Answer:
{f, a}
Step-by-step explanation:
Given the sets:
X = {d, c, f, a}
Y = {d, e, c}
Z ={e, c, b, f, g}
U = {a, b, c, d, e, f, g}
To obtain the set X n (X - Y)
We first obtain :
(X - Y) :
The elements in X that are not in Y
(X - Y) = {f, a}
X n (X - Y) :
X = {d, c, f, a} intersection
(X - Y) = {f, a}
X n (X - Y) = elements in X and (X - Y)
X n (X - Y) = {f, a}
A guide wire of length 108 meters runs from the top of an antenna to the ground. If the angle of elevation to the top of the antenna is 42.3 degrees, then what is the height of the antenna
Answer: Approximately 72.69 meters
Step-by-step explanation:
Antenna height = h[tex]sin(42.3)=\frac{opposite}{hypotenuse} =\frac{h}{108} \\\\108*sin(42.3)=h\\\\h=72.685[/tex]
The height of the antenna by using the Pythagoras theorem is 72.68 meters.
What is trigonometry?"Trigonometry is one of the branches of mathematics that deals with the relationship between the sides of a triangle (right triangle) with its angles".
For the given situation,
Length of guidewire = 108 meters
Angle of elevation = 42.3 degrees
Height of the antenna be 'h'.
By Pythagoras theorem,
[tex]Sine[/tex] θ = [tex]\frac{Perpendicular}{hypotenuse}[/tex]
On substituting the above values,
⇒ [tex]Sine 42.3 = \frac{h}{108}[/tex]
⇒ [tex]0.6730 =\frac{h}{108}[/tex]
⇒ [tex]h=0.6730[/tex] × [tex]108[/tex]
⇒ [tex]h= 72.68[/tex]
Hence we can conclude that the height of the antenna is 72.68 meters.
Learn more about trigonometry here
https://brainly.com/question/13971311
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A 3 phase traffic signal is designed with 2 seconds of all red per phase and phase lengths of 25 seconds, 30 seconds, and 15 seconds. The cycle length is ____ seconds.
Answer:
[tex]CL=76secs[/tex]
Step-by-step explanation:
From the question we are told that:
Traffic Phases p=3
Phase time Lengths
25 seconds, 30 seconds, and 15 seconds
Red Per Phase [tex]T=2sec[/tex]
Generally the equation for Cycle Length is mathematically given by
[tex]CL=Phase\ Length+Red\ Per\ Phase[/tex]
[tex]CL=(25+2)+(30+2)+(15+2)[/tex]
[tex]CL=76secs[/tex]
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:length 30, width 18
Step-by-step explanation:
60% +100%=160%
160% × 2 = 320 %
96/320 = 0.3 ×100 =30 ( length)
30 × 0.6 =18 (width)
Check: (18 + 30) 2 = 96
Consider the following function.
f(x) = x sin(x), a = 0, n = 4, −0.5 ≤ x ≤ 0.5
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T4(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation
f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to four decimal places.)
|R4(x)| ≤
(c) Check your result in part (b) by graphing |Rn(x)|.
A random sample of 35 employees of the local green technologies plant Greenies, who completed two years of college, were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who had only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. Assuming equal variance between the two populations, can we infer at the .10 level of significance that students who completed two years of college had a higher average than students who had only completed high school
Answer:
There is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.
Step-by-step explanation:
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 > μ2
Given :
n1 = 35 ; x1 = 75.1 ; s1 = 12.8
n2 = 50 ; x2 = 72.1 ; s2 = 14.6
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
df1 = n1 - 1 = 35 - 1 = 34
df2 = n2 - 1 = 50 - 1 = 49
(x1 - x2) ÷ Sp(√(1/n1 + 1/n2))
Sp² = (34*12.8^2 + 49*14.6^2) / (35+50-2)
Sp² = (5570.56 + 10444.84) / 83
Sp² = 192.95662
Sp = √192.95662
Sp = 13.89
Test statistic = (75.1 - 72.1) / 13.89 * √(1/35 + 1/50)
Test statistic = 3 / (13.89 * 0.2203892)
Test statistic = 0.980
df = n1 + n2 - 2
df = 35 + 50 - 2 = 83
Using the Pvalue calculator :
Pvalue(0.980, 83) = 0.165
α = 0.1
Pvalue > α ; We fail to reject the H0; and conclude that there is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.
