Write a quadratic function given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
y=(x+3)(x=2)
y=(x-3)(x+2)
y=3(x-3)(x-2)
y=3(x-3)(x+2)

Based on the given task content; the amount of money the customer needs to pay if given a discount of $5 off the second item bought is $38.50

Item 1:

Headphones = $25

Item 2:

CD = $18.50

Amount paid on the second item = original cost - discount

= $18.50 - $5

= $13.50

Total amount the customer needs to pay = cost of item 1 + Amount paid on the second item

= $25 + $13.50

= $38.50

In conclusion, the total amount the customer needs to pay for headphones and CD is $38.50

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In  linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

What are a definition and an example of a linear equation?

   x² + y² = 4 ..........1

   x²/4 - y²/9 = 1

⇒ 9x² - 4y² = 36 ..........2

multiply equation (1) is multiply by 9

      9 x²  + 9y² = 36  ..............3

equation (3) - (2)

   13y² = 0

 y = 0

put y =0 in equation 1

     x² + 0 = 4

      x = ± 2

The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

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Answer:

Yes

Step-by-step explanation:

Winning numbers: 2, 4, 6

Losing numbers:  1, 3, 5

The even numbers are greater.

The average even (winning) number is 4.

The average odd (losing) number is 3.

You can win half a dollar on average.

Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5

Answer:

A

Step-by-step explanation:

[tex]\sqrt{3x+3}=x+1 \\ \\ 3x+3=x^2+2x+1 \\ \\ x^2-x-2=0 \\ \\ (x-2)(x+1)=0 \\ \\ x=-1, 2[/tex]

Upon substituting both of the values back into the original equation, we see they both work.

(a),

The common ratio between the terms is

(b).

The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be

(c).

The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us

The Solution:

Given that the vertices of a quadrilateral are:

We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.

The new x-coordinate will become:

So, the required coordinate of J' is:

Therefore, the correct answer is J'(-8,5)

Answer:

First option is correct.

Step-by-step explanation:

Normally, Pete's dad deposits $25 into his bank account every week.

Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:

8*(25 + x)

He wants to keep the total deposits above 500. So

8*(25 + x) > 500

Now we solve the inequality similarly to how we would solve an equality.

8*(25 + x) > 500

200 + 8x > 500

8x > 500 - 200

8x > 300

x > 300/8

x > $37.50

So the first option is correct.

Answer: ? = 1/2

Step-by-step explanation:

Your question is a bad example, so let me come up with one.

2/8 = 1/4

This is done by dividing both the numerator and denominator by the same value: 2/8 / 2/2

or

2/2 = 1, 8/2 = 4

We now have 1/4

or 9/36

What can we divide 36 by, 9 by? We need to divide by both for it to work.

9/3 = 3

36/3 = 12

3/12 But we can divide this again

3/3 = 1

12/3 = 4

1/4, we could also have divided 9/36 by 6/6 to get 1/4

For 1/8 to get ?/4, we do

8/? = 4

? = 1/2

, so the answer is 1/2/4 = 1/2*4 = 1/8

Answer:

I think about 3.4/4=.85 or 85% of acreage was bought.

Step-by-step explanation:

The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100

From the information, the test in math class has problems with 2 points (x) and problems worth 4 points (y) and the test has 100 points. The equation to illustrate this will be:

2x + 4y = 100

When one answers 30 2-point questions and 8 4-point questions correctly, the score will be:

= 2x + 4y

= 2(30) + 4(8)

= 60 + 32

= 92

The score is 92 points.

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By using the method of division,  they can buy 11 stamps.

The procedure or act of dividing the condition of division one of the pieces or groupings into which a whole is divided or is divisible. Distribution can be an act, a process, or an instance of distribution among a number. something that separates, divides, or marks off the act of dividing into portions or the process of being divided. one of the chunks or groups into which a whole can be split up or divided. the action, procedure, or occurrence of distributing among a group. Division is the act or process of splitting something that is already divided.

Given that,

18k stamps can be bought with #2.00

2.00 ÷ 0.18= 11.11

Hence, they can buy 11 stamps.

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Using integrals, the 90th percentile of the given probability distribution is of $53.58.

The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:

[tex]\int_0^p f(y) dy = 0.9[/tex]

The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.

The function is given by:

f(y) = 3(1 - y)²

Hence the integral is calculated as follows:

[tex]\int_0^p 3(1 - y)^2 dy[/tex]

Applying the integral of the power of y rule, along with the substitution, it is found that:

[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]

Hence:

[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]

Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:

-(1 - p)³ + 1 = 0.9

-(1 - p)³ = -0.1

(1 - p)³ = 0.1

Applying the cube root to both sides:

1 - p = 0.4642.

p = 1 - 0.4642

p = 0.5358.

This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.

The problem is missing, and is given by the image at the end of the answer.

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Answer:

can i see a ss of the question?

Step-by-step explanation:

Answer:

Crow=

50×2

100 leg.

cat=

49×4

196 leg.

Answer:

15th customer

Step-by-step explanation:

to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer

1. Solution of the rational equation [tex]\frac{x}{3} -6=\frac{9}{3}[/tex]   is x = 27

How is the equation solved?

