Write the standard form of the equation of a parabola passing through the point (1, 32) with a minimum point at (-2, 5).

Answer:[tex]-3r+7[/tex]

Step-by-step explanation:

given the equation

[tex](-8r-2)-(-5r-9)[/tex]

Distribute the negative

[tex]-8r-2+5r+9[/tex]

Combine like terms

[tex](-8r+5r)+(-2+9)[/tex]

[tex](-3r)+(7)=[/tex]

[tex]-3r+7[/tex]

Hope this helps!

By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).

The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the greatest power) must be divisible by the fraction's denominator and the constant term (the one without a variable) must be divisible by the fraction's denominator.

It is given that,

x³-5x²-17x+21 = 0x

Factor the left side of the equation,

(x−1)(x−7)(x+3)=0

If any of the factors on the left side of the equation equals 0, the entire expression equals 0.

x−1=0

x−7=0

x+3=0

Set, x−1equal to 0 and solve for x.

x−1 equal to 0.

x−1=0

Add 1 to both sides of the equation.

x=1

Set, x−7 equal to 0 and solve for  x

Set x−7equal to 0.

x−7=0

Add 7 to both sides of the equation.

x=7

Set x+3 equal to 0and solve for x.

Set x+3 equal to 0.

x+3=0

Subtract 3 from both sides of the equation.

x= −3

The final solution is all the values that make (x−1)(x−7)(+3)=0 true.

x=1,7,−3.

Hence, By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).

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The equation of the amount to be paid by anyone using the ride in slope intercept form is; y = 0.5x + 10

The general form of the equation of a Line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, we are told that;

Amount charge by Winter Wonderland per child = $0.50

We are told that there is a separate entrance fee.

Amount of times todd sled down the hill = 16 times

Amount paid by todd = $18

Thus, using the slope intercept form, we have;

18 = 0.5(16) + b

18 = 8 + b

b = 10

Thus, the equation of this amount to be paid in slope intercept form is;

y = 0.5x + 10

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Answer:

>

Step-by-step explanation:

81 is greater than 64

The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

[tex]Ax + By + C = 0[/tex]

Equation of Straight Line or Slope:

[tex]y = mx+b[/tex]

Point-slope form:

[tex]y-y_{1} = m(x-x_1)[/tex]

Slope when 2 points are given:

[tex]m = \frac{(y_2 - y_1)}{(x_2-x_1)}[/tex]

Quadratic Equation:

[tex]Ax^2 + Bx +C = 0[/tex]

When lines are parallel:

Slope of both lines are equal. [tex]m_1 = m_2[/tex]

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line [tex]l_1[/tex] is [tex]\frac{1}{2}[/tex]. The line [tex]l_2[/tex] perpendicular to [tex]l_1[/tex] is [tex]-\frac{2}{1}[/tex].

Work Formula:

Total Work Done = Number of Days [tex]\times[/tex] Efficiency

where Efficiency is inversely proportional to Time Taken.

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Answer:

81 degrees

Step-by-step explanation:

Because of exterior angles u=u-41+u-40

Solve:

u=2u-81

0=u-81

u=81

Answer:

A pair jeans=26$

:. 3 pair jeans=78$

1 t-shirt=10$

No of t-shirt=188$-78$/10$=11

The correct spelling are of the following words is Caucion :caution ,Isle :aisle and Cents :sents

The scent of her perfume is the signifier, and the feminine and romantic association she makes with the scent is the signified.

In linguistics, the concepts of signifier and signified are seen in Saussure's theory of the sign. A sign is formed by the pair signifier/signified. Signifier is a word, an image, anything that has a material form. Signified is the meaning attributed to the signifier by an individual. That means the same signifier can have different signifieds according to the each person. For Mary, the signifier "floral perfume" presents as its signified the "feminine and romantic" feeling. To a different person -  myself, for instance -, a floral perfume does not have the same meaning. I do not see it as romantic or feminine. Instead, because the sweet smell gives me a headache, that has become my signified for it.

The stationary section is on isle 14, one row over from the perfumes and cents.

Hence Caucion :caution

Isle :aisle

Cents :sents

the complete question is

Correct the misspellings in these sentences.

Please use caucion when entering this area as the floor can be slippary.

The stationary section is on isle 14, one row over from the perfumes and cents.

Hence Caucion :caution

Isle :aisle

Cents :sents

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Answer:

Surface area: 502 ft^2

B) Volume
C) Surface area

Step-by-step explanation:

Surface area Formula: 2(lw + wh + lh) = 2(13*15+15*2+13*2)= 502 ft^2

B) Volume because it's asking how much it can hold
C) Surface area because it's asking like how much paint should Cover the thing, not how much it can hold

Answer: 304 Pound of Grapes

Step-by-step explanation:

Sienna has 534 grapes. She eats 18 pounds of grapes.

