Example 4: Find the length of AC? D A 65° 12cm 7cm B​
topic: trigonometry

The value for question 5 is 15 and for the question 6 is 10.

This theorem says that if two chords intersect, the product of its segments will be equal.

The question gives two circles each one with two chords. For solving the exercise, you should apply the Chord Theorem.

        Segments of chord 1 = 23 and x

        Segments of chord 2 = 23 and 15

Applying the  Chord Theorem, you have:

23*x=23*15

23x=345

x=345/23

x=15

        Segments of chord 2= x+5 and 28

        Segments of chord 2 = 2x and 21

Applying the Chord Theorem, you have:

(x+5)*28=2x*21

28x+140=42x

-42x-28x=-140

-14x=-140

x=-140/-14

x=10

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The solution set of an equation is a collection of all the values called "solution set" or "root set" that make the equation true.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The solution set of an equation is a collection of all the values that make the equation true. In mathematical terms, it's the set of all values that satisfy the equation.

The solution set can be represented graphically on a number line or coordinate plane, or it can be expressed as an ordered pair, a set of ordered pairs, or an interval. In some cases, the solution set may be empty, meaning there are no values that satisfy the equation. In other cases, it may contain a single solution, infinitely many solutions, or a range of solutions.

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This problem can be solved by setting up two equations to represent the number of enchilada and taco meals being served. Let x be the number of enchilada meals and y be the number of taco meals. Then we have:

x + y = 250 (representing the total number of meals)

5x + 7y = 1500 (representing the total cost of the food)

Solving these equations using methods such as substitution or elimination will give you the values of x and y, i.e. the number of enchilada and taco meals being served at the party.

Answer:

x + y = 250 (representing the total number of meals)

5x + 7y = 1500 (representing the total cost of the food)

Step-by-step explanation:

There is no way to accurately answer this question as there are too many variables to consider, such as the population size and crime rate of the state.

There is no way to accurately answer this question as there are too many variables to consider. The population size of the state would be an important factor in calculating the number of murders per 100,000 residents. The population size of the state would determine how many people are in the state with an automatic weapon and therefore how many potential murders could occur. Additionally, the crime rate of the state would be an important factor in determining the number of murders per 100,000 residents as it would indicate whether or not there would be a higher propensity for crime in the state. Additionally, the availability of other weapons, such as handguns or knives, would also be a factor as it could reduce or increase the number of murders with automatic weapons. All of these factors, as well as others, make it impossible to accurately determine the number of murders per 100,000 residents in a state with 1 thousand automatic weapons.

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Answer:

24

Step-by-step explanation:

16/12 is 1.333333333

20/15 is 1.333333333

18x1.333333333 is 24

(p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

An expression is combination of variables, numbers and operators.

The given expression is p/6+ ( 7+ 8)

p by six plus seven plus eight.

In the given expression Combine the like terms

p/6 + (7 + 8)

p/6 + 15

LCM 1, 6 is 6

(p + 90)/6

Hence, (p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

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The number of people they use at least two facilities is 37

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

n( of people that use gym and pool only) = 15-1 = 14

n( of people that use pool and track only) = 14-1 = 13

n( of people that use gym and track only) = 10-1 = 9

therefore total number of people that use atleast two facilities = 14+13+9+1 = 37

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Because lines y and x are parallel, we can see that the angles that are congruent to ∠1 are:

∠5, ∠4, ∠6

We know that lines x and y are parllel lines.

So, the angles in the same quadrant of the two intersections will have the same measure, this means that:

∠1 = ∠5

∠2 = ∠6

and so on.

Also, remember that on an intersection the vertical angles have the same measure, that means that:

∠1 = ∠4

∠5 = ∠6

Then, the angles that are congruent to ∠1 are:

∠5, ∠4, ∠6

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Answer: 40.82

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

13 * 3.14 = 40.82

This may be wrong, but I found this on the internet

The player would make or miss 10 shots.

The basketball player with a 50 percent shooting average would make or miss 10 baskets out of 21 shots taken. The pattern of makes and misses would be random, meaning there is no particular pattern for the player to follow. For example, we could see the following sequence of makes and misses: make, miss, make, make, miss, miss, make, miss, make, make, miss, make, make, miss, make, miss, make, miss, make, make, miss. We can calculate the expected outcomes of each shot by dividing the total number of shots (21) by the shooting average (50 percent). This gives us an expected outcome of 10.5, which is rounded to 10. Therefore, the player would make or miss 10 shots.

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Volume of the cone is 178 ft³.

Volume is defined as the space occupied within the boundaries of any three-dimensional shape.

Its SI unit is meter³.

Given,

Radius and height of cylinder and cone are same

Volume of cylinder = 534 ft²

Let radius be r and height be h

Volume of cylinder = πr²h

Volume of cone = 1/3πr²h

⇒ Volume of cone = 1/3 (Volume of cylinder)

⇒ Volume of cone = 1/3 × 534

⇒ Volume of cone = 178 ft³

Hence, 178 ft³ is the volume of cone.

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The probability of selecting exactly 2 white marbles out of 5 marbles from container b is approximately 0.144 or 14.4%.

To calculate the probability of selecting exactly 2 white marbles out of 5, we can use the binomial coefficient formula, which is given by:

P(X=k) = (n choose k) × [tex]p^{k}[/tex] × [tex]1-p^{n-k}[/tex]

where n is the total number of trials (in this case, 5), k is the number of successful outcomes (in this case, 2), p is the probability of success (in this case, the probability of selecting a white marble), and (n choose k) is the binomial coefficient.

First, let's find the probability of selecting a white marble from container B, which is given by:

p = (number of white marbles) / (total number of marbles) = (300 + 1) / (300 + 100 + 1) = 301 / 401

Next, we can use the formula to find the probability of selecting exactly 2 white marbles:

P(X=2) = (5 choose 2) × p² * (1-p)⁽⁵⁻²⁾ = (10) × (301/401)² × (100/401)³ = 0.144

So the probability of selecting exactly 2 white marbles out of 5 is approximately 0.144 or 14.4%.

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Ordered pairs for the image of ABCD after dilated by 3/2 with the center of dilation at the origin is A’(-3, 4.5), B’(-6,-6), C’(6, 0), D’(7.5, 6).

Dilation is defined as for the given geometrical shape when the size of the given shape get changed as per the given condition without changing its shape.

According to the question,

From the given figure ABCD

Ordered pair of A ( -2,3) , B(-4,-4) , C(4,0), D( 5,4)

Dilated  3/2by  with the center of dilation at the origin

New ordered pair after dilation we have,

A¹(-2(3/2)), 3(3/2) =A¹(-3,4.5)

B¹)-4(3/2), -4(3/2) = B¹(-3,4.5)

C¹ (4(32), 0(3/2) = C¹(6,0)

D¹(5(3/2), 4(3/2) = D¹(7.5,6)

Hence, ordered pairs for the image of ABCD after dilated by 3/2 with the center of dilation at the origin is A’(-3, 4.5), B’(-6,-6), C’(6, 0), D’(7.5, 6).

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a. 4x + 8 b. 6x + 8x (???) c. 8x + 13 d. 6x + 6y × 6z

b doesnt make sense. is it x(6+8)?

Answer:1 rose bush costs $11.50

             1 geranium costs $9.50

Step-by-step explanation:

4 rose bushes 3 geraniums = $74.50

7 rose bushes 2 geraniums = $99.50

8 rose bushes 6 geraniums = $149

21 rose bushes 6 geraniums = $298.50

13 rose bushes = $149.50

1 rose bush = $11.50

3 geraniums =$74.50-($11.50x4) = $28.50

1 geranium = $9.50

The value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given the equation is

(x/2) - (2/x+1) = 1

thaking LCM of left side of equation we get,

[x(x+1) - 2*2]/ 2(x+1) = 1

⇒ (x² + x - 4) / (2x +2) = 1

multiply both side by (2x +2) we get,

⇒ (x² + x - 4) = (2x +2)

subtract both side by (2x +2) we get,

⇒ (x² + x - 4) - (2x +2) = 0

⇒ x² - x - 6 = 0

to get the value of x we factorize this equation

⇒ x² - (3-2)x - 6 = 0

⇒ x² - 3x +2x - 6 = 0

⇒ x (x - 3) + 2 (x - 3) = 0

⇒ (x - 3) (x +2) = 0

from x+2 = 0, we get the value of x = -2

and from x-3 = 0, we get the value of x = 3,

So that the value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.

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The system of equations has no solution.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are x=4y-11 --------(I) and 3x-12y=-33 --------(II).

Substitute equation (I) in equation (II0, we get

3(4y-11)-12y=-33

12y-33-12y=-33

0=0

Equations has unique no solution.

Therefore, the system of equations has no solution.

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Answer:

[tex]f(x) = x {}^{2} [/tex]

Answer:

x [tex]\geq[/tex] 64

Step-by-step explanation:

x is the number

x - 14 [tex]\geq[/tex] 50

Now isolate x to solve. So add 14 to both sides

x [tex]\geq[/tex] 64

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There are 15 test scores that are 85 or greater out of a total of 30 test scores.

The third quartile, Q3, is the median of the upper half of the set of data. To determine the number of test scores that are 85 or greater, we must first find the median of the upper half of the data set. The formula to calculate the median is

Median = (n+1)/2

where n is the number of observations in the data set. In this case, n is 30. Plugging this into the formula we get

Median = (30+1)/2 = 15.5

Therefore, there are 15.5 test scores that are 85 or greater.

To calculate the number of test scores that are 85 or greater, we subtract 15.5 from 30. This gives us 14.5 test scores that are 85 or greater. Since 14.5 is not a whole number, we can round up to 15 test scores that are 85 or greater. Therefore, there are 15 test scores that are 85 or greater out of a total of 30 test scores.

