A TV is 20% off the original price amount is $180. What is the original amount?​

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer:

Step-by-step explanation:

30+-60+-90=?

30+60=90

Answer:

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is √3 times smaller than the hypotenuse.

Let x be the length of the hypotenuse, then the side opposite the 60° angle is 6√3. Therefore, we have:

x/2 = 6√3/√3

Simplifying the right side, we get:

x/2 = 6

Multiplying both sides by 2, we get:

x = 12

So the length of the hypotenuse is 12.

To find the length of the side opposite the 30° angle, we use the fact that it is half the length of the hypotenuse:

x/2 = 12/2 = 6

So the length of the side opposite the 30° angle is 6.

Answer:

the answer is c because i took the k12 quiz

Step-by-step explanation:

The correct division equation that represents the relationship between the numbers 0.7 and 0.07 is:

B. 0.07/ 100 = 0.7

Let's break down the given decimals and the options to determine which division equation represents the relationship between the numbers 0.7 and 0.07.

1. The number 0.7:

This number represents seven-tenths, which can also be written as \( \frac{7}{10} \). It's equivalent to the fraction \( \frac{70}{100} \).

2. The number 0.07:

This number represents seven-hundredths, which can be written as \( \frac{7}{100} \).

Now let's consider the options:

A. \(0.7 \div 100 = 0.07\)

This equation is saying that 0.7 (seven-tenths) divided by 100 equals 0.07 (seven-hundredths). However, this is not correct because dividing seven-tenths by 100 would result in a much smaller decimal than 0.07.

B. \(0.07 \div 100 = 0.7\)

This equation is saying that 0.07 (seven-hundredths) divided by 100 equals 0.7 (seven-tenths). This is the correct relationship because dividing seven-hundredths by 100 does indeed result in seven-tenths.

C. \(0.7 \div 10 = 0.07\)

This equation is saying that 0.7 (seven-tenths) divided by 10 equals 0.07 (seven-hundredths). This is not correct because dividing seven-tenths by 10 would result in 0.07, not 0.007.

D. \(0.07 \div 10 = 0.7\)

This equation is saying that 0.07 (seven-hundredths) divided by 10 equals 0.7 (seven-tenths). This is not correct because dividing seven-hundredths by 10 would result in 0.007, not 0.7.

So, option B (\(0.07 \div 100 = 0.7\)) is the correct division equation that represents the relationship between the numbers 0.7 and 0.07. It correctly shows that dividing 0.07 by 100 gives us 0.7.

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Answer:

1. 7/8

2. 1/2

Step-by-step explanation:

y2-y1 /x2-x1 = slope

1. points: (-4,-4) and (4,3)

M = (3+4)/(4+4)

M=7/8

2. points: (-5,-3) and (3,1)

M = (1+3)/(3+5)

M = 4/8 or 1/2

Answer:

0.4

\(\frac{2}{5}\)

Step-by-step explanation:

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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The formula for the nth term of the geometric sequence is given as follows:

\(a_n = 7(-3)^{n - 1}\)

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The formula for the nth term of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

The first term of the sequence is given as follows:

\(a_1 = 7\)

Each term is the previous term multiplied by -3, hence the common ratio is given as follows:

q = -3.

Thus the formula for the sequence is given as follows:

\(a_n = 7(-3)^{n - 1}\)

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Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole

Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.

It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.

To calculate the proportion of red marbles in each sample

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Here, m∠GHI=72° and m∠LMN=108°. Therefore, option B is the correct answer.

Given that, m∠GHI=6x° and m∠LMN=9x°.

We need to find the measure of each angle.

Supplementary angles are thus a set of angles that complete each other to form 180°. Supplementary angles are those angles that sum up to 180°.

Now, 6x°+9x°=180°

⇒15x°=180°

⇒x°=12°

Thus, m∠GHI=6×12°=72° and m∠LMN=9×12°=108°.

Therefore, option B is the correct answer.

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I would use a chart to solve this problem.

This is a good wya to organize your information.

Down the left side, list the people involved.

I put Bob first and the mom second but the order doesn't matter.

Since Bob's mom is 3 times older than Bob, we can represent

Bob's age now as x and Bob's mom's age now as 3x.

Bob's age in 12 years will be x + 12 and Bob's mom's

age in 12 years will simply be 3x + 12.

Since the second sentence starts with in 12 years,

we will be using the information from our second column.

In 12 years, Bob's mom's age, 3x + 12, will be,

equals, twice of her son's age, 2(x + 12).

Solving from here, we find that x = 12.

This means that Bob's age now is 12 and his mom is 36.

The chart is attached below.

Answer:

12 and 36 = bob is 12 and bob's mother is 36

The function y = x^2 - 10x + 2 is written in vertex form as y = (x - 5)^2  - 23.

We are given a quadratic function:

y = x^2 - 10x + 2

We need to rewrite the function in vertex form.

We can see the coefficient of x is 10.

So, we will add and subtract the square of half that.

So, find the square of half of 10, and we will get;

(10 / 2)^2 = 100 / 4 = 25

add and subtract the square of half of 10 from the given function, we will get;

y = x^2 - 10x + 2 + 25 - 25

arrange the expression, we will get;

y = (x^2 - 10x + 25) + 2 -25

write the expression in parentheses as a square, and simplify the constant, we will get;

y = (x - 5)^2  - 23

So, in the vertex form the function is written as y = (x - 5)^2  - 23.

Thus, the function y = x^2 - 10x + 2 is written in vertex form as y = (x - 5)^2  - 23.

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The value of 12x in the expression is 10

You multiply 5 = 6x  by 2 to get 12x

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

2x + 5 = 8x

You subtract 2X from each side to get

5 = 6x

Then multiply both sides by 2

This gives

10 = 12x

So, we have

12x = 10

Why do you multiply both sides by 2

You multiply by 2 because the question requests for the value of 12x

Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x

i.e. 6x * 2 = 12x

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The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Times

s = d/t

d = st

The value of 's' is given as,

s = 828 / 9

s = 92 feet per second

Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.

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Answer:

Step-by-step explanation:

The zeros are where the graph intersects the x-axis

x = 0

x = 2

x = 4

------------------------

Extra Credit

Note x = 2 is a double zero since it touches, but does not cross the x-axis

The equation is

y = -x(x - 2)²(x - 4)

Answer:

140 students......

Step-by-step explanation:

Plz mark brainliest thanks

The number of students 3(1/2) buses can hold is 140 students.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

The number of students the bus can hold = 40

This can be written as,

1 bus = 40 students

Multiply 7/2 on both sides.

3(1/2) = 7/2

7/2 buses =  7/2 x 40 students

3(1/2) buses = 140 students

Thus,

There are 140 students.

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Answer:

not 36 but 64.8

Step-by-step explanation:

filler filler filler filler

Answer:20%

Step-by-step explanation:

Convert fraction (ratio) 36 / 180 Answer: 20%

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Considering the descriptions, angle CEB is found to be 93 degrees

Angle CEB is calculated by investigating the sketch attached

From the sketch, angle CEB and angle AEC are supplementary angles

and angle AEC is given to be 87 degrees.

Supplementary angles are angles that have their sum equal to 180 degrees.

hence In the problem, we have that

angle CEB + angle AEC = 180 degrees

where

angle AEC = 87.

substituting the value into the equation will result to

angle CEB + 87 = 180

angle CEB = 180 - 87

angle CEB = 93 degrees

We can therefore say that angle CEB = 93 degrees

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Answer:

  2√34 ≈ 11.66 units

Step-by-step explanation:

The distance between two points is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

__

For your points, the distance is ...

  d = √((3 -(-7))² +(0 -6)²) = √(10² +(-6)²) = √(100 +36) = 2√34

The distance between the points is ...

  2√34 ≈ 11.66 . . . . units

_____

Additional comment

The distance formula is based on the Pythagorean theorem. It models the distance as the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates of the points.

Answer: $8000 is invested for 6 years

Step-by-step explanation:P=$3,000 r= 7%= 0.07 t= 4 n= 2

The measure of the largest exterior angle of the polygon in discuss is; 100°.

It follows from the task content that the measure of the largest exterior angle of the polygon be determined.

Since the sum of all exterior angles of a polygon is equal to 360°;

x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°

36x° = 360°

x = 10

Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.

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There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

\(1+\cos x\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric Identities}\\\\$\csc \theta=\dfrac{1}{\sin \theta}\\\\\\\cot \theta=\dfrac{\cos \theta}{\sin\theta}\\\\\\\cos^2 \theta + \sin^2 \theta = 1$\\\end{minipage}}\)

\(\begin{aligned}\implies \dfrac{ \sin x}{ \csc x - \cot x} & = \dfrac{ \sin x}{\dfrac{1}{\sin x} - \dfrac{\cos x}{ \sin x}}\\\\& = \dfrac{ \sin x}{\dfrac{1 - \cos x}{\sin x}}\\\\& = \sin x \times \dfrac{\sin x}{1 - \cos x}\\\\& = \dfrac{\sin^2 x}{1-\cos x}\\\\& = \dfrac{1-\cos^2x}{1-\cos x}\\\\& = \dfrac{(1-\cos x)(1+ \cos x)}{1-\cos x}\\\\& = 1 + \cos x\end{aligned}\)

Answer:

y = 8x + 13

Step-by-step explanation:

slope-intercept form: y = mx + b

Given equation: \(y = -\frac{1}{8}x -2\)

Second equation: unknown

Slope: unknown

Given point: (-2, -3)

When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is \(-\frac{1}{8}\), the slope of the line perpendicular to it is 8.

Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:

y = mx + b

-3 = 8(-2) + b

-3 = -16 + b

13 = b

The y-intercept is 13.

Now that we know the slope and the y-intercept, we can write the equation:

y = 8x + 13

Hope this helps :)