Write each expression as a single natural logarithm. ln 18-ln 10

Answer:

n + 3.9 ≤ 16

An inequality is a mathematical expression represented by less than, greater than, or equal to symbols to compare values or to measure and solve complex equations.

Answer:

arccos(51/100)

Step-by-step explanation:

By the Law of Cosines,

[tex]a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=\frac{b^2 + c^2 - a^2}{2bc} \\ \\ m\angle A=\arccos \left(\frac{b^2 + c^2 - a^2}{2bc} \right) \\ \\ =\arccos \left(\frac{10^2 + 5^2 - 8^2}{2(5)(10)} \right) \\ \\ =\arccos(51/100)[/tex]

When two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y, direct variation occurs, whereas indirect or inverse variation occurs when an increase in the value of X results in a decrease in the value of Y and vice versa.

Therefore, direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y whereas indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.

Know more about inverse variation here:

https://brainly.com/question/13998680

#SPJ4

Danladi says that it cannot be rewritten as either of these expressions. He is correct.

It should be noted that 2³ × 42 will be:

= 2³ × 42

= 8 × 42

= 336

Therefore, Zoe says that 2³.42 can be rewritten as 86 and Juana says that it can be rewritten as.85. They're both wrong.

In the other hand, Danladi says that it cannot be rewritten as either of these expressions. Therefore, he is correct.

Learn more about numbers on:

brainly.com/question/25734188

#SPJ1

Answer:

The two smaller angles equal 24 and together they equal 48

Step-by-step explanation:

The bisector tells us that the smaller angles equal each other

3x + 6 = 7x - 18  Subtract 3x from both sides

6 = 4x - 18  Add 18 to both sides

24 = 4x  Divide both sides by 4

6 = x

Now, plug 6 back into each equation.

3x + 6

3(6) + 6

18 + 6

24

7x - 18

7(6) - 18

42 - 18

24

Answer:

[tex]x = 17[/tex].

Step-by-step explanation:

Simplify the given equation:

[tex]2\, (x - 1)^{3/4} = 16[/tex].

[tex](x - 1)^{3/4} = 8[/tex].

[tex]((x - 1)^{1/4})^{3} = 8[/tex].

Take the cubic root of both sides to eliminate the numerator of the exponent. Only roots of even degree could introduce alternative solutions. Since the degree of this root is an odd number, this step would not create extraneous solutions.

[tex]\sqrt[3]{((x - 1)^{1/4})^{3}} = \sqrt[3]{8}[/tex].

[tex](x - 1)^{1/4} = 2[/tex].

Raise both sides to the fourth power to eliminate the denominator of the exponent:

[tex](x - 1) = 2^{4}[/tex].

[tex]x - 1 = 16[/tex].

[tex]x = 17[/tex].

Substitute the solution [tex]x = 17[/tex] into the equation:

[tex]\begin{aligned}& 2\, (17 - 1)^{3/4} \\ =\; & 2\times (16^{1/4})^{3} \\ =\; & 2 \times 2^{3} \\ =\; & 16\end{aligned}[/tex].

Thus, [tex]x = 17[/tex] isn't an extraneous solution since setting [tex]x[/tex] to [tex]17[/tex] satisfies the original equation.

Answer:

#2 Alternate interior angles: 4 & 5 and 3 and 6

#4 :

m∠6 = 55°

m∠3 = 55°

m∠1 = 125°

Reasons: See below

Step-by-step explanation:

Angles 6 and 8 are supplementary angles since they are on the same straight line intersected by another straight line.

So m∠6 + m∠8 = 180
m∠6 + 125 = 180
m∠6 = 180-125= 55°

Angles 3 and 6 are alternate interior angles and equal to each other
m∠3 = m∠6 = 55°

Angles 1 and 3 are supplementary angles whose sum of measures should add up to 180°
m∠1 + m∠3 = 180
m∠1 + 55 = 180
m∠1 = 180-55 = 125°

The equation which models the number of calculators packed by the machine in certain minutes is x = 2.5y

No. of calculators packed after 10 minutes = 25 calculators

No. of calculators packed after 30 minutes = 75 calculators

Using the unitary method for finding calculators packed in a minute,

10 minutes = 25 calculators

1 min = 25/10 = 2.5 calculators

Let x be the number of minutes the machine is running

Let y be the number of calculators packed

Formulation of the equation we get:

x = 2.5y

Hence, the equation which gives the number of calculators packed after certain minutes is given by: x = 2.5y

Learn more about algebra:

https://brainly.com/question/24875240

#SPJ9

Answer: electronics worth $1,650

1500 (1+5%)^2 = $1653.75

3.75 dollars will be left over.

