The points A,B and C have coordinates (2,1), (b,3) and (5,5), where b>5 and angle ABC = 90 degrees. Find b.

Answers

Answer 1

Answer:

b=6

Step-by-step explanation:

modul of the vector AB= sqrt((b-2)^2+(3-1)^2)= sqrt (b^2-4b+8). It is the length of the side AB

modul of the vector BC is equal to sqrt ((b-5)^2+(-2)^2)= sqrt (b^2-10b+29)

modul of the vector AC is sqrt ((5-2)^2+(5-1)^2)= 5

squared modul of AB + squared modul of BC = squared modul of the vector AC.

b^2-4b+8+b^2-10b+29=25

2b^2-14b+12=0

b^2-7b+6=0

b=1    b=6

b>5, s0 b=6


Related Questions

Paul, Than, and Mike have each consumed four beers in the last two hours. Paul weighs 220 pounds, Than weighs 155 pounds, and Mike weighs 197 pounds. Who has the highest blood alcohol concentration (BAC)

Answers

Answer:

Than would

Step-by-step explanation:

since he has the lowest weight then the alcohol concentration has less place to go making his higher.

I need help guys like rn please someone!!

Answers

Answer:

B

Step-by-step explanation:

The correct answer is B, because you have -4 +(-6)+(-2) which is really just

-4-6-2 which is -12. Think of it as getting rid of the plus sign and just leaving the negative sign. Which this would make the answer to the equation be -12, but for the answer of the question, it would be B because it is accumulating the drops in temperatures making the numbers go down in temperature, therefore making them negative.

A is not the answer because although it is similar to letter B, the difference is the final sentence, "What was the overall change in temperature?" Since -4 is listed as the pre-existing temperature, that would make -6 - 2 be equal to negative eight (-8).

C is not the answer because it includes a temperature rising by 18 degrees.

D is not the answer either because it is saying the temperature rose, which is shouldn't have risen.

The only time C and D could be right, is if they included bigger number that equaled out to negative twelve (-12), like saying the temperature rose 18 degrees, but fell by 26 degrees by midnight, that would make the equation look like -4 + 18 - 26 = - 12

Even in that case, C and D would be wrong immediately because of the use of numbers outside of the expression given.

Hope this helps!

PLEASE HELP ME!!!!!!

Answers

Answer:

This is the graph. The 5 points you can plot can be:

roots: (-6, 0) and (-2, 0)

vertex: (-4, -4)

two other random points to complete the 5 points:

(-5, -3) and (-3, -3)

20 labourers complete the construction of a building in 24 days.in how many days would 16 labourers complete the work in 12 days ?​

Answers

Answer:

Step-by-step explanation:

Please help me with this! Write the equation of the line in fully simplified slope intercept form. Explanation and answer please ^^

Answers

Answer:

y = -1/2x - 8

Step-by-step explanation:

y = -1/2x - 8

y=-1/2x-8 would be your answer

2a+3 =(6 + 4a)
Is it true or false

Answers

Answer:

false

I hope it's helps you

Answer:

[tex]2a + 3 = (6 + 4a) \\ \\ it \: is \: false[/tex]

i need help asap can one of yall help me !

Answers

Answer:

(2,-1)

Step-by-step explanation:

please help me with this :(((((​

Answers

Answer:

B

Solution,

2x+8x

.

. . 10x Ans#

Answer the question about the angles below.

Answers

To find angle Y, take 180 degrees (linear pair) minus 35 degrees (angle X).
180-35=145 degrees
Angle Y=145 degrees
Angle W is also 145 degrees since it’s a vertical angle to Angle Y.
To find angle N, take 90 degrees (complementary angle) minus 55 degrees (angle M).
90-55=35 degrees
Angle N=35 degrees
Hope this helped!

What is the equation of the line that passes through the point (8,1) and has a slope
of –3/4?

Answers

Answer:

[tex]y=-\frac{3}{4}x+7[/tex]

Step-by-step explanation:

The slope is already given as [tex]-\frac{3}{4}[/tex] so all we have to do is solve for y-intercept

First, write the equation in slope-intercept form

[tex]y=-\frac{3}{4}x+b[/tex]

Next, use the point to substitute the x and y value and solve for the y-intercept

[tex]y=-\frac{3}{4} x+b[/tex] where b = y-intercept

point: (8, 1)

[tex]1=-\frac{3}{4}(8)+b[/tex]

Then multiply 8 and -3/4

[tex]1=-6+b[/tex]

Finally, solve for the b (y-intercept)

b = [tex]1--6[/tex]

b = 7

so the y-intercept is 7

And the equation of the line that passes through the point (8, 1) and has a slope of -3/4 is [tex]y=-\frac{3}{4}x+7[/tex]

I've been stuck on this for a while now​

Answers

Answer:

-8 1/3 or -8.333

Step-by-step explanation:

10/3 = x/( - 5/2)

Simplify - 5/2

10/3 = x/-2.5

Multiply -2.5 by 10

-25

Divide it by 3

-8.333

Answer:

x = -25/3

Step-by-step explanation:

[tex] \frac{10}{3} = \frac{x}{ (\frac{ - 5}{2} )} \\ = > \frac{10}{3} \times \frac{ - 5}{2} = x \\ = > \frac{ - 50}{6} = x \\ = > \frac{ - 25}{3} = x [/tex]

I wrote a cheque for $10 and he threw my 2 dollar how much do I have left​

Answers

Answer:

you have $ 8

Step-by-step explanation:

cheque wrote ,=$10

and he threw =$2

then total $ left will be $8

please mark me brainleast

how do you find a positive/negative interval?

Answers

Answer:

we need to see that weather it is in positive form or negative form

positive means add

negative means subtract

If ƒ (x ) = 3x2 - x, find ƒ (-2).

I literally have no idea what I'm looking at....maybe I should've paid better attention leading up to the test.

Answers

f(x)=3x^2-x

[tex]\\ \rm\longmapsto f(-2)[/tex]

[tex]\\ \rm\longmapsto 3(-2)^2-(-2)[/tex]

[tex]\\ \rm\longmapsto 3(4)-(-2)[/tex]

[tex]\\ \rm\longmapsto 12-(-2)[/tex]

[tex]\\ \rm\longmapsto 12+2[/tex]

[tex]\\ \rm\longmapsto 14[/tex]

Answer:

14

Step-by-step explanation:

f(x) = 3x² - x

To find f(-2), substitute -2 for x into the function f.

f(-2) = 3(-2)² - (-2)

Now, use PEMDAS to evaluate the function.

Start by evaluating the exponent.

f(-2) = 3(4) - (-2)

Next, multiply 3 and 4 and -2 by -1.

f(-2) = 12 + 2

Add the two terms together.

f(-2) = 14

The correct answer is f(-2) = 14.

P= lw+wh, solve for w

Answers

Step-by-step explanation:

P= w(l+h)

w=P/(l+h)

....

53g=2g-23g+2 solve g

Answers

[tex] \begin{cases}\large\bf{\red{ \implies}} \tt \: 53 \: g \: = \: 2 \: g \: - \: 23 \: g \: + \: 2 \\ \\ \large\bf{\red{ \implies}} \tt \: 53 \: g \: = \: - 21 \: g \: + \: 2 \\ \\ \large\bf{\red{ \implies}} \tt \: 53 \:g \: + \: 21 \: g \: = \: 2 \\ \\ \large\bf{\red{ \implies}} \tt \: 74 \:g \: = \: 2 \\ \\ \large\bf{\red{ \implies}} \tt \:g \: = \: \cancel\frac{2}{74} \\ \\ \large\bf{\red{ \implies}} \tt \: g \: = \: \frac{1}{37} \end{cases}[/tex]

The value of g from the given equation is 1/37.

The given equation is 53g=2g-23g+2.

We need to solve the given equation for g.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 53g=2g-23g+2 can be solved for g as follows:

That is, 53g=-21g+2

⇒53g+21g=2

⇒74g=2

⇒g=2/74=1/37

Therefore, the value of g from the given equation is 1/37.

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Please I need help ASAP, I don’t understand anything and it’s due tomorrow

Answers

Answer:

Alright, here we go.

11. Those are vertical angles.  All vertical angles are equal.

6x + 7 = 8x - 17

2x = 24

x = 12

12. Those are linear angles (adjacent angles on a line).  Linear angles = 180.

(11x - 15) + (5x - 13) = 180

16x - 28 = 180

16x = 208

x = 13

13. If BD is perpendicular to AC, that means ∠ABD and ∠CBD = 90°.  ∠CBD is made up of angle DBE, which equals (2x - 1)° and angle CBE, which equals (5x - 42)°.  

(5x - 42) + (2x - 1) = 90

7x - 43 = 90

7x = 133

x = 19

14. Angles PQS and SQR are equal and halves of angle PQR because of bisector QS.  If PQR = 82°, angle PQS = 41°

10x + 1 = 41

10x = 40

x = 4

15. If the bottom angle is (x + 10)°, then the top angle is also (x + 10)° because they're vertical angles.  Angle (x + 10) and angle (10x - 61) are linear  angles, so they equal 180.

(x + 10) + (10x - 61) = 180

11x - 51 = 180

11x = 231

x = 21

As for y, insert 21 as x for (10x - 61).  

10(21) - 61

210 - 61

149

(18y + 5) should also equal 149° bc of vertical angles.

18y + 5 = 149

18y = 144

y = 8

x = 21

y = 8

(16 is crossed off so I'm going to assume you're not doing that one.)

17. If angle MNQ = (8x + 12)°, and it's bisected by NP, we can say that angles MNP and PNQ are equal halves of  (4x + 6)°.  Now, we were told that angle PNQ = 78°.

4x + 6 = 78

4x = 72

x = 18

This means that angle MNQ = 78 x 2, which is 156.

Now to find y, we see that angles MNQ and RNM are linear angles, so we can say:

(3y - 9) + 156 = 180

3y - 9 = 24

3y = 33

y = 11

x = 18

y = 11

(This took a while.)

If Caleb bought 1.2 pounds of cheese that was selling for 5.95 per pound. How much did Caleb pay for the cheese.​

Answers

Answer:

$7.14

Step-by-step explanation:

If each pound of cheese is $5.95. You just have to find out how much 1.2 pounds is worth. So, you multiply 5.95 times 1.2 pounds and you'll get $7.14

Multiplication is the process of multiplying. The total amount that Caleb needs to make for 1.2 pounds of cheese at a rate of $5.95 per pound is $7.14.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that the rate of cheese per pound is $5.95 per pound. Therefore, the amount that Caleb needs to make for 1.2 pounds of cheese is,

Total Amount = $5.95/pound × 1.2 pounds

                       = $7.14

hence, the total amount that Caleb needs to make for 1.2 pounds of cheese at a rate of $5.95 per pound is $7.14.

Learn more about Multiplication here:

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please guys someone help i need the answer

Answers

Step-by-step explanation:

2x + y + x+ 2y = 180

3x + 3y = 180

3y +20+2x+y=180

4y + 2x = 160

3x + 3y = 180

2x + 4y = 160

elimination

6x + 6y= 360

6x + 12y = 480

= 6y = 120

y= 20

substitute

3x + 3y = 180

3x + 3(20)= 180

3x + 60 = 180

3x = 120

x= 40

x+2y

40+2(20)=80

<4=<8= 80°

<7=180-<8=<180-80= 100°

angle 7 = 100°

angle 8 = 80°

what us the place value of 4965​

Answers

Answer:

thousdand

Step-by-step explanation:

5is in units place

6 is in tens place

9 is in hundreds place

4 is in thousands place

if the distance between town a and b is 1350 KM and the distance between town A and C is in the same direction is approximately two fifth of this. what is the approximate distance of town B and C​

Answers

Answer:

BC = 810 KM

Step-by-step explanation:

It is 2/5 from A to C so the remaining distance 1 -2/5 = 5/5 -2/5 = 3/5 is the distance from C to B

BC = 3/5 * 1350

BC = 810 KM

Expand an expression by using the distributive property.
Example: 3(y + 8) = 3 • y +3 • 8 = 3y + 24
(Reminder: 3 • y is the same as 3 x y or 3y.)
Expand this expression. 8(2x – 4)

Answers

The answer is 16x-32

i got the answer 25 did i do it wrong please help if i did

Answers

You did it right ! Great Job

change 105/7 into a mixed fraction

Answers

Answer:

15 0/1

Step-by-step explanation:



Three-quarters of a number is 2 bigger than two-thirds of the number.
Determine the number.

Answers

Answer:

0

Step-by-step explanation:

3/4.x = 2. 2/3.x

↔ x = 0

The required  number after simplification of the given statement of the equation is equal to 24.

Let's call the number we want to find "x."

According to the given information:

Three-quarters of the number is 2 bigger than two-thirds of the number.

Mathematically, we can express this as the following equation:

(3/4) × x = (2/3) × x + 2

Now, let's solve for "x":

Get rid of the fractions by multiplying everything by the least common multiple (LCM) of 4 and 3, which is 12.

12× (3/4) × x = 12 × (2/3) × x + 12× 2

Simplify both sides:

9x = 8x + 24

Isolate the "x" term on one side. To do this, we need to move the 8x to the left side by subtracting 8x from both sides:

9x - 8x = 8x + 24 - 8x

Simplify further:

x = 24

Therefore, the number after simplification is 24.

learn more about simplification here

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The width of a rectangle
is 11 feet longer than the
length. The perimeter of the The rectangle is 70 feet. Find the length and the width.

Answers

Answer:

Hello! The answer to this problem is Length= 27 and Width= 8

Step-by-step explanation:

2(11+2x) +2x = 70

6x + 22 = 70

6x = 48

x = 8

Answer:

Length = 23 feet and width = 12 feet.

Step-by-step explanation:

The width (W) = x and the length (L)  is x+11 feet   (length must be longer than width).

Perimeter = 2W + 2L = 70

2x + 2(x + 11) = 70

2x + 2x + 22 = 70

4x + 22 = 70

4x =- 70 - 22 = 48

x = 12 = width

So length = 12 + 11 = 23.

Use the story graph of each problem to fill in the blanks of the following sentence frames below.

In problem #1 the motion of the objects starts at ___ seconds and ends at ___ seconds.

The motion of the objects starts at ___ meters and ends at ___ meters.

The objects traveled ___ meters in ____ seconds.

In problem #2 the motion of the objects starts at ___ seconds and ends at ___ seconds.

The motion of the objects starts at ___ meters and ends at ___ meters.

The objects traveled ___ meters in ____ seconds.

Answers

I DONT KNOW WHAT THE ANSWER IS REALLY

Evaluate each expression.(-9)4=

Answers

6561 -9*-9*-9*-9=6561

please answer this question for me. please help.​

Answers

19 divided by 2 is 9.5 meaning both are 9.5 so 9.5x9.5-9.5=80.75 so that should be ur answer also another way to know if the shape are 9.5 u can multiply9.5x4 and it gives u 38 (we multiply by four cuz that’s how many shapes u have)

EASY! Check my work and fill in the blanks!

Answers

Answer:

Step-by-step explanation:

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