Answer:
Step-by-step explanation:
The given trigonometric expression is :
11 cos^2 x +3 sin^2 x+6sinx cosx +5
or, we can write it as,
(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5
Again, after rearranging the terms, we can write the whole expression as,
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
Then if you factor the following underlined section as you would with a polynomial:
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
You get:
(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5
Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.
So, now the whole expression becomes,
(3 cos x + sin x)^2 +7
Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),
The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.
So, I've attached a screenshot from a relevant document below:
Here, a=3 and b=1,
So, R= √10
As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.
Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.
i.e., in our case between (-√10) to √10.
Again, coming back to our original expression,
(3 cos x + sin x)^2 +7
The value of the term in bracket will lie between (-√10) and √10.
But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.
So, the minimum value will be,
(0)^2 + 7=7
and the maximum value will be,
(√10)^2 +7 = 17
solve for z -0.25z= -1.25
Answer:
z = 5Step-by-step explanation:
-0.25z= -1.25
Convert the decimals to improper fractions
That's
[tex] - 1.25 = - \frac{5}{4} [/tex][tex] - 0.25 = - \frac{1}{4} [/tex]So we have
[tex] - \frac{1}{4} z = - \frac{5}{4} [/tex]Multiply through by 4
We have
- z = - 5
Divide both sides by - 1
the final answer is
z = 5Hope this helps you
Answer:
[tex] \boxed{ \bold{ \purple{z = 5}}}[/tex]Step-by-step explanation:
[tex] \mathsf{ - 0.25z = - 1.25}[/tex]
Divide both sides of the equation by -0.25
[tex] \mathsf{ \frac{ - 0.25z}{ - 0.25} = \frac{ - 1.25}{ - 0.25} }[/tex]
Calculate
[tex] \mathsf{z = 5}[/tex]
Hope I helped !
Best regards!
A man makes a profit of 15%6y selling an article for Rs 2500. For what price should he sellituto make a profit of 38%
Find the price before the 15% profit:
2500 / 1.15 = 2173.91
Now multiply the original cost by 1 + 38%:
2173.91 x 1.38 = 2999.99
Answer: 2.999.99 ( may need to round to 3,000)
Consider an experiment in which a marble is tossed into a box whose base is shown in the figure. The probability that the marble will come to rest in the shaded portion of the box is equal to the ratio of the shaded area to the total area of the figure. If the probability is equal to 3/10, find the positive value of x.
Answer:
x = 2
Step-by-step explanation:
Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.
Probability 'P' = [tex]\frac{A'}{A}[/tex]
Area of the shaded region (A')= (x + 1)(x + 2)
Total area of the figure (A) = (2x + 1)(3x + 2)
P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]
10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)
10(x² + 3x + 2) = 3(6x² + 7x + 2)
10x² + 30x + 20 = 18x² + 21x + 6
(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0
8x² - 9x - 14 = 0
x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]
x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]
x = [tex]\frac{9\pm 23}{16}[/tex]
x = -[tex]\frac{7}{8}, 2[/tex]
Therefore, positive value of x = 2 will be the answer.
Which technique is vital for giving an effective presentation?
A.
Focus on the audience’s opinions of your topic.
B.
Use eye contact and speak clearly and deliberately.
C.
Reference only your own thoughts and opinions about the topic.
D.
Use technical terms when speaking to an informal audience.
E.
Analyze the audience right before delivering your speech.
Reset
Answer:
B.
Use eye contact and speak clearly and deliberately.
Step-by-step explanation:
let me know if you have any questions
Answer:
b
Step-by-step explanation:
because
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any
point on the remaining part of the circle.
Answer:
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
Step-by-step explanation:
Let us consider the image attached.
Center of circle be O.
Arc AB subtends the angle [tex]\angle APB[/tex] on the circle and [tex]\angle AOB[/tex] on the center of the circle.
To prove:
[tex]\angle AOB = 2 \times \angle APB[/tex]
Proof:
In [tex]\triangle PAO[/tex]: AO and PO are radius of the circles so AO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PAO = \angle OPA[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)[/tex]
Similarly,
In [tex]\triangle PBO[/tex]: BO and PO are radius of the circles so BO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PBO = \angle OPB[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)[/tex]
Now, we can see that:
[tex]\angle AOB = \angle AOQ+\angle BOQ[/tex]
Using equations (1) and (2):
[tex]\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}[/tex]
Hence, proved.
Hope you could understand.
If you have any query, feel free to ask.
The length of a rectangle is represented by the function L(x) = 4x. The width of that same rectangle is represented by the function W(x) = 7x2 − 4x + 2. Which of the following shows the area of the rectangle in terms of x? (L + W)(x) = 7x2 + 2 (L + W)(x) = 7x2 − 8x + 2 (L • W)(x) = 28x3 − 16x2 + 8x (L • W)(x) = 28x3 − 4x + 2
Answer:
(L ⋅ W)(x) = 28x3 − 16x2 + 8x
Step-by-step explanation:
I took the test hope it helps :3
The area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the length of the rectangle is L(x)=4x, and the width is W(x)=7x²-4x+2. Therefore, the area of the rectangle in terms of x is,
L(x)×W(x) = 4x × (7x²-4x+2)
(L · W) (x) = 28x³ - 16x² + 8x
Hence, the area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.
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Farmer McDonald raises ducks and cows. His animals have a total of 20 heads and
64 legs. How many ducks and how many cows does Mr. McDonald have?
Answer:
8 ducks, 12 cows
Step-by-step explanation:
Let the ducks be x in number and cows be y in number
ATQ, x+y=20 and 2x+4y=64, solving we get y=12 and x=8.
If farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs.
Suppose the number of head and legs be x and y respectively.
If His animals have a total of 20 heads and 64 legs,
x+y=20
2x+4y=64,
Solving the above equations we get y=12 and x=8.
Thus, if a farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.
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A school organised a farewell party of 100 students and school managementn decided three types of drinks distribute in the party
The answer is
i) - c
ii) - b
iii) - b
iv) - a
v) - d
I need help on this question please.
Answer:
27π inch^3
Step-by-step explanation:
5/14, 7/10, 5/6, 11/15, 19/2
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
42°
Х
please help with this
Answer:
X=48degrees.
Step-by-step explanation:
Sum of all angle of traingle=180degrees.
So, 90+42+X=180
132+X=180
X=180-132=48degrees
Express 0.504 as a fraction in its lowest term
Answer:
63/125
Step-by-step explanation:
Turn the decimal .504
=> 504/1000
=> 504/1000 = 252/500
=> 252/500 = 126/250
=> 126/250 = 63/125
=> 63/125 cannot be simplified anymore.
So, 63/125 is the simplified fraction of .504
X = [?]°
Dr.
X Х
As
140°
B
C
Answer:
40°
Step-by-step explanation:
x+140=180°(angle on a straight line)
x=180-140
x=40°
∠DBA and ∠DBC are making linear pair.
Linear pair of angles are formed when two lines intersect each other at a single point.
The sum of angles of a linear pair is always equal to 180°[tex] \rm \large\longrightarrow \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 140 \degree \: [/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 40 \degree[/tex]
Solve the equation for x
Answer:
x = 33
Step 1:
First, let's add the values together from both parentheses.
2x + x = 3x
1 + (-10) = -9
Now we are left with:
3x - 9 = 90.
Step 2:
Add 9 on the left side to cancel out the 9. Add it to the right side.
3x = 99
Finally, divide both sides by 3 to get our answer.
3x / 3 = x
99 / 3 = 33
x = 33
what is x if y is 50, it is equivalent to 9/150. the first peep gets brainliest
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 3
▹ Step-by-Step Explanation
[tex]\frac{9}{150} \\\\150/3 = 50\\9/3 = 3\\\\x = 3[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
SOMEONE HELP ME!!!! I WILL GIVE BRAINLIEST!!!
Answer:
B
Step-by-step explanation:
well if we draw the graph we have the following image, and the only one that applies is
B
because 4>3
Factorise sin²A-5 sinA+6
Answer:
sin²A-5 sinA+6
=sin²A-(3+2)sinA+6
=sin²A-3sinA-2sinA+6
=sinA(SinA-3)-2(sinA-3)
=(sinA-2) (sinA-3)
hope this help you
Answer:
sin²A-5 sinA+6
=sin²A-(3+2)sinA+6
=sin²A-3sinA-2sinA+6
=sinA(SinA-3)-2(sinA-3)
=(sinA-2) (sinA-3)
-4(-w-10)=
i need help don’t know what the answer is
Answer:
[tex]\boxed{4w+40}[/tex]
Step-by-step explanation:
Use the distributive property to evaluate the equation.
-4(-w - 10)
4w + 40
-4 * -w = 4w because two negatives cancel to make a positive value.
-4 * -10 = 40 for the same reason.
Every time Liliana bakes a batch of brownies, she uses 34 cup of chocolate. If she has 128 cup(s) of chocolate remaining, how many batches of brownies can Liliana make? Input your answer as a whole number.
Answer:
3
MARK BRAINLIEST IF THIS HELPED!
i hope u have a great day.
Match each quadratic equation with its solution set.
Answer:
2x²-32 ⇒ x²=16⇒ (-4,4)
4x²-100 ⇒x²=25 ⇒(-5,5)
x²-55=9 ⇒x²=64 ⇒(-8,8)
x²-140=-19 ⇒x²=121 ⇒(-11,11)
2x²-18=0 ⇒x²=9 ⇒(-3,3)
Answer:
2x^2-32 = 0 ===> (-4,4)4x^2 -100=0 ===> (-5,5)x^2 -55=9 ==>(-8, 8)x^2-140= -19 ===>(-11 ,11)Step-by-step explanation: Further explanation
[tex]2x^2-32=0\\\\\mathrm{Add\:}32\mathrm{\:to\:both\:sides}\\\\2x^2-32+32=0+32\\\\2x^2=32\\\\\frac{2x^2}{2}=\frac{32}{2}\\\\\mathrm{For\:}x^2=f\left(a\right)\\\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\x=4,\:x=-4[/tex]
[tex]4x^2-100=0\\\mathrm{Add\:}100\mathrm{\:to\:both\:sides}\\4x^2-100+100=0+100\\4x^2=100\\\frac{4x^2}{4}=\frac{100}{4}\\x^2=25\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{25},\:x=-\sqrt{25}\\\\x=5,\:x=-5[/tex]
[tex]x^2-140=-19\\x^2-140+140=-19+140\\x^2=121\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{121},\:x=-\sqrt{121}\\x=11,\:x=-11[/tex]
[tex]x^2-55=9\\x^2-55+55=9+55\\x^2=64\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{64},\:x=-\sqrt{64}\\x=8,\:x=-8\\[/tex]
[tex]2x^2-18=0\\2x^2-18+18=0+18\\2x^2=18\\\frac{2x^2}{2}=\frac{18}{2}\\x^2=9\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{9},\:x=-\sqrt{9}\\x=3,\:x=-3[/tex]
Solve the inequality for x.
7 > 2x+9
Answer:
x<-1Step-by-step explanation:
[tex]7 > 2x+9\\\\\mathrm{Switch\:sides}\\\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\2x+9-9<7-9\\\\2x<-2\\\\\frac{2x}{2}<\frac{-2}{2}\\\\x<-1[/tex]
a number is multiplied by 5 and the results is twice the number added to 2 find the number
Answer:
5x=2x+2
3x=2
X=2/3
Hope this helps ФωФ
A watermelon weighs 6.45 kilograms. How many grams does the watermelon weigh?
