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2 years ago

Find the gradient of the line 3y + 2x = 1 how to guys

Mathematics

1 answer:

kykrilka [37]2 years ago

5 0

Answer:

-2/3

Step-by-step explanation:

The gradient of a line is its slope. You can just convert the equation to slope-intercept form (y=mx+b where "m" is the gradient/slope):

3y + 2x = 1

3y = 1 - 2x

y = 1/3 - 2/3x

y = -2/3x + 1/3

So, as we can see, -2/3 is the gradient/slope of the line.

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Help me please and thanks

Diano4ka-milaya [45]

I believe it could be option 1

4 0

2 years ago

What is 51/7 by 31/9 in simplest form

konstantin123 [22]

Answer:

25,095238095 = 25 2⁄21

Step-by-step explanation:

Just multiply each denominator and numerator straight across and convert to a mixed number, decimal, or whatever you want.

I am joyous to assist you anytime.

3 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

3 years ago

An online pet store offers the hamster house shown in the figure below

nlexa [21]

Answer:

Step-by-step explanation:

8 0

2 years ago

Determine if y=-2x-7 and -y=2x+13 are parallel, perpendicular, coincide or none of these

Goryan [66]

If you move the negative on the left side of the second equation over to the right side, then we can see that the equation is equivalent to $y={-2x} - 13$ .

Remember that an equation $y = mx + b$ represents a line with slope $m$ and y-intercept $b$ . Since both equations given have a slope of -2, but have different y-intercepts, they are parallel.

4 0

2 years ago