Find a quadratic function that includes the set of values below.
(0,9). (2,15) (3,12)

Answers

Answer 1

Answer:

[tex]f(x) = -2x^2 + 7x + 9[/tex]

Step-by-step explanation:

[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]

Answer 2

Final answer:

To find a quadratic function, substitute each given coordinate into the equation and solve the resulting system of equations.

Explanation:

To find a quadratic function, we need to use the form y = ax^2 + bx + c. From the given set of values, we can substitute each coordinate (x, y) into the equation to get three different equations. So:

When x = 0, y = 9, we get: 9 = a(0)^2 + b(0) + c, which simplifies to c = 9.When x = 2, y = 15, we get: 15 = a(2)^2 + b(2) + 9, which simplifies to 4a + 2b = 6.When x = 3, y = 12, we get: 12 = a(3)^2 + b(3) + 9, which simplifies to 9a + 3b = 3.

Now we have a system of equations that we can solve simultaneously. Solving the second and third equations using any appropriate method, we find that a = -1 and b = 5.

Therefore, the quadratic function that includes the given set of values is y = -x^2 + 5x + 9.

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Related Questions

One number has a prime factorization of 23.32, and another number has a prime factorization of 22.3°. Which of the
following expressions would equal the greatest common factor of these two numbers?
25.35
23.33
22.32
2.3

Answers

Assuming first number is (2^3)(3^2), second number is (2^2)(3^1).

First number: 2 * 2 * 2 * 3 * 3

Second number: 2 * 2 * 3

Both numbers have at least two factors for 2 and one factor for 3.

Their greatest common factor is (2^2)(3).

The measure of the vertex angle of an isosceles triangle is one-fourth
that of a base angle.
(I also need the equation)

measure of each base angle =

measure of vertex angle =

Answers

Answer:

measure of each base angle = 80 each angle

measure of vertex angle = 20

Step-by-step explanation:

x=base angle

2x+ x/4= 180

Multiply everything by 4 to eliminate the fraction

8x+x = 720

9x=720

x=80

80/4=12

Final answer:

In an isosceles triangle where the vertex angle is one-fourth the measure of a base angle, using the properties of a triangle and the Triangle Angle Sum Theorem, we find each base angle measures 80 degrees and the vertex angle measures 20 degrees.

Explanation:

Given an isosceles triangle, where the vertex angle is one-fourth the measure of a base angle, we can find the measures of the angles using the properties of a triangle. From the Triangle Angle Sum Theorem, we know that the sum of the angles in any triangle is 180 degrees.

Let's denote the measure of the base angle as 'b'. Since the triangle is isosceles, both base angles are equal, so we have 2b for the sum of the base angles. The vertex angle, being one-fourth of a single base angle, is ¼×b = b/4. According to the Triangle Angle Sum Theorem, we can write:

2b + (b/4) = 180

Multiplying through by 4 to clear the fraction gives us:

8b + b = 720

Combining like terms:

9b = 720

Dividing both sides by 9 gives us:

b = 80

Now that we have the measure of the base angle, we can find the measure of the vertex angle:

measure of vertex angle = b/4

Substitute b = 80 into the equation:

measure of vertex angle = 80/4

measure of vertex angle = 20

So, the measure of each base angle is 80 degrees, and the measure of the vertex angle is 20 degrees.

help me out pleaseee

Answers

Answer:

Option B is the correct choice.

Step-by-step explanation:

The graph is attached below.

We have to find the [tex]x[/tex] intercept meaning the value of the point on[tex]x-axis[/tex] when [tex]y=0[/tex]

So we will put the value of zero [tex](0)[/tex] instead of [tex]y[/tex] in our given equation.

So here we have solved it algebraically.

[tex]y=\frac{3}{4}x-3[/tex]

Putting [tex]y=0[/tex]

[tex]0=\frac{3}{4}x-3[/tex]

[tex]0=\frac{3x-12}{4}[/tex]

Multiplying [tex]4[/tex] both sides.

[tex]0=3x-12[/tex]

Adding [tex]12[/tex]both sides.

[tex]12=3x[/tex]

Dividing with [tex]3[/tex] both sides.

[tex]x=\frac{12}{3}=4[/tex]

So the x-intercept of the given equation is [tex]4[/tex] which can be written as [tex](4,0)[/tex] in terms of coordinates.

Option B [tex](4,0)[/tex] is the correct choice.

ASAP PLEASE PLEASE HELP The measured dimensions of a rectangle are 6 m by 4 m to the nearest whole unit. Find the minimum and maximum possible areas of the rectangle.

Answers

Final answer:

The minimum possible area of the rectangle is 19.25 m² and the maximum possible area is 29.25 m².

Explanation:

To find the minimum and maximum possible areas of the rectangle, we need to consider the possible values that the length and width can take.

Given that the measured dimensions are 6 m by 4 m to the nearest whole unit, the minimum possible length would be 5.5 m (6 m - 0.5 m) and the minimum possible width would be 3.5 m (4 m - 0.5 m).

Similarly, the maximum possible length would be 6.5 m (6 m + 0.5 m) and the maximum possible width would be 4.5 m (4 m + 0.5 m).

To calculate the minimum and maximum possible areas, we multiply the minimum and maximum possible lengths by the minimum and maximum possible widths respectively. The minimum possible area would be 5.5 m x 3.5 m = 19.25 m² and the maximum possible area would be 6.5 m x 4.5 m = 29.25 m².

Evaluate 6 + 2 • 3 – 1

Answers

Answer:

Step-by-step explanation:

Using the order of operations, that is multiplication before addition/ subtraction.

Given

6 + 2 × 3 - 1 ← evaluate multiplication

= 6 + 6 - 1 ← evaluate from left to right

= 12 - 1

= 11

The answer is 11 PEMDAS

(+4) + (-13) = solve.

Answers

Answer: -9

Step-by-step explanation: When your adding and subtracting positives and negatives, it's a good idea to use a number line to visualize what's going on.

When you're simplifying a problem like (+4) + (-13) we start at zero and +4 moves us 4 units to the right along our number line.

From there, -13 then moves us 13 units back to the left so we end up at -9.

Image provided.

Therefore, (+1) + (-13) = -9

An equivalent fraction for 2/3 is ____

Answers

Answer:

8/12

Step-by-step explanation:

2/3 x 4= 8/12

Answer:

4/6

The drawing will help

Melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of swordfish. She pays a total of $31.25, and the swordfish cost $.20 per pound less than the salmon. What would be the combined cost of 1 pound of salmon and 1 pound of swordfish

Answers

Answer:

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.66

Step-by-step explanation:

Let us assume the cost of 1 pound salmon = $ m

So the cost of 1 pound of 1 pound swordfish cat = $ ( m - 0.20)

Now, the Amount of salmon purchased = 2 1/2 pounds

[tex]2\frac{1}{2} = 2 + \frac{1}{2} = 2 + 0.5 = 2.5[/tex]

So, the amount of salmon purchased = 2.5 pounds

Cost of buying 2.5 pounds = 2.5 x ( 1 pound cost)

= 2.5 ( m) = $ 2.5 m ...... (1)

Also, the Amount of swordfish purchased = 1 1/4 pounds

[tex]1\frac{1}{4} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25[/tex]

So, the amount of swordfish purchased = 1.25 pounds

Cost of buying 1.25 pounds = 1.25 x ( 1 pound cost of swordfish)

= 1.25 ( m - 0.20) = $ 1.25 m - 0.25 .... (2)

Now, the combined cost paid = $ 31.25

⇒Cost of buying (2.5 pounds salmon + 1.25 pounds swordfish) = $ 31.25

or, 2.5 m + 1.25 m - 0.25 = 31.35 (from (1) and (2))

or, 3.75 m = 31.60

or, m = 31.60/3.75 = 8.43

⇒ m = $8.43

So, the cost of 1 pound salmon = m = $8.43

and the cost of 1 pound swordfish = m - 0.20 = $8.43 - 0.20 = $ 8.23

Hence, the combined cost 1 pound of salmon and 1 pound of swordfish = $8.43 + $ 8.23 = $ 16.66

The measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle. Find the measure of the angle

Answers

If the measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle, the required angle will be 40degrees.

Let the measure of the required angle be x

Supplement of the angle = 180 - x ....................1

Complement of the angle = 90 - x

four times the measure of the complement of the angle = 4(90-x)

60 degrees less than four times the measure of the complement of the angle = 4(90-x) - 60 ................................ 2

Equate 1 and 2 to get the unknown value 'x'

180 - x = 4(90-x) - 60

180 - x = 360-4x-60

180 - x = 300 - 4x

Collect the like terms

-x + 4x = 300 - 180

3x = 120

Divide both sides by 3

3x/3 = 120/3

x = 40

Hence the measure of the required angle is 40 degrees

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The measure of the angle is found to be 40 degrees. This was determined by setting up and solving the equation based on the given relationships between the angle's supplement and complement. Therefore, the angle measures 40 degrees.

To find the measure of the angle, let's denote the angle as x. We know the following:

The supplement of the angle is 180 degrees minus the angle: (180 - x).The complement of the angle is 90 degrees minus the angle: (90 - x).

According to the problem, the supplement of the angle is 60 degrees less than four times the complement of the angle. Therefore, we have the equation:

(180 - x) = 4(90 - x) - 60

First, expand and simplify the right-hand side:

180 - x = 360 - 4x - 60

Combining like terms, we get:

180 - x = 300 - 4x

Next, add 4x to both sides to start isolating x:

180 + 3x = 300

Then, subtract 180 from both sides:

3x = 120

Finally, divide both sides by 3:

x = 40

Thus, the measure of the angle is 40 degrees.

The circle with center F is divided into sectors. In circle F , EB is a diameter. The radius of circle F is 3 units

Answers

Answer:

This is only if you are looking to find the Arch AED 11pi/4

Step-by-step explanation:

See photo

Arc length AED of a given circle with a radius of 3 units is 11π/4.

According to the given diagram,

The angle subtended by arc AED or central angle = 360°-120°-45°-30° = 165°

The radius of the circle = 3 units

What is the relationship between arc length, central angle and radius?

Arc length = Central angle(in radians) * Radius

So, arc length AED = 165 *π/180 * 3

Arc length AED = 11π/12 * 3 = 11π/4

Therefore, the Arc length AED of a given circle with a radius of 3 units is 11π/4.

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What is a equation of the line that is parallel to y=-5×+6 and passes through the point (-4,-1)

Answers

The equation of line parallel to y = -5x + 6 and passes through the point (-4, -1) is y = -5x -21

Solution:

Given that, a line passes through (-4, -1) and it is parallel to y = -5x + 6

We have to find the line equation of that line.

Now, as we can see given line equation is in slope intercept form y = mx + c

where "m" is the slope of line and "c" is the y-intercept

So, by comparison, slope of that line is m = -5

We know that slopes of two parallel lines are equal

And as the required line is parallel to given line, it will also have the same slope.

Then, slope of our line = -5

And let us find the line equation point slope form

y – a = m(x - b) where (b, a) is a point on the line

So, line equation is y – (-1) = -5(x – (-4))

y + 1 = -5(x + 4)

y + 1 = -5x – 20

y = -5x -20 – 1

y = -5x -21

Thus the equation of required line is y = -5x -21

The equation of the line parallel to y = -5x + 6 and passing through (-4, -1) is y = -5x - 21, which is determined using the point-slope form of a line with the given point and the parallel line's slope.

To find an equation of a line that is parallel to the given line y = -5x + 6 and passes through a specific point (-4, -1), we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Since parallel lines have the same slope, the line we are looking for will also have a slope of -5. Using the point (-4, -1) and the slope -5, we can substitute these values into the point-slope form:

y - (-1) = -5(x - (-4))
y + 1 = -5(x + 4)
y = -5x - 20 - 1
y = -5x - 21

Thus, the equation of the line is y = -5x - 21.

Dan mows 1/4 of his grandmother's lawn and uses 1/2 gallon of gas. What fraction of the lawn can Dan mow per gallon?
(A) 1/8
(B) 1/6
(C) 1/2
(D) 3/4

Answers

[tex]\frac{1}{2}[/tex] of the grandmother's lawn Dan can mow per gallon.

Option C

Solution:

Given that, mowing [tex]\frac{1}{4}[/tex] uses [tex]\frac{1}{2}[/tex] gallon of gas.

To find: The fraction of the lawn can Dan mow per gallon

According to unitary method,

[tex]\frac{1}{2}[/tex] gallon of gas is required to mow [tex]\frac{1}{4}[/tex] of lawn that is [tex]\frac{1}{2}\rightarrow \frac{1}{4}[/tex]

Therefore, 1 gallon of gas will be required to mow [tex]\frac{1}{2}\times2\rightarrow \frac{1}{4}\frac2[/tex]

[tex]\Rightarrow1 \text{ gallon }\rightarrow \frac{1}{2} \text{ of lawn}[/tex]

Therefore, one gallon will be enough to mow [tex]\frac{1}{2}[/tex] of lawn.

Unitary method:

The unitary method is a technique to solve a problem by finding the value of a single unit first, and then finding the required value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

The equation of line AG is y=_b_x. The midpoint of
B(2a, 2b)
BC is (a + c, b). Does the midpoint of BC lie on Ac?
Why or why not?
no, because bb does not equal a + c
E(a, b)
Fla + c, b)
no, because
(a + c) does not equal b
G
yes, because_b_b= a + c
A(0,0)
Dlc,0)
C(20, 0)'
yes, because ( 6 (a + c) = b

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

9+a=23 need to solve this problem

Answers

Answer:

a = 14

Step-by-step explanation:

Given

9 + a = 23 ( subtract 9 from both sides )

a = 14

Answer:

9+14=23

Step-by-step explanation:

you subtract 9 from 23 and you get 14 so there for the answer is 9+14=23

Find the Greatest Common Factor of the following numbers.
9, 15 and 36

Answers

Answer:

Step-by-step explanation:

Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.

3 is divisible by 9, 15, and 36.

Which of the following is equivalent to -17/9

Answers

If you’re turning this into a decimal it would be: -1.88888888889 (can be rounded up) (-1.9)

If you’re turning it into a percentage it would be: -190%

Remember when you’re converting to a percentage just multiply 100 to the decimal.

alright so ya girl is in 7th grade. i got math hw and i need some help urgent! here's the question: The suspect has been withdrawing money from the ATM machine with a stolen debit card. The account he was stealing from initially contained 5,000 dollars. He's been withdrawing 45 dollars every day, and the account now has 1895 dollars. How long has he been withdrawing money? PS, if you can include an equation that shows what's happening in the problem. xoxo

Answers

He has been withdrawing money for 69 days.

Step-by-step explanation:

Amount of credit card = $5000

Let,

x be the number of days

Amount after withdrawing $45 each day for x days = $1895

Amount left = Total amount - Withdrawal amount per day * number of days

1895 = 5000 - 45*x

[tex]1895=5000-45x[/tex]

Solving for x;

[tex]1895-5000=-45x\\-3105=-45x\\-45x=-3105[/tex]

Dividing both sides by -45

[tex]\frac{-45x}{-45}=\frac{-3105}{-45}\\x=69[/tex]

He has been withdrawing money for 69 days.

Keywords: subtraction, division

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pre- algerba help please

Answers

Answer:

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers.

Answer:

Step-by-step explanation:

my little cousins mock test idk what to do here

Answers

Answer:

the first diagram (circled one in the attached figure)

Step-by-step explanation:

number of pickle slices in each burger = [tex]\frac{78}{26} = 3[/tex] (I hope you know how to find this)

The diagram is nothing but expressing fraction diagrammatically.

The fraction is 78 divided by 26. So assume bar of size 78. Now divide it into 26 equal parts. The same is shown in the diagram.

For example: [tex]\frac{1}{4}[/tex] of a chocolate bar is nothing but one piece when you divide the chocolate bar into four equal parts.

how do you find the equation of a circle if the ends of the diameter are (18,-13) and (4,-3)

Answers

The equation of a circle if the ends of the diameter are (18,-13) and (4,-3) is [tex](x-11)^{2}+(y+8)^{2}=74[/tex]

Solution:

Given that ends of diameter are (18, -13) and (4, -3)

To find the equation of circle, let us first find the center (h, k) of the circle

We know that the center of the circle lies in the center of the diameter also. In order to find the center, get the average of both x and y

[tex]\mathrm{c}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]\begin{array}{l}{c=\frac{18+4}{2}, \frac{-13-3}{2}} \\\\ {c=\frac{22}{2}, \frac{-16}{2}} \\\\ {\mathrm{c}=(11,-8)}\end{array}[/tex]

These are the coordinates of the center of the circle

Now we need to find the radius, we need the center (h, k) and one of the given points (4, -3):

The equation of circle is given as:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

[tex]\begin{array}{l}{(4-11)^{2}+(-3-(-8))^{2}=r^{2}} \\\\ {(-7)^{2}+(-3+8)^{2}=r^{2}} \\\\ {(-7)^{2}+(5)^{2}=r^{2}} \\\\ {49+25=r^{2}} \\\\ {r=\sqrt{74}}\end{array}[/tex]

So the equation of the circle is:

[tex]\begin{array}{l}{(x-11)^{2}+(y-(-8))^{2}=(\sqrt{74})^{2}} \\\\ {(x-11)^{2}+(y+8)^{2}=74}\end{array}[/tex]

9+15 distributive property ?

Answers

Answer:

a(b+c) = axb + axc

3(3+5)= 3x3 + 3x5

of the following is a true statement?
9/12 • 12/9 = 0
3/10 ÷ 7/9 = 3/10 • 9/7
4/5 • 4/5 = 1
1/2 ÷ 1/2 = 1/4

Answers

Answer:

B) (3/10)/(7/9)=(3/10)(9/7)

Step-by-step explanation:

what is the answer too 11 - 18s = - 15?

Answers

Answer: s = 1.44

Step-by-step explanation:

11 - 18*s = -15

-18*s = -15 - 11

-18*s = -26

18*s = 26

s = 26/18

s = 13/9

s = 1.44

The population of a town is represented by the function P(x) = 5000 − 250x, where "x" is the number of years that elapse since 2018. This function model overlooked 200 homeless people and did not include the fact that an average of 50 people per month moved in as people left. Create a new function H(x) that includes this extra information. Graph this new function. Which statement is correct? A) The new function is H(x) = 5200 − 200x. B) The domain of H(x) is [0, 20] and the range is [0, 5200]. C) The x-intercept indicates the population will be zero in 2038. D) The slope of H(x) indicates the population is decreasing at an average rate of 300 people per year.

Answers

Answer:

The answer is A

Step-by-step explanation:

what is the slope of this line ?

Answers

Answer:

slope = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ )= (3, 4) ← 2 points on the line

m = [tex]\frac{4-0}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]

Find the probability P(E or F) if E and F are mutually exclusive, P(E)=0.30, and P(F)=0.45.
The probability of P(E or F) is ___?

Answers

Answer:

P(E or F) = 0.75

Step-by-step explanation:

Given;

P(E)=0.30

P(F)=0.45

We need to find probability of P(E or F).

Now by General theorem of probability addition theorem:

P(E or F) = P(E) + P(F) - P(E and F)

For mutually exclusive events, P(E and F) = 0

So, P(E or F) = P(E) + P(F) = [tex]0.3 +0.45 = 0.75[/tex]

Hence P(E or F) = 0.75

Probabilities are used to determine the chances of an event.

The probability of P(E or F) is 0.75

The parameters are given as:

[tex]\mathbf{P(E) = 0.30}[/tex]

[tex]\mathbf{P(F) = 0.45}[/tex]

[tex]\mathbf{P(E\ or\ F) = P(E) + P(F)}[/tex]

So, the equation becomes

[tex]\mathbf{P(E\ or\ F) = 0.30 + 0.45}[/tex]

[tex]\mathbf{P(E\ or\ F) = 0.75}[/tex]

Hence, the probability of P(E or F) is 0.75

Answers

Answer:

[tex]m\angle B=54^{\circ}[/tex]

[tex]m\angle BAD=36^{\circ}[/tex]

[tex]m\angle CDA=90^{\circ}[/tex]

[tex]BAC=72^{\circ}[/tex]

Step-by-step explanation:

Given:

[tex]\overline{AB}\cong \overline{AC},[/tex]

[tex]\overline{AD}[/tex] bisects angle BAC

[tex]m\angle C=54^{\circ}[/tex]

Triangle ABC is isosceles triangle, because [tex]\overline{AB}\cong \overline{AC}.[/tex] Angles adjacent to the base of isosceles triangle ABC are congruent.

Hence,

[tex]m\angle C=m\angle B=54^{\circ}[/tex]

The sum of the measures of all interior angles is 180°, so,

[tex]m\angle B+m\angle C+m\angle BAC=180^{\circ}\\ \\m\angle BAC=180^{\circ}-2\cdot 54^{\circ}=72^{\circ}[/tex]

Since [tex]\overline{AD}[/tex] bisects angle BAC, angles BAD and CAD are congruent by definition of angle bisector. So,

[tex]m\angle BAD=m\angle CAD=\dfrac{1}{2}m\angle BAC=\dfrac{1}{2}\cdot 72^{\circ}=36^{\circ}[/tex]

AD ia angle bisector in isosceles triangle drawn to the base, so it is the height. Thus, AD and BC are perpendicular. So,

[tex]m\angle CDA=90^{\circ}[/tex]

Select all of the following that are ordered pairs of the given function.
f(x) = 3- 2х
(-2, -1)
(-1, 5)
(0,3)
(1, 0)
(2, -1)

Answers

Answer:

(-1, 5)

(0, 3)

(2, -1)

Step-by-step explanation:

we have

[tex]f(x)=3-2x[/tex]

Remember that

If a ordered pair is a solution of the given function, then the ordered pair must satisfy the given function

Verify each case

case a) (-2, -1)