Select the correct answer.
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?
A. x = -9
B. X=-6
C. y=-9
D. y=-4

Answer:

x = -2

Step-by-step explanation:

We are given the logarithmic base 2 equation of:

[tex]\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}[/tex]

Apply logarithm property of addition where:

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

Therefore, we will write new equation as:

[tex]\displaystyle{\log_2 [4x(x+1)] = 3}[/tex]

Apply logarithm to exponential form using:

[tex]\displaystyle{\log_a M = N \to a^N = M}[/tex]

Thus, another new rewritten equation is:

[tex]\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}[/tex]

Expand the expression in and arrange the terms in quadratic expression:

[tex]\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}[/tex]

Solve for x:

[tex]\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}[/tex]

These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.

( 1 ) 4x > 0, x > 0

( 2 ) x + 1 > 0, x > -1

Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.

Hence, x = -2 is the extraneous solution.

Answer:

Not similar

Step-by-step explanation:

They are not similar because the ratio is not the same. 42/35 = 1.2 and 14/10=1.4

Step-by-step explanation:

what is the problem ? this is very straight forward with a calculator :

cos(64°) = y/8

y = 8×cos(64°) = 8×0.438371147... = 3.506969174... ≈

≈ 3.5

Answer:

Step-by-step explanation:

circumference for A=2π×12=24π

linear velocity=24π÷6=4π cm/sec

circumference for B=2π×15=30π

linear velocity=30π÷6=5π cm/sec

Answer:

4 cups of tea

Step-by-step explanation:

12 ounces ÷ 2/3 ounces = 18 cups of tea.

12/1 ÷ 2/3

12/1 x 3/2

= 36/2

=18

Answer:

4 cups of tea

Step-by-step explanation:

Given Trinity has 12 ounces of tea leaves, and 1 cup of tea requires 3 ounce of tea leaves,

No. of cups of tea = Total amount of tea leaves / Tea leaves required per cup of tea

= 12 / 3

= 4 cups of tea.

The values of the composite functions can be derived from the given tables as follows;

By composite functions definition, we have;

(g•f)(0) = g(f(0))

From the given tables, we have;

f(0) = 1

g(1) = -2

Therefore;

Similarly, we have;

(g•f)(1) = g(f(1))

From the given tables, we have;

f(1) = 0

g(0) = 1

Therefore;

The domain of f(x) are the possible x-values of f(x).

The range of g(x) are the possible y-values of g(x).

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Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters in this problem are given as follows:

[tex]\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5[/tex]

Item a:

The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:

X = 1250:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1250 - 1140}{77.5}[/tex]

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1000 - 1140}{77.5}[/tex]

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is one subtracted by the p-value of Z when X = 1250, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the p-value of Z when X = 1220, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1220 - 1140}{77.5}[/tex]

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

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The fourth term in the Binomial expansion of [tex](e + 2f)^{10}[/tex] is [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]

In elementary algebra, The Binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial [tex](x + y)^{n}[/tex] into a sum involving terms of the form [tex]ax^{b}y^{c}[/tex], where the exponents b and c are nonnegative integers with b + c = n ,  and the coefficient a of each term is a specific positive integer depending on n and b.

The binomial theorem formula is [tex](x + y)^{n}[/tex] = ∑ [tex]nC_{r} x^{n-r}y^{r}[/tex], where n is a positive integer and x, y are real numbers, and 0 < r ≤ n.

The formula to find the nth term in the binomial expansion of [tex](x + y)^{n}[/tex] is [tex]T_{r+1} = nC_{r} x^{n-r}y^{r}.[/tex]

As question demands fourth term of the expansion we need to substitute

r = 3 in the formula of nth term

On substituting we get

[tex]T_{3+1} = 10C_{3} (e)^{10-3}(2f)^{3}.[/tex]

[tex]T_{4} =[/tex] [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]

Hence the fourth term in the binomial expansion of [tex](e + 2f)^{10}[/tex] is [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]

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Step-by-step explanation:

gd seek is sssa eh uiiio if fsssw we to i if i jobs sss

The linear inequality wthat will not have a shared solution set with the graphed linear inequality is C. y > 5/3x + 2.

It should be noted that the graph shows the shaded area as y < 5/3x + 1.. The slope of the line will be 5/3.

The two parallel lines are the same. The graph of the inequality is also attached.

The complete question is:

Which linear inequality will not have a shared solution set with the graphed linear inequality?

A. y < 5/3x – 2

B. y < -5/3x + 1

C. y > 5/3x + 2

D. y > -5/3x + 2

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Answer:

  x = 1

Step-by-step explanation:

The value of x can be found in this one-step linear equation by dividing by its coefficient.

  4 = 4x . . . . . simplify

  1 = x . . . . . . . divide by 4

Answer:

in the 8 is ADB, in the 7 I'm not sure about you need to do sorry, or maybe you need to classify what triangle it is think is a scalene triangle because has a different measurements

The solution to the given equation is x = ±7. The correct option is d. x = ±7

From the question, we are to determine the solution to the given equation

The given equation is

x²-49 = 0

NOTE: I assumed the variable is x

Solving the equation

x²-49 = 0

Writing in the form ax²= c

x² = 49

∴ x = ±√49

x = ±7

Hence, the solution to the given equation is x = ±7

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Hello,

Y = ax + b (where a is the slope) si here the slope is 5/4

Answer:

5/4

Step-by-step explanation:

• Compare the given equation with the general equation of a straight line:

y = 5/4 x  - 7/4

y =   m x  +   c                          [m = slope, c = y-intercept]

As we can see, m in the general equation corresponds to 5/4 in the given equation. This means the slope is 5/4.

(We can also see that the y-intercept is -7/4.)

Answer: 15

Step-by-step explanation:

The rate of change of Function A is 35.

The rate of change of Function B is 50.

So, the difference in the rate of change is 50-35 = 15.

Answer:

990 ft

Step-by-step explanation:

1 yard = 3 feet, using this we can multiply 140 by 3 to convert it from yards to feet.

140 yd * 3 = 420 ft.

Next, to find the perimeter we need to follow this formula:

l + l + w + w.

420 ft + 420 ft + 75 ft + 75 ft = 990 ft

The total distance that needs to be fenced in feet is;

990 ft.

The functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.

It should be noted that function simply means the illustration that shows the relationship between the variables.

In this case, the functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.

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Answer:

17038.94mm

Step-by-step explanation:

The problem proves that the distributor's claim is true and he has a right to complain.

But when the confidence interval is changed from 95% to 90% the distributor's claim proves to be false.

The Confidence Interval for 95%  is 0.9687;0.98532

For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.

The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.

The Confidence Interval for 90%  is 0.97156;0.982431

Here

μ = 0.977

s= σ= 0.03

95 % confidence interval is given by

x~± z∝/2 (s/√n)

Putting the values

0.977 ± 1.96 (0.03/√50)

=0.977 ± 0.008315

0.9687;0.98532

Part B:

x~+ 0.95= 0.977+0.95= 1.927

The critical region is Z ≥ 1.96 therefore the 1.927 lies in the acceptance region that the distributor's claim is true.

Part C:

For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.

Part D:

μ = 0.977

s= σ= 0.03

90 % confidence interval is given by

x~± z∝/2 (s/√n)

Putting the values

0.977 ± 1.28 (0.03/√50)

=0.977 ± 0.005431

0.97156;0.982431

Part D:

x~+ 0.90= 0.977+0.90= 1.877

The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.

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Answer:

77.5° and

102.5°

Step-by-step explanation:

Angles in a linear pair sum up to 180°

Therefore, x + (x +25) = 180

x + x +25 = 180

2x + 25 = 180

2x = 180- 25

2x 155°

dividing bothsides by 2

x = 155/2

x = 77.5

Therefore,

x = 77.5°

(x+25) = 77.5 + 25 = 102.5°

The graph of the functions f(x) and g(x) are the same

The function is given as:

f(x) = log₂(x)

See attachment for the sketch of the graph.

From the graph, we can see that the x values are greater than 0

This means that the domain of f is x > 0

We have:

f(x) = log₂(x)

Rewrite as:

y = log₂(x)

Swap x and y

x = log₂(y)

Express as an exponential function

y = 2ˣ

So, we have:

f⁻¹(x) = 2ˣ

Hence, the equation of f⁻¹(x) is f⁻¹(x) = 2ˣ

We have:

f⁻¹(x) = 2ˣ

Set the function to 0

f⁻¹(x) = 0

Rewrite as:

y = 0

Hence, the asymptote of f⁻¹(x) is y = 0

We have:

f(x) = log₂(x)

g(x) = log₂(x)

Both equations are the same.

Hence, the graph of f(x) and g(x) are the same

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Answer:

1

Step-by-step explanation:

There is one whole 3 inside of 4 1/2 or 4.5.

Multiples of 3 are 3x1=3   3x2=6....

Only a single whole 3 can be inside of 4.5.

Answer:

One

Step-by-step explanation:

ONE

4.5 ÷ 3 = 1 . 5   <=====so there is one and a half 3's in 4.5

Answer:

Step-by-step explanation:

Givens

t1 = 2

r = 3

n = 10

Formula

tn = a*r^(n -1)         Substitute the givens into the this formula

Solution

t10 = 2 * 3^(10 - 1)

t10 = 2 * 3^9

t10 = 2 * 19683

t10 = 39366

Answer: 39366

Answer:

This is the Answer

Step-by-step explanation:

Pls mark as brainliest

Answer:

  6

Step-by-step explanation:

The average of a set of numbers is their sum divided by their number. This fact lets us write an equation to find the missing number.

Let x represent the missing number. The average of the 4 numbers is ...

  (x +18 +11 +25)/4 = 15

Multiplying by 4 gives ...

  x +54 = 60

Subtracting 54, we find the missing number:

  x = 6

The other number is 6.

Answer:

Step-by-step explanation:

for reflection around x-axis.

(x,y)→(x,-y)

so P' is (-7,4)

Answer:

491 mg per dose

Step-by-step explanation:

1 kg ≈ 2.2 lbs

81/2.2 36.82 kg

40*36.82 ≈ 1472.8 mg/day

1472.8/3 ≈ 490.93

to the nearest mg = 491 mg per dose

K=1/3

simplify each bracket, put all numbers on the left hand side, equal it to 0 and solve for k

The rate of return earned on the investment of $475 five years ago in the corporate stock is 312.63%.

The rate of return is the net gain or loss of an investment expressed as a percentage of the investment's initial cost.

It is given by the formula,  R= {Vf - Vi}/{Vi} x 100.

Where:

R = Rate of return

Vf = final value, including dividends and interest

Vi = initial value

Investment cost = $475

Dividends received:

1st two years = $80 ($10 x 8)

Three years = $180 ($15 x 12)

Total dividends received = $260 ($80 + $180)

Total revenue from sale = $1,700

Total proceeds = $1,960 ($1,700 + $260)

Total return = $1,485 ($1,960 - $475)

Rate of return = 312.63%  ($1,485/$475 x 100)

Thus, the rate of return is 312.63%.

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