Tomas makes a photobook online and sends copies to 4 family members. There is a $6 shipping charge for each photobook. He pays a total of $112.

Which equation can be used to find the price, x, of one photobook?

4x + 6 = 112
4(x + 6) = 112
42 - 6 = 112
4(x – 6) = 112

Answer:

The value of c is 8.

Step-by-step explanation:

When a function is divisible by a factor, it will get 0 value. So, you have to substitute x = -2 into p(x) and equals to 0 :

\(p(x) = 4 {x}^{3} + c {x}^{2} + x + 2\)

\(p( - 2) = 4 {( - 2)}^{3} + c {( - 2)}^{2} + ( - 2) + 2\)

\(4( - 8) + 4c - 2 + 2 = 0\)

\( - 32 + 4c = 0\)

\(4c = 32\)

\(c = 32 \div 4\)

\(c = 8\)

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

Line A B and Line C G are parallel.

Line C G and Line R S are perpendicular

Line A B and Line R S must intersect

Line segment C G lies in plane X

Step-by-step explanation:

Given that Planes X and Y intersect at a right angle.

From the image attached, line AB and CG are on the same plane X while line RS is on plane Y. Hence, line CG lies on plane X.

Since both line AB and CG line on the same plane, this means that both lines are parallel to each other.

Since plane X and plane Y are perpendicular to each other and line CG is on plane X and line RS is on plane Y, this means that both Line C G and Line R S are perpendicular.

Also Since plane X and plane Y intersect and line AB is on plane X and line RS is on plane Y, this means that both Line C G and Line R S intersect with each other at right angle.

Answer:

A and  are parallel.

C   and  are perpendicular.

E  lies in plane X.

Step-by-step explanation:

ED22

Answer:2,440,000,000

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

5x3=15, 15+3 =18

Answer:

x = ~2.17 (rounded)

Step-by-step explanation:

First, combine like terms (terms with the same amount of the same variable):

5x + 1 + 18x + 11 = 62

(5x + 18x) + (1 + 11) = 62

(23x) + (12) = 62

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, &  =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 12 from both sides:

23x + 12 (-12) = 62 (-12)

23x = 62 - 12

23x = 50

Divide 23 from both sides to isolate the variable, x:

(23x)/23 = (50)/23

x = 50/23 = 2 4/23 = ~2.17 (rounded to the nearest hundredths).

Answer:

x= -2.17 (rounded to nearest hundredth)

Step-by-step explanation:

5x + 1 + 18x + 11 = 62

     -1            -11      -12

subtract 1 and 11 from both sides which leaves you with:

5x + 18x = 50

add 5x and 18x and you get:

23x = 50

now divide both sides by 23 and get:

x=-2.17

Answer:

x = 1

r+7 = ..

5g = 9

8r = 12

A, C, D and F

Step-by-step explanation:

Q1. By linear pair, I know that 72* + unknown angle = 180*

therefore unknown angle = 180-72 = 108*

Now because this is a pentagon, the total of all interior angles of a polygon equals 540*

so 108* + 100* + 110* + 45* (Half of 90 , written as a semi-square) + Y* = 540

Y* = 540 - 363 = 177*

Q2. 360 - (80+70+110) = q

q = 360 - 220 =  140*


Q3. 160+160+ S* = 360*

360* - 320* = S*

S* = 40*

Hope it helps

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

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Answer: 6 units

Step-by-step explanation:

|-5.4| + |0.6|

5.4 + 0.6 = 6 units

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Domain:

Range:

Function:

Domain:

Range:

Function:

Domain:

Range:

Function:

The number of students who will be going on the trip is B. 40 students.

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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Answer:

The temperature was 80 degrees and it dropped 10 degrees. What is the temperature now?

80 - 10 = 70 degrees

Step-by-step explanation:

Answer:

A cube size is 150mm

Step-by-step explanation:

I think it will be

10.50 x 5 would be the expression.

The answer is $52.5

Answer:

10.50 x 5 would be the expression.

The answer is $-52.5

Step-by-step explanation:

Answer:

A)14 Units is the answer for this question

but check it

The percentage increase is about 16.66%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.

The initial amount was $18 and the final amount is $21.60.

By using the percentage increase formula, we can write

        Percentage increase = (final value - initial value)/|Final value| * 100

                                            = ((21.60 - 18)/21.60)*100

                                            = 16.66%

Hence, the percentage increase is about 16.66%.

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Kaitlin will have $4657 as the total amount in her account after 3 years which was found using the compound interest formula.

What exactly is Compound Interest?

Given: Kaitlin put $4000 into an account earning 5.2% annual compound interest.

We need to find how much will she have in the account after 3 years.

Let,

P = initial sum of money

r = interest rate, 

t = number of years in decimal form

A = total amount in her account

Using the compound interest formula we obtain,

A = P (1+r)^t

A = 4000(1 + 0.052)³

A = 4000(1.052)³

A = 4000(1.164)

A = $4657

Therefore, Kaitlin will have $4657 as the total amount in her account after 3 years.

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The approximate height of the pole in centimeters is 17,500 centimeters.

We have,

Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.

We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.

25 = L/7

where L is the total length of the pole.

We can solve for L by multiplying both sides of the equation by 7:

L = 7 x 25

  = 175 meters

Now we need to convert this length to centimeters.

Since 1 meter is equal to 100 centimeters,

175 meters x 100

= 17,500 centimeters

Therefore,

The approximate height of the pole in centimeters is 17,500 centimeters.

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The complete question.

The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

The system of equation has a solution of x = 8 and y = 6.

In order to remove a variable from a system of equation, we must change the equations so that the variable is removed. In relation to this specific set of equations:

3x - 4y = 0 \s-3x + 9y = 30

By combining the two equations, we can take the variable x out of the equation. This is due to the fact that the x terms cancel out when the two equations are added:

3x - 4y + (-3x + 9y) = 0 + 30

When we simplify this equation, we obtain:

5y = 30

When we multiply both sides by 5, we get:

y = 6

After figuring out y, we can now put this answer back into one of the initial equations to figure out x:

3x - 4y = 0

3x - 4(6) = 0

3x - 24 = 0

3x = 24

x = 8

As a result, the system of equations has a solution of x = 8 and y = 6. By substituting the values of x and y into the two original equations and confirming that they are both true.

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The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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Answer:

30,000

Step-by-step explanation:

10% of 30,000 is 3,000

30,000 - 3,000 = 27,000

The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)

To determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:

\(80/4^{x}\)

This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.

Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.

\(80/x^{4}\)

This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.

Therefore, the expression that is option d.

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The value of 10% as a fraction and a decimal will be 1/10 and 0.1.

From the information, we want to write the percentage as a fraction as well as a decimal. A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.

10% as a fraction will be calculated by dividing 10 by 100. This will be:

= 10 / 100

= 1 / 10

10% as a decimal will be calculated by dividing 10 by 100 and giving it in decimal form.

= 1/10

= 0.1

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. Complete question

Write 10% as a fraction and a decimal

A scalene triangle is a triangle where the lengths of all three sides are different, these are: 14, 6 and 9.

A scalene triangle is a triangle whose three sides are all of various lengths and whose three angles are all of different sizes. A scalene triangle's angles obey its angular summation rule and would always add up to 180.

Properties are:

the triangle with sides of lengths 14, 6, and 9 is: scalene triangle.

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To find the point of intersection for two lines, we can use substitution to solve for the coordinates.

We're given:

With these two equations, we can:

Isolate x in the second equation:

\(x+2y=7\\x =7-2y\)

Substitute the second equation into the first:

\(3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5\)

Solve for y:

\(21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2\)

Solve for x:

\(x+2y=7\\x+2(2)=7\\x+4=7\\x=3\)

The point of intersection of the lines is (3,2).