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4 years ago

10. Determine the equation of a horizontal line that passes through (4,7).

Mathematics

1 answer:

Katen [24]4 years ago

3 0

Answer:

y = 7 is the desired equation

Step-by-step explanation:

If the line is horizontal, then its slope is zero (0). If this horizontal line passes through (4, 7), then y = 7 is the desired equation.

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HELP, WILL MARK BRAINLIEST+100 POINTS. PLEEEEES Square EFGH is drawn on a coordinate plane. Diagonal FH is on the line y − 3 = n

vova2212 [387]

1) Slope of diagonal GE: 3

2) Equation of the line: $x-y=P-Q$

3) Slope of the line: 1

4) y-intercept: 4

Step-by-step explanation:

Here the diagonal FH is given by the line with equation

$y-3=-\frac{1}{3}(x+9)$

This line is written in the form

$y-y_0 = m(x-x_0)$

where m is the slope of the line and $(x_0,y_0)$ are the coordinates of a point on the line.

Therefore, for line FH we have:

$m=-\frac{1}{3}$ (slope)

$(x_0,y_0)=(-9,3)$

Diagonal GE is perpendicular to diagonal FH (the diagonals in a square are perpendicular): this means that its slope must be equal to the inverse reciprocal of the slope of FH. THerefore, the slope of diagonal GE is

$m_{GE}=-\frac{1}{m_{FH}}=-\frac{1}{-1/3}=3$

Two lines are said to be parallel when they have same slope.

Here, we see that the line given in the plot passes through the points

$(x_1,y_1)=(0,5)\\(x_2,y_2)=(-3,2)$

Therefore the slope of the line shown is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{0-(-3)}=1$

This means that also the line that we want to find must have slope of 1:

$m=1$

Now we can use the following form to write the equation of this line:

$y-y_0 = m(x-x_0)$

where:

$m=1$

$(x_0, y_0)=(P,Q)$ is the point that must be on the line

Therefore,

$y-Q=1(x-P)\\y-Q=x-P\\x-y=P-Q$

In order to solve this problem, we have to find the slope of the side WV.

The coordinates of the two points are:

$V(a+5,b-1)\\W(a+3,b-3)$

Therefore, the slope of side WV is given by:

$m=\frac{y_W-y_V}{x_W-x_V}=\frac{(b-3)-(b-1)}{(a+3)-(a+5)}=\frac{-2}{-2}=1$

And we said that two lines are parallel if they have same slope: therefore, the slope of the line parallel to the line that contains side VW is also 1.

The line given in this problem has equation:

$y=\frac{4}{3}x+1$

where

$m=\frac{4}{3}$ is the slope of the line

$q=+1$ is the y-intercept of the line

Here we want to find the line perpendicular to the given line and passing through the point (4,1).

A line perpendicular to the given one must have a slope which is equal to the negative of the reciprocal of the original one, therefore:

$m'=-\frac{1}{m}=-\frac{1}{4/3}=-\frac{3}{4}$

Now we can use the form

$y-y_0 = m'(x-x_0)$

and the coordinates of the point are

$(x_0,y_0)=(4,1)$

Substituting,

$y-1=-\frac{3}{4}(x-4)\\y-1=-\frac{3}{4}x+3\\y=-\frac{3}{4}x+4$

We have written the line in the form $y=mx+q$ , with $q=4$ : so the y-intercept is 4.

Learn more about parallel and perpendicular lines:

brainly.com/question/3414323

brainly.com/question/3569195

#LearnwithBrainly

5 0

3 years ago

Read 2 more answers

The price of a personal computer was 42,000 last year. If there is a decrease of

prohojiy [21]

You'll calculate the amount it was decreased by :

15% is also 15/100

15/100 * 42000

The two 0's in 100 cut 2 of the 0's in 42000 making it :

15/1 * 420

15* 420 = 6300

So, 6300 is the amount that the price is decreased by, but the question says the price of the PC (personal computer) after the decrease has happened not the price it decreased by :

So,

42000 - 6300 = 35700.

4 0

4 years ago

can someone please help and explain to me on how to do this geometry question please?! Thank youuuuu!!! ❤

qaws [65]

There are 13 angles.
We know that $m\angle4=112$ and $m\angle12=105$ (11 angles)

1.

$m\angle2+m\angle3+m\angle4=180\qquad\qquad\text{linear angles}\\\\m\angle3+m\angle3+m\angle4=180\qquad\qquad m\angle2=m\angle3\\\\2m\angle3+m\angle4=180\\\\2m\angle3+112=180\\\\2m\angle3=180-112\\\\2m\angle3=68\quad|:2\\\\\boxed{m\angle3=34=m\angle2}$

(9 angles)

2.

$m\angle3+m\angle12+m\angle11=180\qquad\qquad\text{triangle}\\\\34+105+m\angle11=180\\\\139+m\angle11=180\\\\m\angle11=180-139\\\\\boxed{m\angle11=41}$

(8 angles)

3.

$m\angle12+m\angle13=180\qquad\qquad\text{linear angles}\\\\105+m\angle13=180\\\\m\angle13=180-105\\\\\boxed{m\angle 13=75}$

(7 angles)

4.

$m\angle1+m\angle2+m\angle13=180\qquad\qquad\text{triangle}\\\\m\angle1+34+75=180\\\\m\angle1+109=180\\\\m\angle1=180-109\\\\\boxed{m\angle1=71}$

(6 angles)

5.

$m\angle9=m\angle11\qquad\qquad\text{vertical angles}\\\\\boxed{m\angle9=41}$

(5 angles)

6.

$m\angle10+m\angle11=180\qquad\qquad\text{linear angles}\\\\m\angle10+41=180\\\\m\angle10=180-41\\\\\boxed{m\angle10=139}$

(4 angles)

7. $a||b\text{ and } c||d$ so we have a parallelogram.

$m\angle4+m\angle5=180\qquad\text{consecutive angles are supplementary}\\\\112+m\angle5=180\\\\m\angle5=180-112\\\\\boxed{m\angle5=68}$

(3 angles)

$m\angle8=m\angle5\qquad\qquad\text{opposite angels are congruent}\\\\\boxed{m\angle8=68}$

(2 angles)

8.

$m\angle7+m\angle8+m\angle9=180\qquad\qquad\text{triangle}\\\\m\angle7+68+41=180\\\\m\angle7+109=180\\\\m\angle7=180-109\\\\\boxed{m\angle7=71}$

(1 angle)

9.

$m\angle1+m\angle5+m\angle6=180\qquad\qquad\text{triangle}\\\\71+68+m\angle6=180\\\\139+m\angle6=180\\\\m\angle6=180-139\\\\\boxed{m\angle6=41}$

6 0

3 years ago

PLEASE HELP WILL MARK BRAINLY

Romashka-Z-Leto [24]

Step-by-step explanation:

diameter is 84 thereare 2 time 42 .84.

follow me nice study bye .

7 0

3 years ago

Ellen can buy bottles of water in packages of 6 for $10.98 or in packages of 4 for $8.92. How much money does she save by buying

Alona [7]

Answer:

Step-by-step explanation:

First divide 10.98 by 6 then 8.92 by 4 and subtract the two answers

4 0

3 years ago

Read 2 more answers