Math help please ………….
Answer:
if the terms are approaching zero then it is convergent.
Therefore the stated series is convergent
Step-by-step explanation:
The lengths of the sides of a triangle are 3, 3, 3V2. Can the triangle be a right triangle?
[tex] {\bold{\red{\huge{\mathbb{QUESTION}}}}} [/tex]
The lengths of the sides of a triangle are 3, 3, 3√2. Can the triangle be a right triangle?
[tex]\bold{ \red{\star{\blue{TO \: \: PROVE }}}}[/tex]
IF ITS A RIGHT ANGLED OR NOT
[tex]\bold{\blue{\star{\red{FORMULA}}}}[/tex]
IF IT WILL FOLLOW PYTHAGORAS THEOREM THEN IT WILL BE A RIGHT ANGLE TRIANGLE.
[tex]{HYPOTENUSE}^{2} \\ ={ PERPENDICULAR}^{2}+{BASE}^{2} [/tex]
[tex]\bold{ \red{\star{\orange{GIVEN }}}}[/tex]
1ST SIDE -> 3
2ND SIDE -> 3
3RD SIDE ->3√2
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex]{HYPOTENUSE}^{2}\\ ={ PERPENDICULAR}^{2}+{BASE}^{2} \\{h}^{2}={p}^{2}+{b}^{2} [/tex]
AS HYPOTENUSE is always greater than other 2 sides so 3√2 can only be hypotenuse if it's a right angle triangle
[tex]{(3 \sqrt{2})}^{2} = {3}^{2} + {3}^{2} \\ 9 \times2 = 9 + 9 \\ 18 = 18[/tex]
[tex] {\red{\star}}{ \blue{HENCE \: PROVED}} { \red{ \star}}[/tex]
[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]
Step by step please help answer.
The diameter of a circular reservoir is 840 feet. To walk around the reservoir, you would walk approximately how far? (Use tt = 22/7.)
(1) 267 ft
(2) 2,640 ft
(3) 2,800 ft
(4) 18,480 ft
(5) Not enough information is given.
Answer:
(2) 2,640 ft
Step-by-step explanation:
I'm going to assume that in this question, you are walking 1 full circle around the reservoir. That would mean you need to calculate the circumference of the circular reservoir.
The circumference formula is:
C = ⫪d
C stands for Circumference
d stands for diameter
I will use 22/7 instead of pi, so the formula looks more like this:
C = (22/7)(d)
The diameter is 840 feet, so we will substitute the variable d with 840:
C = (22/7)(840)
You can plug this part into the calculator, but by hand, it'll look something like this:
(22/7)*840 = (22*840)/7
18,480/7 = 2.640
Hope it helps (●'◡'●)
Calculate 20% of 15,998
Answer:
3,199 approximately
Step-by-step explanation:
to find how much 20% of 15,998 does we multiply 15,998 with 20 and then divide it by 100
15,998 x 20 / 100 = 3,199
The length of a rectangle is 6 inches more than the width. The perimeter is 28 inches. Find the length and the width (in inches).
Answer:
The length of the rectangle is 10 inches, and the width is 4 inches.
Step-by-step explanation:
Given that the length of a rectangle is 6 inches more than the width, and the perimeter is 28 inches, the following calculation must be performed to find the length and the width:
(X + X + 6) x 2 = 28
2X + 2X + 12 = 28
4X = 28 - 12
X = 16/4
X = 4
Therefore, the length of the rectangle is 10 inches, and the width is 4 inches.
