Answer:
See proof below
Step-by-step explanation:
[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]
[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]
[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]
Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]
Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]
This is a quadratic equation which can be solved using sum of squars
Note that
[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]
So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]
PROVED
PRACTICING SKILLS & CONCEPTS
1. Complete the square box problem.
.6
2,
According to the question, the first part has square box with two diagonal lines and two values. In a square, all the sides are equal as well as opposite diagonal values are equal.
Therefore, from the figure ABCD is a square in which AC and BD is a diagonal. So the remaining empty boxes will have (-2,6).
In the second part, using probability the arrangement of the alphabets can be done. As per question, total three alphabets are there that is A, B,D. The three alphabets can be arranged as:
Probability = 3! = 6 ways
Hence, the arrangement of alphabets can be done in 6 ways.
What is probability?
Probability defines the occurrence of the events or the outcomes of the occurred events. It is the ratio of favored outcomes to total number of occurred outcomes.
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Helpppppppppppppp meeeeeeee will give brainliest
Answer:90
Step-by-step explanation:
the angle is perpendicular
Choose all the true statements.
A. √√-2= √2
B. √-2=√√2i
C. √-8=2i√/2
D. √√-8=-2√2
E. √-16=4i
F. √-16=-4
Answer:
B,E,A
Step-by-step explanation:
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
G(-3,-4,6) and H(5,-3,-5)
The midpoint is at (1 , -7/2 ,1/2)
In the given statement is
To find the midpoint of the line segment joining the pair of points
G(-3,-4,6) and H(5,-3,-5)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points G(-3,-4,6) and H(5,-3,-5)
Solving for the midpoint , we have,
m = ([tex]\frac{-3+5}{2},\frac{-4+(-3)}{2} ,\frac{6+(-5)}{2}[/tex])
m = (1 , -7/2 ,1/2)
Therefore, the midpoint is at (1 , -7/2 ,1/2)
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The slope of a non-vertical line is the ratio of the ___ to the ____ between any two points on the line
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844)[2] and Todhunter's (1888)[3] formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
According to the given statements;
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points.
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If the dimensions of a photo are 2 inches by 3 inches and the dimensions of a poster are 8 inches by 12 inches, are the photo and poster similar? Explain.
The photo and poster of known dimensions are similar figures at a ratio of 4.
What is a proportion?A proportion is a value that allows us to know variable values of a set of elements that are related by means of a constant.
If we want to know if these two figures are similar or proportional, they must be at a ratio, (both dimensions), for this we formulate the following:
2 is to 83 is to 12This will generate an equation:
2x = 8
3x = 8
When solving for both values of "x" it must be exactly the same:
x = 8/2 = 4x = 12/3 = 4, The picture and poster are similar.Learn more about numerical proportions in:
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please help. two other ppl have answered with wrong answers pls only reply if you know it !!!!!!!!!!!!! high points and brainily for the people who know it fr
Answer:
-12
i hope this helps;/
Answer:
The answer is -12.
Step-by-step explanation:
Basically when it says, "when h = -1 ", we need to substitute t for -1.
So, here's what the equation would look like now,
h(-1) = (-1 + 7) (-1 - 1)
= (6)(-2)
= -12
So, our answer is -12.
Hope this helps!
Determine if the conjectures below are true or false. If false, give a counterexample. Two right angles are always supplemetary.
The conjecture is always true, two right angles are always supplementary.
A pair of angles are supplementary only when the sum of those angles equals to 180°. In such a case each angle is said to be the supplement of another.
In case of parallel lines and a transversal two co-interior angles are supplementary. The opposite angles of a cyclic quadrilateral are supplementary angles .
For two angles to be supplementary only the sum of the angles matter and they should always be 180°.
The numerical value of right angle is 90° .
Therefore the sum of two right angles will be 90°+ 90° = 180°
So the conjecture which states that two right angles are supplementary will always stand as the sum of two 90°s is always 180°.
Hence the conjecture is true.
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Which of the following graphs shows a system of equations with the same end behavior for both functions?
The graph with two functions with the same end behavior is the bottom one.
Which graph shows a system of equations with the same end behavior for both functions?The end behavior tell us how the function behaves as x tends to positive and negative infinity.
Now, let's look at the bottom graph on the given image.
You can see that the red graph goes up on the left side, and down on the right side.
And you also can see the same thing for the line, the blue graph, goes up on the left side, and down on the right side.
So there we can see two graphed equations with the same end behavior, thus, that is the correct option.
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Write each number as a percent.
1/3
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.
The number 1/3 as a percentage is 33.33 %.
What is a percentage?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Let the number be 1/3 then
1/3 = 0.3333
To find percentage multiply it by 100, we get
So, 0.3333 × 100 = 33.33 %
Therefore, the number 1/3 as a percentage is 33.33 %.
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Please help me this is urgent I will give all my points!
Answer:
See below
Step-by-step explanation:
Area of rectangle - area of semicircle =
25 x17 - 1/2 pi (3.5)^2 = 405.8 mm^2 to the nearest tenth ...
what is 8 to the 6 power?
(8⁶) who ever answers first gets brainiest
Answer:
262144
Step-by-step explanation:
8*8*8*8*8*8
64*8*8*8*8*8
512*8*8*8*8
4096*8*8*8
32,786*8
262144
Write the equation of the line in slope-intercept form.
4x=y-11
The equation of the line in slope-intercept form is y = 4x + 11 .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 4x = y - 11 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
4x = y - 11
On adding 11 on both sides in above equation, we will get
y = 4x + 11 equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 4
Intercept = c = 11
The equation of the line in slope-intercept form is y = 4x + 11 .
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WILL MARK BRAINLEST
Write a function g whose graph is a translation 4 units up of of the graph of f(x)=|x|-5
g(x)=
Answer:
Step-by-step explanation:
A company's stock began the day at $27.26 per share. That price drops by $1.02 each hour.
a. What is the price per share after 4 hours?
Mary has 21 coins whose total value is ksh 72.there are twice as many five shilings coins as there are ten shilings coins.the rest are one shilings coin.find the number of ten shilings coin that mary has
Step-by-step explanation:
Value from:
1 shilling coins
=
1
(
21
−
3
x
)
=
21
−
3
x
5 shilling coins
=
5
(
2
x
)
=
10
x
10 shilling coins
=
10
(
x
)
=
10
x
Total value
=
72
shillings
i.e.
21
−
3
x
+
10
x
+
10
x
=
72
shillings
−
3
x
+
10
x
+
10
x
=
72
−
21
17
x
=
51
x
=
51
17
x
=
3
∴
Mary has
3 10
shilling coins.
Compare the two numbers. Use > or < .
-√38, 6
Square root is a factor that, when multiplied by itself, equals the original value.
The values of -√38 = -6.16 then -√38 < 6.
What is a square root?In mathematics, a square root is a factor that, when multiplied by itself, equals the original value. Any time the idea of an object's square is mentioned, square roots can be considered more widely. These include square matrices and function spaces, among other mathematical structures.
Even though it is only one of the two square roots of a positive number, the term "square root" is occasionally used to describe the major square root of a positive number.
Let the values of -√38 = -6.16 then -√38 < 6
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Drag each equation to the correct location on the table.
Solve the equations for the given variable. Then place the equations in the table under the correct solution.
x = 3
x + 3
= 9 -6 + z = -9 2-5 = -2 -² + x = ²²
-14x = -42
Equations x - 5 = -2, -3/5 + x = 12/5, -14x = -42, x/4 = 6/8 will be placed in the x =3 column and equations x/3 = 9, -6 + x = -9 will be placed in the x 73 column.
Here, we are given 6 equations, let us solve each one-
1. x/3 = 9
x= 9 3
x= 27
=x3
2.-6 + x = -9
x= -9 + 6
x
x= -3
X+ 3
3.
3. x - 5 = -2 x= -2 + 5
x=3 4.-3/5 + x = 12/5
x= 12/5 + 3/5
x= 15/5
= x= 3
5. -14x = -42
x= -42/-14
x = 42/14
= x= 3
6. x/4 = 6/8
X/4 = 3/4
x = 12/4
x= 3
Thus, equations x - 5 = -2, -3/5 + x = 12/5, -14x = -42, x/4 = 6/8 will be placed in the x =3 column and equations x/3 = 9, -6 + x = -9 will be placed in the x 73 column.
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 1,4,9,16, . . . . . .
The sequence 1,4,9,16, . . . is neither an arithmetic nor a geometric sequence. In fact, it is a quadratic sequence. The next two terms are: 25 and 36
Given a sequence:
1,4,9,16, . . . .
To determine whether the sequence is an arithmetic, geometric, or neither, we need to check the relation between two consecutive terms.
Arithmetic sequence:
a(n) = a(n-1) + d
or a(n) - a(n-1) = d for all n
where d is a constant and is usually called common difference.
Geometric sequence:
a(n) = a(n -1) . r
or a(n)/a(n-1) = r, for all n
In the given sequence:
a(1) = 1
a(2) = 4
a(3) = 9
a(4) = 16
Check the difference:
a(2) - a(1) = 4 - 1 = 3
a(3) - a(2) = 9 - 4 = 5
Since the difference between 2 consecutive sequence is not a constant, then the sequence is not an arithmetic one.
Check the ratio:
a(2)/a(1) = 4
a(3)/a(2) = 9/4
Since the ratio of 2 consecutive sequence is not a constant, then the sequence is not a geometric one.
Thus the given sequence is neither an arithmetic, nor a geometric sequence. In fact, it is a quadratic sequence. Notice that:
a(n) = n²
Hence, the next two terms are: 25 and 36
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Find a possible value for y when x is -4 in the inequality below y<-2x+3
Answer: y<11
Step-by-step explanation:
y<-2x+3
y<-2(-4)+3
y<-(-8)+3
y<8+3
y<11
Each Graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and range of the relation and determine whether the relation is a function.
Please put it in a way it will enter the portal.
And please tell me which answer is for which.
The domain of the function will be - 2 ≤ x < 0. And the range of the function will be 0 ≤ y < 1. Then the relationship between x and y will be y = √(2² - x²).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
A relation is shown in each graph. Every ordered pair in the relationship has a first and second number that are both real numbers.
From the figure, the domain of the function will be - 2 ≤ x < 0. And the range of the function will be 0 ≤ y < 1.
The function is a part of the circle, then the relationship between x and y will be as,
y = √(2² - x²)
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Answer:
Step-by-step explanation:
A strawberry milk recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk. Part A: How many teaspoons of strawberry syrup per ounce of milk does this recipe use? Show Part B: your work. How many ounces of milk are needed per teaspoon of strawberry syrup? Show your work.
The number of teaspoons of strawberry syrup per ounce of milk this recipe use is 0.375 and the number of ounces of milk needed per teaspoon of strawberry syrup is 2.67
Part A: How many teaspoons of strawberry syrup per ounce of milk does this recipe use?The given parameters are
Teaspoons = 3
Ounces of milk = 8
The number of teaspoons of strawberry syrup per ounce of milk this recipe use is calculated as
Rate = Teaspoons/Ounces of milk
So, we have
Rate = 3/8
Evaluate
Rate = 0.375
Part B: How many ounces of milk are needed per teaspoon of strawberry syrupThe number of ounces of milk needed per teaspoon of strawberry syrup is
Rate = Ounces of milk/Teaspoons
So, we have
Rate = 8/3
Evaluate
Rate = 2.67
Hence, the number of teaspoons of strawberry syrup per ounce of milk this recipe use is 0.375 and the number of ounces of milk needed per teaspoon of strawberry syrup is 2.67
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Work out the equation of the line which has a gradient of -2 and
passes through the point (1, 7)
Answer:
y = -2x + 9
Step-by-step explanation:
1) Use the equation y = mx + c (m being gradient and c being y-intercept)
2) Substitute all the values to get 7 = -2(1) + c
3) Solve to get c:
7 = -2 + c9 = c4) Final answer: y = -2x + 9
Can ya'll help me please? 50 points!!
-3/4
The | \ symbol mean how far it is from 0. - means its negative.
simplify 9w-4y-8w+1+y-12-2w
The simplified form of the expression: 9w – 4y – 8w + 1 + y -12 – 2w is -1w – 3y – 11.
Given,
The expression: : 9w – 4y – 8w + 1 + y -12 – 2w
We have to simplify the expression.
A mathematical expression can be simplified by replacing it with an equivalent one that is simpler (often shorter), for example. Algebraic expressions are simplified in computer algebra. Logic optimization involves the simplification of Boolean expressions.
Now simplify:
9w – 4y – 8w + 1 + y – 12 – 2w
= -1w – 4y + 1 + y – 12
= -1w – 3y + 1 – 12
= -1w – 3y – 11
So, the simplified form of the expression: 9w – 4y – 8w + 1 + y -12 – 2w is -1w – 3y – 11.
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what doe mean (x,y)→(x+2,y-4)
Answer: shift 2 units right, and 4 units down
==================================================
Explanation:
The x+2 means to shift the point 2 units to the right.
For instance, the point (5,13) moves to (7,13) after adding 2 to the x coordinate.
The y-4 means to shift the point 4 units down. Example: (10,8) moves to (10,4) after subtracting 4 from the y coordinate.
Overall, (x,y)→(x+2,y-4) means "shift 2 units right, and 4 units down"
------------
Example:
Let's apply the rule to the point (1, 7)
(x,y)→(x+2,y-4)
(1,7)→(1+2,7-4)
(1,7)→(3,3)
Please answer and explain!!
Answer:
m = 8
Step-by-step explanation:
I looked at the line 8 and looked at m and noticed they're literally the same length. so m = 8.
Determine the slope of the line that contains the given points.
E(5,-1), F(2,-4)
The slope of the line containing (4,2) and (4,-3) is 1.
The slope of a straight line can be written as follows,
m = ( [tex]y_{2} - y_{1}[/tex])/([tex]x_{2} - x_{1}[/tex]) equation1
The line is containing the points (5,-1) and (2,-4). So, we can write
[tex]y_{2}[/tex] = -4 , [tex]y_{1}[/tex] = -1 , [tex]x_{1}[/tex] = 5 , and [tex]x_{2}[/tex] = 2 .
On substituting the values of variables in equation1, we will get
m = (-4-(-1))/(2-5) = (-3/-3) = 1.
As the slope of a line is 1 , so we can conclude that the given line is a straight line.
Here,
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (5 , -1) and ( 2 , -4 ) is 1.
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Find the square of 4+i
Answer:
1i = 1
4 + i = 4 + 1 = 5
Step-by-step explanation:
hope it's helpful
A class of 25 students took a science test. 10 students had an average (arithmetic mean)
score of 80. The other students had an average score of 60. What is the average score of the
whole class?
The required average score of the class is 68.
Given that,
A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80.
The other students had an average score of 60, which is the average score of the whole class is to be detrmined.
The average of the values is the ratio of the total sum of values to the number of values.
Here,
The average of 10 students is 80,
The average of the remaining students is 60 i.e. = 25 - 10 = 15
Now an average of the class,
Average = 80 * 10 + 15 * 60 / 25
= 1700 / 25
= 68
Thus, the required average score of the class is 68.
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