one quarter of a number is 6 what is the one third of the number

The required standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is y = -2x² + 12x - 17.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

To find the quadratic function that has the vertex (3, 1) and passes through the point (5, -7), we can use the vertex form of the quadratic function: y = a(x - h)² + k, where (h, k) is the vertex.

First, we substitute the vertex (5, -7) into the vertex form to find a:

y = a(x - 3)² + 1

-7 = a[2]² + 1
a = -2

Since a = -2, the standard form of the quadratic function is:

y = -2x² + bx + c

Substitute the point (5, -7) into the standard form y = -2x² + bx + c to find b and c:

-7 = -2x² + b(5) + c

-7 = -50 + 5b + c

43 = 5b + c - - - - -(1)

Substitute the point (3, 1) into the standard form y = -2x² + bx + c to find b and c:

1 = -18 + b(3) + c

19 =3b + c - - - - -(2)

Solving equations 1 and 2 we get
43 - 19 = 2b
b = 12 and c = -17

Put a,b and c in the standard equation,
y = ax² + bx + c
y = -2x² + 12x - 17

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The provided parallelogram has angles of 45 degrees and 45 degrees, as well as 48 degrees and 48 degrees.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a quadrilateral with opposing sides that are parallel and equal. It has equal interior opposite angles. In addition, the angles on the same side of the transversal add up to 180 degrees or are additive to each other.

Here,

A parallelogram has two pairs of opposite angles that are equal.

Since one angle of the parallelogram is 48 degrees, its opposite angle must also be 48 degrees.

The other two angles must add up to 90 degrees (since they form a right angle), so they must each be equal to 180 - 90 = 90 degrees / 2 = 45 degrees.

So, the other angles of the parallelogram are 45 degrees and 45 degrees.

The angles of given parallelogram are 45 degrees and 45 degrees as well as 48 degrees and 48 degrees.

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Answer:

6,072

Step-by-step explanation:

5,600 - 4,420 = 1,180

They gained 1,180 people over 5 years.  Now we need to find how many people they gain every year (roughly).

Since it's 5 years, we are going to divide.

1,180 / 5 = 236

They gained 236 people over 1 year.  Since 1998 is two years is before 2000, we're going to multiply 236 by 2.

236 x 2 = 472

Now we add this to the 1998 population.

5,600 + 472 - 6,072

The population in the year 2,000 is 6,072

In multiple regression, we have 4 assumptions listed and explained below. They are valid.

Following are assumptions for multiple regression model:

1. Linear connection: Each predictor variable and the responder variable have a linear relationship.

Making a scatter plot of each predictor variable and the response variable is the simplest technique to check if this premise is true.

2. Lack of Multicollinearity: There is no significant correlation between any of the predictor variables.

Calculating the VIF value for each predictor variable is the quickest approach to see if this premise is true.

3. Independence: Each observation has its own validity.

The Durbin-Watson test, a formal statistical test that informs us whether or not the residuals (and consequently the observations) exhibit autocorrelation, is the easiest approach to find out if this assumption is true.

4. Homoscedasticity: At every point in the linear model, the residuals' variance is constant.

The simplest technique to check if this premise is true is to plot the standardized residuals against the expected values.

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Answer: ez ahh question, the answer is (4,-5)

Step-by-step explanation:

Answer:

[tex]\frac{1}{-6x}[/tex]

Step-by-step explanation:

[tex]\frac{1}{-6x}[/tex]  To get a positive exponent, put the expression over 1.

Answer:

A.  x = -48

Step-by-step explanation:

x/4 = -12

x = (-12)(4) = -48

The correct answers is (a). False (b). False (c). False (d).True

(A). False

If Mrs. Smith and Mr. Smith drive 80 miles each, then the total miles they drive is 80 + 80 = 160 miles. That means James will have to drive 240 - 160 = 80 miles, which is 1/3 of the round-trip distance, not 13/3.

(B). False

If Mrs. Smith and Mr. Smith drive 90 miles each, then the total miles they drive is 90 + 90 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{1}{4})[/tex] of the round-trip distance, not [tex]\frac{12}{4}[/tex].

(C). False

If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then the total miles they drive is 90 + 50 = 140 miles. That means James will have to drive 240 - 140 = 100 miles, which is [tex](\frac{1}{2} )[/tex] of the round-trip distance, not [tex](\frac{5}{12} )[/tex].

