Solve the equation by graphing.
m^2 = 2m + 8

Answer:

  x = 24.10

Step-by-step explanation:

The given sides of the triangle are the hypotenuse (x) and a side of length 20 that is adjacent to the 34° angle and opposite the 56° angle.

The mnemonic SOH CAH TOA reminds you of relationships between the hypotenuse and adjacent or opposite sides:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

If we want to use the "adjacent" side, we would choose ...

  cos(34°) = 20/x

  x = 20/cos(34°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions

__

If we want to use the "opposite" side, we would choose ...

  sin(56°) = 20/x

  x = 20/sin(56°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions

_____

Comment on rounding

If you round correctly (only at the last step), the proper answer is 24.12.

[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:

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:

1/6

Step-by-step explanation:

5/10(3/3)=15/30

2/6(5/5)=10/30

15/30 - 10/30= 5/30 = 1/6

Answer: 1/6

Step-by-step explanation:

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.

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

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: 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:

55510

Step-by-step explanation:

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:

  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:

  x = 8

Step-by-step explanation:

The 12 on the right is 1/3 the number 36 on the segment above. The value of x will have the same proportion to the segment above it, so will be 1/3 of 24, or 8.

  x = 8

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: 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:

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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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:

1.25.

Step-by-step explanation:

The common ratio r  is 1/5 and the first term a1 = (1/5)^(1-1) = 1.

Sum to infinity =  a1 / (1 - r)

=  1 / (1 - 1/5)

= 1 / 4/5

= 5/4

= 1.25 (answer)

Answer:

Step-by-step explanation:

1.25

Answer:

n = 29

Step-by-step explanation:

We need to find an equation that represents the following statement: "Thirteen less than a number is sixteen" which is the same as: "A number minus thirteen equals sixteen"

In that sense, the equation that represents that statement is: n - 13 = 16

Now, the solution is:  n - 13 = 16 → n = 29

Answer:

n = 29

Step-by-step explanation:

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:

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)

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:

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:

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:

Value of log625^5 is 13.95

Step-by-step explanation:

We need to find the value of log625^5

Using log rule log a^n = nloga

log625^5

= 5log625

=5(2.79)

=13.95

So, value of log625^5 is 13.95

Answer with explanation:

We have to find the value of :

  [tex]\rightarrow\log 625^5\\\\\rightarrow 5 \log625\\\\\rightarrow 5 \log 5^4\\\\\rightarrow 4 \times 5 \log 5\\\\ \rightarrow 20 \log 5\\\\\rightarrow 20 \times 0.69897\\\\ \rightarrow 13.9794\\\\=13.98\\\\ \text{Used following properties of log}\\\\ \log a^b=b \log a[/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:

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:

Answer:

The dimensions are 16 meters by 18 meters

Step-by-step explanation:

P = 2(l+w)

is the formula for the perimeter of a rectangle.

We know the length is 2 more than the width ( consecutive even integers)

l = w+2

P = 2 (w+2+w)

P = 2(2w+2)

68 = 2 (2w+2)

Divide each side by 2

34 = 2w+2

Subtract 2

34-2 = 2w+2-2

32 = 2w

Divide by 2

32/2 = 2w/2

16 =w

l = w+2

l =16+2

l = 18

The dimensions are 16 meters by 18 meters

the width of the rectangle is 16 meters and the length is 18 meters.

To find the length and width of a rectangle when given that the length and width are consecutive even integers and the perimeter is 68 meters, we first need to express the length and width in algebraic terms. Let's call the width 'w' and since the length is the next consecutive even integer, it can be expressed as 'w + 2'. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where 'l' is the length and 'w' is the width. In this case, since width is 'w' and length is 'w + 2', the perimeter formula becomes P = 2(w+2) + 2w.

Let's solve for 'w':
68 = 2(w + 2) + 2w
68 = 2w + 4 + 2w
68 = 4w + 4
64 = 4w
w = 16
Now that we have the width, we can easily find the length:
l = w + 2
l = 16 + 2
l = 18

Therefore, the width of the rectangle is 16 meters and the length is 18 meters.

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

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

-4 and -3

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

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.