prove that cos² (45+A) + (45-A)=1
Answer:
Cos²(45°—A) + cos²(45°+A)
= [2 cos²(45°—A) + 2 cos²(45°+A)] /2
= [{2 cos²(45°—A)—1} + {2 cos²(45°+A)—1} + 2] /2
= [cos2(45°—A)+cos2(45°+A)+2]/2
= [cos(90°—2A)+cos(90°+2A)+2]/2
= (sin2A—sin2A+2)/2
= 2/2
= 1
the perimeter of a rectangle is 72 ft. the ratio of the length to width is 5:4. what are the dimensions of the rectangle?
Answer: 20 by 16
Step-by-step explanation:
5:4 OR 5x:4x
Perimeter = 2(l x w)
P = 2(5x x 4x)
P = 10x + 8x = 18 x
18x=72
x=4
5 x 4 = 20
4 x 4 = 16
(5x+3)(-5x+6) box method to distribute and simplify
Answer:
-450
Step-by-step explanation:
please help I having trouble not understanding it thank you I appreciate it
If ABCD is a square and AC= 26, what is the length of BC
Answer:
BC = 18.385
Step-by-step explanation:
You can look at ABC as a right triangle and use the Pythagorean theorem to solve for BC. 26 squared is 676, 676 divided by 2 is 338, and finally the square root of 338 is 18.385. This is the length of BC and AB as well. Hope that helped
Answer: aprox 18.38
Step-by-step explanation:
you have a AC=, which is the hypothenuse of the right triangle, and isosceles
ABC
AB=BC, sides of a square
remember c^2=a^2+b^2 but and b are equal so we can say
c^2= 2a^2
c=a[tex]\sqrt{2}[/tex], 26/[tex]\sqrt{2}[/tex]=a
a=(26[tex]\sqrt{2}[/tex])2=18.38
Mario is playing an online puzzle game. He has 50 points and earns 3 points
for each puzzle he solves correctly. He will advance to the intermediate level
if his score is over 80 points.
Answer:
I think there might be more to this question, but the answer I have is
3x + 50 > 80
Step-by-step explanation:
If he has 50 points, needs higher than 80 points to advance to the intermediate level and receives 3 points for every puzzle he solves correctly, he must multiply the 3 by something to add to 50 to get a total amount higher than 80. Thus, 3x + 50 > 80 is the appropriate answer. Have a good day!
Answer:
the answer is 50x + 3 >80
Step-by-step explanation:
(v^3-2v^2-78v+16) / (v+8)
Answer:
v^2-10v+2
Step-by-step explanation:
(v^3-2v^2-78v+16) /(v+8)
Factor
(v+8)(v^2-10v+2)/(v+8)=v^2-10v+2
Can someone help me on the assignments please!!!
I am not so good at math and show your work do everything you can thank you.
so that's
$300,000
*30*4/100
$36,000
2
prob. = total probs./no of probs
=0.35+0.45/2
=0.575
sweetie please verify tou answer am not 100% sure but that how it should be done
please I need brainliest thanks
A shoe company wants to test an updated model of a running shoe on its wear after one month of running. They recruit 50 people who run on a regular basis to participate in the study. Twenty-five runners will receive a pair of the new model and the remaining 25 will receive a pair of the current model. After one month, the wear on the shoes will be determined using the depth of the tread and the flexibility of the toe box. The wear between the new and current models will then be compared.
Which of the following describes a completely randomized design for this experiment?
The subjects are numbered 1–50 and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the current model.
The subjects’ names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be assigned to the current model group.
The 50 subjects are paired based on running ability. The fastest two runners are paired together, the next fastest, etc. For each pair of runners, the researcher will flip a coin. If the coin lands on heads, the first runner will receive the new model and the second runner will receive the original model.
The 50 subjects are grouped based on running ability. Twenty runners classify themselves as competitive runners and the remaining 30 classify themselves as recreational runners. For the competitive group, the runners’ names are written on equal-sized slips of paper and placed into a hat. The slips are shuffled, and the first 10 runners wear the new model and the other 10 wear the current model. The same procedure is used to assign the shoes to the recreational group.
Answer:
Option A: The subjects are numbered 1–50 and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the current model.
Step-by-step explanation:
We are told that Twenty - five runners will receive a pair of the new model and the remaining 25 will receive a pair of the current model.
Now, a completely randomized design is defined as one where the treatments will be assigned completely at random in such a manner that each experimental unit will posses the same chance of receiving any of the treatments given.
To this effect, the most likely answer will be picking people at random to assign either the new model or current model.
This is usually done by making a list of the treatment combinations and then assigning a random number to each subject.
Looking at the options, the most appropriate will be option A.
A group of 4444 friends is playing cards. The deck has 70707070 cards. To start the game, the dealer makes a pile of 15151515 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone.
