Which linear equation best fits the data ?

Answer:

Step-by-step explanation:

I'll just write log for log base 10.  The important rules about logarithms we need to know are:

[tex] a \log b = \log( b^a) [/tex]

[tex] \log a + \log b = \log( ab) [/tex]

and at the end we'll need something like

[tex]\log a = \log b \implies a=b[/tex]

Suitably armed we can begin,

[tex] \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) [/tex]

First rule,

[tex] \log 3^{ 1 + 1/2x}  + \log 2 = \log (27 - 3^{1/x}) [/tex]

Second rule,

[tex] \log 2(3^{ 1 + 1/2x})  = \log (27 - 3^{1/x}) [/tex]

Third rule,

[tex] 2(3^{ 1 + 1/2x})  = 27 - 3^{1/x} [/tex]

We can rewrite this to be a quadratic equation in [tex]y=3^{1/2x}[/tex].

[tex]  6 (3^{1/2x})  = 27 -  (3^{1/2x})^2 [/tex]

[tex]y^2 +6y - 27 =0[/tex]

[tex](y - 3)(y+9)=0[/tex]

[tex]y=3 \textrm{ or } y=-9[/tex]

First solution:

[tex]3^{1/2x} = 3 = 3^{1}[/tex]

[tex]1/2x = 1[/tex]

[tex]1=2x[/tex]

[tex]x = 1/2[/tex]

Second solution,

[tex]3^{1/2x} = -9[/tex]

No real powers of 3 will be negative, no solution here.

Answer: x=1/2

Check:  

1 + 1/2x = 2 so the left side is log 2(3²) = log 18

Right side, log(27-3^2) = log 18  √

Hi there!  

»»————-　★　————-««

I believe your answer is:  

The x-intercept of the graph is -7. (or (-7, 0). )

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the Slope for the line:}}\\\\m = \frac{8-0}{1-(-7)}\\\\m = \frac{8}{8}\\\\\boxed{m = 1}[/tex]

⸻⸻⸻⸻

Option B is a false statement.

⸻⸻⸻⸻

We can tell with the point (-7,0) that the 'x' intercept of the function is -7.

⸻⸻⸻⸻

The line does not pass (7,0), making option C a false statement.

⸻⸻⸻⸻

The line also does not pass (-1, -8), making option D a false statement.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Find the volume of this prism.

Answer:

24% or d

Step-by-step explanation:

The similarities of two circles is dependent on the radius of circle A and circle B. So the radius of both circles must exist for the circles to be similar.

Given that:

Circles A and B

To prove the similarities of the two circles, the radius of both circles must be known.

Assume the radius of circle A is [tex]r_A[/tex] and the radius of circle B is [tex]r_B[/tex].

The similarity of both circles is proved using:

[tex]r_A = k * r_B[/tex]

or

[tex]r_B = k * r_A[/tex]

where k represents the scale of dilation

Hence, the radius of both circles must exist for the circles to be similar.

Read more about circle similarities at:

https://brainly.com/question/403891

Answer:

A. 10,000

Step-by-step explanation:

A. is 10,000, so it is equivalent to 10,000

B. -10,000    No

C. 100   No.

D. 10   No.

Answer:

third side = 6

Step-by-step explanation:

third side is hypotenuse as it is opposite to 90 degree

using pythagoras theorem

(perpendicular)^2 + (base)^2 = (hypotense)^2

5^2 + [tex](\sqrt{11})^2[/tex] = hypotenuse^2

25 + 11 = hypotenuse^2

36 = hypotenuse^2

[tex]\sqrt{36}[/tex] = hypotenuse

6 = hypotenuse

Answer:

40 L

Step-by-step explanation:

20% empty is the same as 80%full

.8f = .2f + 24

subtract .2f from both sides

.6f = 24

divide both sides by .6

f = 40

Answer:

The length of the third side is approximately 193.14 cm

Step-by-step explanation:

The given dimensions of the sides of triangle ΔVWX are;

X = 160 cm

V = 150 cm

The measure of the included angle, m∠W = 77°

By cosine rule, we have;

w² = v² + x² - 2·v·x·cos(W)

∴ w² = 150² + 160² - 2 × 160 × 150 × cos(77°) ≈ 37,302.35

∴ The length of the third side, w = √37,302.35 ≈ 193.14

The length of the third side, w ≈ 193.14 cm

Answer:

njj

Step-by-step explanation:

Answer:

B=8

Step-by-step explanation:

you add 19 to both sides of the equation to get B by itself.

[tex]B=-11+19\\B=8[/tex]

answer:

8,

reason

11+8=19

alalalalalalalaalalalalal

20character minimum^

9514 1404 393

Answer:

  (x +2)^2 +(y -5)^2 = 9

Step-by-step explanation:

The circle shown has a radius of r = 3 and a center at (h, k) = (-2, 5).

The equation of a circle is ...

  (x -h)^2 +(y -k)^2 = r^2

For the given center and radius, the equation is ...

  (x +2)^2 +(y -5)^2 = 9

Step-by-step explanation:

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Answer:

3n+3

hope it helps

Answer:

32

Step-by-step explanation:

m-án=16, when n = 8

co.op

interest = principle * rate * time in years

8000*0.09*1= 720$

total owed =

principle + interest

8000+720= 8720$

bank

interest = principle * rate * time in years

interest = principle * rate * time in years8000*0.06*1= 480$

principle + interest

8000+480= 8480$

......

6)

Bank A

interest = 1500*2*0.18= 540$

total owed = 1500+540= 2040$

Bank B

compound interest =

1500(1+0.12)^2

compound interest= 1881.6

total owed = 1500+1881.6= 3381.6$

she should choose Bank A less total owed

she'll have to pay the bank 2040$

Answer:

-4 is the correct answer

Answer:

y=18

Step-by-step explanation:

equation:y=3x -7

x=7 then y =?

substitute the vale of x in the equation

y=3x-7

y=3*7-7

y=21-7

y=18

therefore the value of y corresponds to 7 is 18.

Answer:

brainllest f right

a

Step-by-step explanation:

Answer:

[tex]y=-3(x-5)^2+4[/tex]

Step-by-step explanation:

Hi there!

Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:

[tex]y=a(x-h)^2+k[/tex] where the vertex is located at [tex](h,k)[/tex] and a is a numerical value

1) Plug the vertex into the equation

[tex]y=a(x-h)^2+k[/tex]

Plug in the vertex (5,4)

[tex]y=a(x-5)^2+4[/tex]

2) Solve for a

[tex]y=a(x-5)^2+4[/tex]

Plug in the given point (3,-8) and solve for a

[tex]-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4[/tex]

Subtract 4 from both sides

[tex]-8-4=4a+4-4\\-12=4a[/tex]

Divide both sides by 4

[tex]\frac{-12}{4} = \frac{4a}{4} \\-3=a[/tex]

Therefore, a=-3. Plug this back into [tex]y=a(x-5)^2+4[/tex]:

[tex]y=-3(x-5)^2+4[/tex]

I hope this helps!

The answer to the question is C. 5,20,80,320

Step-by-step explanation:

5*4=20

20*4=80

80*4=320

Answer:

134.16 yards or 134.2 if you round to the nearest tenth

Step-by-step explanation:

Using the formula a^2+b^2=c^2

120^2+60^2=c^2

18000=c^2

the square root of 18000 is around 134.16.

Step-by-step explanation:

answer is first option,,,

Answer:

x= -26

Step-by-step explanation:

-14 = x + 12

x = -14-12

x= -26

Answer:

X = -26

Step-by-step explanation:

Move all terms that don't contain  x  to the right side and solve.

Answer:

mkana

Step-by-step explanation:

Answer:

7cm

Step-by-step explanation:

Volume of a prism = base area x height

base area = area of a square = length²

784  = length² x 16

divide both sides of the equation by 16

length² = 784/16

length² = 49

find the square root of both sides

length = 7

Answer:

0

Step-by-step explanation:

3(3x3)(45x6)(45x7)(56x5)(5x5)x0 =0

Answer:

The statement is true.

Step-by-step explanation:

Let the two points are (x', y') and (x'', y'').

The equation of line passing through the two  points is

[tex](y - y')=\frac{y''-y'}{x''-x'}\times (x - x')[/tex]

So, it is true to find the equation of line when the two points is given.  

20- +3

21- -7

22- +4

23- 8

24- 4

ask your teacher for further guidance because explaining negatives is difficult for me

Answer:

20) - 2+5

= 3

21) 8+(-15)

=8 - 15

= - 7

22) - 10 +14

= 4

23) 6-(-2)

=6 +2

= 8

24) - 16-(-20)

= - 16 +20

= 4

Step-by-step explanation:

This is step by step explanation

Please Mark me brainlist

Answer:

Amount of simple interest in three year = 750

Step-by-step explanation:

Given:

Amount invested = 5,000

Number of year = 3 year

Rate of interest = 5% Annually

Find:

Amount of simple interest in three year

Computation:

Simple interest = (P){R)(T)

Amount of simple interest in three year = (5,000)(3)(5%)

Amount of simple interest in three year = (5,000)(3)(0.05)

Amount of simple interest in three year = (5,000)(0.15)

Amount of simple interest in three year = 750

Answer:

40% markup means the scale price is 1.40 times the cost. 1.40 ($20) = $28

Step-by-step explanation:

multiple the price by 1.40

hopefully this helped :)

Answer:

$28

Step-by-step explanation:

We can split this problem into two parts: the original price of the CD set and the 40% extra. We already know the original price of the CD set, so we just need to find the 40% extra. Let's convert 40% to a decimal instead of a percentage. We can do this by dividing by 100.

40/100 = 0.4.

Next, we multiply 20 by 0.4 to find the extra price:

20 * 0.4 = 8

So, the answer is 20 + 8 = $28

We can skip the step of adding the two items together by saying the CD set sells for 140% the original price. 20 * 1.4 = $28

Hope this answer helps you :)

Have a great day

Mark brainliest