Question 1(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Angles A and B are complementary to each other. If mZA = 41° and mZB = (2x + 19), find the value of x.
Ox= 15
Ox=11
Ox= 58
Ox= 30

The length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

The perimeter of the rectangle = 2(length + width)

Let a by b the dimensions for Olive's picture

Let c by d the dimensions for Ryan's picture

b = 1.25d

The perimeter of the picture = 2(9 + 9) = 36

2(a + b) = 36

a + b = 18

a = 18 - b = 18 - 1.25d

Thus, the length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

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Answer:

39%

Step-by-step explanation:

Answer:

Part a) consecutive interior angles

Part b) 

Part c) m∠5=

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Part a) Angles 3 and 5 are consecutive interior angles

therefore

m∠3+m∠5=

Part b) we have

m∠3=

m∠5=

substitute

Part c) solve for x

Find the value of m∠5

m∠5=

m∠5=

Answer:

Step-by-step explanation ma is 9 because p + i=o K/x 798 g ćxΨ / ʥ and 78 / 2 +e =9 then oi x l = j j also = 6 and that's how you do it

a) the acceleration = 0.028 m/s²

b) constant speed = 10m/s

d) Distance travelled during first 10 sec = 50m

e) Distance travelled during last 10 sec = 75m

f) the total distance travelled = 350 m

Total distance travelled during first 10 sec = area of triangle

= 1/2 * 10 * 10

= 50m

Total distance travelled during next 15 sec = area of square

= 15 * 15

= 225

Total distance travelled during last 10 sec = area of triangle

= 1/2 * 10 * 15

= 75m

Total distance travelled = 50 + 225 + 75

= 350m

Velocity = Total distance / Time taken

= 350/ 35

= 10m/s

Acceleration = Velocity / time taken

= 10 / 35

= 0.028 m/s²

c)

= -0.028 m/s²

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The distance the plane traveled from point A to point B is 10952 feet approx.

To solve this we have to use the Pythagoras theorem.

Given that the plane is at a constant height which can be supposed as the perpendicular (i.e 5750 feet) for the triangle which the plane , ground and the makayla make.

Now when the plane is at the A point then the angle of the elevation is 16°, so the distance from the makayla the plane  is :

tanθ = P/B,

B(distance of makayla to plane on ground at point A) = P/tanθ ,

B = 5750 / tan 16°,

B = 5750/ 0.28;

B1 = 20535 feet approx

Similarly when the plane reach at the point B then the angle of the elevation is 31° then the distance from the makayla and the plane would be different, which will be :

tanθ = P/B,

B(distance of makayla to plane on ground at point B) = P/tanθ ,

B = 5750 / tan 31°

B = 5750 / 0.6

B2 = 9583 feet approx

now the distance traveled by the plane is B1 - B2 :

which is 20535  - 9583

10952 feet approx

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Answer:10483

Step-by-step explanation:

The correct answer to reflection of hexagon  is Option B

y=x, x-axis, y=x, y-axis

What is hexagon?

6-sided polygon is called hexagon , it is type of polygon( a plane figure made up of lines).

Main body:

using point B(−3,1)

Across the line y=x(x,y)→(y,x)

so we get (1,−3)

Across the x-axis (x,y)→(x,−y)

we get (1,3)

Across the line y=x(x,y)→(y,x)

we get (3,1)

Across the y-axis (x,y)→(−x,y)

we get (−3,1)

Hence the option B is correct.

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If the side lengths of the state flag of Michigan are in the ratio 4:7. when the flag is 28 feet long the height will be 49 feet

The height of the flag is calculated using the scale factors,  4 : 7

if 4 is equivalent to 28 what would 7 be

4 / 7 = 28 / ?

4 * ? = 7 * 28

? = 7 * 28 / 4

? = 49 feet

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The value of x is 6.67 degrees.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

The (5x + 9)° angle on line m and the (7x -  9)° angle on line n are corresponding angles.

We have given that Line m and Line n are parallel.

t line is the transversal line on the two parallel lines, line m and line n.

We see that,

(5x + 9)° angle on line m is corresponding to the  (7x -  9)° angle on line n.

So,

(5x + 9)° +  (7x -  9)° = 180

12x = 180

x = 80 /12

x = 6.67

Thus, The value of x is 6.67 degrees.

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The solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is (1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is (0, 1)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following set of equations

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graphs that the solution is given for first set is of simultaneous equations as (1, 1) and the second set of simultaneous equations as (0, 1)

Refer to the two graphs attached.

Therefore, the solution for the -

Simultaneous equation [1]

y = 2 - x

6x + 5y = 11

is

(1, 1)

AND

Simultaneous equations [2]

x + 2y = 2

2x + y = 1

is

(0, 1)

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The suitable equation and solution is given by (D) g=48 gifts.

Given that max organized a community toy drive for the holidays.

He asked each family to donate a total of 4 gifts.

12 families participated in the toy drive.

If the total number of gifts is g, then the equation is given by,

g = 12*4 = 48 gifts.

Hence the correct option is (D) g=48 gifts.

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The percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.

Given that, there were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the percentage increase per year be x.

a) According to the question,

500(1+x)³=864

⇒ (1+x)³=864/500

⇒ (1+x)³=1.728

⇒ 1+x= 1.2

⇒ x =0.2

In percentage 20%

b) [tex]500(1+0.2)^1[/tex]

= $600

Hence, the percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.

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Answer:

3.57 × 10⁹

Step-by-step explanation:

Scientific Notation:

*Note: Your problem is already in scientific notation.

Answer: 3,570,000,000

Step-by-step explanation:

Your problem is already in scientific notation but if you are trying to turn it into a standard form, then that is the answer

The equation y = -2x +12 in slope - intercept form.

Find the slope of the line that is parallel to y = -2x +3

Slope (m) = -2

Substitute and calculate ;

m = -2, x = 8 ,y = -4 into y = mx + b

-4 = -2 x 8 + b

Calculate the product :

-4 = -16 + b

Calculate the sum or difference:

-b = -12

b = 12

Again, Substitute m = -2 , b = 12 into y = mx +b :

y = -2x + 12

Rewrite the equation y = -2x + 12 in slope - intercept form:

y = -2x + 12

Hence, The equation y = -2x +12 in slope - intercept form.

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A statement of the equation could be as; "John bought y oranges which are 5 times the apples more than 3".

An equation is an expression that shows the relationship between two or more numbers and variables.

The information provided is that the real-world situation in which opposite quantities combine to make zero.

We have been given an equation as y = 5x + 3

A statement of equation could be as; "John bought y oranges which are 5 times the apples more than 3".

If the number of apple x is 6 then;

y = 5x + 3

y = 5(6) + 3

y = 33

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The number of sticks in the sixth and nth patterns will be 32 and 5n + 2, respectively.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

In the first pattern, the number of sticks is 7. Then in each succession of the pattern, 5 sticks are added, then the number of sticks in the nth pattern will be given as,

aₙ = 7 + (n - 1) × 5

aₙ = 7 + 5n - 5

aₙ = 5n + 2

The number of sticks in the 6th pattern will be calculated as,

a₆ = 7 + (6 - 1) × 5

a₆ = 7 + 5 × 5

a₆ = 7 + 25

a₆ = 32

The number of sticks in the sixth and nth patterns will be 32 and 5n + 2, respectively.

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The ratio of time that the red ball reaches the ground when compared with the green ball is 2:1

By using the equations of motion we first find the acceleration and time of both the balls using [tex]v^{2} -u^{2} =2as[/tex] and [tex]v=u+at[/tex]

where,

v=final velocity,

u=intial velocity,

a=acceleration,

s=height,

t=time

For the red ball,[tex]v^{2} -u^{2} =2as[/tex], v=4m/s, u=0m/s, s=3m by substitiuting in the equation we get ,

[tex]4^{2} -0^{2} =2*a*3[/tex],

acceleration=a=16/6=8/3,

[tex]v=u+at[/tex] by substituting we get,

4=0+8/3*t,

time taken by the red ball to reach ground t=3/2

For the green ball,[tex]v^{2} -u^{2} =2as[/tex], v=8m/s, u=0m/s, s=3m by substituting in the equation we get ,

[tex]8^{2} -0^{2} =2*a*3[/tex],

acceleration=a=64/6=32/3,

[tex]v=u+at[/tex] by substituting we get,

8=0+32/3*t,

time is taken by the green ball to reach ground t=3/4

and their ratio of time red ball/green ball=(3/2)/(3/4)=2/1,

hence time to reach the ground is independent of their mass

therefore, the ratio of time that the red ball reaches the ground when compared with the green ball is 2:1

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The "average" of the "positive distances" of each point from the mean is the mean absolute deviation. There is more variability in the data the higher the MAD (the data is more spread out). The MAD aids in determining if the mean of the set serves as a reliable predictor of the values included therein.

Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. By using the formula |data value - mean|, determine the absolute value of each data value's variance from the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is. The mean absolute deviation may be calculated as shown below.

Step 1: First, determine the mean.

Step 2: Determine the positive distances between each data point and the mean. Absolute deviations are those.

Step 3: Combine those deviations.

Step 4. Multiply the total by the number of data points.

The simplest approach to learn about mean absolute deviation is probably to follow these steps in the example below, however here is a more formal method to express the stages in a formula:

GAD (Greatest Absolute Deviation) = ( ∑ | [tex]x_{i}[/tex] - [tex]x_{mean}[/tex] | ) / n

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First derivative of the given function √2-3x  using first principle method is equal to -3.

As given in the question,

Given function is equal to :

f(x) = √2-3x

First derivative of the given function √2-3x  using first principle method is given by:

    f'(x) = [tex]\lim_{h \to \ 0}[/tex] [ (f(x +h) -f(x) ) / h]

Substitute the value of the function we get,

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] [ √2 -3(x +h ) - (√2 -3x) ] /h

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] [ √2 -3x -3h -√2 +3 x]/ h

⇒f'(x) =  [tex]\lim_{h \to \ 0}[/tex] (-3)

⇒f'(x) = -3

Therefore, first derivative of the given function √2-3x  using first principle method is equal to -3.

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Answer:draw a vertical line on the 4th line on the x axis(the horizontal one)

Step-by-step explanation:

Answer:

last one: 20

Step-by-step explanation:

4 divided by 5 is 0.8

so is 20 divided by 25

If the given quadrilateral is a parallelogram, then the value of x = 8  and the value of y = 9

The given quadrilateral is a parallelogram.

Then the opposite side of of the parallelogram will be equal

Then the equation will be

4x - 17 = 2x - 1

4x - 2x = -1 + 17

2x = 16

x = 16/2

Divide the terms

x = 8

Similarly given angles will be equal

3y + 5 = 5y - 13

5y - 3y = 5 + 13

2y = 18

y = 18 / 2

Divide the terms

y = 9

Hence, the if the given quadrilateral is a parallelogram, then the value of x = 8  and the value of y = 9

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8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.

Answer:Rite aid

Step-by-step explanation:

8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.

Answer:

9.34 billions of pounds

Hope that helps ;)

Answer:1 3/5

Step-by-step explanation:

All you have to do is we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.

Answer:1 3/5

Step-by-step explanation: 8/5-5/5= 3/5 so that leaves you with 1 3/5

a) The lower bound of the length of the line is 12.12

b) The upper bound of the length of the line is 12.25

What is a lower bound?

The least value that would round up to the predicted value is the lower bound. The smallest value that would round up to the following anticipated value is the upper bound.

What is an upper bound?

A value that is greater than or equal to every element of a set of data.

What is the difference between the lower and upper bound?

An element of K that is greater than or equal to each element of S is known in mathematics as an upper bound or majorant of the subset S of some preordered set (K, ), especially in order theory. In addition, each element of K that is less than or equal to each element of S is characterized as a lower bound or minorant of S.

Here,

We have to find the lower bound and upper bound of 12.2

We get a lower bound = 12.12

and upper bound = 12.25

Hence, a) The lower bound of the length of the line is 12.12

b) The upper bound of the length of the line is 12.25

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If the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.

It is given that, the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue.

If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present.

Thus, if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

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Answer:

Let h = number of hours.

[tex]20 + 5h = 10 + 10h[/tex]

[tex]4 + h = 2 + 2h[/tex]

[tex]4 = 2 + h[/tex]

[tex]h = 2[/tex]

In 2 hours, we will have the same amount of money.

The value of the quantity after 99 months is 5228.58.

Given that,  an initial value = 5900, rate of decay = 0.85% and time period = 7 years.

The quantity decreases slowly after which the rate of change and the rate of growth decreases over a period of time rapidly. This decrease in growth is calculated by using the exponential decay formula.

The exponential decay formula formula is [tex]Amount=Initial\ value(1-\frac{r}{100} )^{\frac{t}{n} }[/tex]

Here, the value [tex]=5900(1-\frac{0.85}{100} )^{\frac{99}{7} }[/tex]

= 5900×[tex](0.9915)^{14.14}[/tex]

= 5900×0.8862

= 5228.58

Therefore, the value of the quantity after 99 months is 5228.58.

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