A certain quadratic function has the factors (x + 3) and (2x - 1). What are the solutions of the function?
A- (0,3) and (0, -1)
B- (-1,0) and (3,0)
C- (6,0) and (-3,0)
D- (0,1/2) and (0, -3)

Answer: D

Step-by-step explanation:

There are 14 students who chose vanilla, and 6 of those are male. 6/14 = 3/7.

Answer:

\(y = -2\, x\).

Step-by-step explanation:

Find two points on the original line, \(y = 2\, x\):

Setting \(x = 0\) gives \(y = 0\), which corresponds to the point \((0,\, 0)\).

Setting \(x = 1\) gives \(y = 2\), which corresponds to the point \((1,\, 2)\).

Reflect the two points with respect to the \(y\)-axis by inverting the \(x\)-coordinate of each point. The point \((0,\, 0)\) stays the same, whereas the point \((1,\, 2)\) would be mapped to \((-1,\, 2)\).

Find the equation of the new line. The slope of the new line would be:

\(\begin{aligned}\frac{2 - 0}{(-1) - 0} = \frac{2}{(-1)} = -2\end{aligned}\).

Equation of the new line in point-slope form:

\(y - 0 = (-2)\, (x - 0)\).

\(y = -2\, x\).

Answer:

40 %

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

We are given that the scores are normally distributed.

The mean of the data is 573.

The standard deviation of this data is 72.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

So,

We can write,

μ = 573

σ = 72

Then, the given expression is,

( μ - 3σ < x < μ +3σ ) = 99.7%

So,

μ - 3σ = 573 - 3*72

μ - 3σ = 573-216

μ - 3σ = 357

μ +3σ = 573 + 3*72

μ + 3σ = 573+216

μ + 3σ = 789

Hence, the mean is halfway between these two integers are = 357 and 789

Empirical rule states that for a normally distributed data that

about 68% data lies between μ + 1σ that is one standard deviation from mean.

about 95% data lies between μ + 2σ that is one standard deviation from mean.

about 99.7% data lies between μ + 3σ that is one standard deviation from mean.

Therefore,

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

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Therefore, the only statement that is equivalent to "the price decreased by \(\frac{1}{3}\)" is:

F. The price is now 66, 2/3% of what it was before

Given that the original price of something decreased by 1/3, it means:

the original price is reduced by one-third.

Any option showing or suggesting an increase is definitely the wrong answer.

Therefore, the only statement that is equivalent to "the price decreased by \(\frac{1}{3}\)" are:

F. The price is now 66, 2/3% of what it was before

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Answer:

F

Step-by-step explanation:

Answer:

Option 1 is the answer.

Step-by-step explanation:

Because the domain is x and horse can be between 0 and 6 hours running.

Answer: 2 to the power of 0 can be expressed as 20

Step-by-step explanation: tbf im not sure, explain clearly

Answer:  1 or 2 (see below)

Step-by-step explanation:

any number to the power of 0 = 1

solution 1)  (2w)^0 = 1

solution 2)  2(w^2) = 2(1) = 2

Answer depends on placement of parentheses!

Answer:

22lb.

Step-by-step explanation:

divide 94 by 47 to get 2 than divide 44 divided by 2 and your answer is 22

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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Answer:

y=3d+15

y intercept is 15

slope is 3

Step-by-step explanation:

to graph start at 15 on the y axis. then go up 3 points and over one point. keep doing this until you have a straight line.

Answer:

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

\(h(t) = -4.9t^{2} + 5t + 1\)

How long will it take the ball to hit the ground if no other players touch it?

This is t when h(t) = 0. So

\(-4.9t^{2} + 5t + 1 = 0\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(-4.9t^{2} + 5t + 1 = 0\)

So \(a = -4.9, b = 5, c = 1\)

So

\(\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6\)

\(t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17\)

\(t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)}  = 1.19\)

Since we want a time measure, the answer cannot be negative.

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Answer:

115

Step-by-step explanation:

The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

Given that,

An octahedron is made by connecting the centers of the faces of the right rectangular prism in the illustration below.

We have to find what is the octahedron's volume.

The Greek term "Octahedron," which means "8 faces," is the source of the English word "octahedron." Eight faces, twelve edges, six vertices, and four edges that intersect at each vertex make up an octahedron, a polyhedron. It is one of the five platonic solids with equilateral triangle-shaped faces.

Since two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid. We can compute the volume of one pyramid, then multiply it by two to obtain the volume of an octahedron.

The pyramid's volume is equal to (Base area ×Height)/3.

Since the pyramid's base is square, its base area is equal to a².

Therefore, The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

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Answer:

The relationship between r and V is not linear.

Step-by-step explanation:

The volume increases exponentially as r increases linearly.

Volume of a cylinder is directly proportional to the square of its radius, we can say that there is a linear relationship between the radius and the volume of a cylinder.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Volume of a cylinder is V = πr²h,

where r is the radius

h is the height of the cylinder.

If we keep the height of the cylinder constant and vary the radius, we can see that the volume of the cylinder increases as the radius increases.

In fact, we can express this relationship as a linear equation in the form of y = mx + b,

where y is the volume, x is the radius, m is the slope, and b is the y-intercept.

By rearranging the volume formula, we get V = πr²h, which can be written as y = mx + b, where m = πh and b = 0.

Therefore, since the volume of a cylinder is directly proportional to the square of its radius, we can say that there is a linear relationship between the radius and the volume of a cylinder.

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We can see that since the values that multiply each component (x & y) are less than an unit, the transformation rule would be a reduction.

Answer:

The overall score is 75.6

Letter grade is C

Step-by-step explanation:

The question has missing details (See comment section for complete question).

From the complete question, we have:

Proportion:

\(Midterm = 15\%\)

\(Project = 25\%\)

\(Assignment = 40\%\)

\(Exam = 20\%\)

Scores

\(Midterm = 66\)

\(Project = 90\)

\(Assignment = 75\)

\(Exam = 66\)

Solving (a): The overall score

To do this, we simply calculate the mean of the given data.

The mean is calculated by multiplying each proportion by the scores..

So, we have:

\(Overall = 15\% * 66 + 25\% * 90 + 40\% * 75 + 20\% * 66\)

\(Overall = 9.9 + 22.5 + 30 + 13.2\)

\(Overall = 75.6\)

Solving (b): The letter grade

From the question, we have:

\(A: Mean \ge 90\)

\(B: 80 \le Mean < 90\)

\(C: 70 \le Mean < 80\)

The overall score falls in the following category:

\(C: 70 \le Mean < 80\)

Because:

\(70 \le 75.6 < 80\)

Hence, the letter grade is C

Answer:

The triangles are lined up with their correct pairs already.

Step-by-step explanation:

The leg that is the base is always seen as the bottom, and the leg to the side of it that makes the right angle will always be the height. Though if the base is at the hypotenuse as it is seen in the last photo, the height will be from the point of which the two legs of the triangle meet down to the hypotenuse.

Any value that is raised to the power of zero is 1. The value of the expression given in its simplified form is 1

Any value that is raised to the power of zero is 1. Given the expression

(30^2)^0

Simplify

30^2 = 900

Substitute into the original function to have:

(30^2)^0 = 900^0
(30^2)^0 = 1

Hence the value of the expression given in its simplified form is 1

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Answer:

$2.73

Step-by-step explanation:

$ 0.39 x 7 lbs = $2.73

Answer:

$2.73

Step-by-step explanation:

y=0.39x

y=0.39(7)

y=$2.73

Answer:

16000

Step-by-step explanation:

Simply add the two roughly in your head and round up or down to nearest thousand

The Length of AD is 78 cm.

From the figure, G is Centroid.

The point in which the three medians of the triangle intersect is known as the centroid of a triangle.

It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

The centroid of the triangle separates the median in the ratio of 2: 1.

Centroid divides median in the ratio 2:1 .

As per the given data AG = 52

2 parts is 52 .

3 parts is (52 × 3 )/2= 78

Therefore, the length of AD is 78.

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Answer: Food surpluses led to population growth.

Step-by-step explanation:

Food surpluses led to population growth.

Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

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True!

For example: \(16^\frac{1}{2}\) can also represented as \(\sqrt{16}\), and the answer will still be 4.