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Brums [2.3K]
3 years ago
15

Which equations below represent lines that are perpendicular to the line that contains (1, - 2) and (3,4)^ Select all that apply

Mathematics
1 answer:
Nady [450]3 years ago
3 0

Answer:

Select all the lines with slope -\frac{1}{3}.

Step-by-step explanation:

Use the slopes to help you answer this kind of questions.

The slope of the line going through: (1, - 2) and (3,4) is given by:

m=\frac{y_2-y_1}{x_2-x_1}

We plug in the coordinates to get:

m=\frac{4--2}{3-1}=\frac{6}{2}=3

All lines that are perpendicular to this line has slope -\frac{1}{3}.

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Which Graph Shows a Linear Function?!!
NISA [10]

Answer:

bottom left

Step-by-step explanation:

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8 0
3 years ago
In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track
Aloiza [94]

Answer:

Approximately 0.31\; \rm m, assuming that g = 9.81\; \rm N \cdot kg^{-1}.

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned} .

Weight of the slide:

\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}.

Normal force between the sled and the slope:

\begin{aligned}F_{\rm N} &= W\cdot  \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}.

Calculate the kinetic friction between the sled and the slope:

\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}.

Assume that the sled and its passenger has reached a height of h meters relative to the base of the slope.

Gain in gravitational potential energy:

\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}.

Distance travelled along the slope:

\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}.

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}.

In other words, the sled and its passenger would have lost (approximately) ((137 + 68.1)\, h)\; {\rm J} of energy when it is at a height of h\; {\rm m}.

The initial amount of energy that the sled and its passenger possessed was \text{KE} = 63\; {\rm J}. All that much energy would have been converted when the sled is at its maximum height. Therefore, when h\; {\rm m} is the maximum height of the sled, the following equation would hold.

((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}.

Solve for h:

(137 + 68.1)\, h = 63.

\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}.

Therefore, the maximum height that this sled would reach would be approximately 0.31\; \rm m.

7 0
2 years ago
Branliest and 30 points
nignag [31]
1.
(3/4)^2 = (3/4)* (3/4)
(3/4)*(3/4)= 9/16

Final answer: 9/16

2.
11+6.4= 17.4

Final answer: 17.4

3.
9.5-2.8= 6.7

Final answer: 6.7
3 0
3 years ago
Read 2 more answers
Can someone help w number 4
strojnjashka [21]

Answer:

angle DFG = 49 degrees

angle JKL = 41 degrees

Step-by-step explanation:

When angles are complementary with each other, it means that if you add both of the angles up, it adds up to 90 degrees.

In this question, you would have to add up angle DFG and angle JKL and find the x that makes the equation equal to 90 degrees.

angle DFG = x + 5

angle JKL = x - 3

(x + 5) + (x - 3) = 90

2x + 2 = 90

2x = 90 - 2

2x = 88

x = 44

But since we have to find out the angle measures, we have to the "x = 44" with the x's in the DFG and JKL angles.

DFG = (44) + 5 = 49

JKL = (44) - 3 = 41

7 0
3 years ago
If it is April, then there are 30 days in the month.
dimaraw [331]

Answer:

C.

Step-by-step explanation:

It does not have to be April if there are 30 days. If its not April, it can still have 30 days. April does have 30 days.

6 0
3 years ago
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