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soldi70 [24.7K]
3 years ago
6

Work out the equation of a line which has a gradient of -2 and passes through the point (1 ,7)​

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
7 0

Answer:

Y=-2x+9

Step-by-step explanation:

The first thing is to know the formula which is Y÷x

Then... The line (1,7)use the coordinates Y and X so it will be as follows... Label 1 and 7 as x, y

So it will be Y-7÷X-1 = the gradient which is - 2

So multiply both sides by X-1

So it will be Y-7=2x+2 again be careful because a negative number multiplied by another negative will give you a positive sign

Remember Y-7....... Take 7 to the other side so it will be a positive...... Then work out the integers

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What is the value of the expression 8w−4j2 when w=0.25 and j=0.5?
Alex787 [66]

Answer:

-2

Step-by-step explanation:

3 0
3 years ago
PLZ HELP ME LLZ I WILL DO ANYTHING
____ [38]

Answer:

X=45

Step-by-step explanation:

45+3x=180

180-45=135

135/3=45

x has to be 45

x=45

4 0
3 years ago
What is the value of x, when 10(x + 2) = 5(x + 8)?
tatuchka [14]
The value of x is 4. The steps to solving the equation are to use distributive property first so that the equation then looks like this: 10x+20=5x+40
Next you would combine like terms and then the equation would look like this: 5x+20=40
Then you would use the subtraction property of equality to subtract 20 from 40 so your equation will now look like this: 5x=20
Then you use the division property of equality to divide 20 by 5 to get x=4
7 0
3 years ago
Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio
lina2011 [118]

Answer:

The point of intersection is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

y=0.5x+5

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:

(x-0)^2+(y-5)^2=(3)^2

Simplify:

x^2+(y-5)^2=9

At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:

x^2+((0.5x+5)-5)^2=9

Simplify:

x^2+(0.5x)^2=9

Square:

x^2+0.25x^2=9

Combine like terms:

\displaystyle 1.25x^2=\frac{5}{4}x^2=9

Solve for <em>x: </em>

<em />\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}<em />

Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.

To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:

\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34

So, the point of intersection in QI is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

6 0
3 years ago
A rectangular prism has a length of 114 yards, a width of 212 yards, and a height of 4 yards.
drek231 [11]

Answer: 96,672 yards cubed

Step-by-step explanation: The formula for the Volume of a rectangar prism is Length×Width×Height

114yds × 212yds × 4yds = 96,672yds^3

Its already in simplest form since its all yards

But, you can also convert it into miles

In which 1 mile = 1760 yards

So you'd divide 96670 by 1760, and what ever answer youget would be the answer in miles

8 0
3 years ago
Read 2 more answers
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