Are the two functions inverse of one another ?

The system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Total money Anthony and Joan have to buy apples and oranges = $10

Total pieces of fruit the Anthony and Joan buy is = 25 pieces of fruit

Each Apple's cost = 50 cents

Each orange's cost = 25 cents

Let, x = be the apples

and, y = be the oranges

The equation applied for the number of pieces of fruit they will buy,

x + y = 25

And, the equation applied for cost is,

0.50x + 0.25y = 10.00     (Keep everything in same decimal places)

Hence, the system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

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To find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

The cost of 4 small greeting cards is 4 * $1.80 = 4 * 1.8 = $7.20.

The cost of 3 large greeting cards is 3 * $3.85 = 3 * 3.85 = 11.55.

The total cost of 4 small greeting cards and 3 large greeting cards is $7.20 + $11.55 = 7.2 + 11.55 = 18.75.

To find the cost of x small greeting cards and y large greeting cards, you can use the following equation:

cost = x * $1.80 + y * $3.85

Substituting the values of x and y into this equation will give you the total cost of the greeting cards.

Hence, to find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.

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The value of the correlation coefficient is 0.9866.

By the end of 2014, the number of movie tickets sold would be equal to 1,600,000,000 movie tickets.

In order to determine value of the correlation coefficient and line of best fit that models the data points contained in the table, we would use a graphing calculator (scatterplot).

In this scenario, the year would be plotted on the x-axis of the scatterplot while the number of tickets sold (in millions) would be plotted on the y-axis of the scatterplot.

On the Excel worksheet, you should right click on any data point on the scatterplot, select format trend line, and then tick the box to display an equation and correlation coefficient for the trend line (line of best fit) on the scatterplot.

From the scatterplot (see attachment) which models the relationship between the data points in the table, a linear equation for the line of best fit (trend line) is given by:

y = 20.012x - 38704

Correlation coefficient, R² = 0.9757.

By the end of 2014, the number of movie tickets sold is given by:

y = 20.012x - 38704

y = 20.012(2014) - 38704

y = 40,304.168 - 38704

y = 1,600.168 × 1,000,000 ≈ 1,600,000,000 movie tickets.

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Answer: 21

the hcf of 315 and 42 is 21.

Answer:

HCF of 315 and 42:

Your answer is 21 !

Answer: 24 units.

Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.

The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((4 - (-4))^2 + (4 - 4)^2)

= sqrt(8^2 + 0)

= sqrt(64)

= 8

The length of the side between the second and third vertices can be calculated using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((4 - 4)^2 + (-2 - 4)^2)

= sqrt(0 + (-6)^2)

= sqrt(36)

= 6

The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

= sqrt(8^2 + 6^2)

= sqrt(64 + 36)

= sqrt(100)

= 10

To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.

Therefore, the perimeter of the right triangle is 24 units.

Answer:

Step-by-step explanation:

9 bytes2

To prove <ABC is congruent to <ABD

congruent figures are those that match in terms of size and shape or are the same size and shape. The geometry of congruent angles

Congruent refers to something that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

According to the question

Both the triangles are right-angled

From RHS criterion

∠ABC ≅ ∠ABD

Definition of angle bisector segment addition property

The line or line segment that splits an angle into two equal pieces is known as the internal angle bisector (internal angle bisector)

definition of congruent angle transitive property

According to the transitive property of congruence, all shapes are congruent to one another if two shapes are congruent to a third shape.

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There are at least two restaurants with varying mean delivery times. The required hypothesis are ,

H0: The mean delivery time for all restaurants is the same.

H1: The average delivery time varies between at least two restaurants.

If the data are put through an ANOVA, a different mean delivery time for at least two of the restaurants would be the alternative hypothesis.

According to the alternative hypothesis (Ha), there is a significant statistical association between two variables. As opposed to the null hypothesis, which claims that there is no statistical connection between the two variables.

The analysis of variance procedure, or ANOVA, includes examining the validity of mean hypotheses in light of variances. The equality mean, or H0. All means are equal, is used as the null hypothesis in an ANOVA. Alternative hypothesis, however, includes at least two means that are not equal.

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Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

Answer:

(4,8)

Step-by-step explanation:

First, Let us see the midpoint formula:

m(x,x /2, y,y/2) (That probably looks really confusing online)

Let us label our cords

A: (1x,5y)

B: (7x,11y)

Now, Add the x's together

7x + 1 = 8

8÷2 = 4

Now, Add the y together

11 + 5 = 16

16÷2 = 8

(4,8)

Answer:

Step-by-step explanation:

You want the explicit formula for each of the geometric sequences, and the 7th term.

The explicit formula for a geometric sequence with first term a[1] and common ratio r is ...

  a[n] = a[1]·r^(n-1)

The explicit formula is ...

  a[n] = -4·(-3)^(n-1)

The 7th term is ...

  a[7] = -4·(-3)^(7-1) = -2916

The explicit formula is ...

  a[n] = 12·(1/4)^(n -1)

The 7th term is ...

  a[7] = 12·(1/4)^(7-1) = 3/1024

After Solving the provided question, the Michelle's point value after the third round is -4.5 by the third round

A value is computed using operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or numbers, the math operator's symbol has predetermined rules.

Mathematical operations like addition (+), subtraction (-), multiplication (*), and division (**) take precedence over one another. Neither of the two operators can be used to solve an equation by itself. The brackets in any equation, whether arithmetic or algebraic, must be evaluated first, according to the order of operations principles, which we must abide by. The second place is where the order will be determined. After evaluating addition and subtraction, we'll analyze multiplication and division.

[tex]she starts off with a negative 2.3 of you add positive 4.5 = > (-2.3) + 4.5 = 2.2[/tex]

but after that, she lost another 6.7 points, leaving her with a negative score of 4.5.

[tex]= > 2.2 - 6.7 = ( -4.5 )[/tex]

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Answer:

1) Associative

2) Distributive

3) Distributive

4) Associative

Answer:

Use the formula y-3= 1/4(x--7) ---> y-3= 1/4(x+7)

4.75 is the y intercept

Answer: 38 nickels, 24 quarters

Step-by-step explanation:

x=number of quarters

y=number of nickels

x + y = 62

$0.25x + $0.05y = $7.90

solve for x in terms of y, then substitute into the 2nd equation:

x = 62-y

.25(62-y) + .05y = 7.90

15.5 - .25y + .05y = 7.90

15.5 - .20y = 7.90

-.20y = -7.6

y = -7.6/-.20

y = 38

now solve for x:

x  + 38 = 62

x = 62-38 = 24

x = 24

Using square roots, we know that there are (A) 15 cubes in a row.

The value that a number produces when it is multiplied by itself is known as the square root of the number.

The square root is denoted by the radical sign. For instance, √16 = 4.

The root symbol or surds is another name for the radical symbol.

So, let x be the total number of cubes in a row.

The number of cubes in each row and column is equal because they are organized in a pattern with the same number of cubes in each.

Now,

Total cubes = x * x

Total cubes = x²

We know that the total number of cubes is 225.

So, we got:

x² = 225

Taking square roots:

x² = 225

x = √225

x = 15

Therefore, using square roots, we know that there are (A) 15 cubes in a row.

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Complete question:
A group of cubes is arranged in a pattern with the same number of cubes in each row and column. There are 225

cubes in the shape. How many cubes are in one row?

A) 15

B) 25

C) 56

D) 75

According to given model income level corresponds to the minimum percent of charity contributions is 5%.

The given function is P(x)=0.0014x² - 0.1529x + 5.855, 5≤x≤10.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Check the critical points and end points to test for any absolute extrema over the given interval.

Absolute Maximum: (5,5.1255)

Absolute Minimum: (10,4.466)

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (54.60714285,1.68028392)

Focus: (54.60714285,180.2517125)

Axis of Symmetry: x=54.60714285

Directrix: y=−176.89114464

Now, P(5)=0.0014(5)² - 0.1529(5)+5.855

= 5.1255

≈5%

Therefore, according to given model income level corresponds to the minimum percent of charity contributions is 5%.

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Answer: y= -1x + 2

Step-by-step explanation:

The linear equation is y= mx + b

Y-intercept here is at (0,2), so b is 2

Let pick point (0,2) (2,0)

The slope is rise/run, and we see that the graph is going down by 2 and goes over by 2, so it is -2/2 = -1

So the equation is y=1x +2

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5+2y=13, y-5=2(x-1), y/2 = x+7, x=-4 are linear equations.

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.

A linear equation with two variables has the conventional form Ax + By = C.

Here, the variables x and y, the coefficients A and B, and the constant C are all present.

As explained above about linear equation from given option we can verify that

5+2y = 13 can be written as 2y = 8 or 2y-8=0 which represents linear equation in one variable.

[tex]y = \frac{1}{2x^{2} +7}[/tex] cannot be written in any linear form and its highest degree is 2. So, it is not linear equation.

y-5= 2(x-1) can be written as 2x-y=-3 which is in the form of linear equation in two variables. So, it is linear equation in two variables.

x = -4 can be written as x + 4 = 0 which represents linear equation in one variable.

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Answer: 3

Step-by-step explanation:

The triangles are similar using the angle-angle similarity theorem.

Using the fact that similar triangles have proportional side lengths yields:

[tex]\frac{5x-7}{4}=\frac{18}{9}\\\\\frac{5x-7}{4}=2\\\\5x-7=8\\\\5x=15\\\\x=3[/tex]

Distance between (1,4) and (-2,8) is 5 units.

The separation between two points. The coordinates of two points in space are used in the formula.

In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula.

Let distance between two points ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) be 'd' then,

d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

We are given two points (1,4) and (-2,8)

So, using formula for distance we get,

d= [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

=[tex]\sqrt{(-2-1)^{2} + (8-4)^{2} }[/tex]

d [tex]\sqrt{(-3)^{2} + 4^{2} } \\=\sqrt{25} \\=5[/tex]

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Answer:

(5,0)

Step-by-step explanation:

When graphed the x-intercept meaning the line touching x

is 5 so then your answer is  (5,0) because the x-value comes first so then you'd put the 5 in front.

When working with rational functions, your main concern to not divide by 0.  Dividing by 0 can't be done.

So, you need to look at the denominator of your fraction and figure out what values of g will make that denominator become 0.

Option #1 is to plug in each option from your list to see which ones make the denominator equal 0.  If that g-value makes the denominator equal zero, then it has be excluded.

Option #2 is to set the denominator equal to 0 and solve that equation:
    g^3 - 4g^2 - 12g = 0

To solve this, you could do it by factoring.

    g^3 - 4g^2 - 12g = 0     

     g ( g^2 - 4g -12) = 0

   g ( g - 6 ) ( g + 2) = 0

This splits into:
   g = 0, g = 6, g = -2

So those are the three values of g that you cannot use.

g ≠ 0; g ≠ 6, g ≠ –2

375 hours  should be the warranty period so that only 1% of them fail before the warranty is over.

As per the details share in the above question are as follows,

A certain type of electric bulb is a random variable that is normally distributed with a mean of μ=500 hours

The standard deviation σ=20 hours

We have to determine what should be the warranty period so that only 1% of them fail before the warranty is over?

Now let us consider,

Probablity Z=(X-μ)/σ

Solving further we get,

P(Any bulb fail before 500 hours)

= P(z < (500 - 500)/20)

= P(z < 0) = 0.50

Thus,

P( Failed before 500 hours)

[tex]= (0.50)^3[/tex]

= 0.125

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Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

What is the system of linear equations?

A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations or makes them true.

Let L be the number of lions, T be the number of tigers, and B be the number of bears. We can set up the following system of equations to represent the given information:

L + T + B = 40

L = T + 4

B = T - 3

We can solve this system of equations using substitution. Starting with the second equation, we can solve for T:

T = L - 4

Substituting this expression for T into the third equation, we get:

B = L - 4 - 3

B = L - 7

Substituting this expression for B into the first equation, we get:

L + L - 4 + L - 7 = 40

3L - 11 = 40

3L = 51

L = 17

Now that we know the number of lions, we can substitute this value back into the equation T = L - 4 to find the number of tigers:

T = 17 - 4

T = 13

Finally, we can substitute these values for L and T into the equation B = L - 7 to find the number of bears:

B = 17 - 7

B = 10

Hence, Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

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If the scale of drawing is 1 inches : 10  feet and the real horse height is 25 feet, then the height of the horse in drawing is 2.5 inches

The scale of drawing the horse = 1 inch : 10 feet

Therefore in scale

The height of the horse in drawing = 1 inch

The  height of the horse = 10 feet

The original height of the horse = 25 feet

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 10 feet = x inches : 25 feet

1 / 10 = x / 25

1 × 25 = 10x

10x = 25

x = 25/10

x = 2.5 inches

Therefore, the height of the horse in drawing is 2.5 inches

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