the orthocenter of a triangle is at the origin, and two of the vertices of the triangle are at (-5,0) and (3,4) Find the third vertex of the triangle

Answers

Answer 1

Answer:

  (3, -6)

Step-by-step explanation:

The orthocenter is the point of intersection of the altitudes of the triangle. That is, each altitude goes through the orthocenter. Hence, the line from any given vertex through the orthocenter is perpendicular to the opposite side.

The attached figure shows the given points labeled A and B. Point A lies on the x-axis, as does the orthocenter, so the side opposite will be a vertical line (perpendicular to the x-axis).

The remaining side of the triangle will be perpendicular to the line from B through the origin. The line through B has slope 4/3, so the line containing side AC will have slope -3/4 and will go through point A. Its point-slope equation will be ...

  y -0 = -3/4(x +5)

We already know the x-coordinate of vertex C is the same as that of vertex B, so is x=3. Using this in the equation for side AC, we find the y-coordinate to be ...

  y = -3/4(3 +5) = -6

The coordinates of point C, the third vertex, are (3, -6).

_____

Additional comments

The slope of a line is given by ...

  m = (y2 -y1)/(x2 -x1)

When (x1, y1) = (0, 0), this reduces to ...

  m = y2/x2 . . . . . . the relation we used for the slope of line OB

__

The slope of a perpendicular line is the opposite reciprocal of the slope of a line. The line perpendicular to the one with slope 4/3 will be -1/(4/3) = -3/4.

__

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

The Orthocenter Of A Triangle Is At The Origin, And Two Of The Vertices Of The Triangle Are At (-5,0)

Related Questions

One positive integer is 5 times another positive integer and their product is 320. What are the positive integers?​

Answers

Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
x = 5y
xy = 320

Substitute the first equation into the second equation
(5y)(y) = 320
5y^2 = 320
y^2 = 64
y = 8 (y must be positive)

The integers are (x, y) = (40, 8).

Given: Triangle ABC Prove: m∠A=64°

By the triangle sum theorem, the sum of the angles in a triangle is equal to . Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=64°.

Answers

Answer:

Given: Triangle ABC Prove: m∠A=64°

By the triangle sum theorem, the sum of the angles in a triangle is equal to . Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=150

The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.

Answers

Answer:

width(w)= 20inches

Step-by-step explanation:

solution,

given,

perimeter of a rectangle (P)=68inches

length of rectangle= 14 inches

we know,

perimeter of a rectangle=2L + 2W

or,68=2×14+2×w

or,68-28=2w

or,40=2w

or,w=40÷2

or,w=20inches.

Four squirrels have 30 berries each. But before they start watching, two more squirrels join the group. They share the berries equally amongst themselves. How many berries will each squirrel get to eat?

Answers

Answer:

5

Step-by-step explanation:

4+2=6

30 berrys so you do 30/6=5

line passes through the points (4,-2) and the slope is 5/4 write an equation in slope intercept form

Answers

Answer:

y=5/4x -7

Step-by-step explanation:

Hope this helps!

Based on the graph, what is true about polygon ABCD?

a. The polygon is a hexagon
b. The area of the polygon is 96 square units
c. The perimeter is 20 unit
d. Side AD is congruent to side DC

Answers

Answer:

B

Step-by-step explanation:

The Width of the Rectangle (read Polygon) is 8 units and the Length of the Rectangle is 12 units.

The area of the polygon is 96 square units. Therefore, the correct answer is option C.

From the given graph, we have polygon ABCD.

From the graph, we have AB=DC=12 units and BC=AD=8 units.

Here, the given polygon is rectangle.

Area of a rectangle = Length×Breadth

Now, area of a rectangle = 12×8

= 96 square units

Perimeter of a rectangle = 2(Length+Breadth)

= 2(12+8)

= 2(20)

= 40 units

Therefore, the correct answer is option C.

To learn more about the area of a rectangle visit:

https://brainly.com/question/20693059.

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Which equation correctly uses the law of cosines to solve for y? 92 = y2 + 192 – 2(y)(19)cos(41°) y2 = 92 + 192 – 2(y)(19)cos(41°) 92 = y2 + 192 – 2(9)(19)cos(41°) y2 = 92 + 192 – 2(9)(19)cos(41°) PLS HELP!!

Answers

Answer:

[tex]Fourth \: option: y^2=9^2+19^2-2(9)(19) cos(41°)[/tex]

[tex]The \: law \: of \: cosines \: to \: solve \: for \: one \: side  \: is:[/tex]

[tex]c^2=a^2+b^2-2ab \: cos \: C[/tex]

We must know the other two sides (a and b) and the angle between these sides (angle C, the opposite to the side that we want to determine)

In this case c=y, a=9, b=19, and C=41°, then:

[tex]y^2=9^2+19^2-2(9)(19) \: cos \: (41°)[/tex]

1+3+5+...+X=441
X=? ​

Answers

Answer:

559

Step-by-step explanation:

Please help me with this please

Answers

The answer is 30

1. Find the equilateral triangle angles in this case all of them are 60
2. 90-60 to right the opposite angle that is divided in the right angle
3. The answer should be the same as angle 2

What is the slope of the line?

Answers

3/1 is the answer follow the line

slope:change in x\change in y

Which type of correlation does this scatterplot show?

Answers

Positive correlation. Y varies directly with x. Meaning as x increases or decreases, Y will behave the same as x.

Which of the following is not considered a buying incentive?
a coupon
b. display
C. prize
d. rebate
Please select the best answer from the choices provided
A
B
C
D

Answers

Answer: B) Display

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

Explanation:

A buying incentive is anything that encourages any potential customers to become actual customers. Ideally, those people are repeat customers down the road as well (even if such buying incentives are no longer in place).

If someone sees a coupon or a rebate, then they'll be more likely to buy the item since the price is lower. A coupon is an immediate discount right on the spot, whereas a rebate is when you get a discount later on. A rebate means you have to mail in proof of purchase, and the company will send money back. These are two ways to apply a discount.

A third way to entice customers is to offer prizes. An example of this is a "buy one get one" sale (often abbreviated as BOGO). The company may lose money doing this, but they do so in the hopes of gaining new customers. Plus word of mouth tends to spread more often when such sales occur.

With everything discussed so far, this allows us to rule out choices A, C and D. They are all some kind of way to encourage potential buyers. Choice B is the answer because a display simply shows the price and any other relevant info to the product. Displays are neutral in the sense that they don't encourage a purchase and rather just convey information. When I mention this, I'm not talking about displays that advertise discounts or coupons.

Find the area for each of the given shapes below. If a shape has shading, find the area of the shaded region only.

Answers

Answer:

  a.  39 ft²

  c. 2x² +11x +12

  e. 35 yd²

Step-by-step explanation:

a.

The missing vertical dimension is 5-3 = 2'. The missing horizontal dimension is 11-8 = 3'. Then the figure can be decomposed into a rectangle 11'×3' and one that is 3'×2'. The sum of those areas is ...

  total area = (11 ft)(3 ft) +(3 ft)(2 f) = (3 ft)(11 +2 ft) = (3 ft)(13 ft) = 39 ft²

__

c.

We don't know what to make of the rectangles in each corner, so we'll assume they are distorted right-angle indicators. The area is the product of the dimensions shown:

  A = LW

  A = (2x +3)(x +4) = 2x² +11x +12 . . . area of figure

__

e.

The shaded area is half the area of the rectangle. That is the same area you get if you use the triangle formula for the area of the shaded triangle.

  A = 1/2(14 yd)(5 yd) = 35 yd²

In AJKL, j = 75 cm, k = 23 cm and

Answers

Answer:

The length of side j is 11.85cm

Step-by-step explanation:

Given that

In triangle JKL,

Side k=LJ=3.7cm

To find side j=KL:

By using sine rule,

We can write as

Using property of triangle,

Thus,

The length of side j is 11.85cm

guys help plzz i need your help

Answers

Answer:

it correct because i took this before



Which term has the definition "A relationship in which two variables change at the same rate

Answers

positive correlation

(i believe thats what it is)

Which equation has the same solution as w / 3.9 = 3? A. w+0.6=1.9 B. w-0.6 = 11.1 C. w+1.03=2.93 D. w-1.03=8.24

Answers

The equation has the same solution as w / 3.9 = 3 is w+0.6=1.9

Given:

w / 3.9 = 3

cross multiply

w × 3 = 3.9

3w = 3.9

divide both sides by 3

w = 3.9 / 3

w = 1.3

Check all that applies

A. w+0.6=1.9

w = 1.9 - 0.6

w = 1.3

B. w-0.6 = 11.1

w = 11.1 + 0.6

w = 11.7

C. w+1.03=2.93

w = 2.93 - 1.03

w = 1.9

D. w-1.03=8.24

w = 8.24 + 1.03

w = 9.27

Therefore, the equation has the same solution as w / 3.9 = 3 is w+0.6=1.9

Learn more about equation:

https://brainly.com/question/2972832

23x25 = please help ​

Answers

Answer:

575

Step-by-step explanation:

23/4 = 5.75 times 100

Answer:

575

Step-by-step explanation:

23×25=575 so 575 would be your answer

Find the equation of a line that intersects with y=2x-1 on the y-axis and is parallel to y=-x. Please explain.

