Determine the unknown angle measures?

Thus, Bao age is 27.

acc to our question-

hence,Thus, Bao age is 27.

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The graph of the given linear function is attached below.

A linear function is modeled by the following rule:

y = mx + b

In which m is the slope, which is the rate of change, that is, the change in y divided by the change in x.

Also, b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.

We are given the linear function d(x)=−12x−3

The graph is given below.

Two points on the graph are (2, 4) and (4, 7).

Now,

Hence, Slope of graph = -12

The graph of the given linear function is attached below.

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Answer: 1.467

Step-by-step explanation: All you had to do was divide 22 by 15.

The equation to represent the area of the desk is A=3.5 x 12.  The length of the large office desk is 12.

The area a rectangle occupies on a two-dimensional plane is known as the area of the rectangle. A quadrilateral, a type of two-dimensional shape with four sides and four vertices, is what a rectangle is.

A large office desk is given, with area 42 ft^2. The shape of the desk is rectangle. The area of the rectangle is given by A=l*w.

Given, the area is 42 ft^2.

w=3.5 feet.

A= 42

42=3.5*l

l=42/3.5

l=12 feet.

The length of the rectangular desk is 12 feet. The equation to represent the area of the large office desk is A=12*3.5.

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Answer:

-1

Step-by-step explanation:

An exponential function can be represented by the below four situations.

An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance; and A total population is increasing by about 7.5% each year.

An exponential function is one in which the amount increases or decreases by being multiplied by a fraction or decimal.

In the first situation, 4/5 of the number is found per year; this means we multiply by 4/5.  This is exponential.

In the second situation, the number of miles increases by 38 per gallon of gas used.  This is adding 38, so it is not exponential.

In the third situation, the amount in the checking account is decreased by subtracting $25.75 for every month that passes; this is not exponential.

In the fourth situation, the number of toads increases by 7.5%; this is done by multiplying by 1.075 each time.  This is exponential.

Hence the answer is an exponential function can be represented by the above four situations.

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80 five-card hands (drawn from a standard deck) contain exactly two aces

Permutations and combinations are  ways of representing groups of objects by selecting them  and subsetting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

It's always helpful to try to visualize the problem and how to approach it.

Think of the card arrangements as an array of length 5 named A.

Lets get the total number of ways that 2 slots of the 5 can be selected (Number of possible arrangements of 2 elements in an array of size 5) in A. That's a simple combination. That is:

(5/2)

Now lets get the total number of ways the available Aces can be arranged at those 2 selected slots in A.

(4/2)

Multiplying both combinations given above gives us the number of ways 2 cards of a set of 4 cards can be placed at 5 slots:

(5/2)(4/2)

NOTE: This is not the numbers of 5-card hands that has exactly 2 Aces. This is the total number of arrangements of 2 Aces of the 4 in A.

We have yet to compute the number of arrangements of the remaining cards. We took out 4 cards (The Aces) of the 52 card deck so that leaves us with 48 remaining cards to be arranged at A and took 2 slots from A. So that gives us:

(48/3)

So the answer is:

(5/2)(4/2)(48/3) = 80 five-card hands (drawn from a standard deck) contain exactly two aces

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The number of photos that Sam takes in the afternoon is 224.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, Sam is taking photos for the yearbook and she takes 140 photos in the morning and in the afternoon, she takes 60% more photos.

The photos taken in the afternoon will be:

= Morning photos + Increase in photo

= 140 + (60% × 140)

= 140 + 84

= 224

He took 224 photos.

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$1 is still with you in your pocket.

From the Question:

cost of Shirt=$97

$49 my mom $49 = $50

Amount borrowed from Mum = $50

Total Amount borrowed from dad and mum:

$50 + $50 =  $100

change in hand:

Total t Amount borrowed from dad and mum - the cost of the Shirt

$100-$97 = $3.

Recall:

I gave $1 to dad and $1 to mom and kept $1 for myself

Money owed  my dad = Amount borrowed from Dad - Amout given to Dad

                                      =$50 -  $1

                                     = $49

Money owed my Mum =Amount borrowed from Mum -Amount given to Mum

                                      =$50 -  $1

                                     = $49

change in hand will be = Amount borrowed from dad and mum - (cost of Shirt +Amout given to Dad +Amount given to Mum)

change in hand will be = $100 -( $97+  $1 +  $1 )

                                       = $1

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The GCF of the questions are as follows:

1. 2

2. 12

3. 2

4. 3y

5. 4

6. 2x

7. 1

8. 4ab

9. 7c

10. 1

11. (x+9)(x-9)

12. (x+2)(x-2)

13. (x+12)(x-12)

14. (1+7x)(1-7x)

15. (4x+5)(4x-5)

16. (3x+10)(3x-10)

17. (6x+7)(6x-7)

18. 2(x+5)(x-5)

19. (2x+10)(2x-10)

20. (4x+10)(4x-10)

Define GCF.

The term "greatest common factor" is abbreviated as "GCF." As the greatest number that is a factor of two or more other numbers, the GCF is thus named. The greatest factor that 24 and 36 share, for instance, is 12, hence the GCF of 24 and 36 is 12. 12 is the highest common factor between 24 and 36, while there are others. Since we frequently utilize fractions in our daily lives and hence frequently employ the greatest common factors (GCF), this makes GCF incredibly handy.

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Answer:

The answer is the screenshot shown.

Step-by-step explanation:

How to graph it in that is to check the given first.

y= -5x

x = 0

y = -5

-

So you will have to plot the line at 0 for x and for y, you should put it at -5

Answer: Mean :286.6 Median:294 Mode:169, 294, 188, 295, 487

Charlie needs to sell 1000 packages per month in order to pay himself a monthly salary of $5000. By using the Equation concept we solved this problem.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let the number of packages that Charlie needs to sell is ‘x’

So, According to the question , the below equation has been formed,

10x – (1500 + 3.50x) = 5000

10x – 1500 – 3.50x = 5000

6.50x = 5000+1500

6.50x = 6500

x = 6500/6.50

x = 1000 packages.

So that is how we calculated the number of packages that Charlie needs to sell per month.

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Answer:

3

Step-by-step explanation:

1 foot = 12 inches

Jana can jump 36 inches!

Divide this by 12 to get the feet:

36 / 12 = 3

Check: 12 + 12 = 24 + 12 = 36

so, Jana can jump 3 feet above the ground

Answer:

  450

Step-by-step explanation:

You want the value of (5 × 10⁰) × (9 × 10¹).

  (5 × 10⁰) × (9 × 10¹) = (5) × (9×10) = 450

__

Additional comment

Any number to the 0 power is 1. Any number to the power of 1 is that number.

Your calculator can help you evaluate numerical expressions.

Using the standard form of the equation of line, the slope of the line represented by the equation 3x-4y=7 is 3/4.

In the given question,

We have to find the slope of the line represented by the equation 3x-4y=7.

The given equation is 3x-4y=7.

To find the slope we first express the given equation in the form of standard equation of line.

The standard form of equation is y=mx+c where m is slope of the equation.

Now expressing the equation in standard form.

3x-4y=7

Subtract 3x on both side

3x-4y-3x=7-3x

-4y=7-3x

Divide by -4 on both side

-4/-4 y=7/-4 - (-3)/(-4) x

Simplifying

y=3/4x-7/4

Now comparing from the standard equation to find the slope(m).

m = 3/4

Hence, the slope of the line represented by the equation 3x-4y=7 is 3/4.

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By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = [tex]\frac{15}{2} \ sq. units[/tex]

14) Area of triangle = [tex]\frac{49}{2} \ sq. units[/tex]

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are [tex](x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)[/tex], then area of triangle is calculated by the formula

Area of triangle = [tex]\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|[/tex]

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

[tex]\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units[/tex]

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

[tex]\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units[/tex]

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Answer:

1. a) rectangle, circles.

1. b) circumference.

2. half.

3. 2πr² + 2πrh

4. See below.

Step-by-step explanation:

a) The net of a cylinder is made up of one rectangle and two circles.

b) The width of the rectangle in the net of a cylinder is equal to the circumference of the circle.

The radius of a circle is half the diameter.

[tex]\textsf{Circumference of a circle} = \pi d=2 \pi r[/tex]

Therefore, the formula for the surface area of a cylinder is:

[tex]\begin{aligned}\textsf{S.A. of a cylinder}&=\sf 2\;circles+1\;rectangle\\&=2 \pi r^2+2\pi rh\\&=2\pi r(r+h)\end{aligned}[/tex]

where r is the radius of the circle and h is the height of the cylinder.

Note: It appears from the question sheet that they wish you to use π=3.

Also, as you need to estimate the total surface area, round any decimals to their nearest whole number before carrying out any calculations.

Please note that the formula for Area of Rectangle quoted in the example question is incorrect when comparing it to the answer of question 1b.  In the formula, it says that the length is equal to the circumference of the circle, whereas in question 1b it states that the width of the rectangle is equal to the circumference.  Therefore, I have used the correct formula for the rectangle part of the cylinder:

Given:

Area of One Circle

[tex]\begin{aligned} \pi \times r^2&=3 \times (5)^2\\&=3 \times 25\\&=75\; \sf cm^2\end{aligned}[/tex]

Area of Two Circles

[tex]75 \times 2 = 150\; \sf cm^2[/tex]

Area of Rectangle

[tex]\begin{aligned}2r \times \pi \times h&=2(5) \times 3 \times 6\\&=10 \times 3\times 6\\&=30 \times 6\\&=180\; \sf cm^2\end{aligned}[/tex]

Total Surface Area

[tex]\;\;\;\;180+150\\=330\sf \; cm^2[/tex]

Given:

Area of One Circle

[tex]\begin{aligned} \pi \times r^2&=3 \times (6)^2\\&=3 \times 36\\&=108\; \sf cm^2\end{aligned}[/tex]

Area of Two Circles

[tex]108 \times 2 = 216\; \sf cm^2[/tex]

Area of Rectangle

[tex]\begin{aligned}2r \times \pi \times h&=2(6) \times 3 \times 12\\&=12 \times 3\times 12\\&=36 \times 12\\&=432\; \sf cm^2\end{aligned}[/tex]

Total Surface Area

[tex]\;\;\;\;432+216\\=648 \sf \;cm^2[/tex]

Given:

Area of One Circle

[tex]\begin{aligned} \pi \times r^2&=3 \times (11)^2\\&=3 \times 121\\&=363\; \sf cm^2\end{aligned}[/tex]

Area of Two Circles

[tex]363\times 2 = 726\; \sf cm^2[/tex]

Area of Rectangle

[tex]\begin{aligned}2r \times \pi \times h&=2(11) \times 3\times 17\\&=22 \times 3 \times 17\\&=66 \times 17\\&=1122\; \sf cm^2\end{aligned}[/tex]

Total Surface Area

[tex]\;\;\;\;1122+726\\=1848\sf \;cm^2[/tex]

Answer: 40°

Step-by-step explanation:

First angle can be represented as x, second angle can be represented as y, and the third angle can be represented as z.

x + y + z = 180°

Since the first and second angles are equal, x = y, we can replace y with x.

x + x + z = 180°

The third angle is 2.5 times the first, which can be written as 2.5x.

x + x + 2.5x = 180 (now we solve for x)

4.5x = 180

x = 40°

Check:

40 + 40 + 40(2.5) = 180°

180°=180°

Pre-image Is to image as function is to: B. Relation.

Dilations preserves the following: A. Parallel Lines, C. Perpendicular Lines, and D. Angle.

The scale factor for this dilation (x, y) → (2x, 2y) is: C. k = 2.

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (kx, ky)  = (2x, 2y)

Where:

In conclusion, we can reasonably infer and logically deduce that dilations preserve angle measure, perpendicular lines, betweenness of points, parallel lines, and collinearity in any geometric figure.

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Answer:

Step-by-step explanation:

ED :  DL = FD : DM

or

ED / DL = FD / DM

FD = ED·DM / DL

FD = 88 ·  84  / 48 = 154

profit margin does the stadium anticipate for this year 575050

Given,

This year, a stadium manager has booked five performances with a projected aggregate revenue of $1,050,050.

Profit: 1000 - 425 (85 x 5) = 575

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Answer:

-7x>=22-1

-7x>=21

x>=21/-7

x>=-3

The slopes of both lines that passes through the given points are different, therefore: d. No, they are not perpendicular because their slopes are not reciprocals.

For any two lines that passes through two set of points to be perpendicular to each other, their slopes must have a product that is equal to -1, or be negative reciprocals.

Find the slope of the line that passes through P(0, –9) and Q(2, –8):

Slope of PQ (m) = (-8 -(-9)) / (2 - 0)

m = 1/2

Find the slope of the line that passes through R(1, 4) and S(3, 3):

Slope of RS (m) = (3 - 4) / (3 - 1)

m = -1/2

The slope of both lines are not equal neither are they negative reciprocals of each other. Therefore: d. No, their slopes are not reciprocals.

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The Distance the ship has traveled towards the north and east respectively on a course 50 degrees at and a distance of 10km  is 7.66km respectively

How to find distance traveled by the ship

In a right angled triangle, the square on the hypotenuse side is equal to the sum of the squares on the other two sides

using the trig. ratios of Sine, Cosine and Tangent

From sinβ = opposite/hypotenuse

where; β is the angle made on the course

sin50°=y/10

Where y is the distance towards north

this implies that 10sin50=y

10 x 0.7660=y

y=7.66km

also towards the East

using cosne ratio

cos40=adj/hypo

cos40=x/10

where x is the distance towards east

10 x cos40=x

10x 0.7660

x=7.66km

The ship traveled a distance of 7.66km in each of the directions

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Answer: 144

Step-by-step explanation:

When we go from 4 to 16, we add 12. Then, to get to 36, we add 20. Then, we add 28 to get 64, and finally 36 to get 100. The pattern looks like we add by 8 more every time, so next number is 100 + (36 + 8) or 144.

The sequence of squares of even nos. so the 8th term would be the square of 16 which is 256.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The given sequence is 4, 16, 36, 64, 100...

This is a sequence of squares of even nos.

The first term is the square of 2 and the second term is the square of 4 hence the 8th term would be the square of 16 which is 16² = 256.

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James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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The exact value of the trigonometric equation cos 0.5θ is equal to 2 / 3.

In this problem we have the exact value of a trigonometric function, from which we must determine the exact value of the half angle by means of the following equation:

cos 0.5θ = √[(1 - cos θ) / 2]

If we know that cos θ = 0.8 and cos 0.5θ > 0, then the exact value of the cosine of the half angle is:

cos 0.5θ = √[[1 - (1 / 9)] / 2]

cos 0.5θ = √[(8 / 9) / 2]

cos 0.5θ = √(8 / 18)

cos 0.5θ = √(4 / 9)

cos 0.5θ = 2 / 3

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