Please answer this in the attached screenshot

Answer:

24

Step-by-step explanation:

We are given the logarithmic expression:

[tex]\displaystyle{\log_a \left(\dfrac{x^3y}{z^4}\right)}[/tex]

We are also given by the problem that:

[tex]\displaystyle{\log_a x = 3, \ \log_a y = 7, \ \log_a z = -2}[/tex]

From the expression, we will simplify it using two properties:

[tex]\displaystyle{\log_a MN = \log_a M + \log_a N}\\\\\displaystyle{\log_a \dfrac{M}{N} = \log_a M - \log_a N}[/tex]

Therefore, apply the properties to simplify:

[tex]\displaystyle{\log_a x^3y - \log_a z^4}\\\\\displaystyle{\log_a x^3 + \log_a y - \log_a z^4}[/tex]

Next, we will use another property to take an exponent as a coefficient:

[tex]\displaystyle{\log_a x^n = n\log_a x}[/tex]

Hence:

[tex]\displaystyle{3\log_a x + \log_a y - 4\log_a z}[/tex]

Substitute what are given in the problem and the answer will be:

[tex]\displaystyle{3(3)+7-4(-2)}\\\\\displaystyle{9+7+8 = 24}[/tex]

Hence, the answer is 24.

Answer:

11a − 29b − 50

Step-by-step explanation:

Subtract 7 from − 3

7a − 21b − 10 − 40 + 4a − 8b

Add 7a and 4a

11a - 21b - 10 - 40 - 8b

Subtract 8b from -21b

11a - 29b - 10 - 40

Subtract 40 from -10

11a - 29b - 50

Answer:

11a - 29b - 50

Explanation:

⇒ ‐3 + 7(a – 3b – 1) – 4(10 – a + 2b)

distribute inside parenthesis

⇒ -3 + 7a - 21b - 7 - 40 + 4a - 8b

collect like terms

⇒ 7a + 4a - 21b - 8b - 3 - 7 - 40

add or subtract like terms

⇒ 11a - 29b - 50

The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

The formula for finding the nth term in an arithmetic sequence given as:

= a + (n - 1)d

Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:

= (-1)n + 1

= (-1)5 + 1

= (-1)6

= -6

Here is the complete question:

Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.

Learn more about sequence on:

brainly.com/question/6561461

#SPJ1

[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{1}{5}\left(x+1\frac{3}{4}\right)=-2\frac{1}{2} \end{gathered}$}[/tex]

Multiply both sides of the equation by 20, the lowest common denominator of 5,4,2.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{4+3}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]

Add 4 and 3 to get 7.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]

Use the distributive property to multiply −4 times x 4/7.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-4\times\left(\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]

Multiply −4 by 4/7.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(2\times2+1) \ \ \to \ \ [Multiply \ 2\times2] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(4+1) \ \ \to \ \ [Add] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10\times5 \ \ \to \ \ [Multiply] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=-50 } \end{gathered}$}[/tex]

Add 7 to both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-50+7 \ \ \to \ \ [Add] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-43 } \end{gathered}$}[/tex]

Divide both sides by −4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{-43}{-4} } \end{gathered}$}[/tex]

The fraction [tex]\bf{\frac{-43}{-4}}[/tex] can be simplified to [tex]\bf{\frac{43}{4}}[/tex] by removing the negative sign from the numerator and denominator.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{43}{4} } \end{gathered}$}[/tex]

simplify

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=10\frac{3}{4} \ \ \to \ \ \ Answer } \end{gathered}$}[/tex]

Answer:

[tex]\sf c)\ x=10\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sf -\dfrac{1}{5}\left(x+1\dfrac{3}{4}\right)=-2\dfrac{1}{2}[/tex]

Step 1: Convert the mixed numbers into improper fractions.