Help. I will be guessing on this, but I want to make sure this is on here so no one has to guess like I am. Help a brother out
Answer:
Line 3
Step-by-step explanation:
→ Calculate gradient
[tex]\frac{6-3}{4-2} =1.5[/tex]
Answer:
Line 3
Step-by-step explanation:
(0,0) & ( 4 , 6)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]
Type the correct answer in each box.
Jessica has $24 and plans to spend it all at the grocery store. She wants to purchase bags of carrots and bagels. Bags of
carrots cost $2 each, and bagels cost $3 per bag. Let x represent the number of bags of carrots and y represent the
number of bags of bagels. Complete the equation in standard form that models this scenario.
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y=(
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Step-by-step explanation:
Jessica has $24 and plans to spend it all at the grocery store.Bags of carrots cost $2 each, and bagels cost $3 per bag.Let x represent the number of bags of carrots and y represent the number of bags of bagels.the cost for the 'x' bags of carrots = $2xand the cost for the 'y' bags of bagels = $3ySo, the equation would be,so the equation in standard form that models the given scenario is
2x + 3y = 24
2x + 3y = 24An air conditioning system can circulate 310 cubic feet of air per minute. How many cubic yards of air can it circulate per minute? The air conditioning system can circulate about cubic yards of air per minute.
Answer:
310/[tex]3^{3}[/tex] = 310/27 =11.48
Step-by-step explanation:
Answer:
310/ = 310/27 =11.48
Step-by-step explanation:
Could someone help me
Hello,
I have only found 113 solutions (i have num 15 given)
nb= 1 ::: 27*n + 98= 30*n + 56===> n= 1 4
nb= 2 ::: 28*n + 95= 30*n + 67===> n= 1 4
nb= 3 ::: 29*n + 65= 30*n + 17===> n= 4 8
nb= 4 ::: 29*n + 65= 30*n + 18===> n= 4 7
nb= 5 ::: 29*n + 65= 30*n + 47===> n= 1 8
nb= 6 ::: 29*n + 65= 30*n + 48===> n= 1 7
nb= 7 ::: 29*n + 74= 30*n + 16===> n= 5 8
nb= 8 ::: 29*n + 74= 30*n + 18===> n= 5 6
nb= 9 ::: 29*n + 74= 30*n + 56===> n= 1 8
nb= 10 ::: 29*n + 74= 30*n + 58===> n= 1 6
nb= 11 ::: 30*n + 16= 29*n + 74===> n= 5 8
nb= 12 ::: 30*n + 17= 29*n + 65===> n= 4 8
nb= 13 ::: 30*n + 18= 29*n + 65===> n= 4 7
nb= 14 ::: 30*n + 18= 29*n + 74===> n= 5 6
nb= 15 ::: 30*n + 47= 29*n + 65===> n= 1 8
nb= 16 ::: 30*n + 48= 29*n + 65===> n= 1 7
nb= 17 ::: 30*n + 56= 27*n + 98===> n= 1 4
nb= 18 ::: 30*n + 56= 29*n + 74===> n= 1 8
nb= 19 ::: 30*n + 58= 29*n + 74===> n= 1 6
nb= 20 ::: 30*n + 67= 28*n + 95===> n= 1 4
nb= 21 ::: 36*n + 97= 40*n + 25===> n= 1 8
nb= 22 ::: 38*n + 59= 40*n + 27===> n= 1 6
nb= 23 ::: 38*n + 65= 40*n + 27===> n= 1 9
