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Answer:
(x/y)^(m+n)
Step-by-step explanation:
[tex]\displaystyle\frac{\left(x+\frac{1}{y}\right)^m\left(x-\frac{1}{y}\right)^n}{\left(y+\frac{1}{x}\right)^m\left(y-\frac{1}{x}\right)^n}=\left(\frac{x}{y}\right)^m\left(\frac{x}{y}\right)^n\\\\=\boxed{\left(\frac{x}{y}\right)^{m+n}}[/tex]
If Bobby drinks 5 waters in 10 hours how many does he drink in 1 hour ?
Water drunk by Bobby in 10 hours = 5 units
So, water drink by Bobby in 1 hour
= 5/10 units
= 1/2 units
= 0.5 units
Answer:
1/2 water
Step-by-step explanation:
We can use a ratio to solve
5 waters x waters
----------- = ------------
10 hours 1 hours
Using cross products
5*1 = 10 *x
5 = 10x
Divide by 10
5/10 = x
1/2 waters =x
Which of the following theorems verifies that AABC - ASTU?
A. AA
B. HL
C. HA
D. LL
Answer:
AA
Step-by-step explanation:
See In Triangle ABC and Triangle STU
[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]
Hence
[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]
By AA similarity triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
In the given triangle ABC, ∠C=180°-90°-31°
∠C=59°
In the given triangle SUT, ∠U=180°-90°-31°
∠U=59°
Here, ∠B=∠T (Given)
∠C=∠U (Obtained using angle sum property of a triangle)
So, by AA similarity ΔABC is similar to ΔSUT.
Therefore, option A is the correct answer.
To learn more about the similar triangles visit:
https://brainly.com/question/25882965.
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After leaving an airport, a plane flies for 2 hours on a course of 60 degrees at a speed of 200 kilometers per hour. The plane then flies for 3 hours on a course of 210 degrees at a speed of 100 kilometers per hour What is the distance of the airport from the plane in kilometers? Round to the nearest tenth
Answer: 205.3
I suppose all measures of angles are done from the same axis (for example x-axis)
Step-by-step explanation:
You just have to use the theorem of Al'Kashi:
[tex]d^2=400^2+300^2-2*300*400*cos(30^o)\\\\d\approx{205.3(km)}[/tex]
Suppose that 22 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
cents
Х
?
Answer:
51 cents for 17 inches of wire
Step-by-step explanation:
22 = 66
17 = x
22x = 66 * 17
22x = 1122
x = 51 cents
or
22 inches costs 66 cents
1 inch costs 3 cents (66 / 22 = 3 cents)
17 inches costs 51 cents (17 * 3 = 51 cents)
Given f(x) = 4x - 3 and g(x) = 9x + 2, solve for (f + g)(x).
[tex]\\ \sf\longmapsto (f+g)(x)[/tex]
[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]
[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]
[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]
[tex]\\ \sf\longmapsto 13x-1[/tex]
Answer:
13x - 1
Step-by-step explanation:
f(x) + g(x) = 4x - 3 + 9x + 2
f(x) + g(x) = 4x+9x + 2 - 3
f(x) + g(x) = 13x - 1
a) __m=10km 25m =___km
b) __m=__km__m=1.5 km
Example :
a) 7250m= 7km 250m = 7.250km
Please help me
Answer:
a) 10,025 m = 10km 25m = 10.025 km
b) 1,500 m = 1 km 500 m = 1.5 km
Answer:
a) 10025m = 10km 25m = 10.025km
b) 1500m = 1km 500m = 1.5km
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion.
Unit conversion is the conversion between different units of measurement for the same quantity.
1 km = 1000 m
Solve:
a)
10km 25m = 10×1000 + 25 = 10025 m10km 25m = 10 + 25/1000 = 10.025 kmb)
1.5km = 1 + 0.5 × 1000 = 1km 500m1.5km = 1.5 × 1000 = 1500mHope this helps!! :)
Please let me know if you have any questions
A lottery ticket has a grand prize of $41.7 million. The probability of winning the grand prize is .000000023. Determine the expected value of the lottery ticket. (Round your answer to 3 decimal places.) Expected value
Answer:
000023 because if we take three 0's we can get 000023 and 417 million
A sample of 50 elements from a population with a standard deviation of 20 is selected. The sample mean is 150. The 90% confidence interval for is: a.165.0 to 185.0. b.146.4 to 153.6. c.145.3 to 154.7. d.171.8 to 188.2.
Answer:
c.145.3 to 154.7.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.
The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.
Thus the correct answer is given by option c.
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Chapter 11 part 4:
Of the three functions {f(x), g(x), h(x))} featured on the graph below (on the following page), rank the functions in order of greatest rate of growth to least.
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Answer:
g, h, f
Step-by-step explanation:
A graph of two exponential curves will have the one with the least growth rate crossing under the one with the greater growth rate. Here, f(x) is shown crossing under g(x) and is on its way to a point of intersection with h(x). So, f(x) has the least growth rate.
g(x) and h(x) start out at about the same level, but g(x) curves upward faster, indicating it has the higher growth rate.
In order from greatest to least growth rate, the functions are ...
g(x), h(x), f(x)
How many square inches of sheet metal are used to make the vent transition shown? (The ends are open.)
Answer:
Area of the metal sheet required = 364 square inches
Step-by-step explanation:
Area of the metal sheet required = Surface area of the lateral sides of the vent transition
Since, lateral sides of the vent is in the shape of a trapezoid,
Therefore, surface area of the vent = 4(Surface area of one lateral side)
= [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]
Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.
Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]
= 364 square inches
Therefore, area of the metal sheet required = 364 square inches
What is the product?
(-2a² + s) (5a^2 - 6s)
Answer:
10a²+17a²s-6s²
Step-by-step explanation:
(-2a²+s)(5a²-6s)
= -10a²+12a²s+5a²s-6s²
= -10a²+17a²s-6s²
Answer:
b
Step-by-step explanation:
The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)∀x ∃y(x+y≥0)
The domain of a set is the possible input values the set can take.
It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers
Given that: ∀x ∃y(x+y≥0)
Considering x+y ≥ 0, it means that the values of x + y are at least 0.
Make y the subject in x+y ≥ 0
So, we have:
[tex]\mathbf{y \le -x}[/tex]
There is no restriction as to the possible values of x.
This means that x can take any real number.
Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.
Read more about domain at:
https://brainly.com/question/15110684
1
) Solve the equation
(85) for n.
8n
n =
?
Answer:
n = -10
Step-by-step explanation:
1 / 8^n = 8^5^2
We know that 1/a^b = a^-b
We also know that a^b^c = a^(b*c)
8^-n = 8^(5*2)
8^-n = 8^(10)
Since the bases are the same, the exponents are the same
-n = 10
n = -10
Basketball A basketball player makes 8 of 12 free throws
in the first game of the season. If she shoots with the same
accuracy in the second game, how many of the 15 free
throws she attempts will she make?
At which values of x does the function Fx) have a vertical asymptote? Check
all that apply.
F(x) =
2/3x(x - 1)(x + 5)
I A. -1
B. 2
C. 1
D. -5
E. 0
F. 3
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Answer:
C, D, E
Step-by-step explanation:
Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...
x = 0 ⇒ x = 0 . . . . . . choice E
x -1 = 0 ⇒ x = 1 . . . . . choice C
x +5 = 0 ⇒ x = -5 . . . choice D
If (3a+4b)=16 and ab=4, find the value of (9a^2+16b^2).
Answer:
160
Step-by-step explanation:
(3a+4b) = 16
ab = 4
Square (3a+4b)
(3a+4b)(3a+4b) = 16^2
9a^2 + 12ab+12ab+16b^2 = =256
9a^2 +16b^2 +24ab=256
9a^2 +16b^2 +24ab - 24 ab=256 -24ab
9a^2 +16b^2 =256- 24ab
We know ab = 4
9a^2 +16b^2 =256- 24*4
9a^2 +16b^2 =256- 96
9a^2 +16b^2 =160
Which of the following phrases are expressions?
6-1>L,
-6k = -8,
1/4<3/8,
3 + 5
Answer:
-6k = -8 is an expression
A and C are inequalities
D is arithmetic
nine times a number
Answer:
if we do 9 times a number that will be
9x
Answer:
9x
Step-by-step explanation:
9 times a number (a variable) = 9x
Graph the line.
Y=-1/4x+4
At what rates did she invest?
$1500 invested at___%
$800 invested at ____%
Answer:
4% and 5% respectively
Step-by-step explanation:
Let the intrest rate be x in the first account at x% and (x+1)% in the second account.
ATQ, 100=(x)*1500/100+(x+1)*800/100
x=4.
If a(x + 1) + b(x − 1) − 2 = 0 for all real x, then a =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Answer:
D) 1
Step-by-step explanation:
using the distributive property we have ax+a+bx-b-2=0. because the equation is true for all real x, ax=-bx. this means a-b-2=0 and a=-b. a-b-2=0 becomes a=b+2. then we substitute a for -b and get -b=b+2 which becomes 2b=-2 so b=-1. since a=-b, a=1
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Step-by-step explanation:
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Answer:
B. The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.
Step-by-step explanation:
just did the test
La'Vonn rolled a die 100 times. His results are below. What is the relative frequency for La'Vonn rolling a 3?
Answer:
.15
Step-by-step explanation:
Al gave correct answers to 22 of the 25 questions on the driving test. What percent of the questions did he get correct?
Turner has 6 pounds of pasta. Each time he makes dinner he uses 0.75 pound
of pasta. How many dinners can he make?
Your answer
Answer:
8
Step-by-step explanation:
if you have 6 pounds and you use 0.75 pounds per then you can make 6/0.75 dinners = 8
find the area of right-andled triangled whose sight-angled
making side are 3cm and 4cm
Answer:
3*4=12
Step-by-step explanation:
what is 92 Times 37
Which of the following theorems verifies that abc wxy
Answer:
C. AA
Step-by-step explanation:
Since m<Y = 27°, then m<W = 27°.
We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).
Answer: C. AA
If carpet costs $24.61 per square yard and is available in whole square yards only, find the cost of carpeting the three bedroom floors in the accompanying floor plan.
Answer:
Step-by-step explanation:
The area of each bedroom is the product of its length and width.
Bdrm 1 area = (14 ft)×(14 ft) = 196 ft²
Bdrm 2 area = (11 ft)×(12 ft) = 132 ft²
Bdrm 3 area = (12 ft)×(11 ft) = 132 ft²
Then the total area of carpet needed is ...
196 ft² +132 ft² +132 ft² = 460 ft²
There are 9 ft² in each square yard, so the number of square yards needed is ...
(460 ft²)/(9 ft²/yd²) = 51.11... yd²
Since we can only obtain whole square yards, 52 square yards are needed. The cost of that will be ...
(52 yd²)×($24.61/yd²) = $1279.72
The cost of carpeting for the three bedrooms will be $1279.72.
To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year.
Which type of statistical study is the school conducting?
a) Matched-pair design study
b) Meta-analysis
c) Retrospective observational study
d) Prospective observational study
Answer:
D) Prospective observational study
Step-by-step explanation:
A study which gathers data moving forward is called a prospective study. Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design.