[tex]\sf -\dfrac{1}{5}\left(x+\dfrac{4\times1+3}{4}\right)=-\dfrac{2\times2+1}{2}\implies -\dfrac{1}{5}\left(x+\dfrac{7}{4}\right)=-\dfrac{5}{2}[/tex]

Step 2: Distribute -⅕ through the parentheses.

[tex]\sf-\dfrac{1}{5}(x)+-\dfrac{1}{5}\left(\dfrac{7}{4}\right)=-\dfrac{5}{2}\\\\\implies -\dfrac{1}{5}x-\dfrac{7}{20}=-\dfrac{5}{2}[/tex]

Step 3: Rewrite the equation with a common denominator of 20.

[tex]\sf -\dfrac{1\times4}{5\times4}x-\dfrac{7}{20}=-\dfrac{5\times10}{2\times10}\\\\\implies -\dfrac{4}{20}x-\dfrac{7}{20}=-\dfrac{50}{20}[/tex]

Step 4: Multiply both sides by 20.

[tex]\sf 20\left(-\dfrac{4}{20}x\right)-20\left(\dfrac{7}{20}\right)=20\left(-\dfrac{50}{20}\right)\\\\\implies -4x-7=-50[/tex]

Step 5: Add 7 to both sides.

[tex]\sf -4x-7+7=-50+7\\\\\implies -4x=-43[/tex]

Step 6: Divide both sides by -4.

[tex]\sf \dfrac{-4x}{-4}=\dfrac{-43}{-4}\\\\\implies x=\dfrac{43}{4}[/tex]

Step 7: Convert the answer back into a mixed number.

[tex]\sf x=\dfrac{43}{4}\implies x=\dfrac{40+3}{4}\implies x=10\dfrac{3}{4}[/tex]

Answer:

2-2i

Step-by-step explanation:

So you have the equation:

[tex]\frac{8}{2+2i}[/tex]

and when you have these equations, you want to get rid of the i, and to do that the simplest way is to square it right? If you simply multiply by 2+2i, you're going to get some i in the middle, so to make sure it's eliminated, you use the difference of squares identity: [tex](a+b)(a-b)=a^2-b^2[/tex]. So you multiply by the conjugate, since it's 2+2i, you multiply by 2-2i, that way it evaluates to 2^2-(2i)^2

Multiply both sides by the conjugate of 2+2i

[tex]\frac{8(2-2i)}{(2+2i)(2-2i)}[/tex]

Simplify:

[tex]\frac{16-16i}{2^2-(2i)^2}[/tex]

Distribute square the values below

[tex]\frac{16-16i}{4-4i^2}[/tex]

Rewrite the i^2 as -1, since sqrt(-1) = i

[tex]\frac{16-16i}{4-4(-1)}[/tex]

Cancel out the negatives

[tex]\frac{16-16i}{8}[/tex]

Distribute the division

[tex]2-2i[/tex]

Answer:

Step-by-step explanation:

First, let's turn them both into improper fractions.

3 3/8 = 27/8

Now we can multiply

It is 5*27 / 13 * 8

This equals: 135 / 104

Simplified even further is:

1 31/104

Answer:

3 days

Step-by-step explanation:

Time taken by 2 men to dig  the well = 12 days

Therefore, Time taken by 1 man to dig the well  = 2 * 12 = 24 days

So, Time taken by 8 men to dig the well = 2 * 12/8 days = 3 days

Answer:3 days

Step-by-step explanation: 2 people dig well=12 days right

1 person equal 2x12=24 days

8 people 2x12/8=3

Hello,

Answer:

The length of AB is 17

Step-by-step explanation:

[tex]AB = \sqrt{(x_{B} -x_{A} ) {}^{2} + (y_{B} -y_{A} ) {}^{2} } [/tex]

[tex]AB = \sqrt{(2 - 10) { }^{2} + (19 - 4) {}^{2} } [/tex]

[tex]AB = \sqrt{( - 8) {}^{2} + (15) {}^{2} } [/tex]

[tex]AB = \sqrt{64 + 225} [/tex]

[tex]AB = \sqrt{289} [/tex]

[tex]\boxed{AB = 17}[/tex]

Answer:

Option 1: 4(2y - 4x) -1

Step-by-step explanation:

Hello!

