Rewrite 3x + 15 as the product of two factors

The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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Answer:

1 -  $15

2-  $30

3 - $45

4 - $60

Step-by-step explanation:

$15/hour

1 -  $15 =1*15

2-  $30 =2*15

3 - $45 =3*15

4 - $60=4*15

Answer:

a. [tex]\frac{x+2}{x+6}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]

Answer:

Step-by-step explanation:

Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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Answer:

All Real Numbers

Step-by-step explanation:

I assume you are solving for x.
The Interval Notation would be: (-∞,∞)

The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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The answer to each part is -

        y = mx + c    

        where -

        [m] : slope of line
        [c] : y - intercept                    

Given is the graph of a straight line as shown.

[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -

(0, 4) and (4, 1)

Let the line be -

y = mx + c

m = (1 - 4)/(4 - 0) = -3/4

m = -3/4

So, the equation will be -

y = (-3/4)x + 4

[B] -

For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.

Therefore, the answer to each part is -

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a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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Answer:

i think that answer is correct

Step-by-step explanation:

The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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Answer:

D

Step-by-step explanation:

(7+-6)/2

(7-6)/2

1/2

(-6+(-8)/2

(-6-8)/2

-14/2

-7

(.5,-7)

Answer:

New price = 0.06 x Original price

New price $1,968

Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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Answer:

x + x - x = x

explanation:

give us the actual formula lol

1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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Answer:

 (a) A  and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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Answer:

Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.

Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:

x &= 3y - 4

2x - 2y &= 8

Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12

The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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