Answer:
[tex]25a^6-4[/tex]
Step-by-step explanation:
So if you look at the equation, you'll notice it's being multiplied by it's conjugate which can be expressed as: x+a and x-a. See how only the sign changes? Well if remember the differences of squares, it looks like that, because it is. Essentially the difference of squares says that: [tex]a^2-b^2=(a-b)(a+b)[/tex]. So expanding this out will result in [tex](5a^3)^2-(2)^2[/tex] which simplifies to: [tex]25a^6-4[/tex]. If you're confused on how I got 25a^6. Try to think of a^3 as three a's rather than simply an exponent. and since it has a coefficient of 5. 5a^3 is the same as (5 * a * a * a). Now if you square this you have (5 * a * a * a) * (5 * a * a * a). So if you group like terms you'll end up with 6 a's being multiplied by each other (which can be expressed as a^6) and 5 * 5 which is 25.
The multiplication can be transformed into the difference of squares using the rule:(a−b)(a+b)=a²-b² . Gets the square of 2.
(5a³)²-4
Expand (5a³)².
5² (a³)² -4
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
5²a⁶-4
25a⁶-4 ====> Answer
{ Pisces04 }
A telegraph pole stands on a line joining two points P and Q on the ground.
The telegraph pole is 9 m tall. The angle of depression of the top of the pole to point P
is 4°. The angle of depression of the top of the pole to point Q is 7º. What is the
horizontal distance between P and Q.
Step-by-step explanation:
let's call the top of the pole T, and the ground point of the pole G.
so, the situation gives us 2 right-angled triangles:
PTG and QTB.
from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.
the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).
the inner angle at PTG = 90 - 4 = 86°
the inner angle at QTG = 90 - 7 = 83°
and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :
angle P = 180 - 90 - 86 = 4°
angle Q = 180 - 90 - 83 = 7°
yes, they are the same as the angles of depression (must be the same).
so, we know from both triangles 1 side and all 3 angles.
with the law of sine we can get every missing side.
particularly we need the second legs (sides in the ground) to get the distance between both points.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides always opposite of their related angles.
TG/sin(4) = PG/sin(86)
PG = 9×sin(86)/sin(4) = 128.7059963... m
TG/sin(7) = QG/sin(83)
QG = 9×sin(83)/sin(7) = 73.29911785... m
the distance between P and Q can have now 2 solutions :
if P and Q are on different sides of the pole, then
PQ = 128.7059963... + 73.29911785... = 202.0051142... m
but if they are on the same side of the pole, then their distance is
PQ = 128.7059963... - 73.29911785... = 55.40687846... m
due to the phrasing of the first sentence I suspect the first solution to be right.
but just in case, I gave you also the second possible solution.
Find the length of the hypotenuse on the following right triangle.
Answer:
Step-by-step explanation:
(Round answers to
the nearest hundredth.)
Answer:
28.31
Step-by-step explanation:
So in this case you're going to need to use the law of sines which essentially states that: [tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex] which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).
Given information:
[tex]\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}[/tex]
Law of sines equation:
[tex]\frac{a}{sinA}=\frac{b}{sinB} \text{ can be applied to any two sides }[/tex]
Plug in known information:
[tex]\frac{15}{sin(32)}=\frac{c}{sin (90)}[/tex]
since sin(90) = 1, simplify the fraction
[tex]\frac{15}{sin(32)} = c[/tex]
Calculate sin(32)
[tex]\frac{15}{0.530}\approx c[/tex]
Divide
[tex]28.306\approx c[/tex]
If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c
tan is defined as: [tex]\frac{opposite}{adjacent}[/tex]
[tex]tan(32)=\frac{15}{b}[/tex]
now multiply both sides by b
[tex]b * tan(32)=15[/tex]
Divide both sides by tan 32
[tex]b = \frac{15}{tan(32)}[/tex]
[tex]b\approx 24.005[/tex]
Now use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
[tex](24.005)^2+15^2=c^2\\[/tex]
Square known values
[tex]576.241+225=c^2[/tex]
Add the values
[tex]801.241 = c^2[/tex]
take the square root of both sides
[tex]28.306\approx c[/tex]
Rounding to the nearest hundredth gives you 28.31
answer pleaseeeeeeeeeeeeeee
Answer:
A. Square
Step-by-step explanation:
Hope this helps!
Please mark brainliest! Thanks!
In triangle TUV Y is the centroid if YW=9 find TY
Applying the centroid theorem, the length of TY is calculated as: 18 units.
