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3 years ago

A line contains the points (-1, 6), (6, k) and (20, 3). What is the value of k?

1 answer:

7 0

Consider, pls, this option:
1. if a required line has a form y=ax+b, then points A(-1;6); B(6;k) and C(20;3) belong to it.
2. According to the item 1 it is possible to make up the system of equations for A and C:
$\left \{ {{-a+b=6} \atop {20a+b=3}} \right \ \left \{ {{a=- \frac{1}{7} } \atop {b= \frac{41}{7} }} \right.$
Knowing, that a=-1/7 and b=41/7, it is possible to write the equation of required line:
$y=- \frac{1}{7}x+ \frac{41}{7}$
3. Using coordinates of point B:
$k=- \frac{6}{7}+ \frac{41}{7} =5 \ where \ k=y$

Answer: 5.

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Eight hundred registered voters were asked whether they would vote yes or no on a certain measure. If 38% of those polled said y

Ivan

100%-38%= 62%
To find the decimal of 62%, we will have to divide 62 by 100 to get 0.62.

0.62(800)= 496.

Therefore, 496 people will vote no.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Work out the size of the angle X.<br><br> Give your answer correct to 3 significant figures.

aleksley [76]

Step-by-step explanation:

Recall the Ratio for tan

Tan(theta) = opposite / adjacent

Tan (x) = 9 / 5

solve for x (use Tan^-1(...) )

3 0

2 years ago

Read 2 more answers

Algebra 1

zhannawk [14.2K]

Answer:

The actual wide of the lawn is 24 meters

Step-by-step explanation:

we know that

The scale drawing is

$\frac{2}{1}\frac{mm}{m}$

using proportion

Find out how wide is the actual lawn if the lawn is 48 millimeters in the drawing

Let

x -----> the actual wide of the lawn

$\frac{2}{1}\frac{mm}{m}=\frac{48}{x}\frac{mm}{m}\\\\x=48/2\\\\x=24\ m$

therefore

The actual wide of the lawn is 24 meters

6 0

3 years ago

Rectangle ABCD has vertices at (-7,-2); (1, -2); (1, -8); and (-7, -8) respectively. If GHJK is a similar rectangle where G(2, 5

Minchanka [31]

Answer:

J (6,2) K (2,2)

Step-by-step explanation:

Now distance of AB = [(y2-y1)^2 + (x2-x1)^2]^(1/2)

= 8 units

CB = [(y2-y1)^2 + (x2-x1)^2]^(1/2)

= 6 units by using same formula

Now AB/CB must equal to GH/HJ as rectangles are similar

GH = [(y2-y1)^2 + (x2-x1)^2]^(1/2)

= 4 units

8/6 = 4/HJ

So,

HJ = 3 units

Now if we see the coordinates given carefully, it is obvious that two perpendicular lines lie perfectly parallel to x and y coordinates in rectangle ABCD. A is (-7,-2) and B is (1,-2) which means distance along y-axis doesn't change. Similarly for C (1,-8) and D (-7,-8), one can see that distance between y-axis doesn't change. So lines AB and CD of rectangle are parallel with x and AD and BC are parallel with y-axis.

In rectangle GHJK one can see that in given coordinates, G(2,5) and H(6,5), y coordinate is same so it is parallel to x axis. Now, HJ is perpendicular to GH so it must be parallel to y axis. It means if we know the lengths of sides we can easily determine unknown coordinates by simple addition and subtraction.

So, we know HJ = 3 units

J is (6,2) since HJ is parallel to y axis so distance on x axis will remain unchanged and length of line HJ will effect distance of y axis.

Similarly K is (2,2) for the same reason.

6 0

3 years ago

Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0

maria [59]

The function, as presented here, is ambiguous in terms of what's being deivded by what. For the sake of example, I will assume that you meant

3x+5a
<span> f(x)= ------------
</span> x^2-a^2

You are saying that the derivative of this function is 0 when x=12. Let's differentiate f(x) with respect to x and then let x = 12:

(x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
[x^2-a^2]^2

(144-a^2)(3) - (36+5a)(24)
------------------------------------ = 0
[ ]^2

Simplifying,

(144-a^2) - 8(36+5a) = 0

144 - a^2 - 288 - 40a = 0

This can be rewritten as a quadratic in standard form:

-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.

Solve for a by completing the square:

a^2 + 40a + 20^2 - 20^2 + 144 = 0
(a+20)^2 = 400 - 144 = 156

Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

Finally, a = -20 plus or minus 2sqrt(39)

You must check both answers by subst. into the original equation. Only if the result(s) is(are) true is your solution (value of a) correct.

6 0

3 years ago