Suppose that each semester at a particular community college Manuel has to pay $1478 in tuition and $121 in fees.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for tuition.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for the fees.
If Manuel has × semesters remaining, write an algebraic expression representing the total amount of money he will spend for tuition and

The first step Charlie should use to solve the equation will be to open the bracket on the left side of the equation.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation Charlie wants to solve can be calculated as follows:

-1/4(x - 1) =2/3 x +2

The first step would be to open the parenthesis on the left side of the equation as follows:

-1/4(x - 1) =2/3 x +2

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

Let's subtract 1 / 4 from both sides of the equation

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

- 1 / 4 x + 1 / 4 - 1 / 4  = 2 / 3 x + 2 - 1 / 4

- 1 / 4 x = 2 / 3 x + 7  /4

subtract 2 / 3 x from both sides of the equation.

- 1 / 4 x = 2 / 3 x + 7  /4

- 1 / 4 x - 2 / 3 x = 2 / 3 x - 2 / 3 x + 7  /4

- 11 / 12 x = 7 / 4

cross multiply

-44x = 84

divide both sides by - 44

x = 84 / -44

x = - 21 / 11

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At b= 24 will complete the square in the expression x^2 + bx + 144.

What is perfect square trinomial?

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.

Consider the given expression

x^2 + bx + 144

For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.

Here, c = 144

√144 = 12

So, b√c = 2(12) = 24

The expression becomes,

x^2 + 24x + 144 = (x + 12)^2

This is the perfect square.

Hence, b = 24  will complete the square in the expression x^2 + bx + 144.

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All the improper fractions in mixed or whole numbers are as follows:

So, the given improper fractions in the mixed or whole numbers are:

Therefore, all the improper fractions in mixed or whole numbers are as follows:

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The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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Answer: 2y   or   2 x y

Step-by-step explanation:

2 times the minutes

therefor if carlos answers 4 calls, you would say 2 x 4 and you ranswer would be 8 minutes.

The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.

What is trigonometric functions?

Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.

Consider the given expression.

[tex]3-2tan^2x\\[/tex]

Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:

[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]

Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].

[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]

Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.

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The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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Answer:

  Isiah is correct. The slope is about 0.344.

Step-by-step explanation:

Lyra and Isiah want the slope of the hypotenuse in a triangle with an angle of elevation of 19°.

The slope is the ratio of "rise" to "run". In a right triangle, that is the ratio "opposite"/"adjacent". This ratio is the tangent of the angle of elevation.

  tan(19°) ≈ 0.344

The slope is about 0.344. Isiah is correct.

Isiah knows Lyra is not correct because the slope in a triangle with a 45° angle is 1. Lyra' value of 2.675 is about right for an angle of 69.5°, much greater than either 45° or the given angle of 19°.

__

Additional comment

Unfortunately, the diagram is not drawn to scale. This is often the case with diagrams in geometry problems. The diagram here is misleading in that it seems to show a slope greater than 1 for a 19° angle.

Answer:

21/18 or 1 and 3/18

Step-by-step explanation:

6/9 = 12/18

3/6 = 9/18

12/18 + 9/18 = 21/18 or 1 3/18

Answer:

Elena will need 180 more bats

Let she bats  b more needs

Total bats =  110 + b

Base hits = 24 + 0.35 b

From the question, we have

( 24 + 0.35b) / (110 + b) = 0.300

24 + 0.35b = 33 + 0.3 b

0.05 b = 9

b = 9 / 0.05 = 180

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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Answer:

Step-by-step explanation:

It would be D.

Answer: -3/8 or -0.375

Step-by-step explanation:

you have to get similar denominators to simplify

so times 1/4 by 2 to get 2/8

and then just do 2/8 - 5/8 and you get the answer

If Kelley family went on a tour this afternoon and they bought 4 tickets and 3 pictures. The total cost of the Kelley family's tour is $55.

Given data

Total price =  10t+5p dollars

Where:

t = tickets =4

p = pictures = 3

Now let find the total cost

Total cost =  10t+5p

Total cost = 10(4) + 5(3)

Total cost =40 +15

Total cost =$55

Therefore we can conclude that the total cost is the amount of $55.

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The number of the given statement will be inequality -2 < x <  4.

We have been given the statement "the sum of five times a number and three is between -7 and 23".

Let the number would be x

As per the given statement, we can represent this algebraic form with inequality as:

⇒ -7 < 5x + 3 < 23

Subtract 3 on both sides of the above inequality

⇒ -7 - 3 < 5x  < 23 - 3

⇒ -10 < 5x <  20

Divided by 5 into both sides of the above inequality

⇒ -2 < x <  4

Thus, the number of the given statement will be inequality -2 < x <  4.

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The question seems to be incomplete the correct question would be

Find the number if the sum of five times a number and three is between -7 and 23.

The amount that Sascha will receive in annual interest based on the information is $63.40.

From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.

In this case, it should be noted that the simple interest is calculated as:

Principal × Rate × Time

Principal = $1000

Time = 1 year

Rate = 6.34%

The interest will be:

= Principal × Rate × Time

= 1000 × 0.0634 × 1

= $63.40

The interest is $63.40.

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The correct option A, 266. 9 cm²;  total surface area of the cone given in figure is found as 266.9 sq cm.

For the given question.

Put values -

Total surface area = πr (h + r)

Total surface area = 3.14 x 5 (12 + 5)

Total surface area = 3.14 x 5 x 17

Total surface area = 266.9 sq cm.

Thus, total surface area of the cone given in figure is found as 266.9 sq cm.

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a)4

so it's seven factorial divided by 7-5 factorial

The inequality used to represent games at carnival is 9g - 207.35 > 100

The solution is g > 34.15

Information gotten from the question include

Games at the carnival costs $9 each

The prizes awarded to the winners costs the owner $207.35

How many games must be played for the owner to make more than $100 = ?

Using g as variable which is the number of games to be played we have

total amount gotten from games = 9 * g

prizes of winners = 207.35

The inequality equation as described in the problem is represented using linear function as as follows

9g - 207.35 > 100

for the owner to make more than 100 we have the equation

total amount gotten from games - prizes of winners > 100

9g - 207.35 > 100

100 + 207.35 < 9g

9g > 307.35

g > 34.15

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The value of the expression when z = -19 is 25.

Here we have the expression:

(33 + 2z)²

And we want to evaluate this on z = -19

Evaluating just means that we need to replace the variable in the expression by the given number.

By doing that we will get:

(33 + 2*(-19))^2

(33 - 38)^2

(-5)^2 = 25

The expression is equal to 25.

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Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

__

Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

The solution of the system of equations are x = 4 and y = 4.

The system of equations would be solved using the elimination method.

−10x+2y=−32 equation 1

-2x-2y=−16 equation 2

In order to determine the value of x, take the following steps:

Add equation 2 and equation 1 together

-12x = - 48

Divide both sides of the equation by -12

x = -48 / - 12

x = 4

In order to determine the value of y, substitute for x in equation 1:

-(10 x 4) + 2y = -32

-40 + 2y = -32

Combine similar terms:

2y = -32 + 40

Add similar terms:

2y = 8

Divide both sides of the equation by 2

y = 8 / 2

y = 4

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The table of solutions should be completed based on the given equation (y = 2x²) as follows:

x                    y_

-2                  8

-1                   2

0                   0

1                    2

2                   8

Also, a graph of the solution to the given equation is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would complete the table based on the given equation as follows:

When x = -2, the value of point y is given by:

y = 2x²

y = 2(-2)²

y = 2 × 4

y = 8

When x = -1, the value of point y is given by:

y = 2x²

y = 2(-1)²

y = 2 × 1

y = 2

When x = 0, the value of point y is given by:

y = 2x²

y = 2(0)²

y = 2 × 0

y = 0

When x = 1, the value of point y is given by:

y = 2x²

y = 2(1)²

y = 2 × 1

y = 2

When x = 2, the value of point y is given by:

y = 2x²

y = 2(2)²

y = 2 × 4

y = 8

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Answer:

3x+19

Step-by-step explanation:

Distribute:

14 x − 2 − ( 11 x − 21 ) 1 4 − 2 − ( 1 1 − 2 1 )

14 x − 2 − 11 x + 21 1 4 − 2 − 1 1 + 2 1

Add the numbers:

14x−2−11x+21

14−2−11+2

Combine like terms:

14x+19−11x

14 +19−113x+193+19

Solution: 3x+19

Answer:

3x + 19

Example:

None.

After a counterclockwise 90° rotation, the coordinates of A'B'C' are:

So, the coordinates after the counterclockwise rotation of 90°:

After counterclockwise 90° rotation, coordinates of A'B'C' are:

(Refer to the graph attached below)

Therefore, after a counterclockwise 90° rotation, the coordinates of A'B'C' are:

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Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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Answer:

y=-3/32

Step-by-step explanation:

2-18y=11+78y

-18y-78y=11-2

-96y=9

y=-3/32

The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We have been given the measure of each side of an equilateral triangle whose area is √3 cm².

Let the measure of each side would be "a"

We know that,

Area of an equilateral triangle = √3a² / 4

As per the question,

⇒ √3 cm²= √3a² / 4

⇒ √3a² = 4√3 / √3

⇒ a² = 4 = √4

⇒ a = 2 cm

Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

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The expression is 2z+0.67

From the question, we have

During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%.

z-35%+z-32%

=z-7/20+z-8/25

=2z+0.67

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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