The quadratic function f(x) has roots of 3 and 7, and it passes through the point (1, 12). What is the vertex form of the equation of f(x)?

f(x) = −(x + 5)2 − 4
f(x) = −(x − 5)2 − 4
f(x) = (x + 5)2 − 4
f(x) = (x − 5)2 − 4

The median for the next batch of observations is 5.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=2,5,7,9

n=4

median=(4)/2

=2nd term

=5

The median for following set of observation is 5.

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Answer:

See the picture.

Step-by-step explanation:

Therefore , the solution to the given problem of the equation whose factors are (4x+1)(3x+2) .

How to analyze the equation?

An equation is a mathematical statement made up of two expressions connected together by the equal sign. For instance, 2x – 5 = 15 is an equation. By resolving this equation, we can establish that the variable x has a value of 5.

According to the given question:

Given expression: 12x² +11x+2

=> 12x² +11x+2

Break the expression into groups

=>  (12+3x) + (8x+2)

Subtract 3x from 12x+3x to get 3x(4x+1).

Add 2 to 8x+2 to get 2(4x+1)

= 3x(4x+1)+2(4x+1)

Factor out common term 4x+10

= (4x+1)(3x+2)

Therefore , the solution to the given problem of the equation whose factors are (4x+1)(3x+2) .

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer:

Step-by-step explanation:

Yes, he is correct because writing a negative symbol with a denominator and numerator makes the sense same. Because the negative is as a whole not only the numerator and not only the denominator. As it is a fraction which is a whole single identity.

3/4= 0.75, Therefore in each above three always the

-0.75= -0.75= -0.75 will give same value in each.

Answer:

volume of copper cuboid(V) =10cm×3cm×5cm=150cm³=150/10⁶ m³=1.5×10-⁴ m³

density of copper(d)=9.86×10-³+²=0.986 kg/m

we know,

mass=V/d=1.5×10-⁴/0.986=1.47×10-⁴ kg

The mean of 1, 2, 3, 4, and 5 is 3, and the standard deviation is 1.58.

To find the mean, you add up all the numbers and divide by the number of numbers you have.

To find the standard deviation, you first find the difference between each number and the mean, square each of these differences, add them up, and divide by the number of numbers you have. Then, you take the square root of this result.

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3

Standard deviation = sqrt(((1 - 3)^2 + (2 - 3)^2 + (3 - 3)^2 + (4 - 3)^2 + (5 - 3)^2) / 5) = sqrt((4 + 1 + 0 + 1 + 4) / 5) = sqrt(10 / 5) = sqrt(2) = 1.58

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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The price for an 11-mile ride with taxi company is $12

From the question, we have the following parameters that can be used in our computation:

Taxi cab: Company B:

Given that the number of rides is 1, we have the following equation that represents the total price

Total price = 6.50 * 1 ride + 0.50 * Number of miles

So, we have

Total price = 6.50+ 0.50 * Number of miles

For an 11-mile ride with taxi company B, we have

Total price = 6.50+ 0.50 * 11

Evaluate

Total price = 12

Hence, the price is $12

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Answer:

y<= -1/5x-3

Step-by-step explanation:

x+5y<=-15

5y<=-x-15

y<=-1/5x-3

Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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From Excel 2007 onwards (2010, 2016, etc.) we have exactly 10,48,576 rows and 16,384 columns.

Now, According to the question:

How many rows and columns does Excel 2013 have?

From Excel 2007 onwards (2010, 2016, etc.) we have exactly 10,48,576 rows and 16,384 columns.

Excel sheet:-

In Microsoft Excel, a sheet is often called a worksheet. A sheet is a single page that contains its own collection of cells to help you organize your data. There can be many sheets in your Excel document and you can see the sheets listed as tabs along the bottom of your document.

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By applying the fraction concept, we can conclude that the bunny ate 3/10 food at night.

Application of the concept of fractions in real life

In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.

In the problem above it is stated that initially the bunny has food, which will be eaten in the morning and at night, and some food was left over.

If x is the total food for the bunny, then the given problem can be written mathematically as follows:

breakfast (a) : a = 1/2x

dinner (b)

food left (c) : c = 1/5x

Then the mathematical expression that describes the above situation is as follows:

x = a + b + c

  = 1/2x + b + 1/5x --> then we make the denominators the same, so it becomes:

           x = 5/10x + b + 2/10x

              = 7/10x + b

x - 7/10x = b

     3/10x = b

So, the food that the bunny eats at night was 3/10.

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Answer:

So, the food that the bunny eats at night was 3/10.

:D im jus smart.

