what is Rational Number​

The transformation that maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2.

A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on similarity transformation of both quadrilateral 1 and quadrilateral 2, we can infer and logically deduce that the transformation which directly maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2, as shown in the image attached below.

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Answer:

  (f +g)(2) = -7

Step-by-step explanation:

Functions are added by adding their values.

  (f +g)(2) = f(2) +g(2)

  = (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2

  = -6 +(-1)

  (f +g)(2) = -7

Valerie needs to run [tex]8\frac{1}{8}[/tex] laps.

What are mixed fractions?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

You can divide any fraction into two pieces. These are the denominator and numerator. A improper fraction is one in which the numerator is greater than the denominator. The numerator must then be multiplied by the denominator by the students. They will then receive a specific form of a fraction. That is referred to as a mixed fraction.

Given,

Number of laps valerie ran = [tex]3\frac{1}{4}[/tex] laps

Number of times her coach wants her to run = [tex]2\frac{1}{2}[/tex] times

Therefore,

total number of laps she needs to run = [tex]3\frac{1}{4} \times 2\frac{1}{2}[/tex]

                                                               [tex]= \frac{13}{4} \times \frac{5}{2}[/tex]

                                                               [tex]= \frac{65}{8}[/tex] laps

                                                               [tex]=8\frac{1}{8}[/tex] laps.

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Answer:

Y = 2+- square root of 6

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets solve ~

Let's calculate its discriminant ~

[tex]\qquad \sf  \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16 - ( - 8)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]

So, by quadratic formula :

[tex]\qquad \sf  \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]

Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)

Translating 4 to the right means that you should add 4 to the x value of your coordinate point.

Question 18: C. (3,-5)

This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.

Question 19: A. C’ (0,-2)

We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)

Hope this helps! Let me know if you need more help! Have a fantastic day!

Answer:

416 people

Step-by-step explanation:

The way you get the answer is by adding up the number of people from the sample, which gives you 175 people. After finding that you take the number of people who like pretzels (26) and divide it by 175, giving you 0.16 or 16%.
This means 16% of people will like pretzels, so you apply this to the actual number of people coming, 2600, and find 16% of 2600 (0.16 x 2600) which is 416 people. I hope this makes sense :)

The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

According to the statement

we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.

And we have to find that the yield to maturity on this bond.

So, For this purpose,

The amount given is $911. 10.

Years to maturity = n = 10

Coupon rate = C = 8.25%

Semiannual coupon = $1,000 × (0.0825/2) = $41.25

Yield to maturity = i

Present value of bond = PB = $911.10

Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 9.4%:

= $522.90 + 391.54 ≅ $914.43

The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).

So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

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Answer:

A) the fraction of the week that Jamaar spent in this garden.

Answer:

7 to 22.96

Step-by-step explanation:

Hello!

We can represent each ratio as a fraction:

To find equivalent values, we can convert each fraction into a decimal by dividing them.

The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.

The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1)

First quartile = 1/4 x (n + 1)

The mean absolute deviation is the average of the distance of a data set from its mean.

Mean absolute deviation =  ∑ l x - m(x) l

Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.

Here are the options:

Mean absolute deviation

mean

interquartile range

median

mode

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mean absolute deviation
mean

median

interquartile range

mode

Answer:

Step-by-step explanation:

The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:

  rational roots = ±{divisor of 25} / {divisor of 3}

The list of divisors in each case is pretty short, so this is ...

  rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}

We find the only actual rational root is x = 5/3 when we graph the function.

(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)

The correct option is option (d) 8 hours.

Amelia need to work for 8 hours to buy new sweater $40.

When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.

Let the hours Amelia need to work=h

Amalia paid=$20

Payment of each hour=$2.50

So, we can make an equation with given problem

40=20+2.50h

40-20=2.5h

20=2.5h

[tex]h=\frac{20}{2.5}[/tex]

h= 8

So, Amelia need to work for 8 hours to get $40.

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Intercepts with the axes are where your line touches the x or y axis. An example is a straight line, say, y=4x+2. In this case, the y-intercept is 2 because the line touches the y-axis at (0, 2). With y=mx+b format, the y-intercept is b. To find the x-intercept of an equation in y=mx+b format, set y to zero and solve for x. In a parabola, the x-intercepts would be the roots. An example of this is x^2 - 5x + 4 = 0. The roots here are (4,0) and (1,0). Hopefully this helped.

From the given options, the rational numbers is:

17.156 = 17,156/100

Which is the one in option C.

A rational number is a number that can be written as the quotient of two integer numbers.

When written in decimal form, a rational number has a finite number of digits after the decimal point. Now, for the given options we have:

A: √15

B: 2.6457513110...

C: 17.156

D: √3/85

Now, the square root of a number that is no square, is always an irrational number, so we can discard these two, and also we can see that the number in option B has infinite digits after the decimal point, so we also discard that one.

Now, if we look at the remaining option, which is:

17.156

We can multiply it and divide it by 100 to get:

(100/100)*17.156 = 17156/100

So the number can be written as the quotient of two integers, which means that it is a rational number.

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Answer:

2/9 - 2/15

Solution

LCM = 45

45 ÷9 ×2 = 10

45÷ 15 ×2 = 6

10 - 6 = 4

ANSWER = 4/45

Answer:

l

Step-by-step explanation:

take the lcm of 9 and 15. it will be 45 . than continue

No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.

The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.

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Answer:

3,500 people

Step-by-step explanation:

10% of 35,000 is the same as .10 × 35,000, or 3,500.

The mean, median, and mode of the 5 number 5, 7, 8, a, b. are equal so

the possibilities of a+b is 20.

The" mean" is the" average" you are used to, where you add up all the figures and also divide by the number of figures.

The" median" is the" middle" value in the list of figures. To know the median, your figures have to be listed in numerical order from lowest to largest, so you may have to rewrite your list before you can find the median.

The" mode" is the value that occurs utmost often. However, also there's no mode for the list, If no number in the list is repeated.

Given numbers are: 5, 7, 8, a, b

Total number =5

Then,

The mean = (5+7+8+a+b) / 5

Mean=(20+a+b) / 5          ------------------ (1)

Median=middle value in the list of figures

Median=8                  ------------------(2)

According to the question ,mean and median  are equal

Compare equation (1) and (2),

we get

= (20+a+b) / 5=8  20+a+b

=40a+b=20

there is no repetition of any number, so no mode is there

hence, all the possibilities of a+b is 20.

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The expression that represents the height of the oblique prism is: 1/2x.

What is the Volume of a Prism?

Prism Volume = base area × height of the prism

Given that the oblique prism has:

Volume = 1/2x³ cubic units

edge length = x units

Therefore,

base area = x²

Thus:

1/2x³ = (x²)(height)

Divide both sides by x²

1/2x³ ÷ x² = height

1/2x³ × 1/x² = height

x³/2 × 1/x² = height

height = x³/2x²

height = x/2

Therefore, the expression that represents the height of the oblique prism is: 1/2x.

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The complete question is -

An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?

The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.

Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.

If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :

P(e₁ ∪ e₂) = P(e₁) + P(e₂)

Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.

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from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]

The time in seconds that it took the ball to travel would be = 0.25 seconds.

Speed can be defined as the distance covered by an object per unit time.

The speed used to kick the soccer off the ground = 56 feet per second.

The height equation= −16t² + 56t

The time= ?

The formula for speed = distance/time

56= −16t² + 56t/t

56t = −16t² + 56t/t

−16t² = -56t + 56t

−16t² = 0

Make t the subject formula,

t = √1/16

t = 0.25 seconds.

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The improper fraction is 25 / 6 hours

The mixed fraction is  [tex]4\frac{1}{6}[/tex] hours.

The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.

In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour

0.6 x 60 minutes = 10 minutes

The decimal becomes : [tex]4\frac{10}{60}[/tex] hours

[tex]4\frac{1}{6}[/tex] hours

To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator

The improper fraction is : 25 / 6 hours

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Matt's BAC the equation for is  mathematically given as

X= 4 standard drinks

This is further explained below.

Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.

Generally, One standard drink is equal to twelve ounces of beer.

He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.

In conclusion, the number of standard drinks that Matt consumed

X= 48/12

X= 4 standard drinks

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Answer:

Step-by-step explanation:

Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.

For the first inequality:

4(x + 1) > -4 we distribute through the parenthesis to get

4x + 4 > -4 and subtract 4 from both sides to get

4x > -8 and then divide both sides by 4 to get

x > -2.  That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.

For the other inequality:

2x - 4 ≤ -10 we add 4 to both sides to get

2x ≤ -6 and then divide by 2 to get

x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is

(-∞, -3] or (-2, ∞).  The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.

The expression has 2 factors, and the second factor has 2 terms.

We can write an expression of N factors as:

[tex]y = A_1*A_2*...*A_n[/tex]

Here, the expression is:

4*(8x + 5)

This expression has 2 factors, which are:

4 and (8x + 5)

Now, if we look at the only factor 8x + 5, we have two terms (the terms are the parts that are added), the terms are:

8x and 5.

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Answer:

8

Step-by-step explanation:

Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.

Since the numbers are very small, we can grind out this same number (but be organized):

Jean/white

Jean/tan

Jean/green

Jean/black

Leather/white

Leather/tan

Leather/green

Leather/black

These are the eight choices.

Step-by-step explanation:

she increased the amount from 48g to 54g. that is 54-48 = 6g.

so, the question really is, how many % of 48 is 6 ?

100% = 48g

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%

Answer:

1/9

Step-by-step explanation:

For each of the first die's 6 outcomes, the second die also has a possible 6 outcomes.

6 × 6 = 36

There are 36 different outcomes from

1, 1

1, 2

1, 3

...
6, 6

Many outcomes have the same sum. For example, 3, 4 and 4, 3 both add to 7.

How many outcomes add to 9?

3, 6

4, 5

5, 4

6, 3

4 different outcomes out of a possible 36 different outcomes add to 9.

p(sum of 9) = 4/36 = 1/9

The possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters

convert to centimeters

Perimeter of a square = 4a

where,

Perimeter of a square = 4a

2900 = 4a

divide both sides by 4

a = 2900/4

a = 725 centimeters

Therefore, the possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters

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