Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Circumference of a circle: }[/tex]

[tex]\bullet\ \large\boxed{\mathsf{2\pi r}}}\\\rightarrow\large\boxed{\textsf{Whereas, } \pi \large\textsf{ is your pi and it is approximately equal to 3.14}}\\\rightarrow\large\boxed{\textsf{ And \underline{r} is the radius of the circle.}}[/tex][tex]\huge\textbf{Area of a triangle:}[/tex]

[tex]\bullet\ \large\boxed{\mathsf{\dfrac{1}{2}bh}}\\\\\rightarrow\large\boxed{\textsf{Whereas, }\mathsf{\dfrac{1}{2}} \large\textsf{ is half your triangle, \underline{b} is your \underline{b}ase, and b is your \underline{h}eight}}[/tex]

[tex]\huge\textbf{Surface area of a rectangular prism: }[/tex]

[tex]\bullet \ \large\boxed{\textsf{2(wl + hl + hw)}}\\\rightarrow\large\boxed{\textsf{Whereas, l is your \underline{l}ength, h is your \underline{h}eight, and w is your \underline{w}idth.}}[/tex]

[tex]\huge\textbf{Volume of a rectangular prism:}[/tex]

[tex]\bullet\ \large\boxed{\textsf{whl = v}}\\\rightarrow\boxed{\large\textsf{Whereas, v is your \underline{v}olume, w is your \underline{w}idth, h is your \underline{h}eight, l is}}\\ \ \large\boxed{\textsf{your \underline{l}ength}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The triangle congruence postulate is illustrated below

It should be noted that two triangles are congruent if they have the same shape and size.

AAS: The angle-angle-side theorem illustrates that two triangles are congruent if the two angles and a side note between the two angles are identical to that of another triangle.

SSS: This illustrates that the three sides of a triangle are congruent to the corresponding three sides of the other triangle.

ASA: This illustrates that the triangles are congruent when the two angles and the side are the same as the corresponding angles and sides of the other triangle.

SAS: When two sides and the included angle of a triangle are congruent to the corresponding sides and the included angle if a second triangle then it follows the side-angle-side theorem.

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Answer:

Step-by-step explanation:

So for the 1st one you're going to use your protractor and line it up so that BC is at 0 degrees, that way you can look at the point A to determine the angle. Now that you have the angle you're going to take your protractor and draw one point which will be where the two lines meet, line this up in the middle and then draw a point at 0 degrees and a point at the angle you found. Now draw another point at half the angle (like in the previous answer I answered). Draw a line from the middle point and connect it to all these three points (4 in total but one of them is going connected to all of them, like the point B in the image you sent).

For the second question you're going to take the angle you found in the first answer and multiply it by 2. Now start off by drawing a middle point which will connect the two other lines. Line up your protractor so that point is at bottom but in the middle (Check my photo for clarification). Now go to the value that is twice the angle and draw a point there, and also draw a point at 0 degrees) and then connect the two points to the middle point.

For question 3 you don't really need the hint, all you need is to multiply the angle by 1.5 but I'll send another image explaining what it's trying to explain.

Answer:

Pete's average speed is 12.5 miles per hour

Step-by-step explanation:

Miles per hour means how many miles were driven in 1 hour so :

50 miles in 4 hours = ? miles in 1 hour
4 ÷ x = 1

4/x = 1

x = 4

50÷4 = ?

50/4 = ?

? = 12.5

Pete's average speed is 12.5 miles per hour

Hope this helped and have a good day

The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:

[tex]a_n = 1 + 2(n - 1)[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:

[tex]a_1 = 1, d = 2[/tex]

Hence the rule for the pattern is given by:

[tex]a_n = 1 + 2(n - 1)[/tex].

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False, An exponential growth function represents a quantity that has a constant doubling time.

What does an exponential growth function represent?

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m∠X + m∠Y < 90° is true.

XYZ is a triangle.

We have to find the option that is true about △XYZ.

By angle sum property of a triangle,

The sum of all the interior angles of a triangle is always equal to 180°.

So, ∠X + ∠Y + ∠Z = 180°

Given, m∠Z > m∠X + m∠Y.

This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.

so, ∠X + ∠Y must be less than 90°.

Hence, we can say that ∠X + ∠Y < 90°

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Answer: Option 4 or D. m∠x + m∠y∠90°

Step-by-step explanation: Trust Me! It is correct on Edge!

Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?

A: D. m∠x + m∠y∠90°

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

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1. x < 20

x - 7 < 13

x < 20

2. x > -7

-3(x + 4) < 9

-3x - 12 < 9

-3x < 21

x > -7

Hope this helps!

This exercise refers to the identification of statistics that is misleading or erroneous. In this case, a circle graph and a table are involved.

A circle graph is simply a pie chart. It is used to depict information in percentages. An example is attached.

Although charts and tables are very useful descriptive and or illustrative statistics, they can be misleading.

This can happen when:

This answer is general in nature due to the limited information provided.

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Answer:

C

Step-by-step explanation:

Answer:

[tex]\frac{11}{15} =0.733333333333[/tex]

Step-by-step explanation:

• Here The sample space S is the set of possible outcomes (ordered pairs of marbles) that we can draw at random (without replacement) from the bag.

Then

[tex]\text{cardS} =P^{2}_{10}=10\times 9=90[/tex]

……………………………………………

Drawing two marbles where the marbles are different colors

means

drawing (1green ,1 yellow) or (1green ,1 red) or (1yellow ,1 red)

Remark: the order intervene

=========================

•• Let E be the event “Drawing two marbles where the marbles are different colors”.

CardE = 2×3×3 + 2×3×4 + 2×3×4 = 66  (2 is for the order)

Conclusion:

[tex]p\left( E\right) =\frac{66}{90} =\frac{11}{15} =0.733333333333[/tex]

Method 2 :

[tex]p\left( E\right) =2\times \frac{3}{10} \times \frac{3}{9} +2\times \frac{3}{10} \times \frac{4}{9} +2\times \frac{3}{10} \times \frac{4}{9} =0.733333333333[/tex]

Answer:

[tex]\sf \dfrac{11}{15}[/tex]

Step-by-step explanation:

The bag of marbles contains:

⇒ Total marbles = 3 + 3 + 4 = 10

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

First draw

[tex]\implies \sf P(green)=\dfrac{3}{10}[/tex]

[tex]\implies \sf P(yellow)=\dfrac{3}{10}[/tex]

[tex]\implies \sf P(red)=\dfrac{4}{10}[/tex]

Second draw

As the first marble is not replaced there are now 9 marbles in the bag.

If the first marble was green, the probability of drawing a yellow is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was yellow, the probability of drawing a green is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was red, the probability of drawing a green is now 3/9 and the probability of drawing a yellow is now 3/9.

To find the individual probabilities of picking 2 different colors, multiply the probability of the first draw by the probability of the second draw:

[tex]\implies \sf P(green)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(green)\:and\:P(yellow)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]

[tex]\implies \sf P(yellow)\:and\:P(green)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]

[tex]\implies \sf P(yellow)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(red)\:and\:P(green)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(red)\:and\:P(yellow)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]

To find the probability of drawing two marbles at random and the marbles being different colors, add the individual probabilities listed above:

[tex]\begin{aligned}\implies \sf P(2\:different\:color\:marbles) &=\sf \dfrac{12}{90}+\dfrac{9}{90}+\dfrac{9}{90}+\dfrac{12}{90}+\dfrac{12}{90}+\dfrac{12}{90}\\\\ & = \sf \dfrac{66}{90}\\\\ & =\sf \dfrac{11}{15}\end{aligned}[/tex]

The cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

The cost of one bag of mulch is given as $5.00.

The area covered by one bag of mulch is 5 ft.².

Therefore, the cost to cover 1 ft.² of the garden with mulch is $(5/5) = $1.00.

To find the area of the rectangular plot representing the garden, we do the follows:

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The length of the rectangular plot between points (3, 9) and (5, 9):

Length = √((5 - 3)² + (9 - 9)²) = √(2² + 0²) = √(4) = 2.

The width of the rectangular plot between the points (3, 3) and (3, 9):

Width = √((3 - 3)² + (9 - 3)²) = √(0² + 6²) = √(36) = 6.

Therefore, the area of the rectangular plot = Length*Width = 2*6 = 12 ft.².

Therefore, the cost to cover the rectangular plot with mulch, at the cost of $1.00 per 1 ft.² = $1*12 = $12.00.

Therefore, the cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

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Answer:

The second choice.

Step-by-step explanation:

The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.

Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.

Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.

Therefore, we are left with the second option.

Answer:

AC = 5, BC = √17, AB = √32

Explanation:

Given points: A(-3, -2), B(1, 2), C(2, -2)

Use distance between two points formula:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2} = \sqrt{25+ 0} = 5[/tex]

BC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]

AB length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

Janice estimate is under by approximately 0. 6 units. Option B

The longest part is called the hypotenuse

The formula for finding the hypotenuse, we use the Pythagorean theorem

Hypotenuse = square root of both opposite square and adjacent square

We have that,

Hypotenuse = [tex]\sqrt{16^2 + 20^2}[/tex]

Hypotenuse = [tex]\sqrt{256+ 400}[/tex]

Hypotenuse = [tex]\sqrt{656}[/tex]

Find the square root

Hypotenuse = 25. 6

The length of the longest part = 25. 6

Janice estimated it to be 25

Comparing her estimate with the actual length = Actual length - estimate

⇒ 25. 6 - 25

⇒ 0. 6

Therefore, Janice estimate is under by approximately 0. 6 units. Option B

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Answer: B. It is under by approximately 0.6 units.

Step-by-step explanation: Just did it on edge 2023

Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.

a) Concerned with inspection of products

b) Concerned with decision making regarding products

c) One of the oldest aspects of quality assurance

The Acceptance sampling procedure is necessarily a lot sentencing procedure. It cannot be used to estimate the lot quality or lot conformity to the standard specifications.

The acceptance sampling is used when the test is destructive, or the cost of 100% inspection is quite high, or when we need a continuously monitoring program

The Acceptance sampling procedure is used for decision making of either acceptation or rejection of a lot. It can’t be used as a lot quality estimator

As Acceptance sampling is just a lot sentencing process, it can’t estimate the quality of products in the lot. But designed experiments ensure good quality of the process output before even production

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Answer:

3rd graph from the top.

Step-by-step explanation:

It can't be the top one because the kids shoulder doesn't start at the ground.

It can't be the second or fourth because it shows him not waiting in line.

Therefore it must be the 3rd!

Answer: 3rd option

Step-by-step explanation:

Because the description says that it starts not at 0(from the kid's shoulder), the 1st and 4th options are out.

2nd option is incorrect because the kid had to stand in line so the shoulder height doesn't change(unless he was picking stuff up or something)

That leaves the 3rd option.

Answer:

Copying a line segment or angle is an illustration of transformation. Both are similar, because they are both rigid transformation.

When an angle is copied to a new angle, the new angle and the old angle will have the same measure

Similarly;

When a line segment is copied to a new segment, the new line segment and the old line segment will have the same measure

This type of transformation is referred to as a rigid transformation.

Hence, copying a line segment is similar to copying an angle, because they are both rigid transformations

Step-by-step explanation:

Answer:

2,000

Step-by-step explanation:

⇒ 200/8 = 25

⇒ 25 * 80 = 2,000

Answer:

2000.

Step-by-step explanation:

8 * x = 200

x = 200/8

80x = 80 * 200/8

       = 10 *200

       = 2000.

The amount remaining out the money earned is $37.5

Given the following parameters

Amount earned by kevin = $80

If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;

Total money spent = 51/2 + 68/5 + 22/5

Total money spent = 51/2 + 90/5

Total money spent = 25.5 + 18

Total money spent = 43.5

Amount remaining = 80. - 43.5

Amount remaining = 37.5

Hence the amount remaining out the money earned is $37.5

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Answer:

False.

These are not simultaneous equations.

Step-by-step explanation:

Simultaneous equations are equations involving two or more unknowns that are to have the same values in each equation. In the equations given there is only one unknown value.

The expected value of y when x-value is 45 is 35.06

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. For example, y = 2x+3 and 2y = 4x + 9 are two-variable linear equations.

In the given question value of x is given and value of y is asked.

The given equation : y = -2.61x+152.51 Such questions can be solved by substituting the given value of variable in the equation which will help us find the unknown.

Substituting x = 45 in the given equation , we get

y = -2.61 x 45 + 152.51

y =  -117.45 + 152.51

y = 35.06

Thus the expected value of y when x-value is 45 is 35.06

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The domain of g(x) is [4, 7)

The function is given as:

g(x) = f(x + 3)

Since f(x) is a function, then g(x) is also a function

The domain of f(x) is given as:

[1, 4)

The equivalent of these values in g(x) are

x = 1 + 3 = 4

x = 4 + 3 = 7

Hence, the domain of g(x) is [4, 7)

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Answer: Option (1)

Step-by-step explanation:

The slope of the line is

[tex]\frac{9-6}{4-(-4)}=\frac{3}{8}[/tex]

This eliminates all the options except for (1).

Answer:

1. The volumes are equal.

2. The base areas are equal.

3. The prisms have the same height.

Step-by-step explanation:

I don't see no answered to check all that apply but here is the answers about properties and two prisms

Answer:

a) i) -0.5

   ii) -0.28125

b)  -0.254102 (6 d.p.)

Step-by-step explanation:

Given iteration formula:

[tex]x_{n+1}=\dfrac{\left(x_n\right)^3-1}{4} \quad \textsf{and} \quad x_1=-1[/tex]

Part (a)(i)

Substitute the value of x₁ into the formula and solve for x₂ :

[tex]\begin{aligned}\implies x_2 & =\dfrac{\left(x_1\right)^3-1}{4}\\\\& =\dfrac{\left(-1\right)^3-1}{4}\\\\ & = \dfrac{-1-1}{4}\\\\ & = \dfrac{-2}{4}\\\\ & = -0.5\end{aligned}[/tex]

Part (a)(ii)

Substitute the value of x₂ into the formula and solve for x₃ :

[tex]\begin{aligned}\implies x_3 & =\dfrac{\left(x_2\right)^3-1}{4}\\\\& =\dfrac{\left(-0.5\right)^3-1}{4}\\\\ & = \dfrac{-0.125-1}{4}\\\\ & = \dfrac{-1.125}{4}\\\\ & = -0.28125\end{aligned}[/tex]

Part (b)

To find the solution to 6 decimal places, keep substituting each new value into the iteration formula until the answers are the same when rounded to the required level of accuracy.

[tex]\implies x_4=-0.2555618286...[/tex]

[tex]\implies x_5=-0.2541728038...[/tex]

[tex]\implies x_6=-0.2541051331...[/tex]

[tex]\implies x_7=-0.2541018552...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

[tex]\implies x_8=-0.2541016964...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

[tex]\implies x_9=-0.2541016888...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

Therefore, the solution is -0.254102 (6 d.p.).

Answer:

38,710.

Step-by-step explanation:

This is an arithmetic series  with common difference  8 , first term a = 7 and last term L = 783.

The number of terms n = (783 - 7) / 8 + 1 = 98

Sum of 98 terms = (n/2)[a + L)

= (98/2)(7 + 783)

= 49 * 790

= 38,710.

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

We have:

[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]

Find the common ratio:

[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]

[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]

Substitute:

[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]

[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]

Answer:

Circumference = 18.84 ft

Area = 28.26 ft squared

Step-by-step explanation:

C(circumference) = 2 x [tex]\pi[/tex] x r(radius)

radius = 1/2 circumference

1. divide circumference by two to get the radius, which would be three ft.

2. multiply the radius by pie (3.14) and then multiply that by two and you have your circumference, which is 18.84 ft

area = [tex]\pi[/tex] x r(radius)^2

1. find the radius squared, which would be 9 because 3^2 = 3 x 3 which = 9

2. multiply 9 by pie (3.14) and you get the area which =  28.26

Answer:

3 2/3

Step-by-step explanation:

To do this question, you would need to multiply 7 1/3 with 1/2. The answer is 3 2/3.

Answer:

3 2/3 albums

Step-by-step explanation:

Let's say that the stamp album has 12 stamps (12 is just an arbitrary number used to make calculation easier). If Linda collects half of the album, it means she has 6 stamps. If that is the case, Becky has 6 * 7 1/3 stamps. Since 7 1/3 is equivalent to 22/3, we can determine that Becky has collected 44 stamps (6*22/3). There are 12 stamps in one album, which means there are 44 stamps in 3 2/3 (11/3) albums:

[tex]\frac{12}{1}=\frac{44}{y} \\12y=44\\y=11/3[/tex]

Since the ratio of stamps to albums is constant, the calculation above demonstrates that the number of albums it takes to have 44 stamps is 3 2/3. Please note that the numbers I used are arbitrary. If you substitute 12 for a variable x, you will get the same result.

Answer:

Therefore, we can say that the exponent will be negative if the number is less than 1 and vice versa.

Step-by-step explanation:

We are asked to explain that when we convert a decimal number to scientific notation how will we know whether the exponent is negative.

If the given number is greater than 1 then the exponent is positive and if less than 1 the exponent is negative.