A system of three linear equations in three variables is consistent and dependent. How many solutions to the system
exist?
Onone
Oone
Othree
O infinitely many

Answer:

[tex](f+g)(x)=7x^2-3x-5[/tex]

Step-by-step explanation:

Step 1: What you are given & need to find

Step 2: Set up the problem

Step 3: Simplify

Answer:

Person 2 jogs faster as compared to person 1.

The time taken by the faster jogger finish a five-kilometer race will be, 27.5 minutes.

Step-by-step explanation:

speed = distance/time

Answer:16.e+6.18

Step-by-step explanation:

Answer:

It is A. C. and D.

Step-by-step explanation.

The question is asking for the three different points to be moved, answer choice A is the answer for one point, answer C is for the second point, and answer D is for the third point.

Answer:

[tex]x=10^{\frac{4}{3}}=\sqrt[3]{10000}[/tex]

Step-by-step explanation:

Given equation:

[tex]9^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 3^{\log_3 (\log x)^2}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply log law}: \quad a^{\log_ab}=b[/tex]

[tex]\implies (\log x)^2= \log x-2\log^2x+4[/tex]

Simplify:

[tex]\implies\log ^2 x= \log x-2\log^2x+4[/tex]

[tex]\implies 3\log ^2 x- \log x-4=0[/tex]

Let log(x) = u:

[tex]\implies 3u^2-u-4=0[/tex]

Factor:

[tex]\implies 3u^2+3u-4u-4=0[/tex]

[tex]\implies 3u(u+1)-4(u+1)=0[/tex]

[tex]\implies (3u-4)(u+1)=0[/tex]

Apply the zero-product property:

[tex]\implies 3u-4=0 \implies u=\dfrac{4}{3}[/tex]

[tex]\implies u+1=0 \implies u=-1[/tex]

Substitute u=log(x) back in:

[tex]\implies \log x = -1[/tex]

[tex]\implies \log x= \dfrac{4}{3}[/tex]

On the left side of the original equation, we have log₃ (log x).  

As logs of negative numbers cannot be taken, log(x)=-1 is not a valid solution since this would give log₃(-1) which is undefined.

Therefore, the only valid solution is:

[tex]\implies \log x= \dfrac{4}{3}[/tex]

[tex]\implies x=10^{\frac{4}{3}}[/tex]

[tex]\implies x=\left(10^4\right)^{\frac{1}{3}}[/tex]

[tex]\implies x=10000^{\frac{1}{3}}[/tex]

[tex]\implies x=\sqrt[3]{10000}[/tex]

Note: If a log has no base, assume that the base is 10.

Answer:

The average speed is 80km/h.

Step-by-step explanation:

In order to calculate the average speed you have to divide the total distance by the total elapsed time:

Let t represent time (in hours)

t=12:30-11:30=1

Let D represent distance (in kilometers)

D=80

Therefore, since t=/=0:

D/t=80/1=80km/h

And there you have it! Your answer is 80 km per hour.

Answer:

123.00

Step-by-step explanation:

The correct answer is  H0 : Living in Northern or southern California is not associated with watering habits and  Ha : Living Northern or southern California is associated with watering habits.

Given that,

H0 : Living in Northern or southern California is not associated with watering habits.

Ha : Living Northern or southern California is associated with watering habits.

In independent test in that test we Check the two variables are independent or not. The chi square can be used for any variable. Both the group (independent) and test variable(dependent)   can be nominal, ordinal, or grouped interval.

Therefore, The difference between living in Northern or Southern California and the difference between living in Northern or Southern California is that the former is related to watering practices.

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The sample size will now have to be is 3200.

Given:

the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000.

n = p(1-p)(z/E)^2

800 = 0.5(1-0.5)(z/0.05)^2

800 = 0.5*0.5* z^2/0.0025

800 = 0.25 * z^2/0.0025

800 = 25/100*10000*z^2/25

800 = 1*100*z^2

800/100 = z^2

8 = z^2

z = [tex]\sqrt{8}[/tex]

z = 2.8284

n = p(1-p)(z/E)^2

= 0.25(2.8284/0.025)^2

= 0.25*(113.136)^2

= 0.25*12799.754496

= 3199.938 ≈ 3200

Therefore the sample size will now have to be is 3200.

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The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .

In the question ,

Four equations are given , we need to find the equation that represents the identity property of multiplication .

we know that the identity property of multiplication states that the product of any number and 1 is the same given number .

