Answers
Answer:
[tex]\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Key:
• [tex]-\left(a-b\right)=-a+b[/tex]
Step-by-step explanation:
[tex]\tan \left(2\theta\right)-\left(1-\tan ^2\left(\theta\right)\right)[/tex]
[tex]-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)[/tex]
[tex]=\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Related Questions
(1/7x + 3/8) + (2/9x - 1/8)
Answers
Expand: In (4a)^3
help please
Answers
Answer:
[tex]3\ln 4 + 3 \ln a[/tex]
Step-by-step explanation:
[tex]\ln(4a)^3\\\\=3\ln (4a)~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=3(\ln 4 + \ln a)~~~~~~~~~~~~~~~~~~~~;[\log_b (mn) = \log_b m + \log_b n]\\\\=3\ln 4 + 3 \ln a[/tex]
Find the value of x to the nearest tenth.
4.5
7.2
6.3
5.4
Answers
Answer:
there's no picture dude
AYUDA !!!
hallar el m.c.d por descomposición canónica en cada caso
A) 52 Y 78
B) 56 Y 72
C) 84 Y 96
Answers
Answer:
BStep-by-step explanation:
Always remember:beluga always love answer your question by following these steps:Follow belugaask meBrainliest me first oktake note please: everyone i answer question I got happy:)please don't delete Your question beacause Brainliest Marks & pointswill be lose- a) The volume of a rectangular tank is (2a³ + a² - 2a - 1) cu. ft. where a>4 ft., the length is longer than its breadth and the breadth is longer than its height. (i) Find its length, breadth and height. (ii) Find the area of the its floor.
Answers
The rectangle with:
The volume of (2a³ + a² - 2a - 1) ft³, a > 4 ftThe length > breadth > heightTo find(i) the dimensions(ii) the area of the floorSolution(i)Factorize the volume expression
2a³ + a² - 2a - 1 = 2a³ - 2a + a² - 1 = 2a(a² - 1) + (a² - 1) = (2a + 1)(a² - 1) = (a - 1)(a + 1)(2a + 1)If a > 4, then:
a - 1 > 4 - 1 ⇒ a - 1 > 3a + 1 > 4 + 1 ⇒ a + 1 > 52a + 1 > 2*4 + 1 ⇒ 2a + 1 > 9Since the longest dimension is the length, it is
2a + 1The breadth is the middle dimension, it is
a + 1The height is the smallest dimension, it is
a - 1(ii)The area of the floor is:
Area = length * breadthArea = (2a + 1)(a + 1) = 2a² + 3a + 1Answer:
i) length > 9 ft
breadth > 5 ft
height > 3 ft
ii) Area of floor > 45 ft²
Step-by-step explanation:
Volume of a rectangular prism
[tex]\textsf{V}=lbh[/tex]
where:
l is the lengthb is the breadthh is the heightGiven:
[tex]\sf V=(2a^3+a^2-2a-1)\:\:ft^3, \quad where\:a > 4\:ft[/tex]Part (i)
To find expressions for the 3 dimensions of the tank, factor the expression for Volume.
Using the Factor Theorem, if V(x) = 0 then (a - p) is a factor:
[tex]\implies \sf V(1)=2(1)^3+(1)^2-2(1)-1=0[/tex]
[tex]\implies \sf V(-1)=2(-1)^3+(-1)^2-2(-1)-1=0[/tex]
Therefore (a - 1) and (a + 1) are factors:
[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+p)[/tex]
(where p is a constant to be found)
To find the value of p, expand:
[tex]\implies \sf 2a^3+a^2-2a-1=2a^3+pa^2-2a-1[/tex]
and compare coefficients:
[tex]\implies \sf a^2=pa^2 \implies p=1[/tex]
Therefore:
[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+1)[/tex]
If l > b and b > h then:
length (l) = (2a + 1)breadth (b) = (a + 1)height (h) = (a - 1)If a > 4 ft then:
length > 9 ftbreadth > 5 ftheight > 3 ftPart (ii)
The area of the floor can be found by multiplying the found expressions for breadth and length:
[tex]\begin{aligned}\implies \sf Area\:of\:floor & =(a+1)(2a+1)\\& = 2a^2+3a+1\end{aligned}[/tex]
If a > 4 ft then Area of floor > 45 ft²
The average annual rainfall in Salt Lake City, Utah, is 18.58 inches, and the average annual rainfall in New York City is 46.23 inches. What might be the reason for the difference in the cities’ average annual rainfall?
