Simplify each trigonometric expression. 1-cos² θ
Answer:
[tex]\sin ^2\left(\theta\right)[/tex]
Step-by-step explanation:
Pythagorean identity
[tex]1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\\1-\cos ^2\left(x\right)=\sin ^2\left(x\right)\\=\sin ^2\left(\theta\right)[/tex]
2. Read each question. Then write the letter of the correct answer on your paper.Solve the equation a x²+b x+c=0 for b .
(F) b=-c x-a x² (H) b=-(c x-a x²) (G) b=-c-a x² / x Ib=-(c-ax²)/x
Solution of the equation a x ² + b x + c = 0 for b is b = ( - c - a x ² ) / x
Given,
the polynomial to be solved
a x ² + b x + c = 0
Solving the equation for b implies that we get the value of b from the above given polynomial
We can solve the given polynomial a x ² + b x + c = 0 by rearranging the terms of the polynomial and taking the LHS as b and the RHS as a term consisting of a, c and x
a x ² + b x + c = 0
=> b x = - c - a x ²
=> b = ( - c - a x ² ) / x
This gives us the required answer. It matches with option G among the given multiple choices.
Therefore, we get the solution of the equation a x ² + b x + c = 0 for b as b = ( - c - a x ² ) / x
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Question 7 (1 point)
The use of electricity in the US in 1902 was 6.03 x 10^9 kilowatt-hours.
The use of electricity in the US in 1950 was 4.3 x 10^11 kilowatt-hours.
What was the total kilowatt-hours of electricity used during these two years?
Ob
Oc
Od
(6.03 x 10^9) + (4.3 x 10^11) = 10.33 x 10^20 = 1.033 x 10^19
(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11
(6.03 x 10^9) x (4.3 x 10^11) = 25.929 x 10^20 = 2.6 x 10^19
(6.03 x 10^9) x (4.3 x 10^11) = 25.929 x 10^2 = 2.6 x 10^1
Using scientific notation, the total kilowatt-hours of electricity used during these two years is:
(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For two numbers in scientific notation to be added or subtracted, they need to have the same exponent.
Thus, the first amount has to have an exponent of 10^11, meaning that the exponent has to be added by 2 = equivalent to addition by 100, and to compensate the base has to be divided by 100, hence:
(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11
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simplify the expression 5(2g + 3)
Answer:
10g+15
Step-by-step explanation:
5x2g=10g
5x3=15
Jennifer states that the square root of any number is irrational. Explain why Jennifer is incorrect. PLEASE HURRY!!
Answer:
See explanation below
Step-by-step explanation:
A rational number is one that can be expressed as p/q where p and q are integers. An irrational number, of course, is just the opposite
Rational numbers example: 1/2, 5/6 2, 20/3, - 5/6 0, etc
Irrational numbers example: π, √2 , √3 etc
Basically the square root of a prime number is irrational
Thus √2, √7, √13 are all irrational numbers. They cannot be represented as a ratio of an integer to another integer
However, not all square roots are irrational number.
If the number is a perfect square then its square root will be a rational number
For example √36 is 6 which is a rational number (6/1)
√1 is 1 which is also a rational number
So Jennifer is incorrect in stating that the square root of any number is irrational
1
O What is the value of 6a + 9b?
Answer:
[tex]3(2a + 3b) [/tex]
Step-by-step explanation:
3×2a+3×3b
1. For a fundraiser, the ratio of tickets you sold to tickets your friend sold was 11:5.
Does that mean you sold 11 raffle tickets and your friend sold 5 raffle tickets? Explain your
reasoning.
Answer:
No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.
Step-by-step explanation:
It is given that for a fundraiser, the ratio of tickets you sold to tickets your friend sold was 11:5.
Let us look at the ratio of tickets sold by both the persons.
Now, according to the condition given and the ratio mentioned in the question;
The number of tickets sold by me for the fundraiser be = 11x
and
The number of tickets sold by my friend for the fundraiser be = 5x
It is observed that total number of tickets sold by me and my friend are;
=> 11x + 5x
So, it is inferred that the number of tickets sold by me and my friend are not 11 and 5 respectively and can vary upon the value of x.
For instance, if the value of x = 2 than;
=> 11x + 5x
=> 11 × 2 + 5 × 2
=> 22 + 10
=> 32 tickets
Therefore,
No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.
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I’m the figure below F is between E and G and G is between F and H if FG=5 and EG=11 and FH=8 find EH
Answer:ur mom
Step-by-step explanation:
Here is a graph of the function f.
Use the graph to find the
following.
If there is more than one answer, separate them with commas.
(a) All values at which / has a local maximum : .
(b) All local maximum values of
The required solution of the following are,
(a) All values at which / has a local maximum: -2 and 4
(b) All local maximum values of 3 and 2
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
looking over the curve there are two maxima
first at (-2,3) and the second is at (4, 2)
So the local maximum is at x = -2 , 4
And maximum is y = 3 ,2
Thus, the required solution of the following are,
(a) All values at which / has a local maximum: -2 and 4
(b) All local maximum values of 3 and 2.
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What is the answer to the following : 4/7 times 4/7
Given:
[tex]\frac{4}{7}[/tex] × [tex]\frac{4}{7}[/tex]Solution in Exact Form:
[tex]\frac{16}{49}[/tex]Hope this helps!
HELP ME PLEASEEE TY Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
( ) point
The rational number that can be used to represent the number of points needed for Abraham to get an A will be 1.5.
What is a rational number?It should be noted that a rational number is the number that can be written as a fraction. It can be while numbers and decimals have well.
Therefore, since Abraham needs one-half of a point to get an A– in Math, the rational number that can be used to represent the number of points needed for Abraham to get an A willbe 1.5.
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Meredith lives 24blocks from her friend's house. if she travels 1block every minute, how many minutes will it take her to reach her friend's house? what if she travels 2blocks every minute? show how you calculate each answer.
Answer:
1 block per minute: 24 minutes. 2 blocks per minute: 12 minutes.
Step-by-step explanation:
For the 2 blocks per minute one, it would just be 24/2 because she is going 2 blocks per minute, equaling 12.
A
-5-(-y)
B
-5+y
C
y-5
Part A: Evaluate the 3 expressions when y = 2.
Part B: Are the expressions equivalent to each other?
Explain.
Answer:
-3
Step-by-step explanation:
yes the expressions are equivalent to each other.
as,
A=-5+y, B=-5+y, C=y-5
supongamos que hay una temperatura de 1.3ºF por cada mil pies que un avión sube al cielo, la temperatura en el suelo es -2.8ºF. escriba una ecuación de multiplicación para representar el cambio de temperatura después de que el avión ascienda .10000 fest ¿cuál será la temperatura cuando el avión alcance una altitud de 10.000 pies?
Answer: Total temperature = -6.66ºF
Step-by-step explanation:
Given data,
First temperature = 1.3ºF
Second temperature = -2.8ºF
Fest = 10.000
So,
We can write,
1.3º x + (-2.8º) x = 10.000
x (1.3º - 2.8º) = 10.000
x (-1.5º) = 10.000
x = 10.000/-1.5º
x = -6.66ºF
Therefore,
Total temperature = -6.66ºF
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Multiply and simplify. 6√4 x² . 2√9 x² y²
Solving the problem by multiplying and simplifying we have as a result 72x⁴y²
What is simplification?Simplification is a process of reducing terms to expressions, which do not generate changes or values.
What is multiplication?Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:
a x b the number "a" will be added "b" times.
The algebraic expression that we must simplify to its minimum expression is:
6√4 x² . 2√9 x² y² we can see that it is an expression that has two variables
6×2x² × 2×3x²y²
12x² × 6x²y² ; multiply power of equal base
72x⁴y²
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HELPPPP
Question 11 (1 point)
(02.05 LC)
What number is 70% of 60?
Input only whole numbers. (1 point)
Blank 1:
Answer: 42
Step-by-step explanation:
70% = 70/100 as a fraction. 60 is 60/1 as a fraction.
Using this information, set up your question.
--> 70/100 x 60
Multiply the fractions together and you get 4200/100. This then simplifies/is equivalent to 42. Therefore, 70% of 60 is 42.
What are the domain and the range of this graph?
The domain is x≥0 and the range is y≥0.
The domain is x≥1 and the range is y≤2.
The domain is x≥2 and the range is y≥1.
The domain and range is the set of all real numbers.
The domain and range is the set of all real numbers.
the domain is 0...............
solve each inequality.
[tex]| |3x-1|+5| < 1[/tex]
Solving the inequality for the absolute value of x gives x < 1
What are inequalities?
Inequalities are simply defined as mathematical expressions showing comparison between two equations that are unequal.
They are known for explaining the relationship between values that are not equal to each other.
It is also important to note that absolute values of numbers holds that no number carries the negative sign
It is denoted with the symbol ' | | '
Given the expression;
| | 3x - 1 | + 5 | < 1
expand the bracket
3x - 1 + 5 < 1
Take absolute value
3x - 1 + 5 < 1
collect like terms
3x - 1 < 1 - 5
3x < -4
3x < - 4 + 1
3x < - 3
Make 'x' the subject
x < -3/ 3
x < - 1
x < 1
Thus, solving the inequality for the absolute value of x gives x < 1
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adding and subtracting polynomials
Answer:
1. 9x + 7
3. 7x + 1
5. 5x^2 + 3x
7. 8x + 8
Step-by-step explanation:
I need help. who understands this I really need help here. Please.
