Answers
Answer:
Step-by-step explanation:
angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)
4x^2-6x+40+18x+3+2x^2-7=180
6x^2+12x+36=180
6(x^2+2x+6)=180
x^2+2x+6=180/6
x^2+2x+6=30
x^2+2x=24
x(x+2)=24
x+2=24/x
x=24/x-2
x=24-2x/x
substitute the value of x^2 in angle R
2x^2-7
2(24-2x/x)^2-7(here x and x gets cancel)
2(24-2)^2-7
2*22^2-7
2*484-7
968-7
961
Answer:
Step-by-step explanation:
angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)4x^2-6x+40+18x+3+2x^2-7=1806x^2+12x+36=1806(x^2+2x+6)=180x^2+2x+6=180/6x^2+2x+6=30x^2+2x=24x(x+2)=24x+2=24/xx=24/x-2x=24-2x/xsubstitute the value of x^2 in angle R2x^2-72(24-2x/x)^2-7(here x and x gets cancel)2(24-2)^2-72*22^2-72*484-7968-7961
Related Questions
The probability distribution for a
random variable x is given in the table.
х
-5
-3
-2
0
2
3
Probability
.17
:13
.33
.16
.11
.10
Find the probability that x<-3
Answers
This is the probability that corresponds to x = -5, which is less than x = -3, and it's the only x value of the list smaller than -3. There's not much else to say about this.
If we wanted to find something like P(X < -2), then we would add up the probabilities for x = -5 and x = -3 to get 0.17+0.13 = 0.30
Angle PKL and angle MKN are complementary angles. The measure of angle PKL is twice the measure of angle MKN.
a. Write one equation to find x,
b. What is the measure of angle MKN
c. Solve for x.
Answers
Answer:
∠MKN = 30°
Step-by-step explanation:
∠PKL = 2x
∠MKN = x
2x + x = 90
3x = 90
x = 30
∠MKN = 30°
the radius of a cylindrical water tank is 4ft, and it’s height is 10ft. What is the volume of the tank?
Answers
Answer:
[tex]volume = 502.4ft^3[/tex]
Step-by-step explanation:
[tex]volume = \pi r^2 h = 3.14 \times 4^2 \times 10 = 502.4ft^3[/tex]
solve this: - 6 n = 30
Answers
Answer:
-6n=30
so find value of n
n=30÷(-6)
n=-5
so, value of n = -5
Answer:
-6 n = 30
or,n=30÷(-6)
or,n=-5
Complete the function table
Answers
Answer:
8, 6, 3, 2, 1
Step-by-step explanation:
g(x) = -x + 3
using g(x),
g(-5) = (-1 x -5) + 3
= 5 + 3
= 8
g(-3) = (-1 x -3) + 3
= 3 + 3
= 6
g(0) = 0 + 3
= 3
g(1) = -1 + 3
= 2
g(2) = -2 + 3
= 1
Find the length of side x in simplest radical form with a rational denominator
Answers
Answer:
The answer is "[tex]\frac{7\sqrt{3}}{2}[/tex]"
Step-by-step explanation:
[tex]\to \sin 60^{\circ} = \frac{x}{7} \\\\\to x=\sin 60^{\circ} \times 7 \\\\\therefore \sin 60^{\circ} = \frac{\sqrt{3}}{2} \\\\\to x= \frac{\sqrt{3}}{2}\times 7 \\\\\to x= \frac{7\sqrt{3}}{2}[/tex]
Find the radius of convergence and the interval of convergence.
[tex]\displaystyle \sum \limit_{n=1}^\infty \frac{x^\text{n}}{2^\text{n}(n+1)^2}[/tex]
Answers
Answer:
Radius of Convergence: 2
Interval of Convergence: [-2, 2]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Calculus
Series Convergence Tests
P-Series: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Alternating Series Test (AST)Ratio Test: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{a_{n + 1}}{a_n} \bigg|[/tex]Radius of Convergence (ROC)
Ratio TestInterval boundInterval of Convergence (IOC)
Testing endpointsStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex]
Step 2: Find ROC
Apply Ratio Test
[Series] Set up [Ratio Test]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^{n + 1}}{2^{n + 1}(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Rewrite exponentials [Exponential Rule - Multiplying]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^n \cdot x}{2^n \cdot 2(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Simplify: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x}{2(n + 2)^2} \cdot (n + 1)^2 \bigg|[/tex][Ratio Test] Multiply: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x(n + 1)^2}{2(n + 2)^2} \bigg|[/tex][Ratio Test] Evaluate limit: [tex]\displaystyle \bigg| \frac{x}{2} \bigg| < 1[/tex][Ratio Test] Isolate x: [tex]\displaystyle |x| < 2[/tex]Our ROC is 2.
