Given:
The pair of expressions in the options.
To find:
The two expressions are equivalent for any value of y.
Solution:
Two expressions are equivalent for any value of y, iff they are equivalent.
[tex]3(3y+3)=3(3y)+3(3)[/tex]
[tex]3(3y+3)=9y+9[/tex]
Clearly, [tex]3(3y+3)[/tex] is not equivalent to [tex]6y+6[/tex] or [tex]9y+6[/tex]. So, options A and B are incorrect.
[tex]9(y+3)=9(y)+9(3)[/tex]
[tex]9(y+3)=9y+27[/tex]
[tex]9(y+3)=27+9y[/tex]
The expression [tex]9(y+3)[/tex] is not equivalent to [tex]12+9y[/tex]. So, option C is incorrect.
The expression [tex]9(y+3)[/tex] is equivalent to [tex]27+9y[/tex].
Therefore, the correct option is D.
Marking brainliest please help me
Answer:
I think B
Step-by-step explanation:
Not sure but seems like so. Hope I helped U :)
Can someone please please help me with my math , english and health questions. im failing in all these classes and extremely need help. Some already have one answer but it isnt correct or someone just wrote down stuff just to get points. ( Will Mark Brainliest for each correct answer).
Answer:
okie we will try our best
evaluate without using a calculator sin(90-x)cos(180-x)+tanx.cos(-x)sin(180+x)
1000000
Step-by-step explanation:
son mil ovhomil
Answer this question pls!! (Will give Brainliest)
Answer:
1. Not equivalent
2. Not equivalent
3. Equivalent
4. Equivalent
5. Equivalent
Step-by-step explanation:
I will prove the ones that are equivalent, since the ones that aren't are pretty straightforward.
2(3h + 7) = 6h + 14
3. 6h + 7 + 7 = 6h + 14
4. 3h + 3h + 14 = 6h + 14
5. (3h + 7) + (3h + 7) = 6h + 14
In ΔNOP, the measure of ∠P=90°, PO = 48, NP = 55, and ON = 73. What is the value of the sine of ∠N to the nearest hundredth?
Answer:
[tex]\sin(N) = 0.66[/tex]
Step-by-step explanation:
Given
[tex]\angle P = 90^o[/tex]
[tex]PO = 48; NP = 55; ON = 73[/tex]
Required
[tex]\sin(N)[/tex]
The given parameters is illustrated with the attached image.
From the attached, we have:
[tex]\sin(N) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(N) = \frac{PO}{ON}[/tex]
[tex]\sin(N) = \frac{48}{73}[/tex]
[tex]\sin(N) = 0.66[/tex] -- approximated
Sam is getting ready for a big date when he realizes that he has no money. his roommate, Bill, also has no money, but he has a credit card. knowing that nobody will let Sam use Bill's credit card, Sam asks Bill to put out a cash advance for $120.00. Bill agrees under the condition that Sam is responsible for all interest that accrues on the cash advance which is 30% interest rate, compounded monthly. The $120 cash advance is repaid in monthly installments over 5 years. How much should Bill ask Sam to pay in interest for the cash advance?
Answer:
b 112.80
Step-by-step explanation:
took test on edge
The interest that accrues on the initial down payment at 30% interest rate is $408 .
What is interest?The term interest refers to money that accrues on a principal sum. It is commonly employed in the parlance of borrowing money.
Since it is a compound interest;
A = P(1 + r/n)^nt
Where;
A = amount
P = principal
r = rate
n = number of times compounded per year
t = total time taken
A = 120(1 + 0.025)^12 × 5
A = $528
A = P + I
I = A - P
I = $528 - $120
I = $408
Learn more about compound interest: https://brainly.com/question/25857212
Help plis I don’t understand ✋✋
Trapezoid Area =
[ ( Sum of the rules ) × ( height ) ] ÷ 2
_________________________________
Area = [ ( 2 + 3 ) × 3 ] ÷ 2
Area = [ 5 × 3 ] ÷ 2
Area = 15 ÷ 2
Area = 7.5 m^2
Find P(15,6) The subject is permutations
Answer:
3603600
Step-by-step explanation:
I used my calculator
Lee watches TV for 4 hours per day. During that time, the tv consumes 150 watts per hour. Electricity cost (12 cents)/(1 kilowatt-hour). How much does Lee's tv cost to operate for a month of 30 days?
Answer:
$2.16
Step-by-step explanation:
150 * 4 = 600watt-hours
600 = 0.6kilowatt-hours
0.6 * 30 = 18kilowatt-hours
18 * 0.12 = $2.16
3/2 of a number is less than this number?
true or false, justify your answers
Answer:
False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2
Answer:
false
if the number is X
3/2 of X= X 1/2
[tex]x \frac{1}{2} > x[/tex]
In ΔQRS, r = 1.5 inches, ∠S=23° and ∠Q=22°. Find the length of s, to the nearest 10th of an inch.
Answer:
0.8 inches
Step-by-step explanation:
< R = 180-23-22 = 135°
the length of s = 1.5 × sin 23° / sin 135°
= 1.5 × 0.391 / 0.707 = 0.5865/0.707
= 0.8 inches
Find the value of x.
where happened if you have sex
Answer:
you have a chance of having a baby...
Answer:
chance of relief stress and having a baby
Step-by-step explanation:
hope it helps you
Help Please. Can't seem to understand how to do this. I have tried and watch over 5 videos. Can't seem to get it.
Answer:
The solutions are the following:
z=2(cos(π6)+isin(π6))=√3+12iz=2(cos(2π3)+isin(2π3))=−1+i√3z=2(cos(7π6)+isin(7π6))=−√3−12iz=2(cos(5π3)+isin(5π3))=1−i√3hope this helps!! :) --Siveth
12 bars of soap for $8.69
jonathan walks to school on a sidewalk by going 8 blocks to the east and then 6 blocks south. how much distance (in blocks) would he save if he cut across the field to go to achool instead of walking along the sidewalk?
Answer:
Is there an image to visualize the field?
Step-by-step explanation:
I would love to help.
the figure above, not drawn to scale, consists of a triangle resting on a square of side 5cm. the height of the triangle is 4cm. what is the total area of the figure?
Answer:
5x4x2
Step-by-step explanation:
The total area of the figure id 35 square cm.
What is area?The amount of space taken up by a two dimensional space is called area.
What is the formula for the area of triangle?The formula for the area of a triangle is
[tex]A = \frac{1}{2} (b)(h)[/tex]
Where,
A is the area of triangle.
b is the base of a triangle.
h is the height of the triangle.
What is the formula for the area of square?The formula for the area of square is
[tex]Area = a^{2}[/tex]
Where,
a is the side length of square.
According to the given question.
A triangle is resting on a square.
Side length of square, a = 5cm
So, the area of square = [tex]5^{2} = 25 square cm[/tex]
Also, a triangle with height 4cm.
Since, the triangle is resting on a square.
⇒ Base length of the triangle = 5cm
So, the area of triangle = [tex]\frac{1}{2} (5)(4)= 10 square cm[/tex]
Therefore,
The total area of the given figure = Area of square + Area of triangle
⇒ Total area of figure = (25 + 10) square cm
⇒ Total area of figure = 35 square cm
Hence, the total area of the figure id 35 square cm.
Find out more information about area of triangle and square here:
https://brainly.com/question/11952845
#SPJ3
If you rolled two dice, what is the probability
that you would roll a sum of 6?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter
Answer:
[tex]\frac{5}{36}[/tex]
Step-by-step explanation:
probability of desired outcome:
Number of desired outcomes/number of total outcomes
To find the numerator just count the number of times the condition is satisfied
I get 5
1,5
2,4
3,3
4,2
5,1
The number of total outcomes is just 6² or 36
So the final answer is just 5/36
KkkjwjwjwiwieieieieieieiejeieieieieieieJ
the side length of a triangle are 9,12 and 15. Which side will be opposite the right angle?
Answer:
The hypotenuse. Since it is the opposite of the right angle
The largest number is the hypotenuse
therefore, 15 is the answer.