Answers

Answer:

so where does that line intersect the y axis? just plug in x=0 and you see y= -1. so (0, -1)

y = -x -1 is parallel because it has the same slope and goes through the right point

A 20 cm long thin wire is used to form a square. What is the area of the square?

Answers

Answer:

25cm^2

Step-by-step explanation:

A square has 4 equal sides so each side will be 20/4 = 5cm

Easily calculate the area by taking 5 x 5 = 25cm^2

Plz help me well mark brainliest only if correct!…

Answers

B. Is the answer. As it is the best simplest form

please help me with this math problem please I need help

Answers

is 1.25 because you just add them together

An office clerk earns $120 for two 4-hour work shifts. How much will she earn
for 15 hours of work?

Answers

Answer:

$225

Step-by-step explanation:

$120 for 2 4-hour shifts, $120 in 8 hours

$15 every 1 hour

Money for 15 hours: 15 x 15 = $225

The office clerk earns $225 for 15 hour of work .

What is unitary method?

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

According to the question

An office clerk earns $120 for two 4-hour work shifts.

i.e

In 2 * 4-hour work shifts office clerk  earns = $120

or

In 8 hour work shifts office clerk earns = $120

Now ,

By using unitary method

In 1 hour  work shifts office clerk earns = $[tex]\frac{120}{8}[/tex]

                                                                = $15

Therefore, for 15 hours of work shifts office clerk earns =  $15 * 15

                                                                                          = $225

Hence, The office clerk earns $225 for 15 hour of work .

To know more about unitary method here:

https://brainly.com/question/23423168

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Evaluate g(10) of g(x) =1/2x -4

Answers

Answer:

g(x)= 1

Step-by-step explanation:

[tex]g(x) = \frac{1}{2} x - 4 \\g(10) = \frac{1}{2} (10) = 5 \\ 5 - 4 = 1[/tex]

Write the square root -10 in simplest radical form

Answers

Answer:

The square root of 10 is expressed as √10 in the radical form and as (10)½ or (10)0.5 in the exponent form. The square root of 10 rounded up to 10 decimal places is 3.1622776602

Step-by-step explanation:

hope this is correct

Can someone check my answer?? PLEASE-

The length of a rectangle is six more than the width. If the perimeter of the rectangle is 40 ft, find the length of the rectangle.

A. 13 ft (what I think) ****

B. 7 ft

C. 23 ft

D. 17 ft

Answers

Answer:

the length of the rectangle is 13 ft.

Step-by-step explanation:

width of a rectangle x ft

length of a rectangle x+6 ft

the perimeter of the rectangle is 40 ft,

2(x+x+6) = 40

2x+6 = 20

2x = 14

x = 7

So the length of the rectangle is x+6 = 7+6 = 13 ft

congrats you're right (≧▽≦)!!

Answer:

The correct answer ia A)13 ft

Step-by-step explanation:

hope this helps

Heheh... uhm, yeah, I don't do best with algebraic questions-

Answers

Answer:it's a for sure I think


[tex]2 log_{3}(8) - 3 log_{3}(2) [/tex]
what is the answer to the question​

Answers

We have:   2log₃(8) - 3log₃(2) = 2log₃(8) - log₃(2³)

= 2log₃(8) - log₃(8) =  log₃(8)

= 1,892789261 ≈ 1,9

ok done. Thank to me :>

Answer:

~1.8928 or 3log_3 (2)

Step-by-step explanation:

change 8 to 2^3 and move to front

=2*3log_3 (2) -3log_3 (2)

=6log_3 (2) -3log_3 (2)

with subtraction

=3log_3 (2)

approx with calculator

~1.8928

.I want a way to solve this question​

Answers

Check the picture below.

so then γ ≈ 180 - 69 - 43, γ ≈ 68.

I need this soon pls

Answers

3 -4 is the answer

Its (x, y) so the x is first and the y is last
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