Step 3: Find IOC
Test endpoints
[ROC] Find interval bound: [tex]\displaystyle -2 < x < 2[/tex]x = -2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-2)^n}{2^n(n + 1)^2}[/tex][Series] Rewrite [Exponential Rules - Multiplying]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n}{(n + 1)^2}[/tex]Test convergence of modified series: Alternating Series Test
[AST] Condition 1 [Limit Test]: [tex]\displaystyle \lim_{n \to \infty} \frac{1}{(n + 1)^2} = 0 \ \checkmark[/tex][AST] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 2)^2} \le \frac{1}{(n + 1)^2} \ \checkmark[/tex]At x = -2, the series is convergent.
∴ Current IOC is -2 ≤ x < 2 or [-2, 2); 2 undetermined
x = 2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{(n + 1)^2}[/tex]Test convergence of modified series: Direct Comparison Test
[DCT] Condition 1 [Define comparing series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^2}[/tex][DCT] Condition 1 [Test convergence of comparing series]: [tex]\displaystyle p = 2 > 1, \ \sum \limit_{n = 1}^\infty \frac{1}{n^2} \ \text{convergent by p-series}[/tex][DCT] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 1)^2} \le \frac{1}{n^2} \ \checkmark[/tex]At x = 2, the series is convergent.
∴ IOC for [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex] is -2 ≤ x ≤ 2 or [-2, 2]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations - Power Series (BC Only)
Book: College Calculus 10e
What is the distance between (-8,2) and (4,4)
Answers
Answer:
d = 2√3
Step-by-step explanation:
Glven that (x + 2) Is a factor of the polynomial f(x) = x ^ 3 - 4x ^ 2 - 19x - 14 , factor completely
Answers
Answer:
Factors of the polynomial are (x+2) (x+1) (x-7)
When 12 radios were left, how many hours had gone by?
Hellpp
Answers
If we look at the graph, we see that when there are 12 radios left, hours is equal to 12.
Please solve!
l = 48.1 m, w = 51.62 m, h = 3.42 m
Answers
Answer:
Volume? Surface area?
Step-by-step explanation:
Volume=8491.59
Surface area=5647.93
Portia has purchased a new aquarium for her fish. It is in the shape of a hexagonal prism. 3a) How much water can Portia’s new aquarium hold? * 1 point a) 166.28 cubic inches b) 790.28 cubic inches c) 956.56 cubic inches d) 3120 cubic inches e) 6240 cubic inches
Answers
Answer:
D. 3120
Step-by-step explanation:
How many sides does a hexagon have? Six. Let's begin our equation with 6. The area of a triangle formula would be: 1/2 bh. And a hexagon is just six triangles put together. Now our equation is: 6 (1/2 bh) What's bh then? B (base)= 8in. The base is usually always at the bottom. Now we take 10 and add it into the equation. Next we would multiply this by 13. Our equation is now: 6(1/2*8*10)*13. What do you get then? 3120.
For Part B: Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?
Now, we're dealing with surface area. What is surface area, anyway? Surface area is the sum of all faces. There are 2 hexagonal faces and 6 sides.
What is 6*1/2 *8? 24! Now what's 10*24? That's right, 240!
8*13=104
6(104)=624
624+240=864
Determine the rate of change of the function given by the table.
A) 2
B) 1
C) -1
D) -2
Answers
All i did was
5-3=2
6-4=2
7-5=2
8-6=2
They all equal to 2 so the answer is 2 :)
The graph above shows the cost, in dollars, of apples as
a function of the number of pounds of apples purchased
at a particular grocery store. The equation above defines
the cost C, in dollars, for p pounds of pears at the same
store. Which of the following statements accurately
compares the cost per pound of apples and the cost per
pound of pears at this store?
A. Apples cost approximately $0.07 less per pound
than pears do.
B. Apples cost approximately $0.04 less per pound
than pears do.
C. Apples cost approximately $0.73 less per pound
than pears do.
D. Apples cost approximately $0.62 more per pound
than pears do.
Answers
Your answer is A
The accurate statement is A. Apples cost approximately $0.07 less per pound.
