Find the measures of the numbered angles for each parallelogram.​

SOLUTION :

a² = hypo² - base²

a² = 13² - 12²

a² = 169 - 144 = 25

a = √25

a = 5 units.

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Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

The steps in evaluating each of the following expressions is shown below.

An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 - 2 + 3 - 4

B. 10 + 2(9 - 5) - 16/18

The equation that describes the new function is y' = x^2 + 5

The function is given as:

y = x^2

Shifting the function up by 5 units, the rule is

(x, y) = (x, y + 5)

So, we have:

y' = x^2 + 5

Hence, the equation that describes the new function is y' = x^2 + 5

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The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

First, we find the vector between the two points by vector sum:

[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]

[tex]\vec r = (- 5, - 9, - 4)[/tex]

The distance between the two points is found by the following Pythagorean expression:

[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]

d ≈ 11.1

And the midpoint is found by linear algebra:

[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]

[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]

[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]

The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

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Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

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The period of simple harmonic motion is T = 4.19 seconds:

For given question,

A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.

So, we have mass (m) = 16 pounds

spring constant (k) = 36 lb/ft.

Let T be the period of simple harmonic motion.

Using the formula for the period of simple harmonic motion,

⇒ T = 2π√(m/k)

⇒ T = 2 × π × √(16/36)

⇒ T = 2 × π × √(0.444)

⇒ T = 2 × π × 0.666

⇒ T = 1.333 × π

⇒ T = 4.19 seconds

Therefore, the period of simple harmonic motion is T = 4.19 seconds

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Answer:

x = 24

Step-by-step explanation:

Since this is a right angle, we can use the Pythagorean Theorem to find x. In the formula, a^2 + b^2 = c^2, variables a and b represent the lengths of the legs, and variable c represents the length of the hypotenuse.

a^2 + b^2 = c^2

18^2 + x^2 = 30^2

324 + x^2 = 900

x^2 = 576

x = 24

The probability is 1/5.

There are 3 red marbles and 3 white marbles, for a total of 6.

The probability that the first marble is red is:

P(red) = 3/6

The probability that the second marble is also red is:

P(red') = 2/5 (because now there are 2 red marbles and a total of 5).

The joint probability is:

P = (3/6)*(2/5) = 1/5

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Answer:27 < AB < 81

Step-by-step explanation:

Answer:

27 < AB < 81

Step-by-step explanation:

in a triangle the sum of any 2 sides must be larger than the third side.

that must be true for every pair of sides you pick.

simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.

so,

AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".

AC + AB = 27 + AB must be longer than CB = 54.

so, AB must be longer than 27.

CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.

so only the other 2 conditions need to be true.

hence the answer.

Answer:

76.25

Step-by-step explanation:

Hello,

y = ax + b where a is the slope ! so here the slope is 6

Answer: 98

Step-by-step explanation: 180 - 82 = 98

180 - 80 = 100, and 100 - 2 is 98.

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:

[tex]r = \sqrt{l^{2}+l^{2}}[/tex]

[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

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Answer:

Answer C: m = 26, f = 22

there is a typo in answer D.

Step-by-step explanation:

There are 48 vehicles, so m + f = 48.

They have 140 wheels, so 2m+4f = 140.

You can rewrite the first as m = 48-f and then plug it into the second:

2(48-f) + 4f = 140 =>

96 - 2f + 4f = 140 =>

2f = 140 - 96 =>

2f = 44

f = 22

m = 48 - 22 = 26

Answer:

D

Step-by-step explanation:

Let m = motorcycles and c = cars

m + c = 48                 2m + 4c = 140

m + c  = 48  Multiple this equation through by -2

-2m -2c = -96  Add this to the second equation above

2m +4c = 140

        2c = 44  Divide both sides by 2

          c  = 22.  There are 22 cars.  Plug this back into the top equation to find the number of motorcycles.

m + c = 48

m + 22 = 48 Subtract 22 from both sides

m = 26

The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

Roots are simply the points where the graph intercepts with the x-axis. ( y = 0 )
That is, y = 0 the roots

Given the roots of the equation;

Now, at x = 4,

x = 4

x - 4 = 0

y = ( x - 4)

Also, at x = -7,

x = -7

x - ( - 7 ) = 0

x + 7 = 0

y = ( x + 7 )

Hence; for the equation with the given roots; 4 and -7 will be;

y = ( x - 4)( x + 7 ).

The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

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One linear equation y=x ......(i)

And quadratic equation y=x^2 .....(ii)

(1)Solving them

y=x=x^2

x-x^2=0

x(x-1)=0

If x=0 then y=0

if x=1 then y=1

(x,y)=(0,0),(1,1)

(2) graphically [refer in attachemet]

What is linear equation ?

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The missing height is 65.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Missing height = (mean x total number of students) - sum of existing heights

Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423

Missing height = (8 x 61) - 423 = 64

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Answer:

a: (-1,0) , (3/5,0)

b:(-0.2,-3.2). It will be a minimum

c: To graph, you would first find the vertex using (-b/2a) and then plug that back into the equation to find the y coordinate of the vertex. Once you have the vertex plotted, you can then find the x-intercepts. This can be found by factoring the equation and finding the zeros. These 3 points you plot are enough to graph the line.

Step-by-step explanation:

For showing work on part a:

Turn 5x^2+2x-3 into

(5x^2+5x) (-3x-3)

5x(x+1) -3(x+1)

Finally:

(5x-3)(x+1)

The zeros from that are -1 and 3/5

There will be total 14 hard centred and 14 soft centred choclates in the box.

The ratio is the division of the two numbers.

For example, a/b where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2

Hard centred/ Soft centred = 5/2

And total

Hard centred + Soft centred = 49

Now let say hard centred is H and soft centred S

H/S = 5/2 and H + S = 49

Now H = (5/2)S put into second equation

(5/2)S + S = 49

S(7/2) = 49

S = 14 now put into second equation

H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.

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The surface area of the oblique prism is equal to 485 square units.

In this question we have an oblique prism with seven faces, consistiting in two regular hexagons and five parallelograms. The surface areas is the sum of these seven faces:

A = 2 · 50 + 5 · 11 · 7

A = 485

The surface area of the oblique prism is equal to 485 square units.

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Answer:

Step-by-step explanation:

The ys have to have the same value. That allows you to equate the right side of each y to each other.

-x^2 + 4 = 2x + 1                             Subtract the right side from the left side.

-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1        Combine

-x^2 - 2x + 3 = 0                            Multiply both sides by - 1

-1(-x^2 -  2x + 3) = 0*-1                    Remove the brackets

x^2 + 2x - 3                                   Factor

(x - 1)(x + 3 )

x - 1 = 0

x =   1

x + 3 = 0

x = - 3

So the line goes through x = 1 or x = - 3

x = 1

y = 2x + 1

y = 2(1) + 1

y = 3

x = - 3

y = 2(-3) + 1

y = - 6 + 1

y = - 5

Does the graph confirm this? See below.

red: y = -x^2 + 4

green: y = 2x + 1

Yes the graph is in agreement.

Answer:

Given PR is perpendicular to QS, and PQ and PS are congruent. Angle PRQ and angle PRS are right angles by the definition of perpendicular segments. Therefore triangle PRQ and triangle PRS are right triangles. Segment PR is congruent to segment PR by the reflexive property of congruence. By the HL Theorem, triangles PRQ and PRS are congruent.

The ratio guest to appetizers at the party was 4 guest per appetizer.

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

Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.

The ratio guest to appetizers at the party was 4 guest per appetizer.

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Answer:

A=3Bz/2

B=2A/3z

Step-by-step explanation:

if you need more explanation you can ask me :)

The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.

When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.

To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.

Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.

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The upper quartile for NFC is 3 points higher than that of AFC.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.

Upper quartile for AFC : 26

Upper quartile for NFC : 23

Difference = 26 - 23 = 3

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They need to sell 5 pieces to cover their expenditures (have a profit of zero).

We know that the costs are:

And the revenue is:

So, the profit (the difference between the revenue and the cost) for selling x pieces is:

p(x) = $8*x - $2*x - $30

p(x) = $6*x - $30

We want to find the value of x such that p(x) = 0, then:

0 =  $6*x - $30

x = $30/$6 = 5

They need to sell 5 pieces to cover their expenditures (have a profit of zero).

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Answer:

26 rows

Step-by-step explanation:

this is like a rectangle length×width situation.

seats per row = s

number of rows = r

s × r = 884

s = r + 8

so, we can use e.g. the second equation in the first :

(r + 8) × r = 884

r² + 8r = 884

r² + 8r - 884 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = r

a = 1

b = 8

c = -884

r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =

= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =

= (-8 ± 60)/2 = -4 ± 30

r1 = -4 + 30 = 26

r2 = -4 - 30 = -34

a negative number did not make any sense for the number of rows, so r = 26 is our answer.