Which expression is equivalent to 4^7 x 4^-5

Answer:

i also needed help on this qustion and the awnser is

Step-by-step explanation:

C.

its the same problem and nothing changed besides the order↑≠≈

Answer:

The answer is C

Step-by-step explanation:

Answer:

Step by step and hope this helps

70=−2.5x

Step 1: Flip the equation.

−2.5x=70

Step 2: Divide both sides by -2.5.

−2.5x−2.5=70−2.5

x=−28

Answer:

-10 and -10

Step-by-step explanation:

Can you use the same number twice?

Answer:

About 6.38$

.........................

Answer:

C. 3 feet.

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

The graph intersects x-axis at (4,0)  and (-3,0)

If function f has zeros at -3 and 4 then the first graph represents the function f.

When a function has zeros at -3 and 4, it means that the function's value is equal to zero at those x-values.

In other words, when x = -3 and x = 4, the function f(x) becomes 0.

To represent this on a graph, you should look for two points where the graph intersects the x-axis at -3 and 4.

When the graph crosses the x-axis at these points, it indicates that the function has zeros at those x-values.

When we observe the graphs, the first graph has zeros at -3 and 4.

Hence, the first graph could represent the function f with zeros at -3 and 4.

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In mathematics, a number is considered to be "even" if it is divisible by 2, and "odd" if it is not divisible by 2. The numbers from 1 to 100 can be divided into two groups: even numbers and odd numbers.

Even numbers are numbers that are divisible by 2, such as 2, 4, 6, 8, and so on. When you divide an even number by 2, the remainder will always be 0. Some examples of even numbers between 1 and 100 include: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, and 100.

Odd numbers are numbers that are not divisible by 2, such as 1, 3, 5, 7, and so on. When you divide an odd number by 2, the remainder will always be 1. Some examples of odd numbers between 1 and 100 include: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, and 99.

It is important to note that 0 is not a positive or negative number and it is not considered as odd or even.

Knowing the difference between even and odd numbers is an important concept in math, especially when working with patterns, sequences, and operations. Understanding even and odd numbers can help you better understand the properties of numbers and how they can be used in different contexts.

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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The solution to the inequality is:

x ∈ (-∞, -21].

The correct option is F.

To solve the given inequality, we'll first simplify the expression:

23 < 3x - 3 ≤ -66

To simplify the inequality,

23 < 3x - 3 ≤ -66

Adding 3 to all parts of the inequality:

23 + 3 < 3x - 3 + 3 ≤ -66 + 3

Simplifying:

26 < 3x ≤ -63

Next, divide all parts of the inequality by 3:

26/3 < 3x/3 ≤ -63/3

Simplifying:

8.67 < x ≤ -21

Therefore, the solution to the inequality is:

x ∈ (-∞, -21]

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The given table of the values of f(x) is used to complete the table for the function \(y = f \left( \frac{1}{5} \cdot x \right) \), to give;

The following values of x and y as follows;

x: -0.8, -0.2, 0, 0.6, 1.2

y: 7, -2, 3, -4, 5

Please also see the attached table

The question is with regards to scaling a graph horizontally.

Using the rule of scaling a graph, we have;

Given that a point on the graph of f(x) is (x, y), the corresponding point in the graph of f(C•x) is (C•x, y).

The given modification of the function is presented as follows;

\(y = f \left( \frac{1}{5} \cdot x \right) = f \left( 0.2 \cdot x \right)\)

The points on the graph that completes the table are therefore;

The completed table is therefore;

x y

-0.8 7

-0.2. -2

0 3

0.6. -4

1.2. 5

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Answer

The Answer is C) 2, -6

Step-by-step explanation:

Look at the graph as you can see there is only one solution to that graph and on the line intersected there is one point which that would be 2, -6.

Note: Understand that when asking about the point or something else look for the lines intersected each other then you could find your answer. If there is only one line then it is infinite solutions but if the lines don't intersect then it is a no solution.

Have a good day :)

Using a system of equations, it is found that:

Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.

The variables of the system of equations are presented as follows:

She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:

8x + 10y = 84.

She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:

2x + 10y = 66.

Simplifying by 2, we have that:

x + 5y = 33.

x = 33 - 5y.

Replacing in the first equation, we can find the time it takes to walk a lap, as follows:

8(33 - 5y) + 10y = 84.

264 - 40y + 10y = 84

30y = 180

y = 180/30

y = 6 minutes.

Then the time it takes to run a lap is obtained as follows:

x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.

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       Hence, OPTION (C) is your answer:  X  =  44

Step-by-step explanation:

       √x + 5 - 3 = 4

        √x +  5   =  3  +  4

        √x +  5   =   7

         (√x  +   5)2     =     (7)2

            x   +   5         =   49

        x   -  44     =   0

             +44      =   44

       X                =   44

       Hence,  X  =  44

        Equation: √x  +  5  =  7

      √(44)  +  5  =  7

    √49  =   7

            Hence,   x   =   44

        I hope this helps!

Answer:

The answers are

A - She used the wrong coefficient for X in her Inequality.

B- NO

C- She interpreted the graph incorrectly.

D-NO

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Took test on edge :)

In the expression 1.5x + 18 = 36.5 - 8 x is 7, hence 4x is 28.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An expression 18 + 1.5x is 8 less than 36.5.

∴ 1.5x + 18 = 36.5 - 8.

1.5x = 36.5 - 8 - 18.

1.5x = 10.5.

x = 10.5/1.5.

x = 7.

Therefore 4x is equal to 4(7) = 28.

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(x+4)(x-2)²(x+3) (option D)

To determine which polynomial was graphed, we look at the roots of the function on the graph with the options given.

The roots of the equation are the x values that make the function equal to zero.

On the graph, we check the values of the line that crosses the x axis.

Each box on the x axis represents 2 units

we have x = 2 (towards the right of the x-axis).

Note that two lines touched x = 2. This means x =2 appeared twice

we also have x = -4 (towards the left x axis)

Then we have value of x that is before the x = -4. Checking the options, the value of x will be equal to -3

Now we rewrite:

x = 2, x = 2, x = -4, x = -3

x-2 = 0, x-2 = 0, x + 4 = 0, x+3 = 0

The roots of the function:

(x-2)²(x+4)(x+3)

Hence, the polynomial functions graphed below is (x+4)(x-2)²(x+3) (option D)

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

3/7

Step-by-step explanation:

Sin (R) = opposite ÷ hypotenuse,

Find the opposite by using pythagorean theorem.

(AY)^2 + (2√10)^2 = 7^2

(AY)^2 + 40 = 49

(AY)^2 = 9

AY = 3

Sin(R) = 3/7

Thus, the probability of drawing 2 red balls (2 successes) from the urn is 1/12.

To calculate the probability of 2 successes (drawing 2 red balls) from the urn, we'll use the following terms: total balls, red balls, and combinations.

There are 9 balls in the urn, 3 of which are red.

To find the probability of 2 successes, we need to determine the number of successful combinations and divide that by the total possible combinations.

Successful combinations: Choose 2 red balls from 3, which can be written as C(3,2) = 3! / (2! * (3-2)!) = 3.

Total possible combinations: Choose 2 balls from 9, which can be written as C(9,2) = 9! / (2! * (9-2)!) = 36.

Now, divide the successful combinations by the total possible combinations to find the probability of 2 successes:

Probability = (Successful combinations) / (Total possible combinations) = 3 / 36 = 1/12.

So, the probability of drawing 2 red balls (2 successes) from the urn is 1/12.

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Answer:

option D. {......-2, -1, 0, 1, 2 ......}

The contour integral \(\(\int_{C} \frac{5z^{2}+3\sqrt{2}z+1}{(z-i)^{3}} dz\)\) along the circle |z|=3 evaluates to \(10\pi i\)\), and the inequality \(\(\left|\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz}\right| \leq (R^2-1)(R^2-4) \cdot \frac{2\pi R}{3} + 4\pi R\)\) holds for the given contour \(\(C_R\)\).

To evaluate the contour integral \(\(\int_{C} \frac{5z^{2}+3\sqrt{2}z+1}{(z-i)^{3}} dz\)\) along the circle |z|=3, we can use the extension of the Cauchy Integral Formula for the derivative of a function. The formula states that if f(z) is analytic inside and on a simple closed contour C, except at a point z=a inside C, then the nth derivative of f(z) at a is given by

\(\[f^{(n)}(a) = \frac{n!}{2\pi i}\int_{C} \frac{f(z)}{(z-a)^{n+1}} dz\]\)

In our case, we have \(\(f(z) = 5z^{2}+3\sqrt{2}z+1\)\) and n = 2 (since we want to evaluate the integral of the third derivative). The point a is i, and the contour C is the circle |z|=3.

Using the formula, we can rewrite the integral as:

\(\[\int_{C} \frac{5z^{2}+3\sqrt{2}z+1}{(z-i)^{3}} dz = \frac{2\pi i}{2!}\left(\frac{d^{2}}{dz^{2}}(5z^{2}+3\sqrt{2}z+1)\right)\bigg|_{z=i}\]\)

Taking the second derivative of f(z), we have:

\(\[\frac{d^{2}}{dz^{2}}(5z^{2}+3\sqrt{2}z+1) = 10\]\)

Substituting z=i into the expression, we get:

\(\[\int_{C} \frac{5z^{2}+3\sqrt{2}z+1}{(z-i)^{3}} dz = \frac{2\pi i}{2!}\cdot 10 = 10\pi i\]\)

Therefore, the value of the contour integral is \(\(10\pi i\)\).

Now, let's prove the inequality:

\(\[\left|\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz}\right| \leq (R^2-1)(R^2-4) \cdot \frac{2\pi R}{3} + 4\pi R\]\)

We can rewrite the integral as:

\(\[\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz} = \int_{C_R} (z^4+9z^2-2)dz\]\)

Using the triangle inequality, we have:

\(\[\left|\int_{C_R} (z^4+9z^2-2)dz\right| \leq \int_{C_R} |z^4+9z^2-2||dz|\]\)

For any point z on the contour \(C_R\)\), we have |z| = R. Using this, we can simplify the expression:

\(\[\int_{C_R} |z^4+9z^2-2||dz| = \int_{C_R} |R^4+9R^2-2||dz|\]\)

Since \(\(|R^4+9R^2-2|\)\) is a constant, we can take it outside the integral:

\(\[\int_{C_R} |R^4+9R^2-2||dz| = |R^4+9R^2-2| \int_{C_R} |dz|\]\)

The length of the contour \(\(C_R\)\) is \(\(2\pi R\)\). Substituting this into the integral, we have:

\(\[\int_{C_R} |R^4+9R^2-2||dz| = |R^4+9R^2-2| \cdot 2\pi R\]\)

Thus, we obtain:

\(\[\left|\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz}\right| \leq (R^2-1)(R^2-4) \cdot \frac{2\pi R}{3} + 4\pi R\]\)

which is the desired inequality.

Note: In the given inequality, there seems to be an error in the expression for the integral. It should be \(\(\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz}\)\) instead of \(\(\int_{C_R} \frac{z^4+5z^2+4z^2-2}{dz}\)\).

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Answer:

y + 3 = \(\frac{4}{5}\) (x - 10)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = \(\frac{4}{5}\) and (a, b ) = (10, - 3 ) , then

y - (- 3) = \(\frac{4}{5}\) (x - 10) , that is

y + 3 = \(\frac{4}{5}\) (x - 10)

All of the values that m could take include the following: -3.5, -5, and -7

In Mathematics and Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

This ultimately implies that, all number lines would primarily increase in numerical value towards the right from zero (0) and decrease in numerical value towards the left from zero (0).

From the number line shown in the image attached below, we can logically deduce the inequality:

x ≤ -3

Therefore, the numerical values for x could be equal to -3.5, -5, and -7

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

60

Step-by-step explanation:

\(0.3 \times x =18 \\ x = 18 \div 0.3 \\ x = 60\)

The number of aircraft departures (in billions) from 2000 to 2006 can be approximated by the polynomial function p(x) = 0.0154x - 0.2618x³ + 1.33x² - 1.54x + 9.1, where x = 0 corresponds to the year 2000.

The given polynomial function p(x) represents the number of aircraft departures in billions for the years 2000 to 2006, with x representing the number of years since 2000. The coefficients of the polynomial determine the behavior of the function over the given range.
The function p(x) is a polynomial of degree 3, meaning it is a cubic function. The terms of the polynomial are multiplied by powers of x, representing the increasing influence of each term as the years progress.
The coefficients of the polynomial, 0.0154, -0.2618, 1.33, -1.54, and 9.1, determine the specific shape and behavior of the function. Each coefficient affects the rate of change, concavity, and intercepts of the function. For example, the coefficient of x³ (-0.2618) indicates a negative concavity, while the constant term (9.1) represents the number of aircraft departures in the year 2000 (x = 0).
By evaluating the function p(x) for different values of x within the given range, we can approximate the number of aircraft departures for each corresponding year.

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The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>\(\frac{P(S U M)}{All}\)

\(\frac{P(S U M)}{All} = \frac{360}{1200}\)

Hope this helps ^-^

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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