 hours. $408 divided by 30 hours is $13.6 per hour.

3 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
Who was the first president of united state
STatiana [176]
George Washington
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System of linear equations:
Vedmedyk [2.9K]

Answer:

x= 500 y= 1500

Step-by-step explanation:

Isolate x or y in the first equation

Isolating for x would be x= -y+2000

Substitute X=-y+2000 into equation 10x+20y=35000

10(-y+2000)+20y=35000

Exapnd the equation above and you should get y=1500

Same steps for finding x by isloating for y

3 0
3 years ago
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