simplify the expression (-6)^-4 using positive exponents

GIVEN

Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.

SOLUTION

The two triangles have equal sides such that:

By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.

Since [tex]BC>DC[/tex]Substitute known values into the inequality:

Solving the inequality:

Recall that the side DC has to be greater than 0. Therefore:

Combining both solutions:

The prime factorization given as 2².3².5 is for the number D. 180.

It should be noted that prime numbers are numbers that can only be divided by itself and one. This include 2, 3, 5, 7, etc

A composite number is one that can be generated by multiplying two smaller positive numbers. It is a positive integer with at least one divisor other than 1 and itself. Prime factorization is defined as the process of determining a number's prime factors so that the original number is evenly divisible by these factors.

In this case, it should be noted that we are given the expression as 2². 3². 5. It simply means that we have to multiply them to get the original number.

This will be:

= 2² × 3² × 5

= 4 × 9 × 5

= 180

Therefore, the number is 180.

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Answer:

$26

Step-by-step explanation:

65 x 60% = 39

65 - 39 = 26

The equation of the line in slope intercept form is y = -7x/2 - 5.

For the given question,

The graph of the straight line is given.

Select two points which lies on the line.

(x₁, y₁) = (0, -5)

(x₂, y₂) = (-2, 2)

Find the slope using the formula.

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 + 5)/(-2 - 0)

m = -7/2

The equation of the line in slope intercept form is given as;

y - y₁ = m(x - x₁)

Put the values.

y + 5 = (-7/2)(x - 0)

y = -7x/2 - 5

Thus the equation of the line in slope intercept form is y = -7x/2 - 5.

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Answer:

y = 3x-8

Step-by-step explanation:

Answer:

Output= -31

Step-by-step explanation:

f(x)= -3x²+8x-3

Therefore, f(-2)= -3(-2)²+8(-2)-3

                        = -3×4 -16 -3

                         = -12-16-3

                          = -31

Answer:

8

Step-by-step explanation:

[tex] \frac{72h}{9h} = 8[/tex]

The h is common in the numerator and the denominator, so it cancels out. We are left with 72/9 = 8.

Answer:

Step-by-step explanation:

You want an expression for area, maximum area, and dimensions of a rectangular pen fenced on three sides with a total of 120 m of fencing.

The first attachment shows a sketch of the pen with x defined as the dimension the pen extends from the barn wall. The total length of fence is 120 m, so the side parallel to the barn will be (120 -2x) m in length.

The area is the product of the length and width of the rectangle:

  A = (x)(120 -2x)

The second attachment shows a graph of the area as a function of x.

The value of x that gives the greatest area is the x-coordinate of the vertex of the parabola. It is halfway between the zeros at x=0 and x=60. The maximum area will be had when x=30.

The dimensions of the pen are ...

  x = 30

  120 -2x = 120 -2(30) = 60

The pen is 30 m by 60 m, with the 60 m dimension parallel to the barn wall.

The area function only makes sense for values of x between 0 and 60 meters.

The domain of x is 0 ≤ x ≤ 60.

Answer:

jhhuibhhhiihhuuuuuuuuuuuuuuuuuuuuuuuu

Answer:

Answer should be 3

Step-by-step explanation:

prove me wrong

Answer:

(−12,2)

Step-by-step explanation:

1:

Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value

(4) and divide it by 2 to get 2

.

Therefore, the new point is

(−12,2)

2:

Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value

(−12) to get −10

.

Therefore, the new point is

(-10,4)

3:

Making the input of the function negative will multiply every x-value by

−

1

. To get the new point, we will take the x-value

(−12) and multiply it by −1 to get 12.

Therefore, the new point is

(12,4)

4:

Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value

(−12) by 4 to get −3

.

Therefore, the new point is

(−3,4)

5:

Multiplying the whole function by

4

increases all y-values by a factor of

4

, so the new y-value will be

4

times the original value

(4), or 16.

Therefore, the new point is

(−12,16)

6:

Multiplying the whole function by

−1

also multiplies every y-value by

−1

, so the new y-value will be

−1

times the original value

(4), or −4.

Therefore, the new point is

(−12,−4)

A linear equation is an algebraic equation of the form y = mx + b. The cost of renting the truck if the truck is driven 107 miles exists $32.63.

A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Number of miles travel exists represented by "x"

cost per mile is represented by "c"

therefore we have equation,

c = 23 + 0.09 x

For 1 mile that is x = 1, cost c = $25.07

For 220 miles that is x = 220

c= 23 + 0.09 × 107

c= $32.63

For 107 miles the cost will be $32.63.

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Answer: answer to A: Clockwise rotations clockwise, while counterclockwise rotations rotate in the opposite direction  

Answer to B: i have no idea but i hope the first one helps

Step-by-step explanation:

Answer:

$3,289.90

Step-by-step explanation:

65,798 times 5%

The percent markup is 124.30%.

The wholesale cost of one candle is $5.35

The selling price of the candle is $12

The profit she earns = 12 - 5.35

                                  = $6.65

Here we have to find the percent markup.

The formula for the percent markup =( profit/ wholesale cost )× 100

Markup percent = 6.65 / 5.35 × 100

                          = 1.24299 × 100

                          = 124. 30%

Therefore the markup percentage is 124.30%.

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Answer:

40

Step-by-step explanation:

According to the radioactive isotope disintegration model, the remaining mass of the radioactive isotope after 40 years is approximately equal is 129.622 grams.

The deceasing exponential expression described in the statement models the mass of the radioactive isotope (m), in grams, as a function of time (t), in years, which represents the solution of an ordinary differential equation that represents a simple disintegration.

Now, we need to evaluate the function at t = 40 to find the amount remaining after 40 years:

A(40) = 500 · exp(- 0.028171 · 40)

A(40) = 129.622

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The image's coordinates are:

A = (-2,5),

B = (3,-3),

C = (-4,-1).

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair od numerical coordinates, that are the signed distances from two lines that are fixedly perpendicular to the point and are measured in the same length.

The reverse is done in order to determine a point's coordinates in a coordinate system. Start at the point and move along a vertical line either up or down to the x-axis. Your x-coordinate is located there. To get the y-coordinate, repeat the previous steps while following a horizontal line.

The graph's coordinates are as follows:

A = (-2,5)

B = (3, -3)

C =  (-4,-1)

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Answer:

Carlos will end up paying 80£ in that month, the standard data plan cost 20£ plus 60£ the price of the extra 4 GB of data used.

Carlos has to pay total $80 in a month if he uses 4 GB data over the limit and if he uses x GB data over the limit then have to pay $20+15x.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of 7 GB data plan = $20,

Cost for extra data = $15 per GB.

Since, Carlos use extra 4 GB data in a month,

Cost of 1 GB extra data = $15

Cost of 4 GB extra data = $60

Total cost = cost of 7 GB data plan + Cost of 4 GB extra data

                 = $20 + $60

                 = $80

Total $80 Carlos have to pay, where he used 4 GB over the limit.

If Carlos uses x GB extra data,

Then cost of x GB extra data = $15x

Total cost = cost of 7 GB data plan + Cost of x GB extra data

                =  20 + 15x

Total $20+15x Carlos have to pay, where he used x GB over the limit.

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As per the given condition for the system of equation, the two numbers are equal to 4 and 3.

As given in the question,

To begin with the solution, let the two unknown numbers be x and y. Now, translating the two mathematical statements into system of equations,

When three times the first of two numbers decreased by the second number equals 9.

3 x - y = 9 ____(1)

Twice the first number increased by the second number equals 11,

2 x + y = 11   ____(2)

By solving resultant system of equations we get,

3 x - y = 9

2 x + y = 11

5x        = 20                    (by adding the two equations)

=> x = 4

Substituting the value of x in second equation,

y = 11 - 2x

 = 11 - 2(4)

  = 11 - 8 = 3

Therefore, as per given condition for the system of equation, the two numbers are equal to 4 and 3.

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If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:

Substitute for the coordinates: (-12,1) and (12,-1):

Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.

Taking x and y as the price for each photo, then the equation that represents each situation would be:

For Allen

For Denise

Answer:

30 1/2

Step-by-step explanation:

The slope of the line perpendicular to the line given by equation  2x+2y=-12 is found as 1.

The slope can be calculated using the following formula:

m = Δy/Δx

Where, m is the slope.

The equation of the line is; 2x+2y=-12

Write the equation in slope-intercept form.

2x + 2y = -12

Divide by 2.

x + y = -6

y = -x - 6

Slope m₁ = -1 and y-intercept = -6.

As, both line are perpendicular.

Thus,

m₁ x m₂ = -1

m₂ = -1/m₁

Put the value.

m₂ = -1/(-1)

m₂ = 1

The slope of the perpendicular line is found as 1.

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The domain of the function using interval notation is 4 ≤ y < 8 and the range of the function using interval notation is 4 ≤ y < 6.

A domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:

In interval notation, the domain of this function can be rewritten as 4 ≤ y < 8. In interval notation, the range of this function can be rewritten as 4 ≤ y < 6.

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We are given the following values of the function to be

To find (f.g)(x)

We will find the product of f(x) and g(x)

Upon expanding, we will have

Thus, the answer is:

The product of powers, power of a product, and power of a power laws can be used to evaluate the equivalent numerical expressions such as:

According to the Power of a Product Property, you can distribute the exponent to each factor if a term is raised to one.

According to the rule of a power, when a base is raised to a power and then raised to another power, the exponents are multiplied while the base is left unchanged.

According to the product of powers rule, you can multiply two words with the same base by simply adding their exponents to get the result.

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By using the concept of weighted averages, 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice are needed to produce 70 pints of 55 % pure fruit juice.

The situation describes a mixing process with two fruit juices of different concentrations. All pure fruit percentages are known and we are asked to determine the numbers of pints of 40 % pure fruit juice and 65 % pure fruit juice to produce 70 pints of 55 % pure fruit juice. This can be determined by means of the concept of weighted average:

(55 / 100) · 70 = (40 / 100) · x + (65 / 100) · (70 - x)

38.5 = 0.4 · x + 45.5 - 0.65 · x

0.15 · x = 7

x = 46.667

We need 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice to produce 70 pints of 55 % pure fruit juice.

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