Step-by-step explanation:
We can solve this kind of trigonometric problem
easily by the followings method :
Given :
cos^4a + cos^2a = 1
or, cos4^a = 1 - cos^2a
Therefore; cos^4a = sin^2a
Again,
To prove: cot^4a - cot^2a = 1
L.H.S = Cot^4a - cot^2a
= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a
= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a
= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a
= 1 - cos^2a ÷ Sin^2a
= Sin^2a ÷ Sin^2a
= 1 = R.H.S proved.
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Kyla has the number of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether?
Answer:
92
Step-by-step explanation:
46 + 46 = 92
Solve the following quadratic by
completing the square.
y = x2 - 6x +2
Answer: [tex]3 \pm \sqrt{7}[/tex]
Step-by-step explanation:
[tex]1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}[/tex]
Item 18
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.
A mixed number in simplest form, in the box is 40 5/8 cm^3.
We have given that,
The figure contains a right rectangular prism. The length of the prism is labeled 6 and one-half centimeters, the width is labeled 2 and one-half centimeters, and the height is labeled 2 and one-half centimeters.
What is the volume of the prism?The figure is a rectangular prism, so the formula would be Volume = length x width x height.
length = 6 .5cm
width = 2.5cm
height = 2.5cm
If you plug everything you have in the problem into the volume equation, you would get
volume = 6.5cm x 2.5cm x 2.5 cm.
Without a calculator first, turn the mixed numbers into improper fractions.
6 .5=13/2
2.5 = 5/2
Volume = 13/2 x 5/2 x 5/2
When you multiply everything together you should get.
As a mixed number, that would be 40 5/8.
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what is 3x+2y=6 ordered pair?
The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.
Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).
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Which expressions are equivalent to the one below? Check all that apply.log(10^7)
The value of expression is 7.
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Given:
[tex]log 10^{7}[/tex]
Now, using property of log
[tex]log b^{a} =[/tex] a log b
So,
[tex]log 10^{7}[/tex]= 7 log 10
As log 10 = 1
[tex]log 10^{7}[/tex]= 7 (1)
[tex]log 10^{7}[/tex]= 7
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Does the table of values below represent a proportional relationship?
x
2
3
4
5
y
10
15
24
25
Answer:
No
Step-by-step explanation:
The constant of proportionality is k = y/x. In this case, k is 5. When you multiply k which is 5 with the x value you should get the y value. You will see that 2 X 5 = 10, 3 X 5 = 15, and 5 X 5 = 25 but 4X 5 is not equal to 24. This means the ordered pair (4, 24) does not lie on the straight line that is formed where all the other ordered pairs (2,10), (3,15), and (5,25) lie.
For a proportional relationship in a table, the k is constant for all the ordered pair x and y values. All the ordered pairs in the table should also lie on the same straight line.
So the answer is no.
Solve the equation for 0 <= x < 2pi.
(2sin x - 1)(2cos^2 x - 1) = 0
If
(2 sin(x) - 1) (2 cos²(x) - 1) = 0
then either
2 sin(x) - 1 = 0 or 2 cos²(x) - 1 = 0
sin(x) = 1/2 or cos(2x) = 0
The first equation gives two families of solutions,
x = arcsin(1/2) + 2nπ = π/6 + 2nπ
x = π - arcsin(1/2) + 2nπ = 5π/6 + 2nπ
where n is any integer; we get the solutions x = π/6 and x = 5π/6 in the interval 0 ≤ x < 2π when n = 0.
The second equation also gives two families of solutions,
2x = arccos(0) + 2nπ = π/2 + 2nπ
2x = -arccos(0) + 2nπ = -π/2 + 2nπ
Divide both sides by 2 :
x = π/4 + nπ
x = -π/4 + nπ
Then the solutions we want are x = π/4 and x = 5π/4 (when n = 0 and 1 in the first family, respectively) and x = 3π/4 and x = 7π/4 (when n = 1 and 2 in the second family).
We have 6 solutions, so A is the correct choice.
The value of x must be greater than
0
1
3
7
Answer:
The value of x should be greater than 3.
Step-by-step explanation:
Given that,
The AB is 12 units.
The AC is 15 units.
We need to find the value of BC.
Based on the above information, the calculation is as follows:
As we know that
The sum of two sides length is always more than the 3rd one.
Based on this,
12 + 15 > x
x < 27
15 + x >12
x >-3
12 + x > 15
x >3
find [-4/5]×3/7×15/16×[-14/9]
The given expression is [tex]\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{-14}{9})[/tex].
We need to simplify the given expression.
What is a rational number?In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Now group the rational numbers [tex](\frac{-4}{5}\times \frac{15}{16} ) \times (\frac{3}{7}\times (\frac{-14}{9}))[/tex]
[tex]=(\frac{-4}{16}\times \frac{15}{5} ) \times (\frac{3}{9}\times (\frac{-14}{7}))[/tex]
[tex]=(\frac{-1}{4}\times \frac{3}{1} ) \times (\frac{1}{3}\times (\frac{-2}{1}))[/tex]
[tex]=(\frac{-3}{4} ) \times (\frac{-2}{3})=\frac{1}{2}[/tex]
Therefore, the simplified value of the given expression is [tex]\frac{1}{2}[/tex].
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Which of the following is the missing justification?
picture is provided
Subtraction property of equality
====================================================
Explanation:
Let's say we started with the equation a = b
Subtract c from both sides to get a-c = b-c
This is the subtraction property of equality
-----------------
Example:
x+5 = 12
x+5-5 = 12-5 ... using the subtraction property of equality
x+0 = 7
x = 7
------------------
For this current problem, we're subtracting 3 from both sides in the second step.
A very closely related property is the addition property of equality where we add the same thing to both sides.
Technically we could add -3 to both sides to get the same task done in the second step. But the subtraction property is more direct and straight-forward in my opinion.
Why [tex]\lim _{x\to -3}\left(x^2-2x+4\right)[/tex] is 19 and not 1??? I don't understand how lim x to -3 (x^2) become 9 and not -9???
PLEASEEEEEEEEEEEEE
The quadratic is continuous over its entire domain, which is to say we can evaluate the limit by direct substitution:
[tex]\displaystyle \lim_{x\to-3} (x^2 - 2x + 4) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = \boxed{19}[/tex]
You are mistaking (-3)² for -3². They are not the same number.
(-3)² = (-1 × 3)² = (-1)² × 3² = 1 × 9 = 9
-3² = -1 × 3² = -1 × 9 = -9
Please help me i would really appreciate it, I really dont want to fail the assignment!!!
The ordered pair of the solution for the system of equation area are (2, -3) and (3, -3)
How to solve system of equation?f(x) = x² - 5x + 3
f(x) = -3
Therefore,
-3 = x² - 5x + 3
x² - 5x + 3 + 3 = 0
x² - 5x + 6 = 0
x² - 2x - 3x + 6 = 0
x(x - 2) - 3(x - 2) = 0
(x - 3)(x - 2) = 0
x = 3 or 2
when x = 2
f(x) = 4 - 10 + 3 = -3
when x = 3
f(x) = 9 - 15 + 3 = -3
Therefore, the ordered pair of the solution for the system of equation are (2, -3) and (3, -3)
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Which is the simplified form of x-12?
O 12
O
O
*12
12
17/7/22
Applying the negative exponent rule, the simplified form of [tex]x^{-12}[/tex] is: [tex]\frac{1}{x^{12}}[/tex].
What is the Negative Exponent Rule?The negative exponent rule states that, if [tex]x^{-a}[/tex] then, it can be rewritten as, [tex]\frac{1}{x^a}[/tex].
Given the expression, [tex]x^{-12}[/tex], we can apply the negative exponent rule to rewrite the expression in simplified form as:
[tex]\frac{1}{x^{12}}[/tex].
Therefore, expressing [tex]x^{-12}[/tex] in a simplified form will give us: [tex]\frac{1}{x^{12}}[/tex].
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A cone with radius 2 units is shown below. Its volume is 29 cubic units.
2
h
Find the height of the cone.
Use 3.14 for π and round your final answer to the nearest hundredth.
units
Answer:
It's very interesting 4
{
5x−y=19
13x−3y=51
Can anybody help me to understand this equation ASAP
Answer:
×=-3
y=-4
Step-by-step explanation:
13×-3y=51
(-) 5×-y=19
-5×+y=-19
13×-3y=51
8×-2y=32
2/8x-2y=32
4x-y=16
4×-y=16
-5×+y=-19
-×=-3
×=3
Answer:
x = 3
y = -4
(3,-4)
Step-by-step explanation:
Hello!
We can use the Elimination Method to solve the system.
To eliminate, we want atleast one variable to have the same coefficients on both equations. To do that, we can multiply the first equation by 3 to get -3y.
[tex]5x - y = 19[/tex][tex]3(5x - y = 19)[/tex][tex]15x - 3y = 57[/tex]Now, we can vertically subtract them to eliminate -3y.
[tex]-\left \{ {{15x - 3y = 57} \atop {13x - 3y = 51}} \right.[/tex][tex]2x + 0 = 6[/tex]Solve for x
[tex]2x + 0 = 6[/tex][tex]2x = 6[/tex][tex]x = 3[/tex]The value of x is 3.
To solve for y, we can plug in 3 into the original first equation and solve for y.
Solve for y
[tex]5x - y = 19[/tex][tex]5(3) - y = 19[/tex][tex]15 - y = 19[/tex][tex]-y = 4[/tex][tex]y = -4[/tex]The value of y is -4.
The solution to the system is (3,-4).
the answer to this question
Answer:
positive 1!
Step-by-step explanation:
i got it right on the test trust me!
2.2.5a (Part 1): For the graph below, what is the x-intercept? *
-4 -2
2
-2
-4
y
2
4
0 points
X
An x-intercept is the point where the line of a graph passes through the x-axis. Thus, you should look for this point on the given graph.
What is a graph?A graph can be defined as a type of chart that is used for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
In Mathematics, x-intercept refers to the point where the line of a graph passes through the x-axis as shown in the image attached below. Since the graph wasn't provided for this question, you should look for the point where the line passes or crosses through the x-axis.
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The price of one kilograms of apple at a fruit mart is $4.00. If there is a special price this week with a
15% discount, how much do I need to pay if I buy 3 Kg of apple?
(02.01)
Solve for x: (x+20)/2=3x
a and b are positive integers and 7a+5b=49. Find the values of a and b.
a and b are positive integers and 23a+17b=320. Find the values of a and b.
please hel you can get 30 points
Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
7a + 5b = 49.23a + 17b = 320.Multiplying the first equations by 17 and the second by -5, we have that the system is:
119a + 85b = 833.-115a - 85b = -1600.Then, adding them:
4a = -767
a = -767/4
a = -191.75
Then:
[tex]b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25[/tex]
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What is the area of Victor’s storage space?
The area of victor's storage space is 28 square inches
What is a polygon?A polygon is a plane shape with at least three sides.
Analysis:
Area of storage = area of triangle + area of rectangle
Height of triangle = 5 - 3 = 2 inches
Base of triangle = 12 - 4 = 8 inches
length of rectangle = 5 inches
width of rectangle = 4 inches
Area of storage = 5 x 4 + 1/2 x 8 x 2 = 28 square inches
In conclusion, the area of the storage space is 28 square inches.
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24. Kyla has 2/7the amount of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether
Answer:
207
Step-by-step explanation:
Denise has 46(7/2) = 161 cherries.
So, they have a total of 161 + 46 = 207 cherries
Can someone help me please?
Answer:
C.
Step-by-step explanation:
The reds are counting up in whole numbers by one integer.
Hope this helps!
If not, I am sorry.
This question is based on the box plot below: How is the data distributed?
The distribution is right skewed.
What is the data distribution?A box plot is graph that is used to display data. The box plot is made up of two whiskers that are on either sides of a box. The first line on the box is the first quartile, the second line is the median and the third line is the third quartile.
When the median is closer to the bottom of the box, and if the whisker is shorter on the lower end of the box, the data is right skewed.
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The subject of the formula below is y.
y=X+p-q
Rearrange the formula to make x the subject.
Answer:
x=y-p+q
Step-by-step explanation:
y=x+p-q
x=y-p+q
Please give answer
It’s for a school work
Answer:
x=60
Step-by-step explanation:
x+2x=3x
180/3=60(interior angles add up to 180)
What is the difference between -5 and 3?
Answer:
8
Step-by-step explanation:
3 - -5 = 8
filling space here dont mind this
What is the probability of drawing a red card, replacing it, and then drawing an odd card?
4 red 5 blue 6 red 7 blue 8 blue
Answer:
4
Step-by-step explanation:
5
share 518 in ratio 2:5
please answer fast with the steps
Answer:
148:370
Step-by-step explanation:
2+5=7 parts
518÷7=74
1 part =74
2×74=148
5×74=370
HELP ME PLEASE AND JUST GIVE ME THE ANSWER NO EXPLANATION
The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).
How to locate the missing end of a line segment
In this question we know an end and a midpoint of a line segment. The missing end can be found from the following formula:
M(x, y) = G(x, y) + 0.5 · [H(x, y) - G(x, y)]
M(x, y) = 0.5 · G(x, y) + 0.5 · H(x, y)
0.5 · H(x, y) = M(x, y) - 0.5 · G(x, y)
H(x, y) = 2 · M(x, y) - G(x, y) (1)
If we know that M(x, y) = (5, 3) and G(x, y) = (1, -5), then the coordinates of the point H are:
H(x, y) = 2 · (5, 3) - (1, -5)
H(x, y) = (10, 6) - (1, -5)
H(x, y) = (9, 11)
The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).
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Answer:
its A
Step-by-step explanation:
