Lesson
6-10
Find the values of x and y,
given that AABC ~ AMNC.
B
Sy
A
Lv=600
4x/2x
C
M
60
N

Check the picture below.

Answer: 59°

Step-by-step explanation:

Sum of opposite angles in a cyclic quadrilateral equal to 180°

180 = 121 + A
A = 180 - 121

A = 59°

Answer:

Let the no. of adults be x and no. of children be y

Cost of ticket if there are x adults = 6x

Cost of ticket if there are y children=3y

Step-by-step explanation:

Hope this helps!!

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Answer:

6 children and 4 adults

Step-by-step explanation:

b³-12b²+b²

Step-by-step explanation:

using laws of algebra

Answer: b³-12b²+b

Step-by-step explanation:

The exact values of a and b are [tex]5[/tex] and [tex]5\sqrt{3}[/tex]  respectively. Thus, option A is correct.

A right-angled triangle's sine function is defined as the ratio of the opposite side's length to the hypotenuse's length.

Sin α= Opposite/ Hypotenuse

In trigonometry, the cos is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse

cos α = Adjacent Side/Hypotenuse

In ΔACB,

AB is the hypotenuse, AB=10

Sin 30=BC/AB

[tex]1/2 = a/10[/tex]

Multiply both sides by 10:

[tex]a = 10 \times (1/2) = 5[/tex]

Therefore, the value of a is 5.

Cos 30=AC/AB

[tex]\sqrt3/2 = b/10[/tex]

Multiply both sides by 10:

[tex]b = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt3[/tex]

Therefore, the value of b is 5√3.

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The exact value of a and b is 5 and [tex]5\sqrt{3}[/tex] which means option a is correct.

The triangle is a right-angle triangle.

The hypotenuse is given = 10

By applying the trigonometric ratios we can find the value of a and b.

Apply sine formulae to find value a.

[tex]sin30 = \frac{opposite side of the angle 30}{hypotenuse} \\sin30 = \frac{a}{10} \\\frac{1}{2} = \frac{a}{10} \\2a = 10\\a = 5[/tex]

Apply cosine formulae to find value b.

[tex]cos30 = \frac{adjacent side of the angle 30}{hypotenuse} \\cos30 = \frac{b}{10} \\\frac{\sqrt{3} }{2} = \frac{a}{10} \\2a = 10 *\sqrt{3} \\a = 5\sqrt{3}[/tex]

Therefore the values of a and b are 5 and [tex]5\sqrt{3}[/tex]

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No, it is not sufficient for the environmentalist to use a simple random sample of 101 cars. The reason is that the sample size should be determined based on the required level of precision and the desired level of confidence in the hypothesis test.

In this case, since the environmentalist is claiming that the percentage of hybrids in the city is higher than the national percentage of 3%, it would be appropriate to use a one-tailed hypothesis test. The null hypothesis would be that the percentage of hybrids in the city is equal to 3%, and the alternative hypothesis would be that the percentage of hybrids in the city is greater than 3%.

To determine the sample size needed for this hypothesis test, the environmentalist would need to specify the desired level of significance (e.g., 0.05) and the desired level of power (e.g., 0.80). Based on these parameters, the environmentalist could use a statistical power calculator to determine the required sample size.

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The first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

A mathematical entity with both magnitude (size) and direction is called a vector. It can be depicted graphically as an arrow, with the direction and length of the arrow representing the magnitude and direction, respectively.

To describe the location of the ship at 2:30 pm, we need to find its position vector relative to the port. Since the ship travels at a bearing of 214°, we can represent its motion by a vector with magnitude 15 (the average speed in miles per hour) and direction 214° (measured counterclockwise from due south).

First, let's convert the direction to radians:

214° = (214/180)π = 1.1868π

Then, we can write the vector in component form as follows:

v = (15 cos(1.1868π), 15 sin(1.1868π)) ≈ (-6.20, -13.56)

So the ship's position at 2:30 pm can be represented by the vector v ≈ (-6.20, -13.56), which means that it is approximately 6.20 miles west and 13.56 miles south of the port.

