Find the distance between the points (−1,0) and (7,6).

64 ^ (-2/3)

Rewrite 64 as 4^3

(4^3) ^ (-2/3)

Using the power rule a^b^c = a^(b*c)

4 ^(3*-2/3)

4^ -2

We know that a^ -b = 1/ a^b

1 / 4^2

1/16

The equation of line passing through(4,-3) and perpendicular to x+3y=-15 is y = 3x - 15.

Using the slope formula, determine the slope.

To find the y-intercept, use the slope and one of the points (b).

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

Given,

coordinates = (4,-3)

equation of line = x+3y=-15

equation of line in standard form

⇒ y = -1/3x -5

Slope of line = -1/3

The slope of the line passing through (4,-3) and perpendicular to line x+3y=-15 is 3.

The equation of line becomes

(y + 3) = 3 (x - 4)

y + 3 = 3x - 12

y = 3x - 15

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The equation that represent the data in the table shown is y = -2x + 3.

Linear systems are sets of equations associated with each other and that have two or more variables. In linear systems, only linear equations are entered, that is, expressions where the greatest exponent of the unknowns is equal to 1.

A linear equation is in the form:

y = mx + b

Where:

From the table, using the point (0, 3) and (1, 1):

y - 3 = [(1 - 3)/(1 - 0)](x - 0)

y - 3 = -2xy = -2x + 3

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Answer:

See below

Step-by-step explanation:

40 ÷ 50 =   40/50 = 4/5 = .8  

Based on the numbers that are all less than 496 and yet divide evenly into 496, the sum is 496

The numbers that are less than 496 and yet are able to divide evenly into it are known as the factors of 496. These numbers will not leave a reminder when they divide 496.

The factors of 496 include:

1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

The sum of these numbers that are less than 496 is:

= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

= 496

In conclusion, the sum of all the numbers less than 496 that are able to divide it evenly is 496.

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Answer:

  an = 7 -3(n -1)

Step-by-step explanation:

You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....

An arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.

In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.

The n-th term of the given arithmetic sequence is ...

  [tex]a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}[/tex]

__

Additional comment

The formula can be simplified to ...

  an = 10 -3n

Answer:

8%

Step-by-step explanation:

divide the after tax price by the before tax price

15.93/14.75=1.08

then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate

The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.

The fraction of counters Adam have now is 4/9.

This is an expression which consists of a numerator and a denominator

A numerator is the upper of top value of a fraction

A denominator is the lower or bottom value of a fraction

Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley

= 18 - 10

= 8

Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has

= 10/18

= 5/9

Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has

= 8 / 18

= 4/9

In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9

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For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.

As given in the question,

Revenue for selling x units of a product is R = 113.95 x

Cost of producing x units is C = 93 x + 750

For profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x >93x-93x +750

⇒20.95x > 750

Divide by 20.95

⇒x > 750/20.95

⇒x>35.7995

Nearest whole number is 36.

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of

C =93x + 750 the value of x is 36units.

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Answer:

Acute

Step-by-step explanation:

Obtuse angles are angles that are larger than 90 but less than 180

Acute angles are angles that are less than 90 degrees

Right angles are angles that is exactly 90 degrees

Complementary angles are two angles whose sum is 90 degrees

Using this info, it seems the answer to this question is B. Acute because it says "the values returned by inverse to angles larger than 90" and since acute is the opposite of obtuse imma say B but im not too sure

the price of the ticket which Disney on ice would make no money at all is:

and here, are two posible solutions:

for the first one 1)

for the second one 2)

and in this problem the realistic answer is the first one, so the solution is $8 dollars

47 had a finished basement with 0 three-car garage .

Thinking and cognition are related to reasoning, which requires using one's intellect. The study of logic focuses on how people can construct logically sound arguments using formal reasoning. Deductive, inductive, and abductive reasoning are three examples of logical reasoning that can be used to further break down reasoning. Aristotle distinguished between logical discursive reasoning (reason proper) and intuitive reasoning, noting that the former may lean toward the subjective and the personal, despite being correct. While logical and intuitive styles of reasoning might clash in certain social and political circumstances, in others they are considered as complimentary rather than competitive.

all the values are given that how many houses had a finished basement with no 3-car garage.

the no. of houses are = 47 .

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An equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0

What is point-slop equation of a line?

The point-slope equation of a line is

                      y - [tex]y_{1}[/tex] = m ( x  -[tex]x_{1}[/tex] )

The equation is useful when we know:

and want to find other points on the line.

Given that,

slope , m =  [tex]\frac{2}{3}[/tex]  and passing through the point is (0,9)

An equation of a line given the slope and a point is

             y - [tex]y_{1}[/tex] = m ( x  -[tex]x_{1}[/tex] )

or          y - 9 =  [tex]\frac{2}{3}[/tex] (x - 0)

or          y - 9 =  [tex]\frac{2}{3}[/tex] x

or          y =  [tex]\frac{2}{3}[/tex] x + 9

or          y = [tex]\frac{2x + 27}{3}[/tex]

or          3y = 2x + 27

or         3y - 2x - 27 = 0

Hence, an equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0

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Answer: f(-7)=-9

Step-by-step explanation:

The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.

For the given question;

The inequality of the function is given as;

= x² - 4x + 3

Find the factors;

(x - 3)(x - 1) = 0

x = 1 and x = 3 are the zeros of the equation.

Now, to graph the equation find the point;

Put x = 0; y = 3

Put x = 1; y = 0

Put x = 2, y = -1

Plot the points on the graph and join the points with solid line.

The vertex of the parabola is found at (2, -1).

Thus, the graph of the parabola is plotted.

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No. there is not a fixed number of trials. The correct option is B.

A variable with only two outcomes is said to be binary. Examples of binary categorical variables are sex (male/female) and having a tattoo (yes/no).

Each trial must be independent, meaning that it must have a defined number of trials and a constant success rate. Its probability needs to range from 0 to 1.

There are only two conceivable outcomes for each individual. They are either filtered or they are not. We are not interested in learning how many people were screened, though.

It is an inverse binomial, we want to know how many persons will be screened before 10, which is a binomial. Therefore, since there are an arbitrary number of trials, this is not a binomial equation, and option B provides the solution.

Therefore, there is not a fixed number of trials. The correct option is B.

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9.16

1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it

2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers

3) So the Geometric mean is 9.16 (approximately).

Answer: 68/5

Hope this helps! :)

Value of x =5 and value of y =2

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.

[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]

Now, by comparison, we get:

[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]

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Answer:

n=2.4

Step-by-step explanation:

The value of n is ∛14.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).

To solve the equation −8 + n³= 6

Add 8 to both sides of the equation to isolate the term with n:

−8 + n³ + 8 = 6 + 8.

Simplifying the equation gives: n³ = 14.

Take the cube root of both sides to solve for n.

Taking the cube root of n³ = 14

∛(n^3) = ∛14.

Therefore, n = ∛14.

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Answer:

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 : Evaluate

14 : Open Sentence

Answer:

Step-by-step explanation:

You want to find the rational function (f/g)(x) and its value for x=1 when f(x) = 4x^4−19x^3−10x^2+35x−50 and g(x) = x-5.

The ratio function is the ratio of the given functions, found by dividing f(x) by g(x). Since g(x) is a binomial with a leading coefficient of 1, synthetic division is recommended. The attachment shows the result.

  [tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{4x^4-19x^3-10x^2+35x-50}{x-5}\\\\\boxed{(f/g)(x)=4x^3+x^2-5x+10}[/tex]

The value of this function when x=1 is ...

  (f/g)(1) = 4·1³ +1² -5·1 +10 = 4 +1 -5 +10

  (f/g)(1) = 10

Answer:

Step-by-step explanation:

[tex]m^{a}[/tex] × [tex]m^{b}[/tex] = [tex]m^{a+b}[/tex]

[tex](m^{a}) ^{b}[/tex] = [tex]m^{ab}[/tex]

When three of these twelve aircraft are selected at random, the probability that all three of them will be F/A-18E's is 0.018.

Based on the information given, there are are 12 F/A-18 aircraft, where: 3 are F/A-18A's 4 are F/A-18E's 5 are F/A-18F's. The total number of aircraft will be 12.

When three of these twelve aircraft are selected at random, so that every possible selection is equally likely, the probability that all three of them will be F/A-18E's will be:

= 4/12 × 3/11 × 2/10

It should be noted that this is without replacement that's why we have 10, 11 and 12 as the denominator.

= 4/12 × 3/11 × 2/10

= 1/3 × 3/11 × 1/5

= 3 /165

= 0.018

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Answer:

y = -3/2x +11

Step-by-step explanation:

First you have to change the equation from standard form to slope form.

y = mx + b

2x-3y=7 --> subtract 2x from both sides

-3y = -2x + 7 --> now divide both sides by -3 to get y by itself

y = 2/3x - 7/3  --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.

now you have to use point slope form y - y1 = m (x - x1)

x1 and y1 would be your point. 2 is x1 and 8 is y1

y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope

next distribute the -3/2

y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self

now you have y = -3/2x + 11

Answer: The correct answer is 62.5% and not 67.5 %

Step-by-step explanation: Yes you do 5 divided by 8 and then you move the decimal point two places to the right.

Hope this helped!!!!

Given:

The equation of the graph is x + y = 500.

The objective is to change the equation as inequality and to choose the correct region for shading.

Explanation:

As the equation is given as x + y = 500, the sum of the values of x and y lies within the 500. As its total sum is also equal to 500, the graph must lie with in the maximum range of 500 that is at A along with solid line. (If sum is not equal to 500, the graph will contain dotted line).

Representation of inequality:

The given equation can be represented in the form of inequality as,

Graph:

Then, the graph of the inequality will be,

Hence, the inequality is x + y ≤ 500 and the graph contains solid line with shaded region in A.

Answer:

A

Step-by-step explanation:

The centroid cuts the median in a 2:1 ratio from vertex to side.