Answer:
180= (2x-24 )+ (x+5)
180= 3x-21
+21 +21
201=3x
/3 /3
67=x
Nadira made this table of all the possible outcomes of rolling two 6-sided number cubes and finding the sum of the numbers facing up on the cubes. What is the probability of rolling a sum greater than 10?
Answer:
am pretty sure its 1/4 bc the first guys answer wasn't provided in the answer choices so i had to ask my teacher for help and the answer is 1/4 for those still stuck on this problem !!
Step-by-step explanation:
pls help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I did number 11 and 13 for you and gave an explanation, I hope this helped, if you need more help just comment and let me know, have a great day! <3
Step-by-step explanation:
If the equation is addition like number 11, all you have to do is subtract 1.7 from the solution; which is 4.98. It will look like this:
4.98 - 1.7 = 3.28
if the equation is subtraction like number 13, then you have to add 6.55 with the solution, which is 2.45, it will look like this:
6.55 + 2.45 = 9
find x. pls asap
i need explanation as well
Answer:
7/5 or 1.4
Step-by-step explanation:
1. Cross multiply. 5(2x-1)= 3(3)
2. Simplify and add 5. 10x -5= 9. 10x = 14
3. Divide by 10. 10x/10 = 14/10
X= 14/10= 7/5 or 1.4
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A small child weighs 60N. If mommy left him sitting on the top of stairs, which are 10 m high, how much energy does the child have?
The energy is 6000 joules.
What is Energy?The stored energy that depends upon the relative position of various parts of a system.
Given:
weight = 60N
height = 10 m
So, the energy is
Energy=mgh,
Energy =60*10*10
Energy =6000 joules
Hence, the energy is 6000 joules.
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Solve the equation for the indicated variable. Ax+By=C; y
Answer:
y = (C-Ax)/B
Step-by-step explanation:
We first move Ax to the right by subtracting from both sides
Ax+By=C
Ax+By - Ax = C - Ax
By = C - Ax
Now we divide by B
y = (C - Ax)/B
note that it only works if B ≠ 0
Answer:
y = [tex]\frac{C-Ax}{B}[/tex]
Step-by-step explanation:
Ax + By = C ( subtract Ax from both sides )
By = C - Ax ( divide both sides by B )
y = [tex]\frac{C-Ax}{B}[/tex] (B ≠ 0 )
Please Help its A Geometry Question I will AWard Brainlist thank you
I just answered something very similar to this haha, but the sum of all exterior angles, regardless of the polygon's sides is always equal to 360 degrees, so our sum is 360°
A vehicle travels 55 miles per hour and 20 miles per gallon.
a. Write an equation that represents the distance d (in miles) that the vehicle travels in t hours. Then write an equation that represents the distance d (in miles) that the vehicle travels using g gallons of gasoline.
b. Write an equation that relates g and t. Then solve the equation for g.
c. Thevehicletravelsfor6hours.Howmanygallons of gasoline does the vehicle use? How far does it travel? Explain.
Step-by-step explanation:
The distance d (in miles) you travel in a car is given by d=55t where t is the time (in hours)
The distance d (in miles) you travel in a car is given by d=20g where g is the number of gallons of gasoline the car uses.
1. Write an equation that relates g & t.
20g=55t20g=55t
2. Solving for g.
20g=55t20g=55t
=> g=\frac{55t}{20}g=
20
55t
Hence, g= 2.75tg=2.75t
3. You travel for six hours. How many gallons of gasoline does the car use
We will use this equation g= 2.75tg=2.75t to solve the question.
Putting t = 6
g= 2.75(6)g=2.75(6)
g = 16.5 gallons
4. How far do you travel?
We can use equation d=55td=55t here
d=55\times6=330d=55×6=330 miles
A carpenter cuts a piece of lumber into two pieces. One piece is twice the size of the other.
If the smaller piece is 16 inches. How long was the whole piece of lumber before it was cut
Answer: 32
Step-by-step explanation: If the second piece is twice the size of tee smaller one then you’d want to multiply 16 by 2 or add 16+16 which would give you 32
Answer:
48
Step-by-step explanation:
16x2=32 32+16=48
is the relationship between the time spent swimming and the number of weeks proportional? the points a straight line that through the orgin.
The relationship is proportional because, the points lie on a straight line that goes through the origin.
What is a Proportional Relationship?A relationship that is proportional has a straight line graph that must pass through the origin, whereby the constant of proportionality, k = y/x, where x and y are the variables of the proportional relationship.
An example of a graph that represents a proportional graph is shown in the attachment below. The graph is a straight line graph that passes through (0, 0), which is the origin. The constant of proportionality, k = 21/7 = 3.
Thus, for the relationship between time spent swimming and the number of weeks to be proportional, it means that:
the points lie on a straight line that goes through the origin.
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Cassie has a small cube-shaped box.its volume is 125 cubic centimeters what is the area of the area of one face of the box ?
Answer: 5
Step-by-step explanation: