A student was assigned 40 math problems for homework. The student correctly answered 85% of the problems. How many homework problems did the student correctly answer?​

Equation is \(y = \frac{8}{147} (x + \frac{1}{2} )^2 - \frac{3}{7}\)   and the line of symmetry is \(x=-\frac{1}{2}\)

The parabola is split into two congruent halves by a vertical line, which is the line of symmetry for a quadratic function. It also goes by the name of the axis of symmetry.

For a standard form quadratic function:

\(f(x) = ax^2 + bx + c\)

The equation gives the line of symmetry: x = -b/2a

As a result, the vertex of the parabola serves as the intersection of the line of symmetry, which is a vertical line. The point on the graph where the function reaches its minimum or highest value is known as the vertex of the parabola.

Given that the three points are: (-3, 2), (-4, -1), (0, -1)

To find the line of symmetry of a quadratic function, we need to find the x-coordinate of the vertex of the parabola. Since the three given points lie on the graph of the quadratic function, we can use them to find the vertex.

First, let's write the quadratic function in vertex form:

\(y = a(x - h)^2 + k\)  where (h, k) is the vertex of the parabola.

Using the given points, we can set up a system of equations to solve for a, h, and k:

\(2 = a(-3 - h)^2 + k\)

\(-1 = a(-4 - h)^2 + k\)

\(-1 = a(0 - h)^2 + k\)

We can simplify this system by subtracting the third equation from the first two to eliminate k:

\(1 = a(-3 - h)^2 - a(0 - h)^2\)

\(-2 = a(-4 - h)^2 - a(0 - h)^2\)

Simplifying further, we get:

\(1 = 9a - h^2a\)

\(-2 = 16a - h^2a\)

Solving for h, we get h = -1/2. Substituting this into one of the equations, we can solve for a:

\(2 = a(-3 - (-1/2))^2 + k\)

\(2 = a(25/4) + k\)

Subtracting this equation from one of the other equations, we can solve for k:

\(-3 = a(-4 - (-1/2))^2 + k\)

\(-3 = a(147/4) + k\)

Substituting a = 8/147 and h = -1/2 into the vertex form equation, we get:

\(y = \frac{8}{147} (x + \frac{1}{2} )^2 - \frac{3}{7}\)

So the line of symmetry is  \(x=-\frac{1}{2}\)

To select two points on the coordinate plane, we can choose any two points that are not on the line of symmetry. For example, we can choose (1, 1) and (-2, 4). To connect these points with a line, we simply plot them on the coordinate plane and draw a straight line passing through both points.

To know more about quadratic function, visit:

https://brainly.com/question/1214333

#SPJ1

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

Learn more about quadratic equation here

https://brainly.com/question/30098550

#SPJ4

The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

About maximum height here:

https://brainly.com/question/29081143

#SPJ11

Answer:

BElabora un esquema y resuelve el problema.​

Step-by-step explanation:

Answer:

because the answer is 6.601 not 6.501

Step-by-step explanation:

you must have done the work wrong

Answer:

\(y=\) \(-\frac{5}{6}x - 1\) is the answer

Step-by-step explanation:

Equation of the line: y = 6/5x + 1

                        = 5y = 6x + 5

                        = 6x - 5y + 5

Equation of the perpendicular line: bx - ay + k = 0

                                                       = -5x -6y + k = 0

Equation passes through (6,-6),

-5(6) -6(-6) + k = 0

-30 + 36 + k = 0

6 + k = 0

k = -6

Substituting,

-5x -6y + k = 0

-5x -6y -6 = 0

-6y = 5x + 6

\(y=\) \(-\frac{5}{6}x - 1\) (Slope-Intercept form)

Answer:

-25 ,B

Step-by-step explanation:

The probability of a z-value less than -1.02 is similar to getting the area to the left of z = -1.02 in a normal curve.

Using the standard normal distribution table, the area to the left of z = -1.02 is 0.1539. Therefore, P(Z < -1.02) = 0.1539.

The price of a new pair of pants including tax is $46.06.

A word problem is a math issue that has been expressed as a scene from a tale. It basically asks you to picture how you would use arithmetic to solve a real-world situation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Given that,

Sales tax = 6%

Price of pants = $49

Total price including tax = price of the pants + sales tax = 46+6% = 46+0.06 = 46.06

Thus, the price of a new pair of pants including tax is $46.06.

To know more about word problems visit: brainly.com/question/29203255

#SPJ4

Answer:

-2

Step-by-step explanation:

At first, you might think that -5 is bigger than -2 because 5 > 2, right? Actually, no, that's not how it works. The "rules" for numbers are flipped when you are dealing with negative numbers, so therefore, -2 is bigger. Basically, what I'm saying is that the smaller the number after the negative sign, the bigger the number is and vice versa.

Answer:

Answer is - 2

Step-by-step explanation:

Because in case of negative numbers the number which is smaller in negative no is bigger in negative

numbers I hope you understand....Mark me as brainliest

Answer:

wew so wha do you need help withhhhhhh

Answer: COOOOOOOOOOOOOL

Answer:

Step-by-step explanation:

\(\frac{5^{-2} }{4^{6} } =\frac{1}{5^{2} 4^{6} }\)

Step-by-step explanation:

since this is a symmetric figure, both diagonals have the same length.

let's calculate the one from the top left corner to the bottom right corner.

the length of the diagonal is simply the distance between these 2 points.

we get this via Pythagoras :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

in our case, the distance is c, and the x-coordinate difference and the y-coordinate difference are a and b.

diagonal² = (-b - a)² + (c - 0)² = b² + 2ab + a² + c²

diagonal = sqrt(a² + b² + c² + 2ab)

Answer:

Center (-13 , -2); Radius = 9

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

plz mark me brainlest

Yes. The price vary directly with the number of toppings.

It is given that a large pizza with one topping costs $15.50 and with four toppings it cost $20.

We have to tell that does the price vary directly with the number of toppings.

What will be the cost of one pen if 10 pens cost $ 120 ?

The cost of 1 pen can be calculated by dividing cost of 10 pens by no. of pens and that will be 120 ÷ 10 or $ 12.

As per the question ;

The large pizza with one topping costs $15.50.

A large pizza with four topping costs $20.

So ,

The cost of pizza with one topping is less as compare to the pizza with four toppings.

i.e.,

15.50 < 20

So , we can conclude that with the increase in number of toppings the cost of pizza also increases.

Thus , it is true that the price of pizza vary directly with the number of toppings.

To learn more about algebra click here ;

https://brainly.in/question/6577457

#SPJ2

Value of angle m∠1 is 53°

Alternate angles, also known as alternate interior angles, are pairs of angles that are formed when a straight line, known as a transversal, intersects two parallel lines. Alternate angles are located on opposite sides of the transversal and between the two parallel lines.

In the given figure;

g║h and e║f

m∠1=(2x+3)°

m∠3=(5x+2)°

Since, e║f

m∠2 will be equal to adjacent angle of m∠1  (Alternate angle)

Sum of angles in a straight line is 180°

m∠2+m∠3=180°

m∠2=m∠1 (Co interior angle)

m∠1+m∠3=180°

Putting the values of angle, we get

2x+3+5x+2=180

7x+5=180

7x=175

x=25

m∠1=(2x+3)°

m∠1=2×25+3

=50+3

=53°

Hence, Value of angle m∠1 is 53°

To know more about intersects, visit:

https://brainly.com/question/30792974

#SPJ1

Answer:

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

Step-by-step explanation:

Step(i):-

Given mean of the population = 500

Given standard deviation of the Population = 75

Let 'X' be the variable in normal distribution

      \(Z = \frac{x-mean}{S.D}\)

Given X = $410

\(Z = \frac{410-500}{75} = - 1.2\)

Step(ii):-

The probability that a family spends less than $410 per month

P( X < 410) = P( Z < - 1.2 )

                  =  0.5 - A( -1.2)

                 = 0.5 - A(1.2)

                = 0.5 - 0.3849  ( ∵from normal table)

                = 0.1151

Final answer:-

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

Answer:

Step-by-step explanation:

Answer:

X=-1

Step-by-step explanation:

X=-1 is just a vertical line since it only tells where the x point is.

Answer:

(the letter 'x' represents the amount of miles he hiked)

x≤8

Answer & Step-by-step explanations:

I assume they want probability as a decimal as opposed to a fraction. I will do two questions for you, apply the same logic to all the rest.

P(Black or heart):
There are 26 black cards in a deck, and 13 (red) hearts.

26 + 13 out of 52 cards.

39 / 52 as a decimal is 0.75
P(Black or heart) = 0.75 or 75%
If wanted as a fraction, simplify your fraction down

39/52 has a common factor of 13, divide both numbers by 13

P(Black or heart) = 3/4

P(Red or 10):
There are 26 red cards and four 10's in a deck. Two of these 10's are red, so we will not double count them.

26 + 2 out of 52 cards.
28 / 52 as a decimal is about 0.54 or 54%

P(Red or 10) = 0.54 or 54%
If wanted as a fraction, simplify your fraction down

28/52 has a common factor of 4, divide both numbers by 4

P(Red or 10) = 7/13

Answer:

3x + 1

Step-by-step explanation:

plz mark as the brainliest

Answer:

Diagonals are congruent

Step-by-step explanation:

The diagonals of a parallelogram are not congruent; one is longer than the other

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

To know more about expression, refer here:

https://brainly.com/question/31800038

#SPJ4

Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

try B if wrong sorry

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

ab=48

Step-by-step explanation:

96/2=48

Answer:

If you distribute 4(x+2) using the distributive property, which states that multiplying each number individually by a same # is the same as multiplying the #s' sum by that #.

Thus, 4*(x+2) is the same as 4*x+4*2 which simplifies to 4x+8, Option 2

Answer:

up 1 over 7 (1,7) 1 = x and 7 = y

Step-by-step explanation:

0 plus 1 is 1. 1 plus 1 is 2. 2 plus 1 is 3. 3 plus 1 is 4

-6 plus 7 is 1. 1 plus 7 is 8. 8 plus 7 is 15. 15 plus 7 is 22