Answer:
6450g
Step-by-step explanation:
1kg = 1000g
6.45kg = 6450
The watermelon weighs 6450 grams.
Given that a watermelon weighs 6.45 kilograms.
We need to convert its unit into grams.
To convert kilograms to grams, you need to multiply the weight in kilograms by 1000, as there are 1000 grams in 1 kilogram.
The watermelon weighs 6.45 kilograms, you can use the following formula to convert it to grams:
Weight in grams = Weight in kilograms × 1000
Let's do the math:
Weight in grams = 6.45 kilograms × 1000 = 6450 grams
So, the watermelon weighs 6450 grams.
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please help!!! which of these illustrates the associative property of multiplication?
Answer:
B
Step-by-step explanation:
The association property of multiplication states that if we have three numbers such as:
[tex]a\cdot b\cdot c[/tex]
Then the order of parentheses will not matter. In other words:
[tex](a\cdot b)\cdot c=a\cdot (b\cdot c)[/tex]
For instance:
[tex](3\cdot4)\cdot5=3\cdot(4\cdot5)[/tex]
For the choices, it must have at least three terms. Thus, eliminate A.
It must also have parentheses. Eliminate D.
Choice C represents the distributive property, where you distribute a factor into the expression.
Thus, the correct answer is choice B.
And as previously mentioned, the order of the parentheses does not make the product any different.
[tex]6*(9*1)=6*(9)=54\\(6*9)*1=(54)*1=54[/tex]
Answer:
The correct answer choice is B.
Step-by-step explanation:
The digits should still be in order, so A is incorrect. 6 * 91 does not even equal 69 * 1!
B shows that be can multiply 6 * 9 * 1 in any order. This means we can place a pair of parentheses around any of these numbers and the answer will still be the same.
C is incorrect. We want an equation that helps give us a better understanding of MULTIPLICATION, not ADDITION. The equation is also false.
Finally, D illustrates the commutative property of multiplication- you can multiply your numbers in any order and it will still have the same value. Put simply, it's incorrect.
Let me know if you need more elaboration!
what is the no solution, the one solution, and the infinitely many solution of 2x+5+2x+3x
Answer:
This problem shows an expression, not an equation.
It cannot be solved.
An equation needs an equal sign.
I had $20.00 My Mom gave me $10.00. My Dad Gave me $50.00 My Aunt & Uncle gave me $100.00. I had another $5.00. How much did I have? I had $20.00 My Mom gave me $10.00. My Dad Gave me $50.00 My Aunt & Uncle gave me $100.00. I had another $5.00. How much did I have?
Answer:
you have $185 in total unless the aunt and uncle gave you 100 each, then your answer would be $285
Step-by-step explanation:
Answer:
0$
Step-by-step explanation:
simple
1. Solve each equation.
a. 5x – 2=8
b. 4x – 3= 2x + 9
C. 6x + 3 = 2x + 8
And show work
Answer:
a. 5×=8+2
5×=10
b. 4×-2×=9+3
2×=13
c. 6×-2×=8-3
4×=5
The area of a square of side 2.4 cm is
Answer:
area of cube = a^2 ( a is side)
2.4^2 = 5.76 cm^2
Answer:
5.76 cm^2
Step-by-step explanation:
Hey there!
Well if the side length is 2.4 cm then the area would be,
A = l•l
A = 2.4 • 2.4
A = 5.76cm^2
Hope this helps :)
Create a figure with half the perimeter of a given figure.
you don't have to actually make a shape, can someone explain how to do this pls
Step-by-step explanation:
First you have to add up all of the numbers that make up the perimeter of this arrow.
3+3+1+.5+.5+1.8+1.8=11.6
You than want to divide this number by 2 to find the half perimeter you have to work with, which is 5.8.
A simple shape you can make is a square, with each side being 1.45 m.