3x2+14x=−11 solve for x

Answer:

BC is 22.5 mi

Step-by-step explanation:

Using the pythagorean theorem formula. c² = a² + b²

BC² = AB² + AC²

BC² = 19² + 12²

BC² = 361 + 144

BC² = 505

√BC² = √505

BC = 22.5

Therefore BC is 22.5 mi

x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).

Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.

The given expression is x² + 12.

We have the identity (a + b) (a - b) = a² - b²

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²

                                = x² - (2² × √3² × i²)

We know that i² = -1, where i is the imaginary number in complex numbers

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)

                                = x² + 12

Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.

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Answer:

Step-by-step explanation:

the numerator goes in side of the radical

Answer:

5/17

Step-by-step explanation:

If we do the multiplication first, we get:

[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]

If we do the division next, we get:

[tex]\frac{4+1}{13+4} = 5/17[/tex]

It is not okay to conduct the simulation because people generally favor some numbers.

From the information given, the student wants to simulate 37 birthdays, but she does not have a calculator or software program available.

In this case, it's not okay to conduct the simulation because people generally favor some numbers.

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Answer:

$12.

Step-by-step explanation:

1) if price of one doll is 'x', of one dress is 'y', then the condition 'buys one doll and one dress, it will cost her $21.00' can be written as x+y=21;

2) the condition 'buys two dolls and three dresses, it will cost her $51.00' can be written as 2x+3y=51;

3) it is possible to make up the system:

[tex]\left \{ {{x+y=21} \atop {2x+3y=51}} \right. \ = > \ \left \{ {{x=12} \atop {y=9}} \right.[/tex]

4) the price of one doll is 12$.

Answer: 2 3/4 > 2.68 is correct (only)

Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68

The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.

Sqrt(63) = 7.93, and 7.93 > 8.11 is false.

Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2

Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

Answer:

x² + 4x + 3

---------------

       2

---- => fraction line

Answer:

B

Step-by-step explanation:

when x is 0 y=4(0)+12 y=12

y is 0 y=4(-3) +12 = 12=12

Answer:

f'(1)=-1

Step-by-step explanation:

You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.

I used the limit definition of the derivative to find the slope in the picture attached

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

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Rewriting the equation of the given line in slope-intercept form,

[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]

The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.

Substituting into point-slope form,

[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]

Answer:

C. 4x²√(3x)

Step-by-step explanation:

if x > 0

[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]

          [tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]

          [tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]

          [tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]

          [tex]=4\times x^{2}\times \sqrt{3x}[/tex]

Answer:

u should add 118/9

Step-by-step explanation:

please mark me as brainlest

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions

Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

Answer:

[tex] {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{5} }{ \sqrt[4]{5} } = {5}^{ \frac{1}{3} } \div {5}^{ \frac{1}{4} } = {5}^{ \frac{4}{12} } \div {5}^{ \frac{3}{12} } = {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

THIS IS THE ANSWER: 5 to the power of one-twelfth (Take a look at the image if this does not make sense) :))

:))

:)))   HAPPY SLAPPY!!!!

:))))

"UPDATE" : This was correct on my test. Also I realized to see the image in this answer keep your cursor on the side of your screen, not on the image :D

Step-by-step explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]

Set these equations equal to zero

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

[tex]x = 2[/tex]

[tex] {x}^{2} - 2x + 4 = 0[/tex]

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

[tex]1 + i \sqrt{ 3 } [/tex]

and

[tex]1 - i \sqrt{3} [/tex]

Answer:

A.

Step-by-step explanation:

The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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The equation for the red graph is f(x) = -x².

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

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According to the FIFO method, the ending inventory balance for Commodity Z is $1,405

FIFO means that earlier inventory is sold first and later inventory would be the last goods left.

Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:

= (16 x 62) + (7 x 59)

= 992 + 413

= $1,405

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Answer: 54%

Step-by-step explanation:

You will need to divide these numbers.

[tex]6/11=0.54[/tex]

After you divide that, simplify that to a percentage by multiplying it by 100.

[tex]0.54 *100=54%[/tex]%

I hope this helps!!

Answer:

y = 1, 9.

Step-by-step explanation:

They are the y values of the points of intersection of the 2 parabolas.

y = 1, 9.