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3 years ago

If JM = 5x – 8 and LM = 2x – 6, which expression represents JL?

Mathematics

1 answer:

muminat3 years ago

8 0

Answer:

The expression represents JL is<u> 3x - 2</u>.

Step-by-step explanation:

Given:

JM = 5x – 8 and LM = 2x – 6.

Now, to find expression represents JL.

JM = JL + LM

<em>Subtracting both sides by LM we get:</em>

JM - LM = JL.

JL = JM - LM

Now, putting the expression to get JL:

$JL=5x-8-(2x-6)$

$JL=5x-8-2x+6$

$JL=3x-2.$

Therefore, the expression represents JL is 3x - 2.

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There are 24 hours in a day. If you want to convert days to hours, should you multiply or divide by 24?

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2 years ago

Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

What is the slope of this graph?

larisa [96]

Since the slope is falling, instead of rising, it would be negative.

Now, on the line, I plotted (0, 2) and (-2, 10).

You would now plug this into the rise/run formula.
The formula is $\frac{y2 - y1}{x2 - x1}$

The equation would become,
$\frac{10 - 2}{-2 - 0}$ = $\frac{8}{-2}$ = -4

I believe the answer would be -4.

I hope this helps!

6 0

3 years ago

For each graph below, state wether it represents a function.

Paul [167]

Answers:

Row 1: No, No, No

Row 2: Yes, Yes, Yes

===============================

Explanation:

Use the vertical line test. If it is at all possible to draw a single vertical line through more than one point on the relation curve, then the relation is not a function. This is because a function is only possible when any x input leads to exactly one y output.

So that's why graphs 1,2,3 are not functions, while graphs 4,5,6 are functions.

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3 years ago