What is an equation of the line that passes through the points (-2, 3) and (6, -1)?

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Answer:

  (b)  f(x) = log(x) +4

Step-by-step explanation:

The x-intercept of any log function is (1, 0). The graph here has been shifted 4 units up from that, so is a graph of ...

  f(x) = log(x) +4

Answer:

k=18, general solution does not exist.

Step-by-step explanation:

If f(t)=y=e3t is a solution to the differential equation

d2ydt2−9dydt+ky=0,

then

y = e^(3t)

y' = dy/dt = 3y

y'' = d2ydt2 = 9y

y'' - 9y' + ky = 0

9y - 9(3y) + ky = 0

(9-27+k)y = 0

solve for y

(9-27+k) = 0

k = 18

general solution is when y=e^(3t)=0, or t-> -infinity

Answer:

bbbb,

bbbg, bbgb, bgbb, gbbb,

bbgg, bgbg, bggb, gbgb, gbbg, ggbb,

bggg, gbgg, ggbg, gggb,

gggg

Step-by-step explanation:

3 children: bbb, bbg, bgb, gbb, bgg, gbg, ggb, ggg

4 children: bbbb, bbbg, bbgb, bgbb, gbbb, bbgg, bgbg, bggb, gbgb, ggbb, bggg, gbgg, ggbg, gggb, gggg

You need to take a methodological approach;

The 2 easiest are the possibility of all boys and all girls;

Then consider 3 boys and 1 girl:

bbbg, bbgb, bgbb, gbbb

Then 2 boys and 2 girls:

bbgg, bgbg, bggb, gbgb, gbbg, ggbb

Lastly, 1 boy and 3 girls:

bggg, gbgg, ggbg, gggb

In total, there are 16 possibilities

P.S. interesting to note is that the number of possibilities here follows the pattern of Pascal's triangle:

       1

     1   1

   1  2  1

 1  3  3  1

1  4  6  4  1

The last row is relevant here;

There is 1 possibility where there are 4 boys;

There are 4 possibilities (in terms of the order of birth) where there are 3 boys and 1 girl;

There are 6 possibilities where there are 2 boys and 2 girls

There are 4 possibilities where there is 1 boy and 3 girls;

There is 1 possibility where there are 4 girls;

The pattern ∴ is 1 4 6 4 1, as the 5th row of Pascal's triangle reads;

If your talking about 3 children, it would match the 4th row of Pascal's triangle;

So, 1 possibility of 3 boys;

3 possibilities of 2 boys and 1 girl;

3 possibilities of 1 boy and 2 girls;

And 1 possibility of 3 girls;

If your talking about 10 children, it would match the 11th row of Pascal's triangle.

(Maths can be so cool XD)

Answer:

64 outcomes

Step-by-step explanation:

Given the following data;

Number of coins = 6

Number of outcomes for a single coin = 2

A single coin comprises of a head (H) and a tail (T), thus, the number of outcomes for a single coin is two (2).

To find how many possible outcomes we would have from tossing six coins at the same time, we would use the following formula;

[tex] Number \; of \; outcomes = X^{n} [/tex]

Substituting the values, we have;

Number of outcomes = 2⁶

2⁶ = 2 * 2 * 2 * 2 * 2 * 2

2⁶ = 64

Number of outcomes = 64

Therefore, the number of outcomes for a single coin tossed at the same time is equal to sixty four (64). It would have a total of 32 heads (H) and a total of 32 tails (T).

Answer:

h(2) = 7/4

h(-3) = -2

h(-2) = 11/(-8)

h(-3) - h(-2) = -(5/8)

Step-by-step explanation:

h(x) = (2x^2-x+1) / (3x-2)

h(2) = (2*2^2 - 2 + 1) / (3*2 - 2)

       = (8 - 2 + 1) / (6 - 2)

       = 7/4

h(-3) = {2*(-3)^2 - (-3) + 1} / {3*(-3) - 2}

        = (18 + 3 + 1) / (-9 - 2)

        = 22/(-11)

        = -2

h(-2) = {2*(-2)^2 - (-2) + 1} / {3*(-2) - 2}

        = (8 + 2 + 1) / (-6 - 2)

        = 11/(-8)

h(-3) - h(-2) = (-2) - {11/(-8)}

                  = -(5/8)

Hope this will help. Please give me brainliest.

[tex]h(3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]

[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]

[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]

[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]

[tex]h(2) = \frac{ 8 - 1}{4} [/tex]

[tex]h(2) = \frac{7}{4}[/tex]

[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]

[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]

[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\=-2 + \frac{11}{ 8} \\ =- \frac{5}{ 8} [/tex]

Answer:

A. The graph is a line that goes through the points (9,0) and (0,6).

Step-by-step explanation:

Given

[tex]4x + 6y = 36[/tex]

Required

Select the true options

[tex](a)\ (9,0)\ and\ (0,6)[/tex]

This implies that"

[tex](x_1,y_1)= (9,0)[/tex]

[tex](x_2,y_2)= (0,6)[/tex]

So, we have: [tex](x_1,y_1)= (9,0)[/tex]

[tex]4x + 6y = 36[/tex]

[tex]4 * 9 + 6 * 0 = 36 + 0 = 36[/tex]

So, we have: [tex](x_2,y_2)= (0,6)[/tex]

[tex]4 * 0 + 6 * 6 = 0 + 36 = 36[/tex]

Hence (a) is true.

Answer:

the answer would be a-The graph is a line that goes through the points (9,0) and (0,6).

Step-by-step explanation:

i took the test

[tex] \huge \underline \mathcal{Answer}[/tex]

The given angles forms linear pair, and we know the angles forming linear pair are supplementary,

Therefore,

Angle MHJ + Angle MHL = 180°

Let's solve :

Value of variable m = 10°

[tex] \mathrm{✌TeeNForeveR✌}[/tex]

Answer:

a. 105.84 cm²

b. 136 cm²

Step-by-step explanation:

a. The prism is a cube

Surface area of the cube = 6a²

a = 4.2 cm

Plug in the value

Surface area = 6*4.2²

Surface area = 105.84 cm²

b. The prism is a triangular prism

Surface area of triangular prism = bh + L(s1 + s2 + s3)

b = 6 ft

h = 4 ft

L = 7 ft

s1 = 5 ft

s2 = 5 ft

s3 = 6 ft

Surface area = 6*4 + 7(5 + 5 + 6)

Surface area = 24 +7(16)

Surface area = 24 + 112

Surface area = 136 cm²

Step-by-step explanation:

|6p + 3| > 15

6p = 15 - 3

6p = 12

divide both sides by 6

6p÷6 = 12 ÷ 6

p = 2

hence, p >2 or p < - 3

the inverse of ƒ(x) = x²– 16

[tex] {f}^{ - 1} (x) = \sqrt{x + 16} [/tex]

Answer:

The inverse function should be f

[tex] {f}^{ - 1}( x) = \sqrt{x + 16} [/tex]

this is the correct answer

Answer:

cos x° = adjacent ÷ hypotenuse

Step-by-step explanation:

Option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given trigonometric ratios in the options.

As we know the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

In the right angle triangle (It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base)

cos is the ratio of the side adjacent to the angle to the hypotenuse

cos x° = adjacent ÷ hypotenuse

tan is the ratio of the side opposite to the angle to the side adjacent to the angle.

tan x° = opposite ÷ adjacent

Thus, option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ5

Answer:

1.  27cm3

2.  64cm3

3.   512cm3

4.  ?

Step-by-step explanation:

Answer: 24- b 25- c 26- b 27- c

Step-by-step explanation:

Answer:

D) 1 3/4

Step-by-step explanation:

Answer:

12 ft

Step-by-step explanation:

we know the areas of the 2 top squares.

the area of a square is simply the square of its side length.

