Lance and 7 other friends go to an activity center together. They each pay $5. 95 for dinner, 84 for laser tag, $3. 60 for bowling

shoes, and $2. 25 for video games. The total amount they spent is 8 (5. 95) +8 (4) +8 (3. 60) +8 (2. 25).

Part A

Rewrite the expression so that it only has one multiplication operation

Enter the correct answer in the box

1. The union of set B and C, BUC using interval notation is (3, ∞) U (-∞, 5]

2. The intersection of set B and C, B∩C using interval notation is (4, 5]

We'll begin by obtaining the elements of set B and C. Details below:

With the above information we can determine BUC in interval notation as follow:

BUC = (3, ∞) U (-∞, 5]

We can obtain B∩C in interval notation as follow:

B∩C = (3, ∞) ∩ (-∞, 5]

B∩C = (4, 5]

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Complete question:

B and C are sets of real numbers defined as follows.

Write BUC and B∩C using interval notation.

If the set is empty, write Ø.

B= {x|x>3}

C= {x|x≤5}

A) x²  - 2x - 13 in the form of (x + c)²  + d is (x - 1)²  - 15, and the value of

c = -1, d = -15

B) The solutions of the equation are 1+ √15 and 1- √15.

A quadratic equation is a type of polynomial equation that has the general form of ax² + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero.

a) To write x²  - 2x - 13 in the form (x + c)²  + d, we can complete the square.

First, we add and subtract (2/2)²  = 1 to get:

x²  - 2x - 13 = x²  - 2x - 13 + 1 - 1

Next, we group the terms:

(x²  - 2x) - 14 = (x²  - 2x + 1) - 15

Now, we can see that the left side of the equation is a perfect square trinomial. To complete the square, we add the square of half of the coefficient of the x term, which is (1)² = 1 to both sides:

(x - 1)²  - 15 = 0

So, x² - 2x - 13 = (x - 1)²  - 15

c = -1, d = -15

b) Using the answer from part a, we know that x² - 2x - 13 = (x - 1)² - 15

=0

so (x-1)² = 15

x-1 = ± √15

x = 1 ± √15

The solutions of the equation are 1+ √15 and 1- √15.

In the form a = fg, where f and g are integers:

a = 1, f = 1, g = √15

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Answer:

  45

Step-by-step explanation:

You want to know the expected number of free throws Cynthia will make in 58 attempts, if her success rate is 37 out of 48.

We assume the number of successful free throws is proportional to the number of attempts:

  37/48 = x/58

  x = 37/48·58 ≈ 45

Cynthia could be expected to make 45 free throws this season.

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The number of laps swum by Rita: L

The number of laps swum by John: 3L

The number of laps swum by Rodell: 3L + 25

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Tomika and Mark claim a medical deduction in the amount of $1,839.8.

What is the percentage?

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. It is represented by the symbol “%

Given that the gross income is $101,598

Medical insurance = 7.5 % of $101,598

                              = 7.5% x $101,598

                             =  $7,619.88.

The insurance covered 60% of the medical expenses.

Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800

                                       = $7,619.88 - 40% x $3,800

                                        = $7,619.88 - $1,520

                                        = $6,099.88

Therefore, they can claim a medical deduction in the amount of $1,839.8.

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The volume of the cone with the given radius of the base and height is given by  30π cubic meters ( in terms of π ).

Radius 'r' of the base of the cone is equal to 3m

Height 'h' of the cone is equal to 10m

Volume 'V' of a cone is given by :

V = ( 1 / 3 ) × π × r² × h

Substitute the value of radius and height of the cone in the formula we get,

⇒ V = ( 1 / 3 ) × π × ( 3 )² × ( 10 )

⇒ V = 30π cubic meters ( in terms of π )

Therefore, the volume of the cone for the given radius and the height is equal to  30π cubic meters ( in terms of π ).

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Answer: 12x + 15y = 4140, x+y = 300

Step-by-step explanation:

12x represents $12 tickets, 15y represents $15 tickets, x + y is total tickets

Answer:

that a huge prob but yeah

For the given parallelogram, AC is congruent to BD

The term parallelogram in math is defined as a two-dimensional geometrical shape whose sides are parallel to each other.

Here we have know that ABCD is a parallelogram and angle ABC is a right angle.

And we need to proved that AC is congruent to BD.

=> AC = BD

To show that, ABCD is a rectangle if the diagonals of a parallelogram are equal

To show ABCD is a rectangle we have to prove that one of its interior angles is right angled.

Here we have know that in ΔABC and ΔBAD,

Here we all know that the common side that is BC and BA and here we have also know that the sides AC and AD as Opposite sides of a parallelogram are equal.

Then it can be written as,

=> AC = BD

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Answer: Number 4

Step-by-step explanation:

5/6 = 0.83333...

-9 5/6 = -9.8333333..., which is number 4

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse.

Let's review some information regarding the sin function before learning the sin formula. The sine function, often known as the sin function, is a periodic function in trigonometry.