nb= 24 ::: 38*n + 69= 40*n + 15===> n= 2 7
nb= 25 ::: 39*n + 78= 45*n + 6===> n= 1 2
nb= 26 ::: 39*n + 82= 40*n + 15===> n= 6 7
nb= 27 ::: 39*n + 82= 40*n + 17===> n= 6 5
nb= 28 ::: 39*n + 82= 40*n + 65===> n= 1 7
nb= 29 ::: 39*n + 82= 40*n + 67===> n= 1 5
nb= 30 ::: 40*n + 15= 38*n + 69===> n= 2 7
nb= 31 ::: 40*n + 15= 39*n + 82===> n= 6 7
nb= 32 ::: 40*n + 17= 39*n + 82===> n= 6 5
nb= 33 ::: 40*n + 25= 36*n + 97===> n= 1 8
nb= 34 ::: 40*n + 27= 38*n + 59===> n= 1 6
nb= 35 ::: 40*n + 27= 38*n + 65===> n= 1 9
nb= 36 ::: 40*n + 65= 39*n + 82===> n= 1 7
nb= 37 ::: 40*n + 67= 39*n + 82===> n= 1 5
nb= 38 ::: 46*n + 87= 50*n + 39===> n= 1 2
nb= 39 ::: 46*n + 87= 52*n + 9===> n= 1 3
nb= 40 ::: 47*n + 68= 50*n + 29===> n= 1 3
nb= 41 ::: 47*n + 83= 50*n + 26===> n= 1 9
nb= 42 ::: 47*n + 98= 51*n + 6===> n= 2 3
nb= 43 ::: 47*n + 98= 53*n + 2===> n= 1 6
nb= 44 ::: 48*n + 63= 50*n + 29===> n= 1 7
nb= 45 ::: 48*n + 73= 52*n + 9===> n= 1 6
nb= 46 ::: 49*n + 63= 51*n + 7===> n= 2 8
nb= 47 ::: 49*n + 72= 53*n + 8===> n= 1 6
nb= 48 ::: 49*n + 78= 52*n + 30===> n= 1 6
nb= 49 ::: 49*n + 87= 56*n + 3===> n= 1 2
nb= 50 ::: 50*n + 26= 47*n + 83===> n= 1 9
nb= 51 ::: 50*n + 29= 47*n + 68===> n= 1 3
nb= 52 ::: 50*n + 29= 48*n + 63===> n= 1 7
nb= 53 ::: 50*n + 39= 46*n + 87===> n= 1 2
nb= 54 ::: 52*n + 30= 49*n + 78===> n= 1 6
nb= 55 ::: 57*n + 92= 63*n + 8===> n= 1 4
nb= 56 ::: 58*n + 72= 60*n + 34===> n= 1 9
nb= 57 ::: 58*n + 73= 60*n + 49===> n= 1 2
nb= 58 ::: 58*n + 79= 60*n + 31===> n= 2 4
nb= 59 ::: 58*n + 97= 60*n + 13===> n= 4 2
nb= 60 ::: 59*n + 47= 62*n + 8===> n= 1 3
nb= 61 ::: 59*n + 71= 60*n + 23===> n= 4 8
nb= 62 ::: 59*n + 71= 60*n + 28===> n= 4 3
nb= 63 ::: 59*n + 71= 60*n + 43===> n= 2 8
nb= 64 ::: 59*n + 71= 60*n + 48===> n= 2 3
nb= 65 ::: 59*n + 74= 63*n + 2===> n= 1 8
nb= 66 ::: 59*n + 78= 61*n + 30===> n= 2 4
nb= 67 ::: 59*n + 84= 61*n + 30===> n= 2 7
nb= 68 ::: 59*n + 87= 61*n + 3===> n= 4 2
nb= 69 ::: 60*n + 13= 58*n + 97===> n= 4 2
nb= 70 ::: 60*n + 23= 59*n + 71===> n= 4 8
nb= 71 ::: 60*n + 28= 59*n + 71===> n= 4 3
nb= 72 ::: 60*n + 31= 58*n + 79===> n= 2 4
nb= 73 ::: 60*n + 34= 58*n + 72===> n= 1 9
nb= 74 ::: 60*n + 43= 59*n + 71===> n= 2 8
nb= 75 ::: 60*n + 48= 59*n + 71===> n= 2 3
nb= 76 ::: 60*n + 49= 58*n + 73===> n= 1 2
nb= 77 ::: 61*n + 30= 59*n + 78===> n= 2 4
nb= 78 ::: 61*n + 30= 59*n + 84===> n= 2 7
nb= 79 ::: 65*n + 89= 70*n + 24===> n= 1 3
nb= 80 ::: 68*n + 59= 72*n + 3===> n= 1 4
nb= 81 ::: 68*n + 91= 70*n + 45===> n= 2 3
nb= 82 ::: 69*n + 43= 70*n + 15===> n= 2 8
nb= 83 ::: 69*n + 43= 70*n + 18===> n= 2 5
nb= 84 ::: 69*n + 43= 70*n + 25===> n= 1 8
nb= 85 ::: 69*n + 43= 70*n + 28===> n= 1 5
