Find the unique solution to this system of equations. Give your answer as a point

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

43.96

Step-by-step explanation:

ok so you use the formula: A= 3.14•r•2 next you plug in your values a=3.14•7•2 3.14•7= 28.98•2=43.96

Answer:

43.96

im dying on the question before that one it says "What issues are you having when it comes to area and circumference" you typed nothing really and here you are asking us whats the circles area lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's a little over 60 mph

110 km = 110 km * 0.6 miles / km = 66 miles

110 km/hour = 66 miles / hour

Answer:

197

Step-by-step explanation:

So, if you catch 100 fish on both days, that means that you have caught 200 fish. 100 on one day and 100 on the next. But, since you've caught 3 fish twice, that means that three out of 200 fish are the same and cannot be counted as new fish. So 3 from 200 is 197 fish. Hope this helped!

Day 1: 100 (3 tagged)

Day 2: 97 (3 tagged)

100+97=197

or

Day 1: 100 (3 tagged)

Day 2: 100 (3 tagged)

100+100= 200

200-3=197

Answer, 197 fish.

Answer:

Grater than ( < ), and less than ( > ).

The z-score for a score 15 points below the mean in a normal Distribution with a standard deviation of 10 is -1.5.

To find the z-score for a score 15 points below the mean in a normal distribution, we need to know the mean of the distribution. The z-score is a measure of how many standard deviations a particular score is from the mean.

Let's assume the mean of the normal distribution is denoted by μ. Since we know the standard deviation is 10, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where x is the given score, μ is the mean, and σ is the standard deviation.

In this case, the given score is 15 points below the mean, so we can represent it as x = μ - 15. Substituting these values into the formula, we get:

z = (μ - 15 - μ) / 10

 = -15 / 10

 = -1.5

Therefore, the z-score for a score 15 points below the mean in a normal distribution with a standard deviation of 10 is -1.5.

The negative sign indicates that the score is below the mean, and the value of 1.5 indicates that the score is 1.5 standard deviations below the mean.

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Answer:

y = (x + 4)²

Step-by-step explanation:

Given equation is,

y = x²+ 8x + 16

By using identity (a + b)² = a² + 2ab + b²

y = x² + 2(4)(x) + 4²

Here a = x and b = 4

y = (x + 4)²  

Therefore, factored form of the given equation is y = (x + 4)²

Answer:

A. Margin of error=0.0346

B. Confidence interval=0.4854 to 0.5546

Step-by-step explanation:

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let plug in the formula

Confidence level= 1-0.95

Confidence level= 0.05

Second step is to find Z using this formula

Zα/2

Let plug in the formula

Z= 0.05/2

Z=0.025

Third step is to find the Z score of Z=0.025

Zα/2=1.96

Now let calculate the margin of error using this formula

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009

Computation for the boundaries of confidence interval

Using this formula

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546

In linear equation, The total number of hours it will take to remove the dirt will be 9 3/10 hours.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Convert the mixed fraction number into a fraction number. Then we have

5 ¹/₆ = 31 / 6

The total number of hours it will take to remove the dirt will be given as,

5/9 = (31/6) / Time

Time = (31/6) / (5/9)

Time = (31 x 6) / (6 x 5)

Time = 279 / 30

Time = 9 3/10 hours

The total number of hours it will take to remove the dirt will be 9 3/10 hours.

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SOLUTION

From the graph, the root of the equation is the point where the graph touches the x-axis

Hence the equation that models the graph becomes

Since the solution to the equation are x=-4 and x=0

Hence the equation has two real zeros

The minimum of g(x) is at the point

The minimum of g(x) is at x=-2

The vertex of g(x) is given by

Hence the vertex of g(x) is (-2,-4)

The domain of the function g(x) is the set of input values for which the function g(x) is real or define

Since there is no domain constrain for g(x), the domain of g(x) is

hence the domain of g(x) is (-∞,∞)

The decreasing function the y-value decreases as the x-value increases: For a function y=f(x): when x1 < x2 then f(x1) ≥ f(x2)

Hence g(x) decreasing over the interval (-∞,-2)

Therefore for the graph above the following apply

g(x) has two real zeros (option 2)

The minimum of g(x) is at x= - 2(option 3)

the domain of g(x) is (-∞,∞) (option 4)

g(x) decreasing over the interval (-∞,-2)(option 4)

Answer:

IIUIOIOIO

Step-by-step explanation:

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

From the question, we have the following parameters that can be used in our computation:

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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Answer:

6552 ÷3 =2184

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

If they are only units of one then it should just be 5 and if they are bigger units than just multiply so 5

Step-by-step explanation:

I hope this helps u out

Answer:

9th min?

Step-by-step explanation:

lol sorry im set 4 maths

144π cm²/min is the surface area of the ball increasing when the radius is 9 cm.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given,

Radius of a spherical ball is increasing at a rate of 2 cm/min.

We need to find exactly what rate (in cm2/min) is the surface area of the ball increasing when the radius is 9 cm

S = surface area at time t,  and r = radius at time t

r=9cm

dr/dt = 2 cm/min

S = 4πr²

Differentiate with respect to t

ds/dt=2.4πrdr/dt

=8πr(2)

=16πr

=16π(9cm)

=144π cm²/min

Hence 144π cm²/min is the surface area of the ball increasing when the radius is 9 cm.

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i think the answer is at 15 months

The probability of choosing one of the vegetarians at random is 4/55.

The given data is;

The formula for probability;

probability = favourable outcome/ total outcome

P(one vegetarian) = 20/275

P(one vegetarian) =  4/55

Thus, the probability of choosing one of the vegetarians at random is 4/55.

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Answer:

52800 cm^3

Step-by-step explanation:

Given:

Rectangular prism

h = 6 cm (height)

l = 11 m = 1100 cm (length)

w = 8 cm (width)

\(v =a(base) \times h\)

\(a(base) = l \times w = 1100 \times 8 = 8800 \: {cm}^{2} \)

\(v = 8800 \times 6 = 52800 \: {cm}^{3} \)

Answer:

60

Step-by-step explanation:

25÷5=5

5×12=60

have a great day! :)

Answer:

60

Step-by-step explanation:

We are given:

25/5 = 5

Since the relationship is directly proportional,

x/12 = 5

Multiply both sides by 12 to isolate x:

x = 60

Answer:

a 90° angle is a right angle

Hence, option (C) is the correct answer.

What is an equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here the given expression is

\(\frac{m-2}{m-1}\)

So, here we use equation third

i.e.,

\(\frac{m^{2}-m-2}{m^{2}-1}\\\frac{m(m-1)-2}{m^{2}-1}\\\\\frac{m-2}{m-1}\\\\\)

Hence, option (C) is the correct answer.

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Answer: The number of scores represented in the blue section of the boxplot is 12.

Answer:

\(y=\dfrac{5}{4}x^3+10\)

Step-by-step explanation:

Given information:

Create two equations by substituting the given points into the given equation:

Equation 1:  point (0, 10)

\(\implies a(0)^3+d=10\)

\(\implies 0+d=10\)

\(\implies d=10\)

Equation 2:  point (2, 20)

\(\implies a(2)^3+d=20\)

\(\implies 8a+d=20\)

Substitute Equation 1 into Equation 2 and solve for a:

\(\implies 8a+d=20\)

\(\implies 8a+10=20\)

\(\implies 8a+10-10=20-10\)

\(\implies 8a=10\)

\(\implies \dfrac{8a}{8}=\dfrac{10}{8}\)

\(\implies a=\dfrac{10}{8}\)

\(\implies a=\dfrac{5}{4}\)

Finally, substitute the found values of a and d into the original formula:

\(\implies y=\dfrac{5}{4}x^3+10\)

Check by substituting the x-values of the two given points into the found equation:

\(x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}\)

\(x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}\)

Put(0,10)

Now

Put again (2,20) this time

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Given that,

Slope of the line, m = -6/7

It contains the point (-5,-8)

To find,

The equation of line.

Solution,

Use the formula as follows :

y = mx+b

Put x = -5 and y = -8

\(-8=\dfrac{-6}{7}(-5)+b\\\\b=-8-\dfrac{6}{7}\times 5\\\\b=-12.28\\\\=-\dfrac{86}{7}\)

So, the equation of line is :

\(y=\dfrac{-6}{7}x-\dfrac{86}{7}\)

Answer:

0.58333333....

can i have brainliest plz