Can someone please explain how to solve this step by step with answer? Thank you.

Answer:

A

Step-by-step explanation:

given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12

for the y- intercept let x = 0

f(0) = - 12 → y-intercept is the point (0, - 12) → True

for x-intercepts let y = 0

3(x + 2)(x - 2) = 0

x + 2 = 0 ⇒ x = - 2

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)

since f(x) = 3x² - 12 is symmetric about the y-axis

the vertex is at (0, - 12 ) → not (- 2, 2)

Answer:

Option C is correct.

[tex]y = 0.9673x^2-0.8475x + 10.4334[/tex] is an quadratic model equation for the data set

Step-by-step explanation:

To find the equation of the quadratic model for the given data set:

x               y

4              20

10             86

13            174

17             274

8              72

12             135

6               44

Therefore, the quadratic model for the given data is given by;

[tex]y = 0.9673x^2-0.8475x + 10.4334[/tex]

Answer:x=4 and y=4

Step-by-step explanation: if you divide 9 by 3 it would be 3 and 6 divided by 3 would be 2 so if you multiply 2 by 4 and 3 by 4 and you add them together it will equal 20

Answer: [tex]3x+2y=20[/tex]

Step-by-step explanation:

Let  x be  the number of boxes of crackers and y be the number of boxes of granola bars that Mr. Logan bought at the grocery store.

Given : The price of the crackers is $9 for 3 boxes, and the price of the granola bars is $6 for 3 boxes.

i.e. price of one box of crackers = $9 ÷3 = $3

Price of one box of granola bars=$6÷3 = $2

Mr. Logan ends up buying $20 worth of crackers and granola bars.

i.e.  (Cost of each box of crackers) x + (Cost of each box of granola bars) y

i.e. [tex]3x+2y=20[/tex]

Hence, the equation represents the relationship between the number of boxes of crackers, x, and the number of boxes of granola bars, y, that Mr. Logan bought at the grocery store :

[tex]3x+2y=20[/tex]

Answer:

38.94

Step-by-step explanation:

To find the area, multiply the length times the width. In this case 9.5 times 4.1.

Answer:

1. ∠LOQ = 80°

2. ∠LRQ = 40°

3. ∠LBQ = 40°

Step-by-step explanation:

It is given that ARC QL has a measure of 80.

1.

m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.

∠LOQ = 80°

2.

m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.

∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LRQ = 40°

3.

m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.

∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LBQ = 40°

Answer:

12

Step-by-step explanation:

Change the percentage into a decimal

30% = 30/100 = 0.30

Multiply 40 with 0.30

40 x 0.30 = 12

12 more people adopted, making 52 in all.

~

Answer:

52

Step-by-step explanation:

30% more means the original 100% plus 30% more of the original 40

That's 130% = 130/100 = 1.3

"of" means x, so it's 40 x 1.3 = 52 people

Answer:

see below  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

2020 -2010 = 10 YEARS

375,000 X .09 = 33,750                  2011 VALUE  33750 + 375000 = 408,750

408750 X .09 = 36787.50               2012 VALUE  445537.50

445537.50 X .09 = 40,098.38         2013 VALUE  485635.88

485635.88 X .09 = 43707.23           2014 VALUE  529343.11

529343.11 X .09 = 47640.88            2015 VALUE  576983.99

576989.99 X .09 = 51928.56          2016 VALUE  628918.55

628918.55 X .09 = 56602.67          2017 VALUE 685521.22

685521.22 X .09 = 61696.91           2018 VALUE  747218.13

747218.13 X .09 = 67249.63           2019 VALUE 814467.76

814467.76 X .09 = 73,302.10          2020 VALUE $887,769.86

                                                   Rounded to the nearest dollar: $887,770.00

Answer:

Step-by-step explanation:

We can set up an equation:

4(3x+4)=76

We can distribute the left side and get:

12x+16=76

Subtract 16 from both sides:

12x=60

Divide 12 from both sides:

x=5

Check:

4(3*5+4)

4(15+4)

4(18)

76

So x=5

Answer:

2A /b = h

Step-by-step explanation:

A=1/2 bh

We want to isolate h

First we multiply by 2

2A = 2 * 1/2 bh

2A = bh

Then we divide by b to isolate h

2A /b = bh/b

2A /b = h

Answer:

5 years.

Step-by-step explanation:

She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.

Lina invested for 5 years.

According to the problem,

So, we can say $ 1,696.50 is the interest

∴ Prt = 1696.50

⇒ (7800)(4.35/100)t = 1696.50

⇒ t = 5

∴ Line invested for 5 years.

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Answer:

Scatter plots resembles line graphs in that they are plotted on the x and y axis. The are used because they show how much one variable is affected by another.

Scatter diagrams are important since in statistics they can show the extent of correlation, if any, between the values of observed quantities or a behavior.

Answer:

A scatter plot is defined as a diagram which uses Cartesian coordinates to display values about two variables, one indepedent, the other one dependent.

This diagrams are used in statistics to display information about surveys to a certain sample in a population. The purpose of a scatter plot is to shows if the variables are related, that is, if they have any type of linear correlation between them. If they have linear correlation, then the data is represented by a line.

Now, in this case, the independent variable is time in minutes and the dependent variable is texting. Basically, with this data, the company will be able to stablish the relation between words written in a certain time, that is, the speed of texting actually.

With a scatter plot, they would find the relation that forms the speed of texting. It could be "the more time, more text is written", or "the less time, more text is written".

If we need to establish a possible relation, the most logical would be "the more time, more word are texted".

Answer: 7/16 or .4375

Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!

Answer:

The area is 1/2×3×3= 4.5

Step-by-step explanation:

Answer:

16(3x - 1)

Step-by-step explanation:

the greatest common factor of 48 and 16 is 16, hence

48x - 16 = 16(3x - 1)

Final answer:

After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.

Explanation:

To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:

16(3x - 1)

This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.

Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.

Answer:

C

Step-by-step explanation:

$4.50 x 4 = $18.00          $6.00 x 2 = $12.00          $18 + $12  = $30

$4.50 + $6.00 = $10.50

Answer:

[tex]y-6=5(x-1)[/tex]

Step-by-step explanation:

To make the line parallel, it has to have the same slope as the other. Because it is in slope-intercept form, we can see that the slope of the line is 5.

Now we have all of the numbers we need for point-slope form. The point-slope form looks like this:

[tex]y-y_{1}=m(x-x_{1})[/tex]

So when we input our values for the variables, the equation is:

[tex]y-6=5(x-1)[/tex]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (relevant later)

Point-slope form:

y - y₁ = m(x - x₁)        "m" is the slope

For lines to be parallel, their slopes have to be the SAME

The given line's slope is 5, so the parallel line's slope is also 5.

So you know:

m = 5

(x₁ , y₁) = (1 , 6)

Now you can plug this in:

y - y₁ = m(x - x₁)  

y - 6 = 5(x - 1)

Answer:

0.65

Step-by-step explanation:

0.6 is short for 0.60

0.7 is short for o.7

0.61,0.62,063,0.64,0.65,0.66,0.67,0.68,0.69,0.70

0.65 is in the middle

Answer: The answer is 0.65

Step-by-step explanation:

Answer:

tn = a*2^(n - 1)

Step-by-step explanation:

a = 4

r = 2

tn= a*2^(n-1)

Try it

t3 = 4*2^(3 -1)        Combine the power

t3 = 4 * 2^2            Find 2^2

t3 = 4 * 4                Multiply

t3 = 16                     Answer for t3

Answer:

2^(n+1)

Step-by-step explanation:

You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.

4 is the term 1

8 is term 2

2=term # (1) + 1 for 4

3 = term # (2) + 1 for 8

And so on

So it is 2 to the power of (term # + 1)

Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:

... s = 2t

... g = t/2

... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total

_____

Solution

Substituting for s and g, we have ...

... 2t +t +t/2 +9 = 65

... (3 1/2)t = 56 . . . . . collect terms

... t = 56/3.5 = 16 . . . . divide by the coefficient of t

The shoes are 2t, so $32.

The t-shirt is t, so $16.

The sunglasses are t/2, so $8.

The hat is $9.

Answer:

the probability of getting the exact coins that make $0.15 is 33.3% (1/3)

Step-by-step explanation:

Answer:

a/b =6

Step-by-step explanation:

We want to evaluate a/b

a=24, b=4

Substitute these values into the expression

a/b =24/4

    = 6

Final answer:

When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.

Explanation:

The expression to evaluate is a/b, where a=24 and b=4.

To calculate this, simply divide the value of a by the value of b:

Step-by-step calculation:

Insert the known values into the expression: a/b = 24/4.

Divide 24 by 4 to get the result.

24 divided by 4 equals 6.

Therefore, if a=24 and b=4, the value of a/b is 6.

The domain is the set of all numbers. The range is also the set of all real numbers.

Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.

-----------------------

To write "the set of all real numbers" in interval notation, you would write [tex](-\infty, \infty)[/tex]

This is the interval from negative infinity to positive infinity, spanning the entire real number line.

The number of solutions exist for the given equation (x + 12) = 4x – 1

is one.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We are given that;

The equation=(x + 12) = 4x – 1

Now,

We can simplify the given equation as follows:

x + 12 = 4x - 1

Adding 1 to both sides:

x + 13 = 4x

Subtracting x from both sides:

13 = 3x

Dividing both sides by 3:

x = 13/3

Therefore, by solving equation answer will be one.

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The x-intercept is for y = 0.

substitute y = 0 to the equation of the function:

[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]

Answer:

(-45,0)

Step-by-step explanation:

I took the test

Answer:

(21,5)

Step-by-step explanation:

To find the slope that passes through the points (7,5) and (21,15) , we use the formula

m = (y2-y1)/ (x2-x1)

   = (15-5)/(21-7)

   = 10/14

  =5/7

We want a slope that is 1/3 this slope so we will multiply by 1/3

5/7 * 1/3= 5/21

We know the slope and one point (0,0)  we can use the same formula to figure out x and y

m = (y2-y1)/ (x2-x1)

5/21 = (y2-0)/ (x2-0)

Let the tops be equal and the bottoms be equal

5 = y2-0

5 =y2

and the bottoms

21 = x2-0

21= x2

We have the point

(21,5)

Answer:

here you go

View the picture for your answer!

have a wonderful day :))

Answer:

300 dollars of interest

Step-by-step explanation:

5000 (0.06)

300

Answer:

$30

Step-by-step explanation:

You are being asked to figure out simple interest, I think.

Givens

Formula

i = P*r*t

Solution

Edit

You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).

So it comes to the same thing.

Answer:

changing by one

Step-by-step explanation:

[tex]n,\ n+1-\text{ two consecutive whole numbers}\\57-\text{the sum}\\\\n+n+1=57\qquad\text{subtract 1 from both sides}\\2n=56\qquad\text{divide both sides by 2}\\n=28\\\\n+1=28+1=29\\\\Answer:\ \boxed{\text{The greater of the two numbers is 29}}[/tex]

The two consecutive whole numbers that sum to 57 are 28 and 29. The solution was achieved by setting up an equation and solving for x which represents the smaller number. The greater number is 29.

The sum of two consecutive whole numbers is 57 pertains to a simple arithmetic problem. If two consecutive numbers sum to 57, we can set up an equation to solve for the numbers. Let's call the smaller number 'x'. This means the next number would be 'x + 1' since it's consecutive, or next in line. The equation for your problem would then be x + (x + 1) = 57. Simplifying the equation gives us 2x + 1 = 57, and then subtracts 1 from both sides to get 2x = 56.

The last step is to divide both sides by 2, which gives us: x = 28. So, the smaller number is 28 and the greater number is 29.

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let's find its first derivative for "y"

[tex]\bf y=x^3-3x^2+5x-1\implies \cfrac{dy}{dx}=3x^2-6x+5[/tex]

now, we can run the quadratic formula on that derivative, and it turns out we end up with a negative radicand and therefore an imaginary/complex solution, which is a way to say there are no solutions for it, so the quadratic never touches the x-axis.

so hmmm what is the smallest value it goes down to, for the derivative, before it goes right back up?

well, for that we can simply check her vertex location.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \cfrac{dy}{dx}=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{(-6)}{2(3)}~~,~~5-\cfrac{(-6)^2}{4(3)} \right)\implies \left( 1~~,5-\cfrac{36}{12} \right) \\\\\\ (1~,~5-3)\implies (\stackrel{x}{1}~,~\stackrel{y}{2})[/tex]

so, "y" or dy/dx goes as low as 2 before going back up, and that happens when x = 1.

Check the picture below.

Step-by-step explanation:

We need to find minimum slope for y = x³ -3x² +5x -1

Slope is derivative of y

                [tex]\texttt{Slope,}\frac{dy}{dx}=3x^2-6x+5[/tex]

Now we need to find minimum of 3x² -6x +5

At minimum derivative of  3x² -6x +5 is zero

That is

                6x - 6 = 0

                  x = 1

So the slope is minimum at x = 1

At x = 1,

           Slope = 3 x 1² -6 x 1 +5 = 2

Minimum slope possible for x³ -3x² +5x -1 is 2