Using the graph below, select all statements that are true.

A. f(0.6)=0
B. f(-3.2)=-3
C. f(5.1)=5
D. This is the graph of the greatest integer function.
E. This graph is one-to-one.

Answer:

  1. (-10x -5) -(-7x -4)

  2. (-10x -5) -(-3x -1)

Step-by-step explanation:

The process of simplifying an expression generally involves eliminating parentheses, collecting terms, simplifying fractions, rationalizing denominators, removing appropriate factors from under radicals, and generally putting expressions into general form.

So, to accomplish what the problem is asking, you can create an expression that requires you accomplish as many or as few of these steps as you may like.

In general, you will want to both "do" and "undo" whatever operation(s) you may choose. For example, consider a couple of expressions "a" and "b". For this example, we want our final result to simplify to "a".

If we choose to add "b", we might have ...

  (a+b) -b . . . . . we have both added and subtracted b, so the simplified result is "a"

If we choose to multiply by "b", we might have ...

  (ab)/b . . . . . . we have both multiplied by b and divided by b, so the simplified result is again "a"

_____

We can solve both these problems at once by using ...

If we choose the first approach, we want an expression that is (a+b). That will be ...

  a+b = (-3x -1) +(-7x -4) = -10x -5

By subtracting "b" from this expression, we get "a"--and vice versa. That is ...

_____

Alternate solution to 2

Suppose we choose to multiply instead. Let "b" be -3x+2. Then, using the template for multiplication above, we can write the expression

  (-7x -4)(-3x +2)/(-3x +2) = (21x^2 -2x -8)/(-3x +2)

and we know this rational expression simplifies to -7x -4.

_____

Of course, we can be as elaborate as we might like in modifying the original expression. Whatever we do, we must also include the "undo" so the original expression is recovered when we simplify. To illustrate the point, we can add and subtract 2x from the above rational expression.

  ((21x^2 -2x -8)/(-3x +2) + 2x) - 2x = (21x^2 -2x -8 +2x(-3x +2))/(-3x +2) - 2x

  = (21x^2 -2x -8 -6x^2 +4x)/(-3x +2) -2x

  = (15x^2 +2x -8)/(-3x +2) -2x . . . . . . another alternate solution to #2.

If we're not careful, we can create an expression that is extremely difficult to simplify. The one we have here can be factored to be ...

  (-5x -4)(-3x +2)/(-3x +2) -2x = -5x -4 -2x = -7x -4 . . . our original #2 expression

Knowing that it can be factored is a big help.

Answer:

  1.5

Step-by-step explanation:

The slope is given by ...

  (change in dependent variable)/(change in independent variable)

  = (65 -80)/(74-84) = -15/-10 = 1.5

The slope of the line of best fit is 1.5.

Answer:

The slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is

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

The given two points are (84,80) and (74,65).

The slope of the line of best fit is

[tex]m=\frac{65-80}{74-84}[/tex]

[tex]m=\frac{-15}{-10}[/tex]

[tex]m=1.5[/tex]

Therefore the slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.

Answer:

  No

Step-by-step explanation:

Not all relations have either an infinite domain or an infinite range. Some have no "end behavior". A sine function, for example, continues to oscillate between -1 and +1 forever.

The graphs of some relations are simply a collection of points, so the "end behavior" would be the points at either extreme of the domain.

Answer:

Step-by-step explanation:

Any side to side movement of a function will be reflected inside a set of parenthesis with the x.  For example, if the function was a parabola, the parent graph could be, very simply,

[tex]y=x^2[/tex]

Side to side movement would make the equation look like this:

[tex]y=(x-h)^2[/tex]

where h is the x coordinate of the vertex.

Up or down movment would make the equation look like this:

[tex]y=x^2+k[/tex] for movement upwards, or

[tex]y=x^2-k[/tex] for movement downwards.  The k represents the y coordiante of the vertex in this parabola.

Because our function has NO numbers inside the parenthesis with the f(x), but it has a -1 after, we are moving the parent graph of this function, whatever it is, down one from its starting position.