A.
Utah is close to an ocean, while New York City is landlocked.
B.
New York City is close to an ocean, while Utah is landlocked.
C.
New York City lies in a rain shadow area.
D.
New York City is closer to mountains.
Answers
HELP
The table shows the time in minutes that Naima talked on the phone during the last 3 weeks.
Make a stem-and-leaf graph on your own paper, and then answer the question below.
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
Week 1
12
15
25
45
52
30
31
Week 2
22
25
46
51
10
19
33
Week 3
44
21
30
20
10
24
52
Which stems have the same number of leaves?
a.
Stems 1 and 2 each have 5 leaves
c.
4 and 5 each have 3 leaves
b.
Stems 1 and 3 each have 4 leaves
d.
3, 4, and 5 each have 3 leaves
Please select the best answer from the choices provided
A
B
C
D
Answers
The stems that have the same number of leaves are (c) 4 and 5 each have 3 leaves
How to make the stem-and-leaf graph?The table of values is given as:
Week 1: 12 15 25 45 52 30 31
Week 2: 22 25 46 51 10 19 33
Week 3: 44 21 30 20 10 24 52
Remove the week tags:
12 15 25 45 52 30 31
22 25 46 51 10 19 33
44 21 30 20 10 24 52
Sort the data values in tens
10 10 12 15 19
20 21 22 24 25 25
30 30 31 33
44 45 46
51 52 52
Now, we can now plot the stem-and-leaf graph.
This is represented as follows:
Stem | Leaves
1 0 0 2 5 9
2 0 1 2 4 5 5
3 0 0 1 3
4 4 5 6
5 1 2 2
In the above plot, we can see that stems 4 and 5 have 3 leaves each
Hence, the stems that have the same number of leaves are (c)
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Solve the inequality 4x - 7> 3
Answers
Answer:
[tex]x > \frac{5}{2} > 2\frac{1}{2}[/tex]
Step-by-step explanation:
group
[tex]4x-7 > 3\\4x-7+7 > 3+7\\4x > 3+7\\4x > 10[/tex]
isolate "x"
[tex]4x > 10\\=\frac{4x}{4} > \frac{10}{4}\\x > \frac{10}{4}\\x > \left(\frac{5\cdot 2}{2\cdot 2}\right)\\x > \frac{5}{2}[/tex]
Answer:
x > 2.5 or in fraction form x > 2 1/2
Step-by-step explanation:
4x - 7 > 3
+7 +7 Add seven to both sides.
4x > 10
÷4 ÷4 Divide both sides by 4.
x > 2.5
Hope this helps!
The endpoints of wx are w (5,-3) and x (-1,-9) what is the length of wx ?
Answers
Using the distance formula, the length of WX is approximately: 8.5.
How to Find the Length of a Segment Using the Distance Formula?Distance formula is, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the endpoints:
W(5,-3) = (x1, y1)
X(-1,-9) = (x2, y2)
Plug in the values:
WX = √[(−1−5)² + (−9−(−3))²
WX = √[(−6)² + (−6)²]
WX = √72
WX ≈ 8.5
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Answer:
6 2 with the little check mark line in the midddle
Step-by-step explanation:
A farmer has 6 pumpkins that are the same size. the mass of each pumpkin is 3 kilograms. what is the total mass of the farmer's pumpkins?
Answers
Answer: 18 kilograms
Step-by-step explanation:
If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.
[tex] \frac{2}{3} n (4p + \sqrt{36} - 2 {n}^{2} [/tex])
n= -3
p=5
need urgent help
Answers
Answer:
-16.
Step-by-step explanation:
2/3 * (-3) * (4*5 + 6 - 2(-3)^2)
= -2(20 + 6 - 18)
= -2 * 8
= -16.
If the exchange rate when converting US dollars to Za rands is $1=R17
1. How much is $100 in ZA rands
Answers
How much is $100 in ZA rands.
Solution:Let the unknown be "x"
[tex]\frac{1}{17}×\frac{100}{x}[/tex]
We'll have to do cross multiplication.
So we'll have to multiply 100 and 17.
[tex]100×17[/tex]
[tex]\huge\boxed{= 1700 \: ZA \: rands}[/tex]
Therefore, $100 is 1700 ZA rands.
Factor the expression.
12x+10
Answers
Work Shown:
12x+10
2*6x+2*5
2(6x+5)
Effectively, we use the distributive property in reverse when it comes to factoring expressions like this.
The distributive property in general is a*(b+c) = a*b+a*c
1) Find the Greatest Common Factor (GCF).
1 What is the largest number that divides evenly into 12 and 10?
It is 2.
2 What is the highest degree of that divides evenly into 12and 10?
It is 1, since x is not in every term.
3 Multiplying the results above,
The GCF is 22.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]2(\frac{12x}{2}+\frac{10}{2})[/tex]
3) Simplify each term in parentheses.
2(6x+5)
find the value of 81 3x
Answers
Answer:
27 I think just divide 81 by 3
At the local pet store, zebrafish cost $2.10 each, and neon tetras cost $1.95 each. if ernesto bought 13 fish for a total cost of $26.70 not including tax, how many of each type of fish did he buy?
Answers
Answer:
zebrafish: 9neon tetras: 4Step-by-step explanation:
The numbers of zebrafish and neon tetras can be found by writing an equation relating the numbers of each to their total cost.
__
setupLet z represent the number of zebrafish Ernesto bought. Then the number of neon tetras is (13 -z), and the total cost of the purchase was ...
2.10z +1.95(13 -z) = 26.70
solution0.15z +25.35 = 26.70 . . . . . . simplify
0.15z = 1.35 . . . . . . . . . . . . subtract 25.35
z = 9 . . . . . . . . . . . . . . . divide by 0.15
Ernesto bought 9 zebrafish and 4 neon tetras.
A binomial experiment has 4 trials in which p = 0.4. What is the probability of 3 successes?
Answers
The probability of 3 successes is 0.0384
How to determine the probability?The given parameters are:
Trials, n = 4Probability of success, p = 0.4The binomial probability is represented as:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]
So, the probability of three successes is:
[tex]P(3) = ^4C_3 * 0.4^3 * (1 - 0.4)^{4 -3[/tex]
Evaluate the factors in the expression
[tex]P(3) = ^4C_3 * 0.0384[/tex]
Evaluate the combination expression
P(3) = 1 * 0.0384
Evaluate the product
P(3) = 0.0384
Hence, the probability of 3 successes is 0.0384
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Answer:
0.1536
Step-by-step explanation:
Find the 24th term of the sequence:
11, 16, 21, . . .
Answers
Answer:
126
Step-by-step explanation:
The difference between the first two terms of this sequence is 5 (16 - 11 = 5). The difference between the second and third terms of this sequence is also 5 (21 - 16 = 5).
So, we can assume that the difference between each term in this sequence is 5. To get from the first term (11) to the second term (16) we had to add 5 once. (or, add 5 x 1 [time])
To get from the first term (11) to third (21), we had to add 5 twice
(or, add 5 x2)
*repeated addition, such as 5+5+5 is the same thing as multiplication. If we are adding 5 three times, we will get the same outcome as 5 x 3.
So, to get from the first term (11) to the 24th term, we will have to add 5 23 times, or 5 x 23
5 x 23 = 115
11 + 115 = 126
Making 126 the 24th term of the sequence
question 3 help me please
Answers
Answer:
3x+(4x-1)+90°=180°{sum of angles in a triangle}
3x+4x-1+90°=180°
7x+89°=180°
7x=180°-89°
7x=91°
divide both sides by 7
x=13
Answer:
The answer is x=13
what is the product of 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°))
Answers
The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Complex number is in the form z = a + bi, where a and b are real numbers.
The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:
z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]
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6+x^4-3x^2-5x
WHAT IS THE CONSTANT AND WHY
Answers
Think of a constant as a bald number
Constant is just a simple number with no xs attached
1 2 3
-1 -2 -3
Answer:
6
Step-by-step explanation:
The constant is the number that's all by itself with no variable.
x is the variable. It can vary (change) as you use different values for x.
There are four terms here in the expression in your question they are separated by the plus or minus signs.
2 and 4 are exponents. 3 and 5 are coefficients.
x^4 is a fourth degree term. 3x^2 is a second degree term. 5x is a first degree term. The whole expression is 4th degree because the highest exponent is 4.
But the 6 is all by itself. 6 is the constant.
Consider triangle ABC. What is b?
Answers
Answer:
A triangle is equal to 540° so you do 112 add 37 which equals 149° then take it away from 540 which gives you 391° as your answer
Step-by-step explanation:
Your Welcome
12. If you buy a bag of pretzels ($0.75 per bag) and a Pepsi ($1.25) every weekday at work from a vending machine, how much do you spend on the vending machine products over the course of a year (52 weeks)
Answers
0.75 + 1.25 = $2 everyday
Since there are 5 weekdays:
5 x 2 = $10 a week
Since there are 52 weeks in a year:
10 x 52 = $520 a year!
There is a pair of parallel sides in the following shape.
6, 7 and 5
What is the area of the shape?
Answers
I think it's 28 units²
enter the value of z when y = 7 and x = 14.
Answers
The value of z is 7 when y = 7 and x = 14.
Complete questionIf x varies directly as y and inversely as z and when y = 16 and z = 14, x = 16. Enter the value of z when y = 7 and x = 14.
How to determine the value of z?The variation involves a direct and inverse variation from x to y and z.
This is represented as:
[tex]x = \frac{ky}{z}[/tex]
Where k is the constant of variation
For the first set of values, we have:
[tex]16 = \frac{k * 16}{14}[/tex]
Solve for k
k = 14
For the second set of values, we have:
[tex]14 = \frac{k * 7}{z}[/tex]
Substitute 14 for k
[tex]14 = \frac{14 * 7}{z}[/tex]
Solve for z
z = 7
Hence, the value of z is 7
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I don’t understand how to solve this question, can I have an explanation? I will give Brainliest.
Answers
Answer:
d
Step-by-step explanation:
the fitness grows into bodyness from good
Find the value of x and y.Please help!
Answers
The value of x and y in the right angle triangle are 6 units and 10.4 units.
How to find side of a right triangle?The sides of a right triangle can be found as follows:
using trigonometric ratio,
sin 60 = opposite / hypotenuse
sin 60 = y / 12
cross multiply
y = 12 sin 60
y = 10.3923048454
y = 10.4 units
Therefore,
cos 60 = adjacent / hypotenuse
cos 60 = x / 12
x = 12 cos 60
x = 6 units
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So we conclude that x measures 6 units and y measures 10.39 units.
How to find the value of x and y?
Here we have a right triangle.
x is the adjacent cathetus to the shown angle, and y is the opposite cathetus. We can see that the hypotenuse measures 12.
Then using trigonometric relations we get:
y = sin(60°)*12 = 10.39x = cos(60°)*12 = 6So we conclude that x measures 6 units and y measures 10.39 units.
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Kat is painting the edge of a triangular stage prop with orange paint. The lengths of the edges of the triangle are (3x-4) feet, (x2-1) feet, and (2x-15) feet. What is the perimeter Of the triangle if x =4
Answers
The perimeter of the triangle is 16 feet
What is the perimeter of a triangle?The perimeter of a triangle refers to the calculation of the total distance bounded by the triangle or around the triangle.
Perimeter of a triangle = (3x - 4) + (x² - 1) + (2x - 15)
Perimeter of a triangle = 5x + x² - 20
If x = 4Perimeter of a triangle = 5(4) + (4)² - 20
Perimeter of a triangle = 16
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yyghhghh pls help jgghdeshr3fwqhqjwgdqe
Answers
Answer: The answer is 22
Step-by-step explanation: you divide the 36 and the 9 to get 4 then you add the 18 and the 4 to get 22
Answer:
22
Step-by-step explanation:
[tex]18+(\frac{36}{9})=?\\ 18+4=?\\22=?[/tex]
RIDDLE ME THIS:
You are in a race. You pass the person in second place. What place are you in now.
Answers
classify the pair of angles. then find the value of x.
(need help with 13 & 15!)
Answers
The value of x from the figures are 18 and 26 respectively
Vertical and complementary angles13) From the diagram, the angles at the corner is 90 degrees. This shows that the sum of the angles is complementary (sum is 90 degrees)
3x + 2x = 90
5x = 90
x = 90/5
x = 18
15) Since the sum of angles on a straight line is supplementary, hence;
6x + x - 2 = 180
7x = 182
x = 182/7
x = 26
Hence the value of x from the figures are 18 and 26 respectively
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