Vertex for y=2(x-3)^2 +1

Answer:

Center ( -8, 1 )

Radius ( 13 )

The volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.

The expression for the volume of a bar magnet can be calculated by multiplying its length, width, and thickness.

In this case, the dimensions provided are:

Length = 0.5 in.

Width = 2.25 in.

Thickness = 0.25 in.

To find the volume, we multiply these dimensions together:

Volume = Length × Width × Thickness

= 0.5 in. × 2.25 in. × 0.25 in.

Simplifying this expression, we get:

Volume = 0.28125 in³

Therefore, the volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.

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Answer:

measure of angle 7 + measure of angle 8 = 180°.

Answer:

Mr Kalada's present age is 45 years old

Step-by-step explanation:

Area of shape 1:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 6 × 8

Area of triangle = 24 cm²

Area of shape 2:

Area of Semicircle = πr²/2

Radius of Semicircle = Diameter / 2

Radius of Semicircle = 3 cm

Then,

Area of semicircle = π(3)²

Area of semicircle = 9π cm²

Total Area = Area of semicircle + Area of triangle

Total Area  = (24 + 9π) cm²

Total Area = 52.27 cm² .

Hence Total area of the figure combining triangle and semicircle is 52.27 cm².

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The value of an automobile company's stock fell 5 points over the last month.  The integer that represents the change in the stock's value is -5.

In the context of stock market performance, positive values typically indicate an increase in the stock's value, while negative values indicate a decrease. In this case, since the stock's value fell by 5 points, we assign a negative sign to represent the change.

By convention, negative numbers are used to represent decreases or losses, while positive numbers represent increases or gains. When the stock's value decreases, it is common to use negative integers to signify the change.

In this scenario, a decrease of 5 points is denoted by the negative sign (-) followed by the numerical value 5. Therefore, the integer -5 represents the change in the stock's value.

Using this notation helps provide clarity and consistency in understanding the direction and magnitude of changes in stock prices. It allows investors, analysts, and market participants to communicate and interpret market movements accurately and effectively.

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The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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The area of the triangle whose dimensions are given in a vertices form would be = 9

To calculate the area of the triangle, the formula that should be used is the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2

Where; W=A, X= B, Y = C

Ax= 8

By= -2

Cy= -4

BX= 5

Ay = -8

CX= 3

That is:

= 8(-2--4)+5(-4--8)+3(-8--2)/2

= 16+20-18/2

= 18/2

= 9

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By algebra properties, the simplified form of the trigonometric equation cot² x / (csc x - 1) is  csc x + 1.

In this problem we find the case of a trigonometric equation, whose simplified form must be found. The simplification can be done both by algebra properties and trigonometric formulas. Now we proceed to determine the simplificated form:

cot² x / (csc x - 1)

(csc² x - 1) / (csc x - 1)

[(csc x + 1) · (csc x - 1)] / (csc x - 1)

csc x + 1

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Answer:

B). No two lines are parallel

Step-by-step explanation:

In spherical geometry, there are no parallel lines. This is because any two lines on a sphere will eventually intersect.

Answer: B

Step-by-step explanation:

The coefficients 9 & 6, divided by 3, equal 3 & 2.

For the exponents, if you divide the entire equation by xy, you need to subtract the corresponding exponents of x and y. Subtract the denominator's exponent from the numerator's exponent.

So, for the first part x^8/x^1=x^7

y^2/y^1=y

For the second part: x^3/x=x^2

y^4/y=y^3

So, if you put the coefficients and both parts of the equation together, you get 3x^7y - 2x^2y^3 (answer letter B).

Hope this helped!

Answer:

Let’s solve this problem step by step. Since a + b = 28 and a = 2b + 7, we can substitute the value of a in the first equation to get 2b + 7 + b = 28. Solving for b, we get 3b + 7 = 28, which means 3b = 21 and b = 7. So, the second number is 7.

This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} [/tex]

Now, check the triangle, sin 37° = 3/5

therefore,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) [/tex]

[ convert degrees on right side to radians ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) [/tex]

There are three more possible values as :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} [/tex]

or in decimals :

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167[/tex]

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 2.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = -5.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 8.385[/tex]

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

Hello!:

24/12 - 8

= 2 - 8

= -6

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 100[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 20[/tex]

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

[tex] \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }[/tex]

Solving :

[tex] \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }[/tex]

Step 2: Subtracting 10 on both sides :

[tex] \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }[/tex]

We get ,

[tex] \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }[/tex]

Step 3: Dividing both sides by 5 :

[tex] \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }[/tex]

On cancelling , we get :

[tex] \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar[/tex]

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

The maximum revenue, to the nearest whole dollar, is $180,625 (option c).

To find the maximum revenue, we need to determine the vertex of the quadratic function represented by the revenue equation.

The revenue equation is given as:

R(p) = -4p² + 1700p

The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:

x = -b / (2a)

For the given revenue equation, a = -4 and b = 1700. Plugging these values into the formula, we have:

p = -1700 / (2 × -4)

p = -1700 / -8

p = 212.5

The maximum revenue occurs at p = 212.5.

To find the maximum revenue, we substitute this value back into the revenue equation:

R(p) = -4(212.5)² + 1700(212.5)

R(p) = -4(45256.25) + 361250

R(p) = -181025 + 361250

R(p) = 180625

Therefore, the maximum revenue, to the nearest whole dollar, is $180,625 (option c).

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Using the trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:

(2). x = √116

(3). x = 90

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(1). sinA = 5/13 {opposite/hypotenuse}

cosA = 12/13 {adjacent/hypotenuse}

tanA = 5/13 {opposite/adjacent}

By Pythagoras rule

(2). x = √(4² + 10²)

x = √(16 + 100)

x = √116

(3). 106² = x² + 56²

x² = 106² - 56²

x = √(11236 - 3136)

x = √8100

x = 90

Therefore, using trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;

(2). x = √116

(3). x = 90

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The new coordinates of the triangle after reflecting in the x-axis are:

(3, -1), (3, -3), and (-2, -3).

We have,

The triangle has the coordinates:

(3, 1), (3, 3), and (-2, 3)

Now,

To reflect a point or a shape in the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same.

Let's reflect each of the three given points in the x-axis:

Point (3, 1):

The reflected point in the x-axis will have the same x-coordinate of 3 but with the y-coordinate sign flipped:

Reflected point: (3, -1)

Point (3, 3):

The reflected point in the x-axis will have the same x-coordinate of 3 but with the y-coordinate sign flipped:

Reflected point: (3, -3)

Point (-2, 3):

The reflected point in the x-axis will have the same x-coordinate of -2 but with the y-coordinate sign flipped:

Reflected point: (-2, -3)

Therefore,

The new coordinates of the triangle after reflecting in the x-axis are:

(3, -1), (3, -3), and (-2, -3).

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The notation which is the most appropriate notation when calculating conditional probabilities is option B.

The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."

In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.

Thus option B is correct.

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The total cost of producing the additional units is $767.50.

In order to determine the total cost of producing 10 additional units assuming 2 units are currently being produced, we would have to integrate the marginal cost function for this handbag manufacturer with respect to x, and over the interval [10, 2].

Based on the information provided above, the marginal cost function for this handbag manufacturer is given by this function;

C'(x) = 0.046875x² − x + 100

₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x² − x + 100)dx

₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x²)dx − ₂∫¹⁰(x)dx + ₂∫¹⁰(100)dx

₂∫¹⁰C'(x)dx = 0.046875x³/3|¹⁰₂ - x²/2|¹⁰₂ + 100x|¹⁰₂

₂∫¹⁰C'(x)dx = 0.015625(10³ - 2³) - 1/2(10² - 2²) + 100(10 - 2)

₂∫¹⁰C'(x)dx = 0.015625(1000 - 8) - 0.5(100 - 4) + 100(8)

₂∫¹⁰C'(x)dx = 0.015625(992) - 0.5(96) + 800

₂∫¹⁰C'(x)dx = 15.5 - 48 + 800

₂∫¹⁰C'(x)dx = $767.50

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Derek is saving money for the down payment on a used car. So far, he has saved $200. His parents have said they help him put aside money, they will pay him 6% interest each month on the money Derek has saved. It will take Derek approximately 28 months to save at least $1,000 for the down payment on the used car if the only additions to his savings account are his parents' interest payments.

Month Process

0 Derek saves $200 (initial savings)

1 Derek receives 6% interest on $200 (interest = $200 * 0.06 = $12), total savings = $200 + $12 = $212

2 Derek receives 6% interest on $212 (interest = $212 * 0.06 = $12.72), total savings = $212 + $12.72 = $224.72

3 Derek receives 6% interest on $224.72 (interest = $224.72 * 0.06 = $13.48), total savings = $224.72 + $13.48 = $238.20

4 Derek receives 6% interest on $238.20 (interest = $238.20 * 0.06 = $14.29), total savings = $238.20 + $14.29 = $252.49

5 Derek receives 6% interest on $252.49 (interest = $252.49 * 0.06 = $15.15), total savings = $252.49 + $15.15 = $267.64

6 Derek receives 6% interest on $267.64 (interest = $267.64 * 0.06 = $16.06), total savings = $267.64 + $16.06 = $283.70

It will take Derek approximately 28 months to save at least $1,000 for the down payment on the used car if the only additions to his savings account are his parents' interest payments.

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The new height above sea level would be Option (C) 3980m.

New sea-level = Previously given sea level + 20m

Given,

Height above sea previously = 4000m

Increase in sea level = 20m

Now, since there has been a rise in sea level due to global warming the distance between the previous 4000m mark and the sea level would decrease. This shall now be less than 4000m. The distance/height would reduce by 20m. It can also be observed that the distances below the sea level would increase due to a rise in the sea level mark.

∴ New height above sea level = 4000m - 20m

                                                 = 3980m.

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Answer: A

Step-by-step explanation: 32.07 cm^2

The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

The unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.

The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.

The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.

If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.

Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

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The meaning of "The field of a relation R" is a constraint on the values that can be stored in that attribute.

We are given that;

The statement The field of a relation R

Now,

According to the web results, the field of a relation R is the set of all values that appear in the relation R. In other words, it is the union of all the attributes (columns) of R. For example, if R is a relation with attributes A, B, and C, then the field of R is the set of all values that appear in A, B, or C. The field of R can also be denoted by F.

The field of a relation is different from the domain of an attribute, which is the set of all possible values that an attribute can take. For example, if A is an attribute that can only take integer values, then the domain of A is the set of all integers. The domain of A may be larger than the field of A, which is the set of all values that actually appear in A. The domain of an attribute defines a constraint on the values that can be stored in that attribute.

Therefore, by the domain the answer will be a constraint on the values that can be stored in that attribute.

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Answer:

There are 6 countries with more than 60 confirmed cases

Step-by-step explanation:

- Draw your stem and leaf plot

-There is a stem without a leaf (There are no values in this class)

-Count the values in the stem and leaf plot and ensure they are 15. Each value represents the number of confirmed case in a county.

There are six numbers greater than 60 which are 62,63,63,67,65 and 97

Hence, there are 6 countries which have more than 60 confirmed cases

The required median is 110- 120 and the upper quartile of the scores is 110-120.

Given that, the data from the histogram is

CI                 |             f

80-90          |            5

90-100,        |            3

100-110,        |            4

110-120,        |            4

120-130,       |             3

130-140,       |             3

140-150,       |             2

150-160        |             2

To find the median and upper quartile of the given scores, make the cumulative frequency table.

The cumulative frequency table is given below.

CI                 |             f               |             cf            

80-90          |            5               |             5

90-100,        |            3               |             8

100-110,        |            4               |            12

110-120,        |            4               |             16

120-130,       |             3               |             19

130-140,       |             3               |             22

140-150,       |             2               |             24

150-160        |             2               |             26

N = 26.

The median is the N/2 th score when N is even.

Median  = 13th score = 110-120 scores

To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.

Upper quartile = (3/4 x 26)th score.

Upper quartile = 19.5th  score.

The upper quartile score range is 110 - 120.

Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.

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Answer:

Step-by-step explanation:

ll hypothesis The critical value for this test is 9.488. Based on the test statistic of 1.358, we fail to reject the null hypothesis that the amount of smoking is independent of seat belt use. In other words, there is not enough evidence to support the claim that seat belt use and smoking habits are related.

Personal Note:

You really need to study, or you will end taking summer courses. trust me school isn't that easy and one time I failed I took summer courses but then I passed these summer courses with god's help. so please focus on your studys.

The missing sides of the triangle are

x = 6.32

y = 7.48

z = 11.83

The missing side x is calculated using similar triangles rules as below

x / 10 = 4 / x

cross multiply gives

x² = 40

x = √40 = 6.32

Other sides will solved by Pythagoras theorem.

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let y be the required distance

y² = 6.32² + 4²

y² = 55.94

y = √55.94

y = 7.48

z² = 6.32² + 10²

z² = 139.94

z = √139.94

z = 11.83

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