What is the Centroid Theorem?According to the centroid theorem, given a triangle like TUV with Y as the centroid, the theorem states that:
TY = 2/3(TW)
YW = 9 units
TW = TY + 9
Plug the values into the equation
TY = 2/3(TY + 9)
3(TY) = 2(TY + 9)
3(TY) = 2(TY) + 18
3(TY) - 2(TY) = 18
TY = 18
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Jon, Dave, and Kevin collected rocks at the beach. Each boy collected 25 rocks. How many rocks did the boys collect in all?
By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.
How many rocks did the boys collect in all?
We know that there are 3 boys, and each boy collected 25 rocks.
If we take the product between the number of boys and the number of rocks that each boy collected, we get:
R = 3*25 rocks = 75 rocks.
We conclude that the boys collected 75 rocks in total.
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How many outfits can be made with 40 shirts and 15 pairs of pants
Answer:
600
Step-by-step explanation:
So I'm assuming an outfit is considered one shirt, and one pair of pants... But anyways, this can be expressed in a graph. So for each shirt, there are going to be 15 possible pants you can chose. And this goes for each shirt. So in other words you're simply adding up 15, 40 amount of times. Or 15 * 40, which is 600. I attached an image that illustrates this graph. You can also think of it in terms of choosing one of 15 pants and then for each pant, there are 40 possible shirts to choose from. This is essentially adding up 40, 15 times, or in other words 40 * 15, which is going to get you the same result. But in my diagram I used it in terms of choosing a shirt first.
Answer:
600
Step-by-step explanation:
Pair 1 of pants goes with 40 shirts
Pair 2 of pants goes with 40 shirts
Pair 3 of pants goes with 40 shirts
Pair 4 of pants goes with 40 shirts
Pair 5 of pants goes with 40 shirts
Pair 6 of pants goes with 40 shirts
Pair 7 of pants goes with 40 shirts
Pair 8 of pants goes with 40 shirts
Pair 9 of pants goes with 40 shirts
Pair 10 of pants goes with 40 shirts
Pair 11 of pants goes with 40 shirts
Pair 12 of pants goes with 40 shirts
Pair 13 of pants goes with 40 shirts
Pair 14 of pants goes with 40 shirts
Pair 15 of pants goes with 40 shirts
Add up everything (not including the 1,2,3,4,5,...14,15 pairs of pants because each pair of pants goes with 40 different shirts so u just add up all the 40's) and you would get 600 outfits.
Another simple way of doing this would just be multiplying 40x15
an experimental design that permits simultaneous statistical conclusions about two or more factors is a
Factorial design is the correct choice for the answer as an experimental design that permits statistical conclusions about two or more factors is a factorial design.
A factorial experiment is a type of research methodology that allows the study of main and interaction effects between two or more independent variables and on one or more outcome variables.
This is called a mixed factor experiment. For example, a researcher may choose to treat mobile phone use as a factor within a subject by testing the same participant with and without mobile phone use (the order of these two conditions). Balance).
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Find the length of line segments (4,6) and (5,2)
Answer: [tex]\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}[/tex]
Step-by-step explanation:
We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}[/tex]
[tex]\displaystyle d=\sqrt{(1)^2 +(-4)^2}[/tex]
[tex]\displaystyle d=\sqrt{1 +16}[/tex]
[tex]\displaystyle d=\sqrt{1 7}[/tex]
Need asap pls correct answer
Answer: B. G(x) = (x-5)^2
Step-by-step explanation:
This will shift the graph 5 units right
Analyze the diagram below.
Which statements regarding the diagram are correct? Check all that apply.
ST ≅ ST by the reflexive property.
∠RWS ≅ ∠UWT because they are vertical angles.
△RWS ≅ △UWT by AAS.
△RST ≅ △UST by SAS.
∠WTU ≅ ∠WSR because CPCTC.
Based on the relevant congruent theorems, all of the statements are correct except: D. △RST ≅ △UST by SAS.
What is the AAS Congruence Theorem?Two triangles that have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles are proven to be congruent by the AAS congruence theorem.
Thus, △RWS ≅ △UWT by AAS because they have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles.
△RST cannot be proven to be congruent to △UST by SAS because there is no sufficient information.
Based on the reflexive property, ST ≅ ST. Also, using the CPCTC, all parts of the two congruent triangles are equal, therefore, ∠WTU ≅ ∠WSR.
The only statement that is incorrect is: D. △RST ≅ △UST by SAS.
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Answer:
A, B, C and E
Step-by-step explanation:
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y.
x=2, y=5
The equation that relates x and y is y = 2.5x.
How to solve variation?
The values of x and y vary directly. Therefore,
y α x
where
x and y are the variable.Hence,
y = kx
where
k = constant of proportionality.Therefore,
x = 2
y = 5
5 = 2k
k = 5 / 2
k = 2.5
Hence, the equation that relates x and y are as follows;
y = 2.5x
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Rewrite x² - 10x = 4 so that the left side is a perfect square trinomial.
x² - 10x -4 = 0
x² - 10x + 25 = 4
x² − 10x + 25 = 29
x². - 10x + 10 = 14
Answer:
C
Step-by-step explanation:
x²-10x+(-10×0.5)²=4+(-10×0.5)²
x²-10x+25=29
Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest monthly, and to calculate what annual interest rate he needs, he is using the rule of 72. (3 points: Part I – 1 point; Part II – 1 point; Part III – 1 point)
Part I: What is the rule of 72? To represent the annual interest rate, use r.
Part II: What equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?
Part III: What annual interest rate does Miguel need to double his money by the time he retires?
The rule of 72 is a rule of thumb that is used to determine the doubling time for an investment given the annual interest rate.
The equation Miguel needs to set up is r = 72/16.
The interest rate is 4.5%.
What is the rule of 72?
The rule of 72 is used to determine the time it would take an investment to double in value. The doubling time is determined by dividing 72 by the interest rate.
Number of years it would take an investment to double = 72 / interest rate
n = 72 / r
r = 72 / n
72 / 16 = 4.5%
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What is the value of this subject when a =2 and b= -3?
a^3-b^3/5
Answer:
7
Step-by-step explanation:
a^3 = 2^3 = 8
b^3 = -3^3 = -27
(8 - (-27))/5= (8+27)/5 =35/5=7
Find the value of x and y (2^x+y 2^x-y) =(16,1) in order pair
Answer:
i don't know sorry :(
Step-by-step explanation:
Can someone help me with this please?
Answer: 14.79
Step-by-step explanation:
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]
Which rectangular equation represents the parametric equations x = t²-4 and y = 2t?
Oy = 2(x² + 4)
* y = 2(x² - 4)
Oy = 2√x+4
O y = 2√√x-4
Answer:
[tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Step-by-step explanation:
We are given parametric equations of:
[tex]\displaystyle{x=t^2-4}[/tex] and [tex]\displaystyle{y=2t}[/tex]
Isolate t-variable in [tex]\displaystyle{x=t^2-4}[/tex] first by adding both sides by 4:
[tex]\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}[/tex]
Square root both sides then write plus-minus:
[tex]\displaystyle{\sqrt{x+4}=\sqrt{t^2}}\\\\\displaystyle{t=\pm \sqrt{x+4}}[/tex]
Since the choice determines y-term as a function and only positive t-value exists, substitute only [tex]\displaystyle{t=\sqrt{x+4}}[/tex] in [tex]\displaystyle{y=2t}[/tex].
Therefore, the answer is [tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Answer:
c
Step-by-step explanation:
For the regular hexagon below, if BC = 9 m and AP = 8 m, find it's area.
pls help 10 points for whoever helps
Answer:
see image
Step-by-step explanation:
Putting the data on the line plot is not too bad. Just put an x above the number on the numberline. If a number in the data set repeats, just stack those x's up over the numberline. It seems like the hardest part is labelling the number line. Each tick mark can be 1/8. On the image I wrote all the fractions in eighths at the bottom, then to label the numberline I used the simplified fractions. For example I started with 1 3/8 because it was the smallest number in the data set. Next is 1 4/8, but simplified that is 1 1/2. So 1 1/2 is how we label the numberline.
There were 12 pieces of data, but really only six numbers because some were repeated.
Stack x's above the numberline. Done! You have a line plot. See image.
Answer:
1. 1/⅜
2. 1/⅜
3 is 2/¼
4 is 2/¼
5 is 2/¼
6 is 2/⅞
7 is 2/⅞
8 is 2/⅞
9 is 3/⅛
10 is 3/⅛
11 is 3/⅛
Step-by-step explanation:
Mixed number to Improper Fraction
1.9/4
2.13/4
3.23/8
4.25/8
5.23/8
6.25/8
7. 5/2
8.9/4
9. 23/8
10. 5/2
11. 11/8
12. 25/8
then you make it into the same denominator
1. 18/8
2. 26/8
3. 23/8
4. 25/8
5. 23/8
6. 25/8
7. 20/8
8. 18/8
9. 23/8
10. 20/8
11. 11/8
12. 25/8
then what ever numerator is smallest you put at front and it goes onto the biggest one
e.g ASCENDING ORDER
However you'll need to put it back into the normal mixed number, so all you have to do is revert let's say 25/8 into 3/⅛, and put it onto the graph
1. 1/⅜
1. 1/⅜2. 1/⅜
. 1/⅜3 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞7 is 2/⅞
8 is 2/⅞
9 is 3/⅛
9 is 3/⅛10 is 3/⅛
11 is 3/⅛
and number 12 which is the biggest and the last one the you should put(on the end of graph) is
3/¼
I did rush this so I hope this is the correct answers
what is the following product?
√10 10
A)10
B) 10/10
C) 10√10
D) 100
Answer: C
Step-by-step explanation:
[tex]\sqrt10 10=10\sqrt{10}[/tex]
What is the answer to this pythagoras question?
The length of the segment AB will be equal to 9.848 units.
What is the Pythagorean theorem?It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The length of segment AB will be calculated as:-
Points are A(1,7) and B(10,3)
AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
AB = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]
AB = √(81+16)
AB = √97
AB = 9.848
Therefore the length of the segment AB will be equal to 9.848 units.
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Find ST. Help me please. Thank you :)
The value of ST is 3
How to solve for ST?The given parameters are:
RT = 8
RS = 5
To calculate ST, we make use of the following straight line theorem
RT = RS + ST
This gives
8 = 5 + ST
Subtract 5 from both sides
ST = 3
Hence, the value of ST is 3
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Determine the equation, in vertex form, of a parabola that has been:
(a) reflected in the x-axis and horizontally shifted right 4 units.
(b) vertically compressed by a factor of 1/4 and vertically translated 5 units down
(c) vertically stretched by a factor of 4, translated 3 units left and 2 units up
Answer:
[tex]a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).[/tex]
Good luck!
HELPPPPP!!
Sarai loves music and decides to paint a music staff on her bedroom wall. She knows that it is important to make the lines parallel, or the end result will not look correct. She pencils in the image below, but before she uses paint, she wants to make sure the lines are parallel. Remembering what she has learned in Geometry class, she uses a piece of tape to make a transversal and decides to measure some angles.
Using Sarai’s measurements, Line 1 must be parallel to Line 3 according to which postulate or theorem?
Can you also please explain how you got the answer? thank you <3
Using Sarai's measurements, Line 3 must be parallel to Line 5 by option (A) Converse of Alternate Exterior Angles Theorem.
What is the Alternate Exterior Angles theorem?The alternate Exterior Angles theorem states, "If two lines are parallel and they are intersected by the same straight line then the alternative exterior angles formed by the figure are equal to each other."
The converse of this theorem states that "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."
Here in Sarai's measurement, we can conclude that Line 3 and Line 5 are intersected by one straight line, and the formed alternate exterior angles both are 65, which shows they are equal to each other.
Hence by Converse of the Alternate Exterior Theorem, we can say that both lines are parallel to each other.
So, Line 3 must be parallel to Line 5 according to the Converse of Alternate Exterior Angles Theorem.
Hence Option (A) is correct.
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How tall is the tower?
Answer:
93.6 ftStep-by-step explanation:
[tex]\bf \cfrac{AB}{BC} = \tan(60) [/tex]
[tex] \bf \cfrac{x}{50} = \sqrt{50} [/tex][tex]\bf x = 50 \sqrt{3} [/tex]Length of tower:-
[tex]\bf x + 7[/tex][tex]\bf 50 \sqrt{3} + 7[/tex][tex]\bf 93.6025[/tex][tex] \bf = 93.6[/tex]Therefore, the tower is 93.6ft tall.
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Which of these lines are skew to line EF?
The skew lines are CG, DH, AD, BC.
What is skew lines?Two or more lines which have no intersections but are not parallel.
Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.
As, by the definition
The lines skew to EF is CG, DH, AD, BC
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Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?
9.6, –4.8, 2.4, –1.2, 0.6, ...
f(n + 1) = (–0.5)f(n)
f(n + 1) = (0.5)f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)
Answer: f(n + 1) = (–0.5)f(n)
Step-by-step explanation:
This is a geometric series with common ratio -0.5.
A cube shaped suitcase has a length of 3x + 2 units. What is an expression for its area of the
base?
Answer:
[tex]\huge\boxed{\sf 9x^2+12x+4 \ units^2}[/tex]
Step-by-step explanation:
Given that,
Length of cube = l = 3x + 2 units
Base Area:[tex]= l \times l\\\\= (3x+2)(3x+2)\\\\= 3x(3x+2)+2(3x+2)\\\\= 9x^2+6x+6x+4\\\\= 9x^2+12x+4 \ units^2\\\\\rule[225]{225}{2}[/tex]
30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answer:
A. 2640
Step-by-step explanation:
44 feet per second 30 miles per hour is 2640 feet per minute