[tex]534-18[/tex]

[tex]=516[/tex]

She gives 212 pounds of grapes to her brother.

[tex]516-212[/tex]

[tex]=\fbox{304 grapes left}[/tex]

A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.

What are supplementary angles example?

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.

What do you mean by angle bisector?

If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.

The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.

Thus, the black space is to be filled by the angle bisector.

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Answer:

No, they are not the same

Step-by-step explanation:

Mean is simply the average sum of data. When Standard deviation is obtained from the average of the square of data

The supply-demand curve after US removed tariff on imports is provided. The customer surplus is denoted by area A+B+C+D, loss in producer surplus by A and government loss in revenue by C.

When supply is equal to the demand we get the equilibrium quantity produced and equilibrium price.

The initial price P0 is less than the equilibrium price and thus there is excess demand of the product and thus there is import. When tariff is removed price again drops increasing the excess demand and thus more product is imported.

Consumer surplus is the amount the customer saves as price set by the supplier is less than the amount the consumer is ready to pay. As the customer is ready to pay at P0, the customer surplus when price drop to P1 is given by area A+B+C+D.

The loss in producer surplus is denoted by the area A. As the tariff is removed, the loss in revenue for government is denoted by the area C.

--The question is incomplete, answering to the question below--

"The graph at right shows the situation after the U.S. removes a tariff on imports of canned tuna.

Which areas show the gain in consumer surplus?

A. C

B. A+B+C+D

C. A

D. B+C+D

Which area shows the loss in producer surplus?

A. B+C+D

B. A + B

C. A

D. A+B+C+D

Which area shows the loss in government tariff revenue?

A. A

B. C

C. A+B+C+D

D. B+C+D"

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3x - 5y=-9 has a [tex]\frac{-3}{5}[/tex] slope.

A line's steepness can be determined by looking at its slope. To find the slope of a line, you need to have the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 3x - 5y = -9 in this form, you can start by isolating the y term on one side of the equation:

3x - 5y = -9

-5y = -3x - 9

y = (-3/5)x - (9/5)

The slope of the line is therefore -3/5.

The complete question is:-

What is the slope of 3x - 5y =- 9?

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Reflection is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation is not the same.

In mathematics, a reflection is an isometric mapping from a Euclidean space to itself with a set of fixed points called the hyperplane, also referred to as the axis or plane of reflection.

The image created by a reflection is the figure's mirror image in the axis or plane of reflection.

Rotation:

The concept of rotation in mathematics has its roots in geometry.

Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.

So, we can say that flipping a figure over a line is called reflection. Rotation is the process of turning a figure a specific amount around a point.

Therefore, reflection is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation are not the same.

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Answer:

b

Step-by-step explanation:

both sides withdrew

The inequality that can be used to determine v, the minimum number of visits Joshua needs to earn his first free movie ticket is 5.5v + 60 ≥ 245

The minimum number of visits Joshua needs is approximately 34 visits.

5.5v + 60 ≥ 245

Subtract 60 from both sides

5.5v ≥ 245 - 60

5.5v ≥ 185

divide both sides by 5.5

v ≥ 185 / 5.5

v ≥ 33.63636363636363

Approximately,

v ≥ 34

Therefore, the minimum number of visits Joshua needs to earn his first free movie ticket is approximately 34 visits

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When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

The intercept theorem, also referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem, is a crucial concept in basic geometry that discusses the ratios of different line segments that are produced when two intersecting lines are intercepted by a pair of parallels.

It is equivalent to the ratios in similar triangles theorem. It is typically credited to the Greek mathematician Thales. Despite the fact that its first known demonstration may be found in Euclid's Elements, it was known to the ancient Babylonians and Egyptians.

Similarity and the intercept theorem go hand in hand. It is equivalent to the idea of similar triangles in that it may be used to demonstrate both the qualities of similar triangles and the intercept theorem.

Hence, When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

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'5 more than' means that a number is 5 units greater than the original number, using the concept of addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Now, let us understand the meaning.

Let the original number be x.

'5 more than a number' implies x + 5.

This means that the new number, x + 5, is greater than the original number, x, by 5 units. We also have to keep in mind, [tex]x + 5 > x[/tex].

Hence, the final meaning is 5 units greater than the original number.

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Answer: 0 slope; horizontal line

The roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.

The equation x^2 - 3x + 4 = 0 can be factored as (x - 4)(x - 1) = 0.

Therefore, the roots of the equation are x = 4 and x = 1.

To calculate this, we can use the Quadratic Formula:

x = [-b ± Â√(b^2 - 4ac)]/2a

In this equation, a = 1, b = -3, and c = 4

x = [-(-3) ± Â√((-3)^2 - 4(1)(4))]/2(1)

x = [(3) ± Â√(9 - 16)]/2

x = (3 ± Â√(-7))/2

x = (3 ± iÂ√7)/2

Therefore, the roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.

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The inequality could be represented by 59 + 30r ≤ 125

According to the given information

Money charged for first room = $59

Money charged for per additional room = $30

The money that the customer could pay = $125

So

We need to write the inequality to determine the situation

Let the number of carpets be r

Firstly , determining an expression for the cleaner charges

59 + 30*r

Since

The customer cannot pay more than $125  

Hence

According to the given situation

59 + 30r ≤ 125

30r ≤ 66

r ≤ 2.2

The inequality could be represented by 59 + 30r ≤ 125

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Use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.

Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3.

Making points for the graph is simple.

Select a value for the first coordinate, then calculate the second coordinate by evaluating f at that value

To establish if a graph reflects a function, use the vertical line test.

The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.

The graph is not a function if the vertical line crosses it at more than one location.

Therefore, use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.

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For a 60% confidence interval, the number of cis that we expect to contain the true mean is of 60% of the total amount.

The interpretation of a x% confidence interval it is x% likely that the population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

The bounds a and b of the confidence interval are given by the estimate plus/minus the margin of error.

The interpretation also means that out of n samples, the percentage which are expected to contain the true mean is of x, hence the percentage for this problem is of 60%, as it is the confidence level.

The problem is incomplete, hence only the first part could be answered.

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The measure of the angle when a cannonball is shot will be 60°.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

A cannonball is shot with a speed of 90 m/s. Assuming its upward speed at the highest point of its curve is 0 m/s and the flat speed at the highest point of its bend is 45 m/s.

We know that in projectile motion, the horizontal velocity does not change.

Let 'x' be the angle it shot. Then the cosine of the angle x is the ratio of horizontal velocity to the resultant velocity when it is shot. Then we have

cos x = 45 / 90

cos x = 1/2

cos x = cos 60°

x = 60°

The proportion of the point when a cannonball is shot will be 60°.

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Variance's square root is always the standard deviation. √25 thus equals 5.

Saying that the median is 7, the mode is 2, and the variance is squared does not make much sense.

However, it makes sense to state that the data's median, mode, and standard deviation are 7, 2, and 4, respectively.

Thus,

√25 = 5.

Variance's square root is always the standard deviation.

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3 methods used to calculate volume are-

Every physical object takes up space, and you may determine the volume of some of these by counting their individual parts. The volume of objects with straightforward shapes, such as cones, rectangular prisms, sphere, and cylinders, can be determined using this method most easily.

The definition of density is the mass of an object per unit of volume. Therefore, using the equation: If you understand the object's density and can weigh it, you can calculate its volume.

volume = weight / density

You might not be able to precisely gauge an object's physical dimensions if it has an unusual shape.

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Answer: quotient deals with addition and times deal with multiplication

12/(n*4+1)

When plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.

Treat the <, ≤, >, or ≥ sign as a = sign when putting an inequality on a graph.

Graph the equation as a dotted line if the inequality is either < or >. 

Graph the equation as a solid line if the inequality is either ≤ or ≥.

How to Graph Linear Inequalities: Steps

(A) Always begin by separating the variable y from the inequality's left side.

(B) Symbolizing equality instead of inequality is step two.

(C) In the X, Y, XY, XY plane, graph the boundary line from step 2.

(D) The final step is to shade a portion or one side of the borderline.

Therefore, when plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.

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By using fraction, it can be calculated that 416 people choose neither blue nor red as their favorite color.

What is fraction?

Suppose there is a collection and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is called denominator.

This is a word problem on fraction.

Fraction of people choose blue as their favorite color = [tex]\frac{1}{3}[/tex]

Fraction of people choose red as their favorite color = [tex]\frac{2}{7}[/tex]

Fraction of people choose neither red nor blue as their favorite color =

                                                                               [tex]1- (\frac{1}{3}+\frac{2}{7})\\\\1 - (\frac{7 + 6}{21})\\\\1-\frac{13}{21}\\\\\frac{21-13}{21}\\\\\frac{8}{21}[/tex]

Total number of people surveyed = 1092

Number of people choose neither red nor blue as their favorite color =

                                                                                           [tex]\frac{8}{21}\times 1092[/tex]

                                                                                          = 416          

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