Answers
[tex]a - 4 = ( \sqrt{a} - 2)( \sqrt{a} + 2)[/tex]
[tex] \frac{ \sqrt{a} - 2}{a - 4} = \frac{ \sqrt{a} - 2}{( \sqrt{a} - 2)( \sqrt{a} + 2) } = \frac{1}{ \sqrt{a} + 2 } [/tex]
Related Questions
Alejandro kicks a football. The graph below shows the height of the football hh in meters after tt seconds. What is the football’s greatest height?
Answers
Answer:
The answer will be 30.625 m
The graphs below have the same shape. The equation of the blue graph is F(x) = x^3. What is the equation of the red graph?
Answers
Answer:
g(x) = x³ - 2
(option B)
Step-by-step explanation:
because the shape of the graph has not changed, we know that there was no direct change to x
(this would have looked like 2x³ instead of x³)
and because the graph was not shifted along the x-axis (left or right), we know that the change did not happen inside the parenthesis
(this would have looked like (x³ - 3) instead of (x³) )
we know that the only change that has happened to this graph was a downward shift along the y-axis which can be expressed as
g(x) = x³ - 2
The equation of the red graph will be g(x) = x³ - 2.Option B is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
We know that there was no immediate change to x since the graph's form has not altered. Instead of x³, this would have appeared as 2x³.
Thus we can be confident that the change did not occur inside the parenthesis since the graph was not moved down the x-axis.
We may infer that this graph's sole modification was a downward shift along the y-axis, which is written as;
g(x) = x³ - 2
The graph is also attached in the attachment.
The equation of the red graph will be g(x) = x³ - 2.
Hence option B is correct.
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About 10% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. Round your answer to two decimal places.
Answers
Answer:
The standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.
Step-by-step explanation:
Standard deviation: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
The given parameters are:
Proportion, p = 10%
Sample size, n = 1000
The standard deviation is calculated as:
σ=[tex]\sqrt{np(1-p}[/tex]
So, we have:
σ=[tex]\sqrt{1000*10%*(1-10%)}[/tex]*(1-10%)
Evaluate:
σ= 9.49
Hence, the standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.
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Please answer this question i really want answers :(
Answers
Step-by-step explanation:
[tex] \sqrt{10} = 3.2 \\ then \: the \: sign \: there \: is \: = \\ \sqrt{10 } = 3.2 \\ \\ \: \sqrt{12} = 3.5 \\then \: the \: sign \: there \: is \: = \\ \: \sqrt{12} = 3.5 \\ \\ 6 \frac{1}{3} = 6.3 \: and \: \sqrt{40 } = 6.3 \\ therefore \: 6 \frac{1}{3} = \sqrt{40} \\ \\ 2 \frac{2}{5} = 2.4 \: and \: \sqrt{5.76} = 2.4 \\ then \: \: 2 \frac{2}{5} = \sqrt{5.76} \\ \\ 5 \frac{1}{6} = 5.16 \: and \: 516 \: \: therefore \: \\ 5 \frac{1}{6} = 5.16 \\ \\ \sqrt{6.2} = 2.5 \\ and \: 2.4 \: therefore \: \\ \sqrt{6.2} > 2.4[/tex]
Work out the bearing of D from C.
(Hint: bearings are written with three digits.)
Answers
Answer:
050°
Step-by-step explanation:
The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.
From the diagram, the angle is 050°
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Answers
Using translation concepts, the sequence that is used to obtain the translated image is:
Reflection over the y-axis.Shift right of one unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For all the vertices, the transformations follow the given pattern:
(x,y) -> (-x,y) -> (-x + 1, y).In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) -> (-x + 1, y), the function is shifted right one unit.
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If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The corresponding sides of the triangles are congruent. B. The triangles have the same shape and size. C. The corresponding angles of the triangles are congruent. D. The triangles have the same shape, but not the same size. If two triangles are congruent , which of the following statements must be true ? Check all that apply . A. The corresponding sides of the triangles are congruent . B. The triangles have the same shape and size . C. The corresponding angles of the triangles are congruent . D. The triangles have the same shape , but not the same size.
Answers
Answer:
Step-by-step explanation:
A. Correct
B. Correct
C. Correct
D. False
2.
A. Correct
B. Correct
C. Correct
D. False
Hope I helped!
Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing? State your answer as a reduced fraction. Find an equation of a line in the form y = mx + b that describes the amount of gas in your tank.
Answers
The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.
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.
Given that:-
Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank.The rate of gas will be calculated as:-
Suppose the hours are represented by x and the gallons are represented by y.
The rate of the gas will be the slope so the slope will be calculated as:-
[tex]m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \dfrac{2-20}{3-0}[/tex]
[tex]m =\dfrac{-18}{3}[/tex]
m = -6
The equation will be given as:-
y = mx + c
y = -6x + 20
Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.
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find the value of x? thanks
Answers
Answer:
x=1
Step-by-step explanation:
20(3x-3/5) = 20(2x-2/4)
12x-12= 10x-10
12x-10x =12-10
x= 1
Answer:
Step-by-step explanation:
Solution
3x - 3 2x - 2
===== = ====== Cross Multiply
5 4
4(3x - 3) = 5(2x - 2) Remove the brackets. Distributive Property
12x - 12 = 10x - 10 Subtract 10 x from both sides
12x-10x - 12 = 10x-10x - 10 Combine
2x - 12 = - 10 Add 12 to both sides
2x-12+12 = -10 + 12 Combine
2x = 2 Divide by 2
2x/2 = 2/2
Answer
x = 1
Can someone help me? I’ll give brainliest to whoever gets it right first
Answers
Answer:
the measure of line AD is 8
Step-by-step explanation:
lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8
Simplify this equation 10 ^-8
Answers
———
10^8
1
—
100000000
Consider the function shown on the graph.
Answers
Answer:
C.) y = 3(x - 3)(x - 7)
For the function:
x intercept: (3, 0), (7, 0)vertex point: (5, -12)point: (8, 15)Writing equation:
y = a(x - h)² + k
15 = a(8 - 5)² - 12
15 = 9a - 12
9a = 15 + 12
9a = 27
a = 3
So the equation is:
y = 3(x - 5)² - 12
y = 3(x² - 10x + 25) - 12
y = 3x² - 30x + 63
y = 3(x - 3)(x - 7)
Please help me
14.7 ÷ 4.2
Answers
Answer:
how many times does 4.2 go into 14.7
1. 4.2
2. 8.4
3. 12.6
14.7-12.6=2.1 or one half of 4.2
3.5
Hope This Helps!!!
Find the radius of this sphere The calculate the volume of the sphere?
Answers
Answer: r = 121.92 cm
Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]
7587404.65
Step-by-step explanation:
The radius is given. It's the distance from the center of the sphere to the end. The radius is 4 ft. 1 ft is 30.48cm so 4ft is 121.92cm
(radius) r = 121.92 cm
Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]
= 4/3 x 3.14 x 1812278.18
= 4/3 x 5690553.49
= 7587404.65
Translate to an equation then solve the equation. Seven times the difference of some number and 2 amounts to the quotient of 196 and 14. (Type the question using x as the variable. Do not simplify.) x= ____
Answers
Answer:
x = 4
Step-by-step explanation:
7 * ( x-2) = 196/14
7x -14 = 14
7x = 28
x = 4
its about efficiency in systems
Answers
.......................
Please answer all four of the questions I would really appreciate it <3
Answers
B
A
C
These are the answers in order.
Answer:
1)A because 3 < 3.9 < 4
2)C because 8.2<8.23<8.3
3) D because 6.1>5.9
4)B because 3.6<3.625<3.7
Hope it helps!
Which of the following best describes the graph below?
Answers
The correct option is option D: This is the graph of one to one function.
Function is a relationship between two sets X and Y where set X is domain and set Y is codomain.
If we draw a vertical line and it crosses the graph only once at all locations, the relation is a function and this relation will be one-one.
by checking all the options
Option A: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So it is a function with one-one relation. Therefore option A is incorrect.
Option B: Linear function is a function in which highest degree of variable is 1 and it also describes the straight line. From the graph, it is clear that it is not a straight line. Therefore option B is incorrect.
Option C: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a function. Therefore option C is incorrect.
Option D: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a one-one function. Therefore option D is correct.
The correct option is option D: This is the graph of one-to-one function.
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A building casts a shadow of 40 feet on the ground. A wooden figure of a man is placed on the building and casts a shadow an additional 10 feet beyond the building's shadow. What is the height of the man?\
Answers
The height of the man from the given question is; 37.5 ft
How to solve trigonometric ratios?This question will form a triangle where;
Height of building = 30 ft
Height of man = h ft
Initial height of shadow = 40 ft
Additional height of shadow = 10 ft
Using similarity theorem, we have;
h/30 = (40 + 10)/40
h/30 = 5/4
h = (30 * 5)/4
h = 37.5 ft
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What is the volume of a regular pyramid having a base area of 24 inches and height of 6 inches
Answers
Answer:
V= 48 in^2
Step-by-step explanation:
Formula
Since the base has a known area, we do not need the full volume formula. This formula is
V = B * h / 3
B is the area of the base and h is the height measured from the top of the pyramid to the base meeting the base at right angles.