Given:

Plug in the values for x and y into each equation and see which one outputs 15.

The only option that works is the first option.

Answer:

[tex]4 (2y-4x)-1[/tex]

Step-by-step explanation:

Given:

To find which expressions equal 15, substitute the given values of x and y into the expressions and evaluate:

[tex]\begin{aligned}4(2y-4x)-1 &= 4 \left(2(3)-4 \left(\dfrac{1}{2}\right)\right)-1\\& = 4 \left(6-2\right)-1\\& = 4 \left(4\right)-1\\& = 16-1\\& = 15\\\end{aligned}[/tex]

[tex]\begin{aligned}(x^2+1)+2x+3y & = \left(\left(\dfrac{1}{2}\right)^2+1\right)+2 \left(\dfrac{1}{2}\right)+3(3)\\& = \left(\left\dfrac{1}{4}+1\right)+1+9\\& = \dfrac{5}{4}+1+1+9\\& = \dfrac{45}{4}\end{aligned}[/tex]

[tex]\begin{aligned}4x^2+2y^3-10 & = 4\left(\dfrac{1}{2}\right)^2+2(3)^3-10\\& = 4\left(\dfrac{1}{4}\right)+2(27)-10\\& = 1+54-10\\& = 45\end{aligned}[/tex]

[tex]\begin{aligned}xy+3+20x & = \left(\dfrac{1}{2}\right)(3)+3+20\left(\dfrac{1}{2}\right)\\& = \dfrac{3}{2}+3+10\\& = \dfrac{29}{2}\end{aligned}[/tex]

Therefore, the only expression that equals 15 is:

  [tex]4(2y-4x)-1[/tex]

4.62 × 10⁹  divided by 4.2 × 10³  in standard form  is 1.1 × 10⁶

Lets divide 4.62 × 10⁹ by 4.2 × 10³

since, its division we will subtract the powers.

Therefore,

4.62 × 10⁹ ÷ 4.2 × 10³ = 4.62 × 10⁹ / 4.2 × 10³

Hence,

4.62 / 4.2 = 1.1

Therefore,

4.62 × 10⁹ / 4.2 × 10³ = 1.1 × 10⁹⁻³ = 1.1 × 10⁶

learn more division here: https://brainly.com/question/16366730

#SPJ1

Answer:

Retype your question. That question made me nauseous

The expected gain of this company by the policy that they have here is given as $77.

The stated probability about a person dying is given as 0.0023

This tells us that out of this 10000, the number of people that would die would be 10000*0.0023 = 23 persons

Out of these 23, each of the number that would get the $10000 form the company.

23 * 10000 = $230000

Amount of policy sold at unit price is $100 for 10000

= 100 * 10000

= $1000000

The net earning = 1000000 - 230000

= 770000

The total earning = 770000/10000

= $77

Hence the expected gain of this company is going to be $77.

Read more on expected gain here:

https://brainly.com/question/24175866

#SPJ1

Answer:

(0,4)

Step-by-step explanation:

Because the problem gives you the value of what m would equal in terms of n you would substitute n - 4 for m in the equation above, resulting in:

n - 4 + 5n = 20

6n - 4 = 20

6n = 24

n = 4

Now that you know n = 4, you already can see that the answer would be (0,4), however to check you can substitute 4 for n into the second equation.

m = 4 - 4

m = 0

Because this results in m = 0, that tells you that (0,4) is the right answer.

Answer:

(0, 4)

Step-by-step explanation:

So you can solve the equation by substitution. The solution of a systems of equations, is when they both intersect, or when the (x, y) values are exactly equal, which is why I can substitute the m of the second equation into the first equation, because I'm looking for when they're equal, and that is when m is going to be equal in both equations, as well as the n value.

original equation:

m + 5n = 20

substitute n-4 as m in the equation

(n-4) + 5n = 20

simplify:

6n-4 = 20

add 4 to both equations

6n = 24

divide both sides by 6

n = 4

Now to find m, simply substitute 4 as n in either equation:

Original equation:

m = n - 4

substitute 4 as n

m = 4-4

m=0

so m=0, and n=4, so the solution in the form (m, n) = (0, 4)

[tex]\begin{aligned}&9P(n,5)=P(n,3)\cdot P(9,3)\\&9\cdot\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot\dfrac{9!}{6!}\\&\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot7\cdot8\\&\dfrac{1}{(n-5)!}=\dfrac{56}{(n-3)!}\\&(n-4)(n-3)=56\\&n^2-3n-4n+12-56=0\\&n^2-7n-44=0\\&n^2-11n+4n-44=0\\&n(n-11)+4(n-11)=0\\&(n+4)(n-11)=0\\&n=-4 \vee n=11\end[/tex]

[tex]n[/tex] can't be negative, therefore [tex]n=11[/tex]

Answer:

Step-by-step explanation:

9P(n,5)=P(n,3).P(9,3)

9n(n-1)(n-2)(n-3)(n-4)=n(n-1)(n-2)×9×8×7

(n-3)(n-4)=8×7

(n²-4n-3n+12)=56

(n²-7n+12)=56

n²-7n+12-56=0

n²-7n-44=0

n²-11n+4n-44=0

n(n-11)+4(n-11)=0

(n-11)(n+4)=0

n=11,-4

n=-4(rejected as n is a natural number.)

Hence n=11

Answer:

Step-by-step explanation:

What you do is multiply the previous number and add 1 to get the next answer.

Equation An = 2(An-1)+1

n = The Term

The sequence 1 will be 3(n – 1) + 1. And the sequence 2 will be 9(n – 1) / 2 + 40.

A sequence is a list of elements that have been ordered sequentially, such that members come either before or after.

Let n = natural number.

The sequence 1 will be multiplied by 2 then add 1 starting from 1. Then we have

⇒ 2(n – 1) + 1(n – 1) + 1

⇒ 3(n – 1) + 1

The sequence 1 will be divided by 2 then add 4 starting from 40. Then we have

⇒ (n – 1 / 2) + 4(n – 1) + 40

⇒ 9(n – 1) / 2 + 40

More about the sequence link is given below.

https://brainly.com/question/21961097

#SPJ1

Answer:

f(-2)= 15

Step-by-step explanation:

f(-2)= 2(-2)² - 3(-2) + 1=15

The bulldozer will apply  520n of force to the mound of soil if the top of a ramp is 15 m high and ramp is at an angle of 35° to the ground.

Given Work = 4500 j , Height of top of a ramp is 15m , the ramp is at an angle 35° to the ground.

Work is the . product of the force vector and displacement vector.

[tex]W=F . x[/tex]

It is the multiplication of magnitudes of the vectors and the vectors and the cosine of the angle between them.

W=F * cos ∅

Displacement of the soil is 15 m . The force is parallel to the ramp. So the angle between the vectors is 90°-35°=55°.

Plugging in the values and solving for F:4500 J =F(15 m)( cos55 °)

F=523N

rounded to the significant figures the force is 520 n.

Hence bulldozer needs to apply force of 520 N.

Learn more about force at https://brainly.com/question/12970081

#SPJ4

Answer:

520N

Step-by-step explanation:

(2 one)

(2,2) is the answer

Answer:

log10(1000)=3

Note: The ten is the base number and should be placed slightly lower and be smaller than shown.

Answer:

16

Step-by-step explanation:

f(x) = 2x² when x>4

We cannot use this expression of f to calculate f(4)

because ,this expression define f for the value of x

that are greater (not equal) than 4.

………………………………………………………

f(x) = 4x when x ≤ 4 , here x is can be equal to 4

(notice the sign ≤ )

Therefore

f(4) = 4 × (4) = 16

The area of the border around the pool is determined as 145.97 ft².

Diameter of the circle = 20 ft

Radius of the circle = 10 ft

Area = π(10²) = 314.16 ft²

A = 40 ft x 20 ft = 800 ft²

Pool area = 314.16 ft² + 800 ft² = 1,114.16 ft²

Diameter of the circle = 20 ft + 1ft + 1 ft = 22 ft

Radius of the circle = 11 ft

A = π(11²) = 380.13 ft²

A = 22 ft x 40 ft = 880 ft²

Total area = 880 ft² + 380.13 ft² = 1,260.13 ft²

Area of border = Total area - pool area

Area of border = 1,260.13 ft² - 1,114.16 ft²

Area of border = 145.97 ft²

Thus, the area of the border around the pool is determined as 145.97 ft².

Learn more about area of circle here: https://brainly.com/question/12269818

#SPJ1

Answer: -42v + 70

Step-by-step explanation: You’d multiply -7 with the figures in the brackets, then you’d group like terms then subtract -7v from -35v.

1. -35v + 70 - 7v

Negative multiplied by negative is a positive

2. -35v - 7v + 70

Group like terms

3. -42v +70

Subtract

Hope this was helpful

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{-7(5v - 10) -7v}[/tex]

[tex]\huge\textbf{Solving for your equation:}[/tex]

[tex]\mathbf{-7(5v - 10) -7v}[/tex]

[tex]\huge\textbf{Distribute -7 within the parentheses:}[/tex]

[tex]\mathbf{= -7(5x) -7(-10) - 7v}[/tex]

[tex]\mathbf{= -35v + 70 - 7v}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (-35v - 7v) + (70)}[/tex]

[tex]\mathbf{= -35v - 7v + 70}[/tex]

[tex]\mathbf{= -42v + 70}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{-42v + 7}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

A motor vechicle is motor cycle

Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,

Lemonade left = 14,000 - 9,500 = 4,500 ml

Hence, the lemonade left with Tony is 4500ml.

Learn more about Units conversion:

https://brainly.com/question/4736731

#SPJ1

The number of people who plays only footfall will be 15. The percentage of the class plays only football will be 15.79%.

The quantity of anything is stated as though it were a fraction of a hundred.

In a class of 95 students, 48 play basketball, 35 play football and 32 play neither basketball nor football.

Let x be the number of student who plays basketball as well as football.

48 – x + x + 35 – x + 32 = 95

                           115 – x = 95

                                    x = 20

The number of people who plays only footfall will be

⇒ 35 – 20

⇒ 15

Then the percentage of the class plays only football will be 15.79%.

⇒ 15/95 × 100

⇒ 15.79%

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ1

Answer:

[tex]\huge\boxed{\sf 49\ inches}[/tex]

Step-by-step explanation:

Length of the ladder = 4 feet 1 inch

We know that,

So,

4 feets = 12 × 4 inches

4 feets = 48 inches

So,

= 48 inches + 1 inch

= 49 inches

[tex]\rule[225]{225}{2}[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If a ladder is 4 feet and 1 inch tall, how tall is it in inches?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{7cm} \\ The length of this ladder is 4 feet and 1 inch.\\The measure of one foot is 12 inches. \end{minipage}}[/tex]

Thus,

[tex]\fbox{The measure of 4 feet is 12*4=48 inches.}[/tex]

We add 1 inch more.

[tex]\bf{48+1=49\;inches}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

               [tex]\bf{The\;ladder\;is\;49\;inches\;long.}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

There are 4.29 cases in the units

The given parameters are:

Units = 60

Rate = 14 units per case

The number of cases is then calculated as:

Case = Unit/Rate

This gives

Case = 60/14

Evaluate

Case = 4.29

Hence, there are 4.29 cases in the units

Read more about unit rates at:

https://brainly.com/question/19493296

#SPJ1