What are the possible values of x for the following functions? F(x)=2-x / x(x-1)

Answer:

Step-by-step explanation:

b=4c-s2

4(25)-9(2)

100-18=82

b=82

The length of the side of Amy’s printed picture is 6 inches.

A square is a two-dimensional closed shape with four equal sides.

Now, as per the given question;

The original length of the side of the square was 4 inches.

Thus, the area of the old photo was;

A = side²

A = 4²

A = 16 square inch.

Now, as the picture is increased by 225%.

Then, increase the area by 225%.

New area = 225% of old area

                = (16×225)/100

New area = 36

The length of the side of the new photograph is;

New area = length²

length = √New area

length = √36

length = 6 inches.

Therefore, the length of the side of Amy’s printed picture is 6 inches.

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2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

Given two numbers

1)2.7×1012

2) 1.5×108

Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.

1)2.7×1012=2,732.4

2) 1.5×108=162

The value of the 1st number is 2,732.4 and the value of the 2nd number is 162

1st given number is greater than the 2nd number i.e. 2,732.4>162

Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

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Julie is correct because:

[tex]\frac{\sin A}{\tan A}=\frac{a/c}{b/c}=a/b=\tan A \\ \\ \frac{\sin B}{\cos B}=\frac{b/c}{a/c}=b/a =\tan B[/tex]

Total path coered by the javelin in horizontal direction is domain

Maximum height achieved by the javelin is its range

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x). The roots of the quadratic equation are the values of x that fulfill the equation (α,β ).

It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

Total path coered by the javelin in horizontal direction is domain

Maximum height achieved by the javelin is its range

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Answer: 28 units

Step-by-step explanation:

A=area of parallelogram. h=height. b=base

A=h*b

7=1/4 *b

(7=1/4 *b)*4    ==>Multiply both sides by 4 to get rid of fractions

28=b

b=28 units

Answer:

9x8=72

Step-by-step explanation:

I didn't use a calculator I memorized it?

Answer: Table  which had a constant of proportionality between y and x of 1/6

is table C

Step-by-step explanation:

The meaning of constant proportionality is very simple and that is

ratio of y and x

here

y/x=1/6;

therefore we have to check various options

checking option C

first part:

3/18=1/6;

second part:

(9/2)/27=1/6;(convert mixed fraction into improper fraction)

third part:

(11/2)/33=1/6;

hence ;

Table  which had a constant of proportionality between y and x of 1/6

is table C

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∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.

∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.

∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.

∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.

∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.

∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.

Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.

Right Angles Theorem states that two right angles(90° angles) are congruent to each other.

Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.

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a = amount invested at 4%.

b = amount invested at 7%.

we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.

how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.

how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.

we also know that the earned interest by those two interest amounts is 1440, so

[tex]\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}[/tex]

The horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

An airplane is flying at a speed of 300 mi/h at an altitude of one mile.

As we know,

From the relation between time-distance-speed

distance = time×speed

Speed = 300 mi/h

let distance be d and time be t

d = 300t

We can write the above equation as:

The horizontal distance that the plane has flown:

d(t) = 300t

Thus, the horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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The midpoint of the line segment of the endpoints (6,-6) and (1,2) is given as:

(3½,-1)

What is the midpoint of a line segment in geometry?

The midpoint of a line segment is simply the centre point of a give segment that cuts or divides it into two congruent segments.

That is for example, if there are two points with coordinates (x1,y1) and (x2,y2), then their midpoint will be ; [(x1+x2)÷2,(y1+y2)÷2]

From the given question!

x1=6, x2=1 and y1=-6,y2=2

Thus, the midpoint is derived as;

[(6+1)÷2,(-6+2)÷2]

[(7)÷2,(-4)÷2]

(3½,-1).

Answer:

5 hours and 48 minutes

Step-by-step explanation:

The equation for finding average speed is:  [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]

Let x represent the distance for both the journey from Riley's college to home and back. We can use one variable to represent this because both distances are the same.

We also know that the total round trip took 12 hours. Let y represent the time it took for Riley to drive from college to home. Therefore the time it takes for Riley to drive from home to college is 12 - y.

Using this information, we can set up a system of equations.

[tex]65.1=\frac{x}{y}\\\\69.6=\frac{x}{12-y}[/tex]

Multiply both sides of the first equation by "y" and both sides of the second equation by "12 - y".

[tex]65.1y=x\\\\835.2-69.6y=x[/tex]

Since both 65.1y and 835.2-69.6y are equivalent to x, we can set them equal to each other.

[tex]65.1y=835.2-69.6y[/tex]

Now, we have to solve the equation for time or "y".

[tex]65.1y=835.2-69.6y[/tex]

Add 69.6y to both sides

[tex]65.1y+69.6y=835.2[/tex]

[tex]134.7y=835.2[/tex]

Divide both sides by 134.7

[tex]y\approx6.2 $ hours = Six hours Twelve Minutes[/tex]

This is the time it took for Riley to drive from college to home, therefore the time it took for Riley to drive from home back to college is:

[tex]12-6.2=5.8=5$ hours and 48 minutes[/tex]

5 hours and 48 minutes

The value of x in given diagram is x=3;

The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.

Area of triangle SXY = 1/2 × SX × (x-2);

Area of triangle STR = 1/2 × ST × (x+3);

Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;

Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;

SX × (x-2) = ST × (x+3) - (2x + 1) × XT;

As; SX = TX = ST/2;

(x-2)/2 = (x+3) - (2x+1)/2;

x - 2 = 2x + 6 -2x -1

x = 3;

A triangle is a closed figure that has three vertices, three sides, and three angles.  It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.

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Answer:

di mo po alam yan

oh di po kayo makain tindi tagalog

Answer:

c) 144

Step-by-step explanation:

Since A is between Y and Z,

[tex]YZ = YA + AZ[/tex]

[tex]116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9[/tex]

however, the question asks for [tex]the length of AZ[/tex], not the value of x.

Thus,

[tex]AZ = 16x[/tex]

[tex]AZ = 16\\[/tex] × [tex]9[/tex]

[tex]AZ = 144[/tex]

The segment bisector of line segment XY is line n.

The length of the line segment XY is 6 units.

A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.

As per the given diagram in the question.

It is clear that the line segment XY is being divided by another line named n.

Thus,

The two segment of the line segment XY must be equal.

XM = MY

Substitute the values from the diagram;

5x + 8 = 9x + 12

Simplifying;

4x = -4

x = -1

Put the values in each segment;

XM = 5x + 8

XM = 5(-1) + 8

XM = 3 units.

Put the value in MY

MY = 9x + 12

MY = 9(-1) + 12

MY = 3 units.

As, it is clear from above values that the both segment are equal of 3 units each.

XY = XM + MY

XY = 3 + 3 = 6

Therefore, the value of XY is 6 units.

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Cofunction equivalent to [tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex].

You use the formula for the sine of a sum:

[tex]$$\sin (a+b)=\sin a \cos b+\cos a \sin b$$[/tex]

Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as [tex]$\pi$[/tex]:

[tex]\frac{5 \pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}[/tex]

With that in mind, put [tex]$a=\frac{\pi}{4}, b=\frac{\pi}{6}$[/tex] into the sine formula given above:

[tex]$$\sin \left(\frac{5 \pi}{12}\right)=\sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{6}\right)+\cos \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$$[/tex]

Plug in the familiar values [tex]$\sin \left(\frac{\pi}{4}\right)=\cos \left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}, \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$[/tex], [tex]$\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$[/tex], and you get the answer given above. And, yes, putting that expression into a calculator gives [tex]$0.9659$[/tex] (four significant digits).

The cofunction of an angle θ is the trigonometric complement of an angle. It shows the relationship between trignometric functions:

List the cofunction formula for [tex]$\sin$[/tex]

[tex]$$\sin (\theta)=\cos (\pi / 2-\theta)$$[/tex]

Plug in [tex]$\theta=5 \pi / 12$[/tex] for our cofunction formula:

[tex]$$\sin (5 \pi / 12)=\cos (\pi / 2-5 \pi / 12)$$[/tex]

Determine common denominator in radians

We use a common denominator of [tex]$(12 \div 2)=6$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (6 \pi / 12-(5 \pi / 12))$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex]

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Answer: y = 8x + 9

Step-by-step explanation: Descartes begins with only $9.00, so 9 is the y-intercept. He makes $8.00 every hour, so that is the slope.

y = mx + b

m is the slope, and b is the y-intercept.

y=8x + 9

The expression that represents the given situation is y = $49.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it isgiven that,

Descartes has Money = $9

Each hour earning = $8

Total time of work = 5 hours

So, total money earned in 5 hours = 8*5 = $40

Let y be the total money Descartes has.

So total money Descartes has = Money + total money earned in 5 hours

⇒ y = $9 + $40

⇒ y = $49

This is the required expression for the present situation.

Thus, The expression that represents the given situation is y = $49.

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The simplified form of the following expression is 51.3.

Given,

11(9²-5²)/(2²+8)

= 11(81-25)/(4+8)

= 11(56)/(12)

= 51.3

Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When simplifying an expression, we combine all similar terms and, if necessary, solve all of the supplied brackets, leaving just the, unlike words that cannot be further reduced.

Combining like terms together and leaving unlike terms alone is the fundamental principle for simplifying phrases. The following is a list of some of the guidelines for simplifying expressions:

Add the coefficients of two or more similar terms together, then include the common variable in the equation.

In the phrase a (b + c) = ab + ac, open the brackets using the distributive property.

Change the sign of all the phrases placed inside that bracket if there is a negative sign right outside the parenthesis to make things simpler.

Simply remove the bracket and put the words as they are, keeping the terms' original signs if there is a "plus" or other positive sign outside of it.

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A linear pair is formed of ∠1 and ∠2. The measures of the angle ∠1 is 20 and ∠2 is 160.

Given that,

A linear pair is formed of ∠1 and ∠2.

We have to find the measurements of both angles if m∠1 is eight more than m∠2.

When they refer to something as "linear," they mean that two angles create a straight line (or, 180 degrees). In other words, the two angles add up to 180.

Let us take the ∠1 as x

Then ∠2 will be 8x.

Now, we can write as

x+8x=180

9x=180

x=180/9

x=20

Therefore, the measures of the angle ∠1 is 20 and ∠2 is 8×20=160.

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3m+(m-43)+m

3m=page 3

m-43=page 2

m=page 1

Answer: 4.5

Step-by-step explanation:

To break even, we need the total profit to be equal to 0. If we make x dollars in 2012, then we need to solve

2.5 + 1.75 + (-3.3) + (-1.4) + x = 0

This gives us x = 0.45 in thousands.

Since the question asks us to give the answer in hundreds, we multiply by 10 and get 4.5. Thus the profit in 2012 must be 4.5 (in hundreds) to break even.

The length of KL is 35 units

The given parameters are:

The above means that

JL = JK + KL

So, we have

5x - 8 + 9x + 2 = 12x

Evaluate the like terms

2x = 6

Divide by 2

x = 3

Substitute x = 3 in KL = 9x + 2,

KL = 9 x 3 + 8

Evaluate

KL = 35

Hence, the length of KL is 35 units

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The number of students from country C using mathematical operations is 113,115.

The mathematical operations are addition, subtraction, multiplication, and division.

These mathematical operations are used to determine the output value, given some input values.

The number of foreign students from country B = 138,000

Students from country B are 22% more than the number of students from country C.

Assume that the number of students from country C = 100%

Then the number of students from country B = 122% (100 + 22)

If the number of foreign students from country B is 138,000, which is 22% more, then the number of students from country C is as follows:

The number of students from country C = 113,115 (138,000/1.22)

Thus, the number of students from country C using mathematical operations is 113,115.

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This number is 22​% more than the number of students from country C.

Answer:

Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.

The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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