The ratio of the hypotenuse's length to the perpendicular's length in a right-angled triangle is another way to describe the sine function. Sin is a periodic function that has a period of 2 and a domain and range of (, ), respectively.

To determine the sides of a triangle, use the sin formula. The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle.

hypotenuse/perpendicular = sin.

For every time sin() = sin(), sin( + 2n) = sin()

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g(x) is the vertical stretch and reflection about the x-axis. Hence option (B) is the correct answer.

Vertical compression by a factor M: g(x) = m*f(x)  (m<1)

m = -1.4

it means for given value of xg(x) < f(x)

Vertical stretch by a factor m: g(x) = (1/m)*f(x) (|m|>1)

hence given vlaue of x g(x) > f(x)

reflection about x axis : y = -f(x)

So, In the given plot, we can say that g(x) is a reflection of f(x) about the x-axis,

and g(x) > f(x) for any value of x it denotes stretch

Therefore, g(x) is the vertical stretch and reflection about the x-axis.

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Answer:

-79.9

Step-by-step explanation:

-60.7-19.2=-79.9

Answer: -79.9

Step-by-step explanation:

Subtract 19.2 from both sides of the equation to isolate the X.

0 + X = -60.7 - 19.2

X = -79.9

You can also check your answer by plugging in X into the equation and seeing if it equals -60.7

Answer:

Step-by-step explanation:

THE DARK IS GONNA BE RIGHT OVER LEWFT TO PLAY THE Gme

Note that the rule that describes the transformation shown is: (x,y) → (x+7,-y)(Number 2)

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure. The Pre-Image is the original shape of the item, and the Image is the final shape and location of the object after the transformation.

Thus, with regard to the transformation above,

At Point A: The original coordinate of point A was (-6,-6).

The coordinate after the transformation is A'(1,6), which eliminates option 3.

At Point B:

The original coordinate of point B was (-2,4).

After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. It is therefore right to state that (x,y) → (x+7,-y) is the correct representation of the transformation.

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Full Question:

The missing options are:

Which rule describes the transformation shown?

1. (x,y) → (-y, x+7)

2. (x,y) → (x+7,-y)

3. (x,y) → (-x, y+7)

4. (x,y) → (y+7, -x)

The solution for the given system of inequalities is the ordered pair (-0.43,4.15).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to depict the relationship between two expressions. An inequality sign has non-equal expressions on both sides. It signifies that the expression on the left should be more or smaller than the expression on the right, or vice versa.

We are given a graph on which there are two inequalities plotted

As the first step, we need to frame the equations of both from the points.

For the blue line, we have points (0,2) and (-1,7)

So, using slope-intercept form, we get the equation as

y+5x≥2

For the red line, we have points (0,4) and (3,3)

So, using slope-intercept form, we get the equation as

y+0.33x >4

Now, in order to find the solution, we will subtract both the equations

On subtracting, we get

⇒(y+5x) - (y+0.33x) = 2 - 4

⇒y+5x - y-0.33x = -2

⇒4.67x = -2

⇒x = -0.43

Substituting this value in the equation, we get

⇒y+5(-0.43) = 2

⇒y-2.15 = 2

⇒y = 4.15

Hence, the solution for the given system of inequalities is the ordered pair (-0.43,4.15).

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A. The equation is: x = (30/100) * 140

B. The equation is: y = (100/64) * 40

C. The value of x is 160.

A. To write an equation that shows the relationship of 30% of 140 is x, use the formula: x = (percentage/100) * 140

So for this case, we have:

x = (30/100) * 140 = 42

So the equation is: x = (30/100) * 140

B. To write an equation that shows the relationship of 64% of y is 40, use the formula:

y = (100/percentage) * 40

So for this case, we have:

y = (100/64) * 40 = 62.5

So the equation is: y = (100/64) * 40

C. To find the value of x, given that 45% of x is 72, use the formula:

x = (100/percentage) * 72

So for this case, we have:

x = (100/45) * 72 = 160

So the value of x is 160.

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Answer:

x - 2/3 = 2/3

Answer: x-2/3=2/3

Step-by-step explanation:

The conversion of the equation from slope-form to standard form is 2x + y = 1.

In Mathematics, the slope-intercept form of a line is generally modeled by using this linear equation:

y = mx + b

Where:

Generally speaking, the standard form of a linear function is is generally modeled by this mathematical expression:

Ax + By = C

Where:

A, B, and C represents a number, numeral or numerical value.

Next, we would convert the given linear function in slope-intercept form to standard form as follows:

2x + y = 1.

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The factored form of 26x^5 - 13x is 13x(2x^4 - 1).

What is the greatest common factor?

The greatest common factor (GCF), also known as the greatest common divisor (GCD) or highest common factor (HCF), is a concept in mathematics that refers to the largest positive integer that divides two or more integers without a remainder.

To factor 26x^5 - 13x using the greatest common factor, we need to find the greatest common factor of the two terms.

26x^5 = 213x^5

13x = 13*x

The greatest common factor of the two terms is 13x.

So we can factor it out:

26x^5 - 13x = (13x) (2x^4 - 1)

Hence, the factored form of 26x^5 - 13x is 13x(2x^4 - 1).

