The value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.
How to find geometric mean?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
For Geometric sequence, the value of geometric mean can be found out using the following formula,
[tex]x=\sqrt{ab}[/tex]
Here, (a and b) are the two terms of geometric sequence.
The geometric mean of a and 12 is 8√6. Thus,
[tex]x=8\sqrt{6}[/tex]
[tex]b=12[/tex]
Put this value in formula to find the value of a,
[tex]8\sqrt{6}=\sqrt{a\times12}\\[/tex]
Square both side of equation,
[tex](8\sqrt{6})^2=(\sqrt{a\times12})^2\\64\times6=12a\\a=\dfrac{64\times6}{12}\\a=32[/tex]
Thus, the value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.
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find (a) pq to the nearest tenth and (b) the coordinates of the midpoint of pq p(2,2) q(-3,-6)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[-3 - 2]^2 + [-6 - 2]^2}\implies PQ=\sqrt{(-5)^2+(-8)^2} \\\\\\ PQ=\sqrt{25+64}\implies PQ=\sqrt{89}\implies \boxed{PQ\approx 9.4}[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -3 + 2}{2}~~~ ,~~~ \cfrac{ -6 + 2}{2} \right)\implies \left(\cfrac{-1}{2}~~,~~\cfrac{-4}{2} \right)\implies \left( -\cfrac{1}{2}~~,~~-2 \right)[/tex]
Find triangle angle A when a=4, b=8, c=6
Answer:
A=28.95502437A=28.95502437B=104.47751218B=104.47751218C=46.56746344C=46.56746344a=4a=4b=8b=8c=6
Find -3A if A=…………….
Answer:
Option A is correct !------- HappY LearninG <3 ------
The inverse of G(x) is a function.
G(
Answer:
False
Step-by-step explanation:
To determine if the inverse of g(x) is a function, we will use the horizontal line test.
A horizontal line will pass through more than one point, so it is not a function
can anyone help me find the area of these two pls ? ty
Heeeeeeeelp
Find the sum of the even numbers from 66 to 152, inclusive.
Answer:
72+30=102
Step-by-step explanation:
0+2=2
7+3=10 so the answer
10
+002
102
14 2/3 yards into feet?
Answer:
44.000000001 (exact) or rounded up 44
Step-by-step explanation:
14.666666667*3 because 1 yard= 3 feet
One yard is 3 feet, which means we will have to mutliple 14 2/3 by 3.
14 x 3 =42
2/3 of a yard is 2 feet, which means we must add 2 to 42--->
42+2= 44
14 2/3 yards is 44 feet.
Hope This Helps <3
Analytically show that the equation below represents trigonometric identity statements for questions 1-4.
help pls and ty :D !!
Try this suggested option, answers are marked with colour.
a farmer bought cylindrical bales of Lucerne at a price of R350/bale for his herd of 1500 dairy cows. iii) iii. Determine the approximate space required to store the bales: If the bale has a diameter of 1.5m and a height of 2.6m.
The approximate space required to store the bales is 4.6 cubic meters if the bale has a diameter of 1.5 m and a height of 2.6 m.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
We know the radius will be half of the diameter:
r = 1.5/2 = 0.75 m
h = 2.6 m
V = π(0.75)²(2.6)
V = 4.59 ≈ 4.6 cubic meters
Thus, the approximate space required to store the bales is 4.6 cubic meters if the bale has a diameter of 1.5 m and a height of 2.6 m.
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Simplify. (1/2k)(4k)+12
14 k
2 k^2+12
14 k^2
2 k+12
Answer:
2k^2+12
Step-by-step explanation:
remove parentheses, simplify calculate
Can someone help me with these
Answer:
29 center (3,-5) radius=2
30 center (0,0) radius=2/3
A family drives 412 miles in 110 of an hour. What is their rate of speed in miles per hour?
Answer:
3.74 mph
Step-by-step explanation:
412÷110=3.74
a 1 Mrs. Erskine spent $40.50 for a pair of shoes, $56.95 for jeans, and $25.75 for a shirt. Which of the following shows two equivalent expressions, using the associative property of addition, that can be used to find the amount Mrs. Erskine spent? A (40.50 + 56.95) + 25.75; 25.75 + (40.50 + 56.95) B 40.50 +(56.95 + 25.75); (40.50+ 56.95) + 25.75 C 40.50 + (56.95 + 25.75); (40.50. 56.95) + (40.50 .25.75) D (40.50 +56.95) + 25.75; (40.50 + 56.95 +25.75) • 1 o
Answer:
A
Step-by-step explanation:
Commutative Property(a + b) + c = c + (a + b)(40.50 + 56.95) + 25.75 ; 25.75 + (40.50 + 56.95) correctly represent the situation using the commutative property.
(square root of -5 +2square root of 20) (-square root of -5). Simplify please
Answer:
I got 5-20
Step-by-step explanation:
does anyone know the square root of 65
Answer:
8.062257748
If you need any other help , please let me know ! [ you'll have to pay ]
If the temperature is 11 degrees and overnight it drops by 20 degrees, what is the new temperature in the morning? Explain how you arrived at your answer.
Answer:
-9 degrees.
Subtract 20 from 11 to get -9.
Use the Venn diagram to calculate probabilities.
Circles A, B, and C overlap. Circle A contains 3, circle B contains 9, and circle C contains 6. The overlap of A and B contains 1, the overlap of B and C contains 4, and the overlap of C and A contains 7. The overlap of the 3 circles contains 6. Number 8 is outside of the circles.
Which probability is correct?
P(A|B) = One-half
P(B|A) = StartFraction 7 Over 20 EndFraction
P(A|C) = StartFraction 6 Over 23 EndFraction
P(C|A) = StartFraction 13 Over 17 EndFraction
Using the probability concept and the Venn diagram described, the correct option is given by:
P(C|A) = 13/17.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
P(A|B) is given by the sum of the values that involve both A and B by the sum of all values that involve B, hence:
D = 1(overlap of A and B) + 6(Overlap of the 3).T = 9 + 1 + 4 + 6 = 20.Hence:
P(A|B) = 7/20.
Following the same logic, we have that:
P(B|A) = (1 + 6)/(3 + 1 + 7 + 6) = 7/17P(A|C) = (7 + 6)/(6 + 4 + 7 + 6) = 13/23P(C|A) = (7 + 6)/ (3 + 1 + 7 + 6) = 13/17.Hence the last option is correct.
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Answer:
the correct answer is 13/17
I got it right on edge 2022
Step-by-step explanation:
how many minutes have it been if the start time is 5:30 p.m. and the end time is 5:49
Answer:
19 minutes.
Step-by-step explanation:
49 - 30
= 19 minutes.
Please I really need help
Answer:
85°
Step-by-step explanation:
The two angles are known as vertical angles, which are always congruent
Answer:
∠DEB = 85°
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Angles AEC and DEB are vertically opposite angles, therefore:
∠AEC = ∠DEB
As ∠AEC = 85° then ∠DEB = 85° also.
a line passes through (1, - 1) and (3,5) what is the equation of the line in slope-intercept form?
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{5 +1}{3 -1}\implies \cfrac{6}{2}\implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \\\\\\ y+1=3x-3\implies y=3x-4[/tex]
(2/3)x+4(y-2)=0 slope intercept form
Question 22: 4 pts Find the probability of rolling a 4 on a number cube and then choosing a red ball at random from a bag of 8 blue and 6 red balls.
Answer:
1/14
Step-by-step explanation:
a four out of possible 6 rolls = 1/6
6 red out of 14 balls 6/14
1/6 * 6/14 = 1/14
The Probability of rolling a 4 on a number cube and then choosing a red a ball at random is 1/14.
What is Probability?Probability is "possibility that deals with the chance of occurrence of random event" .
According to the question,
A cube has 6 faces that is (1,2,3,4,5,6). Total number of faces n(s) = 6.
Probability formula = (Number of favorable event)/(Total number of event).
Probability of taking 4, P(4) = 1/6.
A bag containing 8 blue and 6 red balls. Total number of balls in a bag n(s) = 14.
Probability of taking red balls P(red balls) = 6/14.
In order to find that probability of rolling a 4 on a number cube and then choosing a red a ball at random only if multiply P(4) by P(red balls).
P(4) × P(red balls) = [tex]\frac{1}{6}[/tex] × [tex]\frac{6}{14}[/tex] = [tex]\frac{1}{14}[/tex].
Hence, probability of rolling a 4 on a number cube and then choosing a red a ball at random is 1/14.
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For each set of three measures, determine if they can be angle measures of a triangle.
Angles Can be angle measures of a triangle Cannot be angle measures of a triangle
The sum of the angles in the triangle must be equals to 180 degrees for it to be the angle measure of a triangle.
Angles in a triangle
The sum of angles in a triangle is equals to 180 degrees.
Therefore, adding up the three angles in a triangle must be equals to 180 degrees.
Hence,
42 + 34 + 56 = 132 degrees
This does not form a triangle.
35 + 80 + 65 = 180 degrees
This can be the angle measure of a triangle.
15 + 51 + 24 = 90 degrees
This cannot be the angle measure of a triangle.
18 + 42 + 120 = 180
This can be the angle measure of a triangle.
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i really need help with this
Answer:
The second answer is decreases.
Step-by-step explanation:
As X -value increases, the y-value decreases. If you reply back with the options for the first half of the question I'll do my best to answer that as well
couldddddddddd i have some help super fast?
Answer:
[tex]\textsf{a)} \quad P=-20(x-2)^2+3380[/tex]
b) cost of ticket = $13
max profit = $3380
number of tickets sold = 260
Step-by-step explanation:
Profit equation: [tex]P=20(15-x)(11+x)[/tex]
Part (a)Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and [tex]a[/tex] is some constant)
First, write the given profit equation in standard form [tex]ax^2+bx+c[/tex]:
[tex]\begin{aligned}\implies P&=20(15-x)(11+x)\\& = 20(165+4x-x^2)\\& = -20x^2+80x+3300\end{aligned}[/tex]
Factor -20 from the first two terms:
[tex]\implies P=-20(x^2-4x)+3300[/tex]
Complete the square:
[tex]\implies P=-20(x^2-4x+4)+80+3300[/tex]
[tex]\implies P=-20(x-2)^2+3380[/tex]
Part (b)The vertex of the profit equation is (2, 3380).
Therefore, the cost of the ticket is when x = 2 ⇒ $11 + 2 = $13
The maximum profit is the y-value of the vertex: $3380
The number of tickets sold at this price is:
⇒ max profit ÷ ticket price
= 3380 ÷ 13
= 260
In ΔTUV, u = 330 inches, t = 800 inches and ∠T=53°. Find all possible values of ∠U, to the nearest degree.
Answer: 19
Step-by-step explanation:
What is the value of the expression below when f = 2.5
8 + 4f
A. 132
B. 18
C. 42
D. 28
Answer:
x = 48
Step-by-step explanation:
(x - 6)⁰ + ( 2x + 42)⁰ = 180⁰
x - 6⁰ + 2x + 42⁰ = 180⁰
x + 2x - 6⁰ + 42⁰ = 180⁰
3x + 36⁰ = 180⁰
3x + 36⁰ - 36⁰ = 180⁰ - 36⁰
3x = 144⁰
3x / 3 = 144⁰ / 3
x = 48
Hope this helps, thank you :) !!
Jill was looking at a picture of herself and 3 friends. She measured the height of her image as 10 centimeters. If Jill is actually 60 inches tall, which equation can she use to find h, the actual height in inches, of one of her friends who is c centimeters tall in the picture?
The actual height in inches,will be [tex]\dfrac{1}{6} c[/tex] of one of her friends who is c centimeters tall in the picture
What is hieght?Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position.
lets call the height x :
[tex]\dfrac{10}{60} = \dfrac{h}{x}[/tex]
[tex]x = \dfrac{1}{6} h[/tex]
Hence the actual height in inches,will be [tex]\dfrac{1}{6} c[/tex] of one of her friends who is c centimeters tall in the picture.
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In 1900 Kansas City had a population of 163,000In 2020 it has a population of 1,686,000Show me exponential growthHow many years after 1900Did it take for the population to double
The exponential growth is 1.95% and after 35.72 years the population will double.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where a is a constant and a>1
Let's suppose the exponential growth function is:
[tex]\rm y = Ae^{rt}[/tex]
A = 163,000
y = 1,686,000
t = 2020 – 1900 = 120 years
Plug all the values in the function:
[tex]\rm 1686000 = 163000e^{120r}[/tex]
[tex]\rm e^{120r} = 10.343[/tex]
Taking ln both side and solving:
r = 0.0194
r = 1.946 ≈ 1.95%
[tex]\rm 2A = Ae^{0.0194t}[/tex] (the population to double)
After solving:
t = 35.72 years
Thus, the exponential growth is 1.95% and after 35.72 years the population will double.
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