Answers
The last choice is the correct one
Explanation:
We can solve this question using "difference between squares" which has the following general rule:
a^2 - b^2 = (a+b)(a-b)
For the given question:
p^4 - 16 = (p^2 - 4)(p^2 + 4)
Now, p^2 - 4 can be further factorized using difference between squares, therefore:
p^4 - 16 = (p-2)(p+2)(p^2 + 4)
Hope this helps :)
Related Questions
helpppppppppppppppppppppppp
Answers
1 / 4x
Explanation:
(4x^3) * (2x)^-4 = 4x^3 * 2^-4 * x^-4
= (4x^3) / (2^4 * x^4)
= (1/4) * (1/x)
= 1 / 4x
Hope this helps :)
(4x ^ 3) * (2x) ^ - 4
Using properties of exponents we have:
(4x ^ 3) / (2x) ^ 4
Rewriting:
(4x ^ 3) / 16x ^ 4
(x ^ 3) / 4x ^ 4
(1) / (4x)
answer:
An equivalent expression is:
(1) / (4x)
option 1
Aisha owns an apparel store. She bought some shirts and jeans from a wholesaler for $3,900. Each shirt cost $12 and each pair of jeans cost $28. If she sold the shirts at 70% profit and jeans at 125% profit, her total profit was $3,885. How many shirts and jeans did she buy from the wholesalers? 101 shirts and 96 jeans
Answers
x: shirt
y: jeans
We write the following system of equations:
12x + 28y = 3900
8.4x + 35y = 3885
We solve the system of equations:
x = 150
y = 75
Note: see attached image for the solution of the system:
Answer:
she bougth from the wholesalers
150 shirts
75 jeans
Answer:
The correct answer would be:
Step-by-step explanation:
150-shirts
75-jeans
Solve the equation using square roots. x2 + 10 = 9
A. Plus or minus the square root of 1.
B. no real number solutions
C. 1
D. –1
Answers
Subtract 10 from both sides.
[tex] x^2 = -1 [/tex]
Since the square of a number, x, equals a negative number, -1, the answer cannot be a real number because the square of a real number is always non-negative. Therefore, there is no real number solution to this equation.
Answer: B. no real number solutions
Answer:
no real number solutions
Step-by-step explanation:
The current San Francisco cable railway is driven by two large 14-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270°on each sheave. Find the length of cable riding on one of the drive sheaves at any given time.
Answers
The angle θ in this case is 270°, while the radius is 7 feet, diameter is 14 feet
Thus the length of the of the cable will be;
=(270/360)× 22/7×14
= 0.75 × 44
= 33 feet
Answer:
The length of the cable is around 32.97 feet.Step-by-step explanation:
The problem is about a circular sector, where the angle is 270° and the lenght of the subtended arc is the arc is the unknown variable.
The radius of the drive wheel is
[tex]r=\frac{d}{2}=\frac{14}{2}=7ft[/tex]
The central angle is 270°.
The length of the arc is
[tex]L=\frac{2\pi r \theta}{360\°}[/tex]
Replacing all values, we have
[tex]L=\frac{2(3.14)(7)(270\°)}{360\°}=\frac{11869.2}{360} \approx 32.97[/tex]
Thereofre, the length of the cable is around 32.97 feet.
How to estimate the square root of a number that is not a perfect square?
Answers
The marketing department of a sports supply store wants to estimate the percentage of adults in the town who belong to a gym.
Which statement describes a method that will help the marketing department accurately estimate this percentage?
A)Select the store’s first 20 customers every day for one week, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.”
B)Take a random sample of adults at the local park, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.”
C)Take a random sample of adults in the town, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.
D)Take a random sample of the store’s adult customers, and ask what percentage of their friends belong to a gym. Calculate the mean of the responses.
Answers
B) While it does not have necessarily the same amount of bias as sampling people in the sports supply store, people that go to a park are generally more likely to be people that exercise or have a gym membership.
C) Taking a random sample of people in town is a good way to get a non-biased sample. They are not necessarily predisposed to answer your question one way or another.
D) For the same reason as choice A, this is a biased sample.
C is the best choice.
marion is making trail mix for a group camping trip. she buys 3 pounds of granola for $3 per pound and 0.75 pounds of raisins for $2 a pound. what equation can you use to find the price per pound of the trail mix?
Answers
x-------------> pounds of granola-----------> $3 per pound
y-------------> pounds of raisins-----------> $2 per pound
z------------ > price per pounds of the trail mix
we have that
z=3x+2y--------------------- > this is the equation
for x=3 pounds of granola and y=0.75 pounds of raisins
z=3*3+2*0.75=$10.5 of trail mix
It's B on edg. 3(3) + 0.75(2) = (3 + 0.75)x
Simplify the expression.
A) –24n + 8mn – 100np
B) –6n – 2mn + 25np
C) –6n + 2m – 25np
D) –6n + 2mn – 25np
Answers
-24 /4n will equal -6n because the n won't go away
8m/4n will equal 2mn because you can always have two variables on one number and the n is not going anywhere
-100p/ 4n will equal -25np because of the same reason as the upper one.
so -6n + 2mn -25np is the simplified expression
Solve the system of equations using the substitution method.
{4x+5y=7
{y=3x+9
Enter your answers in the boxes.
x=
y=
Answers
y=3x+9
1) 4x+5(3x+9)=7 2) y=3(-2)+9
y= -6 +9
4x+15x+45=7 y=3
19x+45=7
19x= -38
x= -2
x is -2 and y is 3
(Please Answer Quickly)
Algebra 2 Question! I will make sure to give a medal and pin the most helpful answer!
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola. The equation for this parabola is y = -x^2 + 36. (Graph of a parabola opening down at the vertex (0,36) crossing the x–axis at (-6,0) and (6,0))
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created with your table positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice.
Answers
y=x+8
"Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow."
To find the intersection points we need to solve system of two equations:
[tex]y=- x^{2} +36 \\ y=x+36[/tex]
Solution are two points:
(-1,35) and (0,36)
Now we can create a table
x -1 0 1 2
f(x) 35 36 37 38
"What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?"
The domain represents all possible values that x can have. The range represents all possible values that y can have.
In this example not all values make sense. Rainbow goes above ground and touches it.
Limitations exist if we have fraction, root, logarithm, trigonometric function... We do not have any of these so there are no limitations, so x can have any value.
Domain: -6≤x≤6 because x can not have smaller values than those at ground touch.
The formula for parabola is:
[tex]y=a x^{2} +b[/tex]
Depending on sign of [tex] x^{2} [/tex] the maximum or minimum value of y is equal to b. All other smaller or greater values are possible.
Range: 0≤y≤36 because y can not have smaller values than those at ground touch.
"What are the x- and y-intercepts of the rainbow? Explain what each intercept represents."
x- and y- intercepts represent points at which function touches x- and y- axis.
To find y- intercept we insert x=0 into equation:
y=0+36
y=36
To find x- intercept we insert y=0
0=-[tex] x^{2} [/tex]+36
[tex] x^{2} =36 \\ x_{1} =-6 \\ x_{2} =6[/tex]
"Is the linear function you created with your table positive or negative? Explain."
Function is positive if it lies above x-axis. Function is negative if it lies below x-axis.
Positive on interval: x ∈ <-6,∞>
Negative on interval: x ∈ <-∞,-6>
Not defined: x= -6
"What are the solutions or solution to the system of equations created?Explain what it or they represent."
We already found these solutions:
[tex]y=- x^{2} +36 \\ y=x+36[/tex]
Solution are two points:
(-1,35) and (0,36)
These solutions represent points of intersection of linear function and parabola.
"Explain, using complete sentences, the steps for graphing the function."
Step 1) we need to find domain and range
Step 2) we need to find x- and y- intercepts
Step 3) if the function is exponential we find minima and maxima
Step 4) we find at least three values for the function
Which of the following best explains why one graph appears skewed and one graph appears symmetric?
The intervals on the x-axis of the histogram are too large.
The interval on the y-axis of the histogram is too small.
The interval on the x-axis of the histogram is inconsistent.
The interval on the box-and-whisker plot is too small.
Answers
The interval on the X-Axis of the Histogram is inconsistent:
An Histogram is a graphic representation of the frequency of values. It should include all the data range on the x-axis. In this case, the x-Axis should include all intervals from 0 to 24 years, but in the graph the intervals "jump" from 10-14 to 20-24.
This inconsistency causes the difference between the two graphics because the two of them should be skewed to the left, according to the age distribution.
Answer:
The interval on the X-Axis of the Histogram is inconsistent
Step-by-step explanation:
edge
The sum of three numbers is 12. The first number is the difference of the other two numbers. When you add the other two numbers and subtract 8, the result will be the first number. Find the numbers.
2, 4, 6
2, 5, 5
3, 7, 2
5, 10, -3
Answers
50 POINTS PLEASE HELP show work answer all 3
Answers
Answer:
b.) The graph's x-intercepts are similar to ½(x - 5)(x + 2).
a.) [-2, 0], [5, 0]
__________________________________________________________
b.) The graph has a maximum value because the graph opens down [-2 = A].
a.) [-3, -4]
__________________________________________________________
d) [0, -5]
c) -2 = x
b) [-2, -9] → [h, k]
a) -1, 5 = x
Explanation:
b) Both graphs have the binomial of [x - 5][x + 2], so the x-intercepts never altered.
a) Set the binomial equal to zero, and you will get your x-intercepts of [-2, 0] and [5, 0].
__________________________________________________________
b) When A is negative, your graph will have a maximum value [opens down], whereas when A is positive, your graph will have a minimum value [opens up].
a) According to the Vertex Formula, y = A[X - H]² + K, [H, K] represents the vertex, plus, -H gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL labeling your vertex. Additionally, K gives you the NORMAL TERMS.
__________________________________________________________
d) The y-intercept is your C-term, so in this case, it is [0, -5].
c) To find the axis of symmetry, use this formula:
[tex] \frac{-b}{2a} = x[/tex]
Whatever the opposite of your B-term is, you take that and divide it by twice your A-term.
b) To find the vertex, in this case, you have to go from Standard Form to Vertex Form by completing the square, using this formula to get part of your new C-term:
[tex][\frac{b}{2}]^{2} [/tex]
When done, you get this:
[tex]y = {x}^{2} + 4x + 4 \\ \\ y = [x + 2]^{2} [/tex]
Then, you have to deduct some number from 4 that gave you -5 in the first place, and that integer is -9. So, here is the result:
[tex]y = [x + 2]^{2} - 9[/tex]
From here, we can see that our vertex is [-2, -9].
a) When the binomial is set to equal to zero, you get this:
[tex]{x}^{2} + 4x - 5 \\ \\ [x - 1][x + 5] = 0 \\ \\ 1, \: -5 = x[/tex]
e) See above photograph
I am joyous to assist you anytime.
Use systems of equations to solve the problem.
A farmer raises wheat and oats on 180 acres. She plants wheat on 20 more acres than she plants oats on. How many acres of each crop does the farmer plants?
Answers
Y = wheat, x = oats
Y = x + 20. In the 1st equation, get y by itself getting y = 180 - x.
So 180 - x = x + 20. Subtract x on both sides to get 180 - 2x is 20. Subtract 180 to both sides is -2x = -160. Divide -2 to both sides is x = 80. So 80 + 20 is 100 wheat, and 80 oats of acres.
80 acres oats
100 acres wheat
Describe how to find linear expressions for the possible dimensions of a rectangular prism with a volume of 8k^3 +26k^2+ 6k.
Answers
For this case, the first thing you should do is rewrite the expression.
We have then:
Step 1:
Take out common factor.
8k ^ 3 + 26k ^ 2 + 6k
2k * (4k ^ 2 + 13k + 3)
Step 2:
Factor quadratic expression.
2k * (4k ^ 2 + 13k + 3)
2k * (4k + 1) * (k + 3)
Answer:
to find linear expressions for the possible dimensions of a rectangular we rewrite the expression:
2k * (4k + 1) * (k + 3)
The area of a circle A is 85π ft2. ∠BAC is a central angle of the circle, and m∠BAC = 36°
What is the area of the 36° sector?
Question 1 options:
8.5πft2
10πft2
17πft2
21.25πft2
Answers
the magnitude of the central angle in the circle is 360°
Area for 360° central angle - 85π ft2
then the area for 1° = 85π ft2/360°
the area of 36° sector = 85π ft2/360° x 36°
= 8.5π ft2
8- 2 to the root of 4+8*2^3-(3+14-5)/12
I don't know if this makes sense but I need help with it.
Answers
[tex] = 8 -2^{2} +8 \times 8 -\frac{12}{12} [/tex]
[tex] = 8-4+64-1 = 67 [/tex]
Can someone please help me I would appreciate it please!?!
I well mark brainliest if its explained and right.
Answers
_____________________________________________________
The formula for the surface area, "S.A.", of a "cylinder":
S.A. = 2 π r² + 2 π r h ;
in which:
"S.A." = "surface area" of the cylinder; for which we wish to solve;
π = 3.14 (approximation we shall use) ;
r = radius = 5 cm (given; from figure);
h = height = 2 cm (given; from figure);
______________________________________
To solve for the surface area, "S.A." . let us plug in our known values, and solve:
S.A. = 2 π r² + 2 π r h ;
S.A. = 2 * (3.14) * (5 cm)² + 2 * (3.14) * (5 cm) * 10 cm) ;
= 2 * (3.14) * (5²) * (cm²) + 2 * (3.14) * 5* 10 * cm² ;
= 2 * (3.14) * (25) * (cm²) + 2 * (3.14) * 5* 10 * cm² ;
= 157 cm² + 314 cm² ;
= 471 cm² .
________________________________________________
The answer is: " 471 cm² " .
________________________________________________
Mrs. Smith and her daughter Laura want to learn ballet. The cost of beginning ballet classes for kids is $3,200 per year, and it increases by 2% every year. The cost of beginning ballet classes for adults is $4,800 per year, and it increases by 2.7% per year. Which function can Mrs. Smith use to determine the total cost of their ballet classes, T(x), after x years?
Answers
Since it increases by a percentage every year we will use an exponential function.
C(x) = 3200(1+0.02)ˣ. This comes from the $3200 for the first year, and 2% increase every year is 0.02. Add this to 1 because we have all of the first year's cost, 100%, and the additional 2%.
A(x) = 4800(1+0.027)ˣ. This comes from the $4800 for the first year, and 2.7% increase every year is 0.027. Add this to 1 because we have 100% of the first year's cost with an additional 2.7%.
T(x) = 3200(1+0.02)ˣ+4800(1+0.027)ˣ=3200(1.02)ˣ+4800(1.027)ˣ
You earn $10 a week for doing chores, and you have just been paid for completing eight weeks of chores. If you were paid $8 a week doing chores, how many weeks would it take to earn the same amount of money? weeks
Answers
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. if field has a length that is twice its width, find the area of the field in square meters. ________________________________________
Answers
12:2=6 km..............30 min
6000 m :10=600 m (the perimeter)
600m= 2(l+w)=2(2w+w)=2*3w=6w
⇒ w=600:6
w=100m
l=2*100=200m
A=w*l=200*100=20.000 m^2
One leg of a right triangle measures 8 inches and the hypotenuse 17 inches. determine the length of the other leg.
a. 9 inches
b. 13 inches
c. 15 inches
d. 17 inches
Answers
A quadrilateral has angles that measure 71°, 74°, 113°, and x°. What is the measure of x?
Answers
Bascially for answer 360-258
Are elite runners thinner than the average person? Devon thinks that skin thickness of elite runners is thinner than the average person. He compares a data set of elite runners to regular people by looking at the skin thickness. Which statement correctly compares the two groups?
A) The skin thickness of the elite runners varied by about 11 mm.
B) The skin thickness of the average person varied by about 11 mm.
C) The skin thickness of elite runners is on average about 11 mm thinner than that of the average person.
D) The skin thickness of the average person is on average about 11 mm thinner than that of the elite person.
Answers
I hope it's right!!!!
Answer:
c is the answer
Step-by-step explanation:
Which graph represents the function?
Answers
f(x) = (x +7)(x -7)/(x +7)
f(x) = x -7 . . . . . . . . . . . . . . x ≠ -7
The graph will be a line with a slope of 1 and a y-intercept of -7. It will have a "hole" at (-7, -14).
The lower-left selection is appropriate.
What is the sum of a 6-term geometric series if the first term is 23 and the last term is 1,358,127? 1,395,030 1,461,460 1,527,890?
Answers
The sum of 6 terms is
.. 23*(9^6 -1)/(9 -1) = 1,527,890 . . . . . . . . . . selection 3
Answer:
Last term is 1,527,890.
Step-by-step explanation:
In this question a geometric series has been given with
first term A = 23
6th term = 1,358,127
Number of terms n = 6
we have to calculate the sum of this geometric series
we know [tex]T_{n}=a(r)^{n-1}[/tex]
[tex]T_{6}=23.(r)^{6-1}=1358,127[/tex]
[tex]r^{5}=\frac{1358127}{23}=59049[/tex]
[tex]r = 59049^{\frac{1}{5} }[/tex]
r = 9
Now we know the formula to sum a geometric series is
[tex]S=a.\frac{r^{n-1} }{r-1}[/tex]
S = 23 × [tex]\frac{(9^{6-1)} }{(9-1)}[/tex]
S = 23 × [tex]\frac{(531441-1)}{8}[/tex]
S = [tex]\frac{23.(531440)}{8}[/tex] = 23 × 66430
S = 1,527,890
The medicine capsule shown consists of a cylinder with a hemisphere at each end. The total length of the capsule is 18 millimeters. The diameter is 7 millimeters. Which choice is the best approximation of the total surface area of the capsule? Use 3.14 to approximate pi.
Answers
Answer:396
Step-by-step explanation:
Graph the following inequality and then select the correct graph below.
x - y - 2 ≥ 0
Answers
Answer:
Second graph
Step-by-step explanation:
Given inequality,
x - y - 2 ≥ 0
⇒ x - y ≥ 2
The related equation of the inequality,
x - y = 2
Having x-intercept = (2, 0)
y-intercept = (0,-2),
Also, 0 - 0 ≥ 2 ( False )
Thus, the inequality will not contain the origin,
Again,
'≥' shows the solid line.
Hence, by the above explanation it is clear that the SECOND graph would be the graph of given inequality.
Describe the number and type of roots for the polynomial (how many real and complex?). x3 + 5x2 – 4x – 2 = 0
Answers
A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.
Anita brings 6 dolls to her grandmas house. These dolls represent 20% of Anita's doll collection. What is the total number of dolls in Anita's dolls collection?
Answers
6=20%*x
6=20/100 *x
6*100/20=x
30=x
the total number of dolls is 30
Answer:
30 is your answer
Step-by-step explanation: