A zoologist needs to dive into the shark exhibit to supervise its cleaning. The depth of the water in the exhibit is 40 feet, and the divers can safely descend at a rate of 2 feet per minute. Which number expresses how deep below the water the divers are after 15 minutes? − 30 feet − 15 feet − 40 feet − 2 feet

The correct options are (a) , (14,3) , (d), (-8,6) and (e) , (-6,2)

By concept of translation, the coordinates of new triangle A'B'C' are given as follows:

A' (14, 3), B' (-6,2), C (-8, 6).

A translation can be define or represented by a change in the graph of a function, which are done by the means of operations such as multiplication, addition or subtraction either in it’s range(i.e. the values of y) or in it’s domain(i.e. the values of x). Examples are compression of points or shifting  left right or bottom up, stretching and reflections over the axis that is the x-axis or the y-axis, or rotations around the origin.

For the given question, the translation rule is given as follows:

(x , y) -> (2x, y-3).

Applying the rule to each point of triangle, we have that:

A': (2(7), 6-3) = (14, 3).

B': (2(-3), 5-3) = (-6, 2).

C': (2(-4), 9-3) = (-8, 6).

Thus, the coordinates of triangle formed i.e. A'B'C' are given as follows:

A' (14, 3), B' (-6,2), C' (-8, 6).

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The complete question is:

Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.

Question 1 options:

a. (14,3)

b. (9,3)

c. (-6,10)

d. (-8,6)

e. (-6,2)

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.

The reciprocal of the divisor 5 1/5 divided by 1/10

To the reciprocal of the divisor.

Equation: 5 1/5 divided by 1/10

1st: Flip the 1/10 to become 10/1

2nd: Change division to multiplication

New equation: 5.1/5.10/1

⇒ 50/5

       ⇒ 10.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

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Since the rate of change is constant, the relation is linear, and is modeled by:

y = 4x - 4.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that when x changes by 1, y always changes by 4, hence we have a linear relation with a slope of 4, given as follows:

y = 4x + b

When x = 1, y = 0, hence we use it to find b as follows:

0 = 4 + b

b = -4.

Hence the relation is:

y = 4x - 4.

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Answer:

No

Step-by-step explanation:

1/10 = 0.1

0.05 x 0.1 = 0.005

Answer: -1.4,1 1/25,1.25

Step-by-step explanation:

-1.4,1 1/25,1.25

1 1/25=

1+0.04=1.04

Order: -1.4, 1.04, 1.25 ==> -1.4,1 1/25,1.25

Statement (C) "Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44" is the correct explanation of the above-given situation.

So, 4 × 305 = 1220

Therefore, statement (C) "Lynn's method will not yield the correct result. Multiplying by 4 and then doubling the result is equivalent to multiplying by 8, not 44 "is the correct explanation for the situation described above.

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The complete question is given below:

Lynn wants to multiply 44 × 305 44×305. She says that all she has to do is find 4 × 305 4×305 and then double that number. Which explains whether or not Lynn's method will give her the correct answer?

A. Lynn's method will give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 44.

B. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 6, not by 44.

C. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44.

D. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 16, not by 44.

So the correct answer is a. f(-3)=-5.

Solution :

Cartesian coordinate system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

Cartesian Plane:

A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.

Abscissa and Ordinate

The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis and it is known as Abscissa.

The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis and it is known as the Ordinate.

So,

the point (-3, -5) corresponds to the graph of the function.

A point on a graph in the Cartesian coordinate system then that point consists of coordinates (x, y).

In, y=f(x) and x so (x, f(x))

x is a x-coordinate and y=f(x) is y-coordinate.

So if we have a point (-3, -5) the corresponding coordinates are x=-3 and

y=f(x)=-5. So it must be true that y=f(-3)=-5.

So the correct answer is a. f(-3)=-5.

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The contribution of the first data point, (54, 60) to correlation is given by the option with the equation equation;

The correlation coefficient is given by the formula;

[tex]r = \frac{1}{n - 1} \times \sum( \frac{x - \bar{x}}{s_{x} })( \frac{y - \bar{y}}{s_{y} })[/tex]

Where;

(x, y) are the coordinates of a data point.

[tex] \bar{x}[/tex] = The mean for the x-values

[tex]S_{x}[/tex] = The standard deviation of the x-values

[tex] \bar{y}[/tex] = The mean of the y-values

[tex]S_{y}[/tex] = The standard deviation of the y-values

The given parameters are;

[tex] \bar{x}[/tex] = 58.4

[tex]S_{x}[/tex] = 16.87

[tex] \bar{y}[/tex] = 60.8

[tex]S_{y}[/tex] = 21.89

The formula for the contribution of the first data point, (54, 60) to correlation, r, is therefore;

[tex] \displaystyle{\left( \frac{54 - 58.4 }{16.87}\right)\cdot \left( \frac{60 - 60.8}{21.89 }\right)}[/tex]

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The number of f(x) = g(x) solutions is an option (2) The right answer is 2, thus.

A graph is a diagram or visual representation that organizes the presentation of facts or values. The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph.

For the predicament,

f(x) = In(x + 2) and g(x) = e(x - 1) throughout the range [(-2,3].

In the graph below,

plot the two functions f(x) and g(x).

These two functions cross at two locations in the range [(-2,3]).

The function's solution is revealed at the intersection point.

Consequently, we might say that the number of solutions.

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Answer:

Step-by-step explanation:

10 would be the total, since 2/10 are green. 1/2 of 10 is 5, so 5 candles are pink. 5+2=7. 10-7=red candles (3), there is ultimately 3 candles that are red.

Because the angles are vertical angles, the value of x is 1

The angles are given as

A = 7x + 26

B = 4x + 29

The angles are vertical angles

So, we have

A = B

This gives

7x + 26 = 4x + 29

Evaluate the like terms

3x = 3

Divide by 3

x = 1

Hence, the value of x is 1

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Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos

It is given that Juan Dela Cruz is paid 45 peso for every hour he works for up to 40 hours and 1.5 times i.e. 67.5 pesos for every hour after 40 hours.

The first part asks for Juan's earning if he works 35 hours

Therefore , according to the function,

Juan's pay = 35 x 45 = 1575 pesos

The second part asks for Juan's earning for 40 hours

Therefore, according to the function,

Juan's pay for 40 hours = 40 x 45 =1800 pesos

The third part asks for Juan's earning for 45 hours

Juan's pay for 45 hours according to the function=

67.5h-900 = 67.5 x 45 -900 = 2137.5 pesos

Hence, Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos

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The wholesale price of the TV will be 0.40 x where x represents the retail price.

Percentage :

In mathematics, it is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Let the retail price of TV be x

Now, we are given that it is sold off at 60 percent discount.

Whole sale price = x - 60 % of x

Whole sale price = x - 60 / 100 x

Whole sale price = x - 0.60 x

Whole sale price = 0.40 x.

Therefore, the wholesale price of the TV will be 0.40 x where x represents the retail price of the TV.

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Answer:

x = 2.638

Step-by-step explanation:

Answer

Unless you need a different version of this answer?

Step-by-step explanation:

(27in(3)

x=___4_______ True

In(3)

with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.

We are given that Yossi has a garage of area = 230 feet²

We know that area of square is:

A = side²

230 = s²

s = √ 230

s = 15.17 feet

Now area is increased by 50 %

New area = 230 + 50% of 230

A' = 230 + 115

A' = 345 feet²

s² = 345

s = √ 345

s = 18.57 feet

Percent increase in length = 18.57 - 15.17 / 15.17 × 100

Percent increase in length = 22.41 %

Therefore, with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.

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Answer:

The answer to the inequality is

x < -5

x > 15

The equation of the bisector of angle OAB is y=x

If E is the point of intersection of this bisector and line through A and B then the co-ordinates of E is (40/3,40/3)

Since E is the point of intersection of the bisector of angle OAB and line A and B  hence we can say OA:OB=AE:EB

Since point O is the origin hence we can say the co-ordinates of point O are (0,0) and the angle bisector of the angle OAB makes and angle of 45 degree from x axis, So by the formula of Line passing through origin (y= mx )

where ,

∅=angle made by the bisector the angle OAB to the x axis(i.e. 45 degree)

m=tan∅

now using substitution method ,

m=tan45

m=1

the equation of the bisector of angle OAB is  y=x

Now, the equation of the line passing through point A(5,0) and point B(0,8) by formula,

(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)

here , y1=0, x1=5, y2=8, x2=0

again by substitution method,

(y-0)={(8-0)/(0-5)}*(x-5)

y={8/-5}*(x-5)

8x - 5y = 40

point E is the intersection of 8x - 5y = 40 and y=x the solving these two equations by substitution method we get;

x=40/3

y=40/3

the co-ordinates of point E are  (40/3,40/3)

E is the intersection point of the bisector of the angle OAB and the line through point A and B ,

on comparing triangle OEA and triangle OEB we can say that,

OA:OB= AE:EB

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Answer:

0.000345 in standard form would be:

3.45 times 10 to the -4 power

Step-by-step explanation:

The number tells use that we have to divide by 10 and we are working with a negativenumber equal to the power of 4.

Answer:

3.45 × 10^-4

Step-by-step explanation:

Move from the decimal point till you you get to after the first number.

Then you put the decimal point there and because it's starts with 0. i.e it is not up to one

You put minus in front of it when raising it to the power of 10

Using a system of equations, it is found that it sold 27 lower-priced speaker docks.

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

For this problem, the variables are given as follows:

Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks, hence:

x = 3y -> y = x/3.

Combined sales totaled $3,870, hence, considering the price of each speaker:

80x + 190y = 3870.

Since x = 3y:

240y + 190y = 3870.

430y = 3870

y = 3870/430

y = 9.

Hence:

x = 3y = 3 x 9 = 27.

It sold 27 lower-priced speaker docks.

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Answer:

done it step by step

Step-by-step explanation:

The value of the constant π is located between 3 and 4 on a number line

The value is given as

Value = π

As a general rule, the value of π is

π = 22/7

So, we have

Value = 22/7

Evaluate the quotient of 22/7

So, we have

Value = 3.143

The number 3.143 is greater than 3 but less than 4

This means that, 3.143 is between 3 and 4

In other words, the value of the constant π is located between 3 and 4 on a number line

Hence, the value of the constant π is located between 3 and 4 on a number line

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Answer:

  (d)  c = ab/x

Step-by-step explanation:

You want to solve the proportion x/a = b/c for the variable c.

The usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."

  [tex]\dfrac{x}{a}=\dfrac{b}{c}\qquad\text{given}\\\\\\\dfrac{x}{a}\cdot ac=\dfrac{b}{c}\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}[/tex]

At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.

  [tex]\dfrac{xc}{x}=\dfrac{ab}{x}\\\\\boxed{c=\dfrac{ab}{x}}[/tex]

Answer:58.73

Step-by-step explanation:

28.37+30.36=58.73

The number of children wearing both black and orange costumes is 7.

Let P denote the universal set, the number of children going to a party.

Then n(P) = 46

Let B denote the number of children wearing black costumes to the party.

Then n(B) = 18

Let O denote the number of children wearing orange costumes to the party.

Then n(O) = 12

We are asked to find how many children will wear both orange and black. That is to find n(B ∩ O).

We are also given that half of the guests are wearing costumes that are neither black nor orange.

Then n(B ∪ O)' = n(P)/2 = 46/2 = 23, where n(B U O)' denotes the complement of n(B U O).

We also know that n(B ∪ O) = n(P) - n(B U O)' = 46 - 23 = 23

⇒ n(B U O) = n(B) + n(O) - n(B ∩ O)

⇒ 23 = 18 + 12 - n(B ∩ O)

⇒ 23 = 30 - n(B ∩ O)

⇒ n(B ∩ O) = 30 - 23 = 7

⇒ n(B ∩ O) = 7.

Therefore, the number of children wearing both black and orange costumes is 7.

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Answer:

$5.30 for two gallons

Step-by-step explanation:

The measure of the sides is 27, 23 and 16 and the perimeter is 56 respectively

The triangle is a 2 dimensional shape that has 2 sides.

Given the following sides

l = m + n - 12

n = m - 7

m = l - 1/4n

l = m + 1/4n

Substitute

m + 1/4n = m + m - 7 - 12

m + 1/4(m-7) = 2m - 19

m + 1/4m - 7/4 = 2m - 19

-m + 1/4m = -19 + 7/4

-3/4m = -19(4)+7/4

-3/4m = -69/4

-3m = -69

m = 23

Hence the value of m from the given expression is 23

n = 23 - 7

n = 16

l = 23 + 16 -12

l = 39 - 12

l = 27

n = 23 - 7

n = 16

Hence the measure of the sides is 27, 23 and 16 respectively

Perimeter = 27+23+16

Perimeter = 56

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The correct inequality will be 53.46d + 45.5 ≤ 260

What does a math inequality look like?

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Given That:

She plan to drive 350 miles and each mile cost $0.13 which is total $45.5

and she have to pay $53.46 for each day

So the correct inequality will be 53.46d + 45.5 ≤ 260

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