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2 years ago

Which is the graph of the line y - 2 = 3(x - 1)?

Mathematics

1 answer:

nirvana33 [79]2 years ago

5 0

Answer:

Graph D

Step-by-step explanation:

- Distribute 3 to x and -1 to get 3x-3

- To isolate y, add 2 to -3 to get -1

- -1 is your y-intercept, so the line starts there, and graph D is the only graph with a line that starts at -1

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What is 52,437 rounded to the nearest hundred?

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52400

Round the 400 down

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According to the graph, which range value corresponds to a domain value of 2?

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Simply put, domain means the x value and range means the y value.

The question asks for the corresponding range (y-value) for domain (x-value) of 2.

Looking at the graph, x value of 2 corresponds to y value of 4. So the answer is 4.

Correct answer is D

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Perform the Indicated Operation. (-18)-(4)

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3 years ago

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A ball is thrown vertically upwards with an initial velocity of 22 m/s. When will its speed be 10

gogolik [260]

Answer:

The ball's speed will be 10 m/s at t=1.22 seconds

Step-by-step explanation:

The vertical motion of an object is controlled by the force of gravity. This means that there is a non-zero net force acting on the object that makes it accelerate downwards.

If the object is thrown upwards at speed vo, its speed at time t is:

$v_f=v_o-g.t$

Where g is the acceleration of gravity $g=9.8 m/s^2.$

Our ball is thrown upwards with v0=22 m/s. We need to calculate the time when its speed is vf=10 m/s.

Solving the above equation for t:

$\displaystyle t=\frac{v_o-v_f}{g}$

Substituting:

$\displaystyle t=\frac{22-10}{9.8}=\frac{12}{9.8}$

t=1.22 seconds

The ball's speed will be 10 m/s at t=1.22 seconds

8 0

2 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

2 years ago