nb= 86 ::: 69*n + 48= 72*n + 3===> n= 1 5
nb= 87 ::: 69*n + 52= 70*n + 14===> n= 3 8
nb= 88 ::: 69*n + 52= 70*n + 18===> n= 3 4
nb= 89 ::: 69*n + 52= 70*n + 34===> n= 1 8
nb= 90 ::: 69*n + 52= 70*n + 38===> n= 1 4
nb= 91 ::: 69*n + 54= 71*n + 8===> n= 2 3
nb= 92 ::: 69*n + 58= 73*n + 2===> n= 1 4
nb= 93 ::: 69*n + 82= 75*n + 4===> n= 1 3
nb= 94 ::: 69*n + 85= 74*n + 20===> n= 1 3
nb= 95 ::: 70*n + 14= 69*n + 52===> n= 3 8
nb= 96 ::: 70*n + 15= 69*n + 43===> n= 2 8
nb= 97 ::: 70*n + 18= 69*n + 43===> n= 2 5
nb= 98 ::: 70*n + 18= 69*n + 52===> n= 3 4
nb= 99 ::: 70*n + 24= 65*n + 89===> n= 1 3
nb= 100 ::: 70*n + 25= 69*n + 43===> n= 1 8
nb= 101 ::: 70*n + 28= 69*n + 43===> n= 1 5
nb= 102 ::: 70*n + 34= 69*n + 52===> n= 1 8
nb= 103 ::: 70*n + 38= 69*n + 52===> n= 1 4
nb= 104 ::: 70*n + 45= 68*n + 91===> n= 2 3
nb= 105 ::: 74*n + 20= 69*n + 85===> n= 1 3
nb= 106 ::: 76*n + 93= 80*n + 45===> n= 1 2
nb= 107 ::: 79*n + 45= 82*n + 6===> n= 1 3
nb= 108 ::: 79*n + 54= 83*n + 6===> n= 1 2
nb= 109 ::: 80*n + 45= 76*n + 93===> n= 1 2
nb= 110 ::: 87*n + 64= 90*n + 25===> n= 1 3
nb= 111 ::: 87*n + 65= 90*n + 23===> n= 1 4
nb= 112 ::: 90*n + 23= 87*n + 65===> n= 1 4
nb= 113 ::: 90*n + 25= 87*n + 64===> n= 1 3
The graph of f(x)=x^2 is shown. Compare the graph of f(x) with the graph of g(x)=x^2+8
Answer:
D
Step-by-step explanation:
Number 8 is not related to the x, but is related to the the function. so g(x) is 8 units above f (x)
Answer:
D. 8 units above the graph
Step-by-step explanation:
y = mx + b
this formula is basically y = x^2 + 8
+8 part means where it is on the y axis
if it were y = (x+6)^2 + 8
it would also be on 6 places to the left on the x axis
The hypotenuse of a 45°, 45°, and 90° triangle is 26 sqrt(2) inches. What is the length of each of the other sides?
(A)13 sqrt(2) inches
(B)13 inches
(C)13 sqrt(3) inches
(D)26 inches
remember the pythagorean theorem:
a² + b² = c²
where c is the hypotenuse.
so:
[tex] {a}^{2} + {b}^{2} = { ( \sqrt{26)}}^{2} [/tex]
the square and the square root cancel each other out, so...
a² + b² = 26
we know that a and b are of equal length given the angles.
so it's
[tex] { \sqrt{13} }^{2} + { \sqrt{13} }^{2} = 26[/tex]
here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B
Option A is correct,
[tex] \sqrt{13} inches[/tex]
Which choice is equivalent to √10*√5
Answer:
5√2
Step-by-step explanation:
Given √10*√5
Using surd, the expression can be evaluated further as :
√10*√5 = √50
√50 can be expressed as :
√50 = √25*2 = √25 * √2
√25 = 5
Hence,
√50 = √25 * √2 = 5√2
Hence, √10*√5 = 5√2
16.3 m 16.7 m What is the perimeter of the whole garden? LI m busti 2027
The perimeter of the whole garden would be 66m.
Hope this helps! :)
What is the median of Restaurant A's food quality ratings?
4
5
1
3
2
on the provided graph, plot the points where the following function crosses the x-axis and the y-axis g(x) = -5^x + 5, what does the graph look like?
Answer:
see image
Step-by-step explanation:
1. S = 10 mm
V= S×S×S
=___×___×___
=____ mm3
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]V=1000\text{mm}^3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
I am assuming by the infomation given that the figure is a cube.
⸻⸻⸻⸻
[tex]\boxed{\text{Finding the volume of the cube...}}\\\\S = 10mm; V= s^3\\--------------\\\rightarrow V = 10^3\\\\\rightarrow V = 10 * 10 * 10\\\\\rightarrow \boxed{V=1000\text{mm}^3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
PLEASE HELP THIS IS MY LAST QUESTIONNNN
- The electric company charges Dalton a monthly service fee of $30 plus $0.15 per kilowatt-hour of electricity used. This month, Dalton's bill is $105.
- How many kilowatt-hours of electricity did Dalton use?
500 kwh
$105 - $30 = $75
$75 / $0.15 = 500
Answer:
$105-$30 service fee, this leaves only the electricity used. $75. now to find how many kilowatt hours used you divide $75/.15=500 answer 500 kilowatt hours.
Step-by-step explanation:
see above
Z varies directly as Square x and inversely as y. If z = 187 when x = 64 and y = 6, find z if and 9. (Round off your answer to the nearest hundredth.)
Answer:
Z = 50
Step-by-step explanation:
Given the following data;
Z = 187
x = 64
y = 6
Translating the word problem into an algebraic expression, we have;
Z = k√x/y
First of all, we would find the constant of proportionality, k;
187 = k√64/6
187 * 6 = k√64
1122 = 8k
k = 1122/8
k = 140.25
To find z, when x and y = 9
Z = 140.25√9/9
Z = (140.25 * 3)/9
Z = 420.75/9
Z = 46.75 ≈ 50
Note: The values in the latter part of the question isn't explicitly stated, so I assumed a value of 9 for both x and y.
Jan is as old as Gary was 15 years ago. Six years from now, Gary will be twice as old as Jan will be then. How old is Gary now?
Answer:
Gary is now 24years
Step-by-step explanation:
let the age of Jan be x and that of Gary be x+15
in six years time they will be as follows
Jan =x+6
Gary=x+15+6=x+21
2(x+6)=x+21
2x+12=x+21
collect the like terms
2x-x=21-12
x=9
Gary =9+15=24years
Is AABC-ADEF? If so, name which similarity postulate or theorem applies.
75
A. Similar - SSS
B. Similar - AA
0
C. Similar - SAS
D. Cannot be determined
Answer:
B. Similar - AA
Step-by-step explanation:
Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.
Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.
prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Multiply the polynomials 3(x+7) (show work pls)
Answer:
3x + 21
Step-by-step explanation:
(3)(x+7)
Now, we distribute the 3 in each term of (x+7)
So, 3*x = 3x and 3*7 = 21.
So our resulting term would be 3x+21.
If a student answered 77 exam questions correctly out of 100, what fraction
and what percentage of questions did the student answer incorrectly?
Choose two answers.
A. 0.77%
B.
20
100
IC
23
100
I D. 23%
O E. 77%
OF
77
100
Answer: 23%
Step-by-step explanation: 77 + 23 is 100
Answer:
77 out of 100
Step-by-step explanation:
For a fraction, it would look like 77/100,
and for percentage, 77%.
