complete the square in vertex form y=x^2+18x-2​

ANSWER

18. No extraneous solution.

19. The extraneous solution is x=-2

EXPLANATION

18. The given radical equation is:

[tex] \sqrt{3x - 2} = x[/tex]

Solving this radical equation yields

[tex]x=1,x=2[/tex]

We check for an extraneous solution by substituting each value into the equation.

Checking for x=1,

[tex] \sqrt{3 \times 1 - 2} = 1[/tex]

[tex]\sqrt{3- 2} = 1[/tex]

[tex]\sqrt{1} = 1[/tex]

[tex]1 = 1[/tex]

This is true.

Checking for x=2

[tex]\sqrt{3 \times 2- 2} = 2[/tex]

[tex]\sqrt{6- 2} = 2[/tex]

[tex]\sqrt{4} = 2[/tex]

[tex]2 = 2[/tex]

This is also true. Hence there is no extraneous solution.

19. The given radical equation is:

[tex] \sqrt{x + 6} = x[/tex]

Solving this equation yields,

[tex]x=3,x=-2[/tex]

Checking for x=3,.

[tex]\sqrt{3+ 6} = 3[/tex]

[tex] \sqrt{9} = 3[/tex]

3=3.

This is a true solution.

Checking for x=-2.

[tex]\sqrt{ - 2 + 6} = - 2[/tex]

[tex] \sqrt{4} = - 2[/tex]

[tex]2 \ne - 2[/tex]

Hence x=-2 is an extraneous solution.

Answer:

25%

Step-by-step explanation:

Percentages are one of several ways of describing quantities' relationships to one another. Specifying one number as a percentage of another means specifying the fraction of the second quantity the first comprises. The percentage value is the number that, divided by 100, equals that fraction. To express the percentage as a whole number, round it accordingly. Some applications, however, don't require percentages as exact whole figures.

Divide the first number the second. For instance, if you want to find what percentage 43 is out of 57, divide 43 by 57 to get 0.754386.

Answer: 20

Step-by-step explanation:

The area= 25

The square root of 25=5

So we know that 2 sides are 5

5×4=20

Multiply 5 by 4 because squares have all sides of the same length, so the remaining 2 sides are 5.

The definition of a number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Answer: [tex]y=-\frac{1}{2}x+6[/tex]

Step-by-step explanation:

The equation of the line is slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b thte y-intercept.

The lines are parallel, then they have the same slope.

Solve for "y"  from  [tex]2x+4y=10[/tex] to find the slopes of the lines :

[tex]2x+4y=10\\4y=-2x+10\\y=-\frac{1}{2}x+\frac{5}{2}[/tex]

The  value of the slopes of the lines is:

[tex]m=-\frac{1}{2}[/tex]

Substitute the slope and the point into the equation of the line and solve for "b":

[tex]2=-\frac{1}{2}(8)+b\\2=-4+b\\b=6[/tex]

Then the equation of this line is:

[tex]y=-\frac{1}{2}x+6[/tex]

The answer is:

The equation of the new line will be:

[tex]y=-0.5x+6[/tex]

or

[tex]y=-\frac{1}{2}x+6[/tex]

To solve the problem, we need to remember the slope intercept form of a line.

The slope intercept form of a line is given by the following equation:

[tex]y=mx+b[/tex]

Where,

y, is the function.

x, is the variable of the function.

m, is the pendant of the line.

b, is the y-axis intercept of the line.

So, we are given the line that will be parallel to the line that we are looking for:

[tex]2x+4y=10\\4y=-2x+10\\4y=-2(x-5)\\y=\frac{-2}{4}*(x-5)\\\\y=-\frac{1}{2}*(x-5)\\\\y=-\frac{1}{2}x+\frac{5}{2}[/tex]

Where,

[tex]m=-\frac{1}{2}[/tex]

Then,

We need to use the same slope to guarantee that the new line will be parallalel to the given line-

So, our new line will have the following form:

[tex]y=-\frac{1}{2}x+b[/tex]

We need to substitute the given point to isolate "b" in order to guarantee that the line will pass through.

Now, substituting the given point,  to calculate"b", we have:

Calculating b, we have:

[tex]2=-\frac{1}{2}8+b[/tex]

[tex]2=-4+b[/tex]

[tex]2+4=b[/tex]

[tex]6=b[/tex]

Hence, we have that the equation of the new line will be:

[tex]y=-0.5x+6[/tex]

or

[tex]y=-\frac{1}{2}x+6[/tex]

Proving that the line will pass through the given point, by substituting it into its equation, we have:

[tex]2=-0.5(8)+6[/tex]

[tex]2=-4+6[/tex]

[tex]2=2[/tex]

So, since the equality is satisfied, we know that the line pass through the new line.

Have a nice day!

Answer:

Step-by-step explanation:

(5) x^2 + 16 is a perfect square binomial only if imaginary roots are allowed.

x^2 + 16 = (x + 4i)(x - 4i)

(6)  x^4 + 12x^2 + 36 is a perfect square trinomial.  

The square root of x^4 is x^2 and the square root of 36 is 6.

Experimenting, we find that  x^4 + 12x^2 + 36 = (x² + 6)²

so we can conclude that x^4 + 12x^2 + 36 = (x² + 6)(x² + 6) = (x² + 6)².

Answer:

answer in the image attached above

Step-by-step explanation:

Hope it helps

Answer: 314÷13

..............................................................................

Answer:

13/314

Step-by-step explanation:

3, because 12/4=3. And 12:4 is equal to 3:1 or 3.

Answer:

For every 1 cup of sugar there needs to be 3 cups of flour

Step-by-step explanation:

You add 3 more cups of flour for every one cup of sugar you add.

1 cup of sugar = 3 cups of flour

2 cups of sugar = 6 cups of flour

3 cups of sugar = 9 cups of flour

4 cups of sugar = 12 cups of flour

5 cups of sugar = 15 cups of flour

And so forth.

Hope this help you!

The quadratic formula is [tex]\frac{-b+-\sqrt[2]{b^2-4ac}}{2a}[/tex]

and in the equation ax^2+bx+c=0

so now all you have to do is substitute the numbers into the quadratic formula

Answer:

818.4 in²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of circle - ( area of white sector + area of triangle )

  = ( π × 27.8²) - (π × 27.8² × [tex]\frac{210}{360}[/tex] +(0.5 × 27.8 ×27.8 × sin150°)

  = 2427.95 - (1416.30 + 193.21 )

  = 2427.95 - 1609.51 ≈ 818.4 in²

Step-by-step explanation:

[tex]\sqrt{m^6}=\sqrt{m^{3\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\=|m^3|\\\\\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3[/tex]

Answer:

20 disparos

Step-by-step explanation:

Primera etapa es de determinar cuantos tiros de Camilo acertaron al blanco.

Sabemos que en su última práctica, obtuvo 99 puntos con una mezcla de 5, 8 y 10 puntos.  Eso puedo se exprimir así:

5x + 8y + 10x = 99

Sabemos también que el obtuvo tantos tiros de 8 puntos que de 10 puntos, entonces

y = z

Podemos mezclar las 2 ecuaciones y substituir y por z:

5x + 8y + 10y = 99

5x +18y = 99

Una ecuación, dos variables... no es fácil... pero son números pequeños y se puede intentar soluciones.  Entonces, cuantas veces podemos multiplicar 5 y 18 para obtener 99?

El más simple es de hacer la tabla de multiplicación de 18 y ver cual número nos deja con un multiple de 5.

18 x 1 = 18 (99 - 18 = 81, no un multiple e 5)

18 x 2 = 36 (99 - 36 = 63, no un multiple de 5)

18 x 3 = 54 (99 - 54 = 45, SI, un multiple de 5)

18 x 4 = 72 (99 - 72 = 27, no un multiple de 5)

18 x 5 = 90 (99 - 90 = 9, no un multiple de 5)

Entonces, sabemos que y = 3 y z = 3

5x + 18 (3) = 99

5x + 54 = 99

5x = 45

x = 9

El tiró 9 veces por 5 puntos, 3 veces por 8 puntos y 3 veces pour 10 puntos.

En total tiró 15 veces.

Si acertó 75% (3/4) de las veces, cuantos tiros total?

[tex]\frac{15}{3/4} = \frac{15 * 4}{3} = 20[/tex]

Camilo tiró 20 veces en total.

Answer:

29119.66666...+14561.3333...=43681, 209ft^2, not square feet.

Step-by-step explanation:

"One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared"

Ok, so this is a tricky one- 209 feet squared, not 209 square feet, therefore the area is 209^2, or 43,681.

Next, let's define our variables-

x= the "other side"

z= 3 feet shorter than twice side

We can now make these (useful) equations

z=2x-3

43681= (2x-3)+x

We will focus on the latter for now-

Simplify

43681= (2x-3)+x

43681= 2x-3+x

43681= 3x-3

+3

43684=3x

/3

14561.3333...=x

z=2x-3

z=2*(14561.3333)-3

z=29119.66666....

29119.66666...+14561.3333...=43681

Answer:

Area of new patio = 65 ft^2.

Step-by-step explanation:

For the new patio:

Width = x-4 feet

Length = x+4 feet.

Given that x = 9, the new patio has dimensions 9-4 and 9+4 = 5 by 13 feet and its area = 5*13 =  65 ft^2.

The area of the new square brick patio is 65 ft².

Given that, the original patio measures 9 feet by 9 feet.

The formula to find the area of a square is a².

Where, a=side.

Now, for the new patio:

Width = x-4 feet and Length = x+4 feet.

Given that x = 9, the new patio has dimensions 9-4=5 and 9+4 = 13 feet and its area = 5*13 =  65 ft².

Therefore, the area of the new patio is 65 ft².

To learn more about the area of a square visit:

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Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

leg² + leg² = hypotenuse²

We have

leg = 40in

hypotenuse = 41in

Let other leg = x.

Substitute:

x² + 40² = 41²

x² + 1600 = 1681           subtract 1600 from both sides

x² = 81 → x = √81

x = 9in

Answer:

C log (20) - log (3)

Step-by-step explanation:

log (a/b) = log (a) - log (b)

log (20/3) = log (20) - log (3)

Answer: C. log (20) - log (3)

Step-by-step explanation: a p e x /\ dude above me is right too

Answer:

-0.6

Step-by-step explanation:

we know that

The correlation coefficient is a measure of the strength of the straight-line or linear relationship between two variables. Correlation coefficients are expressed as values between +1 and -1

we have

(1,8),(2,3),(3,0),(4,1),(5,2),(6,1)

using a Excel tool (CORREL function)

see the attached table

The correlation coefficient is -0.68

Answer:

X Values

∑ = 21

Mean = 3.5

∑(X - Mx)2 = SSx = 17.5

Y Values

∑ = 15

Mean = 2.5

∑(Y - My)2 = SSy = 41.5

X and Y Combined

N = 6

∑(X - Mx)(Y - My) = -18.5

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -18.5 / √((17.5)(41.5)) = -0.6865

Meta Numerics (cross-check)

r = -0.6865

Answer:

Step-by-step explanation:

Put x = -4 to f(x) = 2x² - x + 9:

f(-4) = 2(-4)² - (-4) + 9 = 2(16) + 4 + 9 = 32 + 4 + 9 = 45

Answer:

1336 phones

Step-by-step explanation:

The average battery life of 2800 manufactured cell phones has a normal distribution.

The mean battery life is 14 hours, therefore: μ = 14 hours.

The standard deviation is 0.5 hours, therefore: σ = 0.5 hours.

To find the number of phones who have a battery life in the 13 to 14 range, we're going to ask for the help of a calculator. The probability of finding phones who have a battery life in the 13 to 14 range is: 0.4772. (See attached picture)

Therefore, the number of phones who have a battery life in the 13 to 14 range is: 0.4772×2800 = 1336,16 ≈ 1336 phones.

Final answer:

To find the number of phones with a battery life between 13 and 14 hours, calculate the z-scores, find the corresponding percentage using the standard normal distribution, and then multiply by the total number of phones, resulting in approximately 1336 phones.

Explanation:

The question asks for the number of cell phones with a battery life in the 13 to 14 hour range out of 2800 phones where the mean battery life is 14 hours with a standard deviation of 0.5 hours. The battery life is normally distributed.

To find this number, we need to calculate the z-scores for 13 and 14 hours and then determine the percentage of phones between those z-scores. The z-score for 13 hours is (13 - 14)/0.5 = -2 and for 14 hours is (14 - 14)/0.5 = 0. Using the standard normal distribution table, the area under the curve from -2 to 0 is approximately 47.7%. Therefore, the number of phones with battery life between 13 and 14 hours is 0.477 * 2800 ≈ 1336 phones.

ANSWER

A.

[tex] \frac{1}{64} [/tex]

EXPLANATION

The given expression is:

[tex] {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } [/tex]

Recall that:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

We apply this property to obtain:

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - \frac{11}{3} - - \frac{2}{3} } [/tex]

Collect LCM

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 11 + 3}{3}} [/tex]

Simplify;

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 9}{3}} [/tex]

.

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - 3} [/tex]

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{ {4}^{3} } [/tex]

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{64} [/tex]

The first choice is correct

Answer:

A rotation is when a shape rotates across the x or y axis on a coordinate plane :)

Step-by-step explanation:

Answer:

(4, - 2 )

Step-by-step explanation:

To find the x- coordinate substitute y = - 2 into the equation

y + 2 = - 3(x - 4), thus

- 2 + 2 = - 3x + 12

0 = - 3x + 12 ( subtract 12 from both sides )

- 12 = - 3x ( divide both sides by - 3)

4 = x

Answer:

75

Step-by-step explanation:

Square both sides. 225=3x^2

divide both sides by 3

x^2=75

x=√75= 5√3

[tex]15 = x \sqrt{3} \\ \\ 1. \: 15 = \sqrt{3x} \\ 2. \: \frac{15}{ \sqrt{3} } = x \\ 3. \: x = \frac{15}{ \sqrt{3} } [/tex]

Answer:

C

Step-by-step explanation:

Arc length is:

s = 2πr (θ/360)

Given θ = 80° and r = 7 ft:

s = 2π (7 ft) (80 / 360)

s = 1120π/360

s = 28π/9

Answer is C.

Answer: y= 4/3x-9

Step-by-step explanation:

The equation 8x - 6y = 54 can be converted to slope-intercept form (y = mx + b) by isolating y. The steps involve rearranging terms and simplifying to yield the equation: y = (4/3)x - 9.

First, you want to manipulate your equation: 8x - 6y = 54 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Here are the steps:

Therefore, the equation 8x - 6y = 54 in slope intercept form is y = (4/3)x - 9.

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Answer:

15

Step-by-step explanation:

Answer:

y = -5

Step-by-step explanation:

You are solving for y. You want to know which value of y makes the equation true. You must end up with y alone on the left side equaling a number.

12y + 25 = -35

First, subtract 25 from both sides.

12y + 25 - 25 = -35 - 25

12y = -60

Now divide both sides by 12.

12y/12 = -60/12

y = -5

Answer: y = -5

Answer:

y - 3 = a(x + 1)^2

Step-by-step explanation:

The vertex equation of a vertical parabola is:

y - k = a(x - h)^2.

If the vertex is at (-1, 3), then the equation becomes:

y - 3 = a(x + 1)^2, where a is a constant.

Next time, would you please share the answer choices.  Thank you.

Answer:

Step-by-step explanation:

all parabola have equation : y = a(x +1)²+3   a in R

Answer:

Bruh its D.

Step-by-step explanation:

D has the exact same values as the original matrix.

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}-6&-6.5&1.7\\2&-8.5&19.3\end{array}\right]}[/tex]

Step-by-step explanation:

Equal matrices are identical. We have the same numbers in the same places. Therefore, the matrix equal to a given matrix is ​​the same matrix.