(D). True

If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then the total miles they drive is 60 + 120 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{7}{12} )[/tex] of the round-trip distance.

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Answer:

Your answer should be: TRUE FALSE TRUE FALSE

The values for g and f for the length of sides of the trapezium are 8 and 6 respectively.

Given the area of trapezium = 60 cm², then:

1/2 × (g + 4g) × f = 60 cm²

by simplification

f(g + 2) = 60 cm²...(1)

for the area of ABCD = 48 cm², then:

f × g = 48 cm²

f = 48/g...(2)

put 48/g for f in equation (1) to get g;

48/g(g + 2) = 60

60g = 48g + 96 {cross multiplication}

60g - 48g = 96 {collect like terms}

12g = 96

g = 96/11 {divide through by 11}

g = 8

put 8 for g in equation (2) to get f;

f = 48/8

f = 6.

Therefore, the values for g and f for the length of sides of the trapezium are 8 and 6 respectively.

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Answer:

33 containers

Step-by-step explanation:

total gallons needed=8×30=240

gallons in 15 containers=15×5=75

gallons needed=240-75=165

no. of containers needed to buy=165÷5=33

The area of the triangle is calculated to be equal to 7.5 square inches.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

we have the base of the triangle to be 6 inches and the height as 2.5 inches, so we solve for the area as follows:

1/2 × 6 inches × 2.5 inches

6 inches can be divided by 2 to give;

3 inches × 2.5 inches

7.5 square inches

Therefore, the area of the triangle is calculated to be equal to 7.5 square inches

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The test is determined whether the population variance is less than 7.

The hypothesis formulation-

‘H0: σ² ≥ 7’

‘H1: σ² < 7’

Now let us solve this question options-wise:

Option a is incorrect because we should always contain the ‘=’ or ‘≥’ or ‘≤’ sign, and in the null hypothesis, and also this option denotes the standard deviation, not the variance.

Option b is correct because it contains a ‘≥’ sign and it is the right complement to the alternative hypothesis.

Option c is incorrect because it measures the standard deviation instead of the variance.

Option d is incorrect because it has the lower limit of the variance as 49 instead of 7

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full question:

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ< 7.

b.σ^2≥7.

c. σ< 49.

d.σ^2≥ 49

Answer:

Below

Step-by-step explanation:

2/3 x = 9 - 2(-1/3 x +3 )     Expand the parentheses

2/3 x = 9 -  -2/3x -6          simplify the R side a bit

2/3 x = 9 + 2/3x - 6

2/3 x = 3 + 2/3 x        subtract 2/3 x from both sides

0 = 3     <===== obvously not true,    NO SOLUTION

The functions that we have are;

1) y = 2.2x + 104

2) y =5.06e^-0.011t

3) The dependent variable is the number of organisms while the independent variable is the time in years.

4) This is an exponential decay

5) The decay rate is 1.1%

We know that an equation is often used to show a function. The equation is a mathematical rule that is used to express the particular situation that we have.

In the case of the problems that we have here, there is a mathematical function that can be used in the representation of each of the cases that have been shown as we can see above.

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AO in terms of P and/or Q is OA = Q = Q

OB in terms of P and/or Q is OB = P =Q

EB in terms of P and/or Q is EB = 2P =2Q

A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any basic hexagon has a total internal angle of 720°.

In a regular hexagon, all sides are equal

Which means:

AB= BC

5p + q -5p = 6p-5p

q = p

So, every side of the hexagon is p = q

Which means that AB = BC = CD = DE = EF = FA = p =q

Recall that at the center, each side forms an angle

There are six sides in a hexagon.

Total angle = 360°

6x= 360°

x= 60°.

By the symmetry of regular hexagon, OA = OB

<OAB = <OBA

<AOB = x = 60°

Sum of all angles in a triangle is 180°

We add the values

<OAB = 60°.

<OAB is an equilateral triangle, thus every side is equal

Hence,

a. OA = Q = Q

b. OB = P =Q

c. EB = 2P =2Q.

From the figure, <BOE= 180° which makes it a straight line.

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Answer:

43 chickens

Step-by-step explanation:

1) 250*8%=20

2) 250-20=230

3) 230*10%=23

4) 20+23=43

The fraction cannot be worked out, given the information on the numerator being even and the denominator being odd.

When fractions are said to be in their simplest forms as 1 / 1, then it means that both the numerator and the denominator are the same. This way, they can divide each other and leave one.

