Caley is trying to find the best deal on a flight from New York to Orlando. She checks the price each week and tracks how much it changes.

Answer:

(6x-1)(2x+1)

Step-by-step explanation:

12x²+4x-1 (find two numbers that when you add or subtract them the ANS will be the coefficient of x and those same numbers when you multiply them the ANS will be the product of 12 and -1) then replace the middle term with those numbers.

12x²+6x-2x-1

(12x²+6x)(-2x-1)

6x(2x+1)-1(2x+1)

(6x-1)(2x+1)

No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100.  So, they cannot be compared as percentages crossed out.

It is a branch of Mathematics. It is a number or ratio expressed in the form of a fraction. A percentage can be denoted by the symbol %. It is a dimensionless number and it does not have any unit of measurement. The percentage is mainly used in shopping malls for giving discounts on clothes to customers. And the percent is used in salary increments in the company. The percentage is a very easy concept to learn by students or any other person. Percentage plays a key role in our daily life.

The number of students cannot be compared as percentages as the total number of students for both grades are not given.

So, the correct option is (c) No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100.  So, they cannot be compared as percentages crossed out.

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Answer:

x=9, x=2

Step-by-step explanation:

Since both expressions (x^2 - 14x + 23 and -3x+5) are equal to y, set those expressions equal to each other and solve for x.

x^2 - 14x + 23 = -3x + 5

subtract 5 from both sides

x^2 - 14x + 23 - 5 = -3x + 5 - 5

x^2 - 14x + 18 = -3x

add 3x to both sides

x^2 - 14x + 3x + 18 = -3x + 3x

x^2 - 11x + 18 = 0x

factor.

(x-9)(x-2) = 0

Because the product of these two things equals 0, we know that one of these terms must equal to zero.

x-9 = 0 or x-2 = 0

it can be either, so solve for both.

x-9 + 9 = 0 + 9     or      x-2 + 2 = 0 + 2

x = 9 or x=2

The actual solution of the mathematical statement is -6.93

From the question, we have the following statement that can be used in our computation:

negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths

Mathematically, this statement can be expressed as

-15 + -3.7 + 9.15/5 * 3² - 4.7

Evaluate the quotient and the exponents in the expression'

So, we have

-15 + -3.7 + 1.83 * 9 - 4.7

Evaluate the product exponents in the expression'

So, we have

-15 + -3.7 + 16.47 - 4.7

Evaluate the sum and the difference

-6.93

Hence, the solution is -6.93

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In order to draw a straight line on a graph at least two points are needed.

The graph for the given straight line is shown in the diagram.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equation is as below,

y = 12x − 3

Substitute x = 0 in the above equation to get,

y = 12 × 0 - 3

=> y = -3.

Substitute y = 0 in the above equation to get,

0 = 12x - 3

=> x = 3 / 12

=> x = 1 / 4

Now, draw a line through these two points on the coordinate plane to get the graph of  y = 12x − 3.

The graph of y = 12x − 3 is given in the following diagram.

Hence, the graph of the given equation is drawn by finding the intercepts.

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Answer: 0.049

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.061

Answer:

A.  (1/6) mile is the maximum height.

B.  The maximum height occurs (3/36) miles from the base of the bridge.

Step-by-step explanation:

The answer of (1/6) mile to the point of maximum height is correctly given by 001466952.  I'll add a little more perspective as well as a second approach in addition to graphing.

Graphing

As suggested by 001466952, one may graph the function and look for the point at which the maximum (vertex) is located.  The attached graph shows this approach.  The maximum height of 0.83 miles is also found on the graph [point (0.1667, 0.083)].

First Derivative

One may also take the first derivative of the function.  The first derivative will provide the slope at any point x on the original curve.  The slope at the vertex will be 0 (the top point where the slope turns from positive to negative).  The slope will be zero at the very top.

y = -3x^2 + x

dy/dx = -6x + 1

0 = -6x+1

x = (1/6) mile

Use x = (1/6) in the original equation to find the height at this point.

y = -3x^2 + x

y = -3(1/6)^2 + (1/6)

y = (-3/36) + (6/36)

y = 3/36 or 0.083 miles from the bridge's base.

The solution is

a) The maximum height occurs at x = 1/6 where x is the number of miles from the base of the bridge

b) The maximum height of the bridge is ( 1/12 ) miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the height of the bridge be represented by the equation ,

y = -3x² + x   be equation (1)

where y is the height of the bridge

and x is the number of miles from the base of the bridge

Now , to find the number of miles at which the maximum height occurs

Take the first derivative of the function and substitute it to 0

So , ( dy / dx ) = 0 ( at maximum height )

On simplifying the equation , we get

dy / dx = -6x + 1

when ( dy / dx ) = 0 ( at maximum height )

-6x + 1 = 0

Adding 6x on both sides of the equation , we get

6x = 1

Divide by 6 on both sides of the equation , we get

x = 1/6

Now , the maximum height of the bridge is at when x = 1/6

Substitute the value of x = 1/6 in equation (1) , we get

y = -3x² + x

y = -3 ( 1/6 )² + 1/6

y = -3/36 + 1/6

On simplifying the equation , we get

y = 3/36 miles

y = 1/12 miles

Hence , the maximum height of the bridge is 1/12 miles

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Answer:

exponential

Step-by-step explanation:

Answer:

$5,550.

Explanation:

The sales price = $185,000

The closing cost = 3% of the sales price.

Thus:

The closing cost is $5,550.

Answer:

n general, greater frequency and intensity of climate hazards are more likely to prompt people to migrate when the population is more vulnerable and has a lower capacity to adapt. Climate events can be divided into fast- and slow-onset events.

Step-by-step explanation:

Answer: No, It is not a right-angled triangle.

Step-by-step explanation:

Find the length of the last side first. To do this, add AB and BC together, then deduct that sum from the 22 cm circumference of Triangle ABC.

ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)

              22cm - 13cm = 9cm

Since the hypotenuse of a triangle is always its longest side, we can be certain that the side we identified is the hypotenuse. The Pythagorean Theorem can now be used to determine whether the triangle is a right triangle.

Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse. The triangle is a right triangle if a2 + b2 do equal c2.

8² + 5² = 9²

64 + 25 = 81

89 > 81

The triangle is not a right triangle, but since a and b are longer than c, we can conclude that it is obtuse.

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To minimize the cost, the builder should but 200 meters of fence costs at $2 per meter and 800 meters of fence costs at $1 per meter. The minimum cost is $1,200.

Recall that if we have a function f(x), then at the extremum point, its derivative is equal to zero.

f ' (x) = 0

In the given problem, let:

p = length of the rectangle

q = width of the rectangle

Then,

p x q = 60,000 or q = 60,000/p

Assume that the front side is p, then the function that describe the cost is:

f(p,q) = 2xp + 1 x (p + q + q)

f(p,q) = 3p + 2q

f(p) = 3p + 2 x 60,000/p

f(p) = 3p + 120,000/p

Take the derivative:

f '(p) = 3 - 120,000/p² = 0

p² = 40,000

p = 200 meters

Substitute p = 200 to get q,

q = 60,000/200 = 300

Hence, the type of fences the builder have to buy to minimize the cost is:

200 meters fence with cost $2 per meter and 200+300+300= 800 meters fence with cost $1 per meter.

The minimum cost is:

f(p) = 3p + 120,000/p

f(min) = f(200) = 3x200 + 120,000/200 = $1,200

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Answer:

6

Explanation:

To know the median, we first need to organize the data from least to greatest, so:

5 6 6 6 7 9 9

Then, the median will be the value that is in the middle, so:

5 6 6 6 7 9 9

Therefore, the median is 6 because there are 3 values to the left of 6 and 3 values to the right of 6.

The given inequality is always true for all real numbers.

Given, the inequality is :

4(2x - 3) < 8(x + 1)

Reduce the greatest common factor for both of the sides of the inequality:

2x - 3 < 2(x+1)

Apply Multiplicative distribution law:

2x - 3 < 2x + 3

Rearrange unknown terms to the left of the side of the equation:

2x - 2 < 2 + 3

Combine the like terms:

0 < 2+3

Calculate the sum or the difference.

0 < 5

The solution of the inequality is always true.

Hence we get the solution as the inequality being true to all real numbers.

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Answer:

162 bracelets

Step-by-step explanation:

1st - 82 bracelets

2nd - 98

3rd - 114

4th - 130

5th - 146

6th - 162

Given the equation :

It is a cubic function because the power of x = 3

The cubic function is not linear function

The linear function has the form : y = m * x + b

The power of x for the linear function = 1

so, the answer is : No

Answer:

a)

b)

c) x-intercept is 0

Explanation:

Given:

a) See below the graph of different transformations of the given function;

The equation of the vertical asymptote as shown on the graph is x = -4

b) The domain of a function is the set of possible input values for which the function is defined. The domain of a graph is the set of possible values from left to right.

Looking at the given graph, we can see that the domain of the function is;

The range of a graph is the set of values from the bottom to the top of the graph. Looking at the graph, we can see that the range is;

c) We'll follow the below steps to determine the x-intercept of the function;

Step 1: Substitute f(x) with 0;

Step 2: Add 2 to both sides;

Step 3: Apply the below rule;

So the x-intercept is 0

Answer:

Slope = -2/3

y-intercept= (0,4)

Step-by-step explanation:

Hope this helps!!!

Answer:

slope= - 2/3

y-intercept = 4

Step-by-step explanation:

convert to y=mx+b where m = slope and b= y-intercept

2x+3y=12

3y= -2x+12

y = -2/3x+4

slope= - 2/3

y-intercept = 4

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The scale factor that was used in the dilation is 3

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, say, 2.

The image of XYZ after dilation through point C is X'Y'Z. X'Z' = 10 and XZ = 30

For Calculating the scale factor, er divide XZ and X'Z'

So, we have :

[tex]\frac{XY}{X'Y'} =\frac{30}{10} =3[/tex]

Hence, the scale factor that was used in the dilation is 3.

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In general, the compound interest formula is

In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,

a) Set t=1

b) Set t=2,

Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.

Answer:

angle E

Step-by-step explanation:

Have 109% in geometry

The perimeter of the triangle is 31 feet when the value if y is 3 feet.

Perimeter of the triangle:

Perimeter of the triangle is obtained by the total distance around the edges of a triangle.

The standard form for the perimeter of the triangle is

P = a + b + c.

where

a, b and c refers the edges of the triangle.

Given,

Here we have the triangle with the side values are (y + 5) feet, (3y + 5) feet, and (4y - 3) feet.

Then we have to find the perimeter of the triangle when the value of y is 3 feet.

We know formula of the perimeter of triangle, so first we have to calculate the side values of it, by apply the value of y as 3,

Apply the value of y as 3 feet then we get the value of the edges are

=> y + 5 => 3 + 5 = 8 feet

=> 3y + 5 => 3(3) + 5 = 14 feet

=> 4y - 3 => 4(3) - 3 = 9 feet.

Therefore, the edges of the triangle are 9ft, 14 ft and 9 ft.

Now, we have to apply the values on the formula of the perimeter of the triangle is, then we get

=> P = 8 + 14 + 9

Then the value of P = 31

Therefore, the value of the perimeter of the triangle is 31 feet.

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(63)

From the question, we are to evaluate the given binomial coefficient.

(90)

( 2 )

Using the formula:

(n) = n! = n! = 1

(0) 0!(n - 0)! 1 * n!

inputting into the formula

90C2 = 90!

2!(90-2)!

90C2 = 90!

2!(88)!

90C2 = 14857159644817614973095227336

2 * 18548264225739843911479684564

90C2 = 14857159644817614973095227336

3709652845179687822959369129

90C2 = 4005

step 1

Find the slope of the line

the slope is giving by the formula

m=(y2-y1)/(x2-x1)

we need two points

From the graph we take the points

(0,80) and (4000, 140)

substitute

m=(140-80)/(4000-0)

m=60/4000

m=6/400

m=3/200

m=0.015

step 2

Find the equation of the line in slope intercept form

P=mx+b

we have

m=0.015

b=80

therefore

P=0.015x+80

Remember that the y-intercept is the value of y when the value of x is zero

In this problem

the y-intercept represent a base pay amount each day

so

$80

Answer:

the first : y = -3(x + 2)² + 10

Step-by-step explanation:

let's do the operations :

-3(x + 2)² + 10 = -3(x² + 4x + 4) + 10 = -3x² - 12x - 12 + 10 =

= -3x² - 12x - 2

and that's exactly the original expression.

twenty-three of the students were in mr. x's class, 31 were in mrs. x's class, 9 were in both mr. and mrs. x's classes, and 18 other students were in neither class. then there are 63 students in the party

twenty-three of the students were in mr. x's class,

31 were in mrs. x's class,

9 were in both mr. and mrs. x's classes,

and 18 other students were in neither class.

therefore 23+31 - 9 =45

and 18 were other students

hence it becomes 45+18= 63 students were in the party

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We could write the following equations according to the problem:

Hours equation:

And, the payment equation: (cents)

We could solve this system of equations using the elimination method:

We're going to multiply the first equation by -620:

Now, we're going to sum both equations eliminating variable a, so we get a linear equation in terms of b:

Now we know that he did 12 hours at job b.

As he worked 22 hours in total, then he worked 10 hours at job a.

Answer:

Step-by-step explanation:

a+b = 22                --  equation 1

6.20a + 7.40b = 150.80    replacing decimals

620a + 740b = 15080      --- equation 2

From eq. 1            a = (22 - b)

putting a's value in equation 2

620(22 - b) + 740b = 15080

13640 - 620b + 740b = 15080

120b = 15080 - 13640

b =  1440/120 = 12

From equation 1            a + 12 = 22

a = 10

Verify your answer by equation 2 putting the value of a and b

620*10 + 740*12 = 15080

The ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds.

A second-order polynomial equation in one variable with the notation x = ax2 + bx + c = 0 and a 0 is known as a quadratic equation. It is a second-order polynomial problem, which guarantees that it has at least one solution according to the fundamental theorem of algebra.

s = 213 solve for t

213 = -16t² + 128t

in standard form

16t² - 128t + 213 = 0

using shridharacharya formula

t = 2.4 , 5.6

so the ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds

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The value of G⁻¹(G(x)) is x , So the correct answer among the following options  is A) x

A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.

An inverse function, sometimes known as an antI function, is a function that can change into another function. In other words, if any function "f" takes x →  y, then the inverse of that function will take y to x. The inverse of a function denoted by "f" or "F" is denoted by "f-1" or "F-1." Not to be mistaken with an exponent or a reciprocal in this case is (-1).

Given, function G(x)

inverse of the given function G⁻¹(x)

Let G(x) = x

Then G⁻¹(x) = x

So value of G⁻¹(G(x)) is,

Put G(x) = x,

Hence, G⁻¹(G(x)) = x

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