Cost of Apples per pound using the given graph:The constant of proportionality would give us the cost of per pound. From the graph, when number of pounds (p) = 3, cost in dollars (C) = 4.
Constant of proportionality = C/p = 4/3
Therefore, Cost of apples per pound = 4/3 = $1.33 (approximated)
Cost of Pears per pound using the given equation:[tex]C = \frac{7}{5} p[/tex]
The constant of proportionality of the equation function will give us the cost per pound for pears.
From the equation, the we can deduce that [tex]\frac{7}{5}[/tex] represents the cost of pears per pound (constant of proportionality).
Thus:
Cost of pears per pound = 7/5 = $1.40
The difference between the cost per pound of pears and the cost per pound of apples would be:
$1.40 - $1.33 = $0.07
Therefore, we can conclude that apples cost approximately $0.07 less per pound.
Learn more about constant of proportionality here:
https://brainly.com/question/11703625
Can some one please help me ?
Answers
9514 1404 393
Answer:
a) 1/2
b) 1/2
Step-by-step explanation:
a) The average rate of change is the slope of the segment whose end points are the ends of the interval. On the interval [2, 8] the average rate of change is ...
m = (f(8) -f(2))/(8 -2) = (4 -1)/6 = 3/6 = 1/2
The average rate of change on the interval [2, 8] is 1/2.
__
b) In this context, "slope" and "average rate of change" mean the same thing. A line with the same slope will have a slope of 1/2.
What is 6 1/3 yards in feet with explication
Answers
Answer:
6 1/3 yards = 19 feet
Step-by-step explanation:
1 yard = 3 feet
So we'll take the number of yards and multiply that by 3
6 yards x 3 feet/yard = 18 feet
for the 1/3 of a yard, you can either ask, "what's 1/3 of 3?" (= 1) or you can multiply 1/3 yard x 3 feet/yard = 1 foot.
Add up the parts, 18 + 1 = 19 feet
The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?
Answers
Step-by-step explanation:
Area=2(L+W)
A=2(6+3)
A=2(9)
A=18in²
therefore, 7500/18
=416.66in²
In the number 3,941,608,572, which digit is in the hundred millions place?
Answers
Answer:
9
Step-by-step explanation:
A hundred millions is: 100,000,000
looking at the number the number in the place hundred millions place is 9, so the answer is 9.
Answer:900,000,000
The digit is 9
Step-by-step explanation:
Rob can complete his bus route in 4 hours. Joan can complete her bus route in 3 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
Answers
Answer:
3:00 pm
Step-by-step explanation:
Given
[tex]Rob = 4\ hrs[/tex]
[tex]Joan = 3\ hrs[/tex]
[tex]Start\ Time = 3:00\ am[/tex]
Required
The next time they leave at the same time
To do this, we first list out the multiples of 4 and 3 (i.e. their time of completing each route)
So, we have:
[tex]Rob: 4, 8, 12, 16, 20...[/tex]
[tex]Joan: 3,6,9,12,15,18....[/tex]
The least common multiple in the above is:
[tex]Least = 12hrs[/tex]
This means that they will meet at the terminal after 12 hours
So, their meeting time is:
[tex]Time = 3:00am + 12\ hrs[/tex]
[tex]Time = 3:00\ pm[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP QUICKK
Answers
9514 1404 393
Answer:
A. The volumes are equivalent.
Step-by-step explanation:
The volume of a pyramid can be found using the formula ...
V = 1/3Bh
where B is the base area, and h is the height.
Both of these pyramids have the same height, so we can compare volumes by looking at the base area.
Prism X has a rectangular base with an area of A = LW = (6 cm)(5 cm) = 30 cm². Prism Y has a triangular base with an area of A = 1/2bh = 1/2(7.5 cm)(8 cm) = 30 cm².
The two base areas are the same, so the volumes are the same.
Which is the most reasonable measure for the capacity of a bathtub?
O 5 liters
© 159 liters
O 159 milliliters
1000 milliliters
Answers
Which Which value of x makes this equation true? -3x+10=5x-8
value of x makes this equation true? -3x+10=5x-8
Answers
Answer:
9/4
Step-by-step explanation:
-3x+10=5x-8
or, -3x-5x = -8-10
or, -8x=-18
or, 8x=18 (i.e. - is cancelled)
or, x=18/8
i.e. x=9/4
Hence, the value of x is 9/4
Answer:
The value of x is 9/4
Step-by-step explanation:
-3x+ 10 = 5x - 8
Add 3x both side
-3x + 3x + 10 = 5x + 3x - 8
10 = 8x - 8
Now, Add 8 both side
10 + 8 = 8x - 8 + 8
18 = 8x
8x = 18
Now, Divide by 8 from both side
8x/8 = 18/8
x = 9/4
Thus, The value of x is 9/4
FOR VERIFICATION ONLY:-3x + 10 = 5x - 8
-3(9/4) + 10 = 5(9/4) - 8
-27/4 + 10 = 45/4 - 8
-27 + 4 × 10/4 = 45 - 8 × 4/4
-27 + 40/4 = 45 - 32/4
13/4 = 13/4
Hence, L.HS = R.H.S
-TheUnknownScientist
Solve for x.
4x - 14
x + 85
x = [?]
Answers
Answer:
x = 33
Step-by-step explanation:
4x - 14 = x + 85
3x = 99
x = 99/3
x = 33
[(-18)+(+7)]×(-10)
i will you 10 point for this
Answers
PLEASE HELP!
Find the x value.
Answers
Answer:
72
Step-by-step explanation:
every angle in a triangle adds up to 180
57 + 51 + x = 180
x = 72
Answer:
The answer to the question is:
x=72°
Step-by-step explanation:
The total angles of a triangle is 180°
x+51°+57°=180°
x+108°=180°
x=180°-108°
x=72°
The graph of the function f(x) = cos(x) is shown.
What is the range of the function?
A. [-3,3]
B. (-00, 00)
C. [-1, 1]
D. (0, 2m)
Answers
Answer:
C
Step-by-step explanation:
bottom to top
it goes from -1 to 1
The required range of the function y= cosx is [-1, 1]. Option C is correct.
From the graph range of the function y = cosx is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is independent while Y is the dependent variable.
What is range?The range is defined as the difference between higher and lower values of y = f(x).
In a graph the value of y = f(x) = cosx is defined for every x of its domain (-∞, ∞) it varies from minimum -1 to maximum +1 on the y axis, so the range of the function is [ -1, 1].
Thus, the required range of the function y= cosx is [-1, 1]. Option C is correct.
Learn more about function here:
brainly.com/question/21145944
#SPJ5
Find the radius and circumference of this pizza. Round to the nearest hundredth if necessary
Answers
I need the answer fast pls
Answers
Answer:
B
Step-by-step explanation:
It's B because that's the only answer that talks about the highest temperature, which is mentioned in the question
Hope this helps
The average time for 100-meter race that Usain Bolt used is 9.6 seconds on average. He wants to test whether his speed has decreased or not. His speed was tested for 16 times, and the average time is 9.7 seconds. Assume the population standard deviation is 0.1 second. At a 5% significance level, the decision is to _________.
Answers
Answer:
At a 5% significance level we reject the Null hypothesis [tex]H_0[/tex]
Step-by-step explanation:
From the question we are told that:
Distance [tex]d= 100[/tex]
Mean [tex]\mu=9.6[/tex]
Sample size [tex]n=16[/tex]
Sample mean [tex]\=x=9.7[/tex]
Standard deviation [tex]\sigma= 0.1[/tex]
significance level [tex]\alpha=5%=>0.05[/tex]
Generally the Hypothesis is mathematically given by
[tex]H_0=\mu=9.6[/tex]
[tex]H_a=\mu=9.6[/tex]
Generally the equation for t test statistics is mathematically given by
[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]t=\frac{9.7-9.6}{\frac{0.1}{\sqrt{16} } }[/tex]
[tex]t=4[/tex]
Therefore P-Value from table
[tex]P-Value=0.000[/tex]
[tex]\alpha>P-value[/tex]
Therefore
At a 5% significance level we reject the Null hypothesis [tex]H_0[/tex]
The diagram shows two lighthouses A and B and a port P
A boat is on a bearing of 340° from lighthouse A and 245° from lighthouse B.
a) Mark, with a cross, the position of the boat on the map.
b) What bearing should the boat sail on to enter the port?
Answers
Answer:
B) is 085 degrees
Step-by-step explanation:
A) From point 'a', measure around 336 degrees bearring and then put the line there. Then, from point 'b' measure around 250 degrees when measuring north.
I hope this makes sense lol, I pretty much guessed the answered so don't expect a proper explanation. :'(
Anyways, there is a screenshot attached that might help.