Identify the key features of the parabola that is formed by the equation.
F(x)=-x2+4x+12

The x-intercepts

The inverses of g and h give:

Here we have the function:

g(x) = -2x + 3

If its inverse is g⁻¹(x), then the composition must be equal to the identity, so we can write:

g( g⁻¹(x)) = x

-2*g⁻¹(x) + 3 = x

g⁻¹(x) = (x - 3)/-2

g⁻¹(x) = - (x - 3)/2

Now we also want to get:

(g *g⁻¹)(-7)

That is the product of the two functions evaluated in -7.

(g *g⁻¹)(-7) = (-2*-7 + 3)*-(-7 - 3)/2 = 85

Now for h(x), we want to get h⁻¹(9)

By looking at the table, we can see that h(-7) = 9

Then the inverse is h⁻¹(9) = -7

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Answer:

D. -7.2y - 49.5  is the correct answer.

Step-by-step explanation:

Distributing the 3 to the terms inside the parenthesis, we get:

3(-2.4y - 16.5) = -7.2y - 49.5

-2.4 x 3 = -7.2

16.5 x 3 = 49.5

so the expression that is equivalent to 3(-2.4y - 16.5) is -7.2y - 49.5

hope this helps

The True statement is parallelogram DEFG is the pre-image because it is not the result of the transformation.

What is Transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

Parallelogram DEFG is transformed to parallelogram VSTU.

It changes from parallelogram DEFG to parallelogram VSTU.

According to how it is said, DFEG is the initial parallelogram or pre-image that is changed to create VSTU, VSTU is changed from DEFG.

The following is an accurate statement concerning the transformation:

As the parallelogram DEFG is not the outcome of the transformation, it is the pre-image.

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The correct Question attached here are as follow:

(Q). Parallelogram DEFG is transformed to parallelogram VSTU. Which statement about the transformation is true?

Answer:

She needs to win 6 more consecutive tournament games.

Step-by-step explanation:

[tex] \frac{3 + x}{4 + x} = \frac{9}{10} [/tex]

[tex]10(3 + x) = 9(4 + x)[/tex]

[tex]30 + 10x = 36 + 9x[/tex]

[tex]x = 6[/tex]

The angle measure of the triangle are;

m< A = 53 degrees

m<B = 90 degrees

m<C = 37 degrees

It is important to note that the sum of the angles in a triangle is equal to 180 degrees

From the diagram shown, we have that;

m< A = 4x + 1

m< B = 7x - 1

m< C = 3x - 2

Equate the angles, we have;

4x + 1 + 7x - 1 + 3x - 2 = 180

collect the like terms, we get

14x = 180 + 2

14x = 182

make 'x' the subject

x = 13

Then, m< A = 53 degrees

m<B = 90 degrees

m<C = 37 degrees

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For the given diameter d=20 cm, the radius is 10 cm.

What is radius?

Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface respectively. It is a fundamental measurement used in geometry and is denoted by the letter "r". The radius is half the diameter of a circle or sphere, and it is used to calculate important properties of the circle or sphere, such as its circumference, area, and volume.

If d = 20 cm, then d represents the diameter of a circle.

To find the radius (r) of the circle, we divide the diameter by 2:

r = d/2 = 20 cm/2 = 10 cm

Therefore, for diameter d=20 cm, the radius of the circle is 10 cm.

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Answer:

3yz^3 + 1

Step-by-step explanation:

let b = the binomial we are looking for.

divide and receive your answer

Answer: x-3=0

Step-by-step explanation: With the equation it is basic algebra. So right now the equation is x-3=0. You will go plus 3, plus 3 on both sides. That would get rid of your negative 3 and make your 0, 3. So what you should have left is, x=3.

Answer:9

Step-by-step explanation: it’s nine because 6×9 = 54

a) the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

b) the probability of guessing a number less than 7 is 6/10 or 3/5.

c) the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

Since the marble is replaced after the first draw, the probability of drawing a yellow marble is 6/18 = 1/3.

Similarly, the probability of drawing a blue marble on the second draw is 8/18 = 4/9.

Therefore, the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

There are 6 numbers less than 7 (1, 2, 3, 4, 5, 6) and 10 total numbers, so the probability of guessing a number less than 7 is 6/10 or 3/5.

Since the marble is not replaced after the first draw, the probability of drawing a white marble is 4/18 = 2/9.

The probability of drawing a red marble on the second draw, given that a white marble was drawn first, is 6/17.

Therefore, the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

Hence, a) the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

b) the probability of guessing a number less than 7 is 6/10 or 3/5.

c) the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

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Answer:

17 - a

Step-by-step explanation:

1. Open parentheses: 25 - 2 x 4-a

2. Follow the Order of Operations to simplify:

-PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction):

- 25-2 x 4 - a

- 25 - 8 - a

- 17 - a

The length of the segment indicated in the circle is 12 units

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

The circle

Since the radius is perpendicular to the chord and intersects the chord at its midpoint, then the radius will divide the chord into two equal segments.

Using the above as a guide, we have the following:

x = 12

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Farmers Products Inc. should disclose a contingent liability in its 2016 financial statements for the lawsuit filed against them due to a collision caused by one of their delivery truck drivers.

Based on the information provided, it appears that as of the date of the financial statements (March 3, 2017), Farmers Products would need to disclose a contingent liability related to the lawsuit filed against them by the other driver.

A contingent liability is a potential liability that may arise from past events but the outcome is uncertain and will depend on future events. In this case, the lawsuit filed against Farmers Products by the other driver represents a potential liability that may result in damages being awarded against the company.

Under accounting standards, a contingent liability should be disclosed in the notes to the financial statements if it is probable that a liability has been incurred and the amount of the liability can be reasonably estimated. In this case, it is probable that Farmers Products may be liable for damages resulting from the accident and the estimated damages fall within a reasonable range of $6,000 to $10,000.

Therefore, in the notes to its 2016 financial statements, Farmers Products should disclose the existence of the lawsuit and the potential liability that may result. The disclosure should also include an estimate of the potential damages, if any, and any other relevant information about the lawsuit.

The question is incomplete; please see below for the whole question -

On December 4, 2016, Dan Johnson, a Farmers Products Inc. delivery truck driver, ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other car filed a lawsuit against Farmers Products for vehicle damages. Damage to this vehicle was estimated to be between $6,000 and $10,000, with no value within that range being more likely than any other. Farmers Products' 2016 financial statements were released on March 3, 2017.

1. Prepare the disclosures and/or journal entries that Farmers Products should include in its financial statements for the fiscal year ending December 31, 2016.2. How would the disclosures and/or journal entries alter if Farmers Products employed IFRS versus US GAAP?

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The statement can be read as "If the sky is clear, then the plane is not on time."

What is the conditional statement?

A conditional statement is a logical statement that has two parts: an antecedent (also called a hypothesis) and a consequent (also called a conclusion). The statement asserts that if the antecedent is true, then the consequent must also be true.

The statement "Q -> ~P" is an example of a conditional statement in symbolic logic.

In this case, Q represents "The sky is clear" and ~P represents "The plane is not on time" (the tilde symbol ~ negates the truth value of P).

The arrow symbol -> means "implies" or "if...then". Therefore, the statement can be read as "If the sky is clear, then the plane is not on time."

In other words, the statement is saying that if the sky is clear, then it is not possible for the plane to be on time.

This is because the statement implies that the plane being on time is dependent on the sky not being clear. So if the sky is clear, it means that the conditions for the plane to be on time are not present, and therefore the plane is not on time.

It's worth noting that the statement does not say anything about what happens if the sky is not clear.

It's possible that the plane could still be on time even if the sky is not clear, according to this statement.

Hence, the statement can be read as "If the sky is clear, then the plane is not on time."

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Answer: If 60% of the members are males, then 40% of the members are females. We can calculate the number of males and females as follows:

Number of males = 60% of 200 = 0.6 * 200 = 120

Number of females = 40% of 200 = 0.4 * 200 = 80

To find out how many percent more males there are than females, we can use the following formula:

% more males = (number of males - number of females) / number of females * 100%

Substituting the values we found, we get:

% more males = (120 - 80) / 80 * 100% = 50%

Therefore, there are 50% more males than females in the club.

Step-by-step explanation:

1. x + 30 = 98 equation says that Jerome's total earnings y for the day is equal to his wages.

2. y = 68 + 30 equation says that Jerome's total earnings y for the day is equal to his wages.

A statement that affirms the equality of two expressions connected by the equals symbol "=" is known as an equation. For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

There are different ways to represent this situation algebraically, but here are two possible equations:

1. Let x be the amount of money Jerome earns in wages, then the equation can be written as:

x + 30 = 98

This equation says that the sum of Jerome's wages x and his tips of $30 is equal to his total earnings of $98 for the day.

2. Alternatively, we can let y be the total amount of money Jerome makes for the day (including tips), then we can write:

y = 68 + 30

This equation says that Jerome's total earnings y for the day is equal to his wages of $68 plus his tips of $30.

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Thus the shaded area of the given rectangular figure is found as : 60 sq. ft.

Area of rectangle = length x width

Complete rectangular area = 12 ft x 7 ft

Complete rectangular area = 84 sq. ft.

Inner rectangular area = 8 ft x 3ft

Inner rectangular area = 24 sq. ft

Shaded area = Complete rectangular area - Inner rectangular area

Shaded area = 84 sq. ft. - 24 sq. ft

Shaded area = 60 sq. ft

Thus the shaded area of the given rectangular figure is found as : 60 sq. ft.

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Complete question:

find the shaded area of the given rectangular figure.

The answer of the given question based on the graph is  the coordinates of point B are (-8, 4).

A quadrant is one of four regions into which coordinate plane is divided by x-axis and y-axis. The x-axis is horizontal axis and the y-axis is vertical axis. The quadrants are labeled using Roman numerals, starting in upper right quadrant and moving counterclockwise.

Since point B is 11 units away from point A, we know that the distance between them is:

d = √((x2 - x1)² + (y2 - y1)²) = 11

where (x1, y1) = (-3, -5) are the coordinates of point A, and (x2, y2) are the coordinates of point B.

We also know that point B is located in quadrant 2, which means that its x-coordinate is negative and its y-coordinate is positive.

To find the coordinates of point B, we can use the distance formula and the fact that point B is in quadrant 2:

d = √((x2 - x1)² + (y2 - y1)²) => 11 = √((x2 - (-3))² + (y2 - (-5))²)

Since point B is in quadrant 2, its x-coordinate is negative and its y-coordinate is positive:

x2 < 0, y2 > 0

We can choose any values for x2 and y2 that satisfy these conditions and the distance formula equation. Let's choose x2 = -8 and y2 = 4:

11 = √((-8 - (-3))² + (4 - (-5))²)

11 = √(25 + 81)

11 = √106

Therefore, coordinates of point B is (-8, 4).

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Answer: 30.4

Step-by-step explanation:

Let's assume that Terrell attends x number of classes in a month. Then, the total cost of the first membership plan would be:

Cost of the first membership plan = $30 + $1 * x

Similarly, the total cost of the second membership plan would be:

Cost of the second membership plan = $15 + $4 * x

As per the problem statement, both membership plans cost the same when Terrell attends a certain number of classes in a month. So, we can equate the above two expressions and solve for x:

$30 + $1 * x = $15 + $4 * x

$2 * x = $15

x = 7.5

Since the number of classes cannot be a fraction, we can round up to the nearest integer, which is 8. Therefore, Terrell needs to attend 8 classes per month to make both membership plans cost the same.

To find the total amount, we can substitute x = 8 in either of the above expressions:

Total amount = $30 + $1 * 8 = $38

Therefore, Terrell needs to attend 8 classes per month, and the total amount would be $38.

We can use the formula for compound interest to calculate the amount of money we will have at the end of 3 years:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money we will have at the end of 3 years

P = the principal (the initial amount we start with)

r = the interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values, we get:

A = 5000(1 + 0.045/12)^(12×3)

A = 5000(1.00375)^36

A ≈ $5,622.16

Therefore, we will have approximately $5,622.16 at the end of 3 years.

Answer:

$8.73 --> 8.73

Step-by-step explanation:

We need to add their costs together to find the total price of the three items.

The cost of Bagels is given as $2.17.

The cost of Cream Cheese is given as $2.82.

The cost of Raisins is given as $3.74.

Adding these three costs together gives us:

$2.17 + $2.82 + $3.74 = $8.73

Therefore, the total price of the three items is $8.73.

Thus, equation of line in slope intercept form: y = 5x + 3.

One approach to calculating the equation of a straight line is the slope-intercept form. The two point form, point-slope form, plus intercept form are the further approaches.

Passing points - (-2, -7)

slope m = 5

The standard slope intercept form for equation of line:

y = mx + c

m is the slope and c is the y-intercept.

Put the given values and find c.

-7 = 5(-2) + c

c = -7 + 10

c = 3

Thus, equation of line in slope intercept form:

y = 5x + 3

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personal experience based .

maths gives us a way to understanding patterns ,define relationships , and predict the future.

One of my friends wanted to host a dinner party at her house, and she asked me to help her plan the menu. She told me that she was expecting around 10 guests, and she wanted to make sure that she had enough food for everyone. The difficult part was that she had a limited budget and wanted to keep the cost of ingredients low.

Mathematical approach:

To help my friend plan the menu, I used math to estimate the amount of food we needed to buy. I researched online to find the average portion sizes for the dishes we were planning to serve and calculated the total amount of ingredients needed based on the number of guests. Then, I compared the cost of the ingredients at different grocery stores to find the best deals and estimated the total cost of the meal.

Outcome:

By using math, we were able to plan a menu that was within my friend's budget and had enough food for all the guests. We were also able to find the best deals on ingredients, which helped us save money.

Approach for next time:

Next time, I would try to involve my friend more in the mathematical calculations to make sure she understands how to plan a meal within her budget. I would also consider making a list of alternative dishes that we could serve in case we were unable to find a certain ingredient or if it was too expensive.

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Answer:

[tex]\frac{24}{5}[/tex]

Step-by-step explanation:

We Know

The test has 6 questions.

Each question has 5 answers.

What would be the probability of getting at least one question wrong?

Each question can only have one correct answer, so the probability of getting a wrong answer for each question is [tex]\frac{4}{5}[/tex]

There are 6 questions on the test, so we take

[tex]\frac{4}{5}[/tex] x 6 = [tex]\frac{24}{5}[/tex]

So, the probability of getting at least one question wrong is [tex]\frac{24}{5}[/tex]

The bar diagram is attached and the equation is amount of trail mix in each bag = x/6

Let's say that Aarón has a total of "x" amount of trail mix.

To divide this equally into 6 bags, each bag will have "x/6" amount of trail mix.

We can illustrate this using a bar diagram as follows:

See attachment

Here, the total amount of trail mix "x" is divided equally into 6 parts, with each part representing "x/6" amount of trail mix.

The equation to represent this is:

x/6 = amount of trail mix in each bag.

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Answer:

The answer is 4.5 miles.

Step-by-step explanation:

To solve this problem, we must remember that the shortest distance between two points lies along a straight line. In this case, this straight line is the hypotenuse of the triangle formed with the 2 mile and 4 mile legs. As a result, we can use the Pythagorean Theorem to find the distance between Lisa's house and the pool.

Pythagorean Theorem:

a² + b² = c²

2² + 4² = c²

c² = 4 + 16

c = √20

c = 4.5 miles (rounded to the nearest tenth)

Therefore, the shortest distance between Lisa's house and the pool is 4.5 miles.

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[tex]\blue{\huge {\mathrm{PYTHAGOREAN \; THEOREM}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

*Please read and understand my solution. Don't just rely on my direct answer*

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

We can use the Pythagorean theorem to find the shortest distance between Lisa's house and the pool.

Let's call the distance we're trying to find "d". We know that Lisa's school is 2 miles north of her house and the pool is 4 miles east of her school, so we can draw a triangle with the following sides:

Using the Pythagorean theorem, we can find d:

[tex]\qquad\qquad\qquad\begin{aligned}\sf c^2& =\sf a^2 + b^2\\\sf d^2& =\sf 2^2 + 4^2\\\sf d^2& =\sf 4 + 16\\\sf d^2& =\sf 20\\\sf d& =\sf \sqrt{20}\\\bold{d}& =\sf \boxed{\bold{\: 4.5\: miles\:}}\end{aligned}[/tex]

[tex]\\[/tex]

Therefore, the shortest distance between Lisa's house and the pool is 4.5 miles (rounded to the nearest tenth of a mile).

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]

If the measure of m∠A = 61°, the angle measure m∠B = 29°.

What is an angle?

Since ΔABC is a right-angled triangle with C as the right angle, we can use the trigonometric ratios to find the missing side lengths and angles.

Given that A = 61°, we know that m∠B = 180° - 90° - 61° = 29° (by the angle sum property of a triangle).

Now, we can use the trigonometric ratios to find the side lengths. Let's start with side AC = x.

From the definition of the sine ratio, we have:

sin(A) = opposite/hypotenuse

sin(61°) = z/x

Therefore, we have:

x = z/sin(61°)

Similarly, from the definition of the cosine ratio, we have:

cos(A) = adjacent/hypotenuse

cos(61°) = y/x

Therefore, we have:

x = y/cos(61°)

Since both expressions equal x, we can set them equal to each other and solve for z:

z/sin(61°) = y/cos(61°)

z = y*tan(61°)

Finally, we can use the Pythagorean theorem to find the length of side BC:

y² = x² - z²

y² = (y/cos(61°))² - (y*tan(61°))²

Simplifying, we get:

y = x*cos(61°)

So, the lengths of the sides are:

AC = x = z/sin(61°)

BC = y = x*cos(61°)

And the missing angle is:

B = 29°

What is trigonometric ratio?

In mathematics, a trigonometric ratio is a ratio of the lengths of two sides in a right-angled triangle. The three primary trigonometric ratios are:

Sine (sin) = Opposite / Hypotenuse

Cosine (cos) = Adjacent / Hypotenuse

Tangent (tan) = Opposite / Adjacent

In these ratios, the hypotenuse is the longest side of the triangle, and it is always opposite to the right angle. The opposite side is the side opposite to the angle of interest, and the adjacent side is the side that is adjacent to the angle of interest (but not the hypotenuse).

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Complete question is: If the measure of m∠A = 61°, the angle measure m∠B = 29°.