Answers
Answer:
3
Step-by-step explanation:
Given expression:
[tex]\dfrac{(14^2-13^2)^{\frac{2}{3}}}{(15^2-12^2)^{\frac{1}{4}}}[/tex]
Following the order of operations, carry out the operations inside the parentheses first.
Apply the Difference of Two Square formula [tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
to the operations inside the parentheses in both the numerator and denominator:
[tex]\implies \dfrac{((14+13)(14-13))^{\frac{2}{3}}}{((15+12)(15-12))^{\frac{1}{4}}}[/tex]
Carry out the operations inside the parentheses:
[tex]\implies \dfrac{((27)(1))^{\frac{2}{3}}}{((27)(3))^{\frac{1}{4}}}[/tex]
[tex]\implies \dfrac{(27)^{\frac{2}{3}}}{(81)^{\frac{1}{4}}}[/tex]
Carry out the prime factorization of 27 and 81.
Therefore, rewrite 27 as 3³ and 81 as 3⁴:
[tex]\implies \dfrac{(3^3)^{\frac{2}{3}}}{(3^4)^{\frac{1}{4}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^{(3 \cdot \frac{2}{3})}}{3^{(4 \cdot \frac{1}{4})}}[/tex]
[tex]\implies \dfrac{3^2}{3^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(2-1)}[/tex]
[tex]\implies 3^1[/tex]
[tex]\implies 3[/tex]
Given that,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
Evaluating the problem,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
→ ((196 - 169)^⅔)/((225 - 144)^¼)
→ (27^⅔)/(81^¼)
→ ((3³)^⅔)/((3⁴)^¼)
→ (3²)/3
→ 9/3 = 3
Therefore, the solution is 3.
Related Questions
find the unit price of a six pack of water for $6.90 fill in the amount per bottle of water
Answers
Given:
six pack of water = $6.90
To find:
Unit(one) price of water bottle(Price of one water bottle).
[tex]\frac{6.90}{6}=1.15[/tex]Therefore,
The price of one water bottle is $1.15.
Kaylee drove 160 miles in 5 hours. If she continued at the same rate, how far would she travel in 17 hours?
Answers
The distance covered by Kaylee in 17 hours at the same rate is 544 miles.
According to the question,
We have the following information:
Distance covered by Kaylee = 160 miles
Time taken by Kaylee = 5 hours
We know that the following formula is used to find the speed:
Speed = distance/time
Speed = 160/5 mile/hour
Speed = 32 miles/hour
Now, we have to find the distance when time taken is 17 hours and the speed is the same.
Now, from the formula of speed, we can find the distance:
Distance = speed*time
Distance = 32*17
Distance = 544 miles
Hence, the distance covered by Kaylee in 17 hours is 544 miles.
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Simplify. -(-6w + x - 3y)
Answers
Answer: 6w - x + 3y
Step-by-step explanation:
identify the terms ,coefficients constants in 5c2 + 7d
Answers
Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.
In the given expression:
[tex]5c^2+7d[/tex]There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.
The net of a cone is shown below. What is the surface area of the cone rounded to the nearest tenth of a square inch? Use π = 3.14.A. 125.6 in²B. 1,256.6 in²C. 175.8 in²D. 251.3 in²
Answers
ANSWER
[tex](C)175.8in^2[/tex]EXPLANATION
The surface area of a cone can be found using the formula:
[tex]A=\pi r^2+\pi rl[/tex]where l = slant height
r = radius
The diameter of the cone is given, but we can find the radius since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{8}{2} \\ r=4\text{ units} \end{gathered}[/tex]From the figure, the slant height of the cone is 10 units.
Hence, its surface area is:
[tex]\begin{gathered} A=(\pi\cdot4^2)+(\pi\cdot4\cdot10) \\ A=50.24+125.6 \\ A\approx175.8in^2 \end{gathered}[/tex]The answer is option C.
how do i evaluate 8!4!/7!2!
Answers
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Hello Just Want to make sure my answer is correct
Answers
So,
Let's remember that:
The three point postulate states that:
Through any three noncollinear points, there exists exactly one plane.
The Plane-Point Postulate states that:
A plane contains at least three noncollinear points.
As you can notice, the diagram illustrates that:
Given that a plane exists, then, there are three collinear points.
That's the three point postulate.
Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 milesfrom city B, how far is city A from city B?City Ais 20 miles due east of city B.City A is 35 miles due east of city B.City A is 42 miles due east of city B.City A is 122 miles due east of city B.
Answers
Given:
City A is due east of city B.
City C is located 35° west of north from city B.
Distance between city C and city A is 100 miles.
Distance between city C and city B is 70 miles.
The objective is to find the distance between city A and city B.
The above situation can be represented as,
Thus the total angle of ∠B = 90°+35° = 125°.
Now the measure of angle A can be calculated by law of sines.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{100}{\sin125\degree}=\frac{70}{\sin A} \\ \sin A=70\cdot\frac{\sin 125\degree}{100} \\ \sin A=0.573 \\ A=\sin ^{-1}(0.573) \\ A\approx35\degree \end{gathered}[/tex]By the angle sum property of triangle the value of angle C can be calculated as,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 35\degree+125\degree+\angle C=180\degree \\ \angle C=180\degree-35\degree-125\degree \\ \angle C=20\degree \end{gathered}[/tex]Now, the distance between A and B can be calculated by,
[tex]\begin{gathered} \frac{AB}{\sin C}=\frac{BC}{\sin A} \\ \frac{AB}{\sin20\degree}=\frac{70}{\sin 35\degree} \\ AB=\sin 20\degree\cdot\frac{70}{\sin 35\degree} \\ AB\approx42\text{ miles} \end{gathered}[/tex]Thus, the distance of city A is 42 miles due east of city B.
Hence, option (C) is the correct answer.
Solve. Your answer should be in simplest form. 2/5 (−3/7)
Answers
Answer:
2/5 (-3/7) = -6/35 ≅ -0.1714286
Step-by-step explanation:
and that’s how you do it
Add: 2/5 + 3/7 = 2 · 7/5 · 7 + 3 · 5/7 · 5 = 14/35 + 15/35 = 14 + 15/35 = 29/35.
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 7) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two fifths plus three sevenths is twenty-nine thirty-fifths.
Determine whether the ratios are equivalent.
2:3 and 24:36
O Not equivalent O Not equivalent
Answers
We can conclude that the given ratios 2:3 and 24:36 are equivalent.
What are ratios?A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ratios are equivalent or not:
2:3 and 24:362/3 = 24/362/3 = 2/3 (Divide by 12)Then, 2:3 :: 2:3
Therefore, we can conclude that the given ratios 2:3 and 24:36 are equivalent.
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Describe where the function has a hole and how you found your answer.
Answers
Step 1:
Write the function
[tex]f(x)\text{ = }\frac{x^2+\text{ 7x + 10}}{x^2\text{ + 9x + 20}}\text{ }[/tex]Step 2:
Factorize both the numerator and the denominator.
[tex]\begin{gathered} f(x)\text{ = }\frac{x^2\text{ + 2x + 5x + 10}}{x^2\text{ + 4x + 5x + 20}} \\ f(x)\text{ = }\frac{x(x\text{ + 2) + 5(x + 2)}}{x(x\text{ + 4) + 5 (x + 4)}} \\ f(x)\text{ = }\frac{(x\text{ + 5)(x +2)}}{(x\text{ + 5)(x + 4)}} \end{gathered}[/tex]Step 3:
A hole is a common factor between the numerator and the denominator.
Hole: x + 5 = 0
x = -5
Final answer
Hole is -5
Which of the following is the horizontal asymptote for the graph below?10A x=-7B. X=0ООC. y - 0C D. y = -7
Answers
A horizontal like y = k, where k is not part of the graph, but guides the function for x-values “far” to the right and/or “far” to the left.
The horizontal asymptote can be observed in the figure below:
Answer: y = 0.
The one-to-one function f is defined below.
Answers
The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively
How to determine the inverse function?The definition of the function is given as
f(x) = 6x/7x - 5
Rewrite the function as
y = 6x/7x - 5
Next, we swap or switch the variables x and y
So, we have the following equation
x = 6y/7y - 5
Cross multiply in the above equation
This gives
x(7y - 5) = 6y
Open the brackets
7xy - 5x = 6y
Collect the like terms
7xy -6y = 5x
Factor out y
y(7x -6) = 5x
So, we have
y = 5x/(7x -6)
Express as inverse function
f-1(x) = 5x/(7x -6)
Using a graphing calculator, we have
Domain: x < 6/7 or x > 6/7
Range: f(x) < 5/7 or f(x) > 5/7
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Find the value of z such that 0.03 or f the area lies to the right of z Round your answer tom2 decimal places
Answers
ANSWER
z = 1.88
EXPLANATION
We have to find z such that the area under the normal curve to the right of that value is 0.03,
This is the same as finding z such that the area to the left of that value is 1 minus 0.03,
[tex]1-0.03=0.97[/tex]These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,
The z-score whose area to its left is closest to 0.97 is z = 1.88.
Hence, for z = 1.88, the area under the curve to its right is 0.03.
you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Answers
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]A population of a certain species of bird is 22,000 animals and is decreasing by 700 birds per year..Write an equation for y, the population at time t (in years), representing the situation.y= How many birds are in the population after 7 years?
Answers
We can solve that problem using a linear function, we know that
[tex]y=mx+y_0[/tex]Where y0 is the initial population and m is the rate of decreasing, we know that for each "x" years we have -700 birds, therefore
[tex]y=-700x+22000[/tex]Let's use t instead of x
[tex]y=-700t+22000[/tex]That's the equation that represents the population at time t
[tex]\begin{gathered} y=-700t+22000\text{ \lparen t = 7\rparen} \\ \\ y=-700\cdot(7)+22000 \\ \\ y=-4900+22000 \\ \\ y=17100 \end{gathered}[/tex]Therefore after 7 years, the population will be 17100 birds.
On a recent survey, students were asked if they ice skate, snowboard, or ski. The Venn diagram below shows the results of the survey
Answers
The number of students who took the survey was 47 (option B).
How to identify the number of students who took the survey?To identify the number of students who took the survey, we must look at the number of students in each of the Venn diagram spaces. In this case, the number of students who practice each sport are:
Ice Skate: 7 students.Snowboarding: 10 students.Ski: 13 students.Ice Skate and Snowboard: 4 students.Ski and Snowboard: 8 students.Ice Skate and Ski: 2 students.Ice Skate, Snowboard and Ski: 3 students.To know the number of students who took the survey, we must add the number of students in each space as shown below:
7 + 10 + 13 + 4 + 8 + 2 + 3 = 47According to the above, the correct answer is option B, since 47 students took the survey.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
How many students took the survey?
Options
A.32
b.47
c.53
D.56
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Add the complex numbers 3 + 11i and -3 - 11i.6 + 0i0 + 0i0 + 22i- 9 + 121i
Answers
SOLUTION
The given complex unbers are:
[tex]3+11i,-3-11i[/tex]Add the complex numbers:
[tex]3+11i+(-3-11i)[/tex]Simplify the expression:
[tex]\begin{gathered} 3+11i-3-11i \\ =3-3+11i-11i \\ =0+0i \end{gathered}[/tex]Therefore the required answer is: 0+0i
Given that events A and B are independent with P(A) = 0.08 and P(B) = 0.25,determine the value of P(A and B), rounding to the nearest thousandth, ifnecessary.
