Practice
Solve each equation. Check your solution (Example 1-3)
1. -2a-9=6a+15
2. 14+3n = 5n-6
3. 1/2 x -5=10 - 3/4 x
4. 7/3 y+1=1/6 y+8

We need to write the equation of the family of the lines with the following characterizing property.

j) x - intercept is twice y - intercept

X- intercept is the value of x when y= 0

Y- intercept is the value of y when x = 0

so, let y- intercept = a

x- intercept = twice y- intercept = 2a

So, the line will pass through the points: ( 2a , 0 ) and ( 0 , a )

The general equation of the line is : y = m * x + b

Where m is the slope and b is y - intercept

So, the equation of the family will be :

Answer:

B is the correct answer

hope this helped:)

Mia's gross pay was $794 at the end of the week.

To calculate Mia's gross pay, we have to find how much she earned working 37 hours at a rate of $12 per hour.

We can simply multiply both variable to determine how much she earned working for 37 hours.

[tex]37 * 12 = 444[/tex]

Mia earned $444 for that week.

We can add this to her 5% commission which would be 5% of $7000

[tex]5\% of 7000 = 350[/tex]

The sum of Mia's gross pay for the week is

[tex]444 + 350 = 794[/tex]

She earned $794 in gross pay at the end of the week.

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Answer:/Step-by-step explanation:

10. Write the phrase "20 divided by x minus 3 is 12" as a variable expression.

  20

---------- = 12

 x - 3

11. Write the phrase "4 plus the quotient of 9 and y equals 6" as a variable expression.

4 + (9 ÷ y) = 6

I hope this helps!

Answer:

The correct option is 3.

Step-by-step explanation:

The parent cube root function is

From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.

If the parent cube root function is reflected across the y-axis, then x is replaced by -x.

Now, the graph of new function sifts 1 unit down. So, the required function is

The graph shows the function .

From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).

Check the above function by these points.

At x=-8,

At x=0,

At x=8,

All these points satisfy by the abobe function. It means the above function is correct.

Therefore the correct option is 3.

The interval notation for the change in temperature are-

For the given function;

Increasing temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the interval notations are-

Increasing temperature; (1, 3) ∪ (6, 8).

Decreasing temperature: It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-

Decreasing temperature; (0, 1) ∪ (3, 6).

Thus, the interval notations for the function are found.

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Answer:

B. −18g^2 − 12g

Step-by-step explanation:

Hope this helps!
Please tell me if its incorrect

We are given the following quadratic equation

The vertex is the maximum/minimum point of the quadratic equation.

The x-coordinate of the vertex is given by

Comparing the given equation with the general form of the quadratic equation, the coefficients are

a = 2

b = 7

c = -10

The y-coordinate of the vertex is given by

This means that we have a minimum point.

Therefore, the minimum point of the given quadratic equation is

Answer:

Exact Form:x=±√6/2

Decimal Form:x=1.22474487,−1.22474487

Step-by-step explanation:

Answer: =111e3t(33cosh11−−√t+711−−√sinh11−−√t)

Step-by-step explanation:

Answer:

x=40/13

Step-by-step explanation:

tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]

[tex]x=\frac{40}{13} hours[/tex]

the form or the slope-intercept form of the equation of the line is

where m is the slope and b is the y-intercept

we have the next equation

as we can see the slope is m=-1/2, because we have the same form of the slope-intercept form

The algebraic expression for 5 more than z is Z + 5.

Given,

5 more than z.

We need to find the algebraic expression.

What are the different algebraic expressions?

We have,

Examples:

- 3 more than M =  M + 3

- 3 less than M =  M - 3

- 3 times M = 3 x M

- 3 times M less than 2 = 3M - 2

- 3 times M more than 2 = 3M + 2

Find the algebraic expression for 5 more than Z.

We have,

5 more than Z = Z + 5

Thus the algebraic expression for 5 more than z is Z + 5.

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I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING

IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.

[tex]12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15[/tex]

THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P

EXPRESSION BY 3

[tex] = 3(4 {x}^{2} - x + 5)[/tex]

HOPE THIS HELPS.

Given:

Required:

To find the value of the given expression.

Explanation:

Consider the given expression,

Final Answer:

The value of the given expression is 10.

MotoWin can expected to make money from offering these warranties.

In the long-run, they should expect to make 514 dollars from each warranty sold

What is expected value of replacement?

The expected value to MotoWin Auto Superstore of a replacing a car is the sum of the costs to be incurred when there is replacement multiplied by its probability of occurrence plus the cost of no replacement multiplied by its likelihood of occurrence expressed in percentage terms

expected value of replacement=(cost of replacement*its probability)*(cost of no replacement*its probability)

cost of replacement=$13,800

probability of replacement=7%

cost of no replacement=$0(when there is no to replace no cost is incurred)

probability of no replacement=93%

expected value of replacement=($13,800*3%)+($0*97%)

expected value of replacement=$414

profit on replacement=replacement price-expected value of replacement

profit on replacement=$928-$414

profit on replacement=$514

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Answer:

x=2log(2)−3log(4)log(4)−log(2)

Step-by-step explanation:

I hope this matches one of your answers

The decimal form is -4

After simplifying the expression to a singles complex number, it becomes 1+√3i.

A complex number is a unique kind of number in the number system, it has two parts. One it called the real part which is a real number and an imaginary part which is also a real part but accompanied by the specific notation called iota.

Here a complex number Z is provided to us,

Z = [2+√(-12)]/2

As we can see,

Here we have √-12

We can write it as,

√(-2×2×3)

= 2√(-3)

Here, √-1 is given that special notation "IOTA (i)" which we mentioned earlier.

=2√3i

So, Z becomes,

Z = (2+2√3i)/2

Z= 1+√3i

So, the simpler form of Z = [2+√(-12)]/2 is Z= 1+√3i.

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The maximum value of the linear equation is obtained as 52.

For the given question;

The linear equation is defined as;

C = x + 4y

The constraints are-

x ≥ 0

x≤ 12

y ≤ 10

2x + 3y ≥ 24

From the constraints, the maximum value for x and y are taken as;

x = 12 and y = 10.

Put the the equation, to find the maximum value.

C = x + 4y

C = 12 + 4×10

C = 52

Thus, the maximum value of the function is obtained as 52.

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Given the equation:

Required: sum and product of the roots of the equation

solution:

For a quadratic equation of the form

the sum of the roots is expressed as

the product of the roots is expressed as

The given quadratic equation can be rewritten in the form as in equation 2 to be

In comparison to equation 2,

Thus,

Sum of roots:

thus, the sum of the roots is

Products of roots:

thus, the product of the roots is

The distance Mr. Jackson drove from when he got in his car to when he got home is 200.5 km.

Given:

The odometer reading when Mr.Jackson got in his car = 187,198.9 km

The odometer reading when Mr.Jackson got home = 187,399.4 km

An odometer is a device used to calculate the distance traveled by a vehicle.

To determine the distance Mr.Jackson drove we subtract the odometer readings from when he got home minus when he got into his car.

⇒ (187,399.4 - 187,198.9) km

⇒ 200.5 km

Therefore, Mr. Jackson drove 220.5 km from when he got in his car to when he got home.

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Answer: The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Domain: (−∞,∞)

Range: (−∞,∞)

Hope this helps! :)

SOLUTION:

Step 1:

In this question, we are given the following:

Compare and contrast the formulas for calculating the volume of a cone and the volume of a pyramid.

Give a mathematical example to illustrate your discussion.

Step 2:

The details of the solution are as follows:

The formula for calculating the volume of a cone:

The formula for calculating the volume of the pyramid:

Solution

we are given the sequence

The first term = 2

Common difference = 6

The sequence is an arithmetic progression

The nth term is given as

Therefore, the answer is

Recall that the general form of a third-degree polynomial is:

where k is a constant, and a, b, and c are the zeros of the polynomial.

Therefore:

Now, to determine the value of k, we consider the y-intercept:

Solving for k, we get:

Finally:

Angle ABE & angle DBC are right angles then ∠ABE≅ ∠EBC

What is complementary angle theorem?

If two angles are complementary to the same angle, then they are congruent.

1.∠ABE and ∠DBC are right angles(Given)

2. m∠ABE=90⁰

m∠DBC=90⁰

By definition of right angles

3.∠ABE and ∠DBE are complementary.

∠DBE and  ∠EBC are complementary.

(By complementary theorem)

two angles are complementary to the same angle, then they are congruent.

4. ∠ABE≅ ∠EBC (is complementary to same)

Hence  ∠ABE≅ ∠EBC.

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Consider first the general case of the equation

The general formula that solves this problem is given by

In this case, the number of real solutions depends on the value that is inside the square root. For it to have a real value, it must happen that

So first, let's check if this is our case. In our case a = 2, b = 3 and c = -20.

Then

So in this case, the equation has real values. Now, recall that

So our general solution becomes

Then,

The symbol in the middle means that we get one different solution whenever we take either the plus sign of the minus sign. So the first solution would be

And the other solution would be

The terms in the given expression are

The common factor in all the three time is

Take the common factor outside the brackets and write the remaining inside the brackets.

Given

4

18

Procedure

The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive

When solving

The answer would be 18

Let x be the number of minutes they read and y the number of pages they read.

Since Alejandro read one page per minute and he has so far read a total of 28 pages he the total amount of pages he read is:

Now, Carly reads twice as much in the same time but she has read only 12 pages so far, then the amount of pages in her case is:

The graphf of this equations are:

The rate of change:

Alejandro: 1

Carly: 2

Given equation is

Now