find the slope of the line that passes through the two points (0,1) and (-8, -7)

Answer:

[tex]\huge \boxed{x=3}[/tex]

Step-by-step explanation:

[tex]6(x+2)=30[/tex]

[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]

[tex]x+2=5[/tex]

[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]

[tex]x=3[/tex]

Answer:

3

Step-by-step explanation:

30 = 6(x+2)

30/6 = 5

5 = x+2

5-2 = 3

3=x

This is a pretty simple question and I tried to make it as simple as possible when explaining it.

Answer:

1/9

Step-by-step explanation:

easy 2/3 is equivalent to 6/9. So there is 1/9 of a pint left

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

Answer:

x = 32

but

I would say anything from 30 to 33

but truly i have no clue about the range

Step-by-step explanation:

3x-9=87 (because 180 -93 =87)

3x = 96

x = 32

Answer:

it is 32

Step-by-step explanation:

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

Step-by-step explanation:

42 is your answer according to bodmas

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

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

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

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

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Answer:  A)  g(x) = 3x - 14

Step-by-step explanation:

Solve the equation for y and replace y with g(x):

y - 3x = -14

y        = 3x - 14

  g(x) = 3x - 14

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

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

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

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

Answer: g = w + 8    g=w-2

Step-by-step explanation:

We could represent the word phrases by the equations.

g = w + 8  

g = w - 2  

Answer:

g = w + 8

g = w - 2

Step-by-step explanation:

Assuming that g and w exists, then we can show the relation as described:

"Variable g is 8 more than variable w."

g = w + 8

"Variable g is also 2 less than w."

g = w - 2

These are the two equations of the described relationship between g and w.

Note that g could not actually exist in the real number system:

g = w + 8

g = w - 2

w + 8 = w - 2

w - w = -2 - 8

0 != -10

This is impossible within the real number system.

Cheers.

Answer:

[tex]\huge\boxed{y = 8}[/tex]

Step-by-step explanation:

-4x + 3y = 12

Given that x = 3

-4 (3) + 3y = 12

-12 + 3y = 12

Adding 12 to both sides

3y = 12+12

3y = 24

Dividing both sides by 3

y = 8

Answer:

y =8

Step-by-step explanation:

-4x + 3y = 12

Let x = 3

-4(3) +3y = 12

-12+3y = 12

Add 12 to each side

-12+12+3y =12+12

3y =24

Divide each side by 3

3y/3 = 24/3

y =8

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Answer:

197 = 10(31-1) + a

197 = 300 + a

-103 = a

Answer:

The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]

The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]

So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Answer:

a) dV(s)  =  15,386 cm³

b) dS(s) = 4,396 cm²

c) dV(s)/V(s) = 1,07 %    and   dS(s)/ S(s)  =  0,71 %

Step-by-step explanation:

a) The volume of the sphere is

V(s) = (4/3)*π*x³        where x is the radius

Taking derivatives on both sides of the equation we get:

dV(s)/ dr  =  4*π*x²    or

dV(s)  =  4*π*x² *dr

the possible propagated error in cm³ in computing the volume of the sphere is:

dV(s)  = 4*3,14*(7)²*(0,025)

dV(s)  =  15,386 cm³

b) Surface area of the sphere is:

V(s) = (4/3)*π*x³  

dV(s) /dx  =  S(s) = 4*π*x³

And

dS(s) /dx  = 8*π*x

dS(s) = 8*π*x*dx

dS(s) = 8*3,14*7*(0,025)

dS(s) = 4,396 cm²

c) The approximates errors in a and b are:

V(s) =  (4/3)*π*x³     then

V(s) = (4/3)*3,14*(7)³

V(s) = 1436,03 cm³

And  the possible propagated error in volume is from a)  is

dV(s)  =  15,386 cm³

dV(s)/V(s)  = [15,386 cm³/1436,03 cm³]* 100

dV(s)/V(s) = 1,07 %

And for case b)

dS(s) = 4,396 cm²

And the surface area of the sphere is:

S(s) =  4*π*x³        ⇒   S(s) =  4*3,14*(7)²    ⇒ S(s) = 615,44 cm²

dS(s) = 4,396 cm²

dS(s)/ S(s)  =  [ 4,396 cm²/615,44 cm² ] * 100

dS(s)/ S(s)  =  0,71

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

Answer:

Use the student t distribution

Step-by-step explanation:

Here is the formula

t = (x - u) ÷(s/√N)

From the information we have in the question:

n = 150

s = 550

x = 3400

u = mean = 2400

= 3400 - 2400÷ 500/√150

= 1000/44.9

= 22.27

At 0.05 significance level, df = 149 so t tabulated will be 1.65.

Answer:

69

Step-by-step explanation:

The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.

We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.

[tex]\frac{5(x)}{2} -6[/tex]

[tex]\frac{5(30)}{2}-6[/tex]

[tex]\frac{150}{2}-6[/tex]

[tex]75-6[/tex]

[tex]69[/tex]

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2

Answer:

D.  2i√3

Step-by-step explanation:

You have the expression √-12.  You can divide the number in the radical sign into the numbers that make up the expression.  After you do this, you will be able to take numbers out of the radical sign

√(-12)

√(-1 × 4 × 3)

√-1 = i

√4 = 2

√3 = √3

2i√3

The answer is D.

Answer:

x=9; one ticket is $9

Step-by-step explanation:

4x+12=48

4x=48-12

4x=36

x=36/4

x=9

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

Answer:

x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

6x - 10 = 4(x+3)

6x - 10 = 4*x + 4*3

6x - 10 = 4x + 12

6x - 4x = 12 + 10

2x = 22

x = 22/2

x = 11

check:

6*11 - 10 = 4(11+3)

66 - 10 = 4*14 = 56

Answer:

Nothing further, the simplest answer is 32 1/2

Step-by-step explanation:

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.

[tex]5x+3+8x-4=90[/tex]

Combine like terms:

[tex]13x - 1 = 90[/tex]

Add 1 to both sides:

[tex]13x = 91[/tex]

Divide both sides by 13:

[tex]x = 7[/tex]

Hope this helped!

Answer:

x = 7

Step-by-step exxplanation:

5x + 3 + 8x - 4 = 90

5x + 8x = 90 - 3 + 4

13x = 91

x = 91/13

x = 7

probe:

5*7 + 3 + 8*7 - 4 = 90

35 + 3 + 56 - 4 = 90