Answer:
c
Step-by-step explanation:
The hypotenuse. Since it is the opposite of the right angle
The largest number is the hypotenuse
therefore, 15 is the answer.
Anthony can either play 4 hours of video games or read 12 chapters of a book. What is Anthony's opportunity cost of playing one hour of video games?
Answer:
The opportunity cost of playing an hour of video games is not reading 3 chapters of a book.
Step-by-step explanation:
Given that Anthony can either play 4 hours of video games or read 12 chapters of a book, to determine what is Anthony's opportunity cost of playing one hour of video games, the following calculation must be performed:
4 = 12
1 = X
1 x 12/4 = X
12/4 = X
3 = X
Therefore, the opportunity cost of playing an hour of video games is not reading 3 chapters of a book.
you have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2.Which of these statements is true?
Answer:
c
Step-by-step explanation:
right on plato
For each expression in the table, select which number line model, If any, can be used to represent the expression. Select all appropriate cells in the
table.
Answer:
I don’t know
Step-by-step explanation:
You didn’t attach a photo lol
use the double-angle formulas for sine and cosine to verify these identities:
tan(2theta) = 2tan(theta) / 1 - tan^2 (theta)
sin
(
2
θ
)
=
2
(
3
5
)
(
−
4
5
)
=
−
24
25
Write the double-angle formula for cosine.
\displaystyle \cos \left(2\theta \right)={\cos }^{2}\theta -{\sin }^{2}\thetacos(2θ)=cos
2
θ−sin
2
θ
Again, substitute the values of the sine and cosine into the equation, and simplify.
)Answer:
In the previous section, we used addition and subtraction formulas for trigonometric functions. Now, we take another look at those same formulas. The double-angle formulas are a special case of the sum formulas, where \displaystyle \alpha =\betaα=β. Deriving the double-angle formula for sine begins with the sum formula,
\displaystyle \sin \left(\alpha +\beta \right)=\sin \alpha \cos \beta +\cos \alpha \sin \betasin(α+β)=sinαcosβ+cosαsinβ
If we let \displaystyle \alpha =\beta =\thetaα=β=θ, then we have
Deriving the double-angle for cosine gives us three options. First, starting from the sum formula, \displaystyle \cos \left(\alpha +\beta \right)=\cos \alpha \cos \beta -\sin \alpha \sin \betacos(α+β)=cosαcosβ−sinαsinβ, and letting \displaystyle \alpha =\beta =\thetaα=β=θ, we have
Using the Pythagorean properties, we can expand this double-angle formula for cosine and get two more interpretations. The first one is:
Similarly, to derive the double-angle formula for tangent, replacing \displaystyle \alpha =\beta =\thetaα=β=θ in the sum formula gives
\displaystyle \begin{array}{c}\tan \left(\alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\\ \tan \left(\theta +\theta \right)=\frac{\tan \theta +\tan \theta }{1-\tan \theta \tan \theta }\\ \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }\end{array}
tan(α+β)=
1−tanαtanβ
tanα+tanβ
tan(θ+θ)=
1−tanθtanθ
tanθ+tanθ
tan(2θ)=
1−tan
2
θ
2tanθ
A GENERAL NOTE: DOUBLE-ANGLE FORMULAS
The double-angle formulas are summarized as follows:
\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ
\displaystyle \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }tan(2θ)=
1−tan
2
θ
2tanθ
HOW TO: GIVEN THE TANGENT OF AN ANGLE AND THE QUADRANT IN WHICH IT IS LOCATED, USE THE DOUBLE-ANGLE FORMULAS TO FIND THE EXACT VALUE.
Draw a triangle to reflect the given information.
Determine the correct double-angle formula.
Substitute values into the formula based on the triangle.
Simplify.
EXAMPLE 1: USING A DOUBLE-ANGLE FORMULA TO FIND THE EXACT VALUE INVOLVING TANGENT
Given that
and \displaystyle \thetaθ is in quadrant II, find the following:
\displaystyle \sin \left(2\theta \right)sin(2θ)
\displaystyle \cos \left(2\theta \right)cos(2θ)
\displaystyle \tan \left(2\theta \right)tan(2θ)
SOLUTION
If we draw a triangle to reflect the information given, we can find the values needed to solve the problems on the image. We are given \displaystyle \tan \theta =-\frac{3}{4}tanθ=−
4
3
, such that \displaystyle \thetaθ is in quadrant II. The tangent of an angle is equal to the opposite side over the adjacent side, and because \displaystyle \thetaθ is in the second quadrant, the adjacent side is on the x-axis and is negative. Use the Pythagorean Theorem to find the length of the hypotenuse:
Now we can draw a triangle similar to the one shown in Figure 2.
Diagram of a triangle in the x,y-plane. The vertices are at the origin, (-4,0), and (-4,3). The angle at the origin is theta. The angle formed by the side (-4,3) to (-4,0) forms a right angle with the x axis. The hypotenuse across from the right angle is length 5.
Figure 2
Let’s begin by writing the double-angle formula for sine.
\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ
We see that we to need to find \displaystyle \sin \thetasinθ and \displaystyle \cos \thetacosθ. Based on Figure 2, we see that the hypotenuse equals 5, so \displaystyle \sin \theta =\frac{3}{5}sinθ=
. Substitute these values into the equation, and simplify.
Thus,
Solution
EXAMPLE 2: USING THE DOUBLE-ANGLE FORMULA FOR COSINE WITHOUT EXACT VALUES
Use the double-angle formula for cosine to write \displaystyle \cos \left(6x\right)cos(6x) in terms of \displaystyle \cos \left(3x\right)cos(3x).
SOLUTION
c
Analysis of the Solution
This example illustrates that we can use the double-angle formula without having exact values. It emphasizes that the pattern is what we need to remember and that identities are true for all values in the domain of the trigonometric function.
Using Double-Angle Formulas to Verify Identities
Establishing identities using the double-angle formulas is performed using the same steps we used to derive the sum and difference formulas. Choose the more complicated side of the equation and rewrite it until it matches the other side.
EXAMPLE 3: USING THE DOUBLE-ANGLE FORMULAS TO ESTABLISH AN IDENTITY
Establish the following identity using double-angle formulas:
\displaystyle 1+\sin \left(2\theta \right)={\left(\sin \theta +\cos \theta \right)}^{2}1+sin(2θ)=(sinθ+cosθ)
2
θ
)
Step-by-step explanation:
Answer this question pls!!
Answer:
(6, 7)
Step-by-step explanation:
A rectangle means that opposite sides are parallel to each other and that opposite sides are equal in measurements.
If we look at the opposite side starting at (2, 1), we can count how long the other side should be. Counting the next point of the rectangle is (6, 1) which is a difference of 4. This means if we count from (2, 7) 4 spaces to the right, we will find our missing vertex.
(2 + 4, 7) = (6, 7)
Probability Event:
You ask 5 people what month their birthday is in. What is the probability that they will all be in the summer?
Label the probability event above as either
A
Independent
B
Dependent
Answer:
Dependent
Explanation:
All of the birthdays being in summer depends on the birthdays of each person.
Find the sum of the measures of the interior angles of the indicated covex
Very confused
Answer:
Step-by-step explanation:
Hope it helps u!!
8
The median of 3 numbers is 7. If one of the numbers is 10, which of the following is a possible value for one of
the other numbers?
0/
6
8
ОООО
13
17
Review Questions
Mathematics
9514 1404 393
Answer:
(a) 6
Step-by-step explanation:
The median is the middle number when they are sorted into order. If one of the numbers is 10, the remaining number must be any number less than 7. Of the offered choices, the only one less than 7 is 6.
__
The three numbers are 6, 7, 10.
Plz hurry in need help !!
BRAINLIEST if correct
Answer:
A=38.88 or 38.9
Step-by-step explanation:
If both are similar then the 9 and the 7.2 are the same
9-7.2= 1.8
9x6=54
7.2-1.8=5.4
7.2x5.4=38.88 or 38.9