write the point-slope equation of the line that contains the point (1, -4) and has slope - 1/3.​

Answer:

a) 86,314.

b) 9,162,500.

Step-by-step explanation:

(a) 838(100 + 3)

= 83800 + 2514

= 86314.

(b) 91625 x 179 - 91625 x 79

= 91625(179 - 79)

= 91625 x 100

= 9162500.

Answer:

a,b are the right answers

Step-by-step explanation:

Answer:

(a) aₙ = 22 + 6(n - 1)

(b) The 14th row has 100 seats

Step-by-step explanation:

1. (a) Remember that an arithmetic series has the general formula a + (n - 1)d. Here a = the first term, and d = difference between first and second term, or in other words the difference between the nth and (n + 1)th terms.

aₙ = 22 + 6(n - 1)

This is our iterative rule for this arithmetic series, aₙ = 22 + 6(n - 1).

(b) Here n = the row number. We want to know the row number that has 100 seats. Let's equate the expression '22 + 6(n - 1)' to 100, and solve for n.

100 = 22 + 6(n - 1),

100 = 22 + 6n - 6,

100 = 16 + 6n,

6n = 84,

n = 84 / 6 = 14

=> the 14th row has 100 seats

Answer: 14

Step-by-step explanation: 9 small squares with one teddy bear in each, 4 medium squares with 4 bears in each medium square, and 1 big square for the entire thing.

The total number of square is 14

In the counting of figures, you have a shape or a figure. From the given shape you will have to identify a given known shape and count the number of times it is present in the given shape.

According to the question

9 small squares with one teddy bear in each,

4 medium squares with 4 bears in each medium square.

1 big square for the entire thing.

Total square = 9 + 4 + 1

                     = 14

Hence, the total number of square is 14

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Answer:

A

Step-by-step explanation:

A contains √3 --> irrational number because 3 is not a square number

For other choices:

- All numbers in the form a/b (a,b are integer numbers) are rational numbers

- √36, √9, √4, √25, √49, √100 are integer numbers because (36, 9, 4,....) are square numbers

- All given decimal numbers can be written in the fraction form

0.5 = 1/2

39.77 = 39 + 77/100 = 3977/100

0.15151578 and 0.00010001 are finite decimals, 0.303030... is infinite repeating decimal, so technically they are rational numbers.

Answer:

k = 3/4

Step-by-step explanation:

Parallel lines have the same slope so first, we need to find the slope of 8x + 6 = 2y. To do so, we can do the following:

8x + 6 = 2y

2y = 8x + 6

y = 4x + 3 (This is now in slope intercept form - y = mx + b where m = slope and b = y-int.)

Therefore, the slope is 4. Now, we can do:

3x = ky - 10

3x - 10 = ky

(3x / k) - (10 / k) = y

y = (3x / k) - (10 / k)  (where k ≠ 0)

Now that the second line is in slope-intercept form, we can set the two x terms equal to each other, therefore:

3x / k = 4x

3x = 4x * k

3x / 4x = k

k = 3/4

Answer:  B  

Step-by-step explanation:

They've given you two functions  f(x) = x^2 + 1 and g(x) = 3x +1  And they are you to find 2 * f(4) then g(x) is not needed so input in  4 for the function f(x) and multiply the output by 2.

F(4) = 4^2 + 1

F(4) = 16 +1

f(4) =  17  

   17  * 2 = 34

Answer:

Step-by-step explanation:

[tex]f( x ) = x^ 2 + 1 \\ g( x ) = 3 x + 1\\\\f(4) \times 2 = ?\\f(4) = 4^2 +1\\\\=( 16+1) \times 2\\\\= 17\times 2\\\\= 34[/tex]

Answer:

[tex]g( x) = \frac{2}{3}x[/tex]

Step-by-step explanation:

Given:

Composite Function:

[tex]h( x)=f( g( x))[/tex]

Also,

[tex]h( x)=\frac{4}{3}x-1[/tex]

To find:

[tex]g( x ) = ?[/tex]

Solution:

First of all, let us learn about a composite function.

Composite function [tex]f( g( x))[/tex] means to write [tex]g( x)[/tex] in place of [tex]x[/tex] in the function [tex]f( x)[/tex].

Let [tex]g( x) = y[/tex]

So, [tex]f( g( x))[/tex] =  [tex]f( y )[/tex].

Therefore,

[tex]h( x) =f( g( x)) = f( y)[/tex]

So, [tex]f( y) = 2y-1[/tex]

We have to solve for [tex]y[/tex] in terms of [tex]x[/tex] to find the value of [tex]g(x)[/tex]:

[tex]\Rightarrow \frac{4}{3}x-1 = 2y-1\\\Rightarrow 2y=\frac{4}{3}x\\\Rightarrow y = \frac{2}{3}x[/tex]

Hence, the answer is [tex]g( x ) = \frac{2}{3}x[/tex].

Checking whether the answer is correct or not:

[tex]f( g( x)) = f( \frac{2}{3}x) = 2\times \frac{2}{3}x -1 = \frac{4}{3}x-1[/tex]

which is [tex]h( x)[/tex].

