Question 10 of 10
What is tan 60°?
4
60⁰
2
90⁰
30⁰
√3
2
OA. 3
O B. 7/3
O. C. 1
O'D. √3
O E.
E. √3
OF. √3
2

Answer:

32 water bottles

Step-by-step explanation:

8x=425-175

425-175=250

250 is how much more they need.

8x=250

x=31.25

You can't have half of a bottle... so round up to at least 32 water bottles

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B) Rounded to the nearest dollar, each employee would receive $ 209.

Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:

A)

Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B)

Therefore, rounded to the nearest dollar, each employee would receive $ 209.

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Answer:

y=200/9. x= 329/9

Step-by-step explanation:

3x=-43-3y; x=-43/3-y. 5(43/3-y)-8y=5; y=200/9. x= 329/9

Answer:

Answer: (second option) (-4,1)

Step-by-step explanation:

Transformations of Points and Shapes

The image shows a trapezoid ABCD where point A has coordinates (-4,1).

The following transformations are performed:

Reflection over the y-axis: If a point (x,y) is reflected over the y-axis, it becomes (-x,y). Thus point A becomes A'=(4,1)

Reflection over the x-axis: If a point (x,y) is reflected over the x-axis, it becomes (x,-y). Thus point A' becomes A''=(4,-1)

Rotation 180°: If a point (x,y) is rotated 180°, it becomes (-x,-y). Thus point A'' becomes A'''=(-4,1)

Answer: (second option) (-4,1)

Spencer has a bag with 10 marbles. There are 6 white marbles and 4 black marbles.

Spencer picks a marble at random.

Write as a decimal the probability of Spencer picking a black marble

4 Black Marbles

+

6 white Marbles

=10

THE ANSWER IS :

4/10

Lowest Term :

2/5

As a Decimal:

The probability of Spencer picking a black marble is approximately 0.4 or 40%.

To find the probability of Spencer picking a black marble, we can use the formula for probability:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the number of favorable outcomes (picking a black marble) is 4, as there are 4 black marbles in the bag. The total number of possible outcomes (picking any marble) is 10, as there are 10 marbles in total.

Now, we can calculate the probability:

Probability = 4 / 10

Simplifying the fraction, we get:

Probability = 2 / 5

To express the probability as a decimal, divide the numerator (2) by the denominator (5):

Probability = 2 ÷ 5

Probability ≈ 0.4

The probability represents the likelihood of an event occurring, and in this case, it tells us the chance of Spencer picking a black marble out of the 10 marbles in the bag.

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The constant income stream that needs to be invested over 9 years at a continuously compounded interest rate of 6% per year to provide a present value of $3000 is approximately $1746.20.

To determine the constant income stream that needs to be invested over a period of 9 years at an interest rate of 6% per year compounded continuously to provide a present value of $3000, we can use the formula for continuous compound interest:

P = A * e^(rt)

Where P is the present value, A is the constant income stream, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time period.

Rearranging the formula to solve for A, we have:

A = P / (e^(rt))

Substituting the given values, we have:

A = 3000 / (e^(0.06*9))

Calculating the exponential term, we find:

A ≈ 3000 / (e^0.54) ≈ 3000 / 1.716 ≈ 1746.20

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Answer:

a) i) The equation is satisfies of the values x = 6 and y=9

ii) The greatest possible value of 3x-2y is  20

iii) The least possible value of 3x – 2y is 2 and '0'

b)

The value of 5(a – 4b)  =  -55

Step-by-step explanation:

Given x and y are two numbers taken from the list below

5  6   7   8   9  10

i)

I will choose  x = 6 and y = 9

3x - 2y = 3 (6) - 2(9) = 18 - 18 = 0

The equation is satisfies of the values x = 6 and y=9

ii)  

we will choose x =10 and y = 5

3x - 2y = 3(10) - 2(5) = 30 -10 =20

The greatest possible value = 20

iii)

we will choose x =6 and y =8

3x - 2y = 3(6) -2(8) = 18-16 =2

we will choose x =6 and y =9

3x - 2y = 3 (6) - 2(9) = 18 - 18 = 0

b)

Given value of 5(a – 4b)

substitute  a = -7 and b = 1​

5(a – 4b) = 5(-7-4(1)) = 5 (-11) = -55

Step-by-step explanation:

I think it should be right angle

The maximum value of the product of two number whose difference is 14 is 49.

The maximum or minimum value of a function is the highest or lowest value of that function.

Let the numbers be x and y

Their product f(x,y) = xy

Since their difference is 14, x - y = 14

So, x = 14 - y

Substituting x into f(x,y), we have

f(x,y) = xy

= (14 - y)y

= 14y - y²

To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.