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The explicit formula for the given sequence is -

a{n} = 8(2)ⁿ ⁻ ¹

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.

Given is the sequence as -

8, 4, 2, ....

The given sequence is a geometric sequence with common ratio of -

{r} = 8/4 = 4/2 = 2

{r} = 2

We can write the explicit term as -

a{n} = 8(2)ⁿ⁻¹

Therefore, the explicit formula for the given sequence is -

a{n} = 8(2)ⁿ ⁻ ¹

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There are 504 multiple ways to go about doing something. the probability that perhaps a specific event (or group of events) would happen.

either as a range between 0 and 100% or even as a percentage on either a line plot between 0 (impossibility) to 1 (certainty).

THE PROCEDURE IS HERE.

The three airports will each receive a fleet of nine taxis.

Three people travel to airport A, five to airport B, and one to airport C.

There are several different methods that this can be done, including:

(9C3) (6C5) (1C1)

(84) (6) (1) (1)

= 504

The result is that this could be done in 504 different ways.

Based on the probability equation, the likelihood that a will take place is related to the ratio of favorable outcomes to all outcomes. Amount of favorable outcomes/Total Number of outcomes determines the probability that an event will occur, P(E).

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

If the store sells 80 feet of rope, it makes a profit of $6.4.

The money made from selling a product, which should be higher than its cost price, is referred to as the profit. It is the gain from any type of commercial activity. In other words, a gain or profit is judged to have occurred when the selling price (SP) of a product exceeds its cost price (CP).

Given the amount a hardware store pays for buying nylon rope is represented by the equation,

y = 0.12x

the cost price of rope is y = 0.12x

and the amount the hardware store charges when selling the rope is represented by the graph,

from graph,

we find the coordinates (1, 0.20) (2, 0.40)

the equation of a line is y = mx + c

since the graph passes from the origin (0, 0) so the equation of the graph will be,

y = mx

and  m = (.40 - 0.20)/(2 - 1)

m = 0.20

selling price of rope = y = 0.20x

where x is the length of rope in feet and y is the amount,

If the store sells 80 feet of rope,

the cost price of  80 feet of rope is

y = 0.12x

y = 0.12(80)

y = $9.6

and the selling price of 80 feet of rope is

y = 0.20x

y = 0.20(80)

y = $16

and profit = selling price - cost price

profit = 16 - 9.6

profit = $6.4

Hence profit is $6.4.

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Answer:use a plane and then you plot the points then count the spaces then u count to half the spaces and then look for the numbers on the places and then u have the central point.

Step-by-step explanation:

The solution to the system of linear equations is (x, y) = (- 8 / 5, 6 / 5).

In this problem we need to build and solve a system of two linear equations with two variables. Linear equations are expression of the form:

y = m · x + b

Where:

And the slope is calculated by following formula:

m = Δy / Δx

First, determine the linear equations associated with each table:

First line - Slope

m = (- 2 - 0) / [- 1 - (- 2)]

m = - 2 / 1

m = - 2

First line - Intercept

b = y - m · x

b = 0 - (- 2) · (- 1)

b = - 2

y = - 2 · x - 2

Second line - Slope

m = (3 - 1) / [2 - (- 2)]

m = 2 / 4

m = 1 / 2

Second line - Intercept

b = y - m · x

b = 3 - (1 / 2) · 2

b = 3 - 1

b = 2

y = (1 / 2) · x + 2

Second, find solution the system of linear equations:

Find x:

(1 / 2) · x + 2 = - 2 · x - 2

(5 / 2) · x = - 4

5 · x = - 8

x = - 8 / 5

Find y:

y = (1 / 2) · (- 8 / 5) + 2

y = 6 / 5

The system of linear equations has the following solution: (x, y) = (- 8 / 5, 6 / 5)

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The required general solution of the differential equation in implicit form y = [tex][(3/2) * (15x + C) * x^{-3}]^{-3/2}[/tex].

The differential equation is a nonlinear equation and cannot be solved exactly by standard methods. One way to approach a solution is to try to find a substitution that transforms the equation into a separable form, where the variables can be separated and integrated separately. A common approach is to make the substitution y = v^(-2/3), which transforms the equation into:

3x^2 * (2/3) * v^(-5/3) * v' + 6x * v^(-2/3) = 15 * v^(-5/3)

Dividing both sides by v^(-5/3), we get:

3x^2 * (2/3) * v' + 6x * 3 * (2/3) * v^(1/3) = 15

This is now a separable differential equation, and we can integrate both sides to find the general solution:

∫(3x^2 * (2/3) * v' dx) = ∫(15 dx) + C

(2/3) * x^3 * v = 15x + C

v = (3/2) * (15x + C) * x^(-3)

Finally, substituting back for y = v^(-2/3), we get the general solution:

y = [tex][(3/2) * (15x + C) * x^{-3}]^{-3/2}[/tex]

This is the general solution of the differential equation in implicit form. To find an explicit form, one could solve for C using initial or boundary conditions.

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