Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan A = [tex]\frac{sinA}{cosA}[/tex] , cot A = [tex]\frac{cosA}{sinA}[/tex]
Consider the left side
(1 + cotA + tanA)(sinA - cosA)
each term in the second factor is multiplied by each term in the first factor.
1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)
= sinA - cosA + cosA - [tex]\frac{cos^2A}{sinA}[/tex] + [tex]\frac{sin^2A}{cosA}[/tex] - sinA ( collect like terms )
= [tex]\frac{sin^2A}{cosA}[/tex] - [tex]\frac{cos^2A}{sinA}[/tex]
= ( sinA × [tex]\frac{sinA}{cosA}[/tex] ) - ([tex]\frac{cosA}{sinA}[/tex] × cosA )
= sinAtanA - cotAcosA
= right side ⇒ proven
Please answer !!!!!!!! Will mark brainliest correct answer !!!!!!!!!!!
Answer:
B
Step-by-step explanation:
I had that same answer. I did it with my teacher and he said it was b
The synthesis of a large collection of information that contains well-tested and verified hypotheses about certain aspects of the world is known as a scientific
A) fact.
B) hypothesis.
C) law or principle.
D) theory.
E) none of these.
Answer:
it's a B because it's the best answer for this quistion like they are saying IF I do this Then this should happen
The numbers x and y are inversely proportional. When the sum of x and y is 42, x is twice y. What is the value of y when x = -8? PLEASE HELP
Answer:
y= -4
Step-by-step explanation:
x+y=42. We know that x plus y equals 42.
x=2y . We also know that x equals twice y.
2y+y=42. Since we know that x=2y, we're going to replace x with 2y from the original equation, simplified would be 3y=42.
y=14. 3y=42 simplified is y=14, this is because we divided both sides by 3 (since 3 and 42 are both divisible by 3) (btw divisible by 3 simply means that it can be divided by 3)
x+14=42. Now that we know what y equals, let's replace y with 14 from the original equation.
x=28. Now that we know that x=28 and y=14, we know that y is always x/2.
When x=-8, we divide it by 2 and get, -4.
Not absolutely positive as this was all mental math, but hope this helps! :)
The value of the variable y at x = -8, will be negative 49.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The numbers x and y are inversely proportional. Then we have
y ∝ 1/x
y = k/x ...1
When the sum of x and y is 42. Then the equation will be
x + y = 42 ...2
x is twice y. Then the equation will be
x = 2y ...3
From equations 2 and 3, we have
2y + y = 42
3y = 42
y = 14
Then the value of x will be
x = 2(14)
x = 28
Then the value of k will be
14 = k / 28
k = 392
Then the equation will be
y = 392 / x
Then the value of the variable y at x = -8, will be
y = 392 / (-8)
y = -49
Thus, the value of the variable y at x = -8, will be negative 49.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
A large rectangle is made up of 3 smaller identical rectangles, the perimeter of one small rectangle is 21cm. What is the perimeter of the large rectangle.
Answer:
63 units
Step-by-step explanation:
If the perimeter of 1/3 of the rectangle is 21, multiply 21 by 3 to find the perimeter of the entire rectangle.
21 x 3 = 63
Find the value of x.
Answer:
x = -7
Step-by-step explanation:
Make an equation:
3x + 33 = 12
3x = -21
x = -7
Answer:
x = -7
Step-by-step explanation:
form an equation.
14 + x + 2x + 19 = 12
like terms together;
x + 2x = 12 - 14 - 19
simplify;
3x = -21
divide both sides by 3;
x = -7
The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.
Which expression represents the width of the rectangle?
1. x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).
2. x2+10 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2+10)−20).
3. x2−30 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2−30)+20).
4. x2+30 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2+30)−20).
Answer:
[tex]1. x^2-10[/tex] because the area expression can be rewritten as [tex](x^2-10)(x^2+10)[/tex]which equals [tex](x^2-10)((x^2-10)+20).[/tex]
Step-by-step explanation:
Area of the rectangle [tex]=(x^4-100)[/tex]
[tex]x^4-100=(x^2)^2-10^2\\$Applying difference of two squares: a^2-b^2=(a-b)(a+b)\\(x^2)^2-10^2=(x^2-10)(x^2+10)[/tex]
Since the length of a rectangle is 20 units more than its width.
[tex]Width: x^2-10\\Length=x^2+10=x^2-10+20[/tex]
The correct option is therefore 1.
Answer:
x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).Step-by-step explanation:
The area of the rectangle is [tex]x^{4} -100[/tex], which can be factored as [tex](x^{2} +10)(x^{2} -10)[/tex], because it's the difference of two perfect squares.
But, we know that [tex]l=20+w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
Additionally, [tex]l=x^{2} -10+20[/tex] and [tex]w=x^{2} -10[/tex], which means [tex]l=x^{2} +10[/tex].
Therefore, the right answer is A.
A. A worker with 1700 hours of training is paid $40 per month.
B. A worker who works 40 hours is paid $1700.
C. There are 40 workers who are paid $1700 per month.
D. A worker with 40 hours of training is paid $1700 per month
Answer:
d.
Explanation:
Look at the title of the categories in the chart. 40 is categorized under “hours of training,” meaning 40 hours of training. 1700 is categorized under “monthly pay.” Put the information together and it means $1,700 for 40 hours that month.
a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?
Answer:
x=8
Step-by-step explanation:
Area of a rectangle=length×width
Area=104
Width=x
Length=5+x
104=x*(5+x)
104=5x+x^2
104-5x-x^2=0
x^2+5x-104=0
Can also be written as
-x^2-5x+104=0
Solve the quadratic equation using formula
−x2−5x+104=0
using the Quadratic Formula where
a = -1, b = -5, and c = 104
x=−b±√b2−4ac/2a
x=−(−5)±√(−5)2−4(−1)(104)/2(−1)
x=5±√25−(−416)/−2
x=5±√441/−2
The discriminant b^2−4ac>0
so, there are two real roots.
Simplify the Radical:
x=5±21/−2
x=-26/2 or 16/2
x=-13 or 8
The value of x can't be negative
So, x=8 is the answer
3× + y = 8, 4× - 3y=2
Answer:
x=2
y=2
Step-by-step explanation:
You can use the process of elimination
x can't be 3 because than the first question would be 9+y=8 which is even bigger than the answer.
So now, we try 2. x=2
6+y=8 which =
6+2=8
So y must be two
Then we try it on the
Second one.
8-6=2 which makes sense.
Hope it helps
Answer:
x = 2
y = 2
Step-by-step explanation:
3x + y = 8..…...(1)× -3
4x - 3y = 2......(2)× 1
-9x - 3y = -24.......(3)
4x - 3y = 2..…..........(4)
Cancel -3y - 3y
-9x - 4x = -24 - 2
-13x = -26
Divide both sides by -13
x = 2
Substitute for the value of y
3x + y = 8
3(2) + y = 8
6 + y = 8
y = 8 - 6
y = 2
What is the measure of the supplementary angle of the 65˚ angle?
A.50˚
B.40˚
C.130˚
D.310˚
Answer:
115
Step-by-step explanation:
When two angles are supplementary, their measures must add up to 180 degrees. Therefore, if we call the other angle x:
x+65=180
x=180-65=115 degrees
Hope this helps!
Answer:
None of them
Step-by-step explanation:
Supplementary angles have 180 degrees
50+65=115
40+65=105
130+65=185
310+65=375
Determine the value of the variables a, b, and c when simplifying and evaluating the expression. 3^8/3^4 = a^b = c
Answer:
3, 4, 81
Step-by-step explanation:
plz thank
The value of a is 3, value of b is 4 and value of c is 81.
To understand more, check below explanation.
Exponential identity:The exponential identity is,
[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]
We have to solve, [tex]\frac{3^{8} }{3^{4} }[/tex]
[tex]\frac{3^{8} }{3^{4} } =3^{8-4} \\\\\frac{3^{8} }{3^{4} } =3^{4} \\\\\frac{3^{8} }{3^{4} } =3*3*3*3=81[/tex]
Hence, the value of a is 3, value of b is 4 and value of c is 81.
Learn more about the exponential expression here:
https://brainly.com/question/8844911
the slope of the line below is -2. which of the following is the point-slope form of the line? 4, -8
Answer:
D
Step-by-step explanation:
Point: (4,-8)
Slope: -2
y-y1=m(x-x1)
y+8=-2(x-4)
3x2 + 5x - 7 = 0 is a quadratic equation.
True
False
Answer:
True
Step-by-step explanation:
Quadratic equations have the highest degree on x as 2. The given equation has 3x^2, meaning that it is quadratic.
what is 222 times 5
no explanation please
Answer:
1110
Step-by-step explanation:
Hey there!
222 multiplied by 5 is 1110.
You can also use a calculator to find that out haha!
Have a wonderful day!
PLEASE HELP WILL MARK BRAINLIEST
Find the area of the right triangle.
Answer:
Step-by-step explanation:
This right triangle is on a grid.
The area is the height * base/2
The base is on a line segment parallel to the x axis which is 6 squares.
The height is on a line segment parallel to the y axis which is 2 squares
The area is the height * base /2
Area = 6 * 2 /2 = 12/2 = 6 square units.
Factor −1/9 out of −1/9x−3.
Answer:
-1/9 (x+27)
Step-by-step explanation:
Divide the whole expression by -1/9.
-1/9x becomes x
-3 becomes + 27
7(+5)=21
can you please help with math problem
can someone help me to find TSA of this figure?
Answer :
is approximately 100 cm ²
Step -by-step explanation
[tex]r \: = 10 \\ l \: = 21.81 \\ T.S.A \: of a \: cone\: = \pi \times r(r + l)[/tex]
[tex] \frac{22}{7} \times 10(10 + 21.81) \\ \frac{22}{7} \times 10(31.81) \\ \frac{22}{7} \times 318.1[/tex]
[tex] \frac{22}{7} \times 318.1 \\ = 999.7 \\ = 100 {cm}^{2} [/tex]
What is the nth term rule of the linear sequence below? − 4 , − 1 , 2 , 5 , 8 ,
Answer:
a
n
=
3
n
−
7
Step-by-step explanation:
Explain why a sample of 30 dentists from a large city taken to estimate the median income of all residents of that large city is not representative
Answer: Because all individuals in the sample have the same job, so the sample is biased.
Step-by-step explanation:
Ignoring the fact that 30 is a small sample for a large city, we already know that all the people in the sample has the same profession.
Now, we can expect that two dentists win have around the same income, but not all the residents in the city are dentists
A lot of them work in fast food, others may be lawyers, others may be freelancers.
We have a lot of jobs where the income does not coincide with the average income of a dentist, so with the sample of 30 dentists we are not actually representing all the other possible jobs that there are in the city.
If we want a sample that represents the income of all the residents, we should have a random sample (so the sample is not biased, like in this case).
The volume of a sphere is 45001 m3. Find the length of the radius
of the great circle.
Answer:
[tex]\large \boxed{\text{22.07 m}}[/tex]
Step-by-step explanation:
The formula for the volume (V) of a sphere is:
V = ⁴/₃πr³
We can use this equation to calculate the radius (r).
[tex]\begin{array}{rcl}45001 & = & \dfrac{4}{3} \pi r^{3}\\\\33750 & = &\pi r^{3}\\10740 & = &r^{3}\\r & = & \textbf{22.07 m}\\\end{array}\\\text{The radius of the great circle is $\large \boxed{\textbf{22.07 m}}$}[/tex]
identify the x- intercepts for
y = (x+3)^2+2
Answer:
No solutions
Step-by-step explanation:
This function would place the parabola above the x axis, so there are no x intercepts
Answer:
D
Step-by-step explanation:
There are no x-intercepts, so this has no solutions.
Hope this helps!
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.
Answer: - 2.5
Step-by-step explanation:
The point R is - 2.5,
The numbers on the number line are arranged sequentially and in regular increment of 1 with only the integer numbers being displayed and ticked. The point R sits directly in between - 3 and - 2. Therefore, to accurately obtain the position of the blue dot, we take the average of both positions binding the blue dot. That is - 3 and - 2
Average = ( - 3 + - 2) / 2
Average = - 5 / 2 = - 2.5
Answer: yea it it - 2.5 i just did that test and got it right <3
Step-by-step explanation:
What value of n makes the statement true?
6x^n• 4x^2=24x^6
n =
Answer:
n =4
Step-by-step explanation:
6x^n• 4x^2=24x^6
Combine like terms
24 x^n *x^2 = 24 x^6
We know that a^b * a^c = a^(b+c)
24 x^(n +2) = 24 x^6
Divide each side by 24
x^(n +2) = x^6
The bases are the same so the exponents are the same
n+2 = 6
Subtract 2
n+2-2 = 6-2
n=4
Answer:
4
Step-by-step explanation:
just did it
The perimeter of a room is 43 ft. The width is 9 1 2ft. What is the length?
[tex]answer = 12 \: ft \\ solution \\ perimeter = 43 ft\\ breadth = 9 \times \frac{1}{2} = \frac{19}{2 } = 9.5 \: ft\\ now \\ perimeter \: of \: \: rectangle = 2(l + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: 43= 2(l + 9.5) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: 43 = 2l + 19 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: - 2l = 19 - 43 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: - 2l = - 24 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: l = \frac{ - 24}{ - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: l = 12 \: ft \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex]length = 12ft[/tex]
Step-by-step explanation:
Given that,
[tex]width =9 \frac{1}{2} = 9.5[/tex]
Let's find the length
[tex]perimeter \\43 = 2(l + w) \\ 43= 2(l + 9.5) \\ 43 = 2l + 19 \\ 43 - 19 = 2l \\ 24 = 2l \\ \frac{24}{2} = \frac{2l}{2} \\ l = 12[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Please help.. I don't understand.. Please show workings
[tex]answer \\ = £59.25 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps[/tex]
Elsa used the multiplication table below to write ratios that are equivalent to StartFraction 12 Over 4 EndFraction.
A multiplication table.
One number is missing from the equivalent ratio, as shown.
StartFraction blank Over 12 EndFraction
What is the missing number?
6
18
24
36
Answer:18
Step-by-step explanation:because it was in the same column
Answer:
Its actually 24 because 4 times 6 is 24 and 12 times 2 is 24
A survey of 720 adults nationwide asked, "What irks you most about the actions of other motorists?" The response "tailgaters" was given by 231 people. What percent of those surveyed were most irked by tailgaters? Round to the nearest tenth of a percent
Answer: 32.08%
Step-by-step explanation:
From the question, a survey of 720 adults nationwide asked, "What irks them most about the actions of other motorists? and the response "tailgaters" was given by 231 people.
The percentage of people that responded with tailgaters will be the number of people who responded with tailgaters divided by the total survey of adults asked and then multiplying by 100. This can be mathematically written as:
= 231/720 × 100
= 32.08%
Help me!
A spinner can land on either red or blue. You spin the spinner and then roll a six-sided number cube.
What is the sample space of outcomes?
{(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
{(R, B), (B, R), (R, 1), (B, 2), (R, 3), (B, 4), (R, 5), (B, 6)}
{BR, 123456}
{1, 2, 3, 4, 5, 6, B, R}
A sample set contains every possible outcome.
The answer would be:
(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
The sample space of the outcomes is {(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
How to determine the sample spaceThe sample space of the spinner is:
S1 = {R, B}
The sample space of the six-sided number cube is:
S2 = {1,2,3,4,5,6}
When the two sample spaces are merged together, we have:
S = {(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
Hence, the sample space of the outcomes is (a)
Read more about sample space at:
https://brainly.com/question/5750471
Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30. The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (3) minus 6 = negative 42. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (negative 2) minus 6 = 18. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answer:
The correct option is;
The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18
Step-by-step explanation:
The parameters given are;
First expression 3 × X × (5 - 4) + 3 ×(X - 6)
Second expression -12 × X - 6
Therefore;
For the first expression, for all X, e have;
3 × X × 1 + 3 ×(X - 6) = -3·X + 3·X -18 = -18
The second expression gives -12·X - 6
When both expressions are equal, we have;
-12·X - 6 = -18
∴ X = (-18 + 6)/(-12) = 1
Hence the correct option is that the expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answer:
The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30
Or
Answer A
Step-by-step explanation:
Apparently, we're trying to see if ...
-3(x)(5 -4) + 3(x -6) = -12(x) -6
by evaluating the expressions for x=2:
-3(2)(5-4) +3(2 -6) ?= -12(2) -6
-6 -12 ?= -24 -6
-18 ≠ -30 . . . . . . . . . shows expressions are not equivalent
