three points have coordinates A(-1,2),B(3,10)and C(p,8).Find the value (s) of p if AC is perpendicular to BC.

Answer:

x=2, y=2

Step-by-step explanation:

3x + y = 8

2x + 4y = 12

Multiply the first equation by -4

-12x -4y = -32

Then add to the second equation

-12x -4y = -32

2x + 4y = 12

------------------------

-10x + 0y = -20

-10x = -20

Divide by -10

-10x/-10 = -20/-10

x =2

Now find y

3x+y = 8

3(2)+y = 8

6+y = 8

y = 8-6

y =2

Answer:

[tex]\huge\boxed{\sf Solution Set = \{(2,2)\}}[/tex]

Step-by-step explanation:

3x + y = 8 ----------------------(1)

2x + 4y = 12 -------------------(2)

Multiply Eq. (1) by 4

4(3x+y) = 8*4

12x + 4y = 32 -----------------(3)

Subtract Eq. (3) from (2)

2x + 4y - (12x + 4y) = 12 - 32

2x + 4y - 12x - 4y = -20

2x - 12x = -20

-10x = -20

Divide both sides by -10

x = 2

Put x = 2 in Eq. (1)

3(2) + y = 8

6 + y = 8

Subtract 6 to both sides

y = 8 - 6

y = 2

Solution Set = {(x,y)} = {(2,2)}

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

Among all shapes with the same area, a circle has the smallest/shortest perimeter.

Answer:

B

Step-by-step explanation:

According to the Factor Theorem, if (x - a) is a factor (where a is a zero) of the polynomial P(x), then P(a) must equal zero.

Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.

Testing each choice, we can see that only choice B is true. That is:

[tex]\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0 \end{aligned}[/tex]

In conclusion, our answer is B.

Answer:

x = 7

Step-by-step explanation:

RT= RS+ST

70 = (7x +2 ) + (2x+5)

70 = 9x + 7

9x= 70 - 7

9x = 63

x= 63/ 9

x = 7

I hope I helped you^_^

Answer:

[tex]given \: that \: total \: length \: rt = 70 \\ \: then \: rs + st = rt \\ 7x + 2 + 2x + 5 = 70 \\ 9x + 7 = 70 \\ 9x = 63 \\ x = \frac{63}{9} \\ x = 7 \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

Perimeter = 2W +  2L

160 = 2W + 2L

width = 16 feet less than length

W = L - 16   ------------(I)

Finding the dimensions of the court:

2W + 2L = 160

2*(L-16) + 2L = 160       {from (I) }

2*L - 2*16 + 2L = 160     {Distributive property}

2L - 32 + 2L = 160

2L + 2L - 32 = 160         {Combine like terms}

4L - 32 = 160              {Add 32 to both sides}

4L = 160 +32

4L = 192         {Divide both sides by 4}

L = 192/4

L = 48

W = 48 - 16

  W = 32

Answer:  Area = 16*pi m^2

               Circumference = 8*pi

Step-by-step explanation:  The circumference and area of a circle are given by:

Area = pi*r^2

Circumference  = 2 pi*r

Radius = Diameter/2, or 4 meters (m)

Area = 16*pi m^2  (50.27 m^2)

Circumference = 8*pi  (25.13 m)

Answer:

20 is the mean length of rainbows

Step-by-step explanation:

x1=6

y1=8

x2=1

y2=6

then ,

distance =

[tex] \sqrt{(6 - 1) {?}^{2} { + (8 - 6)}^{2} } \\ \sqrt{25 + [/tex]

Answer:

(-2,4)

Step-by-step explanation:

-2+6=4

Hello :D

2 x $4.52 = $9.04

$9.04 + $11.47 = $20.51

2 x $20 = $40.00

$40.00 - $20.51 = $19.49

With change:

$40.00 + $7.72 = $47.72

$47.72 - $20.51 = $27.21

Find total collected by multiplying the amount per person by number of people:

1000 x 0.12 = $120.00

Total collected = $120.00

Divide total collected by number of people:

120.00 / 109 = $1.20

Each person gets $1.20

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{x_1+x_2}{2}_\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{6+9}{2},\dfrac{2+4}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{15}{2},\dfrac{6}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=(7.5,3)[/tex]

Answer: y = -1/2x

8(x - 2y) = 16x

8x -16y = 16x

-16y      = 16x-8x

-16y      = 8x

-16y/-16= 8x/-16

        y = -1/2x

Answer:

12,04

Step-by-step explanation:

17^2 - 12^2 (pythagoras theorem)

=145

=square root of 145

=12.04 (rounded off)

Answer:

Below.

Step-by-step explanation:

396,242,002

Answer:

Step-by-step explanation:

buenas tardes .....

solucion

Volumen de un cilindro: es igual al área de la tapa por la altura del mismo

A = πD² * h / 4

Lata grande y lata pequeña

Para la lata grande, el diámetro y la altura han aumentado un 20%.

Lata pequeña:

d = 4 cm

h = 3 cm

A 1 = π * (4) ² * 3/4

A1 = 37,70 cm²

Lata grande:

d = 4 * 1,2 = 4,8 cm

h = 3 * 1,2 = 3,6 cm

A2 = π (4,8) ²3,6 / 4

A2 = 65,14 cm²

Si 37,7 representa el 100%

  65,14 representación x

x = 170%

El incremento del volumen es de un 70%

Answer:

5.5

Step-by-step explanation:

3x + 15 - 7x = -7

-4x + 15 = -7

-4x = -7 -15

-4x = -22

x = -22/-4 = 5.5

Step-by-step explanation:

Let 5 consecutive no. be

n, n+1,n+2,n+3,n+4

n+n+1+n+2+n+3+n+4=110

5n+10=110

5n=110-10

5n=100

n=100/5

n=20

4th term is n+3=20+3=23

                                                    Thank You

Step-by-step explanation:

let : the pair of jeans = X

a. the equation is :

4(X-3) + 8 = 92

b. 4(X-3) = 92-8

4X -12 = 84

4X = 84+12

4X = 96

X = 96/4

X = 24

so, the price of each pair of jeans = $24

_________

For the solution x = 2.6, the left side of equation

(2x - 6) => would be 2(2.6)-6 = 5.2-6 = -8 ( the negative value),

but on the right side of the equation 4x+8 => 4(2.6) +8 = 18.4 ( the positive value)

this difference indicates that x=2.6 is not the right solution.

Answer:

a)  Let x be the cost of one pair of jeans

    [tex]4(x-3)+8=92[/tex]

b)  $24

Step-by-step explanation:

Given information:

Define the variable:

Let x = the cost of one pair of jeans

Create an equation using the defined variable and the given information:

[tex]4(x-3)+8=92[/tex]

To find the price of each pair of jeans, solve the equation for x:

[tex]\implies 4(x-3)+8=92[/tex]

[tex]\implies 4(x-3)+8-8=92-8[/tex]

[tex]\implies 4(x-3)=84[/tex]

[tex]\implies \dfrac{4(x-3)}{4}=\dfrac{84}{4}[/tex]

[tex]\implies x-3=21[/tex]

[tex]\implies x-3+3=21+3[/tex]

[tex]\implies x=24[/tex]

Therefore, the price of each pair of jeans was $24.

----------------------------------------------------

Solving  3(2x - 6) = 4x + 8  mentally:

Expand the brackets:

⇒ 16x - 18 = 4x + 8

Subtract 4x from both sides:

⇒ 12x - 18 = 8

Add 18 to both sides:

⇒ 12x = 26

Two times 12 is 24.  As 26 is very close to 24, then x ≈ 2.

(The actual value of x is 2.2 to 2 decimal places).

Assessing the student's solution:

As x = 2.6 rounds to x ≈ 3 then the student's solution is incorrect because:

⇒ 3(2(3) - 6) = 4(3) + 8

⇒ 3(6 - 6) = 12 + 8

⇒ 3(0) = 20

⇒ 0 = 20

Answer: D

Step-by-step explanation:

-6a + 10 = -27

First step: subtract 10 from both sides:

-6a = -37

Now divide both sides by -6:

A = -37/-6

Simplify:

A = 37/6

Answer:

a = 37/6

Step-by-step explanation:

-6a +10 = -27

Subtract 10 from each side using the subtraction property of equality

-6a+10-10 = -27-10

-6a = -37

Divide each side by -6 using the division property of equality

-6a/-6 = -37/-6

a = 37/6

Answer:

[tex]x - 3(x + 2) > 4 \\ x - 3x - 6 > 4 \\ - 2x > 4 + 6 \\ - 2x > 10 \\ x = 10 \div ( - 2) \\ x = - 5[/tex]

Answer:

[tex]g(x) = |x-3|[/tex]

Step-by-step explanation:

We are given the parent function:

[tex]f(x) = |x|[/tex]

And we want to find the equation after a reflection in the y-axis followed by a translation of three units right.

To reflect a function over the y-axis, we multiply the input by a negative. That is:

[tex]\displaystyle f(x) \rightarrow f(-x)[/tex]

In other words, a reflection over the y-axis will be given by:

[tex]f(-x) = |-x|[/tex]

To shift horzontally, we add if we are moving leftwards or subtract if we are moving rightwards. That is:

[tex]f(x) \rightarrow f(x-k)[/tex]

Where k is the horizontal translation.

Since we are translating three units rightwards, k = 3. Hence:

[tex]\displaystyle f(-(x-3)) = |-(x-3)|[/tex]

Recall that |ab| = |a||b|. Hence:

[tex]\displaystyle f(-(x-3)) = |-(x-3)| = |-1||(x-3)| = |x-3|[/tex]

Hence, f reflected over the y-axis followed by a translation of three units right is given by:

[tex]g(x) = |x-3|[/tex]

Answer:

(x - 4)³

Step-by-step explanation:

"The cube of x" would be x³.  The difference of a number and 4 would be x - 4.

Therefore, "the cube of the difference of a number and 4" would be

(x - 4)³

Answer:

11

Step-by-step explanation:

d=√(5-(-6))²+(-7-(-7))²

d=√(11²+0²)

d=11

Answer:

[tex]\boxed {\boxed {\sf d= 11}}[/tex]

Step-by-step explanation:

We are asked to find the distance between 2 points. We will use the distance formula.

[tex]d= \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2[/tex]

In this formula, (x₁ , y₁) and (x₂ , y₂) are the points. We are given the points (-6, -7) and (5, -7). If we match the value and the corresponding variable, we see that:

Substitute these values into the formula.

[tex]d= \sqrt{(5- -6)^2 + (-7--7)^2[/tex]

Solve inside the parentheses. Remember that two back-to-back negative signs become a plus sign.

[tex]d= \sqrt{ (11)^2+(0)^2[/tex]

Solve the exponents.

[tex]d= \sqrt{(121)+(0)[/tex]

Add.

[tex]d= \sqrt{121}[/tex]

[tex]d=11[/tex]

The distance between (-6, -7) and (5, -7) is 11.

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Answer:

235.34

Step-by-step explanation:

122×193-12 = 23534

23534/100

23534/100 = 235.34

Answer:

158

Step-by-step explanation:

4+16 = 20

20×8-2= 158

the dot means multiply and u must first find the answer in the bracket

if there is no bracker, then u must start with multiply first

Step-by-step explanation:

4+ 16 is equal to 20

8-2 is equal to 6

20×6 is equal to 120

120 is ans