Answer:
true
Step-by-step explanation:
Answer: true
step by step explanation:
If tan a = x + 1 and tan ß = x - 1, then verify that: 2cot(a - B) = x²
[tex]
\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]
Hence verifying that 2cot(α - β) = x².
Angle Relationship
Find mLTSU if SU bisects LTSV,
mLTSU = 4y + 11, and m∠USV = 6y + 5.
< TSU = 4y + 11 = 23 degrees
What does angle relationship mean?
We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles
we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5
SU bisects < TSV
=> < TSU = < USV
4y + 11 = 6y + 5
-2y = -6
y = 3
< TSU = 4y + 11 = 23 degrees ( put the value of y=3)
∠USV = 6y + 5 = 23 degrees ( put the value of y=3)
Hence ,< TSU = 4y + 11 = 23 degrees
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Find x and y, i only need the answer so no need to show work
Step-by-step explanation:
X=48 becase 42+90=132
180-132= 48
Round 3.691 to the nearest hundredth
Answer: 3.69
Step-by-step explanation:
Answer:
3.69
Step-by-step explanation:
If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.
Solve for x.
5(2+1)<5x+3
You're to prepare 850 mL of D8W form D10W and sterile water for injection. How many milliliters of D10W will you need?
The volume of D10W solution required to be diluted to make 850 mL of D8W solution is 680 mL.
How can the dilution contents be calculated?The dilution formula can be presented as follows;
[tex]C_1 \cdot V_1 = C_2 \cdot V_2[/tex]
Where;
[tex]C_1 = Initial \: concentration = D10W [/tex]
[tex]V_1 = Initial \: volume [/tex]
[tex]C_2 = Final \: concentration = D8W[/tex]
[tex]V_2= Final \: volume = 850 \: mL [/tex]
Which gives;
[tex]V_1 = C_2 \cdot V_2/C_1[/tex]
V1 = 8×850/10 = 680
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after seven years , an intitial investment of $600 earned $84 find the interest rate
The interest rate 2% per year
How to calculate the interest rate ?The time period is 7 years
The initial investment is $600
The current investment is $84
The interest rate can be calculated as follows
84/600 × 7
= 84/4200
= 0.02
The interest rate is
= 0.02 × 100
= 2%
Hence the interest rate is 2%
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They wrote the model `n=40\cdot1.5^{t}` , where `n` is the total number of squirrels and `t` is the number of years since the biologists started counting. How many squirrels do the biologists predict there will be `2` years after they started counting
The number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.
How to illustrate the information?It should be noted that a function is used to show the relationship between the variables.
It should be noted that the function that's given is illustrated as:
n = 40 + 1.5t
In this case, it should be noted that t = 2 years.
Therefore, the number of squirrels that the biologists predict there will be 3 years after they started counting will be:
n = 40 + 1.5t
n = 40 + 1.5(2)
n = 40 + 4
n = 43
Therefore, the number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.
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Put these winning lottery numbers in the correct order.
Select the boxes and type in the correct answers.
lowest
48
5
23
11
9
20
Find each of the following by first summing all the negative and positive numbers separately
and then combining the final positive and negative. Show your work.
(a) -8+-9+7+4
(b)-18+6+-22+28
(c) 24+19+-6+10+-12
(d) -18+32+14+21+-50
Applying addition of integers, the final results of the expressions are given as follows:
a) -6.
b) -6.
c) 35.
d) -1.
How do we add two integers?To add two integers, we have to keep in mind their signals, if they are the same or different, as follows:
If they have the same signal, we keep the signal and add the numbers.If they have the different signal, we take the signal of the largest absolute number(largest number without the signal), then subtract the amounts.Hence, for item a, we have that:
-8 - 9 = -17.7 + 4 = 11.-17 + 11 = -6.For item b, the solution is found as follows:
-18 - 22 = -40.6 + 28 = 34.34 - 40 = -6.For item c, the solution is found as follows:
-6 - 12 = -18.24 + 19 + 10 = 53.53 - 18 = 35.For item d, the solution is found as follows:
-18 - 50 = -68.32 + 14 + 21 = 67.67 - 68 = -1.More can be learned about addition of integers at https://brainly.com/question/17695139
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Kim went to the store and bought three shirts.
She spent $26.30. One shirt cost $8.72, and
another cost $10.79. How much did the third shirt
cost?
Answer:
$6.79
Step-by-step explanation:
You add the cost of the first two then subtract that by the total she spent to get the answer
$10.79 + $8.72 = $19.51
$26.30 - $19.51 = $6.79
Ten times the sum of a number and nine is 290. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
Step-by-step explanation:
10+290=x is the answer
x=290-10
x=280#
write 25x + 2 as a verbal expression
The required verbal form of the expression is two more than 25 times of a number.
Given that,
An expression is given we have to determine the verbal expression of the given algebraic expression.
The algebraic expression consists of constant and variable. eg x, y, z etc.
Here,m
Given expression = 25x + 2
Where x is any variable number 25 times and further added 2.
So.
The verbal expression can be given as
two more than 25 times of a number.
Thus, the required verbal form of the expression is two more than 25 times of a number.
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Answer the question.
The distance from the Earth to the Sun is about 1.5 x 108 km, while the distance from the Earth to the
moon is about 3.8 x 105 km. If a scale model of the solar system is constructed so that the distance
from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon?
Select one:
O a. 39, 474 m
O b.
39.5 m
O c. 6.36 m
O d. 0.25 m
The distance from the Earth to the moon, in the scale model, is d. 0.25 m
As per the known fact, ratio of measurement in real is equal to the ratio of measurement on scale. Further, ratio will be calculated in this case as -
Distance from Earth to Sun in real : Distance from Earth to Moon in real = Distance from Earth to Sun on scale : Distance from Earth to Moon on scale
Keep the values in mentioned relation to find the distance from Earth to Moon.
1.5×10⁸:3.8×10⁵ = 100:distance from Earth to Moon on scale
Distance from Earth to Moon on scale = 100×3.8×10⁵/1.5×10⁸
Distance from Earth to Moon on scale = 0.25 m
Therefore, the correct option for distance is d. 0.25 m.
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Randi went to Lowe’s to buy wall-to-wall carpeting. She needs 111.02 square yards for downstairs, 31.82 square yards for the halls, and 161.92 square yards for the bedrooms upstairs. Randi chose a shag carpet that costs $15.01 per square yard. She ordered foam padding at $3.12 per square yard. The carpet installers quoted Randi a labor charge of $3.77 per square yard.
What will the total job cost Randi?
Round your answer to the nearest cent.
help please
Using proportions, it is found that the total job cost for Randi is of $6,674.24.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The total amount of square yards that she needs is given by:
111.02 + 31.82 + 161.92 = 304.76.
The cost per square yard is given by:
15.01 + 3.12 + 3.77 = $21.9.
Hence the total cost is given by:
304.76 x 21.9 = $6,674.24.
The total job cost for Randi is of $6,674.24.
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Building A is 251 meters taller than building B. If the height of building A is subtracted from twice the height of building B, the result is 223 meters. How tall is each skyscraper?
Answer:
Step-by-step explanation:
All students in the 6th grade either purchased their
lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the 6th grade?
i need a really detailed answer
The number of students in the 9th grade is 250.
How to calculate the value?Based on the information, the percentage of those who brought their good from home will be:
= 100 - 24%
= 76%
Therefore, 76% of x = 190
0.76x = 190
x = 190/0.76
x = 250
Therefore, the number of students in the 9th grade is 250.
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Explain how you would estimate the value of 57−−√ by determining the two consecutive whole numbers that it lies between. Write the two numbers and explain the process you used to select them.
The two consecutive whole numbers that it lies between are 28 and 29.
What are the consecutive numbers?The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.
Let the two consecutive numbers be x and x + 1
x + x + 1 = 57
Combine like terms;
2x + 1 = 57
Now Subtract 1 from both sides;
2x = 57- 1
2x = 56
Divide both sides by 2
x = 56/2
x = 28
Thus, x + 1 = 28 + 1 = 29
The two consecutive whole numbers that it lies between are 28 and 29.
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Can someone please help me I will mark u brilliant I need the points for Q R and S
Select the correct answer.
Why is the responsibility for maintaining roads and streets given to municipal governments?
O A.
The federal government would not have time to get to all the roads.
O B.
The local government has better knowledge about the needs in its area.
O C. The state government does not want to pay maintenance crews.
O D.
The county government does not have the power to pave roads.