The transformation from the graph of a function f(x) describes the graph of f(x) - 1 is a vertical shift down by 1 unit

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

The function f(x)

Also, we have

The function f(x) - 1

Subtracting a value from a function means that the function is shifted down

In this case, the subtracted value is 1

This means that f(x) - 1 is a vertical shift down by 1 unit from f(x)

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric sequence:

# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position of the

  number in the sequence

- Ex: U5 = ar^4  ,  U7 = ar^6  ,  U10 = ar^9  ,  U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term  U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

Answer:

B edge

Step-by-step explanation:

[tex]\dfrac{k}{6.4}=8.7\Longrightarrow k=6.4\cdot8.7=\boxed{55.68}[/tex]

Hope this helps.

r3t40

For this case we have the following equation:

[tex]\frac {k} {6.4} = 8.7[/tex]

We must find the value of the variable "k":

Then, we must multiply by 6.4 on both sides of the equation:

[tex]6.4 * \frac {k} {6.4} = 6.4 * 8.7\\k = 55.68[/tex]

Thus, the value of the variable "k" is 55.68.

Answer:

[tex]k = 55.68[/tex]

Option D

Answer:

I think is a for the answer

the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, an expression 2y (x+z) = w

Simplifying the given expression for z

=> 2y (x+z) = w

divide by 2y into both sides

=> x + z = w/2y

subtract by x into both sides

=> z = w/2y - x

=> z = w-2xy /2y

thus,

z = (w- 2xy)/2y

therefore, the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.

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23.

If we take the triangle on the right and put it on the left we have a rectangle, 15 by 11, so area 165.

Answer: 165

24.

Perimeter: 11 + 14 + 11 + 14 = 50

Area: 9 by 14 = 126

Answer:

15092cm^3

Step-by-step explanation:

The total thickness of the strip of metal sheet  would be 2*10=20cm

the new radius of the cylinder would be 9/2+20=24.5cm

Volume of a cylinder: ((pi)r^2)h

the height is 8cm

Volume : (22/7)*24.5^2*8

=15092cm^3

Answer: D) 5832

Step-by-step explanation:

The y values are the x values cubed. Since the x values are increasing by 3, the last x would be 18. 18 cubed is 5832.

Answer:

20 seconds

Step-by-step explanation:

We just need the x-coordinate of the vertex...so find -b/(2a) and we are done:

-b/(2a)=-640/(2*-16)=-640/-32=20

20 second

Answer:

[tex]\boxed{\text{20 s}}[/tex]

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

Your function is

h(t) = -16t²+ 640t

a = -16; b = 640; c = 0

a is negative, so you have a downward-opening parabola.

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

Your parabola opens downward, so the vertex is a maximum.

Calculate h

[tex]h = \dfrac{640}{-2(-16)}} = \dfrac{640}{32} = 20\\\text{The projectile reaches maximum height }\boxed{\textbf{20 s}} \text{after it is thrown}\\[/tex]

The figure below shows the graph of h(t).

Answer:

A 2sqrt(7)

Step-by-step explanation:

Use similar triangles and ratios of lengths of corresponding sides.

2/x = x/14

x^2 = 28

x = 2sqrt(7)

One number to the right of the decimal will mean there are two numbers to the left of the decimal.

When rounding to 50 as the nearest ten the number needs to be between 45 and 54.

Using the 3 numbers shown that would be 48.3

[tex]n,n+1[/tex] - two consecutive integers

[tex]n+n+1=-7\\2n=-8\\n=-4\\n+1=-3[/tex]

-4 and -3

The first attachment is one way that quadrilaterals can be classified. If you've never studied a diagram like this before, it would certainly be mysterious.

There is a little more to it in that a "kite" is not the only kind of quadrilateral with no parallel sides.

Your diagram apparently doesn't recognize the special sorts of trapezoids you might have other than isosceles.

___

The classifications on the first diagram are numbered. The numbers on the second diagram are the way I'd match up the descriptions to the bubbles in your diagram.

Answer:

  20

Step-by-step explanation:

The ratio of rise to run is 5:2, so if the run is 8, the rise is correspondingly 4 times as much:

  rise : run = 5 : 2 = 20 : 8

A similar right triangle would be created by a run of 8 and a rise of 20.

Answer:

20

Step-by-step explanation:

Answer:

(B) -8,4

Step-by-step explanation:

Answer:

(-8,4)

Step-by-step explanation:

Given in the picture is a right triangle and a square sharing one commonside

Area of triangle = area of square

ie [tex]1/2 bs = s^2[/tex] (is s is one side of square)

i.e. b = 2s where b = EA

In other words A divides line EB in the ratio 2:1

Using section formula

Coordinates of A=

[tex](\frac{2(-7)+1(-10)}{3} ,\frac{2(2)+1(-8)}{3})\\=(-8, 4)[/tex]

[tex]2e^x=14\\e^x=7\\x=\ln 7[/tex]

Step-by-step answer:

Between similar figures, if the ratio between the sides is k, then

- ratio between linear measurements, such as diagonals, perimeter, width, heights, etc, are also linear.

Therefore, if the ratio of the corresponding sides is 1:4, the ratio of their perimeters is also 1:4.

Note:

the ratio of area measurements,  or surface areas of similar solids, are proportional to k^2.

Similarly, the ratio of volumes of similar solids are proportional to k^3.

Answer:

See explanation

Step-by-step explanation:

You are given the equality

[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]

where x, y are two positive integers with x>y.

1. x=2,y=1, then

[tex]c=x^2+y^2=2^2+1^2=5\\ \\a=x^2-y^2=2^2-1^2=3\\ \\b=2xy=2\cdot 2\cdot 1=4[/tex]

First Pythagorean triple is (3,4,5)

2. x=3,y=1, then

[tex]c=x^2+y^2=3^2+1^2=10\\ \\a=x^2-y^2=3^2-1^2=8\\ \\b=2xy=2\cdot 3\cdot 1=6[/tex]

Second Pythagorean triple is (6,8,10)

3. x=3,y=2, then

[tex]c=x^2+y^2=3^2+2^2=13\\ \\a=x^2-y^2=3^2-2^2=5\\ \\b=2xy=2\cdot 3\cdot 2=12[/tex]

Third Pythagorean triple is (5,12,13)

4. x=4,y=1, then

[tex]c=x^2+y^2=4^2+1^2=17\\ \\a=x^2-y^2=4^2-1^2=15\\ \\b=2xy=2\cdot 4\cdot 1=8[/tex]

Fourth Pythagorean triple is (8,15,17)

5. x=4,y=2, then

[tex]c=x^2+y^2=4^2+2^2=20\\ \\a=x^2-y^2=4^2-2^2=12\\ \\b=2xy=2\cdot 4\cdot 2=16[/tex]

Fifth Pythagorean triple is (12,16,20)

6. x=4,y=3, then

[tex]c=x^2+y^2=4^2+3^2=25\\ \\a=x^2-y^2=4^2-3^2=7\\ \\b=2xy=2\cdot 4\cdot 3=24[/tex]

Sixth Pythagorean triple is (7,24,25)

7. x=5,y=1, then

[tex]c=x^2+y^2=5^2+1^2=26\\ \\a=x^2-y^2=5^2-1^2=24\\ \\b=2xy=2\cdot 5\cdot 1=10[/tex]

Seventh Pythagorean triple is (10,24,26)

8. x=5,y=2, then

[tex]c=x^2+y^2=5^2+2^2=29\\ \\a=x^2-y^2=5^2-2^2=21\\ \\b=2xy=2\cdot 5\cdot 2=20[/tex]

8th Pythagorean triple is (20,21,29)

9. x=5,y=3, then

[tex]c=x^2+y^2=5^2+3^2=34\\ \\a=x^2-y^2=5^2-3^2=16\\ \\b=2xy=2\cdot 5\cdot 3=30[/tex]

9th Pythagorean triple is (16,30,34)

10. x=5,y=4, then

[tex]c=x^2+y^2=5^2+4^2=41\\ \\a=x^2-y^2=5^2-4^2=9\\ \\b=2xy=2\cdot 5\cdot 4=40[/tex]

10th Pythagorean triple is (9,40,41)

Answer:

2/15

Step-by-step explanation:

There is a 4/10 probability that she chooses blue the first time, but the second time it is a 3/9 chance because she didn't put the marble back so there are 9 marbles in total, 3 blue ones.

4/10 x 3/9 = 2/5 x 1/3 = 2/15

I hope this helps :)

Edit: Messed up the multiplication, whoops!

[tex]|\Omega|=10\cdot9=90\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{90}=\dfrac{2}{15}[/tex]

Answer:

False

Step-by-step explanation:

False, because 3 can not be an even number; it's an odd number.  So the condition cannot be satisfied.

Answer:

Los Angeles

Step-by-step explanation:

Los Angeles has the least variability in temperatures.

To determine which location has the least variability in temperatures, we need to calculate the range or variance of the temperatures for both Miami and Los Angeles.

For Miami:

Temperatures: 76 75 83 73606676 81 83 85 83 87 8080 74

To calculate the range, we subtract the minimum temperature from the maximum temperature:

Range = Maximum temperature - Minimum temperature

Range = 87 - 73

Range = 14

For Los Angeles:

Temperatures: 63 62 65 72 67 | 65 | 6565 69 64 64 61 3639 62

Again, to calculate the range, we subtract the minimum temperature from the maximum temperature:

Range = Maximum temperature - Minimum temperature

Range = 72 - 61

Range = 11

Comparing the ranges, we see that Miami has a range of 14, while Los Angeles has a range of 11. Therefore, Los Angeles has the least variability in temperatures.

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Answer:

  d.  1/4

Step-by-step explanation:

The common ratio will be the ratio of any two adjacent terms:

  (3/12)/(3/3) = (1/4)/1 = 1/4

Answer:

d

Step-by-step explanation:

If the sequence is geometric then a common ratio r will exist between consecutive terms.

[tex]\frac{3}{12}[/tex] ÷ 1 = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{48}[/tex] ÷ [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{192}[/tex]  ÷ [tex]\frac{3}{48}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{768}[/tex] ÷ [tex]\frac{3}{192}[/tex] = [tex]\frac{1}{4}[/tex]

A common ratio of r = [tex]\frac{1}{4}[/tex]

Hence sequence is geometric

Answer:

  A)  -12

Step-by-step explanation:

The point of intersection on the graph is (-6, -6). That is the solution to the system of equations. The sum of the solution values is ...

  (-6) +(-6) = -12

Answer:

A

Step-by-step explanation:

The solution to the system of equations is at the point of intersection of the 2 lines, that is

(- 6, - 6) ⇒ A = B = - 6, thus

A + B = - 6 + (- 6) = - 6 - 6 = - 12 → A

Answer:

[tex](f+g)(x)=6x^2+13x+14[/tex]

Step-by-step explanation:

(f+g)(x) simply means that you are adding f(x) to g(x) to get a new equation that is the sum of them.

[tex]6x^2+9x+8+4x+6[/tex]

simplifies down to, by combining like terms,

[tex]6x^2+13x+14[/tex]

Answer:

2x

Step-by-step explanation:

Solve the equation for a as follows:

First multiply both sides by 2a:

[tex](2a)x=-b[/tex] and then divide both sides by 2x:

[tex]a=-\frac{b}{2x}[/tex]

The denominator will be equal to 2x.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Given that:-

The value of the denominator will be:-

x    =   -b/2a

From the given information the expression will be written as

a  =  -b / 2x

Therefore the denominator will be equal to 2x.

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Answer:

55510

Step-by-step explanation:

Answer: Option A

[tex]h(x) = -0.01 (x-150) (x + 4)[/tex]

Step-by-step explanation:

The javelin will have reached its maximum horizontal distance when it touches the ground.

Then the maximum horizontal distance occurs when the height h (x) is equal to zero.

So we must equal h(x) to zero and solve the equation for x.

Therefore the form that is most useful to determine the horizontal distance that the javelin covers is the one that is factored. Because it allows us to find the zeros of the quadratic function more easily

[tex]h(x) = -0.01 (x-150) (x + 4) = 0[/tex]

[tex]-0.01 (x-150) (x + 4) = 0[/tex]

The equation is equal to zero when [tex]x = 150[/tex] or when [tex]x = -4[/tex]

Therefore the solution is [tex]x = 150[/tex].

The horizontal distance that covers the javelin is 150 feet

Answer:

The answer is A

Step-by-step explanation:

I am 100% sure cuz I just did the test:)

Answer:

I believe you mean what square number that is less than 100 has the most factors.  

The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.  

1 obviously only factors to 1*1.

4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1*n or p*p. example: 1*4, 2*2 .We can eliminate those.  

16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1*n, (p^3)*p, or (p^2*p^2). Example: 1*16, 8*2, or 4*4.

But 36 is 2*2*3*3 as it’s prime factoring. This allows us to find more combinations of factors: 1*36, 2*18, 4*9, 12*3, or 6*6.

Final answer:

The largest even square number smaller than 100 is 64, which is the square of 8.

Explanation:

To find an even square number smaller than 100, we can look at the squares of the even numbers less than 10, since 10² (which is 10 times 10) equals 100. Squaring each even number from 2 to 8, we get the following even square numbers: 2²=4, 4²=16, 6²=36, and 8²=64. Among these, 64 is the largest even square number that is less than 100.