Is the point (4,-3) a solution for this system?

Answer/Step-by-step explanation:

Square all three numbers. If the largest number squared is equal to the sum of the squares of the other two, then the numbers form a Pythagorean triple.

or

Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25

either one works

Answer:

-4 1/26

Step-by-step explanation:

You will want to Reduce the expression, if possible, by cancelling the common factors.

Answer:

4.2

Step-by-step explanation:

Four and one-sixth is equal to 4.2. One-sixth is the same as 1/6, which is equal to 0.16666666666666666. When you add this fraction to 4, you get 4.166666666666667, which can be rounded to 4.2. Four and sixteen hundredths is equal to 4.16, which is close to 4.2 but not exactly the same. Six twenty-fifths is equal to 0.24, which is also not equal to 4.2. 416% is equal to 4.16, which is also not equal to 4.2.

If you draw a histogram for this data, it will be B. Positively skewed.

x Freq(x)

11 3

12 8

13 3

14 4

15 2

Now, we need to find the following measures:

Mean of the data:

Mean is calculated as:

\(�ˉ=∑�=1���⋅��∑�=1���xˉ = ∑ i=1n​ f i​ ∑ i=1n​ x i​ ⋅f i​\)

​

We know that:

$x$ $~~$ $F(x)$ $~~~$ $x\cdot F(x)$

11 3 33

12 8 96

13 3 39

14 4 56

15 2 30

Total= 20 179

\(�ˉ=17920xˉ = 20179​\)

Mean, $\bar{x}=8.95$

Variance of the data:

Variance is calculated as:

\(��2=∑�=1�(��−�ˉ)2⋅��∑�=1���S x2​ = ∑ i=1n​ f i​ ∑ i=1n​ (x i​ − xˉ ) 2 ⋅f i​ ​ Now, we know that $\bar{x} = 8.95$ and $f_1=3,~f_2=8,~f_3=3,~f_4=4,~f_5=2$ and $x_1=11,~x_2=12,~x_3=13,~x_4=14,~x_5=15$\)

Variance, $S_x^2=2.87$ (approx)

Standard Deviation of the data:

Standard deviation is the square root of variance.

\(��=��2S x​ = S x2​ ​\)

Standard Deviation, $S_x=1.69$ (approx)

Now, if we draw a histogram for this data, it will be positively skewed as the mean (8.95) is greater than the median.

Therefore, the correct answer is:

B. Positively skewed.

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Douglas will need approximately 13.12 quarters, or approximately 3 years and 4 months to accumulate $3774, with two decimal places.

We can apply the compound interest formula:

A = P(1 + r/n)^(nt)

Where

Douglas presently has $2880, thus in order to reach his goal of $3774, he must earn the following amount in interest:

$3774 - $2880 = $894

We can set up the equation as follows:

$2880(1 + 0.057/4)^(4t) = $3774

Simplifying the left side, we get:

$2880(1.01425)^(4t) = $3774

Dividing both sides by $2880, we get:

(1.01425)^(4t) = 1.31042

Taking the natural logarithm of both sides, we get:

4t * ln(1.01425) = ln(1.31042)

Dividing both sides by 4 ln(1.01425), we get:

t = ln(1.31042) / (4 ln(1.01425)) = 13.12 quarters

Therefore, Given that there are 4 quarters in a year, Douglas will need approximately 13.12 quarters, or approximately 3 years and 4 months, to accumulate $3774, with two decimal places.

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It will take Douglas approximately 3.02 years to accumulate $3,774 by investing his initial $2,880 in an account that earns 5.7% annually, compounded quarterly.

We use the formula for compound interest to estimate how long it will take Douglas to accumulate the needed amount.

The compound interest formula we shall to solve the problem is:

A = P(1 + r/n)\(^(nt)\)

where:

A = amount of money after t years

P = principal amount (or initial investment)

r = annual interest rate (as a decimal)

n = number of compound interest per year

t = number of years

Filling in the values:

P = $2880

r = 0.057 (5.7% as a decimal)

n = 4 (compounded quarterly)

A = $3774

$3774 = $2880 (1 + 0.057/4)\(^(4t)\)

Simplifying the equation, we get:

1.308125 = (1.01425)\(^(4t)\)

We take the natural log from both sides:

ln(1.308125) = ln((1.01425)\(^(4t)\)

Using the logarithm, we can simplify the right-hand side:

ln(1.308125) = 4t * ln(1.01425)

Now we can solve for t by dividing both sides by 4ln(1.01425):

t = ln(1.308125) / (4 * ln(1.01425))

t ≈ 3.02

Therefore, it will take approximately 3.02 years, for Douglas to accumulate $3,774.

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==============================================

Further Explanation:

Whenever you are doing a proof, always start with the given info. It may seem silly to literally repeat (word-for-word) what your teacher has given you, but this is how all proofs start out. It helps place an anchor point in which you can connect to what you want to prove.

So this is why the first line is literally a repeat of what your teacher has stated. The reason you'll state is "given".

------------------

For reason 2, we use the vertical angle theorem. Vertical angles are always congruent.

Vertical angles form whenever we have an X shape like this of two segments crossing. The angles are opposite one another (almost like mirror images of sorts).

-----------------

Lastly, reason 3 uses the SAS (side angle side) similarity theorem.

This is the theorem which says that if you have two pairs of sides in proportion and a pair of congruent angles between those sides, then we can prove the triangles similar.

Statement 1 handles the sides being in proportion. Statement 2 handles the congruent angles.

As you can see, everything in this proof builds step by step toward the final goal of saying triangle ABC is similar to triangle EBD.

Answer:

well 1 plus 1 is 2 so i dont know

Step-by-step explanation:

:)

Answer:

1

Step-by-step explanation:

10a and -10a would combine and cancel eachother out leaving you with 1

The true intercept and slope are both different from the estimated values based on statistical significance.

The p-value of the intercept coefficient and that of the slope coefficients are 0 and 0.02(2%) respectively. This means that they are statistically significant. Thus we can infer that the true intercept and slope is not equal to 0.

The standard error of the intercept coefficient is 6, which means that the true intercept is likely to be within 6 units of the estimated intercept. The standard error of the slope coefficient is 1, which means that the true slope is likely to be within 1 unit of the estimated slope.

Therefore, the true slope and intercept will be different from the estimated slope and intercept.

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Answer:

9 x a x a x a x a x a x a

Step-by-step explanation:

\((3a^{3})^{2} = 9a^{6} \\\)  Here, we use the law of indices. Everything inside the bracket has to be squared, so 3^2 = 9 and (a^3)^2 = a^6 We use the rule of when one power is within a bracket and one outside, we multiply the two powers together instead of adding.

3^2 can be simplified to 9 as this is simply 3 x 3, but a^6 (this is still a value with an exponent) cannot be simplified so we break this down into the notation of a x a x a x a x a x a

Therefore 9 x a x a x a x a x a x a is the answer.

I hope this helps you!! ^-^

The expansion of (3a³)² without exponents will be 9 x a x a x a x a x a x a.

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

When a mathematical object is increased by a multiplier that is bigger in actual values than one, an expansion follows.

In another word, if you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.

In mathematics, all real-life problems can be converted into equations which are sometimes in form of factors and we need to expand them to create solutions.

Given the expression,

(3a³)²

By the law of indices

(3a³)² = 3²(a³)²

(3a³)² = 9a⁶

But we cannot write it in exponent form

So,

9a⁶ = 9 × a x a x a x a x a x a.

Hence "The expansion of (3a³)² without exponents will be 9 x a x a x a x a x a x a".

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Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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For the figure shown in the image having TV as the midsegment, the length of TV is 40

When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.

In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.

For the given figure, the proportionate sides are

UV and TV, UW and WX

Calculating for s

UV / TV = UW / WX

1 / (-2s + 42) = 2 / (3s + 77)

cross multiplying

3s + 77= 2(-2s + 42)

3s + 77= -4s + 84

collecting like terms

3s + 4s = 84 - 77

7s = 7

s = 1

solving for TV

= -2s + 42

= -2 * 1 + 42

= 40

the value of TV is 40

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Answer:

range =18-2

=16

mean=(n+1)/2

=6+1/2

=3.5

Step-by-step explanation:

range =largest value subtract by smallest value

Answer:

x=12

Step-by-step explanation:

Since the triangles are congruent, you can set each equation equal to each other and solve to find x:

11x-70=5x+2

6x-70=2

6x=72

x=12

I hope this helped!

Answer:

(A) Linear positive association

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

The answer is 0.71

Step-by-step explanation:

I divided it

Answer:

1.4 hours or 83 minutes

Step-by-step explanation:

90 mi / 65 mph = 1.4 hr

Melissa will take 1.4 hour to travel 90miles at a speed of 65 mph.

Speed is the rate of distance covered in a particular time.

It is equal to distance/time

We know that speed=distance/time

so the time will be =90/65

which will be equal to1.44 hour

Hence Melisa will take only 1.4 hour to travel 90 miles at a speed of 65 mph.

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Answer:

what......................

Answer:

Step-by-step explanation:

Answer:

$40.5.

Step-by-step explanation:

if 1/5 of the book costs $13.5. then to find 3/5 you just have to times the answer by 3.

Answer:

1. \(27^{\frac{2}{3} } =9\)

2. \(\sqrt{36^{3} } =216\)

3. \((-243)^{\frac{3}{5} } =-27\)

4. \(40^{\frac{2}{3}}=4\sqrt[3]{25} =4325\)

5. Step 4: \((\frac{343}{27}) ^{-1} =\frac{27}{343}\)

6. \(D. -72cd^{7}\)

Step-by-step explanation:

Use the following properties:

\(a^{\frac{x}{y} } =\sqrt[x]{a^{y} }\)

\(\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}\)

\(a^{-n} =\frac{1}{a^{n} }\)

\((xy)^{z} =x^{z} y^{z} \\\\\)

\((x^{y}) ^{z} =x^{yz}\)

\(x^{y} x^{z} =x^{y+z}\)

So:

1. \(27^{\frac{2}{3} } =\sqrt[3]{27^{2}} =\sqrt[3]{729} }=9\)

2. \(\sqrt{36^{3} } =\sqrt{36*36*36} =\sqrt{36} \sqrt{36} \sqrt{36} =6*6*6=216\)

3. \((-243)^{\frac{3}{5} } =\sqrt[5]{-243^{3} } =\sqrt[5]{-14348907} =-27\)

4. \(40^{\frac{2}{3}}=\sqrt[3]{40^{2} } =\sqrt[3]{2^{6} 5^{2} } =\sqrt[3]{2^{6} } \sqrt[3]{5^{2} } =2^{\frac{6}{3} } 5^{\frac{2}{3} } =4 *5^{\frac{2}{3} } =4\sqrt[3]{5^{2} } =4\sqrt[3]{25}=4325\)

5. \((\frac{343}{27}) ^{-1} =\frac{1}{\frac{343}{27} } =\frac{27}{343}\)

6.

\((-8c^{9} d^{-3} )^{\frac{1}{3} } *(6c^{-1}d^{4})^{2} =\sqrt[3]{-8} c^{3} d^{-1} 36c^{-2} d^{8} \\\\-2c^{3} d^{-1} 36c^{-2} d^{8}=-72cd^{7}\)

The correct choice is B

Let's solve the following triangle using the Law of Cosines for this given information, b = 10, c = 12, A = 59°. The Law of Cosines is expressed as;c² = a² + b² - 2ab cosCUsing the given values,

we can calculate the measure of the missing side of the triangle;a² = b² + c² - 2bc cosAa² = (10)² + (12)² - 2(10)(12) cos(59°)a² ≈ 144.1a ≈ 12 (rounded to one decimal place)Now we can use the Law of Sines to find the values of B and C.

The Law of Sines is expressed as;a/sinA = b/sinB = c/sinCa/sinA = b/sinBsinB = b (sinA / a)sinB = 10 (sin59° / 12)sinB ≈ 0.6914B ≈ sin⁻¹(0.6914)B ≈ 44.2°(rounded to one decimal place)C = 180° - A - BC = 180° - 59° - 44.2°C ≈ 76.8°(rounded to one decimal place),

the solution with the smaller angle B is;a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.Hence, the correct choice is;B. There are two possible solutions for the triangle. The measurements for the solution with the smaller angle B are as follows. a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.

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The domain of the function f(x) = 40t, which represents the number of pecans produced per tree, is all real numbers.

In this context, the variable t represents the number of trees, and since the number of trees can be any real number, the domain of the function is also all real numbers.

This means that the function can be evaluated for any real value of t, including positive and negative numbers, fractions, decimals, and zero.

Therefore, the domain of the function f(x) = 40t is all real numbers.

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As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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Answer:

the picture wont show for the x

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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Answer:

-22 /3 + (-94/5)

-22/3 + -89/5

Step-by-step explanation:

-110/15 + - 257/15

-367/15

The shadow is cast by a person 5 feet tall while a flagpole 20 feet tall casts a shadow 40 feet long is 10 feet.

The mathematics, a ratio indicates how many times one number contains another. A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

Given that, the shadow cast by a person is 5 feet.

The flag pole height = 20 feet.

The flagpole shadow = 40 feet.

Using proportion, we get

20/40 = 5/x

20x = 40 × 5

20x = 200

Therefore, the person casts a shadow 10 feet long.

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Answer:

3, 4, 5

Step-by-step explanation:

We can check each one by seeing if they satisfy the Pythagorean theorem (which is a^2+b^2=c^2; we are going to make the 2 shorter sides a and b, and the longer side c):

\(1^2+5^2=1+25=26\neq 10^2\\3^2+4^2=9+16=25=5^2\\2^2+5^2=25+4=29\neq 5^2\\2^2+2^2=4+4=8\neq 2^2\)

We can see that the only pythagorean triple here is 3, 4, 5.

Alternatively, you could memorise some easy pythagorean triples, like (3, 4, 5), (5, 12, 13), and (7, 24, 25).

Side note: if you multiply each one of these values by any number, it's still going to be a pythagorean triple. For example, (3*2,4*2,5*2) = (6,8,10) is still a pythagorean triple.

The 3,4,5 shows the Pythagorean Triple.

The information regarding the Pythagorean Triple is as follows:

Based on the above information, the calculation is as follows:

\(3^2 + 4^2 = 5^2\)

9 + 16 = 25

25 = 25

Therefore we can conclude that the 3,4,5 shows the Pythagorean Triple.

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