What is the greatest number of cards any player will have after all the cards are dealt?
cards
Answer:
12502 cards
Step-by-step explanation:
Given:
» total of 70707070 cards of the deck
» 15151515 cards were taken and put in a pile
Solve:
1. So, you can subtract 15151515 from 70707070 to find how many cards are left:
70707070 - 15151515 = 55555555
2. Now, there are 55555555 cards remaining in the deck since 15151515 cards were taken to put in a pile. Since the dealer deals the remaining cards to 4444 people, you can just do 55555555 divided by 4444 to find how many cards each person gets:
55555555 ÷ 4444 = 12501.25
3. 12501.25 is the exact number of cards each person gets, but you can’t have a fraction/part of a card. You have to find a specific remaining number:
0.25 is the same as [tex]\frac{1}{4}[/tex], and so convert [tex]\frac{1}{4}[/tex] into a fraction with a denominator of 4444, but is still equivalent to [tex]\frac{1}{4}[/tex]: You’ll get [tex]\frac{1111}{4444}[/tex], which is correct because it’s still equivalent to [tex]\frac{1}{4}[/tex]
4. So, the remaining 55555555 cards divided by 4444 people is 12501 cards and a remainder of 1111 cards. The 1111 cards can be distributed upon the players, but not everyone can get it. Since 12501 were to given to the players and after the remaining 1111 were also distributed, this means that some will have 12501 cards and others will have 12502 cards.
Answer: So, the greatest number of cards any player will have after all the cards are dealt is 12502 cards.
20 POINTS PLS HELP
(((95*26)-470)/16)-35=______________
not 4 a test
Answer:
90
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
(((95 × 26) - 470)/16) - 35
Step 2: Evaluate
(Parenthesis) Multiply: ((2470 - 470)/16) - 35(Parenthesis) Subtract: (2000/16) - 35(Parenthesis) Divide: 125 - 35Subtract: 90if a,b,c,d are in continuous proportion then prove that (c+a) (c+d) = (b+c) (b+d)
Answer:
We must prove that (c+a)(c+d) = (b+c)(b+d)
Let us use principles from mathematical induction [tex] \frac{a}{b} = \frac{b}{c} = \frac{c}{d} = x[/tex]a=bx , b=cx, c=dxa+c = b + c c +d = b + d Such that (a+c)(c+d)=(b+c)(b+d)Rate positively and give brainlist
WILL GIVE BRAINLIEST IF CORRECT!!
Adam and Simon start on bicycle trips from the same point at the same time. Adam travels east at 8mph and Simon travels south at 6mph. After how many hours are they 60 miles apart?
If Adam and Simon start on bicycle trips from the same point at the same time and Adam travels east at 8mph and Simon travels south at 6mph then after 4.28 hours the distance between them is 60 miles.
What is speed?Speed is the distance an object covers in a particular time period. It can be calculated as under:
Speed=Distance/ Time.
How to calculate time?We have been given the speed of Adam and Simon as 8 mph and 6 mph and we are required to find the time taken by both to be 60 miles apart.
Time=Distance/speed
We cannot find individually but we can find the average time.
Time=60/(6+8)
=60/14
=2.28 hours
Hence if If Adam and Simon start on bicycle trips from the same point at the same time and Adam travels east at 8mph and Simon travels south at 6mph then after 4.28 hours the distance between them is 60 miles.
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I really need help. It would mean a lot ❤️!
Answer: The domain has to be x and the range y. But for independent and dependent variable I can't help. So srry. The picture doesn't show the work. Have a nice day :)
PLEASE HEEELP
Select the correct answer from each drop-down menu. Max used these steps to find the inverse of function f. 5 Step 1 given 5 Step 2 y = change f(x) to y 5 Step 3 1 = 64 6 switch x and y 5 Step 4 + 6y 1 add 6 to each side Step 5 + + 5 36 5 multiply each side by 6 y 6x + = 1-1 (3) Step 6 replace y with 1-1(4) Use this information to complete the statement. Max made a mistake in y he should have
Answer:
Step-by-step explanation:
part 1
Solve the following equation
3(2y + 4) = -2y + 20
(show steps)
part2
what is the value of y?
Answer:
1
Step-by-step explanation:
3(2y+4)=-2y+20 distribute
6y+12=-2y+20 isolate variable
8y+12=20 subtract number
8y=8
y=1
Hope this helps plz hit the crown :D
Could someone please help me with this equation, thank you.
-8 + x/5 = 12
Answer:
x = 100
Step-by-step explanation:
1. To get rid of the denominator of 5, multiply both sides of the equation to get 5
-40 + x = 60
2. Add 40 on both sides to get the variable x by itself
x = 60 + 40
3. Solve
x = 100
Answer:
x=100
Step-by-step explanation:
-8+x/5=12
--8+x/5=12+8
x/5=20
5*20=100
x=100
Write an equation in slope-intercept form of the line with slope −45 that contains the point (−5,−4).
Answer:
(-5,-4)x=45
Step-by-step explanation:
Jason says the quotient 517 ÷ 5 is 103 r 2. Use multiplication to show if Jason's answer is correct.
Answer: No Jason is not orrect the anwser is 103.4 x 5= 517
Step-by-step explanation:
ok so first you have to multiply 103.2 times 5 but that gives you 516 so the correct anwser is 103.4 x 5 = 517
Please help 1/2P-10=15
Answer:
if I'm supposed to solve for P, the answer is 50
Step-by-step explanation:
1/2p-10=15
1/2p=25, subtraction property of equality
p=50, multiplication property of equality
therefore, P is equal to 50
Triangle A'B'C' with coordinates of A' (-6,2)
Answer: (A), (B) and (E).
Step-by-step explanation: Given that ΔA’B’C’ with coordinates of A(-6,2),B’(-4,2), and C’(-6,-2) is the image of ΔABC after a translation of (x-3,y+2). We are to find the possible coordinates for the original vertices of ΔABC.
For vertex A, we have
So, the coordinates of vertex A are (-3, 0).
For vertex B, we have
So, the coordinates of vertex B are (-1, 0).
For vertex C, we have
So, the coordinates of vertex C are (-3, -4).
Rewrite the following equation into slope-intercept form (y = mx + b).
3x - y = 7
Answer:
y=3x-7
Step-by-step explanation
Subtracted 3x, then divided by -1, made the 7 negative and the 3x positive
In the accompanying diagram, lines AB and CD
intersect at point E. If m
m
The required value of x is 40 which is determined by the substitute that equals the vertical angles.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
As per the given accompanying diagram, lines AB and CD intersect at point E.
Since ∠AED and ∠BEC are vertical angles then they are congruent, thus
⇒ ∠AED = ∠BEC
⇒ (x + 10) = 50
Subtract 10 from both sides of the above equation,
⇒ x + 10 - 10 = 50 - 10
⇒ x = 40
Thus, the required value of x is 40.
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Missing length?? Please help me out
Answer:
The missing length is 12
Step-by-step explanation:
Required
Determine the missing length (LS)
If RS = 28 and KS = 14
Then
[tex]KR = RS - KS[/tex]
[tex]KR = 28 - 14[/tex]
[tex]KR = 14[/tex]
The sides of the given shape are directly proportional.
This implies that:
[tex]KS : LS = RS : QS[/tex]
[tex]KS = 14[/tex]
[tex]RS = 28[/tex]
[tex]QS = 12 + LS[/tex]
[tex]LS = ??[/tex]
So, the expression becomes:
[tex]14 : LS = 28 : 12 + LS[/tex]
Represent as a fraction
[tex]\frac{14}{LS} = \frac{28}{12 + LS}[/tex]
Cross Multiply:
[tex]14(12 + LS) = 28 * LS[/tex]
Divide through by 12
[tex]12 + LS = 2 * LS[/tex]
[tex]12 + LS = 2 LS[/tex]
Collect Like Terms
[tex]2LS - LS = 12[/tex]
[tex]LS = 12[/tex]
The length of the missing side is 12
True or False: Only items that cannot be replaced or that would be expensive or hard to replace should be put in a safe deposit box.
MERYY CHRISTMAS!PLEASE HELP! I need help I will give brainlist
1. Write an equation of a line that has a slope of "negative one-half" in each
form: a) point-slope form b) slope-intercept form.
2. Describe how linear data given in a table can help you write an equation of
a line in slope-intercept form.
if a rectangle have length of 10 inches and width of 8 inches what is the new area if each corner is cut by x^2
Answer:
[tex]80 - 4x^2[/tex]
Step-by-step explanation:
Area of a rectangle
A rectangle of width W and length L has an area of:
A = W.L
The given rectangle has a length of L=10 inches and a width of W=8 inches, thus its area is:
A = 8*10 = 80
[tex]A = 80\ in^2[/tex]
If each corner is cut by a square of x*x, then the total area will be:
[tex]A' = 80 - 4x^2[/tex]
The new area is [tex]\mathbf{80 - 4x^2}[/tex] square inches
How do I know if the function is a linear function?
Answer:
This is not a linear function.
Step-by-step explanation:
It is a quadratic function. If you were to make a table of the x and y values of the function it would look like this:
x y
0 -4
1 -1
2 8
Just by looking at these three values, we can see that they do not increase at a consistent rate. It increases by 3 from 0 to 1, but increase by 9 from 1 to 2. You can tell if a function is linear by seeing if it increases at a constant rate. (In this case it does not)
The mean diastolic blood pressure for a random sample of people was millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be millimeters of mercury, find a confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit.
Answer:
(85.62, 90.38).
Step-by-step explanation:
The missing data can be assumed to be we have the following information:
¯x =88, s=10, n=70
Substituting the values in the following formula, we compute the 95% C.I for true population mean diastolic pressure as shown below:
95% C.I.=¯x±t(0.95,n−1)⋅Sm=¯x±t(0.95,70−1)⋅s√n=88±1.99⋅10√70=(85.62,90.38)
The answer is (85.62, 90.38).
Answer this please thanks
12.21%
In his bowling league last year he averaged 115. not his average is 131. so the average increases by 12.21% because the rest are two high because this is a percentage
Answer:
A. 12.21
Step-by-step explanation: