Solve 4- 3x = 6 - 5x
X =

Line c is also perpendicular to line a.

Suppose that c and b are perpendicular. This implies that:

option 1) b and a are the same line or,

option 2) b is parallel to a

Since we know that a and b are different lines, hence, the option 2 is the correct.

Answer:

That is my own idea and I hope it is very helpful

The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)

From the question, the equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

As a general representation, a hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

From the above general representation, the coordinates of the center of the hyperbola is

Center = (h, k)

By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we  have the following representstion

(h, k) = (2, -3)

This means that

Center = (2, -3)

Hence, the center is (2, -3)

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Answer:

(2,-3) See question 10

Step-by-step explanation:

The Solution:

Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.

An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.

From the given graph of f(x), the function f(x) is ODD.

The degree of the function f(x) is odd since the f(x) itself is odd.

-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.

Given the polynomial in the question;

-7u² + 12u + 4

Factor out -1 out of the polynomial

-1( 7u² - 12u - 4 )

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 7 × -4 = -28

and whose sum is;

b = -12

Now, factor -12 out of -12x

-1( 7u² - 12(u) - 4 )

We know that -13 is the same as 2 plus -14

-1( 7u² - ( 2 - 14 )u - 4 )

Apply distributive property

-1( 7u² - 2u - 14u - 4 )

Group the terms

-1( u(7u - 2) - 2(7u - 2 ) )

-1( (7-u)(u-2) )

-( (7-u)(u-2) )

Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).

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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.

An expression is combination of variables, numbers and operators.

The given expression is -7u²+12u+4.

We need to find the factors of this expression.

-7u²+12u+4.

This can be written as

-7u^2+14u-2u+4.

Take 7u from first two terms and 2 from last two terms in the expression.

-7u(u-2)-2(u-2)

(-7u-2)(u-2)

-(7u+2)(u-2)

Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.

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C=34.15+0.65M

Given

so

to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence

so, replace and simplify

therefore, the answer is

C=34.15+0.65M

I hope this helps you

C=34.15+0.65M

Given

so

to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence

so, replace and simplify

therefore, the answer is

C=34.15+0.65M

I hope this helps you

Answer:

total distance = 654.5

Total gas used = 27.5

Distance per gallon = 654.5 ÷ 27.5 = 23.8

We drove 23.8 miles for each gallon of gas

The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}

Sample space:

Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

Given,

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.

Here we need to find the sample space for the event.

Let us consider,

P represents Patty

Q represents Quinlan

R  represents Rashad

And through the question we have know that, the teacher drawn two card at a time,

So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.  

The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.

Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.

So, the resulting sample space is

S = {PQ, QP, PR, RP, QR, RQ}

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Answer: x-3y=6

Step-by-step explanation:

so first subtract x to get -x+3y = -6 because standford is ax+by = c

and then multiply by -1 since x has to be positive

x-3y = 6 That is your answer

Answer:

x³ + 4x² + 3x + 1

Step-by-step explanation:

fg(x) + f(x)

= x³ + 4x² + 3x + 1

Answer:

16

Step-by-step explanation:

Two negatives make a positive:

18-7+5

Solve the problem left to right:

18-7=11

11+5=16

SOLUTION:

Case: Interpreting slopes from linear equations

Method:

V(x) = 20.6 + 2.2x

Compared to

y = mx + b

Where m is the slope and it is being interpreted as the rise for every single run on the line graph.

As it applies,

V(x) = 20.6 + 2.2x

m = 2.2 thousand ie. 2200

It is interpreted as the amount the value increases by each month.

Final answer:

The value of this investment is increasing at a rate of $2200 each month

Answer:Answer: number 2 is correct

Firstly, let's draw a picture of the distribution:

Graphically, we want to calculate the blue area. To put it differently, we want to calculate

To do this, we need to find the z-score associated with 6. We can calculate it by

Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.

The probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.

Proportion = 0.2119

P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119

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Table A shows a proportional relationship

What is proportional relationship?

When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.

In the figure we are given 2 tables

We plot both the curve on the graph we get

Table A shows a linear relationship where are Table b Does not shows a proportional relationship

Hence Table A shows a proportional relationship

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Answer:

Step-by-step explanation:

We are asked to determine the degree of the polynomial given its graph. To do that we can count the number of bumps in the graph. We notice that it has 4 bumps:

This type of behavior is usual of polynomials of degree 5.

EXPLANATION

Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:

g(x) = |x+1| - 3

Therefore, the solution is the last option.

The slopes formed by each of the pairs of points are given as follows:

The slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.

For the first case, the points are:

(2, 11.9) and (4, 10.5)

Hence:

The slope is:

m = -1.4/2 = -0.7.

The other slopes are calculated as follows:

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Answer:

  72 cm²

Step-by-step explanation:

You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.

The area of the rectangle is ...

  A = bh

  A = (8 cm)(7 cm) = 56 cm²

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(8 cm)(4 cm) = 16 cm²

The total area is the sum of the areas of the parts:

  total area = rectangle area + triangle area

  = (56 cm²) +(16 cm²) = 72 cm²

The area of the shape is 72 cm².

__

Additional comment

You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm  wide rectangle with the same base.

The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.

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The data collected in [n] days is collected in 24n hours.

The SI unit of time is Seconds. In 1 second, there are (1/60) minutes.

Given is Dr. Choi who just started an experiment and he will collect data for days.

Assume that he collects the data for [n] number of days. In one day, we have 24 hours. Therefore, in [n] number of days, there will be total of 24n hours.

Therefore, the data collected in [n] days is collected in 24n hours.

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The measure of ∠C in the given triangle is 58°.

According to the question,

We have the following information:

ACD is a triangle where we have BD as an altitude on the side AC.

Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.

Now, we have two right-angled triangle: ABD and CBD.

We have ∠ADB = 32°.

Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).

We know that the sum of the three angles in a triangle is 180°.

In ΔCBD, we have:

∠B + ∠C + ∠CDB = 180°

90° + ∠C + 32° = 180°

∠C + 122° = 180°

∠C = (180-122)°

(Moving 122 from the left hand side to right hand side will result in the change of sign.)

∠C = 58°

Hence, the measurement of ∠C in the given triangle is 58°.

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Answer:

28°

Step-by-step explanation:

AB and CD are straight lines, all angles in a straight line add up to 180

The relation which represents a function is the mapping diagram.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).

In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.

Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.

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Answer:

Step-by-step explanation:

12 times 2 =24 60 into 10 so i think it will be 6

Solution

Solution

The final answer

253.75 gallons remain in the tank when the depth of oil is 3.5 ft

To find the number we can create the following equation and solve for x:

Let x be the missing number, use inverse operations to solve the equation:

The number is 40.

[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]

without given any restriction x is all the numbers greater than 0.

NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

Answer: 31

Step-by-step explanation:

The numbers are increasing by 1, then 2, then 3, ...

In other words, the second difference is 1.

So, the next number is likely [tex]24+7=31[/tex].