Two angles of a quadrilateral are of measures 75° and 117° respectively and the other two angles are equal find the measure of each of the equal angles​

The value of sin 0 in quadrant 2 is 4/5

Given that cos 0 = -3/5

We have;

Let's find the opposite side, using Pythagorean theorem

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

25 = x^2 + 9

collect like terms

x^2 = 25 - 9

x^2 = 16

x = √ 16

x = 4

We have that

sin 0 = opposite/hypotenuse

sin 0 = 4/5

It is important to note that the trigonometric identity 'sine' is positive in quadrant 2

sin 0 = 4/5

Hence, the value of sin 0 in quadrant 2 is 4/5

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Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Assuming the following parameters for triangle ABC:

For the slope of BC, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2.

For the slope of CA, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3.

For the slope of AB, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4.

Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.

Since side AB is perpendicular to side QC, we have:

m₁ × m₂ = -1

Slope of AB × Slope of QC = -1

Slope of QC = (k - 4)/(h - 2)

4 × (k - 4)/(h - 2) = -1

(4k - 16)/(h - 2) = -1

4k - 16 = -h + 2

4k + h = 18    .......equation 1.

Similarly, we have the following:

Slope of BC × Slope of AH = -1

-3/2 × (k)/(h + 2) = -1

3k/(2h + 4) = 1

3k = 2h + 4

3k - 2h = 4     .......equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

8k + 2h = 36

3k - 2h = 4

11k = 40

k = 40/11.

For the value of h, we have:

h = -4k

h = -4 × (40/11)

h = -160/11

Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

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Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.

The mean for this problem is:

(4 + 6 + 2 + 4)/4 = 4

Hence the MAD is:

(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1

Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.

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Answer:

Step-by-step explanation:

8weeeks bc 22.50*8=180

Answer:

  BE

Step-by-step explanation:

A line and a plane will not intersect if they are parallel. A line is named by naming any two points on it, in any order.

The line containing points B, E, F appears to be parallel to plane L. As such, it will remain at the same distance from plane L throughout its infinite length. The line can be named by 2 points in any of 6 different ways.

Line BE is parallel to plane L.

__

Additional comment

Other names for the same line include ...

  BF, EF, EB, FB, FE.

The solution of the inequality is as follows;

x > 4 or x < -3

The inequality can be solve as follows:

5x - 3 > 17 or -2x + 2 > 8

Let's solve the first inequality,

5x - 3 > 17

add 3 to both sides of the inequality

5x - 3 + 3 > 17 + 3

5x > 20

divide both sides by 5

5x / 5 > 20 / 5

x  > 4

-2x + 2 > 8

subtract 2 from both sides

-2x + 2 - 2 > 8 - 2

-2x > 6

divide both sides by -2

-2x / -2 > 6 / -2

x < -3

Therefore, x > 4 or x < -3

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The ski club has 44 members in all

What is population?

Population refers to the total number of items or individuals that form a group.

In this case, the population means the total  number of all members in the  Mogul Runners ski club.

What is sample?

Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.

We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.

25% of club members=11 members

divide both sides by 25%

25%/25% of club members=11/25% members

club members=44 members

The ski club has 44 members altogether as computed above.

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Answer:

2583000000000

Step-by-step explanation:

[tex]2.583*10^{12} = 2583000000000[/tex]

If Ama and her son Brandon's average age is currently 36 years. then

Brandon's age is 38 years.

Two or more expressions with an equal sign is called as Equation.

Let the Brandon age be x

Ama was 34 years old

Ama and her son Brandon's average age is currently 36 years

(34 + x)/2= 36

Use cross multiplication

34 + x = 72

x=72-34

x = 38

So  Brandon's average age is 38.

Hence Brandon is 38 years old.

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Step-by-step explanation:

sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2

sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha

1+ 2sin alpha* cos alpha

1+sin2 alpha

Answer:that will be c 60

Step-by-step explanation: Because 12/4 but than the machines turn to 20 so 4x5 equals 20 so you got to do it to both sides

12x5=60 so its 60 men to run 20 machines

The domain and range of the given graphs are as follows,

(b) Domain: x ∈ (-∞, ∞), Range: y ∈ (-∞, ∞)

(c) Domain: x ∈ [-2, ∞), Range: y ∈ [1, ∞)

Determining the Domain and Range from a Graph

The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.