Step-by-step explanation:

The answer to this question is: og(x³y⁵) = 3log(x) + 5log(y)

In mathematics, the logarithm is that the function to exponentiation. which means the logarithm of a given number x is that the exponent to which another fixed number, the base b, must be raised, to supply that number x. within the simplest case, the logarithm counts the amount of occurrences of the identical consider repeated multiplication

To solve this question, we need only 2 identities, i.e.,

log(a*b) = log(a) + log(b)   ...(1)

log(aⁿ) = nlog(a)                ...(2)

Using 1, we can expand log x³ y⁵ as: log x³ y⁵ = log(x³) + log(y⁵)       ...(3)

Using 2, we can expand both the terms as: log(x³) = 3log(x)log(y⁵) = 5log(y)

Putting them in equation 3, we get:3log(x) +5log(y)

Therefore, log(x³y⁵) = 3log(x) + 5log(y)

Learn more about Logarithm here: https://brainly.com/question/28041634

#SPJ4

Answer:

212.

Step-by-step explanation:

Given: 3m^2 + 2p^2 - 15

When m = 3 and p = 10

Substituting the values

= 3(3)^2 + 2(10)^2 - 15

By further calculation

= 3(9) + 2(100) - 15

So we get

= 27 + 200 - 15

= 212

Therefore, the value of the expression is 212.

Answer:

1 1/2+4/5 and the vertical would be graphed?

Answer:

y = ± √ 7/2

Step-by-step explanation:

2*y^2-8-(6-2*y^2)=0

(2 • (y2)) - 8) - (6 - 2y2) = 0

(2y2 - 8) - (6 - 2y2) = 0

Pull out like factors :

4y2 - 14 = 2 • (2y2 - 7)

4.2 Factoring: 2y2 - 7

difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

2 • (2y2 - 7) = 0

5.1 Solve : 2 = 0

5.2 Solve : 2y2-7 = 0

Add 7 to both sides of the equation :

2y2 = 7

Divide both sides of the equation by 2:

y2 = 7/2 = 3.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

y = ± √ 7/2

Answer:

B store is cheaper since 790.56<823

B price<A price

Step-by-step explanation:

A:

549(0.5)=274

264+549=823

Josh need to pay the refrigerator for $823 in this store without tax.

B:

549(0.6)= 329.4

329.4+549=878.4

878.4(09)=790.56

Josh need to pay $790.56 in this store without the tax.

C:

B, department store is cheaper so he could pay less

The factoring of the expression 4 x²=-8 x+5 is (2x-1) (2x+5)

By ordering the values, we get:

4 x² + 8 x - 5

To solve this exercise, we have to follow the rules of factoring:

1. Factor 8 from 8x:

4 x² + 8 x - 5

4 x² + (-2 + 10) x - 5

2. Apply the distributive property:

4 x² - 2x + 10x - 5

3. Groups the first two terms and the last two terms:

(4 x² - 2x) + 10x - 5

4. Factorize the greatest common denominator (GCM) of each group:

2x(2x - 1) + 5(2x-1)

5. Factor the polynomial by factoring the greatest common denominator, (2x-1):

(2x-1) (2x+5)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

Learn more about factoring at brainly.com/question/24734894

#SPJ4

We get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.

We are given an equation:

2 x + 2 y = 8

Divide both the sides by 2, we get that:

2 x / 2 + 2 y / 2 = 8 / 2

x + y = 4

Now, we will subtract x from both the sides, so, we get that:

x + y - x = 4 - x

y = 4 - x

Therefore, we get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ9

Answer: = 7.27 × 108                          

(scientific notation)

with calculate significant figures         = 7.3 × 108

                                                           (scientific notation)

Step-by-step explanation: hope this helps

The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

Given that, 0.05 × ----- = 0.5.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Let the number should fill in the blank be x.

So, 0.05 × x = 0.5

⇒ x = 0.5/0.05

⇒ x = 10

The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

To learn more about the multiplication of decimals visit:

https://brainly.com/question/19655879.

#SPJ1

Answer:

10000

Step-by-step explanation:

The total walking distance of the week is 12.1 km.

So, let the total walking distance be 'x'.

Then,

Therefore, the total distance of walking in the week is 12.1 km.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ9

Using proportions, it is found that:

1. a) 1/5 of the marbles are red.

b) 40% of the marbles are yellow.

c) 60% of the marbles are not yellow.

d) 11/20 of the marbles are green or yellow.

2) Event A, B and C are the most likely, each with equal probabilities.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For the first problem, we have that there are 3 + 4 + 5 + 8 = 20 marbles, hence:

a) 4/20 = 1/5 of the marbles are red.

b) 8/20 x 100% = 0.4 x 100% = 40% of the marbles are yellow.

c) 12/20 x 100% = 0.6 x 100% = 60% of the marbles are not yellow.

d) 3 are green and 8 are yellow, hence 11/20 of the marbles are green or yellow.

A die has 6 possible outcomes, numbered 1 to 6, hence the probabilities(number of desired outcomes divided by number of total outcomes) are given as follows:

Event A, B and C are the most likely, each with equal probabilities.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The missing step 7 in the two column proof is; Consecutive ∠s in a ▱ are supplementary

We are told that WXYZ is a parallelogram in which  we have to prove that: WXYZ is a rectangle. The two column proof is as follows;

           Statement                                              Reason

1. WXYZ is a parallelogram,                 1. Given

    ZX ≅WY

2.  ZY ≅ WX                                           2. Opposite sides of parallelogram

                                                                 are congruent.

3.  YX≅YX                                            3. Reflexive property of congruence

4. ΔZYX ≅ Δ WXY                             4.  SSS congruence postulate

5.  ∠ZYX ≅ ∠WXY                                 5. CPCTC

6. m∠ZYX ≅ m∠WXY                            6. definition of congruence.

7.m∠ZYX + m∠WXY = 180°                   7. Consecutive ∠s in a ▱ are

                                                                   supplementary

8.m∠ZYX + m∠ZYX = 180°                    8. By substitution

9. 2(m∠ZYX) = 180°                                9. By simplification

10.m∠ZYX = 90°                                     10. Division property of equality

11. WXYZ is a rectangle                       11. Rectangle angle theorem.

Read more about Two Column Proof at; https://brainly.com/question/7807853

#SPJ1

Go ahead and ask the question!! <3

Answer:

-4

Step-by-step explanation:

-12+3(-8+(-4)^2-6)+2

first the -4^2

-12+3(-8+16-6)+22

now everything in the parenthesis

-12+3x2+2

now the multiplying.

-12+6+2

now calculate this all together.

-4

Answer:

y=-2x-1

Step-by-step explanation:

y=mx+b

-7=-2(3)+b

-7=-6+b

-1=b

y=-2x-1

Answer:

i say it would be "None of these"

Step-by-step explanation:

because say x=sisters age so, x=12     if lisa if 4 years youger, than x-4=8    (x-4)-x=(-2)      x-(x-4)=4      (x+4)-x=4    so therefore it would be none.

Answer:

none of these

Step-by-step explanation:

because we don't know her sisters age we'll use "x" and Lisa is 4 years younger so you deduct 4 from x and the equation will be '4-x'

The inverse of the function y = log₂(2x) is f ⁻¹(x) = 2ˣ⁻¹.

Given the function is :y = log₂ 2x

we are asked to find the inverse of the function.

steps to find inverse function are:

Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.

To get x = ay + b from the equation y = ax + b, replace x with y and y with x.

Here, find y and solve for x = ay + b.

Then we get y = (x - b/a).

Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.

now interchange the positions of x and y in the function.

x = log₂ 2y

the next step is to isolate the dependent variables.

f ⁻¹(x) = 2ˣ ⁻ 1

Learn more about Inverse functions here:

brainly.com/question/11735394

#SPJ4