Quadratic function is 3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
What is quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:
f(x) = ax² + bx + c in standard form, where a 0.
Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.
The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.
Given Data
Roots (-3,0) and (2,0)
Point (1,-12)
y = a(x-(-3) (x-2)
y = a(x+3)(x-2)
Equating points
-12 = a(1+3)(1-2)
-12 = a(4)(-1)
-12 = -4a
a = 3
f(x) = 3(x+3)(x-2)
Function is 3(x+3)(x-2).
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12. A company has bought 3.4 acres of land out of the 4
acres of land that it plans to buy. What percent of the land
has the company already bought? Solve the problem with a
math drawing or a percent table, or both, explaining your
reasoning.
Answer:
I think about 3.4/4=.85 or 85% of acreage was bought.
Step-by-step explanation:
Your test in math class has problems with 2 points (x) and problems worth 4 points (y). Altogether, the test has 100 points. Write an equation that represents the total points on the test, including the 2-point and 4-point problems.
____________x + _____________y = ___________(total points)
If you answer 30 2-point questions and 8 4-point questions correctly, what will your score be?
The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100
How to illustrate the equation?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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Answer the following questions:
pahelp pls
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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Hallie collects beanbag animals. She
started her collection eight weeks ago
with six animals. Each week since then,
she has been given two more animals.
How many beanbag animals does she
have now? Please help meeee
Answer:
can i see a ss of the question?
Step-by-step explanation:
Quadrilateral IJKL with vertices I( 5,2 ), J( 9,5), K( 5,-2 ), and L( 2,-3 ) : Reflect in the line x=1. What are the coordinates of J’?
The Solution:
Given that the vertices of a quadrilateral are:
[tex]I(5,2),J(9,5),K(5,-2)\text{ and L(2,-3)}[/tex]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:
[tex]x=1-9=-8[/tex]So, the required coordinate of J' is:
[tex](-8,5)[/tex]Therefore, the correct answer is J'(-8,5)
Consider a game in which a player rolls one die. If an even number comes up, the player wins the number of dollars showing on the die. If an odd number comes up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game fair? (Assume that there is no cost to play the game.)
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
(9n-4/7z)².
Use the binomial squares pattern to multiply
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?
The square of a binomial is made up of the first term's square, twice the product of the two terms and the last term's square.This approach is crucial for factoring since it makes factoring polynomials more simpler than with other approaches like the FOIL method, for example.For example : [tex](x+ y)^{2} =x^{2} +2xy+y^{2}[/tex]To learn more about binomial squares pattern , refer:
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In a promotion for a local
Subway, every 5th customer will
get a free sandwich and every
3rd customer will get a free
drink. Which customer will be
the first person to get a free
sandwich and drink?
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
When Ms. Paul bought a new office phone, she borrowed $1,200 at a rate of 18% for 9 months. How much interest did she pay?
Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:
[tex]Interest=Principal\times Rate\times Time[/tex]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.
[tex]Interest=1,200\times0.18\times0.75[/tex]Then, solve.
[tex]Interest=162[/tex]Therefore, Ms. Paul paid interest of $162.
HELP!! This is due soon!
From the given quadratic equation, we have that:
The maximum height is of 600 feet.The ball hits the ground after 8.9 seconds.What is the vertex of a quadratic equation?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:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point, as follows::
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.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]
When does the ball hits the ground?The ball hits the ground for the positive root when h(t) = 0, hence after 8.9 seconds.
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1/8=?/4 how does this get solved?
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
help me please!!!!!!!!
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.
Use the sequence below to complete each task. 972, 324, 108, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 6th term (ac)
(a),
The common ratio between the terms is
[tex]\frac{972}{324}=\frac{324}{108}=3[/tex](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
[tex]a_n=\frac{972}{3^n}[/tex](c).
The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us
[tex]a_6=\frac{972}{3^6}=\frac{4}{3}[/tex]The weekly repair cost Y for a machine has a probability density function given by f(y)=3(1−y)^2, 0
Using integrals, the 90th percentile of the given probability distribution is of $53.58.
What is the 90th percentile of the distribution?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.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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Please
50 POINTS! BRAINLIEST!
The graphs of the conics intersect at two points.
x² + y² = 4
x^2/4 - y^2/9 =1
What are the coordinates of these points of intersection?
Enter your answer by filling in the boxes.
and
( , ) and ( , )
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?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.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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Hello I need to find the answer on how to find (-8)(-7)(3)
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
A music store is having its "Black Friday" sale. The store will give
$5 off for the second item a customer purchases. Emma wants
buy a pair of headphones for $25 and a CD for $18.50. How
much does she need to pay in total?
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
The amount paid by the customer after deducting discountItem 1:
Headphones = $25
Item 2:
CD = $18.50
Discount on the second item = $5Amount 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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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the
nearest tenth
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
HELP ASP ILL GIVE BRAINLIEST AND 50 points
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.
Select the correct answer. What is the solution to the equation? √3x+3-1=x A. -1 and 2 B. -2 and 1 C. 2 D. 1
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.
What value(s) of x in the relation below would create a set of ordered pairs that is not a function? Justify your answer. {(0,5) (1,5) (2, 6) (x, 7)}
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.
6. How many 18k stamps can be bought with #2.00?
By using the method of division, they can buy 11 stamps.
What is division?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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Gwen spent $12.50 to purchase 5 bracelets. Each 4.
bracelet costs the same amount. What is the unit rate
for each bracelet?
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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I need help with statements 2,4,5, and 7
We know that:
[tex]\begin{gathered} YW\cong YZ,XY\cong VY \\ XZ=XY+YZ \\ XZ\cong VY+YW=VW \\ XZ\cong VW \end{gathered}[/tex]Above, we use the transitive property
I am having trouble can u help me please
From the given histogram, it is found that Class 4 contains the largest number of exam scores.
What is an histogram?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:
Class 1 contains 5 scores.Class 2 contains 3 scores.Class 3 contains 7 scores.Class 4 contains 19 scores.Class 5 contains 15 scores.Class 6 contains 18 scores.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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Types of Posts Cost of Each Post Base Price Posts with Words Only S5 $5 Posts with Pictures Only $10 $25 Posts with Words and Pictures $10 $35 Samuel ordered 2 posts with words only and 2 posts with pictures only. After placing his order, Samuel realized he could have saved money if he, instead, ordered 2 posts with words and pictures. Let y represent Samuel's savings, in dollars, and let x represent the number of posts. Which equation could be used to determine the amount of money Samuel could have saved if he ordered 2 posts with words and pictures, instead of his original order? A y = 5x – 5B. y = 5.r + 65C y = -5r + 25D y = 2
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
A pyramid is shown.
The pyramid has a base length of 5 centimeters, an altitude of 8 centimeters, and a lateral edge length of 9 centimeters.
What is the volume of the pyramid?
A collection of black cats and crows has a total of 99 heads and legs between them. There
are twice as many crows as there are cats. How many of each is there?
Answer:
Crow=
50×2
100 leg.
cat=
49×4
196 leg.
It takes 3 1/5 teaspoons
of strawberry syrup
to make 1 3/4
strawberry
milkshakes. How
many teaspoons of
syrup would it take to
make just one
strawberry
milkshake?
The quantity of teaspoons of syrup it would take to make just one strawberry milkshake is 1 29/35 teaspoons
RatioThis 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.
It takes 3 1/5 teaspoons of strawberry syrup to make 1 3/4 strawberry milkshakes Number of teaspoons of syrup would it take to make just one strawberry milkshake = xEquate 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
divide both sides by 7/4x = 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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The number of cars sold weekly by a new automobile dealership grows according to a linear growth
model. The first week the dealership sold six-cars (Po= 6). The second week the dealership sold
nine cars (P₁ = 9).
Write the recursive formula for the number of cars sold, Pn, in the (n + 1)th week.
P₁ = Pn-1 +
Write the explicit formula for the number of cars sold, Pn, in the (n + 1)th week.
Pn=
If this trend continues, how many cars will be sold in the fourth week?
_____cars
The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula is P(n) = 6 + 3(n -1)
The recursive formula of the functionThe 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
The explicit formula of the functionFrom 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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