Write and simplify an expression to represent the area. Then determine the area when x = 3

∠BDC and ∠AED are right angles, is  a piece of additional information is appropriate to prove △ CEA ~ △ CDB

Triangle AEC is shown. Line segment B, D is drawn near point C to form triangle BDC.

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Image is attached below,
as shown in figure
∡ACE = ∡BCD ( common angle )
∡AED = ∡BDC ( since AE and BD are perpendicular to same line EC and make right angles as E and C)
∡EAC =- ∡DBC ( corresponding angles because AE and BD are parallel lines)

Thus, △CEA ~ △CDB , because of the two perpendiculars AE and BD.

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Answer:

A

Step-by-step explanation:

The solution of the linear equation is a = 11/4.

Here we have the linear equation:

9 = 4a - 2

We want to solve this for a, so we need to isolate a on one side of the equation.

First, we can add 2 on both sides to get:

9 + 2 = 4a

11 = 4a

Now we can divide both sides by 4 to get:

11/4 = a

The solution of the linear equation is a = 11/4.

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The measure of the ∠Q = 41°

By law of cosines:

a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Which can we stated as:

[tex]{q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)\\\\[/tex]

solving equation using normal algebra:

60cos(Q) = 36 + 25 - 16

60 cos(Q) = 45

cos(Q) = 45/60

cos(Q) = 3/4

[tex]Q = {cos}^{-1} (\frac{3}{4})\\[/tex]

Thus, Q = 41°

Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.

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By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.

Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.

We have to first plot both the equations on the graph.

For plotting we need points which can be calculated as

C=2x

when x=1 ,C or y=2

when x=3 , C or y=6

C=x+5

when x=0 ,C or y=5

when x=1 ,C or y=6

By combining both equations we get

C=(3x+5)/2

Plot this also and finding points

when x=0  , C=5/2

when x=1 , C=4

Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2

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Answer:

So, after

3

years, Impulse Clothing and Opal Essence will own the same number of clothing stores.

The total number of stores during that year will be 8.

Answer: D. -0.002

Step-by-step explanation: You always do the stuff in parenthesis first (P.E.M.D.A.S.). -1/6 is about -0.167. Next you do -0.167 to the fourth power, which is -0.0007777963. Finally, you multiply that number and 2. And BOOM: you get -0.0015555926, which rounds up to -0.002!

Answer:

66.4 in^2

Step-by-step explanation:

Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:

16 + 50.4 = 66.4

Answer:

1/6

Explanation:

$36 in 1:5

so, the total amount of shares is 6 (1+5)

36 / 6 = 6

$6 per share

shared in the ratio of 1:5

5 x 6 = 30

1:5

M:A

$6:$30

Madison gets $6. Or, 6/36 of the total (which, simplified, is 1/6)

Hope this makes sense!

Answer:

60 meter

Explanation:

[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]

Given following:

hypotenuse: 68 meter

---

tan(θ) ratio = opposite/adjacent = 15/8

---

To find ratio of hypotenuse (use Pythagoras theorem):

(hypotenuse)² = (adjacent)² + (opposite)²

(h)² = (8)² + (15)²

h² = 289

h = √289 = 17

The height of the kite above ground is the opposite size.

[tex]\sf real \ size = ratio \ size[/tex]

[tex]\sf \dfrac{height \ above \ ground}{hypotenuse} = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf \dfrac{height \ above \ ground}{68} = \dfrac{15}{17}[/tex]

[tex]\sf {height \ above \ ground}= \dfrac{68(15)}{17}[/tex]

[tex]\sf {height \ above \ ground}= 60 \ m[/tex]

Answer:

60 m

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

The given scenario can be modeled as a right triangle (see attached diagram) where:

As we have been given the hypotenuse (thread) and the angle θ, and need to find the height (side opposite the angle), we can use the sine trigonometric ratio.

The angle θ has been given as a tan trigonometric ratio.  

[tex]\sf \textsf{Therefore, if }\tan \theta=\dfrac{15}{8} \textsf{ then } \cos \theta=\dfrac{8}{17} \textsf{ and } \sin \theta = \dfrac{15}{17}[/tex]

To calculate the height of the kite above the ground, substitute the values into the sine ratio formula and solve for height:

[tex]\implies \sin \theta=\sf \dfrac{height}{thread}[/tex]

[tex]\implies \sf \dfrac{15}{17}=\sf \dfrac{height}{68}[/tex]

[tex]\implies \sf height=\dfrac{15}{17} \cdot 68[/tex]

[tex]\implies \sf height=\dfrac{1020}{17}[/tex]

[tex]\implies \sf height = 60 \:m[/tex]

Therefore, the height of the kite above the ground is 60 m.

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Step-by-step explanation:

First, there is a vertical stretch by a factor of 3,

Next, there is a horizontal compression by a factor of 2.

Reflect about the y axis.

After, shift to the right 3 units horizontally,

Finally , shift upwards 7 units

Answer:

perimeter = 42 units

Step-by-step explanation:

[tex]|\Omega|=8\cdot7=56\\|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{56}=\dfrac{1}{28}[/tex]

[tex]\huge\boxed{25\%}[/tex]

We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.

We know the counts for every category except for "art but not biology", so we can use subtraction.

[tex]26-4-5-5=12[/tex]

This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.

Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).

This is simple division.

[tex]4/16=0.25=25\%[/tex]

Answer:

2√23 cm or  9.59 cm to the nearest hundredth

Step-by-step explanation:

The 12 cm chord is 6 cm away from the centre and the other chord is 7 cm away from the centre.

If we draw 4 radii from the ends of the 2 chords to the centre  and 2 lines perpendicular from the centre to the 2 chords we have   2 pairs of congruent right triangles.

So by Pythagoras:

r^2 =  6^2 + 6^2   ( the given chord)

r^2 = 7^2 + x^2     where x is 1/2 * length of the second chord.

Therefore:

7^2 + x^2 = 6^2 + 6^2

x^2 = 36+ 36 - 49 = 23

x = √23

and length second chord = 2√23.

n^3 + 6

I'll make n stand for the number

Six more means adding extra 6 onto our number cubed.

So, n x n x n = n^3

(n^3 means n cubed)

Thus, answer is n^3 + 6

Hope this helps!

Answer:

Eli is incorrect. He added the exponents even though the bases are not the same.

Step-by-step explanation:

6^5 * 5^-3 = 6^2

5^-3 = 1/5^3 = 1/125

6^5 = 7776

7776*1/125 = 7776/125 = 62.2 approximately

Answer:

Eli is incorrect. He added the exponents even though the bases are not the same.

Step-by-step explanation:

Edge

Answer:

2x+7

Step-by-step explanation:

To Simplify an Expression , we combine Like-Terms

So for our Question , we have Terms with x and Constant Term

Combine Terms with x : 5x-2x-x=2x

Constant Term : 7

Then 5x-2x+7-x = 2x+7

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

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{5x - 2x + 7 - x = }[/tex] ________[tex]\mathbf{\ x \ + }[/tex]________

[tex]\huge\textbf{Simplify the left side of the equation, to}\\\huge\textbf{get the result of the right side of the}\\\huge\textbf{equation.}[/tex]

[tex]\huge\textbf{Simplifying the LEFT side:}[/tex]

[tex]\mathbf{5x - 2x + 7 - x}[/tex]

[tex]\mathbf{= 5x - 2x + 7 - 1x}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (5x - 2x - 1x) + (7)}[/tex]

[tex]\mathbf{= 5x - 2x - 1x + 7}[/tex]

[tex]\mathbf{= 3x - 1x + 7}[/tex]

[tex]\mathbf{= 2x + 7}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{2\mathsf{x} + 7}}\huge\checkmark[/tex]

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

68% of the data lies within one standard deviation from the mean

95% of the data lies within two standard deviation from the mean

99.7% of the data lies within three standard deviation from the mean

The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean

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The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.

Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Given:

x (x-2) (x + 3) = 18

Divide both sides of the equation by x:

x (x-2) (x + 3) / x = 18 / x

(x-2) (x) + 3) = 18 / x

You can use the following simultaneous equations.

(1) y = (x-2) (x + 3)

(2) y = 18 / x

Using a graphing calculator, we get:

x = 3, y = 6 → point = (x, y) = (3,6)

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Answer:20ft

Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20

20x15 equals 300 so it goes both ways

Answer:

x = - 3

Step-by-step explanation:

A vertical line parallel to the y- axis has equation

x = c

where c is the value of the x- coordinates the line passes through

the line passes through (- 3, 0 ) and (- 3, 3 ) with x- coordinates - 3 , then

x = - 3 ← equation of vertical line

The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints

1 pound = 16 ounces

Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces

= 13/4 × 16

= (208) / 4

= 52 ounces

1 gallon = 4 quarts

0.15 gallon = 0.6 quarts

1 quart = 2 pints

0.6 quart = 1.2 pints

Pint of water dispensed in 20 seconds = 1.2 × 20

= 24 pints of water

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The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.

In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.

It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.

Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.

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On the given graph, we can see that we have:

The correct option would be a in both cases.

We want to study the asymptotes of the graph

If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.

the graph has a horizontal asymptote (or two actually) at y = 3.

For the vertical asymptote we just look at the vertical dashed line, it is at x = -2

Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.

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Steve is 1.2 times faster than Paul.

The quantitative relationship between two values indicating how frequently one value is contained within the other.

For example: Speed = Distance / Time

Total distance covered by both Steve and Paul = 100m

Total time taken by Steve = 10s

Steve's speed = 100 / 10 = 10m/s

Total time taken by Paul = 12s

Paul's speed = 100 / 12 = 8.33m/s

Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2

Hence we can say that Steve is 1.2 times faster than Paul.

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Answer:

22.470

Step-by-step explanation:

In this example you have to use the trigonometric function sine which is defined as [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex]

Plug in known values:

[tex]sin(64) = \frac{x}{25}[/tex]

Multiply both sides by 25

[tex]sin(64) * 25 = x[/tex]

Approximate sin(64) using a calculator:

[tex]0.89879 * 25 = x[/tex]

Simplify

[tex]22.470 \approx x[/tex]

Stratified sampling is used by Made Eyewear

Stratified sampling is is where we divide the population into groups by some characteristic such as age or occupation or gender. Then make sure our survey includes people from each group in proportion to how many there are in the whole population.

Example of this sampling is A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age and use of eyeglasses, like 18–29, 30–39, 40–49, 50–59, and 60 and above

So, Stratified sampling is used by Made Eyewear

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Answer: (-4,0), (4,0)

Step-by-step explanation:

x-intercepts are when y=0.

Answer:

8x+55y ≤ 184

Step-by-step explanation:

8x: The x in 8x signifies the amount of books you can buy. So let's say you want to buy 4 books then x would be 4 and 8x would be equivalent to 42.

55y: The y in 55y signifies the amount of video games you can buy. So let's say you want to buy 2 video games then y would be 2 and 55y would be equivalent to 110.

≤: We're using this sign because you can spend a maximum of 184 dollars. Meaning that the amount you spend (which is the 8x+55y) has to be less than or equal to 184 dollars.

184: The amount of money you are able to spend total.

Hope that helps! If you have any questions feel free to ask me :)