Thus, in graph (b),

Since the values of the given curve extends infinitely (denoted by arrowhead of the curve) on positive as well as negative sides for both the axes, x and y, its domain and range both are (-∞, ∞).

Similarly, in graph (c),

The minimum value on x-axis or abscissa is -2 and maximum is infinity. Hence, its domain is [-2, ∞). The minimum ordinate value or y-coordinate is 1 and maximum is infinity. Thus, its range is [1, ∞).

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Answer:

268.08

Step-by-step explanation:

Answer:

803.84 m³

Step-by-step explanation:

The formula to find the volume of a sphere is:

V = 4 π r³

Given that,

radius ⇒ 4m

Let us find the volume now.

V = 4 π r³

V = 4 π × ( 4 )³

V = 4 π × 64

V = 4 π × 64

V = 12.56 × 64

V = 803.84 m³

The net decrease in calories after walking for 5 hours is 50 calorie.

According to the statement

we have given that the

A 25-year old woman burns 200−20t cal/hr and Her caloric intake from drinking Gatorade is 110t calories during the t hour.

And we have to find the net decrease in calories after walking for 5 hours.

So, For this purpose,

We know that the

calories burns in one hour = 200−20t

calories burns in 5 hours = 5(200−20t)

calories burns in 5 hours = 1000 - 100t

Now,

Calorie intake in t hours = 110t

And

net decrease in calories after walking for 5 hours =  100t - 1000 + 110t

put t is 5 then

net decrease in calories after walking for 5 hours = 210(5) - 1000

net decrease is 50 cal.

So, The net decrease in calories after walking for 5 hours is 50 calorie.

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Answer:

Dependent variable: time(months) or [tex]t[/tex]

Independent variable: 6

Step-by-step explanation:

[tex]h=24+6t[/tex]

(h=height)

The equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.

To write the equation that represents the total cost of a given scenario like the one given, you can use variables to represent each component that makes up the total cost in the given situation.

Thus, let:

a = apple = 3a

s = can of soup = 2s

b = box of cereal = b

c = total cost

We know that unit price of each items are:

Apple = $0.89

Can of soup = $2.98

Box of cereal = $4.99

Equation would be:

c = 3a + 2s + b

Plug in the values

c = 3(0.89) + 2(2.98) + 4.99

Therefore, the equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.

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A circle is a shape formed by a curved side. Therefore, the required answers are:

1. An example of an inscribed angle is: <SQT or <QST or <QTS

2. An example of a minor arc is: arc QT or RS or QR

3. An example of a semicircle is: QRS or QTS

4. <QPR =  [tex]\frac{264600}{44r}[/tex] degrees

An angle is said to be formed whenever two or more straight lines intersect or meet. But an inscribed angle is an angle formed within a given circle.

A circle is a shape formed by a curved side. Some of its parts are semicircle, radius, diameter, chord, sector, segment, etc.

Thus the following can be deduced from the given question:

1. An example of an inscribed angle is: <SQT or <QST or <QTS

2. An example of a minor arc is: arc QT or RS or QR

3. An example of a semicircle is: QRS or QTS

4. <QPR.

length of an arc = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r

where r is the radius of the circle

105 =   [tex]\frac{x}{360}[/tex] x 2 x [tex]\frac{22}{7}[/tex] x r

      = [tex]\frac{44xr}{2520}[/tex]

44 xr = 105 x 2520

44xr = 264600

x = [tex]\frac{264600}{44r}[/tex]

Therefore the measure of angle QPR in terms of r is  [tex]\frac{264600}{44r}[/tex] degrees.

5. The length of arc QTR can be determined by;

Arc QTR =  [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r

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If the length of hypotenuse is 95 m ,perpendicular is 57 m then the length of missing leg is 76m.

Given that the length of hypotenuse is 95 m ,the length of perpendicular is 57 m.

We are required to find the length of base or missing leg.

The given triangle is a right angled triangle. We can easily find out the length of the base of the triangle by using pythagoras theorem.

Pythagoras theorem says that the square of hypotenuse of a right angled triangle is equal to the sum of squares of the base and perpendicular of that triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

We have to find the base of the triangle.

B=[tex]\sqrt{H^{2} -P^{2} }[/tex]

=[tex]\sqrt{(95)^{2} -(57)^{2} }[/tex]

=[tex]\sqrt{9025-3249}[/tex]

=[tex]\sqrt{5776}[/tex]

=76 m.

Hence if the length of hypotenuse is 95 m ,perpendicular is 57 m then the length of missing leg is 76m.

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Based on the given parameters in the question, the value of the probability of A and D is 0.30

The given parameters from the tree diagram are:

The probability P(A and D) is calculated using the following probability formula

P(A and D) = P(A) × P(D)

Substitute the known values in the above equation

P(A and D) = 0.5 × 0.6

Evaluate the product of 0.5 and 0.6

P(A and D) = 0.30

Hence, the value of the probability of A and D is 0.30 based on the given parameters in the question

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The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)

The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.  

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example, The number 5 x 10³ is equivalent to 500

Paper produced in the second year = paper produced in the first year x 5.6

(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]

4.704 x [tex]10^{9 + 1}[/tex]

= 4.704 x [tex]10^{10}[/tex]

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Answer:

339

Step-by-step explanation:

The balance that Cody earned after 20 years is 891.57. Using the compound interest formula, the required value is calculated.

The compound interest is calculated by

[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]

Where,

A - Total amount (Future value)

P - Principal amount (Initial value)

r - The rate of interest

n - Number of times compounded per 't'

t - Total number of years the money is invested

It is given that,

P = 600

r = 2% = 0.02

t = 20 years

n = 1 (since the amount is compounded annually)

Then,

[tex]A=600(1+\frac{0.02}{1})^1^*^2^0[/tex]

   = 600 (1 + 0.02)²⁰

   = 600 (1.02)²⁰

   = 891.57

Therefore, the balance after 20 years is 891.57.

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Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]

Answer:

7,647.4?

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

The angle just below 'x' is 40°    (alternate angles/parallel lines)

40 + x + 20 = 180  ( straight line)

x = 120°

Answer: -3/7

Step-by-step explanation:

The first step is to find the slope of the line

y = mx + c where m is the slope of the line
Rearrange the equation and we get

3y = 7x + 7
y = 7x/3 + 7/3

So the slope of the line 7x - 3y = -7 is 7/3

There is another rule that states: The product of the slopes of two lines perpendicular to each other is -1

So, the slope of the line perpendicular to 7x - 3y = -7 is -1/(7/3) = -3/7

a. Let [tex]d[/tex] be the number of daytime calls Eshwa makes, and [tex]e[/tex] the number of evening calls. Then the cost [tex]C[/tex] (in pence) of making [tex]d+e[/tex] calls is

[tex]C = \boxed{50d + 40e}[/tex]

b. £1 = 100p, so the cost [tex]C'[/tex] (in £) is 1/100 of the cost found in part (a),

[tex]C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}[/tex]

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

[tex]C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}[/tex]

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

[tex]C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}[/tex]

d. Let [tex]e=40[/tex] and [tex]C'=42[/tex]. Solve for [tex]d[/tex].

[tex]42 = \dfrac d2 + \dfrac{2\cdot40}5[/tex]

[tex]42 = \dfrac d2 + 16[/tex]

[tex]\dfrac d2 = 26[/tex]

[tex]d = \boxed{52}[/tex]

The system of equations has one solution (-1, 1)

From the question, we are to graph the given system of equations.

The given system of equation is

y + 2x = −1

3y − x = 4

The graph of the given system of equations is shown below.

From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).

Hence, the system of equations has one solution (-1, 1)

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I think the answer is A. The first one

The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

The information that completes the question are added as an attachment

The question requires that we determine the intervals which the original function f(x) concave down

From the attached graph, we have the following turning points

(-2, -4) and (3, 2)

From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)

So, we have:

(-5, 0), (-2, -4), (3, 2) and (5, 0)

Remove the y coordinates

x = -5, -2, 3 and 5

Express as intervals

(-5, -2) and (3, 5)

Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

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Using it's concept, your percentage for the month was of 94.12%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, your goal was of 85, with a grade of 80, hence the percentage is:

P = 80/85 x 100% = 94.12%.

Hence, your percentage for the month was of 94.12%.

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