An airplane flew across the Pacific Ocean. The table shows the amount of time and the distance traveled when the airplane was traveling at a constant speed. What is the distance traveled for 2 hours? *

Answer:f(x) indicates applying the function to the value x and can also represent the actual value obtained by applying the function to x

Step-by-step explanation:

Answer:

f(x) means y

Step-by-step explanation:

You use f(x) when it is representing y in a function

Answer:

The square root of 85

Step-by-step explanation:

The formula to find out the distance between the points is shown below:

The Distance is

[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

x_1 = -3

y_1 = -1

x_2 = 4

And, the y_2 = 5

Now place these values to the above formula

So, the distance is

[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]

= 9.22 units

Hence, the distance between points M and N is 9.22 units or the square root of 85

Hence, the second option is correct

Answer:

X=1/2. X=4/3

Step-by-step explanation:

6x2+5X-4=0

6X2+8X-3X-4=0

2x(3x+4) - 1(3x+4)=0

2x-1) (3X-4)

X=1/2. X=4/3

The Solution of Equation is x = -4/3 or x= 2.

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. LHS = RHS is a common mathematical formula.

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.

We have the Equation:

6x² + 5x - 4 = 0

Solving the Quadratic equation

6x² + 5x - 4 = 0

6x² -3x + 8x - 4 = 0

3x( x- 2) +4 (x-2)= 0

(3x + 4) (x-2) = 0

3x +4 = 0 or x-2 = 0

x = -4/3 or x= 2

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Answer:

the last one

Step-by-step explanation:

i took the test

If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.

Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.

Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.

Answer:

4 7/24

Step-by-step explanation:

Answer:

103/24 or 4.29 or 4 7/24

Step-by-step explanation:

15 5/12 - 11 1/8

185/12 - 89/8

370/24 - 267/24 = 103/24

or

15 10/24 - 11 3/24 = 4 7/24

Answer:

To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.

Answer:

The answer is

Step-by-step explanation:

f(x) = 6x² + 3

To find the inverse of the function above equate it to y

That's

f(x) = y

So we have

y = 6x² + 3

Next interchange the variables that's x becomes y and y becomes x.

x = 6y² + 3

Next make y the subject

Subtract 3 from both sides

That's

6y² + 3 - 3 = x - 3

6y² = x - 3

Divide both sides by 6

That's

Next find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

approximate perimeter is 42.32

Step-by-step explanation:

each side of a square is equal to each other

1. Find the square root of 112

[tex]10.58^2 = 112[/tex]

2. Multiply 10.58 by 4(number of sides)

[tex]10.58(4) = 42.32[/tex]

Answer:

focus and belive on your self

Step-by-step explanation:

Unfortunately, I do not go to Harvard Business School so I am unable to solve this complex equation.

Answer: -9

Step-by-step explanation: you want to take away 12 from 3, which will leave you in the negatives

Answer:

p

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

9+10 > 21

19 >21

This is not true so it cannot make a triangle

Answer:

Step-by-step explanation:

1=

option b= 4

2.

option b=60miles per hour

Hope it helps

Answer:

1

Step-by-step explanation:

Using the sum to product formulae and the exact values

sin x + sin y = 2sin([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

cos x + cos y = 2cos([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Given

[tex]\frac{sin75+sin15}{cos75+cos15}[/tex]

= [tex]\frac{2sin(\frac{75+15}{2})cos(\frac{75-15}{2}) }{2cos(\frac{75+15}{2})cos(\frac{75-15}{2}) }[/tex]

= [tex]\frac{2si45cos30}{2cos45cos30}[/tex]

= (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) ÷ (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= 1

Answer:  1

Step-by-step explanation:

sin 75 = sin(30 + 45) = sin30 · cos45  + cos30 · sin45

                                 [tex]=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}[/tex]

sin 15 = sin(45 - 30) = sin45 · cos30  - cos45 · sin30

                                  [tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]

cos 75 = cos(30 + 45) = cos30 · cos45  - sin30 · sin45

                                   [tex]=\dfrac{\sqrt3}{2}\cdot \dfrac{\sqrt2}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}[/tex]

cos 15 = cos(45 - 30) = cos45 · cos30  + sin45 · sin30

                                   [tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]

       [tex]\dfrac{\sin 75+\sin 15}{\cos 75+\cos 15}[/tex]

   [tex]=\dfrac{\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6-\sqrt2}{4}+\frac{\sqrt6+\sqrt2}{4}}\\\\\\=\dfrac{\frac{\sqrt6}{2}}{\frac{\sqrt6}{2}}\\\\\\=1[/tex]

Answer:

[tex]=7x^2+8x-2[/tex]

Step-by-step explanation:

So, on Monday, Tuesday, and Wednesday, he mowed:

[tex](4x^2+3x-4),(5x-8),(3x^2+10)[/tex]

yards, respectively.

To determine how many yards he mowed in the three days, simply add the three expressions. Thus:

[tex](4x^2+3x-4)+(5x-8)+(3x^2+10)[/tex]

Combine like terms:

[tex]=(4x^2+3x^2)+(3x+5x)+(-4-8+10)[/tex]

Add or subtract:

[tex]=7x^2+8x-2[/tex]

And it cannot be simplified further :)

The answer is C. If the verticle line intersects with the graph more than once, it is NOT a function.

Answer:

The cost in 2007 - 2008  =  $15,795.5

The linear model for the data is y = $650.5·x + $9290.5

Step-by-step explanation:

The given data can be presented as follows;

College year,                         x,                 Estimated tuition, y

1997-1998,                             0,                 $9412

1998-1999,                             1,                  $9941

1999-2000,                            2,                 $10561

2000-2001,                            3,                 $11242

2001-2002,                            4,                  $11965

2002-2003,                            5,                  

2003-2004,                            6,                  

2004-2005,                            7,                

2005-2006,                            8,                

2006-2007,                            9,                  

2007-2008,                            10,                  

With points (1, 9941) and (3, 11242), we have the slope given by the equation;

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Which gives;

[tex]m = \dfrac{11242 - 9941}{3 - 1}= 650.5[/tex]

Therefore;

y - 11242 = 650.5 × (x - 3)

y= 650.5·x - 650.5 ×3 + 11242

y = 650.5·x + 9290.5

Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;

y = 650.5×10 + 9290.5 = $15,795.5

The cost (estimated tuition) in 2007 - 2008  =  $15,795.5

The linear model for the data is y = 650.5·x + 9290.5.

The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the cost of tuition of battery after x years.

From the table using the points (1, 9941) and (3, 11242):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5[/tex]

The linear model for the data is y = 650.5x + 9290.5

At 2007-2008 (x = 10:

y = 650.5(10) + 9290.5 = 15795.5

The cost of college tuition in 2007-2008 is $15795.5

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Answer: 40/7, if you need, the mixed fraction is 5 5/7

Step-by-step explanation:

First of all, convert all the mixed fraction into improper fraction.

2 2/3=8/3

2 1/7=15/7

Then do the multiplication.

8/3 × 15/7=120/21=40/7 (You can directly simplify it to 40/7 since you can use 15 divided by 3 to get 5 left in the numerator)

Hope this helps!! :)

Please let me know if you have any question

Answer:

5.71

Step-by-step explanation:

two two by three × two one by seven

=8/3×15/7

=8×5/7 as 15 and three will divide and 15 will change to 5

=40/7

=5.71

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]

Step-by-step explanation:

Given,

Length of the rectangle ( l ) = 3x + 5

Breadth of the rectangle ( b ) = 2x - 1

Perimeter of the rectangle ( P ) = 52

Finding the value of x

[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]

⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]

⇒[tex] \sf{52 = 2(5x + 4)}[/tex]

⇒[tex] \sf{52 = 10x + 8}[/tex]

⇒[tex] \sf{10x + 8 = 52}[/tex]

⇒[tex] \sf{10x = 52 - 8}[/tex]

⇒[tex] \sf{10x = 44}[/tex]

⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]

⇒[tex] \sf{x = 4.4 \: }[/tex]

Hope I helped!

