Find the equation of the median from B, in ABC whose vertices are A(1, 5), B(5, 3), and
C(-3, -2). Include a sketch.

Answers

Answer 1

Answer:

Step-by-step explanation:

Midpoint of AC = M(-1, 1.5)

Slope of BM = (1.5 - 3)/(-1 - 5) = ¼

Point-slope equation for line of slope ¼ that passes through B(5,3):

y-3 = ¼(x-5)

Find The Equation Of The Median From B, In ABC Whose Vertices Are A(1, 5), B(5, 3), AndC(-3, -2). Include

Related Questions

The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.

The restricted domain for ƒ is ?

Answers

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

-3u-17=(u+8)
simplify

Answers

Answer:

-25/4 = u

Step-by-step explanation:

-3u-17=(u+8)

Add 3u to each side

-3u+3u-17=(u+3u+8)

-17 = 4u +8

Subtract 8 from each side

-17-8 = 4u+8-8

-25 = 4u

Divide by 4

-25/4 = 4u/4

-25/4 = u

The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters

Answers

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

What is expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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I need the answer to this

Answers

Answer:

[tex]A)\:x<12[/tex]

[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]

OAmalOHopeO

Answer:

x < 12.................................

Express the set shown below in roster form. ​{x | x is a natural number less than -2}

Answers

Given:

The set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

To find:

The raster form of the given set.

Solution:

We know that, natural numbers are all positive integers.

Natural numbers: 1, 2, 3, 4,... .

The given set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

Here, x is a natural number and it is less than -2, which is not possible.

Since all natural numbers are greater than or equal to 1, therefore the given set has no element.

[tex]\{x|x\text{ is a natural number less than }-2=\phi[/tex]

Therefore, the roaster form of the given set is [tex]\phi[/tex] or [tex]\{\ \}[/tex].

prove that: cos^2 (45+A)+cos^2 (45-A)=1​

Answers

Answer:

see explanation

Step-by-step explanation:

Using the cosine addition formula

cos(A ± B ) = cosAcosB ∓ sinAsinB

Then considering the left side

cos²(45 + A) + cos²(45 - A)

= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²

= [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA - [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]² + [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA + [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]²

= [tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex] sin²A + [tex]\frac{1}{2}[/tex] cos²A + sinAcosA + [tex]\frac{1}{2}[/tex] sin²A

= cos²A + sin²A

= 1

= right side , then proven

Answer:

Step-by-step explanation:

cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1

2cos²x=1+cos2x

[tex]cos^2x=\frac{1}{2}(1+cos2x)[/tex]

cos²(45+A)+cos²(45-A)

[tex]=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1[/tex]

cos (90-x)=sin x

cos (90+x)=-sin x

Lisa made a shirt using 1/3 m of blue fabric and 3/5 m of red fabric how many meters of fabric did she use in all

Answers

Answer: 14/15 of a meter

Step-by-step explanation:

5 and 3 LCM is 15.

3/5 x 3 + 1/3 x 5= 9/15 + 5/ 15 = 14/15

If x2-y2 = 10 and x+y = 5, what is the value of x-y? 2-5?

Answers

Answer:

x-y=2

I don't get why they are asking you what is 2-5. That seems super basic compared to the other question it is with. Since 5-2=3, then 2-5 or -5+2=-3.

Step-by-step explanation:

We are going to use identity x^2-y^2=(x-y)(x+y)

x^2-y^2=10

(x-y)(x+y)=10

(x-y)(5)=10

Since (2)(5)=10, this implies x-y=2.

Which of the following is equal to -16?

Answers

Answer:

The last one. 4.

Step-by-step explanation:

The square root of a positive or negative number can't be negative. so it's positive 4.

The sum of 3 unequal odd numbers is 203. What may those numbers be? Give four possible answers.

Answers

Answer:

71, 69 and 63

71, 67 and 65

73, 67 and 63

75, 65 and 63

45 points! Hello! The area of a rectangular pool is given by the trinomial 4y2 + 6y – 10. What are the possible dimensions of the pool? Use factoring.
Thank you to however helps me!

Answers

Answer:

The dimensions are (2y+5) by 2(y-1) or 2(2y+5) by (y-1)

Step-by-step explanation:

4y^2 + 6y – 10

Factor the expression

Factor out the greatest common factor

2 ( 2y^2 +3y -5)

2 ( 2y+5) ( y-1)

A = l*w

The dimensions are (2y+5) by 2(y-1) or 2(2y+5) by (y-1)

A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 24 ft 3 / sec . Find the rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 ft. (You must also include the units)

Answers

Answer:

The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.

Step-by-step explanation:

The volume of the cone ([tex]V[/tex]), in cubic feet, is defined by the following equation:

[tex]V = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, in feet.

[tex]h[/tex] - Height, in feet.

And there is the following ratio of the radius to the height is:

[tex]\frac{r}{h} = k[/tex] (2)

By applying (2) in (1):

[tex]h = \frac{r}{k}[/tex]

[tex]V = \frac{\pi}{3\cdot k}\cdot r^{3}[/tex] (3)

And the rate of change of the radius is found by differentiating on (3):

[tex]\dot V = \frac{\pi}{k}\cdot r^{2}\cdot \dot r[/tex] (4)

Where:

[tex]\dot V[/tex] - Rate of change of the volume, in cubic feet per second.

[tex]\dot r[/tex] - Rate of change of the surface of the water, in feet per second.

[tex]\dot r = \frac{k\cdot \dot V}{\pi\cdot r^{2}}[/tex]

If we know that [tex]k = \frac{1}{3}[/tex], [tex]\dot V = 24\,\frac{ft^{3}}{s}[/tex] and [tex]r = 2\,ft[/tex], then the rate of change of the radius of the surface of the water is:

[tex]\dot r = \frac{\left(\frac{1}{3} \right)\cdot \left(24\,\frac{ft^{3}}{s} \right)}{\pi\cdot (2\,ft)^{2}}[/tex]

[tex]\dot r = 0.637\,\frac{ft}{s}[/tex]

The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.

Write the quadratic equation in standard form:
7x + 8 + 2x2
2x + 1 + x2

Answers

Answer:

[tex]3x^2 + 9x +9[/tex]

Step-by-step explanation:

Given

[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]

Required

The result in standard form

We have:

[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]

Remove brackets

[tex]7x + 8 + 2x^2 + 2x + 1 + x^2[/tex]

Collect like terms

[tex]7x+ 2x + 8 + 1 + 2x^2+ x^2[/tex]

[tex]9x + 9+ 3x^2[/tex]

The standard form of a quadratic equation is:

[tex]ax^2 + bx + c[/tex]

So, we have:

[tex]9x + 9+ 3x^2[/tex]

[tex]3x^2 + 9x +9[/tex]

You are walking from home to a grocery store you stop for a rest after 2/5 miles the grocery store is actually 3/4 miles from home how much farther do you have to walk

Answers

Answer:

7/20 mile farther

Step-by-step explanation:

Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:

3/4 - 2/5 = ?

Here the LCD is 20.  Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.

Then 3/4  - 2/5 = 15/20 - 8/20, or 7/20.

You still have 7/20 mile to walk to get home.

work out the equasion 39+(−13)

Answers

Answer:

39-13=26

Step-by-step explanation:

plus(minus)=minus

3 hundreds equal how many tens

Answers

Answer:

There are 30 tens in 3 hundred.

Step-by-step explanation:

there are thirty tens in 3 hundred

Solve 60 ÷ 5(1 + 1(1 + 1))

Answers

Answer:

Creo que es 36

Step-by-step explanation

:D

Answer:

36

Step-by-step explanation:

Find all points of intersection of the given curves. (Assume 0 blank.)
R= 1 - cos(Theta), r = 1 + sin(theta)

Answers

9514 1404 393

Answer:

POLE(1+(√2)/2, 3π/4)(1-(√2)/2, 7π/4)

Step-by-step explanation:

Your have correctly identified the points of intersection, but you need to follow directions in your entry of those answers. "POLE" goes in the first answer slot. You may also be expected to rationalize the denominator, or provide the r value as a single term.

The points of intersection are ...

  POLE

  ((2+√2)/2, 3π/4)

  ((2-√2)/2, 7π/4)

Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.

Answers

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Subtract the second equation from the first.
8x + 3y = 14
(4x + 3y = 8)
-
O A. 6y = 22
O B. 4x = 6
O c. -6y = 6
D. 12x = 22
Please help

Answers

Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

solve by completing the square method 3x²=15-4x ​

Answers

Answer:

Step-by-step explanation:

3x²=15-4x

divide by 3 on both sides

x²=5-[tex]\frac{4}{3}[/tex]x ​ ​

move everything to one side

x²+[tex]\frac{4}{3}[/tex]x ​-5 = 0

add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex]  but also subtract it too

x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]​-5-[tex]( \frac{2}{3} )^{2}[/tex]​ = 0

now use the property of a perfect square to rewrite

[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0

rewrite 5 as a fraction

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0

add up the fractions

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0

move to the other side

[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]

take the square root of both sides :P

[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex]  = [tex]\sqrt{\frac{49}{9} }[/tex]

much easier looking now, just use algebra to solve for x

x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]

subtract  [tex]\frac{2}{3}[/tex]  from both sides

x + [tex]\frac{2}{3}[/tex] -  [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]

x = [tex]\frac{5}{3}[/tex]

:)  

Answer:

x = - 3, x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Given

3x² =15 - 4x ( add 4x to both sides )

3x² + 4x = 15 ← factor out 3 from each term on the left side

3(x² + [tex]\frac{4}{3}[/tex] x) = 15

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + [tex]\frac{4}{3}[/tex] x

3(x² + 2([tex]\frac{2}{3}[/tex] )x + [tex]\frac{4}{9}[/tex] - [tex]\frac{4}{9}[/tex] ) = 15

