Step-by-step explanation:
[tex]8x^3-8=2^3x^3-2^3=(2x)^3-2^3\\\\\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(2x-2)\bigg((2x)^2+(2x)(2)+2^2\bigg)\\\\=(2x-2)(4x^2+4x+4)\\=2(x-1)(4x^2+4x+4)\\=4(2x-2)(x^2+x+1)\\=8(x-1)(x^2+x+1)[/tex]
The equivalent expression of 8x³ - 8 is 8(x-1) (x² + x +1)
How to arrive at the above expression
8x³ - 8 = 2³ x³ -2³
= (2x)³ - 2³
Using a³ -b³ = (a - b) (a² + ab + b²)
= (2x -2) ((2x)² + (2x) (2) + 2²))
= (2x -2) (4x² + 4x + 4)
= 2(x-1)(4x² + 4x + 4)
= 4(2x -2) (x² + x +1)
= 8 (x-1) (x² + x +1)
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which equation has roots of 3plus or minus sqare rt 2?
Answer:
Option D is correct.
The equation with roots 3 plus or minus square root 2 is x² - 6x + 7
Step-by-step explanation:
The roots of the unknown equation are
3 ± √2, that is, (3 + √2) and (3 - √2)
The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation
x = (3 + √2) or x = (3 - √2)
The equation is this
[x - (3 + √2)] × [x - (3 - √2)]
(x - 3 - √2) × (x - 3 + √2)
x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)
= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2
Collecting like terms
= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2
= x² - 6x + 7
Hope this Helps!!!
Rationalize the denominator of 2/√3−1 Please give step by step answer
Answer:
√3 + 1
Step-by-step explanation:
Step below are self-explanatory
2/(√3−1)= 2×(√3 + 1)/(√3 - 1)×(√3 + 1) = multiplied both sides by √3 + 12×(√3 + 1)/(√3² - 1²)= used (a+b)(a-b)= a² - b² formula2×(√3 + 1)/(3 - 1)=2×(√3 + 1)/2= cancelled like terms√3 + 1New packaging for fruit snacks contains 10% less weight than the original packaging. If the new package costs 15% more than the original package, by what fraction did the unit price increase? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
Let's say the original packaging was 1 lb of packaging for $1.
The cost was $1/lb.
Then the weight went down by 10% and the price went up by 15%.
Now 0.9 lb of packaging cost $1.15.
The new unit cost is $1.15/(0.9 lb)
The difference is
$1.15/(0.9 lb) - $1/lb =
= $1.15/(0.9 lb) - $0.9/(0.9 lb)
= $0.25/(0.9 lb)
=$25/(90 lb) = $5/(18 lb)
The price went up by 5/18.
find the difference between the endpoints of the interval on the y-axis. (1) [y-value at x=p] - (2) [y-value at x=p+k]
I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.
The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!
For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.
If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.
For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.
For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.
Hope you understood!
And for part one the answer on part c (-2). It depends on K.
25% of a number is a lb. please help
Answer:
4 lb
Step-by-step explanation:
Helppp!!!! please!!!
Answer: B. rectangular pyramid
the question is 1/2 of 5 =
Answer:
2.5
Step-by-step explanation:
1/2x5=?
5/2=?
2.5=?
Answer:
[tex]\boxed{2.5}[/tex]
Step-by-step explanation:
=> [tex]\frac{1}{2} of 5[/tex]
The word "of" means "to multiply"
=> [tex]\frac{1}{2} * 5[/tex]
=> [tex]\frac{1*5}{2}[/tex]
=> [tex]\frac{5}{2}[/tex]
=> 2.5
Pretty confused on finding the missing line segment. Please help.
Answer:
Option (1). 17
Step-by-step explanation:
Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Coordinates of points A and C are (4, 3) and (19, 11).
To get the length of segment AC we will substitute the coordinates in the formula,
AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]
= [tex]\sqrt{(15)^2+8^2}[/tex]
= [tex]\sqrt{225+64}[/tex]
= [tex]\sqrt{289}[/tex]
= 17
Therefore, length of segment AC = 17 units.
Option (1) will be the answer.
A chemist begins with 120 mL of a radioactive substance that decays exponentially. After 24 hours, only 30 mL of the substance remain. How many mL will remain after 48 hours? 12.5 mL 7.5 mL 4.5 mL 9.5 mL
Answer:
7.5 mL
Step-by-step explanation:
If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.
PLEASE HELP ME I REALLY NEED HELP PLEASEEEE
If a circle has an area of 12πcm² and a diameter line AB, what is the length of arc AB?
A. √3π cm
B. 3π cm
C. 2√3π cm
D. 6π cm
E. 4√3π cm
Answer:
c
Step-by-step explanation:
area of a circle = πr²
area = A²
A =√ 12π
A = 2 √ 3π
Help please ASAP :) please give answers to both questions
Answer:
2 cm
10 cm
Step-by-step explanation:
14/7 = 2
This helps to find because area of rectangle = bh or base times height.
A = 1/2 bh
30 = 1/2 b 6
30 = 3b
b = 10
Answer:
b = 2 cm
b = 10 cm
Step-by-step explanation:
Area of a Rectangle: A = lw
Area of a Triangle: A = 1/2bh
We are given area and length, so simply plug it in:
14 = 7w
w = 2 cm
We are given area and height, so simply plug it in:
30 = 1/2(6)(b)
30 = 3b
b = 10 cm
A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test. Change: Final Blood Pressure - Initial Blood Pressure The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 32 subjects in the study had an average change in blood pressure of 2.5 with a standard deviation of 4.8. Find the p -value for the hypothesis test.
Answer:
The p -value for the hypothesis test is 0.003.
Step-by-step explanation:
In this case, a paired t-test would be used to determine whether the drug increases blood pressure.
The hypothesis can be defined as follows:
H₀: The drug has no effect on blood pressure, i.e. d = 0.
Hₐ: The drug increases blood pressure, i.e. d > 0.
The information provided is:
[tex]n=32\\\bar d=2.5\\S_{d}=4.8[/tex]
The test statistic is:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
[tex]=\frac{2.5}{4.8/\sqrt{32}}\\\\=2.9463\\\\\approx 2.95[/tex]
The degrees of freedom of the test is:
[tex]df=n-1=32-1=31[/tex]
The p-value of the test is:
[tex]p-value=P(t_{31}>2.95)=0.003[/tex]
*Use a t-table.
Thus, the p -value for the hypothesis test is 0.003.
A t-test is an inferential statistic that is used to see if there is a significant difference in the means. The p-value for the hypothesis test is 0.003.
What is a t-test?A t-test is an inferential statistic that is used to see if there is a significant difference in the means of two groups that are connected in some way.
As it is given that 32(n) subjects in the study had an average change in blood pressure of 2.5([tex]\bar d[/tex]) with a standard deviation of 4.8([tex]S_d[/tex]).
Now, in order to solve the problem we need to use t-test, the test will determine whether the blood pressure increases or not under the influence of the drug.
The hypothesis for the test can be defined as:
H₀: The drug has no effect on blood pressure, therefore, d = 0.
Hₐ: The drug has increased blood pressure, therefore, d>0.
The test static is:
[tex]t = \dfrac{\bar d}{\dfrac{S_d}{\sqrt n}}\\\\\\t = \dfrac{2.5}{\dfrac{4.8}{32}} = 2.946 \approx 2.95[/tex]
Further, the degree of freedom of the test can be written as,
[tex]d_f=n-1 = 32-1=31[/tex]
Thus, the p-value of the test is:
[tex]p-value = P(t_{31} > 2.95)\\\\\text{Using the t-table}\\\\p-value = 0.003[/tex]
Hence, the p-value for the hypothesis test is 0.003.
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how to do this question plz answer
Answer: 28
Step-by-step explanation:
The shape is grouped into 4 identical parallelograms.
Thus, as the combined area of the figure is 308, you can divide 308/4 to get 77. Thus, each parallelogram has an area of 77.
Then, divide 14/2 to get that the height of each parallelogram is 7.
The area of a parallelogram is l*w. Thus, because l = 7, each parallelogram has a width of 11 because 77/7 = 11.
Then, simply add 11+11+6 to get y.
Hope this helps <3
Determine the measure of the unknown angles.
PLEASE HELP!!! ASAP!!
(Picture included)
(V.O.A) means vertically opposite angle.
Find the measure of angle b
your answer _____
Answer:
43
Step-by-step explanation:
it looks the same as the other side
The required angle b is 43°.
It is required to find the measure of angle b.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given:
The measure of angle b is 43° due to vertically opposite angle.
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.
Therefore, the required angle b is 43°.
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Please help ASAP :):)
Answer:
b
Step-by-step explanation:
i solved it in my head.
Answer:
4 cm^2
4 cm
Step-by-step explanation:
8/2 = 4
4/2 = 2
each side of the square is 2 cm
sqrt. 16 = 4
4 cm
Two pathways meet at 30° to each other. One pathway has lighting and the other does not.
The distance between successive lights on the lighted pathway is 5 metres. Each light has a
range of effective illumination of 6 metres.
What length of the pathway without lights is illuminated by the pathway with lights?
Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.
find the solution(s) to (x + 3)^2=49
Answer:
x = 4
x = -10
Step-by-step explanation:
(x + 3)² = 49
Take the square root of both sides.
x + 3 = ±7
The equation is x + 3 = 7 or x + 3 = -7.
x + 3 = 7
Subtract 3 on both sides.
x = 4
x + 3 = -7
Subtract 3 on both sides.
x = -10
Answer:
x₁ = -10
x₂ = 4
Step-by-step explanation:
(x + 3)² = 49
x + 3 = ± 7
x + 3 = -7 → x = -10
x + 3 = 7 → x = 4
Hope this helps! :)
.Resolva as equações, sendo U = Q (separe as respostas por vírgulas). A) 3y - 2 = - y + 4 B) 5 - 4x = x + 3 + 2x C) - 12 - 9x = - 4 - 12x D) - x - 6 + 3x = -2x + 8x + 15
Answer:
[tex](A) y=1.5[/tex]
[tex](B)x=\dfrac27[/tex]
[tex](C)x=2\dfrac23[/tex]
[tex](D)x=-5.25[/tex]
Step-by-step explanation:
(A)
[tex]3y - 2 = - y + 4\\3y+y=4+2\\4y=6\\y=\dfrac64\\\\y=1.5[/tex]
(B)
[tex]5 - 4x = x + 3 + 2x\\5 - 4x = 3 +3x\\5-3=3x+4x\\7x=2\\x=\dfrac27[/tex]
(C)
[tex]-12 - 9x = - 4 - 12x\\-9x+12x=-4+12\\3x=8\\x=\dfrac83\\\\x=2\dfrac23[/tex]
(D)[tex]- x - 6 + 3x = -2x + 8x + 15[/tex]
[tex]2x-6 = 6x + 15\\2x-6x=15+6\\-4x=21\\x=\dfrac{21}{-4} \\\\x=-5.25[/tex]
The planet mercury is approximately 6*10^7 miles from the sun. The distance between the sun and mars is approximately 2*10^8 miles. About how many times farther from the sun is mars than mercury.
Answer:
Around 10/3 or 3.33 times farther.
Step-by-step explanation:
We simply divide the larger distance by the smaller distance to find our ratio:
2(10⁸)/6(10⁷)
10/3
*Remember when you divide exponents, you subtract them
The graphs below have the same shape. What is the equation of the blue graph?
g(x) =
A. g(x) = (x + 3)2 + 1
B. g(x) = (x - 3)2 + 1
C. g(x) = (x - 3)2 - 1
D. g(x) = (x + 3)2 - 1
Explanation:
The vertex of a parabola is either the highest point or the lowest point, depending on how the parabola is oriented. In this case, it is the lowest point.
For the red f(x) curve, we see the vertex is (0,0)
The blue g(x) curve has its vertex at (3,1)
In general, the vertex is represented by (h,k)
For the blue curve, (h,k) = (3,1) so h = 3 and k = 1 pair up together
We will plug those values along with a = 1 into the vertex form below
y = a(x-h)^2 + k
y = 1(x-3)^2 + 1
y = (x-3)^2 + 1
The blue curve is the result of shifting the red curve 3 units to the right and 1 unit up. No vertical stretching or compressing has been applied, which is why a = 1 stays the same.
Find the total surface area of this triangular prism...
Answer:
144 cm^2
Step-by-step explanation:
8x6+4x10+4x8+4x6
48+40+32+24
80+40+24
120+24
144
Which statement best describes the function below : F(x)=2x^2-3x+1
Answer:
it is a many to one function:)
Step-by-step explanation:
The statement which best describes the function F(x)=2x^2-3x+1 is it is a many to one function.
How do you find the piecewise function?
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.
What is a function example?f(x) = x2 shows us that function "f" takes "x" and squares it. Example: with f(x) = x2: an input of 4. becomes an output of 16.
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HELPPP DO NOT LOOK IT UP PLS
(x2 + 4x) - 2x = x2 +
X
Answer:
x=0
Step-by-step explanation:
(x^2 + 4x) - 2x = x^2 +x
Combine like terms
x^2 +2x = x^2 +x
Subtract x^2 from each side
2x =x
Subtract x from each
2x-x = x-x
x = 0
Answer:
[tex]x=0[/tex]
Step-by-step explanation:
[tex]x^2+4x-2x=x^2+x[/tex]
Combine like terms.
[tex]x^2+2x=x^2+x[/tex]
Add [tex]-x^2[/tex] and [tex]-2x[/tex] on both sides.
[tex]x^2+2x-x^2-2x=x^2+x-x^2-2x[/tex]
[tex]0=x-2x[/tex]
[tex]0=-1x[/tex]
Divide both sides by [tex]-1[/tex].
[tex]\frac{0}{-1} =\frac{-1x}{-1}[/tex]
[tex]0=x[/tex]
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$?
Answer:
16.59
Step-by-step explanation:
Given:
[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]
Expanding the left hand side, we have:
[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]
Therefore:
[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]
To find the minimum value, we take the derivative and solve for its critical point.
[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]
Recall that:
[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]
The minimum possible value of the coefficient of x is 16.59.
Answer:
173
Step-by-step explanation:
For sympliciy let the box equal y.
Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].
19. Solve for g: 5 / 8 = 12 / g
Answer:
19.2Solution,
[tex] \frac{5}{8} = \frac{12}{g} \\ or \: 5 \times g = 12 \times 8 \: ( \: cross \: multiplication) \\ or \: 5g = 96 \\ or \: g = \frac{96}{5} \\ g = 19.2[/tex]
Hope this helps..
Good luck on your assignment...
Answer:
Step-by-step explanation:
5/8=12/g
*8 *8
5=12*8/g
*g *g
5g=12*8=96
:5 :5
g=96/5
g=19.2
2+2 what does it 1+!
Answer:
4 AND 2
Step-by-step explanation:
Answer:
Hello!
______________________
This question is very easy.
2 + 2 = 4
1 + 1 = 2
Step-by-step explanation: Add.
Hope this helped you!
Can anyone help with this?
Answer:
115/5 23 so 20% =23 23x4 =92
Dos familias asisten a un sitio de comidas rápidas de la ciudad, una de ellas pide 4 perros calientes y 3 hamburguesas y pagan 43000 pesos, la otra familia, piden 5 perros calientes y 1 hamburguesa y pagan 34500 pesos, se desea saber ¿cuál es el valor de cada perro y de cada hamburguesa?.
Answer:
Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.
Step-by-step explanation:
Sea x el precio de los perros calientes y y el precio de las hamburguesas.
Escribiendo los datos de la primera familia en forma de ecuación tenemos:
[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)
Escribiendo los datos de la segunda familia:
[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)
Vamos a resolver este sistema de ecuaciones por el método de suma y resta:
[tex]4x+3y=43,000\\5x+y= 34,500[/tex]
Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:
[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]
Por lo tanto, un perro caliente cuesta 5,500 pesos.
Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:
[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]
Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una