Best regards!! :D

Answer:

9 9/14

Step-by-step explanation:

[tex]4\frac{1}{2}\times\:2\frac{1}{7}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{2}=\frac{9}{2}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{7}=\frac{15}{7}\\\frac{9}{2}\times\frac{15}{7}\\\\\mathrm{Multiply\:fractions}:\\\quad \frac{a}{b}\times\frac{c}{d}=\frac{a\:\times\:c}{b\:\times\:d}\\\\=\frac{9\times\:15}{2\times\:7}\\\\=\frac{135}{14}\\\\[/tex]

[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{135}{14}\\=9\frac{9}{14}[/tex]

Answer:

(x+5) (x=3)

(X+5) (x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

Answer:

No

Step-by-step explanation:

2 to the fourth power is equal to 16.

On the other hand, 2 times 4 is equal to 8.

So, they are not equivalent because 16 [tex]\neq[/tex] 8

4² is the same as the question 4 x 4 which is 16

Answer:

For 7 miles call they Yellow Cab and for 3 miles call Express Cab

In 4 miles it cost $6.00 for both

Step-by-step explanation:

Express Cab= $4.50 for 3 miles, and for 7 miles it cost $10.50

Yellow Cab = $5.75 for 3 miles, and for 7 miles it cost $6.75

add 1.50 to 4.50 and is 6 dollars in 4 miles and add 0.25 to 5.75 and it also makes it 4 miles

Answer: 2(x+y)-25

Step-by-step explanation:

First, we need to show the sum of Roger and Olivia's heights. If Roger is x and Olivia is y, the sum is x+y

Next, we need to double that. To double something we multiply it by 2. Since we need double the expression we found above, we put it in parentheses. So the doubled sum is shown as 2(x+y)

Finally, we need to show that Isabella is 25 centimeters shorter than the doubled sum. To do that, subtract 25.

The final expression for Isabella's height is 2(x+y)-25

Answer:

[tex] \frac{7}{15} [/tex]

Step-by-step explanation:

[tex] \frac{9}{5} - \frac{4}{3} = \frac{27 - 20}{15} = \frac{7}{15} [/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{7}{15} }}}}}[/tex]

Option C is the correct option

Step-by-step explanation:

[tex] \sf{ \frac{9}{5} - \frac{4}{3} }[/tex]

Take the L.C.M ( Lowest Common Multiple ) of 5 and 3.

L.C.M of 5 and 3 = 15

⇒[tex] \sf{ \frac{9 \times 3 - 4 \times 5}{15} }[/tex]

Multiply the numbers

⇒[tex] \sf{ \frac{27 - 20}{15} }[/tex]

Subtract 20 from 27

⇒[tex] \sf{ \frac{7}{15} }[/tex]

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:

The question is lacking appropriate diagram. Find the diagram to the question attached.

From the diagram, it can be seen that AD = AB+BC+CD

Given the following

AD = 23units

AB = 4units

CD = 12units

To get C=BC, we will substitute the given segments into the expression above as shown;

23 = 4+BC+12

23 = BC + 4 + 12

23 = BC+16

Subtract 16 from both sides

23-16 = BC+16-16

7 = BC

Hence the length of segment BC is 7units.

Answer:

The annual depreciation rate is 72.86%.

Step-by-step explanation:

The information provided are:

From the above data we know that the band's popularity depreciated.

The initial cost of a signed Black Diamond poster was, a = $500.

After three years the cost of a signed Black Diamond poster was, y = $10.

It can be seen that the value of a signed Black Diamond poster is decreasing exponentially over the years.

The formula for exponential decay or depreciation is:

[tex]y=a(1-r)^{x}[/tex]

Here,

y = final value

a = initial value

r = rate of depreciation

x = time

Compute the annual depreciation rate as follows:

         [tex]y=a(1-r)^{x}[/tex]

        [tex]10=500\times (1 -r)^{3}[/tex]

[tex](1-r)^{3}=\frac{10}{500}[/tex]

 [tex](1-r)=\sqrt[3]{\frac{1}{50}}[/tex]

    [tex]1-r=0.2714[/tex]

          [tex]r=1-0.2714\\\\r=0.7286[/tex]

Thus, the annual depreciation rate is 72.86%.