Solve for the remaining sides and angles if possible (if not, answer "DNE" in all answer boxes). As in the text, (a, a), (B, b), and (y, c) are angle-side opposite pairs. Round to one decimal places, if necessary a = 11, b = 11 c = 11
Answers
Answer: A = 60°, B = 60°, y = 60°, a = 11, b = 11, c = 11.
Using the law of cosines, we can solve for the remaining angles and sides of the triangle. Let's start by finding angle B:
cos(B) = (a^2 + c^2 - b^2) / 2ac
cos(B) = (11^2 + 11^2 - 11^2) / (2 * 11 * 11)
cos(B) = 0.5
B = cos^-1(0.5)
B ≈ 60°
Next, we can find angle y:
cos(y) = (a^2 + b^2 - c^2) / 2ab
cos(y) = (11^2 + 11^2 - 11^2) / (2 * 11 * 11)
cos(y) = 0.5
y = cos^-1(0.5)
y ≈ 60°
Now, we can use the law of sines to find side a:
a / sin(A) = b / sin(B) = c / sin(y)
a / sin(A) = 11 / sin(60°)
sin(A) = a / (11 / sin(60°))
A = sin^-1(sin(A))
A ≈ 60°
Since we now know that all angles of the triangle are 60°, we can conclude that it is an equilateral triangle. Therefore, all sides and angles are equal, and our answers are:
Angle A = 60°
Angle B = 60°
Angle y = 60°
Side a = 11
Side b = 11
Side c = 11
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Related Questions
ll we know about a function g is g(−1)=3 and g ′
(x)= x 2
+3
for all x. (i) The linearization of g at −1 is X. (Choose A, or B, or C, or D from the list below.) (A) L(x)=−2x+1 (B) L(x)=3x+6 (C) L(x)=2x+5 (D) L(x)=2x−3 (ii) Using linear approximation, we can estimate g(−1.06)≃ (iii) The estimate in part (ii) is an -estimate
Answers
(i) The linearization of g at -1 is (C) L(x)=2x+5.The function g(−1)=3 and g′(x)=x²+3, for all x. To find the linear approximation of a function at some point `a`, the following formula is used:`
(ii) Using linear approximation, we can estimate `g(-1.06) ≃ 2.84`.To estimate `g(-1.06)` using linear approximation, we need to plug `-1.06` into the linearization of `g` at `-1`.`\(L(-1.06) = 4(-1.06) + 7 = 2.84\)`So the estimate of `g(-1.06)` using linear approximation is `2.84`.
Therefore, the correct answer is option `(D)`. (iii) The estimate in part (ii) is an - underestimate. The estimate in part (ii) is an underestimate because we are approximating a function that is increasing with a line that is increasing at a slower rate than the function.
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One number is eight less than a second number. Six times the first is 3 more than 3 times the second. Find the numbers.
Answers
17. Write the first 4 terms of the
sequence defined by the explicit rule.
f(n) = 2n - 5
Answers
Answer:
The first four terms are: -3, -1, 1, and 3
Step-by-step explanation:
First 4 terms are:
f(1) = 2 (1) - 5 = -3
f(2) = 2 (2) - 5 = -1
f(3) = 2 (3) - 5 = 1
f(4) = 2 (4) - 5 = 3
Which equation matches the table?
X 4 5 6 7 8
Y 8 10 12 14 16
y = x - 4
y = x ÷ 2
y = x + 4
y = 2 x
Answers
Answer:
y=2x
Step-by-step explanation
Can u guys help pls? This is due in 10 mins
Answers
Answer:
Question 7: 16n^8 Question 8: 6r^4 Question 4: (-1,-7) Question 6: 6y^7
Step-by-step explanation:
Do i need it?
6. b 6y^7
7. b 16n^8
Scientists trying to calculate the half-life (the time it takes for half of a sample to decay) of Phosphorus-32, took measurements of the sample once every day for five days. On what day should about half of the original amount of P-32 remain? (Round answer to the nearest day.)
Answers
According to the information, on the 11th day, half of the substance should remain.
How to calculate on which day half of the substance will remain?To calculate what day half of the substance will remain, we must carry out the following mathematical procedure.
First of all we must find the range of decrease from one value to another.
4, 4.5, 5.5, 4 and 3
We average these values and it gives us 4.4.
We then subtract 78 - 50 to identify the difference between these two mass values. and then we divide the result in the decreasing range (4.4).
78 - 50 = 2828 / 4.4 = 6.36According to the above, it would take another 6.3 days to reach 50%, so more or less on day 11 half of the substance would remain.
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Alex prepares goody bags for his guests. He has 30 Minifigures and 24 spinners. How many goody bags can he make if he wants to put the same number of Minifigures in each bag and the same number of spinners in each bag with no toys left over?
Answers
Answer:
he can make 6 goodie bags
Step-by-step explanation:
Sort the scenarios according to their variability.
I will mark BRAINLIST if correct, and if you want to explain you can. I will report if wrong.
Answers
Scenario 2: low
Scenario 3: high
Scenario 4: low
Scenario 5: low
8 ÷ 28 *has to be in decimal form*
Answers
Answer: 0.28571428571
Step-by-step explanation: 8 dived by 28
Cody ran 3 miles on his first day of training. The next day he ran 2/12 that distance. How far did he run the second day?
Answers
Answer:
.5 miles
Step-by-step explanation:
2/12 = 1/6
3 miles divided by 1/6 = .5
Putting 100 points to whoever can solve this
check attachment
Answers
Answer:
The syntax ↓
\(1.2 * 4 = 4.8\\3 * 3 * 3 = 27\\14.7 / 7 = 2.1\\+ 27 = 29.1\\- 4.8 = 24.3\)
It's 24.3 try it.
Hope this helps!
Please give brainliest, i need 3 more :)
Answer:
24.3
Step-by-step explanation:
Here we need to evaluate,
\(\longrightarrow 3^3 +14.7\div 7-(1.2\times 4)\)
First of all we need to know about BODMAS , which stands for ,
B = BracketsO = of D = divisionM = multiplicationA = AdditionS = SubtractionThis means first we need to solve brackets , then of , then division , then multiplication, then addition and finally subtraction.
In the given questions, firstly solve the terms inside the brackets ,
\(\longrightarrow 3^3 +14.7 \div 7 -(1.2\times 4)\)
Multiply 1.2 and 4 ,
\(\longrightarrow 3^3+14.7\div 7-(4.8) \)
Now perform division , that is divide 14.7 by 7
\(\longrightarrow 3^3 + 2.1 - 4.8 \)
Simplify 3³ .
\(\longrightarrow (3)(3)(3)+2.1-4.8= 27+2.1-4.8\)
Add ,
\(\longrightarrow 29.1 -4.8\)
Finally subtract,
\(\longrightarrow \underline{\underline{\boldsymbol{ 24.3 }}}\)
And we are done!
add ( 7x^2-5x+3)+(2x^2+7x-8)
Answers
Answer:
A.9\(x^{2}\)+2x-5
Answer:
\( 9{x}^{2} + 2x - 5\)Option A is the correct option.
Solution,
\(7 {x}^{2} - 5x + 3 + 2 {x}^{2} + 7x - 8 \\ \)
Combine like terms:
\(7 {x}^{2} + 2 {x}^{2} - 5x + 7x + 3 - 8\)
Simplify:
\(9 {x}^{2} + 2x - 5\)
Hope this helps..
Good luck on your assignment..
Kiki’s mother cooked a dinner that contained a total of 992 calories. She also prepared a dessert that contained a total of 846 calories. The dinner was divided into 4 equal servings. The dessert was divided into 6 equal servings. Kiki had one serving of dinner and one serving of dessert.
Answers
Graph the function f(x) = -3 log₂ (-x-4) - 8 on the
axes below. You must plot the asymptote and any two points
with integer coordinates.
Answers
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
What is meant by a function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. The sets X and Y are referred to together as the function's codomain and domain, respectively.
Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known approach to the concept of function. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically with the infinitesimal calculus towards the end of the 17th century, and until the 19th century, the functions that were taken into consideration were differentiable.
Given function is,
f(x)= -3 log₂ (-x-4) - 8
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
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the midpoint of uv is m(10, 6). one endpoint is v(10, 7). find the coordinates of the other endpoint u.
Answers
The coordinates of the other endpoint U are found to be (Xu, Yu) = (10, 5).
What is coordinates of a point?The coordinates are a pair of numbers which characterize the exact location of a point on a cartesian plane through using horizontal and vertical lines.
The x and y values of a point on a graph are usually represented by (x, y). Each point or ordered pair has two coordinates.Now, as per the question.
To find the coordinates of U, use the midpoint formula with the coordinates of points u and v (Xv, Yv) and (Xm, Ym) respectively.
Let's refer to them as (Xu, Yu)
Midpoint formula {(Xv + Xu)/2, (Yv + Yu)/2)}
Fill in the recognized coordinates as needed.
Point V at (10, 7) = (Xv, Yv)
Midpoint, point M at (10, 6) = (Xm, Ym)
For the x coordinates;
(10 + Xu)/2 = 10
Xu = 10.
Similarly for the y coordinate;
(7 + Yu)/2 = 6
7 + Yu = 12
Yu = 5
We can test this by plugging U's coordinates into the midpoint formula.
(10 + 10)/2 = 20/2 = 10
(5 + 7)/2 = 12/2 = 6
Therefore, the coordinates of the are (Xu, Yu) = (10, 5).
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5. Find the Fourier coefficients of the periodic ( -5 to 5) function y(t) = -3 when -5
Answers
In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:
c₀ = -3 (DC component)
cₙ = 0 for n ≠ 0 (other coefficients)
To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:
cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt
where T is the period of the function and n is an integer.
In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).
To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:
c₀ = (1/T) ∫[-T/2, T/2] y(t) dt
Substituting the given values:
c₀ = (1/10) ∫[-5, 5] (-3) dt
= (-3/10) \([t]_{-5}^{5}\)
= (-3/10) [5 - (-5)]
= (-3/10) [10]
= -3
Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.
For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:
cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt
Since y(t) is constant, the integral becomes:
cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt
= (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt
The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.
all the coefficients cₙ for n ≠ 0 are zero.
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Find the sum of a third (a+b) and a fifth of (a-b)
Answers
Answer:
(5a+5b+3ab)/15
Step-by-step explanation:
qquy đồng lên thôi !!
A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)
(a)
Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic. (Round your answer to two decimal places.)
Answers
The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.
Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:
p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.
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this is not relly i qustion but i have 10 or qustion i need help with if any one can help me with them text me and it 8th grad math
Answers
Which graph shows the result of dilating this figure by a factor of One-third about the origin? On a coordinate plane, triangle A B C has points (negative 6, 6), (6, 6), (6, negative 6). On a coordinate plane, triangle A prime B prime C prime has points (negative 2, 2), (2, 2), (2, negative 2). On a coordinate plane, triangle A prime B prime C prime has points (negative 3, 3), (3, 3), (3, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (Negative 18, 18), (18, 18), (18, negative 18). On a coordinate plane, triangle A prime B prime C prime has points (negative 12, 12), (12, 12), (12, negative 12).
Answers
answer in scientific notation.
4,672,000
Answers
Answer:
4.672 × 10⁶
Step-by-step explanation:
I need help ring the center, radius, and diameter.
Answers
Answer:
(-2, 5), 6, 12
Step-by-step explanation:
Center: (-2, 5)
Radius: 6
Diameter: 12
find y intercept
y=50+5x
answer needs to be a point ex. (0,0)
Answers
Answer:
(0, 50)
Step-by-step explanation:
The equation of a line is in the form of the y-intercept form
\(y = mx + b\)
where m is the slope and B is the y intercept. So in our case
\(y = 50 + 5x\)
if we use the commutative property we can rewrite our equation as
\(y = 5x + 50\)
therefore b = 50 is our why intercept
In slope-intercept form, y = mx + b, where m = slope, and y-intercept = b:
b represents the y-coordinate of the y-intercept (0, b). Hence, in your given equation: y =5x + 50:
b = 50, and its corresponding x-coordinate is 0.
The y-intercept is (0, 50).
Suppose y = – 3x2 – 15x – 11 was written in the form y = a(x – h)2 + k.
What is the value of a?
a) = -5
b) a= -3
c) a = 5
d) a = -11
Answers
Answer:
b) -3
Step-by-step explanation:
You want the value of 'a' when the quadratic y = –3x² – 15x – 11 is written in the form y = a(x – h)² + k.
Leading coefficientThe leading coefficient in either form is the coefficient of x². It is the same in both forms: -3.
Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
Answers
Answer:
-2x + y = 25
Step-by-step explanation:
just add them together by columns. X-3x = -2x
3y-2y = y
5+20 =25.
done.
suppose nine pairs of similar-looking boots are thrown together in a pile. what is the minimum number of individual boots that you must pick to be sure of getting a matched pair? why? since there are 9 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . it follows that if a minimum of boots are chosen, at least two must be from the same pair.
Answers
the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.
Since there are 9 pairs of boots in the pile, we can determine that each pair has two boots. If at most one boot is chosen from each pair, the maximum number of boots chosen would be 18.
To guarantee that a matched pair of boots is chosen, we must pick at least two boots from the pile, one from each boot of the same pair. Therefore, the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.
Number of pairs of boots in the pile = 9
Number of boots in each pair = 2
Maximum number of boots that can be chosen = 9 x 2 = 18
Minimum number of boots required to guarantee a matched pair = 2
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Which of the following expressions are equivalent to 1/-7 • -6/5
Answers
Solve for v.
5(v+6)=-3(4v-6) + v
Simplify your answer as much as possible.
V=
Answers
Distribute on both sides
5v + 30 = -12v + 18 + v
Add like terms
5v + 30 = -11v + 18
Work backwards
16v + 30 = 18
16v = -12
v = -0.75
Solve y=x^2+4x+6 by using the completing squares method. Fast please :)
Answers
Answer:
x = -2±√-2
Step-by-step explanation:
y = x^2+4x+6
x^2+4x+6=0
move the constant to the right
x^2+4x=-6
add the square of 1/2 of the x variable to both sides
1/2 of 4 is 2
x^2+4x+2^2=-6+4
x^2+2^2=-2
(x+2)^2=-2
square both sides
x+2=±√-2
x=-2±√-2
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mmon Core Algebra I - MA3109 B-IC
Activity
Vertical Stretches and Shrinks of Exponential Functions
Assignment Active
Identifying a Function
Which is a stretch of an exponential decay function?
◎m=²[
Of(x) = -(5)
Of(x) = 5(²)
O fix) = 5(5)*
Answers
The stretch of an exponential decay function is y = 2(1/5)ˣ
Which is a stretch of an exponential decay function?From the question, we have the following parameters that can be used in our computation:
The list of exponential functions
An exponential function is represented as
y = abˣ
Where
a = initial valueb = growth/decay factorIn this case, the exponential function is a decay function
This means that
The value of b is less than 1
An example of this is, from the list of option is
y = 2(1/5)ˣ
Hence, the exponential decay function is y = 2(1/5)ˣ
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Complete question
Which is a stretch of an exponential decay function?
Of(x) = -(5)ˣ
Of(x) = 5(2)ˣ
O fix) = 2(1/5)ˣ