AIR TRAVEL - an airplane traveling at an altitude of 5,900m changes its altitude by - 2,900m. What does this change in altitude mean ?

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Explanation:

Plug in x = 1

f(x) = 17-x^2

f(1) = 17-1^2

f(1) = 17-1

f(1) = 16

Repeat for x = 5 to find that f(5) = -8

Now we'll use the formula below to find the average rate of change from x = a to x = b.

[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(5)-f(1)}{5-1}\\\\m = \frac{-8-16}{4}\\\\m = \frac{-24}{4}\\\\m = -6\\\\[/tex]

The average rate of change is -6

The formula is basically the slope formula, more or less. So that's why I used 'm' to represent the average rate of change.

The average rate of change on the interval [1,5] is the same as finding the slope through the lines (1, 16) and (5, -8)

Answer:

13cm

Step-by-step explanation:

if the area is 117 then to find out the missing length, you divide 117 by 9 which gets you 13.

to check its correct, 13 x 9 = 117cm^2

Answer:

84

Step-by-step explanation:

Score = 90

Standard deviation = 3

Score = mean + 2(standard deviation)

90 = mean + 2(3)

90 = mean + 6

Mean = 90 - 6

Mean = 84

The right answer is a i think i don't known step by step

Step-by-step explanation:

a

a

Answer:

It will take 48 hours for the entire icicle to melt.

Step-by-step explanation:

12 divided by 1/4 = 48

The linear equation to model the situation is f(x) = -1/4x + 12

Write a linear equation in slope-intercept form to model the situation. An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.

The given parameters are:

The above means that:

A linear equation is represented as:

f(x) = mx + c

Where f(x) represents the function and x represents the number of hours.

So, we have:

f(x) = -1/4x + 12

Hence, the linear equation to model the scenario is f(x) = -1/4x + 12

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Answer:

Total number of wreaths = 3.5 wreaths

Step-by-step explanation:

Given:

Number of medium wreaths = x

Number of larger wreaths = 2[Number of medium wreaths]

Number of small wreaths = [1/2][Number of medium wreaths]

Find:

Total number of wreaths

Computation:

Total number of wreaths = Number of medium wreaths + Number of large wreaths + Number of small wreaths

Total number of wreaths = Number of medium wreaths + 2[Number of medium wreaths] + [1/2][Number of medium wreaths]

Total number of wreaths = x + 2x + 0.5x

Total number of wreaths = 3.5 wreaths

Answer:

Part A

a·(a² - a + 1) + 5·a = a³ - a² + 6·a

Part B

The value of a·(a² - a + 1) + 5·a, for a = -2 is -24

Step-by-step explanation:

Part A

The given function is a·(a² - a + 1) + 5·a

The function is simplified by expanding the product of sums into sums of products, as follows;

a·(a² - a + 1) + 5·a = a × a² - a × a + a × 1 + 5·a = a³ - a² + a + 5·a = a³ - a² + 6·a

The function, a·(a² - a + 1) + 5·a, in simplified format is therefore;

a·(a² - a + 1) + 5·a = a³ - a² + 6·a

Part B

When a = -2, we get;

(a³ - a² + 6·a)[tex]_{a = 2}[/tex] = (-2)³ - (-2)² + 6·(-2) = -8 - 4 - 12 = -24

Answer:

C and D

Step-by-step explanation:

Mathematically, a unit circle is one in which the value of the radius is 1 unit

Generally, for a unit circle we have it that;

r^2 = x^2 + y^2

where (x,y) represents the coordinates of a point on the unit circle

But from above, r = 1

Thus:

x^2 + y^2 = 1

Looking at option C, by squaring each coordinate, we have

(6/7)^2 = 36/49 and the second as 13/49

by adding both, we have

36/49 + 13/49 = 49/49 = 1

Thus, we have this as a coordinate on the unit circle

For the last option;

(5/13)^2 = 25/169 and (12/13)^2 = 144/169

Adding both, we have;

25/169 + 144/169 = 169/169 = 1

So this is also a point on the unit circle

Answer:

The mean of x and y is equal to t.

Step-by-step explanation:

Given that,

The mean of t and t+2 is x.

The mean of t and t-2 is y.

i.e.

[tex]x=\dfrac{t+t+2}{2}\\\\x=(t+1)[/tex]

and

[tex]y=\dfrac{t+t-2}{2}\\\\x=(t-1)[/tex]

The mean of x and y is :

[tex]M=\dfrac{x+y}{2}\\\\M=\dfrac{(t+1)+(t-1)}{2}\\\\M=\dfrac{2t}{2}\\\\M=t[/tex]

Hence, the mean of x and y is equal to t.

Step-by-step explanation:

Let's first rearrange so it's easier to look at: y = 2x +6

To find the perpendicular slope you need to find the negative reciprocal of m so flip and change the sign:

m= -1/2

Next plug in the point (0, -2) into the point-slope equation of a line:

[tex]y2 - y1 = \frac{ - 1}{2} (x2 - x1) \\ [/tex]

y-(-2) = -1/2 (x-0)

y + 2 = -1/2x

y = -1/2x - 2

Therefore the equation is y = -1/2x - 2

Answer:

2X+100 =8X+208

8X-2X=100-208

6X=-108

X=-18

8X+208=(8×-18)+208

=-144+208

=64

ANGLE 3=180-64

=116

Answer: The measurement of angle #3 on the photo you provided it would be a 300 Degree angle if that is what you're asking

Step-by-step explanation: If you're asking what measure of an angle #3 is the correct measurement is 300 Degrees

Answer:

The answer would be the first one.

m = -3n

Step-by-step explanation:

Answer:

m = -3n

Step-by-step explanation:

-6 = (-3)2  True

-12 = (-3)4  True

-18 = (-3)6  True

Answer:

5/8

Step-by-step explanation:

SUM OF RATIOS = 5 + 3 = 8

fraction of blue sweet = blue sweet ratio / sum of ratios = 5/8

Answer:

55° because 2and 6 are corresponding angles (they are equal)

6 and 8 are vertically opposite angles (they are equal)

Step-by-step explanation:

hope this is helpful

Answer: (0, -2) or -2

Step-by-step explanation:

Sub in 0 for x since at the y intercept x is 0

[tex]y=5(0)^2+2(0)-2\\y=5(0)+0-2\\y=0+0-2\\y=-2[/tex]

Step-by-step explanation:

A circle equation is represented by

[tex]x {}^{2} + {y}^{2} = r {}^{2} [/tex]

A circle have both terms to the 2nd. degree

The 1st equation, 2nd equation, 4th equation are circles.

A quadratic is represented by

[tex] {x}^{2} + bx + c[/tex]

A quadratic equation only has one term that is second degree.( meaning if x and y are both to the 2nd degree, it will not be a quadratic, it will be a circle.

The 3rd equation is a quadratic.

The fifth equation has a leading coefficient at the degree of 1 so it is other(linear)

This language derives from the area of a square being its side length multiplied by itself. The word "quadratic" comes from quadratum, the Latin word for square.

f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

From the given table we can get the dy/dx which is the slope (m) ,

Therefore,

dy/dx = (7 - 10 ) / ( 4 - 3 )

dy/dx = -3

Now,

( y - y1 ) = m ( x - x1 )

Putting the value from the table,

( y - 10 )  = -3 ( x -5 )

=> y - 10 = -3x + 15

=> 3x + y = 25

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Answer:

no  its not equal

Answer:

403

Step-by-step explanation:

divide 2.75 and 1,1109 and you will get your answer

Answer:

a) Josh likely made the negative and positive multiplication error.

b) -20a-8+12b

= -4(5a+2-3b)

Step-by-step explanation:

To check if you are correct, you can always simplify it again:

-4(5a+2-3b)

=-20a-8+12b

Remember:

Negative times negative equals to positive, negative times positive equals to negative!

I hope this is helpful! :)

Answer:

x = -3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5-4*x-(17)=0

1.1     Pull out like factors :

  -12 - 4x  =   -4 • (x + 3)

2.1      Solve :    -4   =  0

This equation has no solution.

A a non-zero constant never equals zero. 2.2      Solve  :    x+3 = 0

Subtract  3  from both sides of the equation :

                     x = -3

Answer:

a) The equation for the situation = 14.50 = 4.5 + 1.25n

b) The number of oranges she bought = 8 oranges

Step-by-step explanation:

Where n represents the number of oranges.

The equation is written as

Total charge = $0.75 × 6 + $1.25 × n

$14.50 = $0.75 × 6 + $1.25 × n

14.50 = 4.5 + 1.25n

1.25n = 14.5 - 4.5

1.25n = 10

n = 10 / 1.25

n = 8 oranges

Answer:

paint a is cheaper

Step-by-step explanation:

cost price of 1 liter of paint A = 109,95 / 5L

=21.99

cost price of 1 liter of paint B = 599 / 20L

= 29.95

paint A < paint B

Answer:

area = 15 units ^2

Step-by-step explanation:

you look at width times height (just count the blocks vertical and horizontal)

width = 3 units

height = 5 units

area = 15 units ^2

Answer:

There is a mistake in the question. x results in a decimal answer, which is not possible for number of hoops.

Step-by-step explanation:

Aileen: x

Zulie: 3x

Melody: 4 + x

Zoe: x - 3

Abigail: x - 3

82 = (x) + (3x) + (4+x) + (x-3) + (x-3)

Combine Like Terms

x + 3x + x + x + x = 7x

4 - 3 - 3 = -2

7x - 2 = 82

7x = 80

x results in a decimal answer, which is not possible for number of hoops.

Answer:

4 and 3/4

Step-by-step explanation:

Multiplying 3/4 times 5 days will give you 3.75 hours (or 3 and 3/4ths)

1/2 times 2 days will give you one hour

adding these together will give you 4.75 or 4 and 3/4ths

Answer:

C

Step-by-step explanation:

3/4 * 5 + 1/2 * 2 = 15/4 + 1 = (15+4)/4 = 19/4 = 4.75 = 4 3/4

Answer:

962.5 yd²

Step-by-step explanation:

The formula for a trapezoid is:

(a + b) ÷ 2 x h

Where a & b are the two side lengths and h is height.

Use the formula with the given measurements:

(39.2 + 10.8) ÷ 2 x 38.5 = 962.5

Area is measured in square yards, in this case.

FINAL ANSWER:

The area of the trapezoid is 962.5 yd²

Hope this helps!

-SpaceMarsh

Answer:

1. h(x) = x + 5—> f(x) = x² + 4x - 5, and g(x) = x - 1

2. h(x) = x + 3 —> f(x) = x² - 9, and g(x) = x - 3

3. h(x) = x + 4—> f(x) = x² - 16, and g(x) = x - 4

4.h(x) = x - 1—> f(x) = x² - 4x + 3, and g(x)= x - 3

Step-by-step explanation:

A) f(x) = x² - 9, and g(x) = x - 3

We are told that; h(x) = f(x)/g(x)

f(x) = x² - 9 can be factorized to;

f(x) = (x + 3)(x - 3)

Thus; h(x) = (x + 3)(x - 3)/(x - 3)

(x - 3) will cancel out to give;

h(x) = x + 3

B) f(x) = x² - 4x + 3, and g(x)= x - 3

x² - 4x + 3 can be factorized as;

(x - 1)(x - 3)

Thus; f(x) = (x - 1)(x - 3)

h(x) = (x - 1)(x - 3)/(x - 3)

h(x) = x - 1

C) f(x) = x² + 4x - 5, and g(x) = x - 1

x² + 4x - 5 can be factorized as;

(x - 1)(x + 5)

Thus; f(x) = (x - 1)(x + 5)

h(x) = (x - 1)(x + 5)/(x - 1)

h(x) = x + 5

D) f(x) = x² - 16, and g(x) = x - 4

x² - 16 can be expressed as;

(x + 4)(x - 4)

Thus; f(x) = (x + 4)(x - 4)

h(x) = (x + 4)(x - 4)/(x - 4)

h(x) = x + 4

Answer:

(a^9/8)

Step-by-step explanation:

(a/b)^n = (a^n/b^n)