Givens
B = 24 in^2
h = 6 in
Solution
V = B * h / 3
V = 24 * 6/3
V= 48 in^2
A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. What is the expected value of the game?
Answers
The expected value of the game is $2.00.
To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side
Now the question arises how to find the Fair Price
We are told that in the game of rolling the colored die;
A roll of a red loses.
A roll of blue pays 5.00 and A roll of green pays 2.00.
Now, the best game to get the fairest price is to play; RRRGGB i.e (RED, RED, RED, GREEN, GREEN,BLUE)
Fair price = 2(3/6) + 6(1/6) + 0(2/6)
Fair price = $2
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fy= 2x² + 2x + 1
y = 2x + 3
What is the solution to this system of equations?
o (-1, 3) and (0,4)
o (0, 1) and (1,5)
○ (0, 1) only
o (-1, 1) and (1, 5)
Answers
The answer is (-1,1) and (1,5)
The graphs below have the same shapes. What is the equation for the red graph? g(x)= A g(x) = 2^x + 5 B 2^x - 5 C. g{x} = 2^x+5 D G(x) = 2^x-5
Answers
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
Answers
The best buy is a 9 oz box of rice $1.25. (option d)
What is the best buy?In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.
Unit cost = total cost / total oz
$0.90 / 6 = $0.15
$1.93 / 12 = $0.16
$2.42 / 16 = 0.151
$1.25 / 9 = 0.14
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Discrete Math please help
Answers
Considering the given operations, the discrete sets are given as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.What is operation A - B?It is the operation of elements that are in set A but not in set B, hence, since A - B = {1, 5, 7, 8}, we have that:
A = {1,5,7,8}
What is operation B - A?It is the operation of elements that are in set B but not in set A, hence, since B - A = {2,10}, we have that:
B = {2,10}
What is the intersection operation?It contains the elements that are in both sets, hence, since [tex](A \cap B) = \{3,6,9\}[/tex], we have that the sets are completed as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.More can be learned about discrete math at https://brainly.com/question/13309484
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A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Answers
Answer:
51
Step-by-step explanation:
let's set the starting number as x
1. x times 2 = 2x
2. 2x- 138
3. result = 102
So, 2x-138 = 102
Now lets work backwards to solve for x.
1. 2x = 102
x = 51
So the starting number was 51.
2x - 138 = 102
+138 +138
(x=the missing number)
2x =240
240\2 = 120
x=120
Carmen drew this figure to represent the dividend of a division expression.
A number line going from negative 4 to positive 12. An arrow goes from 0 to 9.
What number is represented by the arrow?
Answers
The number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a number line shown in the picture.
As we can see each unit is represented by 1.
So after 2 there will be 3 and after 4 there will be 5 and so on.
So after 8, there will be 9 which is represented by the arrow.
Thus, the number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.
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Answer: 9
Step-by-step explanation:
The number line going from - 4 to + 12 represents the range of possible values for the dividend of the division expression. The arrow going from 0 to 9 indicates the actual value of the dividend. Therefore, the number represented by the arrow is 9.
144 to the 1/2 power
Answers
Answer:
(144)^1/2
(12^2)^1/2
12 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
12
Step-by-step explanation:
Rewrite 144 as 12²
(12²)^1/2
Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
12^2(1/2)
Cancel the common factor of 2.
Cancel the common factor.
Rewrite the expression
12^1
Evaluate the exponent.
12
If 6^(2x)=4 find 36^(6x-2) could anyone help me please?
Answers
Answer:
3.160
Step-by-step explanation:
You can solve for x using logarithm.
Rewrite in logarithm form
[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]
What is the length of CD? In this diagram, AABC~ AEDC.
Answers
The length of CD will be option C. 3
From given diagram, triangle ABC and EDC meet at a common vertex C.
So, triangle ABC and EDC both are congruent to each other.
Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.
Therefore,
AB/ED = AC/EC = BC/CD
AC/EC = BC/CD
18/6 = (12 - x)/x
Simplifying the expression,
We get
18x = 6(12 - x)
Multiplicating the terms in right hand side,
18x = 72 - 6x
Solving 6x on both sides,
we get
18x + 6x = 72 - 6x + 6x
24x = 72
Dividing both the sides by 24, we get
24x/24 = 72/24
x = 3
Hence, the length of CD is 3.
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