3(x + [tex]\frac{2}{3}[/tex] )² - [tex]\frac{4}{3}[/tex] = 15 ( add [tex]\frac{4}{3}[/tex] to both sides )

3(x + [tex]\frac{2}{3}[/tex] )² = 15 + [tex]\frac{4}{3}[/tex] = [tex]\frac{49}{3}[/tex] ( divide both sides by 3 )

(x + [tex]\frac{2}{3}[/tex] )² = [tex]\frac{49}{9}[/tex] ( take the square root of both sides )

x + [tex]\frac{2}{3}[/tex] = ± [tex]\sqrt{\frac{49}{9} }[/tex] = ± [tex]\frac{7}{3}[/tex] ( subtract [tex]\frac{2}{3}[/tex] from both sides )

x = - [tex]\frac{2}{3}[/tex] ± [tex]\frac{7}{3}[/tex], then

x = - [tex]\frac{2}{3}[/tex] - [tex]\frac{7}{3}[/tex] = - 3

x = - [tex]\frac{2}{3}[/tex] + [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]

please help
find 0. ​

Answers

Answer:

0=70!!!!!!!!!!!!!!!!!!!!!!

❤❤❤❤❤❤I WILL MARK AS BRAINLIEST IF RIGHT PLEASE HELP ME PLEASE BE CORRECT BEFORE ANSWERING PLEASE AND THANK YOU.

TELL ME WHERE TO PUT EACH POINT OF THE TRIANGLE TY

Answers

Answer:

Please look at the picture

Step-by-step explanation:

Please look at the picture I have drawn it for you

What are the solutions to the equation

Answers

Answer:

(0,1) and (3,4)

Step-by-step explanation:

It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4

put them in the equation and you'll see the the values satisfies the equation

Answered by GAUTHMATH

use the figure to find y

Answers

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

3) Consider the sequence -11 ; 2sin3x ; 15; ...

3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic. ​

Answers

First term=a=-11
U1=a=-11
U3=a+2d=15
-11+2d=15
2d=26
d=13
2sin3x - (-11)=d
2sin3x=2
sin3x=1
sin(3x)=sin(90)
3x=90
x=30 degrees

I am having troubles finding x, need an explanation

Answers

Answer:

56+35=180 then solve it thanks

Answer:

Step-by-step explanation:

we have a two right triangle, with one side 115

lets say that the other side of the big right triangle is y

-in the big triangle find the third angle

180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180

tan 55 = opp. /adj= y / 115

y = 115 * tan 55

-in the small right triangle

tan 56 = opp./ adj. = 115 / y-x

y-x = 115/ tan 56 , subtract y from both sides

- x=  -y +( 115/tan 56), multiply by -1 both sides

x= y -(115/tan56), substitute y for 115 * tan 55

x= (115*tan 55)- (115/tan56)

x≅86.6685

HJ= 5x -3, JK= 8x -9 and KH= 131

Answers

Answer:

HJ = 52

JK = 79

Step-by-step explanation:

Hello, I want to assume you are trying to determine either HJ or JK. Below is an illustration of how to determine either HJ or JK.

From the question given above, the following data were obtained:

HJ = 5x – 3

JK = 8x – 9

KH = 131

If we draw a straight line, we'll observe the following:

H_______J_______K

KH = HJ + JK

Next, we shall determine the value of x.

HJ = 5x – 3

JK = 8x – 9

KH = 131

KH = HJ + JK

131 = (5x – 3) + (8x – 9)

131 = 5x – 3 + 8x – 9

Collect like terms

131 + 3 + 9 = 5x + 8x

143 = 13x

Divide both side by 13

x = 143 / 13

x = 11

Finally, we shall determine HJ and JK. This can be obtained as follow:

For HJ:

HJ = 5x – 3

x = 11

HJ = 5(11) – 3

HJ = 55 – 3

HJ = 52

For JK:

JK = 8x – 9

x = 11

JK = 8x – 9

JK = 8(11) – 9

JK = 88 – 9

JK = 79

Find the lateral area of this square based pyramid. 10in 5in (in the image)​

Answers

Answer:

100 in²

Step-by-step explanation:

4 triangles, each of them has area = 10*5/2

so total area = (10*5/2)*4

= (10*5*2)

= 100 in²

Answered by GAUTHMATH

The lateral surface area of the pyramid is 100 in²

What is surface area?

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.

4 triangles, each of them has an area = 10 x ( 5/2 )

So total area = (10 x 5/2) x 4

Total area = (10 x 5 x 2)

Total area = 100 in²

Therefore the lateral surface area of the pyramid is 100 in²

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Eddie is using his phone's calculator app to calculate 16,544 × 70. He accidentally enters 16,544 × 7 instead. How can he correct his mistake

Answers

Answer:

Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.

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