Answers
To find: P(AandB)
P(AandB)=P(A)*P(B)
P(AandB)=0.08*0.25
P(AandB)=0.02
Thus the required answer is 0.02
4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6
Answers
To find the value of y
4(y – 4) = 8
Divide both-side of the equation by 4
y - 4 = 2
Add 4 to both-side of the equation
y = 2 + 4
y = 6
D is the correct option
Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Answers
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
Answers
The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]Hi, could you help me figure out why I got 8 points off in this problem?
Answers
In triangle PQR
Construction: Draw PX perpendicular to QR where x lies on QR
Since:
PX perpendicular to QR
In the 2 triangles PXQ and PXR
given
proved up
PX = PX ------- common side in the 2 triangles
Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency
As a result of congruency
PQ = PR ------- proved
In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Answers
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
The statement listed below is false. Let p represent the statement.
Answers
We will have that the negation of the statement would be:
*That product did not emerge as a toy in 1949. [Option B]
With the information given, find the lenght of the prism
Answers
Answer:
The lenght of the prism is 22 cm.
Step-by-step explanation:
From the given drawing, we can conclude that a one-unit line measures 2 cm. Since the prism is 11 unit lines long, we can conclude that it is 22 cm.
Roberts Company has the following sales budget for the first four months and the year:
January February March April
Budgeted units to sell
200
400
800
950
Total - 2,350
Sales price per unit
$25
$25
$25
$25
Total-$25
Total sales
$5,000
$10,000
$20,000
$23,750
Total - $58,750
What is the new amount of budgeted total sales for March if the budgeted number of units is expected to be 1,100 units instead of 800 units?
A. $27,500
B. $10,000
C. $47,500
D. $66,250
Answers
Using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, new amount of budgeted total sales for March:
So, we know that:
2350 × 25 = $58,750And 2350 is further:
2350 = 200 + 400 + 800 + 950.Let's replace 800 with 1100.
Now, solve as follows:
200 + 400 + 1100 + 950 = 2,6502,650 × 25 = $66,250Therefore, using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
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Ishaan started a toy car collection. His grandfather gave him 15 cars to start his collection. He can use his allowance to add 4 cars to his collection every month. Which equation can be used to find y, the total cars in his collection after x months?
Answers
The equation that he can use to find y, the total cars in his collection after x months is y = 15 + 4x.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of months be x.
Let the number of cars be y.
The equation will be:
y = 15 + (4 × x)
y = 15 + 4x
This illustrates the equation.
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Let f(x) = 2x-1 and g(x) = x2 - 1. Find (f o g)(-7).
Answers
Answer: (f o g)(-7) = 95
Step by step solution:
We have the two functions:
[tex]\begin{gathered} f(x)=2x-1 \\ g(x)=x^2-1 \end{gathered}[/tex]We need to find (f o g)(-7) or f(g(-7)), first we evaluate g(-7):
[tex](f\circ g)(-7)=f(g(-7))[/tex][tex]g(-7)=-7^2-1=49-1=48[/tex]Now we evaluate f(48):
[tex]f(48)=2\cdot48-1=96-1=95[/tex]How many solutions does the system formed by x − y = 4 and ay − ax + 4a = 0 have for a nonzero number a? Give your answer and complete the explanation.
Answers
Given system of equations have no solutions that is nonzero.
We have been given the system of equations formed by x − y = 4 and ay - ax + 4a = 0
We need to find the number of non-zero solutions the system have for a nonzero number 'a'
x - y = 4 ............(1)
ay - ax + 4a = 0 ............(2)
From equation (1),
x = 4 + y
Substitute x = 4 + y in equation (2),
ay - a(4 + y) + 4a = 0
ay - 4a - ay + 4a = 0
-4a + 4a = 0
0 = 0
This means that the system have no solutions that is nonzero.
Therefore, given system of equations have no solutions that is nonzero.
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