Hence, our answer [tex]g( x ) = \frac{2}{3}x[/tex] is correct.

The g(x) of the function is:

g(x) = (2/3)x

A function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

We have:

h(x) = (4/3)x - 1

h(x) = f(g(x))

f(x) = 2x - 1.

Thus, we can say:

h(x) = f(g(x)) = 2*g(x) - 1

(4/3)x - 1 = 2g(x) - 1

(4/3)x - 1 + 1= 2g(x)

(4/3)x = 2g(x)

(4/3)x * 1/2 = g(x)

(2/3)x = g(x)

g(x) = (2/3)x

Therefore, g(x) = (2/3)x.

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Answer:

4 playlists

:)

Answer:

15.41

Step-by-step explanation:

Answer:

Ratio of their surface area = 9:16

Step-by-step explanation:

Volume of cube A = a^3

Volume of cube B = b^3

Ratio of their volumes= 27:64

Volume of cube A = a^3

27 = a^3

a= 3√27

= 3

Volume of cube B = b^3

64 = b^3

b =3√64

= 4

Surface area of cube a = 6a^2

=6 × 3^2

= 6 × 9

= 54

Surface area of cube b = 6b^2

= 6 × 4^2

= 6 × 16

= 96

Surface area of cube a : surface area of cube b

= 54:96

= 9:16

Answer:

0.85x - $50

Step-by-step explanation:

Given that :

Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay

Discount on price = 15%

Amount parents agreed to pay = $50

Cost of bike = x

Discount on bike = 0.15x

Cost after discount is removed = (x - 0.15x) = 0.85x

Parent pays $50 of cost price, amount Brandon will have to pay equals :

(0.85x - $50)

Answer:

0.85x - $50

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

x=3

y=6

to find x+y-1, sub in x and y

3+6-1 = 8

Answer: 8

Step-by-step explanation:

x+y+(-1), given x=3, y=6, and z=-4

---------

 x+y+(-1)

=(3)+(6)+(-1) ⇔ substitute x and y

=9+(-1) ⇔ add 3 and 6

=8

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

x2 + 10x + 25

x2 + 5x + 5x + 25

x(x + 5) + 5(x + 5)

(x + 5)(x+ 5) are the factors

x2 - 36

Both are squares so

x2 - (4)2

Answer:

B

Step-by-step explanation:

f(x)=(x-3)(x²+2x+2)

when solve for x using quadratic formula fo x in (x²+2x+2):

x=(-b±√b²-4ac)/2a  a=1,b=2,c=2

x=-1±i

f(x)=(x-3)(x+1-i)(x+1+i)

The complete factored form of the polynomial is F(x) = (x - 3)(x + 1 + i)(x + 1 - i).

To find the complete factored form of the polynomial F(x) = x³ - x² - 4x - 6, we can factor it using various methods such as synthetic division or factoring by grouping.

Factoring the polynomial, we get:

F(x) = (x + 3)(x - 1)(x + 2)

Comparing the factored form with the options provided:

A. F(x) = (x + 3)(x + 1)(x - 1)

This option does not match the factored form of the polynomial.

B. F(x) = (x - 3)(x + 1 + i)(x + 1 - i)

f(x)=(x-3)(x²+2x+2)

When solve for x using quadratic formula fo x in (x²+2x+2):

x=(-b±√b²-4ac)/2a  

x=-1±i

f(x)=(x-3)(x+1-i)(x+1+i)

So, the is the required factored form.

C. F(x) = (x - 3)(x + 1 + i)(x - 1 - i)

This option does not match the factored form of the polynomial.

D. F(x) = (x + 3)(x + 1 + i)(x + 1 - i)

This option does not match the factored form of the polynomial.

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Answer:

<abc=14

Step-by-step explanation:

<abc= 14 ; because if the whole thing is 90 and <CBD is already 76 then you subtract 90-76 to get the rest of the angle which is 14 degrees

Answer:

distance= 9 units to the nearest

Step-by-step explanation:

using the formula

√(∆x)^2+(∆y)^2

√73

= 8.5

= 9 units

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

Work Shown:

d = distance between (-3,1) and (5,-2)

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-5)^2 + (1-(-2))^2}\\\\d = \sqrt{(-3-5)^2 + (1+2)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.5440037\\\\d \approx 8.5\\\\[/tex]

Alternatively, you can plot the two points on the same xy grid. Then form a right triangle with the two points as the endpoints of the hypotenuse. Use of the pythagorean theorem will result in getting the same approximate distance. The distance formula is effectively the same as the pythagorean theorem, but just in a different form.

Answer:

x =-19

Step-by-step explanation:

[tex]-4(x + 1) - 3 = -3(x - 4).\\\\\mathrm{Expand\:}-4\left(x+1\right)-3:\quad -4x-7\\\\\mathrm{Expand\:}-3\left(x-4\right):\quad -3x+12\\-4x-7=-3x+12\\\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\-4x-7+7=-3x+12+7\\\\Simplify\\-4x=-3x+19\\\\\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}\\-4x+3x=-3x+19+3x\\\\Simplify\\-x=19\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{19}{-1}\\\\Simplify\\x=-19[/tex]

Answer:

We have this equation:

-4(x+1) - 3 = -3(x-4)

First of all, we solve the paretheses:

-4x - 4*1 - 3 = -3x - (-3*4)

-4x - 4 - 3 = -3x +  12

-4x -7 = -3x + 12

We sum 7 on both sides and 3x on both too:

-4x - 7 + 7 + 3x = -3x + 12 + 3x + 7

-4x + 3x = 12 + 7

-x = 19

x = -19

Now we can verify:

-4(-19+1) - 3 = -3(-19-4);

-4(-18) - 3 = -3(-23);

72 - 3 = 69 (TRUE)

Answer:

The experimental probability is the same as the theoretical probability.

Step-by-step explanation:

The given data is:

color            observed frequency               relative frequency

Red                            15                                          3/10

Blue                           12                                          6/25

Green                         8                                           4/25

Yellow                        10                                          1/5

Purple                         5                                           1/10

The experiment was repeated 50 numbers of times.

Solution:

Theoretical probability is basically what is expected to happen without experimenting and experimental probability is what actually happens as a   results of an experiment.

Theoretical probability =  favorable outcomes / all possible outcomes

Experimental probability = no. of times outcome occurs / no. of times

                                                                                      experiment is performed The experimental probability  and theoretical probability are same i.e. 1/5

This can be seen from the table:

Experimental probability = 1/5

As the experiment is performed 50 times and the outcome (yellow tile) occurs 10 times so using the formula of experimental probability:

10/50 = 1/5

Now as given, there are 5 number of tiles (red,blue,green,yellow,purple) so number of possible outcomes is 5. Yellow tile among these 5 tiles is 1. So the favorable outcomes is 1. So looking at the given formula of theoretical probability:

1/5

So

experimental probability = 1/5

theoretical probability = 1/5

Hence the experimental probability is the same as the theoretical probability.

Answer: A

Step-by-step explanation: it’s A for the lazy people

Answer:

[tex]y=2x-2[/tex]

Step-by-step explanation:

Because the coordinates for x = 0 is (0,-2) so that's your y- intercept.

Then if you all you have to do is make sure that you have the correct slope.

So i just made a table on paper and started going up and seeing what slope i'd need to match the table on the screen.

[tex]2(0)-2=-2\\2(1)-2=0\\2(2)-2=2\\2(3)-2=4[/tex]

Answer:

$210

Step-by-step explanation:

Answer: x=5 and x=-1

Step-by-step explanation:

X^2-4x-5=0

(X-5) (x+1)=0

X-5=0. And. X+1=0

Answer:

1. x = 10  2. x = 7  3. x = 1  4. x = 6

Explanation:

1. -2x + 81 = 61 (Subtract 81 from 61)

  -2x = -20 (Divide)

   x = 10

2. 9x - 58 = 5 (Add 58 to 5)

   9x  = 63 (Divide)

   x = 7

3. 21 +10x = 3x + 28 (Rearrange expression)

   21 - 28 = 3x - 10x (Combine like terms)

   -7 = -7x (Divide)

    x = 1

4. 9x - 42 = 2x (Rearrange)

   9x - 2x = 42 (Combine like terms)

   7x = 42 (Divide)

   x = 6

Answer:

3.85 + 6.29 = 10.14

Hoped I helped

Step-by-step explanation:

3.85+6.29= 10.14

thank

Answer:

30 ft

Step-by-step explanation:

6 x 5 = 30

you multiply 6 times 5 and you get 30

Step-by-step explanation:

Answer:

Y=40

X=67

Step-by-step explanation:

In a cross line problem, one part of the cross, (such as 63°) is always the same on the other side. (like y+23° and 63°. This means Y=40 because 40+23 is 63.

To find x, you must know that 360° is all the way around in degrees. you know that 126° (63 +63) is already taken up. So you subtract 126 from 360 and then multiply the answer by 1/2 because you trying to find the bottom total.(360-126)=234(1/2)= 117 Lastly, you find X in the equation 2x-17=117.

x=67

Answer:

(r+q)+s

Step-by-step explanation:

The parentheses make it clear that r and q need to be added first.

Step-by-step explanation:

L=2B

P=2(L+B)

48=2(2B+B)

48=2(3B)

48=6B

B=8yd

L=2*8

=16yd

Answer:

length * width = 16 yd * 8 yd

or

length = 16 yd

width = 8 yd

Step-by-step explanation:

take the rectangular pool to have sides a (length) and 2a (width).

we are told that the length is as twice as its width, therefore,

Perimeter is given by (a + 2a) × 2 = 48 yd

Divide both sides by 2 ⇒ [tex]\frac{((a + 2a) * 2)}{2} = \frac{48 yd}{2}[/tex] ⇒ a + 2a = 24 yd

⇒3a = 24 yd

Divide both sides by 3 ⇒ [tex]\frac{3a}{3} = \frac{24 yd}{3}[/tex] ⇒ a = 8 yd

therefore, the width of the pool is 8 yd and its length is 16 yd (Twice as long as it is wide)

Answer:

For

Step-by-step explanation:

the first half of food + the last quarter of door

= F o o d + d o o r

= Fo + r

= For