In the scenario, the ship's average speed of 15 miles per hour means that it travels 15 miles in one hour. Therefore, in two and a half hours (from noon to 2:30 pm), the ship travels 37.5 miles in the direction of 214°. The components of the position vector indicate the distance the ship has traveled in the westward and southward directions, respectively, relative to the port. Therefore, the first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

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Answer:

The answer to your problem is:

AB= 30cm

BD= 16cm

Step-by-step explanation:

Since the one shown is to be dilated by a factor of 2, our new dimensions are 2x / 2y. We multiply each side length by two to get our new dilated image.

Which the side lengths being:

AB= 30cm

BD= 16cm

Thus the answer to the problem is:

AB= 30cm

BD= 16cm

Answer:

- Y-intercept: (0, 2) or just 2

- Slope: -1

- Line: y + x = 2 or y = -x + 2

Step-by-step explanation:

The distance on Ralph's map is 1.89 inches.

To find the number of inches needed to represent 13.2 miles on Ralph's map of Virginia Beach using a scale of 1 inch for every 7 miles, follow these steps
1. Divide the actual distance (13.2 miles) by the scale ratio (7 miles per inch): 13.2 miles ÷ 7 miles/inch = 1.8857 inches
2. Round the result to the nearest inch: 1.8857 inches ≈ 2 inches
So, the closest number of inches needed to represent the 13.2-mile distance on Ralph's map is 2 inches.
Ralph's map of Virginia Beach uses a scale of 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
The closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
The scale of Ralph's map of Virginia Beach is 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
To determine the number of inches needed to represent this distance on Ralph's map, we can use a proportion as follows:
1 inch / 7 miles = x inches / 13.2 miles
Cross-multiplying gives:
7x = 13.2x = 13.2 / 7x ≈ 1.89
So, the closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
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Determine the proper prism's base. The base takes the form of the prism's base. Calculate the base's area. The appropriate prism's height should be measured. Multiply the base's area by the prism's height.

A prism is a three-dimensional geometric object with two parallel, congruent bases and rectangular sides connecting the bases. The prism's name is derived from the design of its base. For instance, the bases of a triangular prism, rectangular prism, and so on, are all triangular. The distance between the two parallel bases of a prism determines its height. The formula V = Bh, where B is the area of the base and h is the height of the prism, can be used to determine the volume of a prism.

The formula V = Bh can be explained as follows:

Determine the proper prism's base. The base takes the form of the prism's base. The base, for instance, might be a triangle, square, rectangle, or any other polygon.

Calculate the base's area. The formula's B stands in for this.

The appropriate prism's height should be measured.

To get the volume, multiply the base's area by the prism's height.

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Answer: Spinner 1 = 1/2, Spinner 2 = 1/4, Spinner 3 = 1/3

Step-by-step explanation:

SPINNER ONE

Explanation: Half of the board (B) is 50%, or 1/2.

~

SPINNER TWO

Explanation: There are 4 sections, and one of those sections is 3. That’s 25%, or 1/4.

~

SPINNER THREE

Explanation: There are 3 segments, which means that one of those is green, so ~33% or 1/3 is the answer.

Hope this helped!

Answer:

The average rate of change of the given function over the interval [2, 4] is -4.

Step-by-step explanation:

To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

Given function:

[tex]f(x) = x^3 - 7x^2 + 10x[/tex]

To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).

[tex]\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}[/tex]

[tex]\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}[/tex]

Substitute the values into the formula for the average rate of change over the interval [2, 4]:

[tex]\textsf{Average rate of change} = \dfrac{f(4) - f(2)}{4 - 2} = \dfrac{-8-0}{4-2}=\dfrac{-8}{2}=-4[/tex]

Therefore, the average rate of change of the given function over the interval [2, 4] is -4.

Answer:

Step-by-step explanation:

O Draw a line that intersects the first line at an acute angle using a straightedge.

O Draw a ray that intersects the first line at an acute angle using a straightedge.

Draw arcs on either side of a given point on the line,

Draw ares on either sig, of a given point of the lin

The lengths of the missing sides are:

x = 6

y = 3√2

Here we can see a right triangle, we want to find the two missing lengths in it.

We know the measure of one angle, and the length of the adjacent cathetus of it, then we can use trigonometric relations:

cos(a) = (adjacent cathetus)/hypotenuse

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the values that we know, we will get:

cos(45°) = 3√2/x

Solving for x:

x = ( 3√2)/cos(45°) = 3√2*(2/√2) = 6

And to get the value of y we use the other:

tan(45°) = y/ ( 3√2)

1 = y/ ( 3√2)

( 3√2) = y

These are the lengths.

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The area of the bases of the second triangular pyramid will be 3 times the first one.

What is a triangular pyramid?

A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.

We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 90 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 90 = A * 5

⇒ A = 18 square inches.

Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 270 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 270 = A * 5

⇒ A = 54 square inches.

Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.

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Therefore, the magnitude of vector v is 6 and its direction is 160°.

Magnitude generally refers to the size or extent of something. The term is often used in different contexts, and its meaning can vary depending on the specific field or area of application. Here are a few examples of how magnitude can be defined in different contexts:

Physics: In physics, magnitude usually refers to the size or amount of a physical quantity, such as distance, speed, acceleration, force, or energy. Magnitude can be measured in various units, such as meters, seconds, meters per second, Newtons, or Joules.

Earthquakes: In seismology, magnitude is a measure of the strength or intensity of an earthquake, which is usually expressed on the Richter scale or the moment magnitude scale. The higher the magnitude, the more energy is released by the earthquake, and the stronger its impact on the ground and structures.

The magnitude of vector v is given by:

|v| = |2u| = 2|u| = 2(3) = 6

Therefore, the magnitude of vector v is 6.

The direction of vector v is the same as the direction of vector u, since multiplying a vector by a scalar does not change its direction, only its magnitude. So the direction of vector v is also 160°.

Therefore, the magnitude of vector v is 6 and its direction is 160°.

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Answer:

The expressions are:

[tex]9 {x}^{2} + 24x + 16 = {(3x + 4)}^{2} [/tex]

[tex] {(7 - 3x)}^{2} [/tex]

[tex](1 - 2x)( - 2x + 1) = {(1 - 2x)}^{2} [/tex]

[tex]4 {x}^{2} + 6x + \frac{9}{4} = {(2x + \frac{3}{2} )}^{2} [/tex]

Answer:

The first three options A, B and C

Step-by-step explanation:

First we should know, what is a perfect square?

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)² or (a+b) (a+b)

If the middle term is positive, then the factors are (a+b) (a+b) and if the middle term is negative, then the factors are (a-b) (a-b).

Now, lets look at the answers:-

[tex]2x^2 + 20x + 100[/tex]

first term is squared, to know if the last term is also squared you can square root it, [tex]\sqrt{100[/tex] is 10 which could be [tex]10^{2}[/tex] is also 100.

Same thing goes with the equation [tex]9x^2 + 24x + 16[/tex] the first and last term are squared except that 16 could be [tex]4^2\\[/tex]  which is still the same.

Now, in this equation it's a bit different;

[tex](7 - 3x)^2[/tex]

Notice, that there is a power 2 on the bracket which means the equation could also be represented as  [tex](7 - 3x ) (7 - 3x)[/tex] and like I mentioned above that from the factors of a perfect square it could also be represented as  (a-b) (a-b) which is similar to [tex](7 - 3x ) (7 - 3x)[/tex], if we would to make it a perfect square trinomial it would look like this [tex]7^2 - 27x + 3x^2[/tex] , first term sqaured as well as the last term.

Other options don't comply with the rules to a perfect square.

Hope this helps.

To determine the probability that any given ant will be within the blue circle but not within the yellow circle, you need to find the difference in the areas of the two circles, and then calculate the ratio of that difference to the total area of the surface. If the blue circle has a radius of R1 and the yellow circle has a radius of R2, the areas of the circles can be calculated using the formula for the area of a circle: A = πr².

First, find the area of the blue circle: A1 = πR1²
Next, find the area of the yellow circle: A2 = πR2²
Then, find the difference in areas: ΔA = A1 - A2

Finally, divide the difference in areas by the total area of the surface, and multiply by 100 to get the probability as a percentage: Probability = (ΔA / Total Area) x 100%

Without the specific measurements of the circles and the surface, it's impossible to give an exact probability. However, once you have those measurements, you can use the steps above to find the probability to the nearest whole percent.

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The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

In mathematics, the unitary approach is a way for handling proportional problems. The unitary technique involves determining the value of one unit and using that value to estimate the worth of other units or the total. It is frequently applied in scenarios found in daily life, such as figuring out the cost of a single item when the cost of several are known, or figuring out how long it will take to finish a task when only a portion of the time is known. The unitary approach is a quick and effective method for resolving a variety of mathematical issues.

given

We must divide the overall number of health clubs by the entire population in order to calculate the number of health clubs per capita:

Health club density is calculated as the sum of all clubs divided by the total population.

Per-person health club availability is 81 out of 581,000.

Per-person health club density = 0.000139

The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

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Answer:

1/6

Step-by-step explanation:

There is a 1/3 chance that you will get either a blue, red or green.
It is also a 1/2 chance that you will get an even number on a die.
1/3x1/2=1/6.

Therefore our answer is 1/6

Step-by-step explanation:

a perfect square is

(a + b)²

as in our case this involves x and y, we can outright write

(ax + by)²

now, let's do the multiplication :

a²x² + 2abxy + b²y²

what do we have ?

9x²

that fits to a²x² and means that a = 3.

-12xy

that must be 2abxy. we know, a = 3.

-12xy = 2×3×bxy

-2xy = bxy

so, b = -2

that means what is missing is b²y² = 4y²

the perfect square would then be

9x² - 12xy + 4y²

Answer:

4y^2

Step-by-step explanation:

[tex]9 {x}^{2} - 12xy[/tex]

9 is a square of 3

Let's write a formula for the square of the difference:

[tex] {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} [/tex]

In the first place we can write 3x, because:

[tex](3 {x})^{2} = 9 {x}^{2} [/tex]

Now, -12xy could be the product of 3x and -4y (but it has to be half the product, so we write -2y instead)

In order to get a perfect square, we need to choose such numbers that can be changed in the form of this formula:

(3x - 2y)^2 = 9x^2 - 12xy + 4y^2

That means, 4y^2 must be added

There were 110 children and 237 adults whο swam at the public pοοl that day.

Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.

Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:

x + y = 347 ....(1)

Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:

1.75x + 2.5y = 785 ....(2)

We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.

Frοm equatiοn (1), we can express y in terms οf x as:

y = 347 - x

We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:

1.75x + 2.5(347 - x) = 785

1.75x + 867.5 - 2.5x = 785

-0.75x = -82.5

x = 110

Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:

110 + y = 347

y = 237

Therefοre, the number οf adults whο used the swimming pοοl is 237.

Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.

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The experimental probability that the next student to sign up for camp this summer will specialize in architecture is approximately 0.371 or 37.1%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

The experimental probability of an event happening is calculated as the number of times the event occurred divided by the total number of trials or experiments.

In this case, the number of trials is the total number of students who signed up for camp last summer, which is:

26 (students who specialized in architecture) + 44 (students who specialized in other areas) = 70

The number of times the event we are interested in (specializing in architecture) occurred is 26.

So, the experimental probability that the next student to sign up for camp this summer will specialize in architecture is:

26/70 ≈ 0.371 or about 37.1%

Therefore, the experimental probability that the next student to sign up for camp this summer will specialize in architecture is approximately 0.371 or 37.1%.

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The dimensions of diameter of the circle is 6 inches which Jessa used to draw her circle.

The circumference of a circle is stated by the formula -

C = 2πr, where r refers to radius of the circle. Calculating radius now.

18.84 = 2πr

Rewriting the equation for radius of circle

r = 18.84/2×3.14

Performing division on Right Hand Side of the equation

r = 3 inches

As known, diameter is double the radius. Hence, diameter of the circle = 2×3

Performing multiplication on Right Hand Side of the equation

Diameter of the circle = 6 inches

Thus, the correct answer is A 6.

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The complete question is -

9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.

A 6

B 15.7

C 3

D 9.42

After answering the presented question, we can conclude that probability Therefore, the probability of not selecting a white shirt is 16/24 = 2/3. So, the answer is (B) 2/3.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

There are 24 t-shirts in the basket, and 4 are navy, 12 are red, so the remaining (24 - 4 - 12) = 8 t-shirts must be white.

The probability of not selecting a white shirt can be found by dividing the number of non-white shirts by the total number of shirts in the basket.

The number of non-white shirts is 4 (navy) + 12 (red) = 16.

Therefore, the probability of not selecting a white shirt is 16/24 = 2/3.

So, the answer is (B) 2/3.

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2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

A circle is a two-dimensional object in geometry made up of all points in a plane that seem to be equidistant from a certain point known as the centre. The radius of a circle is the distance from the centre to any point on the circle. The diameter is the length of a line joining two points on a circle and running through its centre. The area of a circle is the space inside of it, and the circumference is the distances around the edge. Tangent lines perpendicular to radii, inscribed and encircled angles in relation to the diameter, and a constant diameter to diameter ratio (pi) are only a few of the crucial characteristics of circles.

given

The circle has a radius of 7 feet, and its area is:

A=r2 = (22/7)x7/2 = 154 square feet

The circle is divided into six equal sections, each of which will have the following area:

6 / 154 = 25.67 square feet (rounded to two decimal places)

An region of two of the pieces will include:

2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

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The value of f is 72/19.

What is an inverse function?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g(y), a function g is the inverse of a function f. Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the composition of f and g.

Here, we have

Given: If f varies inversely as g, find f when g = -6, f= -12 when g= 19.

f ∝ 1/g

f₁ ×g₁ = f₂ ×g₂

Let the required value of f = x

Inserting in equation (1) and we get

(-12) ×(-6) = f₂ ×19

72/19 = f₂

f₂ = 71/19

Hence, the value of f is 72/19.

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Answer:

4units

4 is 4 units less than 8 and 8 times 4 is 32

:)

Answer:

the width of the rectangle is 4 units

Step-by-step explanation:

Let's assume the length of the rectangle is "L" units.

According to the problem, the width of the rectangle is 4 units less than the length, which means the width is (L - 4) units.

The area of the rectangle is given as 32 square units, so we can write:

Length x Width = Area

L x (L - 4) = 32

Expanding the equation, we get:

L^2 - 4L = 32

Bringing all the terms to one side, we get:

L^2 - 4L - 32 = 0

Now, we can solve this quadratic equation for "L" using factoring or the quadratic formula. Factoring gives:

(L - 8)(L + 4) = 0

This gives two possible solutions for "L":

L = 8 or L = -4

We can reject the negative solution, since length cannot be negative. Therefore, the length of the rectangle is 8 units.

Using the equation for the width we found earlier, we can calculate the width of the rectangle as:

Width = L - 4 = 8 - 4 = 4 units.

Answer:

140.

Step-by-step explanation:

Answer:140

Step-by-step explanation: