The x is a placeholder for a number. Think of x like a box and inside the box will go a number. In this case, -4 will replace x
7 - 2x = 7 - 2(-4) = 7 + 8 = 15
Answer: 15Find the absolute extrema of the function on the closed interval. f(x) = sin 2x, [0, 2π]
Answer:
Minimum -1, maximum 1.
At points (3π/4. -1) and (π/4 , 1)
Step-by-step explanation:
The maximum value for the sine of an angle is 1 and the minimum is -1.
The angle will have values of π/2 and 3π/2 at these points.
As the angle is 2x the angle values will be π/4 and 3π/4.
Both the Galapagos Islands and the island of Naura are on the Equator, but the Galapagos Islands are at 90.30◦W whereas the island of Nauru is at 166.56◦E. How far is it from the Galapagos Islands to Nauru traveling over the Pacific ocean along the Equator, correct to the nearest km ?
Answer:
11,481 km
Step-by-step explanation:
Longitude 90.30° W is equivalent to 360° -90.30° = 269.70° E. Then the difference in longitude of the islands is ...
269.70° -166.56° = 103.14°
The circumference of the earth at the equator is 40,075 kilometers. Hence the distance will be 103.14/360 times that distance:
(103.14/360)(40,075 km) = 11,481 km
_____
Additional comment
As always with global distance measures, the result of a calculation depends on the assumptions you make. Attached is another take on the question. Apparently, the distance depends on precisely where in the islands you're measuring from/to. The distance computed above differs from the one below by 136 km. The extent of the Galapagos Islands is on the order of 265 km. So, the number we have computed is at least approximately correct.
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
[tex]\\[/tex]AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
Now let's calculate the area
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
[tex]AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right][/tex]
AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| = [tex]\sqrt{(-6)^2 + (-6)^2 + (10)^2}[/tex]
|AB X AC| = [tex]\sqrt{172}[/tex]
|AB X AC| = 13.15
Area = 13.15 square units.
PS: ACBD is also a parallelogram. The diagram has also been attached to this response.
-28/((-12+9)-(9+12/3)+1)
I need help with this math question (complex fractions and rational expressions). For the answer, I need a step-by-step explanation so I can understand it, thank you :) I tried putting it into Symbolab to understand it but that wasn't very helpful so I think human assistance would be more beneficial haha. - [tex](\frac{(7x^{2} + 5x) }{x^{2} + 1 } ) - (\frac{5x}{x^{2} -6})[/tex]
Step-by-step explanation:
-(7x² + 5x) / (x² + 1) − 5x / (x² − 6)
To add or subtract fractions, you need a common denominator.
The common denominator of these fractions is (x² + 1) (x² − 6).
Multiply the first fraction by (x² − 6) / (x² − 6).
-(7x² + 5x) (x² − 6) / ((x² + 1) (x² − 6))
-(7x⁴ + 5x³ − 42x² − 30x) / ((x² + 1) (x² − 6))
(-7x⁴ − 5x³ + 42x² + 30x) / ((x² + 1) (x² − 6))
Multiply the second fraction by (x² + 1) / (x² + 1).
5x (x² + 1) / ((x² − 6) (x² + 1))
(5x³ + 5x) / ((x² − 6) (x² + 1))
Subtract the fractions.
(-7x⁴ − 5x³ + 42x² + 30x − 5x³ − 5x) / ((x² + 1) (x² − 6))
(-7x⁴ − 10x³ + 42x² + 25x) / ((x² + 1) (x² − 6))
Write the equation of the line that passes through (3,-2) and has a slope of 4 in point-slope form. (2 points)
A)y + 2 = 4(x - 3)
B)y- 3 = 4(x + 2)
C)X - 3 = 4(y + 2)
D)x + 2 = 4(y - 3)
Plz explain just a bit how you got the answer. Will give brainliest!!
Answer:
[tex]A)y + 2 = 4(x - 3)[/tex]
Kyle is renewing his subscription to his favorite computer magazine . The cost is $24 for 12 issues. What is the cost of each issue
Answer:
$2
Step-by-step explanation:
$24 ÷ 12 issues = $2 per issue
Answer:
$2 / issue
Step-by-step explanation:
We want to find the cost of each issue. We need to find the unit rate.
Divide the cost by the number of issues.
cost / issues
It costs $24 for 12 issues.
cost = $24
issues = 12 issues
$24 / 12 issues
Divide 24 by 12
$2 / issue
It costs $2 per issue.
-6 < 2x - 4<4
Solve the inequality
How much fencing would you need to fence in a rectangular storage that measures 40 feet x 20 feet?
Answer:
Ammount of fencing required = perimeter of the rectangular storage.
Perimeter of a rectangle = 2(l+b), where l = length, b = breadth.
so perimeter = 2(40+20) = 2(60) = 120 feet
so fencing required = 120 feet
HOPE IT WAS HELPFUL!
Answer:
[tex]\Huge \boxed{\mathrm{120 \ feet}}[/tex]
Step-by-step explanation:
The length of the rectangular storage is 40 feet.
The width of the rectangular storage is 20 feet.
The length of fencing is needed to fence the entire rectangular storage.
The perimeter of the rectangle is required.
[tex]P=2l+2w \\ \\ \sf P=perimeter \\ l=length \\ w=width[/tex]
[tex]P=2(40)+2(20) \\ \\ P=80+40 \\ \\ P=120[/tex]
120 feet of fencing is needed to fence the rectangular storage.
A rare mutation only occurs in 1 in every 2048 generations of fruit flies. We can assume that whether or not the mutation occurs is independent of previous generations. (a) Calculate the probability of seeing this mutation at least once in 50 generations. (b) Calculate the probability of seeing this mutation at least once in 3000 generations. (c) Compare the calculation in parts (a) and (b) to the approximation 1 â exp(ânp).
Answer:
(A) 0.0244
(B) 1 (not 1.47 as is calculated) since probability values are between 0 and 1; 0 and 1 inclusive
Step-by-step explanation:
The rare mutation only occurs in 1 generation, out of every 2048 generations. This implies that the next occurrence will fall in or within the next 2048 generations (2 generations in 4096 generations, will have the rare mutation).
(A) The probability of occurrence of this mutation at least once (at most infinity) in 50 generations of fruit flies will surely be less than, as 50 is less than 2048.
The accurate probability is gotten when 50 is divided by 2048
50÷2048 = 0.0244
(B) The probability of seeing this mutation at least once (at most infinity) in 3000 generations would have been 1.47 but for 3 reasons;
- The full question already tells that the mutation will occur once in every 2048 generations and 3000 is greater than 2048, hence there will be a sure occurrence within 3000 generations.
- Question (b) asks you to calculate the probability of seeing this mutation at least once in 3000 generations so, the probability is 1 (representing full probability).
- In probability theory or statistics, all probability values fall within 0 and 1; with 0 representing no occurrence at all and 1 representing full occurrence.
in a particular class of 34 students, 11 are men. What fraction of the students in the class are women?
Please help.
Step-by-step explanation:
34-11= women
women divided by 34
23/34 is the fraction of women in the class.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given that,
Total students in the class = 34 students.
Number of students men = 11
Number of students women = 34 - 11 = 23
Now a fraction of 23 from 34 = 23/34
Hence "23/34 is the fraction of women in the class".
For more about fractions,
https://brainly.com/question/10354322
#SPJ2
The Inka Kola Soda Company has heard cmp1aints that the amount of soda in their 12-oz. cans is less than 12 ounces. A random sample of 36 12-oz soda cans is taken, resulting in a sample mean of 11.85 oz and a sample standard deviation of s = .18 oz. Assuming that the population is normal, a 95% confidence interval for the true mean amount of soda in a 12-oz can will be:_______
a. 11.85 plus or minus 0.0494
b. 11.85 plus or minus 0.0588
c. 11.85 plus or minus 0.0609
d. 11.85 plus or minus 0.0784
Answer:
b. 11.85 plus or minus 0.0588
Step-by-step explanation:
Give the following :
Sample mean (m) = 11.85 oz
Sample standard deviation (s) = 0.18
Confidence interval = 95%
Number of observations (n) = 36
Using the formula:
Mean ± Z95% × (sd/√n)
Z score at 95% confidence interval = 1.96
11.85 ± [1.96 × (0.18/√36)]
11.85 ± [1.96 × (0.18 / 6)]
11.85 ± (1.96 × 0.03)
11.85 ± 0.0588
There are 100 people in a sport centre.
67 people use the gym.
62 people use the swimming pool.
56 people use the track.
38 people use the gym and the pool.
31 people use the pool and the track.
33 people use the gym and the track.
16 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
We need to determinate who doesn't use anything, so first we must know the real number of who are practising: a person can do more things.
For doing this, is better use a three-circles graphic, but we try to do without it.
So
16 pool + gym + track, and this number is sure38 gym + pool, but this number includes the people of 1st point. We must know who do only gym + pool: 38 - 16 = 2231 pool + track, this number also includes people of 1st point, so: only pool + track 31 - 16 = 1533 gym + track, this number also includes people of 1st point, so: only gym + track 33 - 16 = 17now:
67 gym, we must know who use only gym: 67 - 16 (gym + pool + track) - 22 (gym + pool) - 17 (gym + track) = 1262 pool, we must know who use only pool: 62 - 16 (gym + pool + track) - 22 (gym + pool) - 15 (pool + track) = 956 track, we must know who use only track: 56 - 16 (gym + pool + track) - 15 (pool + track) - 17 (gym + track) = 8now we must now who do some facility: let's sum all
16 + 22 + 15 + 17 + 12 + 9 + 8 = 99
99/100 practise something
So only 1/100 doesn't use nothing
The probability is 1%
The function intersects its midline at (-1.25,-3) and a maximum point at (0,4) Find a formula for f(x) Give an exact expression.
Answer: y = 7cos(0.4π x) - 3
Step-by-step explanation:
The equation of a cosine function is: y = A cos(Bx - C) + D where
Amplitude (A) is the distance from the midline to the max (or min)Period (P) is the length of one cosine wave --> P = 2π/BPhase Shift (C/B) is the horizontal distance shifted from the y-axisMidline (D) is the vertical shift. It is equal distance from the max and minMidline (D) = -3
(-1.25, -3) is given as a point on the midline. We only need the y-value.
Horizontal stretch (B) = 0.4π
The max is located at (0,4) and also at (5, 4). Thus the period (length of one wave) is 5 units.
[tex]P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 5=\dfrac{2\pi}{B}\qquad \rightarrow \qquad B=\dfrac{2}{5}\pi[/tex] → B = 0.4π
Phase Shift (C) = 0
The max is on the y-axis so there is no horizontal shift.
Amplitude (A) = 7
The distance from the midline to the max is: A = 4 - (-3) = 7
Equation
Input A = 7, B = 0.4π, C = 0, and D = -3 into the cosine equation.
y = A cos(Bx - C) + D
y = 7cos(0.4π x - 0) - 3
y = 7cos(0.4π x) - 3
Please help me and answer this in 20 mins please
a) The perimeter of question a's shape is 18 units.
b) The answer to question b is 28 ft.
Of the 80 trees planted, 2 out of 5 survived the winter. How many trees died during the winter?
Answer:
32
Step-by-step explanation:
2/5x80
16x2
32
Hope this helps
Answer:
48 died
Step-by-step explanation:
2 out of 5 survived that means 5-2 = 3
3 out of 5 died
Multiply that fraction that died by the total number
3/5 * 80
48
What is the slope of the line with equation y = - 3x + 4
Answer:
-3
Step-by-step explanation:
-3 is the slope y=mx + b m is -3
Answer:
m= -3
Step-by-step explanation:
[tex]y = - 3x + 4\\y = \:mx+b\\where \:m\:is\:slope[/tex]
A set of values is shown belovi
12.7, 22, 23.5, 24, 11, 22
What is the mean absolute deviation of the set of values?
A o
B 3.96
C 4.9
D 19.2
Answer:
sorry yall i can help u
Step-by-step explanation:
What are the solutions to the equation? 4x ^ 3 = 36x
Answer:
x = - 3, x = 0, x = 3
Step-by-step explanation:
Given
4x³ = 36x ( subtract 35x from both sides )
4x³ - 36x = 0 ← factor out 4x from each term
4x(x² - 9) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x² - 9 = 0 ⇒ x² = 9 ⇒ x = ± [tex]\sqrt{9}[/tex] = ± 3
Answer:
4x^3=36x.
4x^3-36x=0.
4x^3=36x.
4x(x^2-9)=0.
4x=0,x^2-9=0.
x=0,x^2=9.
x=0,√9=+3 or -3.
x=0,+3,-3.
Thank you for the question
3. Kirk bought a bag of candy and took 10
pieces. He split the rest evenly among 12
friends. Each friend received 5 pieces. Letc
represent the number of pieces in a bag.
Equation:
Solve it to find how many pieces of candy were in the bag.
Type here
Show your work
Write and solve the equation
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :( Multiply.
Hey there! I'm happy to help!
First, let's multiply the numerators. We will put q+5 in parentheses so we can multiply it by 4q.
4q(q+5)
We use the distributive property to undo the parentheses.
First, we multiply 4q by q.
4q×q=4q²
And we multiply 4q and 5.
4q×5=20q
So, our numerator right now is 4q²+20q.
Now, for the denominators.
2(q+4)
We do 2 by q.
2×q=2q
And 2×4, which is 8.
So, our denominator is 2q+8.
Right now, our fraction is [tex]\frac{4q^2+20}{2q+8}[/tex], and this is your correct answer. However, we can simplify it a bit more. We can divide the 4 by 2, q² by q, and simplify the 20 and the 8.
4/2=2
q²/q=q
20/8=5/2
Now, our final product is (2q+5)/2
But, mark down your answer as [tex]\frac{4q^2+20}{2q+8}[/tex] because that is technically correct.
Have a wonderful day! :D
A Gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed
Answer:
The circumference is 31.42 and the area is 78.54
Step-by-step explanation:
For circumference you use the formula
C=2 r
R= radius and = 3.14
For area use the formula
A= r^2
I hope this helps
Consider the geometric sequence 1/64, 1/16, 1/4, 1, …. What is the common ratio?
Answer:
Identify the Sequence 1, 1/4, 1/16, 1/64 11, 1414, 116116, 164164 This is a geometric sequencesince there is a common ratiobetween each term. In this case, multiplying the previous termin the sequenceby 1414gives the next term.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Sequence:
1/64, 1/16, 1/4, 1Common ratio is the ratio between the next term and the previous term:
1/16 : 1/64 = 1/16 * 64 = 64/16 = 4or
1/4 : 1/16 = 1/4 * 16 = 16/4 = 4or
1: 1/4 = 1* 4 = 4Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4)0=(3x+2)(x−4)0, equals, left parenthesis, 3, x, plus, 2, right parenthesis, left parenthesis, x, minus, 4, right parenthesis Erik said, “The right-hand side is factored, so I'll use the zero product property.” Caleb said, “I'll multiply (3x+2)(x-4)(3x+2)(x−4)left parenthesis, 3, x, plus, 2, right parenthesis, left parenthesis, x, minus, 4, right parenthesis and rewrite the equation as 0=3x^2-10x-80=3x 2 −10x−80, equals, 3, x, squared, minus, 10, x, minus, 8. Then I'll use the quadratic formula with a=3a=3a, equals, 3, b=-10b=−10b, equals, minus, 10, and c=-8c=−8c, equals, minus, 8." Whose solution strategy would work?
Answer:both
Step-by-step explanation:
Answer:
Both :)
Step-by-step explanation:
83,997 to the nearst tenth
Answer:
Hey there!
If you mean, to the nearest ten, this would be 84000.
Let me know if this helps :)
Answer:
84,000
Rounded to the nearest 10 or
the Tens Place.
Witch is a function
Answer:
A
Step-by-step explanation:
a x-vaule can't have more than one y-vaule so a problem like (-4,3) and (-4,5) cant be a function
When two straight lines cross, it is found that the angles opposite each other are the same size. They are known as .............
Answer:
Step-by-step explanation:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.
Answer:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.
Step-by-step explanation:
Adjacent angles are angles that come out of the same vertex.
5/4p=4/3p+3/2 A: The solution set is (_) Simplified B: There is no solution Pick one and if A then simplify the answer
Answer:p= -18
Step-by-step explanation:Let's solve your equation step-by-step.
5/4 P= 4/3 P + 3/2
Step 1: Subtract 4/3p from both sides.
5/4 P - 4/3 P = 4/3 P + 3/2 - 4/3 P
-1/12 P = 3/2
Step 2: Multiply both sides by 12/(-1).
(12/-1) × (-1/12 P) = (12/-1) × (3/2)
P = -18
Answer:
p = - 18
Step-by-step explanation:
5 4 3
--- p = --- p + ---
4 3 2
5 2² 3
--- p = --- p + ---
2² 3 2
5p 2² * p 3
--- = --------- + ---
2² 3 2
p = - 18
ic
А
50
B
(2x + 260 )°
O A. O
B. 2
C.5
OD.7
Answer:
[tex]\Huge \boxed{x=0}[/tex]
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
y + 50 = 180
y = 180 - 50 = 130
We can use Angle formed by a chord and tangent theorem to solve for x.
The angle formed by a chord and tangent is half the measure of the intercepted arc.
130 = 1/2(2x+260)
Expand brackets.
130 = x+130
Subtract 130 from both sides.
x = 0
f (x) = 2(x)2 +59/(x+2)