Hurryyyyyyyy pls
Answer:
OA
Step-by-step explanation:
the federal government only manages the things about the country , that's why there are different types of government becuz each one of them has responsibilities
the table shows the estimated sales for two different prices of bags of chips. Calculate the profit per bag for the bags sold at 3$ each
The profit per bag for the bags sold at 3$ each is $1.5 per bag.
How to calculate the profit?The total cost will be:
= $300000 + (1 × $600000)
= $900,000
The revenue will be:
= $3 × 600000
= $1,800,000
Therefore, the profit per bag will be:
= ($1800000 - $900000) / 600000
= $900000/600000
= $1.5
The profit is $1.5.
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Is (1, 10) a solution to the inequality y ≤ 4x + 1?
Answer:
(1,10) is not a solution to the inequality.
Step-by-step explanation:
First, you want to insert the values of x and y in the inequality.
So, [tex]10\leq 4(1) +1[/tex]
[tex]10\leq 5[/tex]
That inequality is not true, so we know that (1,10) is not a valid solution.
Is this true
4. When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. For example, 12 – 4 is 8 and 11 – 4 is 7
When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.
How to calculate the value?It should be noted that in subtraction when you reduce the first number, you will get a value that's lesser by 1.
In this case, if we have 20 - 5 = 15, then 19 - 5 = 14. We can see that 14 and 15 is a difference of 1.
Therefore, when you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.
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left parenthesis 3 plus 4 right parenthesis plus 5 equals 3 plus left parenthesis 4 plus 5 right parenthesis is an example of the ______________property.
1. inverse
2. associative property
3. identity property
4. commutative property
Answer:
2 associate property
Step-by-step explanation:
(3 + 4) + 5 3 + (4 + 5) On the left side, the 4 is "associating" with the 3", but on the left side the 4 is "associating;" with the 5.
Solve first principle of y=X^3
Answer:
3x^2
Step-by-step explanation:
Explained in image.
Write a slope-intercept equation for a line passing through the point (4,7) that is parallel to y=x+1. Then write a
second equation for a line passing through the given point that is perpendicular to the given line.
Answer:
y = x + 3
y = -x + 11
Step-by-step explanation:
When the slopes are parallel they are the same. When slopes are negative, the slope is the negative reciprocal.
Parallel: The slope is 1. This is the coefficient of the x in the equation given. If you do not see a number before the x like in y = x + 1, then number is 1.
Use this form:
y =mx + b Us the slope of 1 to put in for m. Use 4 for x and 7 for y
7 =(1)4 + b Solve for b.
7 = 4 + b Subtract 4 from both sides.
3 = b
The equation for the parallel line is
y = x + 3.
Perpendicular:
y = mx + b This time the slope is -1 Still use 4 for x and 7 for y
7 = (-1)4 + b
7 =-4 + b add 4 to both sides
11 = b
The equation would be y = -x + 11
11. A trader bought 2 cows and 9 goats for a total of ksh. 98 200. If she had bought 3 cows and 4 goats, she would have spent ksh. 2200 less a) Taking C to be the number of cows and G to be the number of goats, form two equations to represent the above information. b) use substitution method to represent the above information
By using subtraction method we get 55.157.8987
What is subtraction method?
In mathematics, subtraction refers to the act of removing something from a set of related objects or numbers. What is left in the group decreases as a result of subtraction.
Let cost of each cow=x
cost of each goat =y
Given 2x+9y=98200------------(equation 1)
9y=98200-2×Y=98200-2x/9-----------(equation 2)
Also 3x+4y= 9800+2200
3x+4y=1004004y=100,
400-3xY=100400-3x/4---------(equation 3)
From equation 2 and 3 we get
Y=Y98200-2x/9
=100400-3x/4
=196,400-8x
=301200-27x
=19x
=104,800
=x=55.157.8987
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20 cm
13 cm
7 cm what is the area of the shape?
Answer:
270cm2
Step-by-step explanation:
you have to split the figure into 2.
the triangle above is = 1/2 x20cmx13cm=130cm2
the rectangle is = 20cmx7cm=140cm2
total area=140cm2+130cm2
=270cm2
the cost of 1 dorzen of pencils is rs 80 find the cost of 18 pencil
Answer:
soln
given,
1dozen=rs 80
therefore,cost of 18 dozen pencils =80 × 18
=1440 Rs
What is the area, in square units, of the parallelogram shown below? D A 7 units C H5 units O 20 square units O 25 square units 30 square units O 35 square units B
Answer: The answer is C
Step-by-step explanation: