Use triangles to find the sum of the interior angle measures of the polygon. What's the answer?

Answer:

20.4cm²

Step-by-step explanation:

base= 10.2

height= 2

10.2×2=20.4cm²

Step-by-step explanation:

An integer is 3 less than 5 times another. If the product of the two integers is 36, then the integers are: 3 and 12. Solution: x * (5x 3) 36; 5x2 - 3x = 36; 5x2 -3x 36 = 0; (5x + 12)(x - 3) = 0; x = -12/5 or x =3.

Answer:

Associative Property

Step-by-step explanation:

Associative Property= Uses parethesis and it doesnt matter the order you put it in it. You are going to get the same answer.

Answer:

They are vertical.

x = 87°

Step-by-step explanation:

Vertical angles are always the same.

Answer:

y = 3x+3

Step-by-step explanation:

Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

Step-by-step explanation:

x + (-7) ≤ 18

x - 7 ≤ 18

x ≤ 18 + 7

x ≤ 25

Value of x is less than or equal to 25

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Probability is the likelihood of occurrance of an event. It is given by:

Probability = number of occurrence / total number of possible occurence

A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.

Probability of using coupon = 32/40 = 0.8

Hence if 750 people go to this store each day, number of people sampled = 75.

Number of people expected to use the coupon = 75 * 0.8 = 60

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

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We represent it as -5. Thus, the common difference/ratio of the given sequence in the simplest form is -5.

To determine if a sequence is arithmetic or geometric, we have to find the differences (common differences) between the terms in the sequence.

The differences between the terms are calculated to determine if they are consistent for the arithmetic sequence or if they have a common ratio for the geometric sequence.

Therefore, the sequence below is arithmetic:19, 14, 9, ...To determine the common difference, we subtract each term from the previous term.19 – 14 = 5; 14 – 9 = 5Therefore, the common difference is 5. Hence, this is an arithmetic sequence with a common difference of 5.

Also, we can say that 14 - 19 = -5, 9 - 14 = -5, and so on. This is a common difference of 5 in the opposite direction. We can say that the difference is -5.

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The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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The expression -√3 sin x + cos x in the desired form k sin(x+0), where k = -1.732 and 0 = π/2. Therefore, -√3 sin x + cos x = -1.732 sin(x+π/2)

We can start by trying to write the expression in the form k sin(x+0), where k is some constant and 0 is an angle. To do this, we'll need to use some trigonometric identities.

First, note that -√3 is the same as -1.732, which is the negative square root of 3.

Next, we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b) to write:

-1.732 sin(x) + cos(x)

= -1.732 sin(x) + 1 sin(x + π/2)

= sin(x + π/2) (-1.732 cos(π/2) + 1 sin(π/2))

= sin(x + π/2) (-1.7320 + 11)

= sin(x + π/2) (-1.732)

So we have expressed the expression -√3 sin x + cos x in the desired form k sin(x+0), where k = -1.732 and 0 = π/2. Therefore, -√3 sin x + cos x = -1.732 sin(x+π/2)

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The equation of the circular orbit and the parabolic path of the comet are

given by the center, diameter, vertex, and directrix.

Part A: The equation of the planet's orbit is; x² + y² = 50²

Part B: The equation of the comet's orbit is; \(\underline{x = -\dfrac{y^2}{280} + 60}\)

Part C: The planet's orbit and the comet's path do not intersect.

Reasons:

Part A: The center of the orbit = The origin (0, 0)

The diameter of the orbit = 100

Therefore;

\(Radius \ of \ orbit = \dfrac{100}{2} = 50\)

The radius of the planet's orbit, r = 50

The equation of a circle with center (h, k) is; (x - h)² + (y - k)² = r²

Therefore, the equation of the circle is (x - 0)² + (y - 0)² = r²

Which gives;

x² + y² = 50²

Part B: The directrix of the parabolic path is x = 70

The vertex = (60, 0)

Therefore, -p = 70

\(The \ equation \ is \ x = \dfrac{1}{4\cdot p} \cdot (y - k)^2 + h\)

Which gives;

\(The \ equation \ is \ x = \dfrac{1}{4\times (-70)} \times (y - 0)^2 + 60 = -\dfrac{y^2}{280} + 60\)

\(x = \mathbf{ -\dfrac{y^2}{280} + 60}\)

The equation of the comet's path in standard form is \(\underline{x = -\dfrac{y^2}{280} + 60}\)

Part C: At the point where the path intersect, we have;

\(x^2 = \left( -\dfrac{y^2}{280} + 60 \right)^2\)

Therefore;

\(\mathbf{\left( -\dfrac{y^2}{280} + 60 \right)^2} = 50^2 - y^2\)

Let y² = a, we get;

\(\left( -\dfrac{a}{280} + 60 \right)^2 = 50^2 -a\)

a ≈ -2015.693 and a ≈ -42784.31

y ≈ √(-2015.693) or y ≈ √-42784.31) (imaginary numbers)

The planet's orbit does not intersect the path of the comet.

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Answer:

The equation that models the situation is \(y = 8 - 0.75t\)

Step-by-step explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, has the following format:

\(y = mx + b\)

In which m is the slope(how much y changes when x changes by 1 unit) and b is the intercept, which is the value of t when x = 0.

A candle is 8 inches tall and burns at 3/4 inch each hour.

Using t as number of hours and y as the height.

Initial height of 8 inches, that is, when \(t = 0, y = 8\), so \(b = 8\)

Burns at 3/4 inch each hour.

That is, the height decreases by a rate of 3/4 inch each hour, so \(m = -\frac{3}{4} = -0.75\)

So

\(y = 8 - 0.75t\)

is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

Answer:

a

\(\mu_x  =7.5 \ minutes \)

b

\(\sigma_{x} = 4.33 \  minutes \)

c

\(P(5 <  X  <  11 ) = 0.4 \)

d

\(P(W = 4 ) =  0.228\)

Step-by-step explanation:

From the question we are told that

  The  interval is \((w , y) =  (0 , 15)\)

Considering question a

    Generally the mean waiting time is mathematically represented as

              \(\mu_x  = \frac{w + y}{2}\)

=>          \(\mu_x  = \frac{0 + 15}{2}\)

=>          \(\mu_x  =7.5 \ minutes \)

Considering question b

Generally the standard deviation is mathematically represented as

      \(\sigma_{x} = \frac{y - w}{\sqrt{\sqrt{12} } }\)

=>    \(\sigma_{x} = \frac{15 - 0}{\sqrt{\sqrt{12} } }\)

=>    \(\sigma_{x} = 4.33 \  minutes \)

Considering question c

Generally the probability density function for a random variable  X is  

     \(f(x) =  \left \{ {{ \frac{1}{y} \ \ \ \ \  0 <  X  <  y } \atop {0} \\ \ \ \  Otherwise} \right.\)

=>       \(f(x) =  \left \{ {{ \frac{1}{15} \ \ \ \ \  0 <  X  <  15 } \atop {0} \\ \ \ \  Otherwise} \right.\)

Generally the probability that the waiting time is between 5 and 11 minutes is mathematically represented as

     \(P(5 <  X  <  11 )= \int\limits^{11}_{5} {f(x)} \, dx\)

=>    \(P(5 <  X  <  11 )= \int\limits^{11}_{5} {\frac{1}{15}} \, dx\)

=>   \(P(5 <  X  <  11 ) =  \frac{1}{15}  x | \left \  11 } \atop {5}} \right.\)

=>   \(P(5 <  X  <  11 ) =  \frac{1}{15} [ 11 - 5]\)

=>   \(P(5 <  X  <  11 ) = 0.4 \)

Considering question d

      Generally the probability the  waiting time is less than 5 minutes is mathematically represented as

     \(P(X < 5) =  \int\limits^5_{-\infty} {\frac{1}{15} } \, dx\)

Given that time cannot be negetive

     \(P(X < 5) =  \int\limits^5_{0} {\frac{1}{15} } \, dx\)

    \(P(X < 5) = \frac{1}{15} *  x  | \left \  5 } \atop {0}} \right.\)

    \(P(X < 5) =0.33.\)  

Generally the probability that the waiting time is less than 5 minutes on exactly 4 of 10 mornings follows a binomial  distribution because  the number of trial is finite i.e 10  the probability of success is probability that the waiting time is less than 5 minutes and probability of failure is probability that the waiting time is not  less than 5 minutes(i.e there is  only two outcome )

Hence for a random variable K representing the number of times in the total of 10 mornings that the  waiting is less than 5 minutes then

    The probability the random variable(W) is exactly 4 is mathematically represented as

    \(P(W = 4 ) =  ^{10}C_4 * (0.33)^4 *  (1- p)^{10 -4}\)

Here C denotes combination

So

     \(P(W = 4 ) =  0.228\)

Answer:

3 n 2/3

Step-by-step explanation:

i just used a calculator bro

Answer:

X = 15

Step-by-step explanation:

We can tell that the two sides that show the degrees are equal because of the arc. We can set up a simple equation:

x + 45 = 60

x = 15

Answer:

x = 15°

Explanation:

The two marked angles are equal as they are vertically opposite angles.

∴ x + 45°  =  60°

⇒ x =  60° - 45°

⇒ x = 15°

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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The ordered pair (3, - 2) is not a solution to the equation 2x - y = 4

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, an equation 2x - y = 4 now if  (3, - 2) is an ordered pair then putting the numerical value of x must satisfy the y value.

when x = 3,

2(3) - y = 4.

6 - y = 4.

- y = 4 - 6.

- y = - 2.

y = 2.

So,  (3, - 2) is not a solution to an equation 2x - y = 4.

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Answer:

2 13/16

Step-by-step explanation:

1 15

16

+

7

8

=  (1 + 0) + (

15

16

+

7

8

)

=  1 +

15

16

+

7 × 2

8 × 2

=  1 +

15

16

+

14

16

=  1 +

15 + 14

16

=  1 +

29

16

=  1 +

1 13

16

=  

2 13

16

Answer: XY=21 YZ=29

Step-by-step explanation: okay so the entire line (XZ) is equal to 50, and its made up of a and a + 8. So you can make an equation out of that.

a+a+8=50

2a+8=50

2a=42

a=21

then you just have XY equal 21, and YZ equal 21+8 or 29.

Answer:

XY = 21

YZ = 29

Step-by-step explanation:

XZ = 50

XY = a

YZ = a + 8

XY + YZ = XZ

a + (a + 8) = 50

2a + 8 = 50

2a = 50 - 8

2a = 42

a = 42 ÷ 2

= 21

hope this helps

Answer:

40

Step-by-step explanation:

6=110 1=40 because it's not gonna be a higher character

Answer:

a = -2

Step-by-step explanation:

I'm assuming that the equation is a + 8/3 = 2/3, and you are supposed to solve for a.

Answer:

A.

a=-2

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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$5000 would grow to $10,000 in 60 years

In order to determine the number of years it would take for $5000 to double, the rule of 72 can be used.

The rule of 72 is a rule of thumb that is used to determine the number of years it would take for the money in an account to double given the interest rate.

Rule of 72 = 72 / interest rate

72 / 1.2 = 60 years

In order to determine the number of years it would take $5,000 to grow to $10,000 in an account that yields 1.2% interest, divide 72 by the interest rate.

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