In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove that XYZ is also an equilateral triangle.

~Thanks in advance ! ​

The graph and inverse of a function are reflections of each other along the line y = x.

A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).

When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.

Therefore,

The point (x, y)'s reflection over the line y = x is (y, x).

The point (x, y)'s reflection over the line y = - x is (-y, -x).

Thus, the graph and inverse of a function are reflections of each other along the line y = x.

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Step-by-step explanation:

10x2(x-2)2=100x2x2 2x2

Answer:its b

Step-by-step explanation:

trust me its b

The sample standard deviation is 7.6 and the sample variance is 2.76.

for the scores  5, 2, 2, 7, 9.

According to the question,

Sample size n = 5

Sample Mean = [5+2+2+7+9]/5

= 5

Formula for sample standard deviation = (x-mean)²/n

= [(5-5)²+(2-5)²+(2-5)²+(7-5)²+(9-5)²]/5

= [0+9+9+4+16]/5

= 38/5

= 7.6

Formula for sample variance = √sample standard deviation

=√7.6

=2.76.

Hence, the sample standard deviation is 7.6 and the sample variance is 2.76.

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Answer:

Question 2: 4 1/2

Question 10: $7.24

Step-by-step explanation:

Question 2:

1 1/2/x = 3/9

to solve for x, we need to use 1 1/2/x and multiply it by x:

1 1/2/x * x

then we need to have 3/9 multiplied by x:

3/9 * x

this is equal to 1 1/2 = 3/9 * x

now you need to multiply both sides by the opposite of 3/9 = 9/3

3/2 * 9/3 = 3/9 * 9/3 * x which equals 9/2 = 4 1/2

final answer: 4 1/2

Question 10:

Jeff bought 3 boxes of cereal $2.99 each which comes up to $8.97,

he bought one gallon of milk for $4.98,

and 4 bananas for $0.50 each which in total is $2.00.

total amount spent: 8.97 + 4.98 + 2.00 = $15.95

We know there is a 20% off discount so what we have to do is take 20% off $15.95!

20%= $3.19

15.95 - 3.19 = 12.76

The total is now $12.76. But, Jeff payed with a $20.00 bill. Because of this, he will get $7.24 back. 12.76 + 7.24 = 20

Final answer: $7.24

The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2). Option B

The term factorization has to do with the process of obtaining common factors in an expression. It involves dividing each term in the expression with a factor that is common to all the terms in the expression.

The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2).

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Missing parts;

Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)

See below for the organized result in a two-way frequency table

The given parameters are:

Candies = 18

Chocolate and Caramel = 10

None = 3

Chocolate = 12

Using the above parameters, we have the following rows and columns:

                                           Chocolate

                                           Present            Absent     Total

Caramel     Present                  

                   Absent

                   Total

Next, we populate the table as follows:

                                           Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3

                   Absent

                   Total                       12

The total number of candies is 18.

So, we have:

                                    Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3             13

                   Absent

                   Total                       12                 6               18

Subtract the cells from the column total

                                    Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3             13

                   Absent                    2                   3             5

                   Total                       12                   6              18

The above represents the organized result

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The null hypothesis is μ≥700 and alternative hypothesis is μ<700, the type of test statistic is t statistic, the statistical test value is -2.650, the critical value is -1.796 and the null hypothesis is reject.

Given the average monthly rent for apartments on the east side of the cities is $700, and the mean for a random sample of 12-month rents for apartments on the east side is $687, with a standard deviation of $17.

Statistical hypothesis testing is an important technique in inferential statistics. Used to test hypotheses about population parameters. Statistical tests are used to compute test statistics and p-values. Finally, use this test statistic and the p-value to make a decision about rejecting the null hypothesis.

(a) Let μ be the population and monthly rent. the null and alternative hypotheses are given below.

Null Hypothesis: μ≥700

Alternative hypothesis: μ< 700 This is a left-sided hypothesis test.

(b) Here, the sample size is less than 30 and the population mean is unknown. Therefore, a one-sample t-test can be used here. Therefore, the t statistic is the test statistic.

(c) Given [tex]\bar{x}[/tex]=687, s=17 and n=12, the test statistic is computed as

[tex]\begin{aligned}t&=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}\\ &=\frac{687-700}{17/\sqrt{12}}\\ &=-2.64901888216\\ &=-2.650\end[/tex]

(d) For n-1=12-1=11 degrees of freedom

The critical value for a significance level of 0.05 with 11 degrees of freedom is

[tex]\begin{aligned}t_{crit}&=-1.7959\\ &=-1.796\end[/tex]

(e) Reject the null hypothesis because the statistical test value (-2.650) is less than the critical value (-1.796). There is ample evidence to support the claim that the average monthly rent for East Side apartments is lower than stated on the website.

Hence, The value of test statistic and critical value has a mean of $687 and a standard deviation of $17, which are -2.650 and -1.796.

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If Eli ate  one third of a pie on friday ,one fourth proportion of the pie on saturday and 50 ounces of the pie on sunday then it is found that she ate 30 ounces of pie.

Given that Eli ate one third of a pie on friday, one fourth of the pie on saturday, and final 50 ounces of the pie on sunday which is left out.

We have to find the amount of pie that she ate one saturday.

We are given fraction and we know that sum of all fractions of something is equal to 1.

Let the proportion that she ate on sunday be x.

1/3+1/4+x=1

Taking LCM.

(4+3+12x)/12=1

7+12x=12

12x=12-7

12x=5

x=5/12

So the left out out portion that she ate on sunday is 5/12 of the pie.

We are given that she ate 50 ounces on sunday so the total pie will be 12/5*50=120 ounces.

Portion eaten by Eli on saturday =1/4

Pie that she ate on saturday=1/4*120

=30 ounces.

Hence Eli ate 30 ounces of pie on saturday.

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The value of f(x) when x is -6 is 1.

Composite functions are also known as function of a function. In order to get a composite functions f(g(x)).

g(4) = -6 (the value of g(x) when x is equivalent to 4 is -6)

f(g(x))= f(g(4)) = f(-6)

f(-6) = 1

The value of f(x) when x is -6 is 1.

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Mr. Cahn’s total earnings in a year is $18,900.

The total earnings is a function of the annual salary, commission and Christmas bonus.

Total earnings = annual salary + commission + Christmas bonus

Commission = 6% x (160,000 - 20,000)

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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Considering it's asymptotes, the rational function shown in the graph is:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:

(x + 2)(x - 1).

The horizontal asymptote is of y = 0, hence the function can be given by:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

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The values of x and y are 19 and 14 respectively.

Given the hypotenuse = 24

Opposite = x

Adjacent = y

Let's use the sine ratio to find the opposite side

sin of angle = opposite/hypotenuse

sin 54 = x/24

Cross multiplysin 54 × 24 ,= x

x = 19.42

x = 19

To find the adjacent side, we use cosine ratio

cos = adjacent/hypotenuse

cos 54 = y/25

Cross multiply

cos 54 × 24 = y

y = 14

Thus, the values of x and y are 19 and 14 respectively.

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Answer:

B, 2

Step-by-step explanation:

The slope in a y=mx+b equation is m. The m in your equation is 2.

Therfore, your slope is 2.

Answer: x = [tex]\sqrt{y^2 -1}[/tex]

Step-by-step explanation:

The graph that describes the motion of Maria is the graph in Option B.

Displacement is the term that is used to describe the distance covered in a specified direction.

We are told that Maria walked up a hill in 30 minutes, and then she ran back down the hill in 10 minutes. The graph that describes this motion is the graph in Option B.

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There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

Using a system of equations, it is found that Oscar bought 6 markers, 6 notebooks and 15 packs of sticky notes.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

He bought the same number of markers as notebooks, hence:

x = y.

He bought three more packs of sticky notes than markers and notebooks combined, hence:

z = 3 + x + y

z = 3 + 2x.

He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. He spent $49.05 in total, hence:

1.05x + 2.25y + 1.95z = 49.05.

Then:

1.05x + 2.25x + 1.95(3 + 2x) = 49.05.

7.2x = 43.2

x = 43.2/7.2

x = 6.

The amounts are as follows:

He bought 6 markers, 6 notebooks and 15 packs of sticky notes.

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Answer:

P(draw 4) = 1/6

Step-by-step explanation:

Six cards means: n(s) = 6

The equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

The function is given as:

d(t) = a * sin(b * t) + d

The bob is 5 cm away from the wall implies that the vertical shift is 5.

This means that

d = 5

So, we have

d(t) = a * sin(b * t) + 5

The bob reaches the closest point to the wall, which is 3 cm from the wall.

So, the amplitude is

A = 3 - 5

Evaluate

A= -2

So, we have:

d(t) = -2 * sin(b * t) + 5

The period is calculated as:

B = 2π/t

Where

t = (5 + 3)/2

This gives

t = 4

Substitute t = 4 in B = 2π/t

B = 2π/4

Evaluate

B = π/2

So, we have:

d(t) = -2sin(π/2 t) + 5

Hence, the equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

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We can actually deduce here that the following that is characterized by drawing the boundaries of legislative districts in bizarre or unusual ways to favor one party is: A. Gerrymandering.

Gerrymandering is actually known to be characterized by the practice of setting electoral district boundaries in order to favour some specific political interest in some legislative bodies and district.

Gerrymandering usually leads to the creation of convoluted districts rather than compact areas. The gerrymandering is seen in the United States.

The word "gerrymandering" was actually coined when Massachusetts's redistricting maps of 1812 was reviewed by Governor Elbridge Gerry. This was done when it was noted that one of the districts resembled a salamander.

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Answer:38

Step-by-step explanation:4+5×6+4=4+30+4=38

Answer:

(-4,0) and (4,0)

Step-by-step explanation:

The x-intercepts occur for values of x where f(x) = 0.

f(x) = 0 when the nominator ([tex]x^{2} - 16[/tex]) = 0.

[tex]x^{2} -16[/tex] is a difference of squares,
so you can factor it as (x + 4)(x – 4)

When x = –4 or x = 4, the nominator is 0, and f(x) = 0

Answer:

5

Step-by-step explanation

becasue 2x0=0 and 1x0=0

and when you add 5 to 0 you get five

Answer: B. a^4/b^12

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{a}{b^{3} }\right)^{4} \end{gathered}$}[/tex]

Use the rules of exponents to simplify the expression.

To raise the quotient of two numbers to a power, raise each power to the power and then divide it.

To raise a power to another power, multiply the exponents.

Multiply 3 by 4.

We conclude that: the correct option is "B".

A. 6x²-2x+5, is the quotient of the polynomial.