9h - 27 What is the greatest common?factor Expand the expression

Answer:

x is any real number from -infinity to infinity.

1. The value of the expression when q = 13 in q - 10 is 3.

2. The value of the expression when x = 4.2.

34.5x is 144.9

3. The interest will be $5.25.

It should be noted that an expression is simply used to show the relationship between the variables.

1. The expression when q = 13 in q - 10 will be:

= q - 10

= 13 - 10

= 3

2. The value in the expression when x = 4.2 will be:

= 34.5x

= 34.5 × 4.2

= 144.9

3. Principal = $70

Rate = 3%

Time = 2.5 years

Interest = PRT / 100

= (70 × 3 × 2.5) / 100

= $5.25

The simple interest would you earn in 2.5 years is $5.25.

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Based on the slope formula for a line, the value of a is: a = -3.

If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:

Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.

The given line has the following:

(-10, 0) = (x1, y1)

(a, -6) = (x2, y2)

Slope (m) of the line = -6/7.

Plug in the values into the slope formula for a line:

(-6 - 0) / (a - (-10)) = -6/7

-6/(a + 10) = -6/7

Cross multiply and solve to find the value of a in the equation:

-6(a + 10) = -6(7)

Apply the distributive property

-6a - 60 = -42

Add 60 to both sides

-6a - 60 + 60 = -42 + 60 [addition property of equality]

-6a = 18

Divide both sides by -6

-6a/-6 = 18/-6 [division property of equality]

a = -3

Therefore, the value of a is -3.

The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).

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A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.

Simple interest=p*n*r

=300000*6/100*45/365

=2250

Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.

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Answer:

63

Step-by-step explanation:

23 + 94  = 117

180 degrees ( sum of all angles in a triangle)

180 - 117 = 63

Answer:

Step-by-step explanation:

To find the median of a stem and leaf plot, use the equation:

Therefore, for the given plot, there are 16 elements.

When there are two middle values, the median is the mean of these two values:

7r³ + 11r²s  -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.

Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.

Let's review some of the crucial words used during expression simplification:

In an algebraic expression, a variable is a letter with an undetermined value.

We have been asked to simplify the expression

(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

Let's simplify

⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

⇒ 7r³ + 10r²s  −3rs² − 8s + r²s -6rs²

⇒ 7r³ + 11r²s  -9rs² - 8s³

Thus, 7r³ + 11r²s  -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

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The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true

The functions are given as

f(x) = c

Also, we have

f(-x) = c

In the above function definitions, we can see that

The functions f(x) and f(-x) have the same value

i.e. f(x) = f(-x) = c

This means that f(x) =f(-x)

By the symmetric property of an equation, the above can also be rewritten as

f(-x) = f(x)

Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true

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The original price for the desk is $980.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

Given:

Sale price = 343

price was 35% of the original price.

let the original price be x

35% of x = 343

35 / 100 * x = 343

x= 343 * 100/ 35

x=980

Hence, the original price of the desk was $980.

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After 10 years, the money dis she earn is $800 with the interest of 6%.

Interest:

Interest is the amount for a particular principal amount of money at some rate of interest.

Given,

Jackie deposited $500 in an account for 10 years at 6% interest.

Here we need to find the money did she earned.

We know that, the interest for the amount is 6%.

So, the amount after 10 years is,

=> 500 x (6/100) x 10

=> 30 x 10

=> 300

Therefore, the interest amount is 300.

So, the total amount she will receive after 10 years is,

=> 500 + 300

=> 800

Therefore, she will earn $800 after 10 years.

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Matching the given mathematical operation equations to the specified choices, gives;

A•B = B•A ; Commutative Property of Multiplication

A + B = B + A ; Commutative Property of Addition

(A•B)•C = A•(B•C); Associative Property of Multiplication

A•0 = 0; Multiplicative Property of 0

(A + B) + C = A + (B + C); Associative Property of Addition

A•1 = A; Multiplicative Identity

A + 0 = A; Additive Identity

The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties

Commutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.

Therefore;

Commutative property of multiplication is therefore; A•B = B•A

Commutative property of addition is; A+B = B+A

Associative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.

Therefore;

(A•B)•C = A•(B•C) represents the associative property of multiplication

The associative property of addition is represented by (A+B)+C = A+(B+C)

The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0

Therefore, the equation, A•0 = 0, represents the multiplicative property of 0

The multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0

The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively

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Answer:

Step-by-step explanation:

Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.

ive n

lan A

Plan B

Monday: 3 clients - Plan A

5 clients - Plan B

Total 10 hours

Tuesday

6 clients - Plan A

2 clients - Plan B

Total 10 hours

rocedure

Let's define a system of linear equations that represents the above problem.

A: Number of hours of workout in plan A

B: Number of hours of workout in plan B

The goal here is to solve

3A+5B=10 and

6A+2B=10 for the variables A and B.

The solutions to your equations are:

A = 5/4 hour

B = 5/4 hour

The value of a in the magic square is  25

The value of b in the magic square is 3

The value of c in the magic square is 14

The value of d in the magic square is 7

The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.

According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.

The three squares of the diagonal from left to right has all the complete numbers.

Sum of the the squares = 5 + 16 + 27 = 48

a = 48 - 18 - 5 = 25

b = 48 - 18 - 27 = 3

c = 48 - 29 - 5 = 14

d = 48 - 27 - 14 = 7

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SOLUTION

f(x) = x + 3

The provided translated function, f(x), shifts left by two units on the horizontal axis.

One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.

The given graph equation for the translation, as per the query, is g(x) = (x + 2)²

The translation of the given quadratic function is: y = g(x) = (x + 2)²

Consequently, the parent function is written as y = g(x) = x2.

Additionally, the vertex should be known when graphing the translated function:

a(x - h)2 + k = y = g(x);

where the parent function is (0, 0) and the vertex values are (h, k).

(h, k) = is the vertex for the function that is provided (-2, 0)

This information causes the translation function to move the graph two units to the left.

Horizontal translation is the name given to the translation.

As a result, the given function, f(x), shifts horizontally, or left, by 2 units.

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Let the price of black and white brouchers be x

The price of color brochures be y.

A/q,

4x+4y=148.....(1)

4x+3y=125 .....(2)

The equation (1) becomes,

x+y=37

y=37-x.......(3)

Putting (3) in (2) we have,

4x+3(37-x)=125

4x+111-3x=125

x=14

Putting the value of x in (3) we have,

y=37-14=23

The price of black and white brouches is $14

The price of color brouchers is $23.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]

and

[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]

We need to find : (f + g) (x) = ?

[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]

[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]

[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

y = 1

The graph has no gradient and only intersects at the y-axis.

Answer:

x + 15 - 30

x -15

Step-by-step explanation:

Answer:

In order, the answers are d, b, c, a

Step-by-step explanation:

[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]

[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]

[tex] {x}^{0} = 1[/tex]

[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]

Answer:

x = 8

y = 8

Step-by-step explanation:

The two equations are:

x + y = 16    (1)

x = y           (2)

Since x = y substitute for y in terms of x in (1):
x + x = 16

2x = 16

2x/2 = 16/2

x = 8

y = 8

By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.

Here we have the functions:

f(x) = -2x +4

g(x) = 2x - 8

We want to find the value of x such that:

f(x) = g(x).

If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.

The graph can be seen in the image below.

There we can see that the graphs intercept at (3, -2), meaning that the solution of:

f(x) = g(x) is x = 3.

Which is the same thing that if we write:

f(x) = g(x)

-2x + 4 = 2x - 8

4x = 12

x = 12/4 = 3

x = 3

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5 units

Explanation

Step 1

the distance between 2 points P1 and P2 is given by:

Let

P1=A(-3,4)

P2=B(2,-4)

Step 2

put the values into the equation

The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)

An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.

The initial constant, “a,” cannot be 0, and this is an unbreakable rule.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.

Thereafter draw a sloping triangle connecting the two spots you find on the line.

If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:

-2 = a(0+3)(0+1)

-2 = 4a

a = -1/2

So the equation can be written as y = -1/2 (x+3)(x+1)

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The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.

Given that,

The numbers 106 and 104.

We have to find the greatest common factor of 106 and 104.

The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)

The factors of 104 are 1,2,4,8,13,26,52,104;

The factors of 106 are 1,2,53,106.

Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.

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The angles congruent to ∠5 are as follows:

According to the diagram, line l, m and n are parallel lines.

Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.

Hence, the angles that are congruent to ∠5 can be solved as follows:

∠5 ≅ ∠8 (vertically opposite angles)

Vertically opposite angles are congruent.

∠5 ≅ ∠1 (corresponding angles)

Corresponding angles are congruent.

∠5 ≅ ∠4 (alternate angles)

Alternate angles are congruent.

∠5 ≅ ∠9 (corresponding angles)

∠5 ≅ ∠12 (alternate exterior angles)

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Using the law of Sines, the length of side AD, |AD|, is 7.44

From the question, we are to determine the length of side AD

From the given information, we have that

u = 17 and v = 17

Then,

ΔBCD is an isosceles triangle

∴ m ∠DBC = m ∠ BCD

m ∠DBC = x = 25°

∴ m ∠BCD = 25°

Also,

m ∠BCA = ∠y + m ∠BCD

m ∠BCA = 25° + 25°

m ∠BCA = 50°

Now, we will determine the measure of ∠CAD.

m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)

m ∠CAD + 25° + 50° = 180°

m ∠CAD = 180° - 25° - 50°

m ∠CAD = 105°

Now,

From law of Sines, we can write that

|AD| / sin DCA = |DC| / sin CAD

|AD| / sin y = u / sin CAD

|AD| / sin 25° = 17 / sin 105°

|AD| = (17 × sin 25°) / sin 105°

|AD| = 7.43795

|AD| ≈ 7.44

Thus,

Length AD is 7.44

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