A. 2
B. 1/3
C. 5
D. -3​

Answer:

1. Transversal y intersects lines m and n; <1 ~= <2 (Given)

2. <1 ~= <3 (Vertical Angles Theorem)

3. <2 ~= <3 (Transitive Property of Congruence)

4. m || n (Converse of Alternate Interior Angles Theorem)

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]

Answer:

22

I remember this question in school

Applying properties of exponents, the quotient is given as follows:

[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]

The expression is given by:

[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}[/tex]

The 3 can be inserted into the cube root, as follows:

[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}[/tex]

Applying the subtraction, we have that the expression is:

[tex]\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}[/tex]

The denominator can be simplified as follows:

[tex]\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}[/tex]

Then:

[tex]\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}[/tex]

Hence the quotient is given by:

[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]

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The value of x in 6/7x + 1/2 = 7/8 is 7/16

The equation is given as:

6/7x + 1/2 = 7/8

Subtract 1/2 from both sides

6/7x + 1/2 -1/2 = 7/8 -1/2

Evaluate the difference

6/7x = 3/8

Multiply both sides by 7

6x = 21/8

Divides both sides by 6

[tex]x = \frac {7}{16}[/tex]

Hence, the value of x is 7/16

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Answer:

Step-by-step explanation:

The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.

Step-by-step explanation:

step 1: how many dolphins

there are 6 sharks

sharks to dolphins is 3 to 5

3 S to 5 D

we can divide 6 (amount of sharks known) by 3, to get what a ratio of 1 is

6 ÷ 3 = 2

so 2 sharks is = 1 part or ratio

now we can times by 5 to get a ratio of 5

5 × 2 = 10

there are 10 Dolphins

Step 2: How many starfish

repeat the steps above but for the ratio 2: 7 where 2 is the Dolfin ratio and there are 10 dolphins

put in questions answer you got

Answer:

35 starfish

Step-by-step explanation:

shark/dolphin  *  dolphin /starfish = shark / starfish

Now. put in the numbers given:

3/5 * 2/7 =      6/35  = shark / starfish    put in '6' for shark (given)

        6/35 = 6/starfish        cross multiply

        6 * starfish = 35* 6

           starfish = 35  

Answer:

y = 2x - 11.

Step-by-step explanation:

Use the point-slope form of the straight line.

y - y1 = m(x - x1)   where m = slope and (x1, y1) is the given point.

Here m = 2 and (x1, y1) = (7,3) so the equation is:

y - 3 = 2(x - 7)

y - 3 = 2x - 14

y = 2x - 11

For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.

A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.

The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.

A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.

Given 300 2   and p 0.45

p = 0.45 Up

and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287

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[tex] \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c[/tex]

688,747,536 ways in which the people can take the seats.

There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.

When the whistle blows, each person needs to change to an orthogonally adjacent seat.

(This means that the person can go to the seat in front, or the seats in the sides).

This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.

Now, if we take the options that each seat has, and we take the product, we will get:

P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.

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The expression that represent the given statement is p/q - m²

From the question, we are to write an expression for the word problem

We are to write an expression for the statement

"Subtract the square of m from the ratio of p and q"

Square of m = m²

Ratio of p and q = p/q

Thus,

subtract the square of m from the ratio of p and q, becomes

p/q - m²

Hence, the expression that represent the given statement is p/q - m²

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Answer:

[tex] - \frac{ \sqrt{2} }{2} [/tex]

Step-by-step explanation:

The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.

Answer:

0.1 cases

Step-by-step explanation:

100(1-0.90)^3

100(0.10)^3

100(0.001)

0.1

The required minimum sample size to construct a 95% confidence level for the population mean is 267.

In this question,

In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.

The population standard deviation, σ = 25

Confidence level for the population mean = 95%

Margin of error = ±3

Let n be the sample size of the population

The z-score for the confidence level of 95% for the population mean is 1.96.

The formula of margin of error is

[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]

Now, the sample size of the population can be calculated as

[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]

On substituting the above values,

⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]

⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]

⇒ [tex]n=(16.33)^{2}[/tex]

⇒ n = 266.77 ≈ 267

Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.

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The values of trigonometric functions sin(x/2) is [tex]\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex], cos(x/2) is [tex]\frac{1}{\sqrt{14(7+4\sqrt{3})}}[/tex] and tan(x/2) is 7+4√3.

Given that the value of trigonometric function csc(x)=7 for 90°<x<180°.

We are given:

csc(x)=7 Where: 90° < x < 180°

This interval indicates that the angle x in the second quadrant and we know that at that quadrant sin(x) and CSC(x) functions are positive and all other trigonometric functions sign are negative.

Now:

sin(x)=1/csc(x)

sin(x)=1/7

Using the trigonometric identity sin²x+cos²x=1, we get

cosx=±√(1-sin²x)

cosx=±√(1-(1/7)²)

cosx=±√((49-1)/49)

cosx=±(4√3)/7

As x is in second quadrant.

Therefore, cosx=-(4√3)/7

consider the inequality, 90°<x<180°

Divide by 2, we get

45°<x/2<90°

This is the angle x/2 in the first quadrant and in that quadrant all functions sign are positive.

Substitute the value of cosx in half angle formula for sine function,

[tex]\begin{aligned}\cos x&=1-2\sin^2\left(\frac{x}{2}\right)\\ -\frac{4\sqrt{3}}{7}&=1-2\sin^2\left(\frac{x}{2}\right)\\ 2\sin^2 \frac{x}{2}&=1+\frac{4\sqrt{3}}{7}\\\sin \frac{x}{2}&=\pm\sqrt{\frac{7+4\sqrt{3}}{14}}\end[/tex]

As x/2 lies in first quadrant then [tex]\sin \frac{x}{2}=\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex]

Again, Substitute the value of cosx in half angle formula for sine function,[tex]\begin{aligned}\sin x&=2\sin\left(\frac{x}{2}\right)\cos\frac{x}{2}\\ \frac{1}{7}&=2\sqrt{\frac{7+4\sqrt{3}}{14}}\cos\left(\frac{x}{2}\right)\\ \cos \frac{x}{2}&=\frac{1}{14\times\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}}\\\cos \frac{x}{2}&=\frac{1}{\sqrt{14(7+4\sqrt{3})}}\end[/tex]

Now find tan(x/2) as shown below, we get

[tex]\begin{aligned}\tan\frac{x}{2}&=\frac{\sin\frac{x}{2}}{\cos \frac{x}{2}}\\&=\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}\times \frac{\sqrt{14}\sqrt{7+4\sqrt{3}}}{1}\\&=7+4\sqrt{3}\end[/tex]

Hence, when trigonometric function csc(x)=7 for 90°<x<180° then sin(x/2) is [tex]\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex], cos(x/2) is [tex]\frac{1}{\sqrt{14(7+4\sqrt{3})}}[/tex] and tan(x/2) is 7+4√3.

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If I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only.

This ultimately implies that, a numerical data is a data set consisting of numbers rather than words.

An outlier can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.

Assuming I am counting the number of expert tutors on Brainly and I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.

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The speed of private jet is = 252 mph

The speed of commercial jet is =  360 mph

What is speed ?

Let the speed of private jet be x mph.

Then the speed of commercial jet will be = 2x - 144

Equation forms:

10x = 7 ( 2x - 144 )

Solving for x

10x = 14x - 1008

⇒ 10x - 14x =  - 1008

⇒ - 4x = - 1008

⇒ x = 252

So, x = 252

Hence, the speed of private jet is = 252 mph

The speed of commercial jet is =  = 2(252) - 144 = 360 mph

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Answer:

A, C, D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

for the lines to be parallel , then

8x - 14 and 2x + 54 are same- side interior angles and sum to 180°, that is

8x - 14 + 2x + 54 = 180

10x + 40 = 180 ( subtract 40 from both sides )

10x = 140 ( divide both sides by 10 )

x = 14

Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: [tex]a*\frac{x}{100}[/tex] where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: [tex]\frac{96}{100} = 0.96[/tex]. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

[tex]0.96T = 72,000[/tex]

To find the original value of T, we simply divide both sides by 0.96

[tex]T = 75,000[/tex]

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

[tex]1000P = T[/tex]

Substitute 75,000 as T

[tex]1000P = 75,000[/tex]

Divide both sides by 1,000

[tex]75=P[/tex]

This means she sold each for 75

Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)

The coefficient of determination is 1.

Given

Total Sum of squares (SST) = 90

Sum of squares due to error (SSE) = 0

We have to find coefficient of determination.

The correlation of determination is the ratio of the explained variation to the total variation.

The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.

The coefficient of determination is also called r-squared or r-square.

Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.

Coefficient of determination can be found with the following formula:

Formula of coefficient of determination :

[tex]R^{2} = 1 - \frac{SSE}{SST}[/tex]

= 1 - [tex]\frac{0}{90}[/tex]

= 1 - 0

= 1

[tex]R^{2}[/tex] = 1

Therefore,

The coefficient of determination is 1.

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Step-by-step explanation:

Circumference = πd

= π × 12

= 37.6991

=38

Answer:38

Step-by-step explanation:

Answer: A, D

Step-by-step explanation:

A) Correct. [tex](x^3)^2=x^{(3)(2)}=x^6[/tex]. Similar logic for y.

B) Incorrect. The numerators are different.

C. Incorrect. The denominators are not the same.

D. Correct. The denominators are the same by difference of squares.

Answer:

(2030)4

Step-by-step explanation:

Base 6 to decimal calculation:

(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10

Decimal to base 4 calculation:

Divide by the base to get the digits from the remainders:

= (2030)4

Still have any questions?

Do hit me up or contact me

The answer is 2030.

First, convert from base 6 to base 10.

Now, convert from base 10 to base 4.

Connecting the digits, the answer is : 2030

Answer:

B.  -x³ - 9x².

Step-by-step explanation:

- (3x³ + x²) +2 (x³ - 4x²)

= -3x³  + 2x³  - x² - 8x²

= -x³ - 9x²

Answer: [tex]\Large\boxed{-x^3-9x^2}[/tex]

Hi there! By my calculation, I got the answer above. However, it doesn't fit any one of the answer choices. I am not sure if I am totally correct, but I have been double-checking my answers. Please let me know whether it's the answer choices mistaken or I am wrong so that I could modify my answer if necessary.

Step-by-step explanation:

Given expression

- (3x³ + x²) +2 (x³ - 4x²)

Expand parenthesis by the distributive property

= -3x³ - x² + 2x³ - 8x²

Combine like terms

= -3x³ + 2x³ - x² - 8x²

[tex]\Large\boxed{=-x^3-9x^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.

Note that the equation of the functions are stated as:

f(x) = 2x² + 7x + 6

g(x) = 2^x + 5

The right and next thing to do is to plot a graph of both functions (see image attached)

From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)

Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

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The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

The equation can be simplified as follows:

7y + 8 = 9 + 3y + 2y

We have to combine like terms

Hence,

7y + 8  = 9 + 3y + 2y

7y + 8 = 9 + 5y

subtract 5y from both sides

7y - 5y + 8 = 9 + 5y - 5y

2y + 8 = 9

Let's subtract 8 from both sides

2y + 8 - 8 = 9 - 8

2y = 1

Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

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