factorize completely -3c²-4cb+4b²​

Answer:

1

Step-by-step explanation:

f(x) = x² + 3x

g(x) = 5x + 2

f(3) = 3² + 3 x 3

f(3) = 9 + 9

f(3) = 18

g(3) = 5(3) + 2

g(3) = 15 + 2

g(3) = 17

(f - g)(3) = 18 - 17

(f - g)(3) = 1.

Answer:

Sean's rocket lands 3 seconds after Kiara's rocket.

Step-by-step explanation:

Kiara:  f(t)= -16t² + 80t

Sean:  h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time.  We need to be suspicious of Sean's rocket launch.  His equation for height has "+64" at the end, whereas Kiara's has no such term.  The +64 is the starting height iof Sean's rocket.  So Kiara has a 64 foot disadvantage from the start.  But if it is a race to the ground, then the 64 feet may be a disadvantage.  [Turn the rocket upside down, in that case.  :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground).  So we can set both equation to 0 and calculate t:

Kiara:  f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring.  I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5.  Kiara's rocket lands in 5 seconds.

Sean:  h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds.  Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

To learn more about independent populations from the given link

https://brainly.com/question/23989150

#SPJ4

Using compound interest, the rates per compounding period are given as follows:

a) 0.1273 = 12.73%.

b) 0.0833 = 8.33%

c) 0.0617 = 6.17%

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The interest rate per compounding period is given as follows:

[tex]\left(1 + \frac{r}{n}\right)^n - 1[/tex]

For item a, the parameters are:

r = 0.12, n = 52.

Hence:

[tex]\left(1 + \frac{0.12}{52}\right)^{52} - 1 = 0.1273[/tex]

For item b, the parameters are:

r = 0.08, n = 104.

Hence:

[tex]\left(1 + \frac{0.08}{104}\right)^{104} - 1 = 0.0833[/tex]

For item c, the parameters are:

r = 0.06, n = 12.

Hence:

[tex]\left(1 + \frac{0.06}{12}\right)^{12} - 1 = 0.0617[/tex]

More can be learned about compound interest at https://brainly.com/question/25781328

#SPJ1

Answer:

x = 35.

Step-by-step explanation:

since they are odd, the second number isn't x + 1, it is x + 2.

x + x + 2 = 72

2x + 2 = 72

2x = 70

x = 35

Answer:

Given:

Mass of the tennis ball=56.5 g

wavelength=5400 Angstroms

De-Broglie Wavelength = 5400 Angstrom.

= 5400 × 10⁻¹⁰ m.

Now, Using the Formula,

λ = h/mv

here,

h is the Planck's constant = 6.62 × 10⁻³⁴ J-s.

and v is the velocity of the tennis balls.

∴ 5400 × 10⁻¹⁰ = (6.62 × 10⁻³⁴)/ (0.054 × v)

⇒ 0.054v = (6.62 × 10⁻³⁴)/ (5400 × 10⁻¹⁰)

⇒ 0.054v = 0.0012 × 10⁻²⁴

⇒ v = 0.0012 × 10⁻²⁴/0.054

⇒ v = 0.023 × 10⁻²⁴ m/s.

Hence, the velocity of the tennis balls is 0.023 × 10⁻²⁴ m/s.

Learn more about average velocity here:

https://brainly.com/question/13372043

#SPJ4

Answer:

The exact amount of time would be 8 2/9 weeks, but if we are only counting full weeks, it would be finished in 9 weeks.

Step-by-step explanation:

y = xm

18 1/2 = 2 1/4x  Change both numbers into improper fractions

18 1/2 would be 37/2  The denominator (bottom number) stays 2.  To get the top number you would (2 x 18) + 1 or 37.  That makes 37/2 equivalent to 18 1/2.

Now do the same thing to 2 1/4.  The bottom number stays the same.  We get the top number (4 x 2) + 1 or 9.  That makes 9/4 equivalent to 2 1/4.

We know have

37/2 = 9/4 x  We can solve for x by multiplying both sides of the equation by 4/9

37/2(4/9) = (9/4)(4/9)x

148/18 = x  If we divide both the top and the bottom by 2 we would get 74/9 = x  If we divide 74 by 9 we get 8 2/9

The number of terms in the geometric series is 9

The geometric series given as:

96 - 48 + 24 -....,-3/8 .

Calculate the common ratio (r) as follows

r = T2/T1

Substitute the known values in the above equation

r = -48/96

Evaluate

r = -0.5

The number of terms is then calculated as:

Tn = a * r^n-1

Let n = 9

So, we have:

T9 = a * r^9

Substitute the known values in the above equation

T9 = 96 * (-0.5)^8

Evaluate the product

T9 = -3/8

Hence, the number of terms in the geometric series is 9

Read more about geometric series at

https://brainly.com/question/24643676

#SPJ1

Answer:

Graph B

Step-by-step explanation:

Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = -12

2y = 3x + 12

y = 3/2x + 6

Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.

Answer:

First:

5x + 9 < 2

x= 9/5= 1,8 < 2

Second:

x + 6 < 12

x= 12/6= 2 < 12

Answer:

See below

Step-by-step explanation:

An area of  2km  x  2km = 4 km^2    

1 km = .62137 miles

2 (.62137)      x      2  (.62137)    =   1.5444 mi^2

Answer:

(-4,0) , (0,9)

Step-by-step explanation:

x-intercept is the point where the line touches the x-axis, which means, y = 0.

So when y = 0,

-9x + 4(0) = 36

-9x = 36

x = [tex]\frac{36}{-9}[/tex]

x = -4

Therefore, the coordinates of the x - intercept is (-4,0)

y-intercept is the point where the line touches the y-axis, which means , x = 0.

so when x = 0,

-9(0) + 4y = 36

4y = 36

y = [tex]\frac{36}{4}[/tex]

y = 9

Therefore, the coordinates of the y - intercept is (0,9)

Answer:

x - intercept (-4,0)

y -intercept (0,9)

Step-by-step explanation:

Put in 0 for x.

-9(0) + 4y = 36

4y = 36  Divide both sides by 4

y = 9

(0,9) This is where the line will cross the y axis.

Put in 0 for y

-9y + 4(0) = 36

-9y = 36 Divide both sides by -9

Y = -4

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-2)})\implies y+5=6(x+2)[/tex]

Answer:

Associative property of addition.

Step-by-step explanation:

The location of the parentheses makes no difference to the sum of these numbers.

The property shown in the statement "(46 + 17) + 3 = 46 + (17 + 3)" is the associative property of addition.

The associative property of addition states that when adding three or more numbers, the grouping of the numbers does not affect the sum

In the given statement, we have three numbers being added: 46, 17, and 3. The statement shows that the addition is grouped differently on each side of the equation, but the result is the same.

On the left side, we have (46 + 17) + 3.

This means we first add 46 and 17, which equals 63. Then we add 3 to the sum, resulting in 66.

On the right side, we have 46 + (17 + 3). Here, we first add 17 and 3, which equals 20. Then we add 46 to the sum, also resulting in 66.

As we can see, no matter how we group the numbers being added, the final sum is the same. This demonstrates the associative property of addition.

Therefore, the property shown in the given statement is the associative property of addition.

To learn more about addition from given link

brainly.com/question/25421984

#SPJ3

I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.

Hope this helps!

The statement that justifies the relationship is: D. it represents a function because no length has more than one price.

For a relation to be considered a function, any of the following criteria must be met:

In the scenario given:

Length of ribbon = input (x-value)

Price of ribbon = output (y-value).

We can observe that each length of ribbon (input) has its own price (output), therefore, we can conclude that the price of ribbon is a function of the length of the ribbon.

The answer is: D. This relationship represents a function because no length has more than one price.

Learn more about functions on:

https://brainly.com/question/17043948

#SPJ1

Answer:

4/10

Step-by-step explanation:

Let the numerator be 2x and the denominator is 5x. The denominator is 6 more than the numerator so if we add 6 to the numerator both numbers should be equal.

Solve:

2x+6 = 5x

6 = 3x

x = 2

2x = 4

5x = 10

Step-by-step explanation:

Let the numerator be 2x and denominator be 5x,

A.T.Q,

2x+6 = 5x

2x-5x = -6

-3x = -6

3x = 6

x = 2

So, the fraction is 4/10 = 2/5

The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.

Generally, the equation for is zeros  mathematically given as

y=x^4−2x^3−11x^2+12x+36

Therefore

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

x=-2

x=3

since the graph attached has a positive leading coefficient and a positive degree

In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

Read more about graph

https://brainly.com/question/16608196

#SPJ1

Answer:

[tex]x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]

A quadratic can generally be expressed as: [tex]y=ax^2+bx+c[/tex]

So using the equation you gave: [tex]0=x^2-5x-1[/tex]

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

[tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

Answer:

15?

Step-by-step explanation:

2×15=30 i am not fully sure but this should be it

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

To know more about normal distribution........

https://brainly.com/question/4079902

#SPJ4

Answer: [tex]\Large\boxed{2}[/tex]

Concept:

Here, we need to know the idea of the PEMDAS method.

PEMDAS is an acronym for the order of operations.

Solve:

Given expression

[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]

Simplify the exponents

[tex]=\dfrac{27~-~13}{11~-~4}[/tex]

Simplify by subtraction

[tex]=\dfrac{14}{7}[/tex]

Simplify the fraction

[tex]\Large\boxed{=2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4/5 of the students would have protractors.

Step-by-step explanation:

Concluding, there are (2 + 12) boxes of pencils left.

We know that Ms. Bloom had (4 + 7/12) boxes of pencils, and we also know that (2 + 1/12) of the boxes were broken.

The number of boxes of pencils left is given by the difference between the two above numbers, then we get:

N = (4 + 7/12) - (2 + 1/12) = (4 - 2) + (7/12 - 1/12) = 2 + 6/12

Now we can simplify the fraction:

N = 2 + 1/2

Concluding, there are (2 + 12) boxes of pencils left.

If you want to learn more about subtractions:

https://brainly.com/question/25421984

#SPJ1

Answer: (-1, 1)

Step-by-step explanation:

Since the graph is already given, we could directly refer to the intersecting point of the system of equations.

According to the graph, [ y = 2x + 3 ] and [ y = -x ] intersect at (-1, 1).

Therefore the solution is [tex]\Large\boxed{(-1,1)}[/tex]

Given equation

1) y = 2x + 3

2) y = -x

Substitute the y value in the 1) equation by the 2)

(-x) = 2x + 3

Add x on both sides

-x + x = 2x + 3 + x

0 = 3x + 3

Subtract 3 on both sides

0 - 3 = 3x + 3 - 3

-3 = 3x

Divide 3 on both sides

-3 / 3 = 3x / 3

x = -1

Substitute the x value into one of the equations to find the y value

y = -x

y = - (-1)

y = 1

Therefore, the solution is [tex]\Large\boxed{(-1,1)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The slope between these two points is m=-4.

Step-by-step explanation:

Greetings !

[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]

The true statements are:

The independent variable is the variable that determines the value of the dependent variable. There is a positive relationship between the number of people at the picnic and the total cost. This is because it can be seen as the number of people at the picnic increases, the total cost changes.

Rate of change = total cost / number of people

$52 / 6 = $8.67

To learn more about independent variables, please check: https://brainly.com/question/26287880

#SPJ1

Answer:

A, B, D

Step-by-step explanation:

right on edge

Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). For function composition h(x) =  f(g(x)), the value of a exist -4.

Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the outcome of one function into the other one.

Here, h(x) = f(g(x))

which means, h(x) = f(x³+ a)

[tex]$h(x) = \sqrt{x^3+a+2}[/tex]

[tex]$\sqrt{x^3-2} = \sqrt{x^3+a+2}[/tex]

To estimate the value of a, we separate equal terms:

1) Both are squared, so we can "eliminate" the square;

2) x³ = x³

3) -2 = a+2

a = -4

For function composition h(x) =  f(g(x)), the value of a exist -4.

To learn more about function composition refer to:

https://brainly.com/question/17299449

#SPJ4