Sai vì số Nguyên dương nhỏ trừ số nguyên dương lớn bằng số nguyên âm
2^12÷2^(k/2 )= 32 find k
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]
Divide. Write your answer as a fraction in simplest form. − 10 2/7÷(−4 4/11)=
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
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
Trigonometric ratios
class 9
please answer my questions
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.
u4gent help needed
help me with the question of o.math
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
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
the answer is
A. 28, 25, 22
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
The circumference of a circle is 20π. What is the area of the circle?
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.
How many gallons equal 26 liters
Answer:
6.8 gallions i believe. im not quite sure
find the mean value of the following. 5, 11, 4, 10, 8, 6
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.
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.
Help what is x
When x^5 is 225
Answer:
Solution given:
x^5=225
we have
x=[tex] \sqrt[5]{225} [/tex]
x=2.9541
Hello!
[tex] \bf {x}^{5} = 225[/tex]
Extract the radical on both sides of the equation.[tex] \bf x = \sqrt[5]{225} [/tex]
[tex] \bf x ≈2.95418[/tex]
Answer: x ≈ 2,95418
Good luck! :)
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
find the missing length indicated
Answer:
240
Step-by-step explanation:
We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:
Hypotenuse/leg = leg/part
Where,
Hypo = 400
Leg = x
Part = 144
Substitute
400/x = x/144
Cross multiply
400*144 = x*x
57,600 = x²
√57,600 = x
240 = x
x = 240
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
Which ordered pair can be plotted together with these four points, so the resulting graph still represents a function?
•(2, -1)
•(2, -2)
•(-2, 2)
•(-1, 2)
Answer:
-1,2 can be plotted together with these four points ...
428363939+42724289292952926263938
Answer:
4.2724289e
+22
Step-by-step explanation:
mzmznznxnxnznxn no n n j j h h h h h h hh h h &
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)
Answer:
(-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
The coordinates of the other endpoint will be (-1,-6). The correct option is C.
What is the midpoint of the line?Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).
The x- coordinate will be calculated as:-
(13 + x)/2 = 6
13+x= 12
x = -1
The y-coordinate will be calculated as:-
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.
To know more about midpoints of the line follow
https://brainly.com/question/24431553
#SPJ2
Please help me with this problem.
Answer:
1/4a -1/6b + 1/10c
Step-by-step explanation:
1/2 a -1/3 b + 1/5c + -1/4a + 1/6 b - 1/10c
Combine like terms
1/2a - 1/4a -1/3b + 1/6b +1/5c - 1/10 c
2/4a -1/4a -2/6b + 1/6b +2/10c -1/10c
1/4a -1/6b + 1/10c
1 pump can fill a pool in 8 hours the other pump can fill the pool in 10 hours if both of the pumps were turned on at the same time to fill the pool how long will it take
Answer:
4 4/9 hoursStep-by-step explanation:
In one hour pump1 can fill 1/8 of the tank and pump2 can fill 1/10 of the tank.
Two pumps can fill:
1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the tank in one hourTime required to fill the tank:
1/(9/40) = 40/9 = 4 4/9 hoursSelect all that apply.
What are the angle measures in a 30-60-90 right triangles?
90°
150°
60°
120°
30°
Answer:
90°,60°&30°
Step-by-step explanation:
A 30-60-90 triangle is a right triangle with angle measures of 30º, 60º, and 90º (the right angle). Because the angles are always in that ratio, the sides are also always in the same ratio to each other.
Write an equation of a line perpendicular to y = -1/5x + 5
that passes through the point (-1,-3)
Select one:
a. y = 5x + 2
b.y = 2x - 5
c.y = -5x - 5
d. y = -5x + 2
Please help me out . Find x please
Answer:
on my screen I cant see anything sorry!
Step-by-step explanation:
There are 8.54 grams of sugar in 7 servings of grapes. How many grams of sugar are in a single serving of grapes?
Answer:
1.22
Step-by-step explanation:
divide 8.54 by 7 to get one serving
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is , where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle? 7 in. 8 in. 9 in. q 10 in.
Answer:
B) 8in
Step-by-step explanation:
Two traffic lights both turn green at 1:20 pm. One light is on a 72-second 0cycle from green back to green while the other light is on a 1-minute cycle. After how many minutes will they again turn green together?
Answer:
32
Step-by-step explanation:
Answer:
6 minutes
Step-by-step explanation:
1 minute = 60 seconds
LCM of 60 and 72 = 360
360 seconds = 6 minutes
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=-x-1
y= x+3
A. (0,3)
B. (-2,1)
C. (-1,2)
O D. (0, -1)
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
You are setting the combination on a five-digit lock. You want to use the numbers 12345 but you don't care what order they are in.
Answer:
It's a combination, BUT...
Step-by-step explanation:
Definition: A combination is a grouping of outcomes in which the order does not matter. That's the difference between combination and permutation.
Combination Formula: nCr = (n!)/[r!(n-r)!)] where n stands for number of things and r the pair chosen
Applied to this case: We have n=5 (12345) and r=5 for the 5-digit lock combination.
5C5 = (5!)/[5!(5-5)] = 1
But!! As you can see, we cannot have 1 possible combinations so.. We have to assume that this is a permutation!!! Conceptually, this looks pretty much like a combination, but being the same range as number of items, we conclude that it's a permutation.
Permutation Formula: nPr = (n!)/(n-r)!
nPr = (5!)/(5-5)! = 120
Well, this looks way more accurate now, right?
Final Answer: The scenario involves a permutation, and there's 120 possible combinations of those 5 numbers in a 5-digit lock.
Please help urgent!!! Find the value of x in the triangle shown below!
Answer:
Step-by-step explanation:
so we know a few things about t his triangle, it's a special one :P , it's called isosceles because two of the legs are the same length, which also mean that the angle x is the same at the other unknown angle sooo there are 2 x's if that makes sense? and then we can solve this , b/c we also know that the interior angles of a triangle add up to 180°
180 = 32 + 2x
148 = 2x
74 =x
∠x = 74°
Solve the following quadratic function
by utilizing the square root method.
y = 100 – x2
Answer:
x = ± 10
Step-by-step explanation:
To solve the equation let y = 0 , that is
0 = 100 - x²( add x² to both sides )
x² = 100 (I take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
Then solution is x = - 10, x = 10
Answer:
10
Step-by-step explanation:
the guy on top put -10 he's right but it's just 10
