The 3 points plotted below are on the graph of y=b^x. Based only on these 3 points, plot the 3 corresponding points that must be on the graph of y=log_b x by clicking on the graph.

Answer:

18000 m

Step-by-step explanation:

Hey there!

In order to solve this problem, we need to first know how many minutes are in an hour

As you know, there are 60 minutes in an hour so this means in 1 hour, he will climb 9000 meters two times

So 9000 two times is 18000,

Meaning, in 1 hour, Sam will climb 18000 m

Answer:

18,000m in an hour

Step-by-step explanation:

We know this because if its 9000 m in 30 minutes, we can do 9000 x 2 and get 18,000m for an hour.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Answer:

200 < p < 300

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Answer: 20%

Step-by-step explanation: 150 times .2 equals 30

We are going to use the following equation:

Where is the interest paid, P is the principal, r is the annual rate and t is the time in years.

So, the time in years can be calculated as:

Therefore, the annual rate r, can be calculated as:

Answer: 7.8%

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

No, I don't agree with Andre.

The greatest product is the highest number obtained by multiplying the given digits in a manner that gives us the largest number.

In case of 5,6,7,8,9 ; the greatest product is 84,000 which is obtained  by multiplying 875 × 96 = 84000.

According to Andre the greatest product is 987 × 65 = 64155, which you can comprehend is much lower than 84000.

For example, Among 54 × 6 ; 46 × 5 ; 65 ×4 = 324 ; 230 ; 260 , the first  one is the greatest product.

Similarily in 875 × 96, in which the second number i.e., 96 is greater rather than 65 in 987 × 65 ; it gives the greatest product.

Hence, I don't agree with Andre as the greatest product is 875 × 96 .

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

see below

Step-by-step explanation:

We know that we have a right triangle with x^2 + y^2 = 25^2

x^2 + y^2 =625

Taking the derivative with respect to time on each side

d/dt( x^2 + y^2) =d/dt 625

The derivative of x^2 with respect to t is 2 x  times dx/dt and

the derivative of y^2 with respect to t is 2 y  times dy/dt and

and the derivative of a constant is zero

2 x  dx/dt  + 2 y dy/dt = 0

We are trying to find dy/dt or the rate it is sliding down the wall

Subtracting 2y dy/dt

2 x  dx/dt  = -  2 y dy/dt

Divide each side by  -2y

2x/- 2y * dx/dt = dy/dt

-x/y * dx/dt = dy/dt

We know that dx/dt = 2

If the base is 7   x^2 + y^2 =625  7^2 + y^2 = 625  so y = sqrt(625 - 49) =24

-7/24 * 2 = dy/dt

-7/12 ft/sec= dy/dt  when x=7

If the base is 15   x^2 + y^2 =625  15^2 + y^2 = 625  so y = sqrt(625 - 225) =20

-15/20 * 2 = dy/dt

-3/2ft/sec= dy/dt  when x=15

If the base is 24   x^2 + y^2 =625  24^2 + y^2 = 625  so y = sqrt(625 - 576) =7

-24/7 * 2 = dy/dt

-48/7 ft/sec= dy/dt  when x=24

Now we need to find the rate at which the area is changing

A = 1/2 xy

Taking the derivative of each side

dA/dt =d/dt ( 1/2 xy)

Using the product rule of derivatives

        = 1/2 ( x dy/dt + y dx/dt)

 Using the information for 7 ft from the wall

x = 7, dy/dt = -7/12, y = 24 and dx/dt =2

      =  1/2 ( 7 * -7/12 + 24*2)

      = 1/2 ( -49/12+ 48)

  = 527/24 ft^2/ sec

Answer:

  a) -7/12, -3/2, -48/7 . . . feet per second

  b) 21 23/24 square feet per second

Step-by-step explanation:

a) Let x represent the distance of the base from the wall. Then the Pythagorean theorem relates r, x, and the length of the ladder:

  r^2 +x^2 = 25^2

  2r·r' +2x·x' = 0 . . . . . derivative with respect to time

  r' = -x·x'/r

  r' = -x·x'/√(25^2 -x^2)

For x = 7, r' = -7(2)/√(625 -49) = -14/24 = -7/12 ft/s

For x = 15, r' = -15(2)/(√(625 -225) = -30/20 = -3/2 ft/s

For x = 24, r' = -24(2)/√(625 -576) = -48/7 ft/s

__

b) The area is ...

  A = 1/2rx

Then the rate of change of area is ...

  A' = (1/2)(r'x +rx') . . . . differentiate with respect to time

At x=7, this is ...

  A' = (1/2)(-7/12×7 +24×2) = 21 23/24 . . . ft^2/s

Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2

There is no solution to the equation.

An equation is a mathematical statement which is formed when two algebraic expression are equated using an equal sign.

A Trigonometric Equation is given

3 cos\(\rm \theta\) +1 = 4

3cos\(\rm \theta\) =3

cos\(\rm \theta\) = 1

\(\rm \theta\) = cos⁻¹ 1

\(\rm \theta\) = 0 , 2nπ , both the solution does not exist as the limit of the function is   0 < theta < 360 ,

There is no solution to the equation.

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Answer:

using diameter, The Area of the circle is 28.27

Step-by-step explanation:

A = 1/4(3.14)(d^2)

A = 28.27

Answer:

Mean = 2.2

Median = 1

Mode = 0 and 1

Range = 9

Step-by-step explanation:

First arrange the number of calls from least to greatest.

0, 0, 0, 1, 1, 1, 2, 3, 5, 9

Mean is the average. Add the numbers together and divide by 10 since there are 10 numbers in total.

0 + 0 + 0 + 1 + 1 + 1 + 2 + 3 + 5 + 9 = 22

22/10 = 2.2

Mean = 2.2

Median is the middle number. Since there is an even amount of numbers, take the 5 and 6 number in the list, add them together and divide by 2. You are taking the average of the two numbers.

0, 0, 0, 1, 1, 1, 2, 3, 5, 9

1 + 1 = 2

2/2 = 1

Median = 1

Mode is the number that occurs the most.

0, 0, 0, 1, 1, 1, 2, 3, 5, 9

In the list the numbers 0 and 1 both occur 3 times.

Mode = 0 and 1

Range is the biggest number (9) minus the smallest number (0).

0, 0, 0, 1, 1, 1, 2, 3, 5, 9

9 - 0 = 9

Range = 9

The answer is A and D

good luck

The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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Answer:

Step-by-step explanation:

0.0000158

Answer:

dependent care FSA

Health FSA

IRA

Step-by-step explanation:

The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.

Given an expression, -3x²-24x-36;

Factorizing, we get,

-3x²-24x-36 = -3(x²+8x+12)

= -3(x²+6x+2x+12)

= -3[x(x+6)+2(x+6)]

= -3(x+6)(x+2)

Hence, The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

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The coordinates of N are (5,-6)  so that segment MN is 3/7 of MP.

Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).

now we have to find the coordinates of N such that the MN : NP is 3:4 .

We will use the section formula:

The section formula states that:

\({\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}\)

Where the coordinates of the points are given and the ratio in which the points are divided is given.

Now we will substitute the values:

\({\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}\)

Solving we get:

N=(5,-6)

The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.

Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.

Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.

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Answer:

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.

Answer:

The smallest integer is -27 and the integers are -27, -26, and -25

Step-by-step explanation:

We can represent this with:

x + x - 1 + x - 2 = -78

Simplify.

3x - 3 = -78

Add 3 to both sides.

3x = -75

Divide both sides by 3.

x = -25

So, the first integer is -25.

Subtract two to get the smallest integer.

-25 - 2 = - 27

Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

\( 2x^2y^3 - 3x^2 = 149 - 4y^3 \)

\( x^2(2y^3 - 3) = 149 - 4y^3 \)

\( x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} \)

\( x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} \)

Try y = 1

\(x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}\)

For y = 1, x is imaginary.

Try y = 2

\( x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3\)

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5

The value of x + y is 5.

Polynomials are expressions which consist of variables, constants, coefficients and exponents.

We have the equation,

2x²y³ + 4y³ = 149 + 3x²

2x²y³ - 3x² = 149 - 4y³

x² (2y³ - 3) = 149 - 4y³

x² = (149 - 4y³) / (2y³ - 3)

x = √[(149 - 4y³) / (2y³ - 3)]

Now, we have to find two positive integers.

We can use trial and error method here.

Trial putting y = 1.

x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]

  = √[145 / (-1)]

  = √(-145)

There is no real root for √(-145). So y = 1 is not applicable.

Trial putting y = 2.

x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]

  = √[117 / 13]

  = √(9)

  = ± 3

But we need positive integers. So we ignore -3.

So x = 3 and y = 2 ⇒ x + y = 5

Hence x + y = 5.

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Answer:

4

Step-by-step explanation:

10y^2/ z

10(-2)^2/-5

10 ×-2 =-20

-20÷-5=4

The value of the expression is -8.

The expression when y=−2 and z=−5 in 10y²/z will be gotten by putting the values of y and z into the expression that's given. This will be:

10y²/z = 10(-2)²/-5

= 10(4)/-5

= 40/-5

= -8

In conclusion, the value of the expression is -8.

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The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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Step-by-step explanation:

1. if x=-4, then the value of the given function is f(x)=7/0 - impossible to divide by zero; in this case the correct answer is 'any number except -4';

2. if to see the behavior of the given function near x=-4, then:

\(\lim_{x \to -4^+}( \frac{7}{x+4} )=+ \infty;\\ \lim_{x \to -4^-}(\frac{7}{x+4})=- \infty.\)

3. correct answers are marked with green colour (see the attachment).

Answer:

Domain:  all real numbers x except x = -4

\(\textsf{End behaviour}: \quad f(x) \rightarrow - \infty \; \textsf{as} \; x \rightarrow -4^{-}, \;f(x) \rightarrow \infty \; \textsf{as} \; x \rightarrow -4^{+}\)

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{7}{x+4}\)

The domain of a function is the set of all possible input values (x-values).

When the denominator of a rational function is zero, the function is undefined.

To find the value(s) of x for which the function is undefined, set the denominator to zero and solve for x:

\(\implies x+4=0\)

\(\implies x+4-4=-4\)

\(\implies x=-4\)

Therefore, the domain of the given function is:

The vertical asymptote(s) of a rational function are the values of x for which the denominator is zero.

Therefore, there is a vertical asymptote at x = -4.

As x gets very close to x = -4 from the negative side, the function approaches -∞ because the denominator will be an extremely small negative number.

As x gets very close to x = -4 from the positive side, the function approaches ∞ because the denominator will be an extremely small positive number.

Therefore, the behaviour of the function near the excluded x-value is:

\(\\ \sf{:}\dashrightarrow \dfrac{w^2}{25}+45w+155\)

\(\\ \sf{:}\dashrightarrow \dfrac{52}{25}+45(52)+155\)

\(\\ \sf{:}\dashrightarrow \dfrac{52}{25}+2340+155\)

\(\\ \sf{:}\dashrightarrow \dfrac{52}{25}+2495\)

\(\\ \sf{:}\dashrightarrow 2+2495=2498\)

We know that x represents the number of trips to the airport, and y represents the number of trips from the airport. If the taxi driver had 18 fares in total, then we can express the first equation.

The price of a ride to the airport is $3.50 and from the airport is $9, if the driver collected $118 for the day, then we can express the second equation.

In order to solve this system of equations, let's solve the first equation for x.

Then, we combine it with the second equation.

Once we have the value of one variable, we can easily find the value of the other one.