So, f(x,y) = f(y) = 14y - y²

df(y)/dy = d(14y - y²)/dy

df(y)/dy = d(14y)/dy - dy²/dy

df(y)/dy = 14 - 2y

Equating to zero, we have

df(y)/dy = 0

14 - 2y = 0

14 = 2y

y = 14/2

y = 7

To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again

So, df'(y)/dy = d(14 - 2y)/dy

= d14/dy + d(-2y)/dy

= 0 - 2

= -2 < 0.

Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)

So, since y = 7,

x = 14 - y = 14 - 7 = 7

So, f(x,y) is maximum at x = 7 and y = 7

So, f(7,7) = 7 × 7

= 49

So, the maximum value of the product of two number whose difference is 14 is 49.

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Answer:

V=100.53 inch³

Step-by-step explanation:

V=πr²h

V=22/7 x 2 x 2 x 8

V=100.53 inch³

Answer: 300

Step-by-step explanation:

From the question, we are informed that Mr Gaines is catering his company picnic and that he will pay $18.45 for 3 people to eat the barbecue lunch. This means each person spends:

= $18.45/3

= $6.15

With a budget of $1850.00, the number of people that he'll be able to feed will be:

= $1850/$6.15

= $300 people

Answer:  see below

Step-by-step explanation:

8)   3x ≥ 24

   ÷3    ÷3  

     x  ≥  8

Graph:        ·--------→

                 8

Interval Notation: [8, ∞)

The piecewise function for this problem is defined as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

Between x = -3 and x = -1, the linear function has a slope of 1, with a x-intercept of -3, meaning that the parent function y = x was shifted left 3 units, hence it is given as follows:

f(x) = x + 3, -3 ≤ x < -1

Between x = -1 and x = 1, the function is constant at y = 5, hence it is given as follows:

f(x) = 5, -1 ≤ x ≤ 1.

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Answer:

a and d

Step-by-step explanation:

The points (0, 0) and (3, -2) are solutions to the system of inequalities y≤-2x+6 and x−y<6 which are a correct options (A) and (C).

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Given the system of inequalities as

y≤-2x+6 and x−y<6.

To determine the solutions, you first have to graph both of the lines in the problem.

y = -2x+6 and x − y = 6. Then, to shift them to inequality, you have to shade the half-plane that they represent.

The solution is the space that they have in common. In this case, it will be on the right side of the graph.

The points (0, 0) and (3, -2) are included in the shaded region they have in common.

Hence, the points (0, 0) and (3, -2) are solutions to the system of inequalities y≤-2x+6 and x−y<6.

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To show that in every isosceles trapezoid, the interior angles with the base minor are congruent, we can use the given notation ◻ for the isosceles trapezoid.

An isosceles trapezoid has two parallel sides, where the longer side is called the base major and the shorter side is called the base minor. Let's consider an isosceles trapezoid ◻.

Since ◻ is an isosceles trapezoid, it means that the non-parallel sides are congruent. Let's denote these sides as a and b. The base angles of the trapezoid (the angles formed by the base major and the non-parallel sides) are congruent by definition.

Now, let's focus on the interior angles with the base minor. Denote these angles as α and β. Since the sides a and b are congruent, the opposite angles formed by these sides are congruent as well. Therefore, α and β are congruent.

Hence, we have shown that in every isosceles trapezoid, the interior angles with the base minor are congruent.

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Hi there!

We can find the percentage by expressing the amount of oranges to total fruits as a fraction:

\(\text{ oranges to total fruit} = \frac{\text{x Oranges}}{\text{ y total pieces of fruit}}\)

Plug in the given values:

\(\text{ oranges : total fruit} = \frac{\text{6}}{\text{15}} = 0.4\)

Convert to a percentage by multiplying by 100:

0.4 × 100 = 40%.

\(\boxed{\text{40\% of total pieces of fruit are oranges}}\)

Answer:

y = 0.20m + 10, 100 minutes

Step-by-step explanation:

Equation: y = mx + b

Fill it in.

m = slope = 0.20

b = y-intercept = 10

y = 0.20x + 10 (They wanted the variable to be m. So, changing that.)

y = 0.20m + 10

Fill in.

30 = 0.20m + 10

Solve.

20 = 0.20m

100 = m

She was on the phone for 100 minutes.

3.7%

hey im just guessing

Answer:

B. 37%

Step-by-step explanation:

There are 37 students out of 100 that prefer pineapples to peaches and a percent is out of a hundred so therefore 37% is correct

Based on the slopes calculated, Sammy can conclude that quadrilateral EFHG is a rectangle.

To determine whether quadrilateral EFHG is a rectangle using coordinate geometry, Sammy can follow these steps:

1. Calculate the slopes of the opposite sides:

  - Slope of EF: mEF = (yF - yE) / (xF - xE)

  - Slope of HG: mHG = (yG - yH) / (xG - xH)

2. Calculate the slopes of the adjacent sides:

  - Slope of FG: mFG = (yG - yF) / (xG - xF)

  - Slope of EH: mEH = (yH - yE) / (xH - xE)

3. Check if the opposite sides have equal slopes:

  - If mEF = mHG and mFG = mEH, then EFHG is a parallelogram.

4. Check if the adjacent sides have perpendicular slopes:

  - If mEF * mFG = -1 and mHG * mEH = -1, then EFHG is a rectangle.

Let's calculate the slopes using the given coordinates:

mEF = (7 - 10) / (4 - 7) = 3 / -3 = -1

mHG = (5 - 8) / (6 - 9) = -3 / -3 = 1

mFG = (5 - 7) / (6 - 4) = -2 / 2 = -1

mEH = (8 - 10) / (9 - 7) = -2 / 2 = -1

Since mEF = mHG = -1 and mFG = mEH = -1, we have equal slopes for opposite sides and perpendicular slopes for adjacent sides.

Therefore, Sammy is able to determine that the quadrilateral EFHG is a rectangle based on the calculated slopes.

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The goal of this is to get 24 by multiplying the p value with q. q can be any number, as long as it gets to 24 in this scenario.

So your first p value is 4, so you can take 24, and divide it by 4 to get your answer.

24/4=6 then you can check it by multiplying 6*4=24. That means 6 is your first q value.

This will work for the rest of them in that table, except for the 0, because no matter what you multiply that by you cannont get 24. Try it out for yourself, goodluck!

Answer:

q- 24/4=6

24/2=12

24/0=0

24/-2= -12

24/-4= -6

The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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Answer:

Step-by-step explanation:

1) WXYZ is a rectangle              1. Given

2) ∠Z ≅ ∠Y                                 2. Definition of rectangle

3)  WZ ≅ XY                              3.  Definition of rectangle

4) ZY ≅ ZY                                 4. Reflexive property

5) ΔWZY ≅ ΔXYZ                      5. SAS

6) WY ≅ XZ               6. CPCT -Corresponding parts of congruent triangles

The diagonals of rectangle are congruent

The point (-2,2), we need to evaluate each case

In this case, for the real part we need to obtain -2

For the imaginary part, we need to obtain 2

As we can see the complex number that is shown in the graph is

ANSWER

A.

Step-by-step explanation:

KLH is a triangle, and the sum of all angles in a triangle is 180°.

now, we know the angle at L = 134°.

because of the symmetry of the angles in such a regular parallelogram, the upper angle at H is 25°, and the lower angle at H (one of the angles in our triangle) is (4x + 9)°.

and the upper angle at K is (4x + 9)°, and the lower angle at K is 25°.

so, we have

180 = 134 + 25 + (4x + 9) = 159 + 4x + 9 = 168 + 4x

12 = 4x

x = 12/4 = 3

The approximate volume of the solid created by rotating the region under the curve y = sin(x) on the interval [0, π] around the x-axis is approximately 2.094 cubic units.

To find the volume of the solid, we can use the disk method. Considering a small segment on the x-axis between x and x + Δx, the corresponding slice of the solid can be approximated as a disk with radius y = sin(x) and thickness Δx. The volume of this disk is given by V = π * (sin(x))^2 * Δx.

To find the total volume of the solid, we need to sum up the volumes of all the disks. We can do this by taking the limit as the thickness Δx approaches zero and integrating over the interval [0, π]. Thus, the volume can be calculated as V = ∫[0, π] π * (sin(x))^2 dx.

Using a calculator or integration software, we can evaluate this definite integral. The result is approximately 2.094 cubic units. Therefore, the approximate volume of the solid created by rotating the region under the curve y = sin(x) on the interval [0, π] around the x-axis is approximately 2.094 cubic units.

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To find the scale factor, let's first find the center of dilation. The dilation center, the vertice of the segment and its image, they all belong to the same line. If we call the center of dilation as O, we know that O, A, and A' are in the same line, and we can affirm the same for O, B, and B' . The center of dilation will be the interception of those two lines.

A and A' both belong to the line x = 6, B and B' both belong to the line y = -2.

This means, our center of dilation is (6, -2).

To find our scale factor, we can use the fact that Lengths of segments

|OA'| and |OA| relate to each other at the scale factor.

Our scale factor is 3/4.

Answer:

x≥5

Step-by-step explanation:

If x is the quantity of goats he wants x≥5

Answer:

\(150-(65+20x)\)

Step-by-step explanation:

So we know that Amy sets aside a total of $150 to pay her bills.

The cost for the monthly cell phone plan is a $65 access fee plus $20 per gigabyte of data used.

In other words, the total cost when using x gigabytes is given by the expression:

\(65+20x\)

The first term represents the access fee, and the second term represents the cost for x gigabytes.

And since we want to find out the amount of money Amy will have left after using x gigabytes, we subtract this from 150:

\(150-(65+20x)\)

The above expression will give us the amount of money Amy will have left after paying her cell phone plan.

Our answer is the second choice.