An airplane lands at an airport 60 miles east and 25 miles north of where it took off. How far are the two airports?

[tex]y = - 2(x - 2)(x - 10)[/tex]

[tex]0 = - 2(x - 2)(x - 10)[/tex]

[tex]x - 2 = 0 \\ x = 2[/tex]

[tex]x - 10 = 0 \\ x = 10[/tex]

Answer:

The zero's are x=2 and x=10

Step-by-step explanation:

y = -2(x-2) (x-10)

We want to find the zero's so we set y=0

0 = -2(x-2) (x-10)

Using the zero product property

x-2 = 0   and x-10 =0

x-2+2 =0+2     x-10+10 =0+10

x =2      x=10

The zero's are x=2 and x=10

Answer:

1.27 x 17 = 21.59 Product means multiply

Step-by-step explanation:

Answer:

21.59

Step-by-step explanation:

17 x 1.27 = 21.59

21.59/17=1.27

Answer:

Step-by-step explanation:

[tex]-6n-5=31\qquad\text{First step: add 5 to both sides}\\\\-6n-5+5=31+5\\\\-6n=36\qquad\text\qquad\text{Second step: divide both sides by (-6)}\\\\-6n:(-6)=36:(-6)\\\\n=-6[/tex]

Answer:

"(3)"

Step-by-step explanation:

Relation is a mapping between x-values and y-values. Xs are the domain and Ys are the range.

Given x values (0,3,6) and y-values(8, 2, -1), this is a relationship, so it is a relation.

To check whether a relation is a function or not, we simply see if each unique x value is paired with a unique y value.

Is there any y value that is same for x-values? NO! All are different. So this is a function as well!

Answer choice (3) is right.

Answer: (3) both a relation and a function

Step-by-step explanation:

Relation : It is the relation established between two set of values

Function : It is a kind of relation, where only output exist for e ach input.

Generally x values presents input values and y values represents the output values.

The given table :

x -  y

0 - 8

3 - 2

6 - 1

Here, each x value is related to a y-value , so its a relation.

Also, there only one unique y-value for each x-values, thus its a function.

Hence, the set of ordered pairs in the mapping below can be described as  both a relation and a function.

Answer:

12

Step-by-step explanation:

Treat the less than or equal too sign as you would a normal equal sign.

Add 27 to -15 so that x is less than or equal to 12

The length of the bd in the given triangle is 12 cm. This is obtained by applying the Pythagoras theorem.

The Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. I.e., [tex]a^2+b^2=c^2[/tex].

The triangle is perpendicularly divided into two halves looking like right-angled triangles.

The side lengths for the given triangle are bc=13 cm and ac=10 cm

The line segment bd divides the triangle into two right-angled triangles symmetrically.

So, the base ac of the given triangle is divided at the mid-point d.

Thus,

ac = ad + dc

here, d is the mid point, ad = dc

So, ad=dc=5 cm

Now, the triangle forms a right-angled triangle with sides bd, dc, and bc. Where bc is the hypotenuse.

To find the length of bd, applying the Pythagoras theorem

[tex](bc)^2=(bd)^2+(dc)^2[/tex]

⇒ [tex](13)^2 = (bd)^2 + (5)^2[/tex]

⇒ [tex]169 = (bd)^2 +25[/tex]

⇒ [tex](bd)^2 = 169 - 25[/tex]

⇒ [tex](bd)^2 = 144[/tex]

∴ bd = 12 cm

Therefore, the length of the bd is 12 cm.

Learn more about Pythagoras's theorem here:

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ANSWER

[tex] {i}^{31} = - i[/tex]

EXPLANATION

We want to evaluate

[tex] {i}^{31} [/tex]

Use indices to rewrite the expression as:

[tex] = {i}^{30} \times i[/tex]

We know that

[tex] {i}^{2} = - 1[/tex]

So we rewrite the expression to obtain;

[tex] = ({ {i}^{2}) }^{15} \times i[/tex]

This gives us;

[tex]= {( - 1) }^{15} \times i[/tex]

This simplifies to

[tex] = - 1 \times i[/tex]

[tex] = - i[/tex]

Answer:

[tex]10.3\ mi[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(10,8)\\B(1,3)[/tex]

substitute the values

[tex]d=\sqrt{(3-8)^{2}+(1-10)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(-9)^{2}}[/tex]

[tex]d=\sqrt{25+81}[/tex]

[tex]d=\sqrt{106}[/tex]

[tex]d=10.3\ mi[/tex]

The decimal equivalent of 3/7 rounded to the nearest hundreds is 0.428

Answer: 0.43 cause hundredths place is the 3 and its rounded

Step-by-step explanation:

[tex](2x + 1)(3x + 4) \\ = 2x(3x + 4) + 1(3x + 4) \\ = 6 {x}^{2} + 8x + 3x + 4 \\ = 6 {x }^{2} + 11x + 4[/tex]

Interest (I) = Principal (P) X Rate (R) X Time (T)

They tend to use 'Exact Interest' in which Interest calculated using a 365-day year. Time that counts exact number of days in the month that the borrower has the loan

Hope this helps :)

Answer:

Interest (I) = Principal (P) X Rate (R) X Time (T)

Hope this helps you:)

5INGH

Step-by-step explanation:

Answer:

126.2 meters

Step-by-step explanation:

A trapezoid's area is found using the formula A = 1/2 (a+b)h where a and b are the two bases. Substitute A = 12,052.1, a = 82.4 and b=108.6. Then solve for h.

A = 0.5(a+b)h

12,052.1 = 0.5(82.4 + 108.6)*h

12,052.1 = 0.5(191)h

12,052.1 = 95.5h

126.2 = h

Answer: You multiply 1.5 each time.

Step-by-step explanation:

72*1.5=108

108*1.5=162

162*1.5=243

And so on and so forth....  Hope it helped!

243 = 3x3x3x3x3

162 = 3x3x3x3x2

108 = 3x3x3x2x2

72 = 3x3x2x2x2

The next two numbers in the sequence would be

48 = 3x2x2x2x2

32 = 2x2x2x2x2

The answers are:

[tex]f(x)=\frac{5x+3}{2}[/tex]

[tex]f(x)=2x-8[/tex]

[tex]f(x)=7x-2[/tex]

[tex]f(x)=\frac{1}{x+2}[/tex]

To find the inverse function of a function, we need to replace the variable (x for this case) for the function itself (f(x)), where we see "x" we must rewrite with "y" or "f(x) and then, isolate "y" or "f(x).  If we have the inverse function and we want to find the function, we need to reverse the process.

Let's find each function of the given inverse functions in order to match each one with its inverse.

First inverse function,

[tex]f^{-1}(x)=\frac{2x-3}{5}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{2f(x)-3}{5}\\\\5x=2f(x)-3\\\\5x+3=2f(x)\\\\f(x)=\frac{5x+3}{2}[/tex]

Therefore, the function that matches with the first inverse function is:

[tex]f(x)=\frac{5x+3}{2}[/tex]

Second inverse function,

[tex]f^{-1}(x)=\frac{x+8}{2}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{f(x)+8}{2}\\\\2x=f(x)+8\\\\2x-8=f(x)\\\\f(x)=2x-8[/tex]

Hence, the function that matches with the second inverse function is:

[tex]f(x)=2x-8[/tex]

Third inverse function,

[tex]f^{-1}(x)=\frac{x+2}{7}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{f(x)+2}{7}\\\\7x=f(x)+2\\\\7x-2=f(x)\\\\f(x)=7x-2[/tex]

So, the function that matches with the third inverse function is:

[tex]f(x)=7x-2[/tex]

Fourth inverse function,

[tex]f^{-1}(x)=\frac{1-2x}{x}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{1-2f(x)}{f(x)}\\\\xf(x)=1-2f(x)\\\\f(x)x+2f(x)=1\\\\f(x)(x+2)=1\\\\f(x)=\frac{1}{x+2}[/tex]

So, the function that matches with the fourth inverse function is:

[tex]f(x)=\frac{1}{x+2}[/tex]

Have a nice day!

There is not much that can be done to figure out how to write 0.312 as a fraction, except to literally use what the decimal portion of your number, the .312, means. Since there are 3 digits in 312, the very last digit is the "1000th" decimal place. So we can just say that .312 is the same as 312/1000.

Jeremiah's batting average of 0.312 can be expressed as the fraction 312/1,000, which can be further reduced to its simplest form 39/125 by dividing by their greatest common divisor, which is 8.

To express Jeremiah's batting average of 0.312 as a fraction in lowest terms, we need to start by expressing it as a fraction out of 1,000, which gives 312/1,000. From there, we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor to reduce it to its simplest form. The greatest common divisor of 312 and 1,000 is 8. If we divide 312 by 8, we get 39, and if we divide 1,000 by 8, we get 125. Therefore, the fraction in its simplest terms is 39/125.

Expressing decimals as fractions is a common task in Mathematics and it's a handy skill for dealing with real-world data, like a baseball player's batting average.

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Answer:

1.31950791

Step-by-step explanation:

I don't actually know if this is correct

Answer:

y = 2.4

Step-by-step explanation:

first distribute into the parenthesis' -

2(y-3) = 1.2 -y

2y - 6 = 1.2 - y

+y                +y

3y -6 = 1.2

   +6     +6

3y = 7.2

/3      /3

y = 2.4

hope this helps!!

Answer:  y=2.4

Step-by-step explanation:

The work is below Hopefully this helps:)

* Mark me the brainliest:)!!

The data set is

20

32, 34, 36

40, 42, 44, 48

55

65

We can see that each value only shows up one time. Therefore there is no mode. To have a mode, we need to have a value show up more than once, and it must be the most frequent value. For example, the set {1,2,3,3,4} has a mode of 3 since it shows up twice, the most of any value in that set. However we don't have that occur for the data set your teacher gave you.

Answer:

no mode i just got it right

Step-by-step explanation:

Answer:

the third one

Step-by-step explanation:

-b to start is -(-6) which is 6

needs the plus and minus

the first expression is the whole numerator

Answer:   [tex]\bold{c)\quad x=\dfrac{6\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}}[/tex]

Step-by-step explanation:

[tex]3x^2-6x+8=0\quad \rightarrow \quad a=3,\ b=-6,\ c=8\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}}\\\\\\x=\dfrac{6\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}[/tex]

The Pythagorean Theorem says for a right triangle with legs a,b and hypotenuse c,

[tex]c^2 = a^2+b^2[/tex]

Solving for each in turn,

[tex] c= \sqrt{a^2+b^2}[/tex]

[tex]a^2=c^2 - b^2[/tex]

[tex]a = \sqrt{c^2-b^2}[/tex]

[tex]b = \sqrt{c^2-a^2}[/tex]

Looking at our choices, we select the third and fourth.

The pythagorean theorem states that, in every right triangle, the following formula holds:

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs, and c is the hypotenuse.

We can deduce the following expressions for a,b and c:

[tex]a = \sqrt{c^2-b^2},\quad b=\sqrt{c^2-a^2},\quad c=\sqrt{a^2+b^2}[/tex]

Answer:

-3/b

Step-by-step explanation:

The reciprocal of -b/3 is -3/b

Answer:

The correct answer is,

| -8|

| 4 |

Step-by-step explanation:

It is given two matrices,

1)Let Matrix A =   5  -2

                          -6    2

2) Matrix B =       -1

                          -1

Matrix A is 2 x 2 matrix and matrix B is 2 x 1 matrix

To find the product of two matrices

A x B =    5  -2       x      -1     =   -10+2      =   -8

             -6    2              -1             6 -2            4

Therefore the correct answer is

| -8|

| 4 |

Answer:

The answer to your question is that x is equal to 50.

[tex]\bf \stackrel{\textit{range is always the set of y-coordinates}}{f=\{(2,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{7}),(3,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{4}),(9,\stackrel{\downarrow }{1})\}}\qquad \qquad \{3,7,3,4,1\}\implies \{3,7,4,1\}[/tex]

Answer:

{3, 7, 3, 4, 1}

Step-by-step explanation:

Answer:

a = 15

Step-by-step explanation:

The graph of function g(x) is described by g(x)=ax−7, or y = ax−7.

y = g(x)=ax−7 passes through (1/3, -2).  We can subst. -2 for y and 1/3 for x to determine the value of the coefficient a:

-2 = g(1/3) = a(1/3) - 7

Solve for a.  First, add 7 to both sides:  5 = a(1/3).

Next, multiply both sides by 3:  15 = a, or a = 15.

12) D'(3, 1) E'(1, -2) F'(5, 0)

13) Vertex E

14) D'(3, 1)

15) D'(1, 3) E'(3, 0) F'(-1, -2)

16) D'(-11, 11) E'(13, 8) F'(-9, 6)

P'(-9, 10) Q'(-7, 12) R'(-5, 10)

17) Translate 4 units down; (x, y) ---- (x, y - 4)

18) P'(-1, 2) Q'(-3, 4) R'(-5, 2)

19) P'(-2, 1) Q'(-4, 3) R'(-2, 5)

20) P'(-1, -2) Q'(-3, -4) R'(-5, -2); Rotated 180° about the origin

21) P'(3, 6) Q'(9, 12) R'(15, 6)

22) A'(-9, 0) B'(0, 12) C'(9, 0) D'(0, -12)

23) Image (yes, the answer is actually Image)

24) (x, y) → (1.5x, 1.5y)

This took me 45 mins to do, lol.

You're welcome? :) <3

Answer:

Step-by-step explanation: I hope that helps you.

Answer:

12+x/8

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

i hope it helps if not 17 then it is ..................... 12+x/8

Answer:

2,038,711

Step-by-step explanation:

For a continuously compounding rate r, the growth is modeled by ...

P = P0·e^(rt)

where P0 is the initial population, r is the annual growth rate (compounded continuously) and t is the number of years.

Putting your values into this formula, you have

P = 750000·e^(0.04·25) ≈ 2,038,711

Using the formula for continuous compound growth, the population of the district in 2025 is projected to be approximately 1,226,030.

The question is asking about the future population of a district based on continuous compound growth. In this case, the compound interest formula, which includes the principle amount, the rate of growth (interest), and time. The formula often looks as follows: A = P * e^(rt), where A is the amount in the future, P is the principle amount (initial population), r is the rate of growth (interest), and t is the time.

In your case, the calculation would be: A = 750,000 * e^(0.04 * 25). Here, 'e' represents Euler's number (approximately equal to 2.71828), 0.04 is the growth rate, and 25 is the time (years from 2000 to 2025).

Using this formula, we can calculate that the population of the district in 2025 will be approximately 1,226,030 people, assuming a steady growth rate of 4% annually.

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