Represent a quadratic function

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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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

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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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

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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The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.

A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.

It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.

The balance sheet is illustrated below:

Current Assets  

Accounts Receivable  26500

Cash    20500

Merchandise Inventory  26300

Total Current Assets  73300

Property, Plant and Equipment  

Land    10000

Total Property, Plant and Equipment 10000

Total Assets   83300

Current Liabilities    

Accounts Payable   12200

Long Term Liabilities  

Long-Term Notes Payable  17500

Stockholders' Equity  

Common Stock  30000  

Retained Earnings  23600  

Total                                 53600

Total Liabilties          83300

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Answer:

y = 1

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

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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Answer:

x is any real number from -infinity to infinity.

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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SOLUTION

Step1:

hence from the diagram above, the dimension of the rug is

Since we have area of the rug,

then we have

We now solve the equation above quadratically

Then we have

Solve using factor method we obtain

Equating each factor to zero we have

Since x can not be 28, the value of x is 1

The Dimension of the rug becomes

Hence the dimension of the rug is 32 ft by 22ft (22,32)

[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:

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:

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.

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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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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SOLUTION

f(x) = x + 3

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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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 scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.

Now,

That means that 1 inch corresponds to 7ft +7ft= 14ft.

Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.

Answer: The scaled figure will fit in the billboard.

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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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.

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]

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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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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Answer:

x + 15 - 30

x -15

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

23 + 94  = 117

180 degrees ( sum of all angles in a triangle)

180 - 117 = 63

The total possible outcome for the experiment is 36.

The ossible outcomes for same number on each dice is 6.

So probability for the same number on dice is,

So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.