Simplify: squrt 18x⁷
Answers
Answer:
3x^3 ⋅ √2x
Step-by-step explanation:
Related Questions
SEE QUESTION IN IMAGE
Answers
Answer:
B. 48°Step-by-step explanation:
∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)
m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)
m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)
Correct choice is B
The circumference of a circle is 20π. What is the area of the circle?
Answers
Answer:
The area of the circle is 100 square units.
Step-by-step explanation:
We are given that the circumference of a circle is 20π, and we want to determine its area.
Recall that the circumference of a circle is given by the formula:
[tex]\displaystyle C = 2\pi r[/tex]
Substitute:
[tex]20 \pi = 2 \pi r[/tex]
Solve for the radius:
[tex]\displaystyle r = \frac{20\pi}{2\pi} = 10[/tex]
The area of a circle is given by:
[tex]\displaystyle A = \pi r^2[/tex]
Since the radius is 10 units:
[tex]\displaystyle A = \pi (10)^2[/tex]
Evaluate:
[tex]\displaystyle A = 100\pi\text{ units}^2[/tex]
In conclusion, the area of the circle is 100 square units.
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answers
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
find the mean value of the following. 5, 11, 4, 10, 8, 6
Answers
44/6 = 7.33….
answer: 7.33…..
2x²+3x²+3.(-1) =5x.x+5x .1
Answers
[tex]\\ \sf\longmapsto 2x^2+3x^2+3(-1)=5x.x+5x.1[/tex]
[tex]\\ \sf\longmapsto 5x^2-3=5x^2+5x[/tex]
[tex]\\ \sf\longmapsto 5x^2-5x^2-3=5x[/tex]
[tex]\\ \sf\longmapsto 5x=-3[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-3}{5}[/tex]
Trigonometric ratios
class 9
please answer my questions
Answers
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
If you have to invest in an account that pays 5.3 compound annually, after 10 years how much interest is earned
Answers
[tex]\\ \sf\longmapsto Interest=Rate\times Time[/tex]
[tex]\\ \sf\longmapsto Interest=5.3(10)[/tex]
[tex]\\ \sf\longmapsto Interest =53[/tex]
It means that if your principal is $100 after 10years you will receive $53 as interest
Step-by-step explanation:
[tex]thank \: you[/tex]
Find the first three terms of the sequence given by the following.
a
n = 25-3(n − 1), n= 1, 2, 3, ...
A. 28, 25, 22
B. 25, 22, 19
C. 25, 28, 31
D. 28, 31, 34
Answers
the answer is
A. 28, 25, 22
Divide. Write your answer as a fraction in simplest form. − 10 2/7÷(−4 4/11)=
Answers
Answer:
33/14
Step-by-step explanation:
[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]
[tex] = - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]
[tex] = \frac{72}{7} \times \frac{11}{48} [/tex]
[tex] = \frac{3}{7} \times \frac{11}{2} [/tex]
[tex] = \frac{33}{14} [/tex]
stan dreamcatcher
I need help please help me
Answers
Answer:
I found x for you, right there.
Answer: x is 12 and y is 5
Step-by-step explanation:
if A ={1,2,3,4} and B={3,4,5,6} find A-B.
Answers
Answer: {1,2} is the answer.
Step-by-step explanation:
A-B
{1,2,3,4}-{3,4,5,6)
= {1,2}
a sum of money Doubles itself in 5 years what is rate of simple interest
Answers
Step-by-step explanationIf you are reading this say
thank u
u4gent help needed
help me with the question of o.math
Answers
Answer:
1≤f(x)≤5
Step-by-step explanation:
-1≤x≤1
-2≤2x≤2 (Multiplied by 2 both side)
-2+3≤2x+3≤2+3 (Adding three both sides)
1≤f(x)≤5
Atlantic Hurricanes
Number
1925
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
Year
Between which years was
the biggest change in the
number of hurricanes?
Answers
Answer:
1950
Step-by-step explanation:
because 1950 column has the most highest number which is 11
Answer:
Between 1945 and 1950 ( from 5 to 11 ),
Step-by-step explanation:
2^12÷2^(k/2 )= 32 find k
Answers
Answer:
k = 14
Step-by-step explanation:
Prime factorize 32
32 = 2 * 2 * 2 * 2 * 2 = 2⁵
[tex]\frac{2^{12}}{2^{\frac{k}{2}}}= 32\\\\\frac{2^{12}}{2^{\frac{k}{2}}}=2^{5}\\\\2^{12-\frac{k}{2}}=2^{5}[/tex]
Both sides base are same.So, compare exponents
[tex]12-\frac{k}{2}=5\\[/tex]
Subtract 12 from both side
[tex]-\frac{k}{2}=5-12\\\\-\frac{k}{2}=-7\\[/tex]
Multiply both sides by (-2),
[tex](-2)*(-\frac{k}{2})=-7*(-2)\\\\k = 14[/tex]
Is the following number rational or irrational?
-117
Choose 1 answer:
Rational
Irrational
Answers
Answer:
-117 is irrational number
Answer:
Irrational
Step-by-step explanation:
Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.
solve for w.
-9/7=-2/3w-1/2
Answers
Answer: [tex]w=\frac{33}{28}[/tex]
Step-by-step explanation:
To solve for w, we want to isolate w.
[tex]-\frac{9}{7}=-\frac{2}{3}w-\frac{1}{2}[/tex] [add both sides by 1/2]
[tex]-\frac{11}{14}=-\frac{2}{3}w[/tex] [multiply both sides by -3/2]
[tex]w=\frac{33}{28}[/tex]
Now we know that [tex]w=\frac{33}{28}[/tex].
Answer:
[tex]\sf w=\dfrac{33}{28} \\[/tex]
Step-by-step explanation:
[tex]\sf -\dfrac{9}{7} =-\dfrac{2w}{3} -\dfrac{1}{2}[/tex]
First, take -2w/3 to the left side.
[tex]\sf -\dfrac{9}{7}+\dfrac{2w}{3} = -\dfrac{1}{2}[/tex]
Then, add 9/7 to both sides.
[tex]\sf \dfrac{2w}{3} = -\dfrac{1}{2}+\dfrac{9}{7}[/tex]
Make the denominators the same and add the fractions.
[tex]\sf \dfrac{2w}{3} = -\dfrac{1*7}{2*7}+\dfrac{9*2}{7*2}\\\\\sf \dfrac{2w}{3} = -\dfrac{7}{14}+\dfrac{18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{-7+18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{11}{14}[/tex]
Use cross multiplication.
[tex]\sf 2w*14=11*3\\\\28w=33[/tex]
Divide both sides by 28.
[tex]\sf w=\dfrac{33}{28} \\[/tex]
If n equals 5 and b equals 4 what is n + b * 5
Answers
Answer:
25Step-by-step explanation:
Given,
n = 5
and, b = 4
Equation:
n + b × 5
= 5 + 4 × 5
= 5 + 20
= 25 (Ans)
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answers
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
Given the mean of a random variable, X, is 10 and P(X < 11) = 0.67. Find the standard deviation.
Answers
Answer:
Step-by-step explanation:
This is the problem we need to solve:
[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.
If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:
P(z < .43) = .66640 and P(z < .44) = .67003
We'll use z = .44
[tex].44=\frac{11-10}{\sigma}[/tex] and
[tex].44=\frac{1}{\sigma}[/tex] and
[tex]\sigma=\frac{1}{.44}[/tex] so
σ = 2.27 (check it; it works!)
Am I suppose to substitute the variables with random numbers in order to answer these questions???
Translation A maps (x, y) to (x + n, y + 1). Translation B maps (x, y) to (x +s, y + m).
1. Translate a point using Translation A, followed by Translation B. Write an algebraic rule for the final image of the point after this composition.
2. Translate a point using Translation B, followed by Translation A. Write an algebraic rule for the final image of the point after this composition.
3. Compare the rules you wrote for parts (a) and (b). Does it matter which translation you do first? Explain your reasoning.
Answers
9514 1404 393
Answer:
(x, y) ⇒ (x +n +s, y +1 +m)(x, y) ⇒ (x +s +n, y +m +1)they are identical in effect; order does not matterStep-by-step explanation:
Substitute the expressions.
A then BAfter the first translation, the value of x is (x+n). Put that as the value of x in the second translation.
x ⇒ x +s . . . . . . . . . the definition of the second translation
(x+n) ⇒ (x+n) +s . . . the result after both translations
The same thing goes for y. After the first translation, its new value is (y+1).
y ⇒ y +m . . . . . . . . the definition of the second translation
(y+1) ⇒ (y+1) +m . . . the result of both translations
Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).
__
B then AThe same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...
x ⇒ x +n . . . . . . . . . . definition of translation A
(x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B
y ⇒ y +1 . . . . . . . . . . . definition of translation A
(y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B
The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).
__
You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.
The two translations give the same result in either order.
How many gallons equal 26 liters
Answers
Answer:
6.8 gallions i believe. im not quite sure
help please ITS OF TRIGONOMETRY
PROVE
Answers
Answer:
The equation is true.
Step-by-step explanation:
In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation. Please note that each side is named with respect to the angle is it across from.
Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
One is given the following equation,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
As per the attached reference image, one can state the following, using the right angle trigonometric ratios,
[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]
Substitute these values into the given equation. Then simplify the equation to prove the idenity,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]
[tex]1+(-1)=0[/tex]
[tex]1-1=0[/tex]
[tex]0=0[/tex]
Find the surface area of the triangular prism
Answers
1/2 x 6 x 4 = 12
Back: 12 square centimeters
1/2 x 6 x 4 = 12
Right: 15 square centimeters
3 x 5 = 15
Left: 15 square centimeters
3 x 5 = 15
TOTAL: 54 square centimeters
The surface area is the added areas of each face of a 3D figure.
Formulas I’ve used:
Area of a parallelogram:
A = bh
Area of a triangle:
A = 1/2bh
Which is the graph of y = [x]-2?
PLEASE HELP TIMED PLEASE
Answers
Answer:
3rd graph
Step-by-step explanation:
I don't understand need help?
Answers
9514 1404 393
Answer:
2. (only)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.
1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle
2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle
3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle
4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle
K is between J and M. L is
between K and M. M is
between K and N. If JN = 30, KM = 8, and JK = KL = LM, what is MJ?
(please do step-by-step fully)
Answers
Answer:
12
Step-by-step explanation:
for this you need to draw a straight line and plot the points J,K,L,M,N according to the question.
here,
given K lies between J and M, L is between K and M , M is between K and N.
JN= 30, KM=8
JK=KL=LM
MJ= ?
according to the question,
J--------K-------L--------M-------N
KM= 8
KL+LM= 8 (KL+LM=KM)
KL+KL=8 ( given, LM=KL)
2KL= 8
KL=4
so,
JK= KL=4 and LM= KL= 4
now,
MJ= ?
we know
MJ= JK+KM = 4+8= 12
Si Juana tiene dos perros y lo simbolizamos y 2p y le regalan un hato y lo simbolizamos por g como se representa en el leguaje algebraico.
A) 3P
B) 3G
C) 2PTG
D) 2P-G
Answers
An angle measures 73.6° more than the measure of its complementary angle. What is the measure of each angle?
PLEASE help, I'm struggling a lot!
Answers
Answer:
Let ABC = 73.6
Complement = ABD = 16.4
ABx = unknown angle
ABx + (ABx + 73.6) = 90
ABx = 16.4 / 2 = 8.2
The angles are 8.2 and (8.2 + 73.6) = 90
Given: j(x) = x2 - 2x + 1
Which set of values represents the range of the function for the domain {0, 1, 5}?
Answers
Answer:
{1, 0, 16}
Step-by-step explanation:
given..
j(x) = x^2-2x+1
put all given values of domain (1,0 and 5 ) in the equation..
the values you get are range of the function
Answer: 1
Step-by-step explanation
0(2)-2(0)+1=0+0+1= 1
1(1)-(2)(1)+1=1-2+1= 1
(5)(2)-(2)(5)+1=10-10+1= 1
