which exponential equation is equivalent to this logarithmic equation log x5 + log x12 =7

Answer:

∠ BCA = 90°

Step-by-step explanation:

∠ BCA is an angle in the semicircle and equals 90°

Answer:

B

Step-by-step explanation:

The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.

2(x-3) = x + 6

Simplify:

2x -6 p x + 6

Add 6 to both sides

2x = x + 12

Subtract x from both sides:

X = 12

The answer is B) 12

Answer:

35 miles

Step-by-step explanation:

1/5 = 7

so each part is 7, which means that 5 parts would be 7*5.

7*5 = 35

cross check:

35/5 = 7

hope this helps :)

Answer:

[tex]f(126) \approx 5.01333[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{126}[/tex]

Required

Solve using differentials

In differentiation:

[tex]f(x+\triangle x) \approx f(x) + \triangle x \cdot f'(x)[/tex]

Express 126 as 125 + 1;

i.e.

[tex]x = 125; \triangle x = 1[/tex]

So, we have:

[tex]f(125+1) \approx f(125) + 1 \cdot f'(125)[/tex]

[tex]f(126) \approx f(125) + 1 \cdot f'(125)[/tex]

To calculate f(125), we have:

[tex]f(x) = \sqrt[3]{x}[/tex]

[tex]f(125) = \sqrt[3]{125}[/tex]

[tex]f(125) = 5[/tex]

So:

[tex]f(126) \approx f(125) + 1 \cdot f'(125)[/tex]

[tex]f(126) \approx 5 + 1 \cdot f'(125)[/tex]

[tex]f(126) \approx 5 + f'(125)[/tex]

Also:

[tex]f(x) = \sqrt[3]{x}[/tex]

Rewrite as:

[tex]f(x) = x^\frac{1}{3}[/tex]

Differentiate

[tex]f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\\[/tex]

Using law of indices, we have:

[tex]f'(x) = \frac{x^\frac{1}{3}}{3x}[/tex]

So:

[tex]f'(125) = \frac{125^\frac{1}{3}}{3*125}[/tex]

[tex]f'(125) = \frac{5}{375}[/tex]

[tex]f'(125) = \frac{1}{75}[/tex]

So, we have:

[tex]f(126) \approx 5 + f'(125)[/tex]

[tex]f(126) \approx 5 + \frac{1}{75}[/tex]

[tex]f(126) \approx 5 + 0.01333[/tex]

[tex]f(126) \approx 5.01333[/tex]

Answer: The first number is 2, the second number is 3 and the third number is -2

Step-by-step explanation:

Let the first number be 'x', the second number be 'y' and the third number be 'z'

The equations according to the question becomes:

⇒ x + y + z = 3              ....(1)

⇒ x - y + z = -3              ....(2)

⇒ x - z = 1 + y              ....(3)

Rearranging equation 3:

⇒ x - y = 1 + z                .....(4)

Putting in equation 2:

⇒ 1 + z + z = -3

⇒ 1 + 2z = -3

⇒ z = -2

Putting this value in equation 4 and equation 1, we get:

⇒ x - y = -1

⇒ x + y = 5

Cancelling 'y' by eliminiation method and equation becomes:

⇒ 2x = 4

⇒ x = 2

Putting value of 'x' and 'z' in equation 1:

⇒ 2 + y - 2 = 3

⇒ y = 3

Hence, the first number is 2, the second number is 3 and the third number is -2

Answer:

x= -4

Step-by-step explanation:

A line is 180 degrees. This means that we can use the equation

60+x+124=180

Simplify:

184+x=180

x= -4

We can check this answer by plugging it back in:

60 + (-4) +124 =180

180=180

I hope this helps!

Step-by-step explanation:

[tex]60 + 124 + x = 180 \\ 180 - 184 = x \\ x = - 4[/tex]

Answer:

144

Step-by-step explanation:

We can write this as 2 shirts = 16.00 . Then, we can write this as a ratio, where

2 shirts / 16.00 = 18 shirts/ cost of 18 shirts as the cost for a pair of shirts remains the same, so the ratio will as well.

Therefore, writing the cost of 18 shirts as c, we have

2 shirts/16.00 = 18 shirts/c

multiply both sides by c to remove a denominator

2 shirts * c/16.00 = 18 shirts

multiply both sides by 16 to remove the other denominator

2 shirts * c = 18 shirts * 16

divide both sides by 2 shirts to isolate the c, as we want to figure that out

c = 18 shirts * 16/2 shirts

c=144

9514 1404 393

Answer:

  -4, 0

Step-by-step explanation:

The denominator is x^2+4x. This is zero when ...

  x^2 +4x = 0

  x(x +4) = 0

The zero product rule tells you the product is zero when the factors are zero.

  x = 0

  x +4 = 0   ⇒   x = -4

The denominator is zero for x=0 and x=-4.

9514 1404 393

Answer:

  x = 15

Step-by-step explanation:

In this geometry, x is the geometric mean of the segment lengths of the hypotenuse.

  x = √(9×25)

  x = 15

Hello,

3x+9+8x-25=28

11x-16=28

x=44/11

x=4

So, GE=3x+9=3*11+9=42

Answer:

107%

Step-by-step explanation:

Round up all possible algorithms

9514 1404 393

Answer:

  (c)  3x^4

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

___

  [tex]\displaystyle\sqrt[3]{9x^4}\cdot\sqrt[3]{3x^8}=\sqrt[3]{9\cdot3x^4x^8}=\sqrt[3]{27x^{12}}=\sqrt[3]{(3x^4)^3}=\boxed{3x^4}[/tex]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.  

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)  

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) [tex]Z=2.45[/tex]

b) [tex]P Value=0.0073[/tex]

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach [tex]P=21.4=>0.214[/tex]

Population Size [tex]N=498[/tex]

Sample size [tex]n=12[/tex]

Therefore

[tex]P'=\frac{129}{498}[/tex]

[tex]P'=0.2590[/tex]

Generally the Null and Alternative Hypothesis is mathematically given by

[tex]H_0:P=0.214[/tex]

[tex]H_a:=P>0.214[/tex]

Test Statistics

[tex]Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]

[tex]Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}[/tex]

[tex]Z=2.45[/tex]

Therefore P Value is given as

[tex]P Value =P(Z\geq 2.45)[/tex]

[tex]P Value =1-P(Z\leq 2.45)[/tex]

[tex]P Value =1-0.99268525[/tex]

[tex]P Value=0.0073[/tex]

Answer:

Step-by-step explanation:

If you plot this angle in the coordinate plane, you will find yourself in the fourth quadrant with a referencew angle of 30. Constructing the triangle from that reference angle and using the Pythagorean triple for a 30-60-90 triangle, you get that the side adjacent to the reference angle is √3, the side opposite the reference angle is a -1, and the hypotenuse (which is NEVER negative!) is 2. The x and y coordinates of the terminal point result from the cos (related to the x coordinate) and the sin (related to the y coordinate). The cos of 30:

[tex]cos(30)=\frac{\sqrt{3} }{2}[/tex] and the sin of 30:

[tex]sin(30)=-\frac{1}{2}[/tex] so the coordinates of the terminal point on that angle are

[tex](\frac{\sqrt{3} }{2},-\frac{1}{2})[/tex]

You could also just go to your unit circle, find the angle 330 and look at the coordiantes they give you there for (cos, sin). But I'm a high school math teacher so I wanted you to know how to find this outside of the unti circle. Cuz what if you lost it!?

Answer:

Question 1: x = 6

Question 2: Correct!

Question 3: x = 11

Question 4: Correct!

Step-by-step explanation:

Question 1:

Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.

Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:

First, subtract 50 from 180 to find what angle 22x - 2 will equal:

180 - 50 = 130

130 = 22x - 2

Now use basic algebra to solve for x:

130 = 22x - 2

(add 2 to both sides)

132 = 22x

(divide both sides by 22)

x = 6

Question 3:

Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.

With that in mind, to solve for x, add the two equations and set it equal to 180:

5x + 15 + (9x + 11) = 180

Now use basic algebra to solve for x:

5x + 15 + 9x + 11 = 180

(add like terms)

14x + 26 = 180

(subtract 26 from both sides)

14x = 154

(divide 14 from both sides)

x = 11

Hope it helps (●'◡'●)

Answer:

B

Step-by-step explanation:

THere are 52/4= 13 hearts we can draw

The number of ways to draw 3 hearts from 13 is

13C3= 286

The number of ways to draw 3 cards from 52 is

52C3= 22100

divide these

286/22100= 11/850

This is answer B

Step-by-step explanation:

The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)

Answer:

n = 4 is 10

hope it helps and have a good day

Step-by-step explanation:

The Answer Is Provided Below ➳

(2²)² = 2⁴/2⁴ = 2⁰ × 2⁰ = 2⁰/2⁰

Answer:

The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Divide both sides by 3

Take square root of both sides.

Add 9 to both sides.

Answer:

The value of A is 5

......

[tex]\huge{\boxed{\boxed { ⎆ Answer :- }}} \ [/tex]

[tex](x + a)(x - a) = {x}^{2} - 25[/tex]

Use, the algebraic identity ↦

[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]

So,

[tex](x + a)(x - a) = {x}^{2} - 25 \\ \\ ⟹ \sqrt{25} = 5[/tex]

↦So, the value of a is 5.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

put the value of f(x)

I think that you know

hope it is helpful for you

Answer:

4x + 2h - 1

Step-by-step explanation:

[tex]\frac{f(x+h) - f(x)}{h}[/tex]

[tex]\frac{(2(x+h)^2 - (x + h) + 5) - (2x^2 - x + 5)}{h}[/tex]

[tex]\frac{2x^2 + 4xh + 2h^2 - x - h + 5 - 2x^2 + x - 5}{h}[/tex]

[tex]\frac{4xh + 2h^2 - h}{h}[/tex]

4x + 2h - 1

Answer:

paying $1.20 for a 6 roll package of toilet paper

Step-by-step explanation:

to find the answer, double 6 to equal 12 and double the price as well. therefore, it is 2.40. since 2.40 is cheaper than 2.88, it is a better deal.

Answer:

o (h,k)

Step-by-step explanation: