Mrs. Gallas is playing with her class. She picks one of the points on the graph and gives three clues. If the class can correctly guess the point, they win.
Clue #1: y = 0
Clue #2: The distance from the origin is greater than 3 units.
Clue #3: The distance from the origin is greater than 3 units.

Which point did Mrs. Gallas choose?

[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]

The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸

Given: (4×2⁵) / (2³ × 1/16)

In order to write this expression as the power of 2, we need to use some in indices law:

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":   5⁴ x 5³ = 5⁴⁺³ = 5⁷ and  P⁴ x P⁶ = P¹⁰

Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base":   5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and  P⁸  ÷  P² = P⁸⁻² = P⁶

Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:

8⁻² = 1/8²   and b⁻⁶ = 1/b⁶  

Let's use the laws to create the given expressions as the power of 2:

(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴)       Note: 4 = 2² and 16 = 2⁴    

                            = (2²⁺⁵) /(2³⁺⁽⁻⁴⁾)               Note: 1/2⁴ = 2⁻⁴ (reciprocal law)

                            = 2⁷ / 2⁻¹

                            = 2⁷⁻⁽⁻¹⁾                            Division law

                            = 2⁸

Therefore, the expressions as the power of 2 is 2⁸

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|-2.65| can be found between numbers 2.6 and 2.7

Absolute value means to remove any negative sign in front of a number and to think of the number as positive.  This is what the vertical lines |  | surrounding -2.65 means.

Thus,   |-2.65| = 2.65

If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7

Therefore,  |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer

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The probability that the first card is a heart and the second one is not a heart is P = 0.19

A standard deck has 52 cards divided in 4 sets, such that each set has 13 cards.

The probability of randomly drawing a heart is equal to the quotient between the number of cards of the set heart (13) and the total number of cards (52), so we get:

p = 13/52

Now, the probability of not getting a heart is equal to the number of cards that are not hearts (3*13 = 39) and the total number of cards (now is 51 because we already took one).

q = 39/51

The joint probability is equal to the product between the two individual probabilities:

P = q*p = (13/52)*(39/51) = 0.19

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Answer:

24:23

Step-by-step explanation:

Answer:

The slope is -1.

Step-by-step explanation:

When given two points, the formula for slope is [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

4 - 7 / -2 - (-5) = -3 / 3

-3 / 3 = -1, so the slope is -1.

The probability of rolling a number less than 12 is 91.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.

We can have the number 12, the probality will be 1/12

So the probability of rolling a number less than 12 is = (1 -  probability of 12)

=1-1/12

=11/12

=0.916

Hence the probability of rolling a number less than 12 is 91.6%.

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Answer:

Step-by-step explanation:

We know that corresponding parts of congruent figures are congruent.

It means:

Step-by-step explanation:

given

f(x)=6x+9

solve

6(6x+9)+9=0

36x+54+9=0

36x+63=0

36x=_63

36x/36 = _63/36

x=_63/36

Andrew's score on the midterms this week, based on his scores last week and the absolute change, is 95%.

The Midterm score for this week increased by 23 percentage points over the midterm score for the last week. This increase in the midterm score was an absolute change and not a relative change.

As a result of this being an absolute change, the midterm score for Andrew this week would then be:

= Midterm score last week + absolute change in the score

= 72% + 23 percentage points

= 95%

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Answer:

Step-by-step explanation:

these seem complicated,  but just think about what they are asking.  they are giving you a point and a slope to a line.  

That gives you the hint to use the "point-slope"  formula

if you don't have it memorized you might as well start trying to now.  You'll need this over and over and over...

y-y1=m(x-x1)

so plug in the given info

y-4= (-1/4)(x-(-2))

y-4 = -1/4 (x +2)

y-4 = (-1/4)x  -1/2

y = (-1/4)x + 7/2   this is the slope intercept formula. y = mx +b

we can now graph this line with the slope intercept formula.

note the graph does pass through (-2,4)  and has a  -1/4 slope   :)

The domain of the given graph is x≤ 2, option A is correct.

A relation is a function if it has only One y-value for each x-value.

We have to find the domain of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

As we observe the graph the value of x are less than 2

Hence, the domain of the given graph is x≤ 2

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Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

According to question,

slope = (-1/2-3/4)/(5/6-(-2/3))

slope = (-5/4)/(9/6)

slope = -30/36

slope = -5/6

You can ask where you don't understand.

The first number is 8  and the second number is 20

let the first number =  X

the second number = 4 + 2X

sum = 28

X + (4 + 2X) = 28

3X + 4 = 28

3X = 24  

X = 8                                                                  

The first number is 8

and the second number is 4 + 2X = 4 + 2(8) = 20

Addition:

When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.

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Answer:

10%

Step-by-step explanation:

3/30

1/10

10/100

10%

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According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given,

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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Answer:

[tex]5\frac{1}{3} or \frac{16}{3}[/tex]

Step-by-step explanation:

endless 3’s are always 1/3

So now we just add 5 in front of it

5 1/3

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[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

5.333333

= [tex]\frac{16}{3}[/tex]

We see that,

3 ) 16 ( 5.333333

    15

      10

       9

        10

         9

           1

and so on...

Thus,

[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

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The graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

In this question, we have been given  Holly is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly

needs to bring at most 10 drinks but doesn't want to spend more than $50.

Let x be the number of soda cans and y be the number of soda cans(or bottles)

Holly needs to bring at most 10 drinks

So, we get an inequality,

x + y ≤ 10

She doesn't want to spend more than $50.

So, we get an inequality,

2x + 5y ≤ 50

In following graph, an inequality x + y ≤ 10 is represented by blue shaded region and the inequality 2x + 5y ≤ 50 is represented by red shaded region.

The solution set for the given inequalities is represented by a purple region (common region for both the inequalities)

Therefore, the graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

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The amount of gallons of water is 160 and  gallons of the premium antifreeze solution that must be mixed is 80.

Let y represent the volume of water

Hence,

Total volume equation :

x +y = 240 equation 1

Pure antifreeze volume:

0.60 = .20 × 240  gallons equation 2

Hence,

Equation 2

x =  .20 × 240 /.60

x = 48 /.60

x = 80 (Pure antifreeze)

So,

y = 240 -80

y = 160 gallons of water

Therefore the volume of water is 160 gallons.

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Step-by-step explanation:

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Question

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The length of a room is

3

4

times its breadth. The total area of the four walls of this room is

15

28

times the area of the floor of the room. What is the ratio of the height of the room to the length of the room?

Medium

Solution

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Correct option is D)

Let breadth =x units

Then length =

3

4

x units

⇒ Area of floor = x×

3

4

x=

3

4

x

2

square units

Let the height of the room =y units. Then

Area of four walls = 2[xy+

3

4

xy]=

3

14

xy

Now,

3

14

xy=

15

28

(

3

4

x

2

)⇒xy=

15

2

×4x

2

y=

15

8

x ⇒

x

y

=

15

8

⇒ y:x=8:15

Step-by-step explanation:

annual salary (that means the income for a whole year) is

$36,000

1 year = 12 months.

twice a month = 2 times in a month

so, he gets 12×2 = 24 paychecks in a year.

so, the gross income per paycheck is

36,000 / 24 = $1,500

100% = $1,500

1% = 100%/100 = 1500/100 = $15

so, $15 will be withheld from each paycheck for Medicare taxes.

6% = 1%×6 = 15×6 = $90

so, $90 will be withheld from each paycheck for social security taxes.

and then there is the federal income tax of $287.95

so, he will actually get for each paycheck

1500 - 15 - 90 - 287.95 = $1,107.05

Answer:

0.007 pounds a day

Step-by-step explanation:

if he loses 18.5 pounds in 4 weeks then each week has 7 days so you divide 18.5 by 7 four times. HOPE THIS HELPS :)

Answer: 46 ft

Step-by-step explanation:

You didn't specify what those numbers mean, so I'm going to assume they're the length of the sides of the shape.

The perimeter equals the sum of all sides' lengths of the shape.

So, it equals 8 + 8 + 15 + 15 = 46 ft

Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

For given transformation of ΔABC to ΔA'B'C' the line of reflection is x = y

Triangle A'B'C' is the image of ΔABC under a reflection.

Given A(-2, 5), B(0, 9), C(3, 7),

A'(5,-2), B'(9, 0), and C'(7,3)

We need to find the line of reflection.

We can observe that the coordinates (x, y) of preimage are transformed to (y, x) in image.

This means, the line of reflection is x = y

Therefore, for given transformation of  ΔABC to ΔA'B'C' the line of reflection is x = y

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Answer:

To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

Step-by-step explanation:

Answer: 3/10

Step-by-step explanation:

4/5 is equal to 8/10 and 1/2 is equal to 5/10

then we have 8/10-5/10 which is 3/10

this is the answer since expressions can be a number

It is worthwhile to enter the race if it costs $1000.

Total cost is an economic measure that includes not only the initial cash outlay but also the opportunity cost of their choices when producing a product, purchasing an investment, or acquiring a piece of equipment. TVC + TFC = TC

The sum of fixed and variable costs is the total cost. For example, if a company has a fixed cost of $30 per unit and a variable cost of $5 per unit as output increases, the total cost is $35.

In this case, first place pays $4800 to the winner, second place $3300 and third place $1300. It is therefore worthwhile since the amounts are more than $1000.

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