[tex]\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27[/tex]

2.The two numbers = 2, 6

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x+ y =8 --- (1)

1/x+1/y = 2/3 ---(2)

Considering (2),

[tex]\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6[/tex]

Substituting  x in (1)

We have,

When x = 2 ; y= 6

When x = 6 ; y = 2

So, the two numbers = 2, 6

3. The two numbers = 3, 9

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x- y =6 --- (1)

1/y -1/x = 2/9 ---(2)

Considering (2),

[tex]\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9[/tex]

Since x and y are whole numbers we will have y = 3

When y = 3 ; x=9 (substituting in (1))

So, the two numbers = 9,3

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The multiplication of  [tex](9n- \frac{4}{7} z)^{2}[/tex]   [tex]=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

How is the expression  [tex](9n- \frac{4}{7} z)^{2}[/tex]  solved?

[tex](9n- \frac{4}{7} z)^{2} \\\\=(9n- \frac{4}{7} z) (9n- \frac{4}{7} z)\\\\=81n^{2} -\frac{36}{7} nz -\frac{36}{7} nz +\frac{16}{49} z^{2} \\\\=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

What is the binomial squares pattern?

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The quantity of teaspoons of syrup it would take to make just one strawberry milkshake is 1 29/35 teaspoons

This is the number which gives the comparison between two quantities. The ratio of teaspoons of strawberry to make strawberry milkshake is the comparison between the two quantities.

Equate the ratio of teaspoons of strawberry syrup to strawberry milkshakes

Teaspoons of strawberry : make strawberry milkshake

3 1/5 : 1 3/4 = x : 1

16/5 ÷ 7/4 = x/1

cross product

16/5 × 1 = 7/4 × x

16/5 = 7/4x

x = 16/5 ÷ 7/4

x = 16/5 × 4/7

= (16 × 4) / (5 × 7)

= 64 / 35

= 1 29/35 teaspoons

The teaspoons of syrup would it take to make just one strawberry milkshake is 1 29/35 teaspoons

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Answer:

14.2 feet

Step-by-step explanation:

Use the Pythagorean Theorem to solve both parts.

Part 1.

35 is the hypotenuse and 21 is a leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]

28 feet represents how far the base of the ladder is from the house.

Part 2.

Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.

Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]

Round to the nearest tenth and you have 14.2 feet

Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:

In the problem, here are the given information:

Principal (Money borrowed) = $1,200

Rate = 18% or 0.18 in decimal form

Time = 9 months or 0.75 year.

(Take note that the time in the formula is measured in years.)

Let's plug in the given information to the interest formula above.

Then, solve.

Therefore, Ms. Paul paid interest of $162.

From the given histogram, it is found that Class 4 contains the largest number of exam scores.

An histogram of a data-set is a graph that shows the number of times each element of x was observed, or elements in each range of x were observed.

From the histogram in the problem, we have that:

All these number of scores are given at the center of the bars on the graph.

The largest number among these number of scores is of 19 in Class 4, hence Class 4 contains the largest number of exam scores.

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Answer:

168

Step-by-step explanation:

Hello I need to find the answer on how to find (-8)(-7)(3):

This is asking to find: -8 × -7 × 3 = ?

Because a negative times a negative = positive we have:

56 × 3 = 168

First, let's see the points on the coordinate plane:

Now, let's remember that a function has every element of it's domain related with only one element from it's image.

Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:

As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.

We know that:

Above, we use the transitive property

The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula  is P(n) = 6 + 3(n -1)

The given parameters are

Po = 6

P1 = 9

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = P1 - Po

So, we have

d = 9 - 6

Evaluate

d = 3

The recursive formula  is

P(n + 1) = d + Pn

So, we have

P(n + 1) = 3 + Pn

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = 9 - 6

Evaluate

d = 3

The explicit formula  is

P(n) = Po + (n -1) * d

So, we have

P(n) = 6 + (n -1) * 3

Evaluate

P(n) = 6 + 3(n -1)

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Answer:

simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.

Step-by-step explanation:

The cost of each bracelet will be $2.5.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of 5 bracelets = $12.50

Now,

Since, The cost of 5 bracelets = $12.50

So, The cost of 1 bracelets = $12.50 ÷ 5

                                         = $2.5

Thus, The cost of each bracelet will be $2.5.

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Answer:

1. 12 days

2. more than 200 miles

3. 11 lawns

4. at least 9 hours (about 9.92 hours)

Step-by-step explanation:

1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.

2.

[tex]70 + .15x < 50 + .25x[/tex]

[tex]20 < .10x[/tex]

[tex]200 < x[/tex]

[tex]x > 200[/tex]

3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.

4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.

From the given quadratic equation, we have that:

A quadratic equation is modeled by the following rule:

y = ax^2 + bx + c

The vertex has these following coordinates.

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point, as follows::

For this problem, the function is:

h(t) = -16t² + 160t + 200.

Then the coefficients are:

a = -16, b = 160, c = 200.

And the maximum height, in feet, will be of:

[tex]y_v = -\frac{160^2 - 4(-16)(200)}{4(-16)} = 600[/tex]

The ball hits the ground for the positive root when h(t) = 0, hence after 8.9 seconds.

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x = Number of posts

y = samuel's savings

If he order 2 posts with words and pictures:

y = 2(10) + 35 = 55

If he order 2 posts with words only and 2 posts with pictures only.

y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60

Therefore, he could have save 5 dollars

Therefore the equation is:

y = 5x - 5