For such a situation to happen, the numbers will have to either both be even numbers, or odd numbers. The numerator cannot be even while the denominator is odd.

This fraction therefore cannot be worked out.

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The area of the piece of paper left after cutting out the circle is 29.76 in².

Area of a figure:

The amount of unit squares that completely encircle the surface of a closed figure is its area. Area is measured in square units like cm² and m². A shape's area is a two-dimensional measurement. The term “area” refers to the space inside the boundary or perimeter of a closed shape.

You need to first determine the rectangle's area.

8x10=80 in²

determine the circle's overall area.

The diameter is 8 in so you would use 4 as the radius

A=πr²

A=3.14x4²

A=3.14x16

A=50.24 in²

The area of the circle must then be subtracted from the area of the rectangle.

80-50.24=29.76

The area of the piece of paper is 29.76 in ².

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The table for the values when x = 0,5,8,10, will be:

x (minutes) y (altitude in feet)

0                                    1500

5                                1450

8                                1420

10                                1400

30                                  1200

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

When x = 0, y will be:

-10x + 1500

= -10(0) + 1500

= 1500

When x = 5 y will be:

= -10(5) + 1500

= 1500 - 50

= 1450

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Answer:

(-1,-3)

Step-by-step explanation:

See the attached worksheet.  First step is to apply the transformation.  Modifiy the x and y points as per the instructions.  The transformed triangle is shown in blue and the coordinates are listed.  As the directions indicate, it is slipped down by 2 and to the left by 3 (y-2 and x-3).

Next, convert the x values so that they are reflected across the y axis.  The table shows that all x values are the negative of their original values.  The reflected triangle is shown in red.

The new point Z is (-1,-3).

Step-by-step explanation:

jaubslsjsolqmaiBaokmaalo

Based on the information below, a statement which is true include the following: C. the number of female students in School A is more than the number of male students in School B.

In Mathematics, a pie chart is sometimes referred to as a circle graph and it can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

By critically observing the pie chart shown in the image attached below, we can reasonably infer and logically deduce that the total number of male students in School A is less than the total number of female students in School B.

In conclusion, School A has more female students than male students.

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To find three additional polar representations of the point (2, 3π/4), we can add or subtract 2πk to the angle, where k is an integer. Using this method, we get:

   (2, -5π/4) - subtract 2π

   (2, 11π/4) - add 2π

   (2, -3π/4) - subtract 2π

To find the smallest and largest values of the angle, we need to consider the interval −2π < θ < 2π. The given angle of 3π/4 lies in the second quadrant. Adding or subtracting 2π to this angle will give us angles in the third and fourth quadrants. Therefore, the smallest value of the angle is −3π/4, and the largest value is 5π/4. Thus, the polar representations are:

   (2, 3π/4)

   (2, -5π/4)

   (2, 11π/4)

   (2, -3π/4)

   (2, 5π/4)

Answer: 360 = 7n + 12 + 13x — 16 + 6xx = 146 * 14 = 84°

The system of equations is:

y = 19 + 4*x

y = 15 + 6x

And the solution is x = 2 and y = 27.

We know that red is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. Then after x sets he will be lifting:

y = 19 + 4*x

kilograms.

And his partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Here we can write:

y = 15 + 6x

Then we need to solve the system of equations at:

y = 19 + 4*x

y = 15 + 6x

Using substitution, wecan write:

19 + 4x = 15 + 6x

19 - 15 = 6x - 4x

4 = 2x

4/2 = x

2 = x

They will lift the same weight after 2 sets, and the weight is:

y = 19 + 4*2

y = 19 + 8 = 27

They will be lifting 27 kilograms.

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The simplified product of - (2/5).(2/5) is equal to - 4/25.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A product of two fractions - 2/5 and 2/5 is given.

We know in the product of fractions numerator is multiplied by the numerator and the denominator is multiplied by the denominator.

Therefore, - (2/5).(2/5).

= - (2×2)/(5×5).

= - 4/25.

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1.) The "(≠)" means that all of the points on the line will satisfy the inequality.

2.) The solution set for the inequality is the entire region (shaded or unshaded portion) shown in the graph. The shaded region represents the set of all points that satisfy the inequality, while the unshaded region represents the set of all points that do not satisfy the inequality.

What is linear inequality?

A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.

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Value of expression 5 - 3 is 2

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

5 - 3 = ?

we need the difference of 5 and 3

5 - 3 = 2

Hence, 2 is value of expression 5 - 3

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