Which of the following is NOT equivalent to 2x + x - y + 3 + 5?
x + x + x - y + 8
3x - y + 8
2x 2 - y + 5 + 3
x + 2x - y + 5 + 3
Answer:
2x 2 - y + 5 + 3
Step-by-step explanation:
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find the exact value of 6cos(105°)
Answer:
[tex]-\frac{3(\sqrt{6}-\sqrt{2})}{2}\text{ or } \frac{-3\sqrt{6}+3\sqrt{2}}{2}}\text{ or }\frac{3(\sqrt{2}-\sqrt{6})}{2}[/tex]
Step-by-step explanation:
There are multiple ways to achieve and even express the exact answer to this problem. Because the exact value of [tex]6\cos(105^{\circ}})[/tex] is a non-terminating (never-ending) decimal, it does not have a finite number of digits. Therefore, you cannot express it as an exact value as a decimal, as you'd either have to round or truncate.
Solution 1 (Cosine Addition Identity):
Nonetheless, to find the exact value we must use trigonometry identities.
Identity used:
[tex]\cos(\alpha +\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta[/tex]
Notice that [tex]45+60=105[/tex] and therefore we can easily solve this problem if we know values of [tex]\cos(45^{\circ})[/tex], [tex]\cos(60^{\circ})[/tex], [tex]\sin (45^{\circ})[/tex], and [tex]\sin(60^{\circ})[/tex], which is plausible as they are all key angles on the unit circle.
Recall from either memory or the unit circle that:
[tex]\cos(45^{\circ})=\sin(45^{\circ})=\frac{\sqrt{2}}{2}[/tex] [tex]\cos(60^{\circ})=\frac{1}{2}[/tex] [tex]\sin(60^{\circ})=\frac{\sqrt{3}}{2}[/tex]Therefore, we have:
[tex]\cos(105^{\circ})=\cos(45^{\circ}+60^{\circ}}),\\\cos(45^{\circ}+60^{\circ}})=\cos 45^{\circ}\cos 60^{\circ}-\sin 45^{\circ}\sin 60^{\circ},\\\cos(45^{\circ}+60^{\circ}})=\frac{\sqrt{2}}{2}\cdot \frac{1}{2}-\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2},\\\cos(105^{\circ})=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4},\\\cos(105^{\circ})={\frac{-\sqrt{6}+\sqrt{2}}{4}}[/tex]
Since we want the value of [tex]6\cos 105^{\circ}[/tex], simply multiply this by 6 to get your final answer:
[tex]6\cdot {\frac{-\sqrt{6}+\sqrt{2}}{4}}=\frac{-3\sqrt{6}+3\sqrt{2}}{2}}=\boxed{\frac{3(\sqrt{2}-\sqrt{6})}{2}}[/tex]
Solution 2 (Combination of trig. identities):
Although less plausible, you may have the following memorized:
[tex]\sin 15^{\circ}=\cos75^{\circ}=\frac{\sqrt{6}-\sqrt{2}}{4},\\\sin 75^{\circ}=\cos15^{\circ}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]
If so, we can use the following trig. identity:
[tex]\cos(\theta)=\sin(90^{\circ}-\theta)[/tex] (the cosine of angle theta is equal to the sine of the supplement of angle theta - the converse is also true)
Therefore,
[tex]\cos (105^{\circ})=\sin (90^{\circ}-105^{\circ})=\sin(-15^{\circ})[/tex]
Recall another trig. identity:
[tex]\sin(-\theta)=-\sin (\theta)[/tex] and therefore:
[tex]\sin (-15^{\circ})=-\sin (15^{\circ})[/tex]
Multiply by 6 to get:
[tex]6\cos (105^{\circ})=-6\sin (15^{\circ})=-6\cdot \frac{\sqrt{6}-\sqrt{2}}{4}=\boxed{-\frac{3(\sqrt{6}-\sqrt{2})}{2}}[/tex] (alternative final answer).