Answer:
[tex]sin\theta =\pm\dfrac{4}{5}\\tan\theta =\pm\dfrac{3}{4}[/tex]
Step-by-step explanation:
Kindly refer to the attached image of a right angled [tex]\triangle ABC[/tex].
Let [tex]\angle C = \theta[/tex]
Sides BC = a
AB = c and
AC = b respectively.
To prove:
[tex]sin^2\theta+cos^2\theta =1[/tex]
Proof:
Using Sine and Cosine values:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\theta =\dfrac{AB}{AC} = \dfrac{c}{b }[/tex]
[tex]cos\theta =\dfrac{Base}{Hypotenuse}\\\Rightarrow cos\theta =\dfrac{BC}{AC} = \dfrac{a}{b}[/tex]
As per Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow b^{2} = a^{2} + c^{2} .......... (1)[/tex]
Considering the LHS of [tex]sin^2\theta+cos^2\theta =1[/tex]:
[tex](\frac{c}{b})^2+(\frac{a}{b})^2\\\Rightarrow \frac{c^2+a^2}{b^2}[/tex]
Now, using equation (1):
[tex]\Rightarrow \dfrac{b^2}{b^2} = 1 = RHS[/tex]
Hence, proved that : [tex]sin^2\theta+cos^2\theta =1[/tex]
Now, we are given that:
[tex]cos\theta =\frac{4}{5}[/tex]
To find, sine and cosine values of the angle i.e. [tex]sin\theta = ?[/tex] and [tex]tan\theta = ?[/tex]
Using [tex]sin^2\theta+cos^2\theta =1[/tex]:
[tex]sin^2\theta+(\dfrac{4}{5})^2 =1\\\Rightarrow sin^2\theta = \dfrac{9}{25}\\\Rightarrow sin\theta = \pm \dfrac{3}{5}[/tex]
We know that:
[tex]tan\theta =\dfrac{sin\theta}{cos\theta}\\\Rightarrow tan\theta =\pm \dfrac{\dfrac{3}{5}}{\dfrac{4}{5}}\\\Rightarrow \bold{tan\theta =\pm \dfrac{3}{4}}[/tex]
20 POINTS ! An international company has 17,800 employees in one country. If this represents 22.1% of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number. Thankyou!
Answer:
80,543 employees total
Step-by-step explanation:
22.1% of total = 17,800 employees
0.221 of x = 17800
0.221 • x = 17800
x = 17800 / 0.221
x = 80542.98643
x ≈ 80543 employees total
a) What is a tessellation? Give two everyday examples of tessellations (that do not extend
indefinitely). You may insert images or give a verbal description. (5 points)
please help
The tile in a bathroom or kitchen is one example of tessellation. It's where you place geometric shapes together to fill a space. In this case, we have squares placed together to fill the space of the wall or floor. There cannot be any gaps or overlaps.
Another example would be bricks as this is composed of rectangles placed together without any gaps or overlaps. There are many other examples as well usually done as floor or wall patterns of some kind. Some tessellations involve using more than one shape (eg: one pattern uses squares and equilateral triangles placed together).
When statistically analyzing data, a researcher would not look to study which of the
following statistics?
A. central tendencies of the data
B. variability in the data
C. spread of the data
D. time it took to collect the data
Answer:
D. The time it took to collect the data.
In a basketball game, one team's score is two points less than half the other team's score, which is x. What is the difference in the score?
Answer:
1/2x +2
Step-by-step explanation:
Let's say there are 2 teams : A & B
A leads with x points, while B score 2 points less than half of B's score (x)
B = 1/2 of B score - 2
The difference of A - B = x - (1/2x - 2) = x - 1/2x + 2 = 1/2x + 2
The required difference in score is 1/2x + 2.
Given that,
In a basketball game, one team's score is two points less than half the other team's score, which is x. What is the difference in the score is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Let the score of the second team be x,
One team's score is two points less than half the other team's score
= 1/2x - 2
Difference of the score = x - (1/2x - 2)
= x -1/2x +2
= 1/2x + 2
Thus, the required difference in score is 1/2x + 2.
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what is the algebraic expression for 11 more than twice a number x
Answer:
11+2x
Step-by-step explanation:
Answer:
2x + 11
Step-by-step explanation:
"twice a number x": Multiply the variable x with 2 ⇒ 2x
"11 more than...": Add 11 ⇒ + 11
Combine the two terms:
2x + 11 is your answer.
~
what is 1944 divided by 2/3
Answer:
2916
Step-by-step explanation:
1944 ÷ (2/3) = 2916
a printer can print 12 pages in 9 seconds. what’s the closest estimate of the number of pages it can print in one minute?
I need help, please help me
Answer:
See below.
Step-by-step explanation:
The perimeter of a rectangle is simply the distance around the rectangle. The distance will be its two lengths plus the two widths. In other words:
[tex]P=2l+2w[/tex]
We want to solve for l. Therefore:
[tex]P=2l+2w\\2l+2w=P\\2l=P-2w\\l=(P-2w)/2[/tex]
Diego and Max are buying soft drinks for a neighborhood picnic. Each person is expected to drink one can of soda. Diego says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to determine the total cost of the soda. Max says that if you divide the cost of a 12-pack of soda by the number of sodas, you will determine the total cost of the sodas.
Which choices best illustrates who is correct and why?
Max is incorrect because he calculated the cost of one can of soda
Diego is incorrect because he calculated the price of one can of soda
Max is correct because the total cost divided by the number of sodas gives you the total cost of the sodas
Diego is correct because the price of one can of soda multiplied by the number of sodas needed will give you the total cost of the soda.
Answer:
D). Diego is correct because the price of one can of soda multiplied by the number of sodas needed will give you the total cost of the soda.
Step-by-step explanation:
Since every person is expected to drink one can of soda:
Let the price of each can of soda = p
and the total number of people present at the picnic = n
∵ Total price = p(the price of each soda can) * n(number of people)
Thus, Diego correctly asserts that if he multiplies the 'unit price for a can of soda by the number of people attending the picnic', he would be able to deduce the total cost of soda. Hence, Max is incorrect and option D is the correct answer.
Write the expression in simplest form.
Answer:
8
Step-by-step explanation:
(-11x/2 + 3) -2(-11x/4 -5/2)
= -11x/2 + 3 -(2*-11x/4) -(2*-5/2)
= -11x/2 + 3 -(-22x/4) -(-5)
= -11x/2 + 3 +22x/4 + 5
= -22x/4 + 22x/4 + 3 + 5
= 0 + 8
= 8
The value of the simplified expression is 8.
We have,
(-11/2 x + 3) - 2 (-11/4 x - 5/2)
To simplify the expression ((-11/2)x + 3) - 2((-11/4)x - 5/2), distribute the -2 to each term within the second set of parentheses and then combine like terms.
((-11/2)x + 3) - 2((-11/4)x - 5/2)
= (-11/2)x + 3 - 2 x (-11/4)x - 2 x (-5/2)
= (-11/2)x + 3 + (11/2)x + 5
= (-11/2)x + (11/2)x + 3 + 5
Combine like terms.
= 3 + 5
= 8
Therefore,
The simplified expression is 8.
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At an ice carving competition, each carver starts with a block of ice with the dimensions shown. The block is wrapped in a special reflective material to keep it from melting before the competition starts. 1.1 0.8 1.3
Complete question :
At an ice carving competition, each carver starts with a block of ice with the dimensions shown. The block is wrapped in a special reflective material to keep it from melting before the competition starts. The side lengths of the block are 1.1, 0.8, 1.3. How much reflective material is needed to cover the block completely, without any overlaps?
Answer:
6.7 unit^2
Step-by-step explanation:
Taking the dimension of the ice block as :
1.1 by 0.8 by 1.3
The total reflective material which will used to cover the ice block must have the same surface area as the ice block.
Shape of ice block = rectangular prism.
Taking the surface area if a rectangular prism :
Using the relation :
2(lw * lh * wh)
Where l = Length = 1.1
Width w = 0.8
Height h = 1.3
Therefore,
2[(1.1*0.8) + (1.1*1.3) + (0.8*1.3)]
2[(0.88) + (1.43) + (1.04)]
2(3.35)
= 6.7 unit^2
Reflective material should be 6.7 unit^2
The total reflective material required is 6.7 square units
What is a surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.
Given that:-
The dimensions of the ice cube are 1.1 by 0.8 by 1.3The total reflective material which will be used to cover the ice block must have the same surface area as the ice block.
The shape of the ice block = is a rectangular prism.
Taking the surface area of a rectangular prism by using the relation :
SA = 2( lw x lh x wh )
Where l = Length = 1.1
Width w = 0.8
Height h = 1.3
Therefore,
SA = 2 [(1.1 x 0.8) + (1.1 x 1.3) + (0.8 x 1.3)]
SA = 2 [ (0.88) + ( 1.43 ) + ( 1.04 ) ]
SA = 2 ( 3.35 )
SA = 6.7 square units
Therefore the Reflective material should be 6.7 square units
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find the length of a line segment whose endpoints are (-2,3) and (6,3)
Answer:
8
Step-by-step explanation:
Since we want to find the length of a line segment, we can use the distance formula.
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1} )^2 }[/tex]
(x₁, y₁) and (x₂, y₂) are the points given.
The points we are given are: (-2,3) and (6,3). Therefore,
[tex]\\x_{1} =-2\\y_{1}=3 \\x_{2} = 6\\y_{2} =3[/tex]
Plug each value into the formula.
[tex]d=\sqrt{{(6--2})^2+(3-3 )^2} }[/tex]
Evaluate inside of the parentheses first.
[tex]d=\sqrt{(6+2)^2+(0)^2}[/tex]
[tex]d= \sqrt{(8)^2+(0)^2 }[/tex]
Evaluate the exponents.
8²= 8*8=64
[tex]d=\sqrt{64+(0)^2}[/tex]
0²= 0*0= 0
[tex]d=\sqrt{64+0}[/tex]
Add 64 and 0.
[tex]d=\sqrt{64}[/tex]
Take the square root of 64.
[tex]d= 8[/tex]
The length of the line segment is 8
Divide 41 by 15. Give your answer as a recurring decimal
Answer:
2.733333....
Step-by-step explanation:
Jason watched a caterpillar move 16 feet in 8 minutes. Jason says that the caterpillar's unit rate is 0.5 foot per minute. Is Jason correct? Drag and drop numbers and words into the correct boxes to complete the explanation.
Answer:
Jason is incorrect.
The caterpillar's rate is 2 ft/min
Step-by-step explanation:
The rate of motion is defined as the quotient between the distance covered (in our case 16 feet) divided by the time it took to cover that distance (in our case 8 minutes)
Then, the rate is:
[tex]rate=\frac{distance}{time} = \frac{16\,\,ft}{8\,\,min} = 2\,\frac{ft}{min}[/tex]
find the perimeter of an isosceles triangle with side lengths of 5+x, 5+x, and xy. Write in simplest form.
To get the perimeter, you add up all the outer sides
side1+side2+side3 = (5+x)+(5+x)+(xy) = 10+2x+xy
The like terms 5 and 5 add to 10. The other pair of like terms x and x add to 2x. There isn't anything to pair with xy, so we leave it as is.
Parallel lines are coplanar. What characteristics of these geometric figures create the different requirements?
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
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what is the slope of the line y = - 5/4x - 5 ?
Answer:
-5/4
Step-by-step explanation:
Slope is rise over run which means that the -5 will apply to your y values and the 4 will apply to your x values. This slope would have a point move down 5 units and to the right 4 units to get the location of the next point when going left to right. Because the slope contains a negative, the slope will be angled downward left to right. The negative only applies to the 5.
Hello, I hope you are having a splendid day. :)
The slope of this line is -5/4.
This equation is written in slope-intercept form, which looks like this:
y=mx+b
Where
m is the slope and b is the y-intercept.
So the slope is the number before x (in y=mx+b form).
The number before x is -5/4.
Therefore, -5/4 is the slope. Hope it helps. Ask me if you have any queries.
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Good luck.
How can I doo hard math level
Answer:
You can learn math by
Step-by-step explanation:
practicing and remember not to overwork yourself
Help me
Please !! :/
Answer:
The area is 10 cm².
Step-by-step explanation:
The area of a triangle is 1/2 * bh where b = base and h = height. We know that b = 4 and h = 5 so the area is 1/2 * (4 * 5) = 1/2 * 20 = 10 cm².
Jones planted s flowers. He planted fewer flowers than Kerry Kerry planted 50 flowers. Write
the expression that shows how many flowers Jones planted.
Answer:
s < 50
Step-by-step explanation:
s must be less than 50
s < 50
Please help! Offering 15 points with brainiest
Answer:
1/1296
Step-by-step explanation:
P( 5) = number of 5's over total numbers possible
= 1/6
P( 5,5,5,5) = 1/6 * 1/6 * 1/6* 1/6
=1/1296
Answer:
[tex]\Large \boxed{\frac{1}{1296} }[/tex]
Step-by-step explanation:
Outcomes of a dice: 1, 2, 3, 4, 5, 6
There are 6 total outcomes.
The probability of landing a 5 on a dice is 1/6.
P(landing a 5 four times) = 1/6 × 1/6 × 1/6 × 1/6 = 1/1296
What two numbers multiply to 36 and add up to -20?
Answer:
-2 and -18
Step-by-step explanation:
It is useful to consider the factors of 36:
36 = (-1)(-36) = (-2)(-18) = (-3)(-12) = (-4)(-9) = (-6)(-6)
The sums of these factor pairs are -37, -20, -15, -13, -12.
The factor pair of interest is -2 and -18.
–6 < 2x – 4 < 4 solve the inequality
Answer:
The answer is
[tex] - 1 < x < 4[/tex]Step-by-step explanation:
[tex] - 6 < 2x - 4 < 4[/tex]First of all add 4 to both sides of the inequality to make 2x stand alone
That's
[tex] - 6 + 4 < 2x - 4 + 4 < 4 + 4 \\ - 2 < 2x < 8[/tex]Divide both sides of the inequality by 2 inorder to find x
That's
[tex] \frac{ - 2}{2} < \frac{2x}{2} < \frac{8}{2} [/tex]We have the final answer as
[tex] - 1 < x < 4[/tex]Hope this helps you
Given g(x)=2x+1 and f(x)=x-7 find (g•f) (x)
Step-by-step explanation:
(g•f(x))
Where ever you see x in g(x), you put f(x)
2(x-7)+1
[expanding]
2x-14+1
2x-13
I'm not 100% sure
Please help a girl out I’m honestly extremely slow
First, reorder the numbers so they go from least to greatest. It should look like this:
-11, -9, -6, 0, 2, 18, x, 20, 36, 37, 46, 47, 51.
Mean: 19.25
The mean is the average. To find it, add all numbers together and divide by how many numbers there are.
Median: 19
The median is the center number in the ordered line of numbers. I added a bolded variable (x), so you can see where it is. Because it's between two numbers, add those numbers and divide by 2.
Mode: N/A
There's not a mode. A mode is a repeating number in the sequence.
Range: 62
Range is the difference between the largest and smallest number.
[tex]51 - ( - 11) = 62[/tex]
47.)
The range is larger than the highest temperature because the temperature values are both positive and negative. Due to this, the smallest number (-11) becomes positive as the negative sign is distributed to it and adds to the largest number (51).
48.)
Again, mean is the average. Add all values together and divide by the number of values there are.
[tex] = \frac{( - 11) + ( - 9) + ( - 6) + 0 + 2 + 18 + 20 + 36 + 37 + 46 + 47 + 51}{12} [/tex]
[tex] = \frac{231}{12} [/tex]
[tex] = 19.25[/tex]
In a certain Algebra 2 class of 21 students, 11 of them play basketball and 6 of them play baseball. There are 6 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
Step-by-step explanation:
total number of students=21
students play neither sport=6
students who play at least one sport=21-6=15
Let play basketball=X
and play baseball=Y
n(XUY)=n(X)+n(Y)-n(X∩Y)
15=11+6-n(X∩Y)
n(X∩Y)=17-15=2
reqd. probability=2/21
CAN ANYONE ANSWER THIS I WILL GIVE BRAINLIEST! 13
Answer:
option 4
Step-by-step explanation:
so first you would simplify to x>-6 and since there is no line under the greater then it would be and open circle and it is shading to the right because of the greater than symbol and if would start of -6 so option 4 is the correct answer
Answer:
Draw an open circle on-6 and shade to the right.
Step-by-step explanation:
Simplify the inequality, so it looks like this: x > −6When the inequality symbol doesn't have a line under it like these do, ≤ and ≥, then it's an open circle, rather than a closed one on a number line.The last option would be the correct one because it says open circle and -6 like we said in step 1 and 2.Lin created a scaled copy of Triangle A with an area of 72 square units. How many times larger is the area of the scaled copy compared to that of Triangle A
Answer:
Copy's area is 16 times bigger then triangle area.
Step-by-step explanation:
Given:
Area of copy = 72 unit²
Find:
How bigger copy compared to triangle
Computation:
Area of triangle = [1/2][base][height]
Area of triangle = [1/2][3][3]
Area of triangle = 4.5 unit²
So.
Area of copy / Area of triangle
72 / 4.5
16
So,
Copy's area is 16 times bigger then triangle area.
reduce the following rational expression to lowest terms if possible -60/-48 Please answer me fast Will mark as a brainlist ✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️
Answer:
5/4
Step-by-step explanation:
-60/-48
factor the expression
(-15)(4)/(-12)(4)
cancel out 4
-15/-12
divide by -3
=5/4
What is the minimum value of the objective function, C with given constraints? C=5x+6y ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪2x+y≤83x+4y≤17x≥2y≥1
Answer:
The answer is 16
Step-by-step explanation:
I did the test
Answer:
Answer is 16
I just did the test its right i swear.