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Answer:

Step-by-step explanation:

First you go up to your y intercept which in your case would be (0,4) and plot a point.

From there you add your slope. From the point (0,4) go down 2 and left 5 and plot a point there. You do that one p=more time from the new point and then you draw your line.

Hope this helps :)

The value of y from the equation is 2.3

A linear equation is one in which the highest power of the variable is always equal to 1. It is also called a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Where x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

8.4 + y = 10.7

y = 10.7 - 8.4

y = 2.3

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Jane covers a combined 28 miles on her bike and run.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

An expression is a means to include operations like addition, subtraction, multiplication, and division in a statement that has more than two variables or numbers.

An example of an expression is 2 + 3 x y = 7.

Those are

Jane rides a total of 16 miles.

Jane covers 12 miles on her run.

the combined distance Jane covers while jogging and riding.

= 16 + 12

= 28 miles

Thus,

Jane covers a combined 28 miles on her bike and run.

The complete question is:

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. What is the total distance Jane travels biking and running?

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The solution of the trigonometric function in the interval is x = 0

A trigonometric function is an equation that contains the trigonometric ratios.

Given the trigonometric function secx + tanx = 1, we proceed to solve it as  follows.

secx + tanx = 1

Using the trigonometric identity tan²x + 1 = sec²x

⇒ secx = √(1 + tan²x)

So, substituting this into the equation, we have that

secx + tanx = 1

√(1 + tan²x) + tanx = 1

√(1 + tan²x) = 1 - tanx

Squaring both sides of the equation, we have that

√(1 + tan²x) = 1 - tanx

√(1 + tan²x)² = (1 - tanx)²

1 + tan²x = 1 - 2tanx + tan²x

Substracting 1 from both sides, we have that

1 - 1 + tan²x = 1 - 1 - 2tanx + tan²x

0 + tan²x = 0 - 2tanx + tan²x

tan²x = - 2tanx + tan²x

Substracting tan²x from both sides, we have that

tan²x - tan²x= - 2tanx + tan²x - tan²x

0 = -2tanx + 0

0 = -2tanx

tanx = 0/-2

tanx = 0

taking inverse tan, we have that

x = tan⁻¹0

x = 0

So, the solution is x = 0

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The mass of the wine can be found by multiplying the density of the wine (0.8 kg/litre) by the volume of the wine (20 litres). The mass of the wine is 16 kg.

Its density is how much "stuff" can fit into a certain quantity of space. For instance, a block of the more resilient, lighter element gold (Au) will have a higher density than a block of the more substantial element lead (Pb) (Au). Styrofoam blocks are not as dense as bricks. Mass per unit volume serves as its definition.

We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the amount of matter contained therein (its mass). Density can also be defined as the quantity of mass per unit of volume.

mass = density x volume

mass = 0.8 kg/litre x 20 litres

mass = 16 kg

So, the mass of the wine is 16 kg.

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The sum of the given polynomials is 5x² - 2x - 7.

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

The given polynomials are 4x² + 3x - 1 and x² - 5x - 6.

We have to add the given polynomials to find the sum.

(4x² + 3x - 1) + (x² - 5x - 6)

Rearranging with adding the like terms,

(4x² + x²) + (3x - 5x) + (-1 - 6) = 5x² - 2x - 7

Hence 5x² - 2x - 7 is the sum of the given polynomials.

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Answer:

$20239.6

Step-by-step explanation:

The amount financed for the car is $25,800 - $8,000 = $17,800.

To find the monthly payment, you can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where M is the monthly payment, P is the amount financed, i is the monthly interest rate (3.99%/12), and n is the number of payments (60 months).

So,

i = 3.99%/12 = 0.00399

n = 60

M = $17,800 [ 0.00399(1 + 0.00399)^60 ] / [ (1 + 0.00399)^60 – 1]

M ≈ $337.31

So, Michelle will make monthly payments of $337.31 for 60 months.

To find the total amount that Michelle will pay for the car, you can multiply the monthly payment by the number of payments:

$337.31 x 60 = $20239.6

So, the total amount that Michelle will pay for the car is $20239.6

Answer: The method of substitution involves three steps:

Step-by-step explanation:

Solve one equation for one of the variables.

Substitute (plug-in) this expression into the other equation and solve.

Substitute the value into the original equation to find the corresponding variable. here i helped ya

Chelsea wants to add one layer of 3 x 3 cubics and Stephen wants to add one layer of 3 x 6 cubics.

From given figure, the dimension of the rectangular prism are:

6 cm × 3 cm × 3 cm

The volume of the rectangular prism would be,

V = l × w × h

V =  6 × 3 × 3

V = 54 cm³

Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters.

Chelsea wants to add eight layers.

This means 72 = 8 × 3 × 3 cubics, then one layer in this case consists of 3 x 3 cubics;

Whereas Stephen says they only need to add four layers.

This means 72 = 4 × 3 × 6 cubics, then one layer in this case consists of 3 x 6 cubics.

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