For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .

So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is

(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)

Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .

The given question is incomplete , the complete question is

Which equation illustrates the identity property of multiplication?

(a) (a + bi) × c = (ac + bci)

(b) (a + bi) × 0 = 0

(c) (a + bi) × (c + di) = (c + di) × (a + bi)

(d) (a + bi) × 1 = (a + bi)

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Answer:

in the picture

Step-by-step explanation:

Hope this helped! Solve your problem: Use the quadratic formula to solve for x.

8x²-8x-1=0

Answer:

The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

Reasons:

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to

Step-by-step explanation:

Answer:

  5.5%

Step-by-step explanation:

You want the interest rate that can be compounded continuously to give $1490 from an investment of $650 after 15 years.

The formula for account value with continuously compounded interest is ...

  A = Pe^(rt) . . . . P=principal, r=interest rate, t=years

Solving for r, we find ...

  ln(A/P)/t = r

  ln(1490/650)/15 = 0.0553...

The interest rate is about 5.5%.

<95141404393>

Answer:

x = 5

Step-by-step explanation:

Let's say

x = #s of nickels Nina has (we are going to try to get X)

y = # of nickels Maurice has

5x + 9 < The amount Nina has

y = 2x < Amount that Maurice has

Add them both to the total, 84

5x + 9 + 5y = 84

Transfer the 9 to the other side

5x + 5y = 75

Substitute y with it's value

5x + 5(2x) = 75

5x + 10x  = 75

15x = 75

Divide

x = 5

Answer:

90 liters

Step-by-step explanation:

It's given in the question!

74-126+329/2

-52+329/2

277/2

138.5

The length of the side x on the right triangle is 41.06

A right triangle is a triangle that has one interior angle of 90°

The parameters in the right triangle are;

Acute angle = 47°

Leg length of side adjacent to 47° = 28

Length of the hypotenuse = x

From trigonometric ratios, we have;

[tex]cos(\theta) =\mathbf{ \dfrac{Length \, of \, adjacent \, side}{Length \, of \, Hypotenuse}}[/tex]

The cosine of the 47° angle is therefore;

[tex]cos(47^{\circ}) = \dfrac{28}{x}[/tex]

From which we have;

[tex]x= \dfrac{28}{cos(47^{\circ}) } \approx 41.06[/tex]

The length of the side, x ≈ 41.06

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Answer:

The number of candy bars each friend will receive is 1.66.

Step-by-step explanation:

Given that Becky has 5 candy bars

She wants to share them with 3 friends.

To determine the number of candy bars each friend will receive

We need to determine the number of candy bars each friend will receive

So,  the number of candy bars would be

5/3 which would = to 1.66

and that's how much she will give each friend

Answer:

l = 1

Step-by-step explanation:

v = lwh

8 = l(2)(4)

8 = l8  Divide both sides by 8

1 = l

The value of g = 4π²l/T²

Operators are Mathematical operations that emphasize particular actions like summing up, dividing, and adding multiple times, etc.

In Mathematics, the basic arithmetic operations are Addition, Subtraction Division, and Multiplication.  

The symbols which are used for each operation are

Addition  - (+)

Subtraction  - (-)

Division  - (÷)

Multiplication  - (x)  

Given [tex]l = \frac{gT^{2} }{4 \pi ^{2} }[/tex]  

To get the 'g' value we will use Multiplication and Division

Multiply both sides with 4π²  

=> [tex]4 \pi ^{2} (l )= \frac{gT^{2} }{4 \pi ^{2} }(4 \pi ^{2} )[/tex]  

=> [tex]4 \pi ^{2} (l )= gT^{2}[/tex]  

Divide by T² on both sides

=> [tex]4 \pi ^{2} (l )\frac{1}{T^{2}} = g\frac{T^{2}}{T^{2}}[/tex]

=> [tex]\frac{ 4 \pi ^{2} l }{T^{2}} = g[/tex]

=> [tex]g = \frac{ 4 \pi ^{2} l }{T^{2}}[/tex]  

Therefore,

The value of g = 4π²l/T²

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The initial size of the bacteria culture is 33

The count of the bacteria after 10 days = 200

The count of bacteria after 20 days = 1200

The difference in time = 20 - 10

= 10 days

Then the exponential growth equation will be

1200 = 200×[tex]e^{10k}[/tex]

[tex]e^{10k}[/tex] = 1200 / 200

Divide the terms

[tex]e^{10k}[/tex] = 6

10k = ln(6)

10k = 1.79

k = 1.79 / 10

Divide the terms

k = 0.179

Use the same equation to find the initial size of the bacteria culture

200 = x × [tex]e^{10(0.179)}[/tex]

x = 200 / [tex]e^{10(0.179)}[/tex]

x = 200 / 5.99

Divide the terms

x = 33.38

x ≈ 33

Hence, the initial size of the bacteria culture is 33

The complete question is:

The bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially. Find the initial size of the bacteria culture

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Answer:

[tex]-2[/tex]

Step-by-step explanation:

The perpendicular slope is the opposite of the reciprocal of the original slope. So, let's find the slope of this line! I will put it in slope-intercept form (y = )

[tex]x-2y=-8\\-2y=-8-x\\y=4+\frac{1}{2} x\\y=\frac{1}{2} x+4[/tex]

Here, I see that the slope of the line is [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2. The opposite of 2 is [tex]-2[/tex]. The slope of the perpendicular line is [tex]-2[/tex]!

Answer:

1st

Step-by-step explanation:

Explanation in the picture.

Answer:

both

Step-by-step explanation:

because the first one, since the number 4 isn’t next to the parentheses then we are not multiplying so it’s actually adding so it still equals 7

Thus, solving the linear inequalities for y we have

y > 4 - (2/3)x,

y > (3/2)x - 3, and

y ≥ 6x - 6

We have to solve each of the linear inequality for y.

1. The given linear inequality is -

2x + 3y > 12

=> 3y > 12 - 2x

=> y > 4 - (2/3)x

2. The given linear inequality is -

3x - 2y < 6

=> -2y < 6 - 3x

=> 2y > 3x - 6

=> y > (3/2)x - 3

3. The given linear inequality is -

4y - 2x ≥ 4x + 3(y-2)

=> 4y - 2x ≥ 4x + 3y - 6

=> 4y - 3y ≥ 4x + 2x - 6

=> y ≥ 6x - 6

Thus, solving the linear inequalities for y we have

y > 4 - (2/3)x,

y > (3/2)x - 3, and

y ≥ 6x - 6

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Answer:

[3, ∞]

Step-by-step explanation:

In the binomial expansion of (2 + 3x)ⁿ, the value of n = 22/5

Binomial expansion is the expansion of the binomial (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ where ⁿCₓaˣbⁿ⁻ˣ is the general term and x = 0 to n

Since we require the expansion of  (2 + 3x)ⁿ, comparing it with the binomial expansion equation above  (a + b)ⁿ.

So, a = 2 and b = 3x

So, the binomial expansion is (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3x)ⁿ⁻ˣ

= ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ

So, the general term of  (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ and the coefficient term is ⁿCₓ2ˣ(3ⁿ⁻ˣ)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15. Then

For the x³ term, xⁿ⁻ˣ = x³

⇒ n - x = 3

⇒ x =n - 3

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₃2ⁿ⁻ˣ(3³) =

Also, for the x⁴ term, xⁿ⁻ˣ = x³

⇒ n - x = 4

⇒ x =n - 4

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15, we have that

ⁿCₙ₋₃2ⁿ⁻ˣ(3³)/ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴) = 8/15

ⁿCₙ₋₃/(ⁿCₙ₋₄ × 3)= 8/15

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/15 × 3

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/5

n!/(n - 3)![n - (n - 3)]!  ÷ n!/(n - 4)![n - (n - 4)]! = 8/5

n!/(n - 3)![n - n + 3)]!  ÷ n!/(n - 4)![n - n + 4)]! = 8/5

n!/(n - 3)!3!  ÷ n!/(n - 4)!4! = 8/5

n!/3!(n - 3)! ÷ n!/4!(n - 4)(n - 3)! = 8/5

n!/3!(n - 3)! × 4!(n - 4)(n - 3)!/n! = 8/5

4!/3! × (n - 4) = 8/5

4 × 3!/3! × (n - 4) = 8/5

4(n - 4) = 8/5

Dividing through by 4, we have

(n - 4) = 8/(5 × 4)

(n - 4) = 2/5

Cross-multiplying, we have

5(n - 4) = 2

Expanding the brackets, we have

5n - 20 = 2

5n = 20 + 2

5n = 22

n = 22/5

So, the value of n = 22/5

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