Answer:

Z = -15

Step-by-step explanation:

z - 1 +16 = 0

z + 15 = 0

subtract 15 from both side to get z by itself

z+15-15 = -15

so the answer will be z=-15

Answer: $24 after 4 years

Step-by-step explanation:

1.5% = 0.015

Take 400 times 0.015 = $6 per year

6 times 4 = $24 after 4 years

A graph is a diagram representing data in an organized manner.

The examples are line graphs, histograms, pie charts, bargraphs.

A graph can simply be defined as the pictorial representation or given a diagram representing data or values in an organized manner.

Points on a graph mostly represents the relationship between two or more elements.

It is also referred to as a mathematical diagram that explains the relationship between two or more sets of data, measurements or elements.

The data on a graph is mostly arranged in an organized manner.

The examples of a graph;

Hence, a graph is an organized diagram.

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The area of the rectangle is 12 square units which vertices are P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3).

To find the area of the rectangle, we need to first find the side lengths of the rectangle. We can do this by using the coordinates of the points to find the distances between them.

The side length of the rectangle along the x-axis is the distance between points P and Q, which is 4 - 2 = 2 units.

The side length of the rectangle along the y-axis is the distance between points P and S, which is 3 - (-3) = 6 units.

Now that we know the side lengths of the rectangle, we can use the formula for the area of a rectangle, which is length x width, to find the area.

The area of the rectangle is 2 x 6 = 12 square units.

Therefore, the answer is 12 square units.

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Answer:

20+7k=8k+16

Step-by-step explanation:

8(k+2)

8 x k = 8k

8 x 2 = 16

Therefore, its  20+7k=8k+16

Answer:

8k+16

Step-by-step explanation:

20 + 7k = 8(k + 2)

20 + 7k = (8)(k) + (8)(2)

20 + 7k = 8k + 16

The factors of polynomial P(x)= 2x² -7x + 3 is x =1/2 and x =3.

Factoring polynomials is the opposite method of the multiplication of things of polynomials. An expression of the shape

axⁿ + bxⁿ⁻¹+kcxⁿ⁻² + ….+kx+ l, wherein every variable has a regular accompanying it as its coefficient is known as a polynomial of diploma ‘n’ in variable x. hence, a polynomial is an expression wherein a mixture of a regular and a variable is separated with the aid of an addition or a subtraction signal.

For a polynomial of the form:

ax²+ bx +c, rewrite the middle term as a sum of two terms whose product is a × c =2×3 = 6 and whose sum is b= −7.

Now,

Factor −7 out of −7x

2x²−7(x)+3

Rewrite −7 as −1 plus −6

2x²+ (−1−6)x +3

Apply the distributive property.

2x²−1x−6x+3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2x²−1x)− 6x + 3

Factor out the greatest common factor (GCF) from each group.

x(2x−1)−3(2x−1)

Factor the polynomial by factoring out the greatest common factor,

(2x−1)(2x-1)(x−3)

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The coefficient of the expression 3x² is the number 3

The coefficients are the numbers on the left side or before each variable.

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

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The level of a line's slope indicates its steepness.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.

Now, let's take an example ,

2x - 3y ≤ 12

or, - 3y ≤ 12 - 2x

or, 3y ≤ 2x - 12

or y ≤ (2/3)x - 4

So, here slope (m) = 2/3, graph is shown below:

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a) Differential equation (initial value problem) for the mass of the copper sulfate would be dm/dt = 0

b) m(t)=0

What is Differential equation?

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to create a relationship between the two.

a) Solution is flowing out of the tank. This can be expressed mathematically as:

dm/dt = (flow rate of solution into tank) - (flow rate of solution out of tank)

= (2 l/min) - (2 l/min)

= 0

Therefore, the differential equation for the mass of the copper sulfate in the tank is:

dm/dt = 0

This is a simple differential equation with a constant coefficient of 0, and it can be easily solved by integrating both sides of the equation with respect to time.

b. To solve the differential equation, we can write:

m(t) = integral(0, t, dm/dt)

= integral(0, t, 0)

= 0

Since the coefficient of the derivative is 0, the solution to the differential equation is a constant function with a value of 0. This means that the mass of the copper sulfate in the tank will remain constant over time, regardless of the flow rates of the solution into and out of the tank.

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The average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

What is Standard deviation?

Standard deviation is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To determine whether there is evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years at a 5% level of significance, we need to perform a one-tailed t-test. A one-tailed t-test is used to test whether the mean of a sample is significantly greater than (or less than) a certain value.

To perform the t-test, we first need to calculate the t-statistic, which is defined as:

      [tex]t = (mean - null value) / (standard error / \sqrt{n} )[/tex]

where mean is the mean age of the sample of lifeguards, null value is the value that the null hypothesis is testing against (in this case, 24 years), standard error is the standard error of the mean age, and n is the number of lifeguards in the sample.

Plugging in the values from the problem, we get:

           [tex]t = (24.7 - 24) / (standard \ error / \sqrt{36} )\\\\= 0.7 / (standard\ error / 6)[/tex]

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

   [tex]standard \ error = population \ standard\ deviation / \sqrt{(n)}[/tex]

Plugging in the values from the problem, we get:

standard error = / sqrt(36) = / 6 =

Substituting this value back into our expression for t, we get:

    t = 0.7 / ( 6)

      = 1.8

For a one-tailed t-test at a 5% level of significance, the critical value is 1.645. This means that if the t-statistic is greater than 1.645, we can reject the null hypothesis and conclude that there is evidence to support the claim.

So we can reject the null hypothesis and conclude that there is evidence to support the claim that the average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

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The required total number of people in the stadium are 14500.

In math, a percentage is a number or proportion that can be communicated as a small part of 100. On the off chance that we need to compute percent of a number, partition the number by the entire and increase by 100. Thus, the rate implies, a section for each hundred

2% of the fans in attendance were teenagers, and there are 290 teenagers in number.

Let x be the total number of people in stadium.

So, 2% of x = 290

2x/100 = 290

x = 29000/2 = 14500 people

Thus, there are 14500 people in the stadium.

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Yes, since the midpoint of a line segment is at an equal distance from the two endpoints, it is said to be equidistant from them.

A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group.

The perpendicular bisector of two specified (different) points is their location in two-dimensional Euclidean geometry. The locus of points equidistant from two provided points in three dimensions is a plane, and generalizing further, the locus of points equidistant from two given locations in n-dimensional space is a (n1)-space.

The circumcenter of a triangle is a location that is equally spaced from each of the three vertices. This point exists in every non-degenerate triangle. The circumcentre of cyclic polygons is equally far from all of the vertices, and this conclusion may be generalized to them.

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Expression is a constant, variable or constant multiplied by a variable separated by operator.

Identity, as we all know, is equality, which holds true regardless of the variable's value. These identities are algebraic formulas that show that for all possible values of the variable, the Left-Hand Side (LHS) and the Right-Hand Side (RHS) of the equation are equal. A phrase that can have any value is called a variable.

Monomial, polynomial and binomial are the three types of algebraic expression.

An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. For instance: 5x+20y, 6-8x.

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Answer:

Depends on your school. I took Pre-calculus my 11th grade year. Sometimes it is Algebra 2.

No, y = 4 is not a linear function.

A linear function is a function that has a constant rate of change, meaning for every input (x), the output (y) always increases or decreases by the same amount. This can be expressed algebraically as a linear equation in the form y = mx + b, where m is the rate of change (slope) and b is the y-intercept.

For example, y = 3x + 2 is a linear function because for every increase of 1 in the input (x), the output (y) increases by 3.

In contrast, y = 4 does not have a constant rate of change because the output (y) is always 4, no matter what the input (x) is. Therefore, y = 4 is not a linear function.

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To solve an equation for vertical asymptotes using a calculator, just input the denominator of the given equation to calculator to solve for x, the obtained values of x will give the vertical asymptotes for the given equation.

A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a.

Vertical asymptotes are significant because they demonstrate the boundaries of an undefined function. This can be crucial when examining a function's behavior and comprehending its characteristics.

To calculate the vertcial asymptotes on a calculator (eg. fx-991EX) follow the steps below to input the denominator of the given equation:

1. Press MENU button

2. Press Alpha + A to select equation/Func options

3. Press 2 to select Polynomial option

4. Select the degree of denominator

5. Enter the respective coefficients and press equal to button to get the vertical asymptote.

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All the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

SSS Theorem: The Side Side Side (SSS) Theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.

Example of SSS Triangles:
From the figure:

These are SSS triangles. Given that they have the exact same measurements, we can deduce the following:

AB = XY

BC = YZ

AC = XZ

If we know that AB = 5 units, then XY also equals 5 units.

And if BC = 4 units, then YZ also equals 4 units.

Further, if AC = 7 units, then XZ also equals 7 units.

Then the two triangles are said to be congruent by SSS rule.

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Answer:

x = 7/19

Step-by-step explanation:

(3x-2)-3(2x+1)=4(4x-3)

3x - 2 - 6x - 3 = 16x - 12

-19x = -7

x = 7/19

Answer:

x = 7/19

Step-by-step explanation:

(3x-2)-3(2x+1)=4(4x-3)

3x - 2 -6x -3 = 16x -12

-3x -5 = 16x -12

-5 = 19x -12

7 = 19x

x = 7/19