=>

81 ft² means side length is 9 ft.

225 ft² means side length is 15 ft.

these are also 2 of the sides of the right triangle.

the third side we get by using Pythagoras :

c² = a² + b²

with c being the side opposite of the 90 degree angle.

so,

225 = 81 + x²

as x is also the third side of the triangle.

=> 144 = x²

x = 12 ft

Answer:

C. 1 and 3

Step-by-step explanation:

Answer:

( 1.  6 )

Step-by-step explanation:

Use the formula:

x = - b/2a

to find the maximum and minimum.

Answer: (1,  6 )

Step-by-step explanation:

This should help:

x = - b/2a

Answer:

4.2 hours

Step-by-step explanation:

Answer:

If you take 5 sweet out of the basket, then the ratio of the number of chocolate to the number of sweet left in the basket is. \frac{5} {30 - 5} = 5/25 = 1/5

Step-by-step explanation:

Answer:

The one you selected is correct! You can check it by using the four values of m and w given.

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Answer:

  (b) 19.7 ft

Step-by-step explanation:

The perimeter of the figure is the sum of the lengths of the 3 straight sides and half the circumference of a 3-ft circle.

  P = 6 + 3 + 6 + (1/2)(π)(3) = 15 +3/2π ≈ 19.712 . . . feet

The perimeter is about 19.7 feet.

Answer:

A = $3,198.17

A = P + I where

P (principal) = $1,600.00

I (interest) = $1,598.17

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 7.72/100

r = 0.0772 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 1,600.00(1 + 0.0772/12)(12)(9)

A = 1,600.00(1 + 0.006433333)(108)

A = $3,198.17

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $1,600.00 at a rate of 7.72% per year compounded 12 times per year over 9 years is $3,198.17.

Answer:

-4374

Step-by-step explanation:

Given :

a1 = 2 ; r = - 3

The nth term of a geometric series :

A(n) = ar^(n-1)

The 8th term :

A(8) = 2(-3)^(8-1)

A(8) = 2(-3^7)

A(8) = 2(−2187)

A(8) = - 4374

It is airoplane and ambulance

Answer:

4 cookies

Step-by-step explanation:

24 x (1/6) = 24/6 = 4

Answer:

4

Step-by-step explanation:

1/6 can be represented as a percentage 1 divided by 6 = 0.1667...multiply that by 24 and you get 4 with a few decimals that round up to four as you would not want to give them a partial cookie....

QUESTION:- Find the value of x.

A. 30

B. 60

C. 90

D. 120

ANSWER:-

ALL ANGLE SUMS HAVE SAME LOGIC OF STRAIGHT LINE ANGLES = 180°

[tex]y + x + y - x = 180[/tex]

[tex]2y = 180 \\ y = 90[/tex]

[tex]2x + y + x = 180[/tex]

[tex]3x + 90 = 180 \\ 3x = 90 \\ x = 30 \degree[/tex]

Answer:

30 degrees

Step-by-step explanation:

2x + y + x = 180

y + x + y - x = 180

3x + y = 180

2y = 180

y = 90

3x + 90 = 180

3x = 90

x = 30

Answer:

x=11

Step-by-step explanation:

the question would be to find x

3x + 28 + 5x + 52 + 2x - 10=180 (sum of angles in a triangle is equal to 180⁰)

10x + 70=180

10x=180-70

10x=110

x=110/10

x=11

Answer:

07.50086956521739% (round it)

Step-by-step explanation:

Find what percent 43.13 (Number A) is of 575 (Number B). To do this you divide Number A by Number B.

43.13 / 575 = 0.0750086956521739

Move the decimal point two places to the right.

007.50086956521739

Get rid of the zeros.

7.50086956521739

Answer:

07.5%

Step-by-step explanation:

Answer:

b

Step-by-step explanation: