The price of an item has been reduced by 30% . The original price was $90 . What is the price of the item now?

Answer:

6[tex]x^{2}[/tex]y

Step-by-step explanation:

If I ready your explanation correctly it is

2x3xy  We multiply the 2 and 3 and the xx would be [tex]x^{2}[/tex]

Answer:

(a) {-1, 1)

(b) {-11}

(c) {-3, 4}

***(d) { x < -1 or x > 1, I am not sure how else to put it, try {-1, 1} if you are not allowed to put in > or < signs

(e) (-∞, -11] or x ≤ -11

(f) {-3, 4}

(g)  ( -√2, √2)  

***I know the correct solution sets but I am not sure how to represent all of  them given the one box you have in your solution for (a). Maybe the solution boxes for the other parts are different. Without knowing that I am only able to provide what is the correct expression

Step-by-step explanation:

We have
f(x) = x² - 1

g(x) = x + 11

(a) f(x) = 0

=> x² - 1 =

=> x² = 1

x = ± 1  

Answer (a): The solution set is {-1, 1}

(b)
g(x) = 0

=> x + 11 = 0

=> x = -11

Answer (b): Solution set: {-11}

(c)
f(x) = g(x)
=> x² - 1 = x + 11
=> x² -x -12 = 0

This is a quadratic equation which can be solved by factoring:
=> (x - 4)(x+3) = 0

=> x = 4, x = -3

{-3, 4} Answer

(d) f(x) > 0
=>  x² - 1 > 0
Add 1 to both sides

x² > 1

x < -1 or x > 1

[tex]\left(-\infty \:,\:-1\right)\cup \left(1,\:\infty \:\right)[/tex]

(e) g(x) ≤ 0
=> x + 11 ≤ 0

=> x ≤ -11

{-∞, -11}

(f)f(x) > g(x)

=> x²-1 > x +11

=> x² -x - 12 > 0

=> (x + 3)(x +4) > 0

=> x + 3 >0 and x - 4 > 0

=> x > -3 and x < 4

{-3, 4}

(g) f(x) ≥ 1

=> x² - 1 ≥ 1

=> x² ≥ 2

=> x ≥ ± √2

=> x ≤ -√2  or x ≥ √2

=> { -√2, √2}

In the above derivations note that if x² ≥ 1 then two possibilities are
x < - 1 or x > 1

Answer: 3

Step-by-step explanation:

1. 2 packs of 6

2. 6 packs of 2

3. 3 packs of 2 and one pack of 6

The angle not congruent to the angle 4 in the options is angle 7(∠7)

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, corresponding angles are equal, alternate angles are equal and vertically opposite angles are equal.

Therefore,

∠4≅∠6(vertically opposite angles)

∠4≅∠2(corresponding angles)

∠4≅∠8(alternate exterior angles)

Therefore the angle not congruent to ∠4 among the option is ∠7

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Based on the interest compounded by the bank monthly, and the amount deposited by Sean in the account, the amount of money that will be in that account in a year is $3,668.09

First, find the monthly rate because the interest is compounded monthly:
= 4.7% / 12

= 4.7/12 %

The number of periods would be:

= 1 x 12 months a year

= 12 periods

The amount that Sean will have in a year can be found by the formula:

= Amount invested x (1 + periodic rate) ^ number of periods

Solving for the amount in the account after 1 year gives:
= 3,500 x (1 + 4.7%/12) ^ 12

= 3,500 x 1.0480257937581146250656044647993

= $3,668.09

In conclusion, the amount that Sean will have after saving for a year in the account would be $3,668.09

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By using the concept of weighted averages, 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice are needed to produce 70 pints of 55 % pure fruit juice.

The situation describes a mixing process with two fruit juices of different concentrations. All pure fruit percentages are known and we are asked to determine the numbers of pints of 40 % pure fruit juice and 65 % pure fruit juice to produce 70 pints of 55 % pure fruit juice. This can be determined by means of the concept of weighted average:

(55 / 100) · 70 = (40 / 100) · x + (65 / 100) · (70 - x)

38.5 = 0.4 · x + 45.5 - 0.65 · x

0.15 · x = 7

x = 46.667

We need 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice to produce 70 pints of 55 % pure fruit juice.

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In linear relationship, 199.333 million dollers per year is the percent growth rate.

What is linear relationship in math?

Given , t Rs numbers of year since 1997 .

t = 0 corresponds to year 1997

t = 6 corresponds to year 2003

Let  s(t) = sales of the year

So, given that

 sales in 19997 is  $2503 millions

so    s(0) = 2503  million dollers

Sales in 2003 is $3699 millions

so  s(6) = 3699  million dollers

Now apply formula of linear relation ship

               s - s(0) = s(6) - s(0)/6 - 0 ( t - 0)

               s - 2503 = 3699 - 2503/6 (t)

                s = 1196* t /6 + 2503

  so         s(t) = 598t/3 + 2503

 so now average rate of change of function over on interval is given by

                 =     s(b) - s(a)/b - a

                 = s(6) -  s( 0)/6 - 0

                 = 3699 - 2503/6

                 = 598/3

                 = 199.333 million dollers per year .

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We know that

1 m = 100 cm

Then to change from meter to centimeter, multiply by 100

Since the tree in Bob's backyard is 8.5 m

Then to change it to cm, multiply 8.5 by 100

The height of the tree is 850 cm

The length of the bridge that connect the two cities separated by the lake is 3.4 miles.

The mathematical operation that would be used to convert yards to miles is division. Division is the process of putting a number into equal groups using another number. For example, when 6 is divided by 3, 3 divides 6 into 2 equal groups.

In order to convert yards to miles, divide the given length in yards by 1760.

1 yard = 1 / 1760 miles

5927.61 / 1760  = 3.36796 miles

= 3.4 miles

To round off to the nearest tenth, since the hundredth digit is greater than 5, 1 is added to the tenth digit and the digits less than the tenth digit is replaced with zero.

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The inverse statement is If an angle is not obtuse, then it is a right angle False. Option C

An inverse statement can be defined as a type of conditional sentence having a prompt or immediate inference made from original statement.

It carries the negation of both the hypothesis and conclusion from the

It states the opposite of the original statement given.

The statement is formed by negating the hypothesis and conclusion of a given conditional statement.

An inverse statement is expressed  the form:

Original statement:  If p, then q

Inverse statement: If not p, not q

Given the statement as;

Obtuse angles are not right angles

The inverse statement is:

If an angle is not obtuse, then it is a right angle

Hence, the inverse statement is False. Option C

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For the following relations, using the condition for a relation to represent a function, we have that:

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

The input may also be called domain, while the output may also be called range.

For a point in the standard format (x,y), we have that:

Hence, in the context of this problem, we have that:

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Answer:

y = 15x - 30

Hope this helps!

Step-by-step explanation:

The slope can be found with the equation [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex].

Add in the numbers from the two points to get [tex]\frac{15-0}{3-2}[/tex] which is [tex]\frac{15}{1}[/tex] : 15.

That means slope is 15. To get the other numbers, you can do y = 15x and then plug in one of the points, for example (0) = 15(2), which is 0 = 30. To make this equation true, you need to minus 30 so it would be 0 = 30 - 30 and this is true, so putting it all together would get y = 15x - 30.

We were given the following details:

Car registration = $90

Car Insurance (annual) = $520

Home Insurance = $1020

Since we are to calculate for the monthly amount to budget for Car Insurance, we have:

herefore, the correct nanswer is A. ($43.00 per month)

From the provided information we get that Ava's Pin code is 8842.

Ava's pin code is a 4-digit number.

Let the first digit = x                                      equation 1

Reading from left to right, the first and second digits are the same. So,

Second digit = x                                            equation 2

Let, third digit = y

The second digit is twice the third digit. So,

x = 2y

⇒ y = x/2

Third digit = x/2                                            equation 3

Let, fourth digit = z

The first digit is four times the fourth digit. So,

x = 4z

⇒ z = x/4

Fourth digit = x/4                                            equation 4

Sum of the four digits is 22. So, using equation 1 , equation 2 , equation 3 and equation 4 , we can write

x + x + (x/2) + (x/4) = 22

2x + (x/2) + (x/4) = 22

Multiplying both sides by 4 , we get

8x + 2x + x = 88

11x = 88

x = 8

First digit = x = 8

Second digit = x = 8

Third digit = x/2 = 8/2 = 4

Fourth digit = x/4 = 8/4 = 2

So, we can conclude that the Ava's Pin code is 8842.

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Let's summarize the given information:

iles before school: 0.65

Miles after school: 1.5

o find the total mnumber of miles that Franklin jogs we need to add the miles he jogs before and after school:

The result of the addition is:

He jogs 2.15 miles.

nswer: 2.15 miles

We are asked to solve the following system of equations using the elimination method:

x + 2 y = 16

-7 x- 3 y = 24

so we select to multiply the first equation by "7", that way we will be able to eliminate the term in "x" by simple combining term by term the two equations:

7 (x + 2 y) = 7*16

7 x + 14 y = 112

now we combine this new expression term by term with the second equation:

7 x + 14 y = 112

-7 x - 3 y = 24

_____________

0 + 11 y = 136

solve for y by dividing both sides by 11:

y = 136/11

Now we use this value to solve for x in the first equation:

x + 2 (136/11) = 16

x +

Answer:

Step-by-step explanation:

3x−(12x−6)−42=0

−9x+6−42=0

(−9)⋅x+(−36)=0

x=−(−36)/−9

x=-4

The equation of the line is y = -1/3x - 4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Slope, m = -1/3

y-intercept, c = -4

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = -1/3x - 4

Hence. the linear equation is y = -1/3x - 4

See attachment for the graph

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First, we need to calculate the median

13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23

we have 11 values the media is the 6th value in this case 15.

the lower extreme is 13 the upper extreme is 23.

The lower quartile is 14 and upper quartile is 16

the box plot is

Answer:

The top set does not represent a function because -4 corresponds to two y-values.

Answer: $-75

Step-by-step explanation:

She took out money therefore the balance will go down. If we take 43 dollars from $-32 then we will get -75.

The water pressure on a submerged object is given by P = 64d, then the

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

given the role as;

P = 64d

Where;

P stands for pounds per square foot of pressure.

d represents the object's depth in feet.

Let's now make the variable "d" the focus of the formula.

The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.

We get,

P/64 = 64d/64

d = P/ 64

P equals 672 pounds per square foot if there is pressure.

When the variable's value is substituted into the formula, we get;

d = P/64

Then,

d = 672/64

Discover the quotient.

d = 10. 5 ft.

The value is 10.5 feet.

Therefore,

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

plants have developed seeds = 71

total plants = 200

Step 02:

% = part / whole * 100

% = 35.5

The answer is:

35.5 %

Assuming that the total number of people that pay the $120 are the 900 that claim the policy, and assuming that out of the 900 cases only the vehicular and job related policies are covered, then the profit for this policy will be:

So, under those assumptions, the profit would be $99 900.

⇒Parallel line have the same gradient if the gradient of the given equation is m=-6  it means that the gradient of the new equation is also m=-6

The general equation of a straight line is y=mx+c

⇒plug in the points and find the value of the unknown c

[tex]6=-6(9)+c\\6=-54+c\\c=6+54\\c=60[/tex]

⇒This means that the new equation parallel to the given equation is⇒

[tex]y=-6x+60[/tex]

The selling price is $224.75.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Cost price= $155

Cost marks up = 45%

Then the selling price is

=155 + 155 x 45/100

= 155 + 155 x 0.45

=155 + 69.75

= $224.75

Hence, The selling price is $224.75.

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The larger cylinder is 16 times as large as the smaller cylinder.

The formula for calculating the volume of cylinder is expressed according to the equation;

V = πr²h

where:

r is the radius

h is the height.

Determine the volume of the smaller cylinder;

V =  π(4)²(8)

V =  128π cm^3

Determine the volume of the larger cylinder;

V =  π(16)²(8)

V =  2048π cm^3

Determine the ratio

Ratio = 2048π/ 128π

Large/Small = 16

Large = 16 Small

This shows that the volume of the large cylinder is 16 times greater than that of smaller cylinder.

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Based on the direct variation between x and y, the value of y is 48

The given statements are:

From the above points, we understand that:

The variation is a direct variation

A direct variation is represented as

y = kx

Where k represents the constant of variation

The above equation is a linear equation

As a general rule, linear equations are equations that have constant average rates of change.

So, we have

y = kx

y is 120 when x is 15

This means that

120 = 15k

Divide by 15

k = 8

So, we have

y = 8x

The value of y when x is 6 is

y = 8 x 6

Evaluate

y = 48

Hence, the value of y when the value of x is 6 is 42

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