Write y= -4x² -16x -14 in vertex form.

A) y= -4(x-16)² -14

B) y= 4(x+4)² +2

C) y= -4(x+2)² +2

D) y= (x+2)² -14

Answer:

option d

Step-by-step explanation:

Solve each inequality and check which inequality has -12 as a solution

a. [tex]x+6<-8[/tex]

Subtract 6 from both sides

[tex]x<-14[/tex]

b. [tex]x+4>-6[/tex]

Subtract 4 from both sides of the inequality to get x alone

[tex]x>-10[/tex]

c.[tex]x-3>-0[/tex]

Add 3 on both sides

x>3

d. [tex]x+5<-4[/tex]

Subtract 5 from both sides

x<-9

-12 lies below -9. So x<-9 has -12 in its solution

One number is six times as large as a certain smaller number.

i.e., Y  = 6x

Answer is 6x

The larger number in terms of x is 6x.

To write the larger number in terms of x, we know that the larger number is six times as large as the smaller number. Let x represent the smaller number, so the larger number can be written as 6x.

https://brainly.com/question/8306203

#SPJ2

Answer is A

12+x

____. =0.70

24+x

Answer:

A

Step-by-step explanation:

Currently, Andy has a winning record of 50%.

12 /24  = 0.50

To determine a winning record of 70%: add x matches to 12, x matches to 24, and set equal to 0.70.

12 + x /24 + x  = 0.70

x = 16

Therefore, Andy would need to win 16 matches in a row.

-3.

Hope this helped.

Answer:

x = -3

Step-by-step explanation:

Solving for value of x

−x + (−3) = x + 3              

-x -3 = x + 3                     [subtract x from both side]

-x -3 -x = x + 3 -x

-2x -3 = 3                       [add 3 to both side]

-2x -3 + 3 = 3 + 3

-2x = 6                          [divide both side by -2]

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{6}{-2}[/tex]

x = -3

Its x^2 if x > -1

x = 3  so the answer is 3^2  = 9

The regular price of the jeans was $50. We know this because he saved $20 when the pants were 40% off so for every 10% percent it is $5, so 100% is $50 if that makes sense, if you need more thorough explanation let me know. :)

10 -:- 5. This is the answer. Hope this helps:)

The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation is represented as ∑(from n=1 to n=20)[1 + (n-1)*2]. This notation communicates the series' progression and key characteristics.

The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 can be represented in sigma notation as follows: Let the general term of this arithmetic series be a_n = 1 + (n-1)*2, where n is the term number. This formula is for a sequence where the difference between each number is 2 (an arithmetic sequence). Thus, the series 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation can be written as ∑(from n=1 to n=20)[1 + (n-1)*2]. Here, n = 1 is the starting point, n = 20 is the end point which is calculated by (39-1)/2 + 1 because the sequence is an arithmetic sequence with common difference 2 and first term 1, and 1 + (n-1)*2 is the formula for the nth term.

https://brainly.com/question/35665690

#SPJ2

The sum 1 + 3 + 5 + ... + 39 can be written in sigma notation as Σ(1 + (i - 1)2) for i from 1 to 20.

To express the sum 1 + 3 + 5 + 7 + 9 + ... + 39 in sigma notation, we first need to realize that this is an arithmetic series where each term increases by 2. The first term a1 is 1, and the common difference d is 2. We can find the number of terms n in the series by using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d.

Since 39 is the last term, we have 39 = 1 + (n - 1)2, which simplifies to n = 20.Now we know our series goes from the 1st term to the 20th term, and the formula for the ith term is ai = 1 + (i - 1)2. Therefore, the series in sigma notation is written as:  Σ(1 + (i - 1)2) for i from 1 to 20.

Answer:

hours worked; amount of money earned; 0 to 30; $0 to $330

Step-by-step explanation:

Let

y ----> the amount earned per week

x ----> the number of hours worked by week

In this problem

the amount earned per week (variable y) represent the dependent quantity

the number of hours worked by week (variable x) represent the independent quantity

therefore

The domain is the interval -----> [0,30] (the maximum number of hours per week is 30)

The range is the interval -----> [0,11*30] ----> [0,330] (the maximum amount earned per week is $330)

therefore

independent quantity is hours worked

dependent quantity is amount of money earned

domain is 0 to 30

range is $0 to $330

Final answer:

The independent quantity is hours worked and the dependent quantity is the amount of money earned, with a domain of 0 to 30 hours and a range of $0 to $330.

Explanation:

In the given scenario where Uan earns $11 per hour and works at most 30 hours per week, the independent quantity is the hours worked, and the dependent quantity is the amount of money earned. This is because the money earned depends on the number of hours worked.

The domain represents the possible values of the independent variable, which is the hours worked. In this case, it is reasonable to assume that Uan could work anywhere from 0 to 30 hours per week. Therefore, the domain is 0 to 30 hours.

The range represents the possible values of the dependent variable, which is the amount of money earned. Since Uan earns $11 per hour, working 0 hours would yield $0, and working the maximum of 30 hours would yield $330 (30 hours × $11 per hour). Thus, the range is $0 to $330.

The correct answer to the student's question, based on the information, would be: hours worked; amount of money earned; 0 to 30; $0 to $330.

The first thing you would do is "bring" the 10 over by subtracting 10 from both sides

[tex]3x^2+13x-10=0[/tex]

Now, you would want to factor

[tex](3x-2)(x+5)=0[/tex]

Then, set each factor equal to zero, and solve

3x-2 = 0

3x = 2

x = 2/3

AND

x+5 = 0

x=-5

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The determinant is given as:

D = -b ±√(b² - 4ac) / 2a

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

x + 3 = 4 is an equation.

3x + 4x = 4 is an equation.

We have,

3x² + 13x = 10

This can be written as:

3x² + 13x - 10 = 0

Using the Middle term factorization.

3x² + (10 + 3)x - 10 = 0

3x² + 10x + 3x - 10 = 0

This is not possible so,

Using determinant.

3x² + 13x - 10 = 0

a = 3, b = 13 and c = -10

Now,

Determinant is given as:

D = -b ±√(b² - 4ac) / 2a

D = -b + √(b² - 4ac) / 2a

D = [-13 + √(169 + 120)] / 6

D = (-13 + √17) / 6 _____(1)

D = -b - √(b² - 4ac) / 2a

D = -13 - √(169 + 120) / 6

D = (-13 - √17 ) / 6 ______(2)

Thus,

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

For four days it would be $19.8. For seven days it would be $24.9

Step-by-step explanation:

4 days:

$4.70 x 4 + 1= 19.8

7 days:

$4.70 x 7 = $24.9

I took away 1 from the 4 day equation because the question said you get a dollar off if you return the dvd before 5 days.

Hope this helps!

~Starr

Answer:

The man got a 8% raise.

Step-by-step explanation:

Percentage change        = [Increase or decrease in value / Original Value]*100

Increase in hourly wage = [tex]13.5-12.5[/tex]

                                         =[tex]1[/tex]

Percentage raise             = [Increase in hourly wage / Initial hourly wage]*100

                                         =[tex]\frac{1}{12.5} *100[/tex]

                                         = [tex]8[/tex]%

The man got a 8% raise.

The man's hourly wage increased from $12.50 to $13.50 which, following the formula for calculating percentage change, indicates that he received an 8 percent raise in his hourly wage.

Given that the man's hourly wage increased from $12.50 to $13.50, we can use the formula for calculating the percentage change to find out what percent raise he got.

The formula for calculating the percentage change is as follows:

[(change in quantity)/(original quantity)] × 100

In this case, the change in quantity (the man's wage increase) is $1.00 (13.50 - 12.50), and the original quantity (the man's original wage) is $12.50.

Plugging these values into the formula, we get:

[1.00/12.50] × 100

This calculates to an 8 percent wage increase. Therefore, the man got an 8 percent raise in his hourly wage.

https://brainly.com/question/20818421

#SPJ3

The Equation ( x= 11): 3x + 3 = 2(x + 7) and 6(x + 2) - x = 4(x + 4) + 7

The Equation ( x= 3): 0.8x + 5 = 0.2(40 - x), 2(x - 5) + 7 = x and

                                    ½(x + 8) + 3/2x = 10

The Equation ( x= 1/2): 5(x - 1) - 6x = -11x and ½x + 1/4 = x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1.  0.8x + 5 = 0.2(40 - x)

Solving for x, we get

0.8x + 5 = 0.2(40 - x)

0.8x + 5 = 8 - 0.2x

x + 5 = 8

x = 3

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

Solving for x, we get

2(x - 5) + 7 = x

2x - 10 + 7 = x

2x - 3 = x

-3 = -x

3 = x

3. 3x + 3 = 2(x + 7)

Solving for x, we get

3x + 3 = 2(x + 7)

3x + 3 = 2x + 14

3x = 2x + 11

x = 11

4.  5(x - 1) - 6x = -11x

Solving for x, we get

5(x - 1) - 6x = -11x

5x - 5 - 6x = -11x

5x - 6x = -11x + 5

5x - 6x + 11x = 5

10x = 5

x = 1/2

5.  6(x + 2) - x = 4(x + 4) + 7

Solving for x, we get

6(x + 2) - x = 4(x + 4) + 7

6x + 12 - x = 4x + 16 + 7

5x + 12 = 4x + 23

5x = 4x + 11

x = 11

6.  ½(x + 8) + 3/2x = 10

Solving for x, we get

½(x + 8) + 3/2x = 10

½x + 4 + 3/2x = 10

½x + 3/2x = 6

2x = 6

x = 3

7.  ½x + 1/4 = x

Solving for x, we get

½x + 1/4 = x

1/4 = ½x

½ = x

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ2

Afaik you just plug these into y=mx+b (slope intercept form)

I would think the answer to be y = (-3/5)x + 4

Answer:

y=-3/5x+4

Step-by-step explanation:

y=mx+b

Answer:

81

Step-by-step explanation:

x^2 − 18x + 9^2 = 17 + 9^2

=> x^2 − 18x + 81 = 17 + 81

A

f(x) = 2x + 1

f(3) = 2*3 + 1 = 7

B

g(x) = x^2

g(7) = 7^2

g(7)= 49

C

f(g(x)) = 2(g(x) + 1

f(g(x)) = 2 x^2 + 1

f(g(3) = 2* 3^2 + 1

f(g(3) = 19

D

g(f(x)) = (f(x))^2

g(f(x)) = (2x + 1)^2

g(f(3)) = (2*3 + 1)^2 = (6 + 1)^2 = 49

E

f(g(x)) = 2*g(x) + 1

f(g(x)) = 2*x^2 + 1

f(g(3)) = 2*3^2 + 1

f(g(3)) = 2 * 9 + 1

f(g(3)) = 18 + 1

f(g(3) = 19

F

f(g(x)) = 2(g(x)) + 1

f(g(x)) = 2*x^2 + 1  

Answer: 100

Step-by-step explanation:

[(25 - 11) + (15 - 9)] * 5

=[    14      +      6    ] * 5

=             20             * 5

=                     100

Answer:

B

Step-by-step explanation:

I got it correct on edg

Answer:

b

Step-by-step explanation:

The queen might've asked the king to measure the rug to demonstrate humility, responsibility, highlight practical skills, or grasp the concept of measurement. Without specific context, however, it's hard to pinpoint an exact reason.

Without specific context, it's difficult to provide an exact reason for the queen asking the king to measure a rug. However, in general, English literature often showcases rulers partaking in ordinary tasks as a means of demonstrating humility, responsibility, or attention to detail. For instance, the queen might have wanted the king to measure the rug in order to prove that he can attend to ordinary matters as well as royal duties, or perhaps to prove himself practical and not merely ceremonial. It could also be a ploy to make the king grasp the concept of measurement, size or area, by doing the task himself.

https://brainly.com/question/31928608

#SPJ3

Answer:

Option D

0.6

Step-by-step explanation:

Given that there are 5 colour marbles in a large bag.

The colours are red, orange, yellow, blue and green.

Also given that there are equal amounts of each colour

Let n be the no of marbles of each colour.

Then total no of marbles = 5(n) = 5n

No of red,blue and yellow marbles = n+n+n = 3n

Prob of drawing a red or blue or yellow = P(red)+P(blue)+P(yellow)

= [tex]\frac{n}{5n} +\frac{n}{5n} +\frac{n}{5n}  = \frac{3n}{5n}[/tex]

= 0.60

To complete the square for the equation x²-7x = 5, you need to add 12.25 to both sides of the equation, leading to the equation (x - 3.5)² = 17.25.

To complete the square in the equation x²-7x = 5, we will need to find a term (b) to add to both sides where b is one-half of the number being subtracted from x² (-7), squared.

First, we will take half of 7 which equals 3.5. Squaring 3.5, we get 12.25. Therefore, we add 12.25 on either side to complete the square.

The equation then becomes x² - 7x + 12.25 = 5 + 12.25, which simplifies to (x - 3.5)² = 17.25. This represents a completed square.

https://brainly.com/question/4822356

#SPJ12

To complete the square for the equation [tex]x^2-7x=5[/tex], you need to add 12.25 to both sides. This forms a perfect square trinomial (x - 3.5)² on the left side of the equation and results in the number 17.25 on the right side.

The provided equation is a quadratic equation (it's in the form of ax² + bx + c = 0), and you're asked to complete the square.

In order to complete the square, you take half of the coefficient of the 'x' term (which is -7 in this case), square it and add it to both sides of the equation. So, half of -7 is -3.5, and -3.5² equals 12.25.

Therefore, adding 12.25 to both sides of the equation completes the square and forms a perfect square trinomial on the left:

[tex]x^2 - 7x + 12.25 = 5 + 12.25[/tex]

Which simplifies to:

[tex](x - 3.5)^2 = 17.25[/tex]

https://brainly.com/question/4822356

#SPJ12

Answer:

24 ounces.

Step-by-step explanation:

Given that the ratio of blue paint to yellow paint in a green paint mixture is 2:3.

Actual ounces used for blue paint = 16

By ratio and proportion property we have

2:3 = 16:x where x is the actual ounces of yellow paint used.

Simplify using ratio rules

if a:b = c:d then ad = bc

We get

2x=3(16) = 48

Divide by 2

x = 24

Hence 24 ounces of yellow paint to be used.

Answer:

24 ounces. to be exact

Step-by-step explanation:

Answer:

The answer is A) When you want to change cars frequently.

Step-by-step explanation:

Answer with explanation:

Car lease means you don't want to buy the car , you want to use it for various Purposes or you love riding or driving different cars.

⇒Changing cars completely ,means you are interested in distinct brand of cars that is in leasing.

⇒When you want to keep a car for several years , it means you love that thing and either you don't have enough money to buy or you are in two minds ,so either you lease it or take a loan for that thing.

⇒When you like the idea of owning a car, it means you take loan for it,not to lease it.

¬Option A  is most appropriate.

   When you want to change cars frequently

According to picture Jennifer’s grandmother buys = 28 kg of carrots.

Total number of grandchildren = 3.

Number of kilograms of carrots are distributed equally.

In order to find the Number of kilograms of carrots are distributed, we need to divide total Kgs of carrots by total number of grandchildrens.

Therefore ,

28 ÷ 3 .

On dividing 28 by 3, we get 7.

Therefore, Jennifer will get 7 kilograms of carrots.

180° rotation about the origin changes the signs of the coordinates.

(x, y) → (-x, -y)

It is a reflection over the y-axis and a reflection over the x-axis (in either order).

You did not provide the options so hopefully you can figure out the answer based on the information I provided.

Answer:

The transformation of the triangle MNO will be first a reflection respect to the x-axis and second a reflection over the y-axis.

Step-by-step explanation:

By definition a coordinate transformation from 180° rotation round the origen can be expressed as:

(x,y) ---> (-x,-y)

On the other hand, the coordinate transformation of the reflection over x- axis is:

(x,y) ---> (x,-y)

And the reflection over the y-axis of the this transformation is:

(x,-y) ---> (-x,-y)

That result the same transformation than the 180° rotation.