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.
what the hell is a rotation?
Answer:
A rotation is when a shape rotates across the x or y axis on a coordinate plane :)
Step-by-step explanation:
The graph below plots the values of y for different values of x:
Plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What is the correlation coefficient for the data plotted?
−0.9
−0.6
0.6
0.9
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
please help and look at the picture
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
which matrix is equal to [-6,-6.5,1.7,2,-8.5,19.3]
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.
what is the square root of m to the power of 6
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]
Which of these expressions is equivalent to log (20/3)
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
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared
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
Two squares are similar. The first square has sides that measure 4 inches, and the second square has sides that measure 12 inches. The scale factor used to get from the first square to the second one is
3, because 12/4=3. And 12:4 is equal to 3:1 or 3.
erza has a square brick patio. he wants to reduce the width by 4 feet and increase the length by 4 feet.
let x represent the length of one side of the square patio. write expressions for the length and width of the new patio. then find the area of the new patio if the original patio measures 9 feet by 9 feet.
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.
What is the formula to find the area of a square?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:
https://brainly.com/question/1603804.
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Write the equation of a line in slope intercept form that is parallel to 2X plus 4Y equals 10 and passes through the point (8,2)
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]
Why?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!
Determine if the binomial is a perfect square binomial. If so, show the original monomial squared.
5. x2+ 16
6. x4 + 12x2+ 36
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.
How do I do this algebra??
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]
8x-6y=54 in slope intercept form please!!
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.
Explanation: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:
Add 6y to both sides to isolate variables on one side. Now, the equation is 8x = 6y + 54. Divide everything by 6 to solve for y. The equation becomes y = (8x/6) - (54/6). Simplify the equation: y = (4/3)x - 9.
Therefore, the equation 8x - 6y = 54 in slope intercept form is y = (4/3)x - 9.
Learn more about Slope-Intercept Form here:
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The average battery life of 2800 manufactured cell phones is recorded And normally distributed. The mean battery life is 14 hours with a standard deviation of .5 hours. Find the number of phones who have a battery life in the 13 to 14 range.
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.
please help with this thank you
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
I promise BRAINLIST!!! It's simple!!!
Make a stem-and-leaf plot that represents the data set below?
64, 67, 81, 89, 108, 114, 74, 52, 93, 76, 87
Answer:
answer in the image attached above
Step-by-step explanation:
Hope it helps
Camilo practica tiro al blanco. En cada disparo acertado puede obtener 5, 8, o 10 puntos. En su última práctica, su puntuación total fue de 99, él obtuvo 8 puntos tantas veces como 10 puntos. Si en el 75% de las veces acertó al blanco, ¿cuántos disparos hizo Camilo en total?
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.
What are the opposites of 9, -2.6, 1.15, 7 1/3? Enter the answers in respective order, each separated by a comma.
-9, 2.6, -1.15, -7 1/3
To find the opposite of a number, multiply or divide it by -1. These four numbers just each got multiplied by -1 to get the answers.
Please need help
Find area of shaded region.
Round to the nearest tenth
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
What percent of a dozen is 3
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.
What is the meaning of Zero on a number line
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.
Give the polynomial function below find f(-4) f(x) =2x^2 - x+ 9
Answer:
f(-4) = 45Step-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
The vertex of this parabola is at (-1,3) Which of the following could be its equation
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
I only need someone to put it in the quadratic formula I already have solutions. Please answer ASAP!!! I will give brainliest!!!
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
Olivia solved a division problem by subtracting and keeping track as shown. Identify the problem she solved.
Answer: 314÷13
..............................................................................
Answer:
13/314
Step-by-step explanation:
Make your turn please
Answer:
9inStep-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
The answer and how to do it for me homework
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
There is 1 cup of sugar for every 3 cups of flour in an oatmeal raisin cookie recipe. Create a ratio table that shows how much of each item would be needed when wanting to make more than one batch of cookies
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!
math help ^^ will give 10 points ^-^
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.
i am a number. If the area of each square below is 25 square units, i am the perimeter of the figure. i am ___________
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.