Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{4 + \sqrt{45} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{4}{6} + \cfrac{ \sqrt{45} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{3 \times 3 \times 5} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ 3\sqrt{5} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Related Questions
An investment group compares returns on an account against the function represented in the table, where x is the time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the table?
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
Answers
The function over the interval is an increasing exponential function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
The complete question is
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.
For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.
For, Exponential function
When the exponential function then it shows total return on investment is not maximum.
When the exponential function is increasing it shows time goes, total return on investment is maximum.
Hence, the exponential function is increasing.
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Garth is packing boxes with books.the list shows how many books are in each 10 of boxes
Answers
The median of books to a box is 9 and The mean of books to a box is 11
The complete question is
Garth is packing boxes with books. The list shows how many boxes are in each of 10 boxes. 6,14,6,18,9,9,12,10,11,15
Which statement is true about the number of boxes packed to a box?
A) The median # of books to a box is 8
B) The median # of books to a box is 9
C) The mean # of books to a box is 11
D) The mean # of books to a box is 12
What is Mean and Median ?Mean is the average of the data given while the median is the middle point of the data.
It is given that
The data is
6, 14, 6, 18, 9, 9, 12, 10, 11, 15
The mean is
(6 + 14 + 6 + 18 + 9 + 9 + 12 + 10 + 11 + 15)/10 = 11
and the median is 9
Therefore Option B and C is the correct answer.
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A _______ random variable has infinitely many values associated with measurements.
Answers
Answer:
Continuous
A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions.
A store finds that the number of shirts sold increases each week. In the first week, only 15 shirts were sold. In the next week, 22 shirts were sold and in the third week 29 shirts were sold. The number of shirts sold each week represents an arithmetic sequence.
What is the explicit rule for the arithmetic sequence that defines the number of shirts sold in week n?
Answers
The explicit rule for the arithmetic sequence is a(n) = 7n + 8 if the arithmetic series is 15, 22, 29,...
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
In the first week, only 15 shirts were sold. In the next week, 22 shirts were sold and in the third week, 29 shirts were sold.
15, 22, 29,...
The first term a = 15
The common difference d = 22 - 15 = 7
a(n) = 15 + (n - 1)7
a(n) = 7n + 8
Thus, the explicit rule for the arithmetic sequence is a(n) = 7n + 8 if the arithmetic series is 15, 22, 29,...
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What value of k makes the equation true? (5a^2b^3)(6a^kb)=30a^6b^4
Answers
The value of K will be equal to 4 for an expression (5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
We have an expression given as:-
(5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.
The mathematical properties we knew
[tex]x^mx^n = x^{m+n}[/tex]
[tex]x^m[/tex]÷[tex]x^n=x^{m-n}[/tex]
So the expressions will be written as:-
(5. 6 . a². a[tex].^k[/tex] .b³ .b = 30a⁶b⁴.
30 ( [tex]a^{2+k}[/tex])([tex]b^{3+1}[/tex]) = 30a⁶b⁴.
Comparing the terms we will get:-
[tex]a^{2+k}[/tex] = a⁶
2 + k = 6
k = 6 - 4
k = 4
Therefore the value of K will be equal to 4 for an expression (5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.
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Devonte used the change of base formula to approximate log Subscript 8 Baseline 25. Which expression did Devonte use?
Answers
[tex]\frac{log 25}{log 8}[/tex] is the expression Devonte used the change of base formula to approximate log Subscript 8 Baseline 25.
Given that, Devonte used the change of base formula to approximate log Subscript 8 Baseline 25.
We need to determine the expression did Devonte use.
What is the formula of change of base formula?The change of base formula says [tex]log_{a} b=\frac{log_{c}b }{log_{c}a}[/tex]. It means to change the base of a logarithm logb b a, we just use division [tex]\frac{log a}{log b}[/tex] where these logarithms can have any positive number as a base.
Now, log Subscript 8 Baseline 25 [tex]=log_{8}25[/tex]
[tex]=\frac{log_{10}25 }{log_{10}8}=\frac{log 25}{log 8}[/tex]
Therefore, [tex]\frac{log 25}{log 8}[/tex] is the expression Devonte used the change of base formula to approximate log Subscript 8 Baseline 25.
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Answer:
D
Step-by-step explanation:
The mean height of 20 boys and 14 girls is 161 cm. The mean height of 14 girls is 151 cm. Find the sum of the heights of 14 girls.
Answers
Answer: 2114
Step-by-step explanation:
m = sum of the terms / number of terms
151 = a/ 14
14 x 151 = a
2114 = a
Answer:
21.14 m
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
here mean is 151 cm and count = 14 , then
[tex]\frac{sum}{14}[/tex] = 151 ( multiply both sides by 14 to clear the fraction )
sum = 14 × 151 cm = 2114 cm = 2114 cm ÷ 100 = 21.14 m
To solve the equation -2x²-x+1=0 using the quadratic formula, what would be the value of b?
0
-2
-1
1
Answers
Answer: -1
Step-by-step explanation:
The value of b is the coefficient of x.
Find the midpoint of the segment with the following endpoints. (9, 8) and (3, 2)
Answers
Answer:
yoooo how you guys doing?
express x^2 +4x-7 in the form (x+a)^2 -b where a and b are integers
Answers
[tex]x^2+4x-7=x^2+4x+4-11=(x+2)^2-11[/tex]
Yo! Solving linear equations with integers! These are just some practice exercises I need help with! So they should probably be simple, I need these done asap, I’d appreciate work shown C:
1) - 4 + 3x = 4 x - 8
2) -5x - 8 = 2
3) 12 r - 14 = 5 ( 2 - r )
4) 3 x - 8 = - ( 17 + 2x)
Ty!
Answers
Answer:
Step-by-step explanation:
Solving linear equation with one variable:1) -4 + 3x = 4x - 8
Add 4 to both sides
-4 + 3x + 4 = 4x - 8 + 4
3x = 4x - 4
Subtract 4x from both sides,
3x - 4x = -4x + 4x - 4
-x = -4
[tex]\sf \boxed{\bf x = 4}[/tex]
2) -5x - 8 = 2
Add 8 to both sides
-5x - 8 + 8 = 2 + 8
-5x = 10
Divide both sides by (-5)
[tex]\sf \dfrac{-5}{-5}x =\dfrac{10}{-5}[/tex]
[tex]\sf \boxed{\bf x = -2}[/tex]
3) 12r - 14 = 5(2-r)
12r - 14 = 5*2 - 5*r
12r - 14 = 10 - 5r
Add 14 to both sides
12r - 14 + 14 = 10 - 5r + 14
12r = 24 - 5r
Add 5r to both sides
12r + 5r = 24
17r = 24
Divide both sides by 17
r = 24/17
4) 3x - 8 = -(17 + 2x)
3x - 8 = -17 - 2x
Add 8 to both sides
3x - 8 + 8 = -17 - 2x + 8
3x = -9 - 2x
Add 2x to both sides
3x + 2x = -9
5x = -9
Divide both sides by 5
[tex]\sf \dfrac{5}{5}x=\dfrac{-9}{5}\\\\\boxed{x = \dfrac{-9}{5}}[/tex]
Answer:
1) x = 4
2) x = -2
3) [tex]r= \frac{24}{7}[/tex] [tex](1\frac{7}{17})[/tex]
4) [tex]x=-\frac{9}{5}[/tex] [tex](-1\frac{4}{5})[/tex]
Step-by-step explanation:
hope this helps!!
(work shown in photo :) )
What is 10 1/2÷214 ?
Answers
Answer:
21/428 or 0.04 906542056074...
Step-by-step explanation:
f(x) = 2x2 + 3x + 5,
Answers
Answer:
...
Step-by-step explanation:
your favorite basketball player has an 90% free-throw percentage. In the next game that s/he plays they shoot 12 free throws. What is the probability that they make all 12
Answers
The probability that favourite basketball player make all 12 is 0.
Give 90% free- throw percentage of favourite basketball player and he has taken 12 shots in the game.
Probability is the chance of happening an event among all the events possible. It lies between 0 and 1.
This is a binomial probability question "makes" is what some writer call a "success". In the binomial probability distribution, the probability of r successes in trials is :
=[tex]nC^{r}[/tex][tex]p_{r}p^{r}(1-p)^{n-r}[/tex]
p is the probability of "success" n p r=n!/((n-r)!
n [tex]p_{n}[/tex]=0
In this problem , n=12, r=12,p=0.9. the probability of exactly 12 made shots out of 12 attempted is 12[tex]C_{12} (0.90)^{12} (1-0.90)^{0}[/tex].
=12!/12!(12-12)!*[tex](0.90)^{12}(0.10)^{0}[/tex]
=0
Hence the probability that they make all 12 is 0.
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e) If the cheetah made a round-trip and took half the amount of time on the return trip as on the front end of the trip, what would be the relationship between the average rates on each leg of the trip? Using a complete sentence, explain how you arrived at this conclusion.
Answers
The relationship between the average rates is that ; The average rate of return trip is twice the average rate of front trip.
How to determine algebra relationship?From the complete question seen online, we can say that;
Time taken on front trip = t
Time taken on return trip = 1/2 × t = t/2
Relationship between speed(Rate) and time is;
Rate ∝ 1/time
This means that Rate is inversely proportional to time.
Thus, for the front trip, the rate is; r = 1/t
For return trip, the rate is; R = 1/(t÷2)
R = 1 × 2/t
R = 2/t
Rate of front trip = 1/t
Rate of return trip = 2/t
Thus, we can say that the average rate of return trip is twice the average rate of front trip.
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i need this answer a.s.a.p!!!
Answers
Answer:
Should have ended with "at most -15, not "at least -15."
Step-by-step explanation:
[tex]\leq[/tex] -15 means less than or equal to -15
So it can be -15, but also anything less than -15. The phrase "at most -15, not "at least -15" says exactly that.
Please help me with this question
I tried to use the law of cosine but the numbers I get are in decimal places and are too small for the angles.
Answers
Answer:
y = √119 ≈ 10.909θ ≈ 65.376°α ≈ 24.624°sin(θ) = (√119)/12 ≈ 0.909059cos(θ) = 5/12 ≈ 0.416667tan(θ) = (√119)/5 ≈ 2.181742csc(θ) = (12√119)/119 ≈ 1.100038sec(θ) = 2.4cot(θ) = (5√119)/119 ≈ 0.458349Step-by-step explanation:
You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.
The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Find yThe Pythagorean theorem relates the measures of the sides. It tells you ...
y² +5² = 12²
y = √(144 -25) = √119
Find anglesThe trig relations above tell you ...
sin(α) = 5/12 ⇒ α = arcsin(5/12) ≈ 24.624°
cos(θ) = 5/12 ⇒ θ = arccos(5/12) ≈ 65.376°
Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.
Find trig functionsUsing the definitions above for the trig functions, you have ...
sin(θ) = y/12 = (√119)/12
cos(θ) = 5/12
tan(θ) = y/5 = (√119)/5
Using trig identities, you have ...
csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119
sec(θ) = 1/cos(θ) = 12/5 = 2.4
cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119
_____
Additional comment
The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.
We have shown both exact values and decimal values you can round to the desired precision.
A sample has a sample proportion of 0.3 . Which sample size will produce the
widest 95% confidence interval when estimating the population parameter?
Answers
Answer: A 100
I did the text the other day
A sample size of 50 will produce the widest 95% confidence interval when estimating the population parameter.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To produce the widest confidence interval, we need to choose the smallest sample size.
This is because as the sample size decreases, the margin of error increases, leading to a wider confidence interval.
Among the given options, the smallest sample size is 50.
Therefore, selecting a sample size of 50 will produce the widest 95% confidence interval when estimating the population parameter.
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Rashaad leans a 16-foot ladder against a wall so that it forms an angle of 66° with the
ground. What's the horizontal distance between the base of the ladder and the wall?
Round your answer to the nearest tenth of a foot if necessary.
Answers
Trigonometry: Rounded to the nearest tenth of a foot, the answer is 15.2 feet.
What is trigonometry?Trigonometry is a branch of mathematics that studies the relationships between side lengths and angles of triangles. It is used to calculate unknown side lengths and angles of triangles when given other values, and to solve various problems in different fields such as engineering, navigation, astronomy, and physics.
The horizontal distance between the base of the ladder and the wall can be calculated using trigonometry.
The formula for finding the opposite side of a triangle (in this case, the horizontal distance) when given the angle and the adjacent side is: opposite side = adjacent side x tan (angle)
Therefore, the horizontal distance is 16 feet x tan(66°) = 15.2 feet.
Rounded to the nearest tenth of a foot, the answer is 15.2 feet.
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PLEASE HELP ASAP!!!!!
Which equation is the polar equivalent to the equation y=−3√x?
A. 0= pi/6
B. 0=pi/3
C. 0=2pi/3
D. 0=5pi/6
Answers
The value of θ = pi /3 , Option B is the correct answer.
What is an Equation ?A statement in mathematics used to correlate two algebraic expressions by using an equal sign is called an Equation.
x = rcosθ
y = rsinθ
The equation given is
[tex]y = -\sqrt{3} \;x[/tex]
rsinθ = - [tex]\sqrt{3}[/tex] [tex]\rm {r \; cos\; \theta}[/tex]
sin θ / cos θ = - [tex]\sqrt{3}[/tex]
tan θ = -[tex]\sqrt{3}[/tex]
θ = pi /3
Therefore Option B is the correct answer.
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If = 12 –3 a,find the value ofxwhen a= 8
Answers
Answer:
-12
Step-by-step explanation:
x = 12-3a
When a=8:
x = 12-3(8)
x = 12 - 24
x = -12
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
-3x+3y=9
2x-7y=-14
Alse please don't take long
Choices are attached
Answers
Answer:
[tex]\sf C) \ x = -1\dfrac{2}{5} , \ y = \ 1\dfrac{3}{5}[/tex]
Given equations:
a) -3x + 3y = 9b) 2x - 7y = -14Make x the subject in equation 1:
-3x + 3y = 9-3x = 9 - 3yx = y - 3Substitute this into equation 2:
2(y - 3) - 7y = -14
2y - 7y = -14 + 6
-5y = -8
y = -8/-5
y = 1.6
Then x = y - 3
= 1.6 - 3
= -1.4
Solution: (x, y) ⇒ (-1.4, 1.6)
Which inequality represents all the solutions of
9(4x-8) < 4(6x + 9)?
Answers
Answer:
x < 9
Step-by-step explanation:
Our original inequality:
[tex]9(4x-8) < 4(6x+9)[/tex]
Firstly, let's expand the brackets on both sides:
[tex]36x - 72 < 24x + 36[/tex]
Now, we add the 72 over to isolate the [tex]x[/tex]:
[tex]36x < 24x + 108[/tex]
Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:
[tex]12x < 108[/tex]
Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:
[tex]x < 9[/tex]
This means our final answer is [tex]x < 9[/tex].
What is the measure of arc BEC in circle D?
134°
150°
209°
210°
Answers
The measure of arc BEC is 134°. The correct option is the first option 134°
Circle GeometryFrom the question, we are to determine the measure of arc BEC
In the given diagram,
Measure of angle C = 1/2 (measure of arc AB)
Reason: The measure of an inscribed angle is half the measure of the intercepted arc
∴ Measure of angle C = 1/2 (76°)
Measure of angle C = 38°
m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)
m∠A + 75° + 38° = 180°
m∠A + 113° = 180°
m∠A = 180° - 113°
m∠A = 67°
Measure of arc BEC = 2 × m∠A (Angle at the center is twice the angle at the circumference)
Measure of arc BEC = 2 × 67°
Measure of arc BEC = 134°
Hence, the measure of arc BEC is 134°. The correct option is the first option 134°
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what is the polar form of -3+ v3i?
Answers
So
[tex]\\ \rm\Rrightarrow r=\sqrt{a^2+b^2}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{(-3)^2+(\sqrt{3})^2}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{9+3}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{12}[/tex]
[tex]\\ \rm\Rrightarrow r=2\sqrt{3}[/tex]
Find theta
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{y}{x})[/tex]
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{\sqrt{3}}{3})[/tex]
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{-1}{\sqrt{3}})[/tex]
[tex]\\ \rm\Rrightarrow \theta=\dfrac{5\pi}{6}[/tex]
Polar form
[tex]\\ \rm\Rrightarrow r(cos\theta+isin\theta)[/tex]
[tex]\\ \rm\Rrightarrow 2\sqrt{3}(cos\dfrac{5\pi}{6}+isin\dfrac{5\pi}{6})[/tex]
What is the value of 3 x squared minus 5 x y + 5 y squared for x = negative 6 and y = 2?
-68
-4
188
208
Answers
Answer: 188
Step-by-step explanation: If you plug in all the values, you get 188.
So, 3(-6){squared} - 5(-6)(2) + 5(2){squared)
3(36)+60+20
3(36)+80
108 + 80 = 188
I hope this helps!
Answer:
188
Step-by-step explanation:
3x² - 5xy + 5y² for x = -6 and y = 2
3(-6)² - 5(-6)(2) + 5(2)² =
= 3(36) + 60 + 5(4)
= 108 + 60 + 20
= 188
find the surface area of the composite figure
Answers
The total area of the given composite figure is 84.8 ft²
How to find the area of a composite figure?We are given;
Area of Triangle = 5.6 ft²
Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²
Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)
Area of rectangles = 14.4 + 16 + 43.2
Area of rectangles = 73.6 ft²
Total area of composite figure = 73.6 ft² + 11.2 ft²
Total area of composite figure = 84.8 ft²
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Wich seires of transformations will not map figure L onto itself
Answers
Answer:
cheesefnekeeorknfdndndndn
Find ZABC
00
A
38⁰
32⁰
Answers
Answer:
The answer will be 38° + 32° = 70°
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The velocity of a particle can be modeled by the function v(t)=1/10(3t-8)^3+2. Which graph accurately shows the velocity of the park or at any time, t?
Answers
The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.
How to draw a function Graph?Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.
Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.
The velocity of a particle is modeled by the function;
v(t) = ¹/₁₀(3t - 8)³ + 2
The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.
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