Final answer:
Using the quadratic formula, the exact solutions of the equation x² + 7x - 4 = 0 are x = (-7 + √65) / 2 and x = (-7 - √65) / 2.
Explanation:
To solve the quadratic equation x2 + 7x − 4 = 0 using the quadratic formula, we first identify the coefficients as a = 1, b = 7, and c = -4. The quadratic formula is x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]. Substituting the values we have:
x = [tex]\frac{-(7) \pm \sqrt{7^2 - 4(1)(-4)}}{2(1)}[/tex]
x = [tex]\frac{-7 \pm \sqrt{49 + 16}} {2}[/tex]
x = (-7 ± √65) / 2
Therefore, the exact solutions for x are x = (-7 + √65) / 2 and x = (-7 - √65) / 2.
The exact solutions of [tex]\(x^2 + 7x - 4 = 0\) are \(x = \frac{-7 + \sqrt{65}}{2}\)[/tex] and [tex]\(x = \frac{-7 - \sqrt{65}}{2}\).[/tex]
To find the exact solutions of the quadratic equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex] using the Quadratic Formula, we start with the standard form of a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] and apply the formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In the equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex], the coefficients are:
[tex]- \( a = 1 \)[/tex]
[tex]- \( b = 7 \)[/tex]
[tex]- \( c = -4 \)[/tex]
Now, substitute these values into the Quadratic Formula:
1. Calculate the discriminant [tex]\[ b^2 - 4ac = 7^2 - 4(1)(-4) = 49 + 16 = 65 \][/tex]
[tex]\[ b^2 - 4ac = 7^2 - 4(1)(-4) = 49 + 16 = 65 \][/tex]
2. Substitute [tex]\( b \), \( a \)[/tex], and the discriminant into the formula:
[tex]\[ x = \frac{-7 \pm \sqrt{65}}{2(1)} \][/tex]
[tex]\[ x = \frac{-7 \pm \sqrt{65}}{2} \][/tex]
So, the exact solutions of the equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex] are:
[tex]\[x = \frac{-7 + \sqrt{65}}{2} \quad \text{and} \quad x = \frac{-7 - \sqrt{65}}{2}\][/tex]
What’s the correct answer ??
Answer:
D
Step-by-step explanation:
A park ranger spent $208 to buy 12 trees.
Redwood trees cost $24 each and
spruce trees cost $16 each. How many of
each tree did the park ranger buy?
Let x represent number of redwood trees and y represent number of spruce trees.
We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:
[tex]x+y=12...(1)[/tex]
[tex]y=12-x...(1)[/tex]
We are also told that redwood trees cost $24 each, so cost of x redwood trees would be [tex]24x[/tex].
Each spruce tree costs $16, so cost of y spruce trees would be [tex]16y[/tex].
Since the park ranger spent $208 on trees, so we can represent this information in an equation as:
[tex]24x+16y=208...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]24x+16(12-x)=208[/tex]
[tex]24x+192-16x=208[/tex]
[tex]8x+192=208[/tex]
[tex]8x+192-192=208-192[/tex]
[tex]8x=16[/tex]
[tex]\frac{8x}{8}=\frac{16}{8}[/tex]
[tex]x=2[/tex]
Therefore, the park ranger bought 2 redwood trees.
Upon substituting [tex]x=2[/tex] in equation (1), we will get:
[tex]y=12-x\Rightarrow 12-2=10[/tex]
Therefore, the park ranger bought 10 spruce trees.
The park ranger bought 2 redwood trees and 10 spruce trees.
To solve this problem, we can set up a system of equations based on the given information:
Let x represent the number of redwood trees.Let y represent the number of spruce trees.We have two pieces of key information:
The total cost of the trees is $208.The total number of trees is 12.This gives us two equations:
24x + 16y = 208 (total cost equation)x + y = 12 (total number of trees equation)We can solve this system using substitution or elimination. Let's use substitution:
From the second equation, solve for y: y = 12 - x.Substitute y in the first equation: 24x + 16(12 - x) = 208.Simplify and solve for x: 24x + 192 - 16x = 208 → 8x = 16 → x = 2.Substitute x back into the equation for y: y = 12 - 2 → y = 10.Therefore, the park ranger bought 2 redwood trees and 10 spruce trees.
Which equation is represented by the graph below y = In x
y = In X+1
y=et
y = x + 1
Answer:
C y=e^x
Step-by-step explanation:
The equation of the graph of a function is y=e× option (C) y=e× is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
We have a graph of a function shown in the picture.
As we can see in the graph of the function is rapidly increasing.
We have an equation for the functions:
y = In(x)
The above function graph has a logarithmic graph which is decreasing as the x increase.
y = In(x) + 1
The above function graph has a logarithmic graph with 1 unit shift up which is decreasing as the x increase.
y=e×
The above function has a graph of an exponential function
y = x + 1
The graph of a above function is a straight line.
Thus, the equation of the graph of a function is y=e× option (C) y=e× is correct.
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If a pair of dice is rolled what is the probability that the first die rolls 4 and the second die rolls 6
Answer:
there is a 1 in 6 chance, so 1/6. The probability of rolling any side is 1/6.
Step-by-step explanation:
Answer:
1/36
Step-by-step explanation:
The odds of rolling a four on a dice are 1/6. The odds of rolling a six are also 1/6. So if you roll two die to find the probability you multiply the two numbers probability together which would equal 1/36.
Which of the fractions is equivalent to 3/8 ?
2/7, 8/3, 9,24, 5/10
Answer:
3/8 = 9/24
because
3/8 = 0.375
and
9/24 = 0.375
Answer:
9/24.
Step-by-step explanation:
We can see this by finding how 9/24 is simply 3/8 but not simplified down all the way. Notice how when you try simplifying the others, they are either unable to be simplified further or simplify into something else.
2/7--> unable to simplify further.
8/3--> unable to simplify further.
9/24--> simplifies to 3/8.
5/10--> simplifies to 1/2.
Answer will get brainliest
1. outcome
2. probability
3. equally likely
4. likely
5. certain
6. unlikely
7. impossible
Hope this helps! If you have any more questions or need further clarification then please comment down below or message me! Good luck!
In a class, 10 out of 25 students ride the bus. What percent of students ride the bus?
Answer:
25%
Step-by-step explanation:
Answer:
10/25= 45%
45% is the answer
Step-by-step explanation:
7. Find the perimeter of triangle FGH.
9. Determine whether the triangle is equilateral, isosceles, or
scalene.
8. The perimeter of triangle FGH is units.
(Round to the nearest tenth as needed.)
Answer:
9.) Its equilateral
7.) 24
Step-by-step explanation:
Sorry I only have the answer for 7 and 9.
To find the perimeter of a triangle, the lengths of all the sides are required, which are not provided in the question. The type of the triangle (equilateral, isosceles, scalene) also depends on these measurements.
Explanation:In order to find the perimeter of triangle FGH, we need the lengths of all three sides. Unfortunately, as the specific details regarding the lengths of the sides of triangle FGH are not provided, we cannot definitively provide the perimeter. Usually, the perimeter is calculated by adding up the lengths of all the sides.
In terms of the triangle type, it could be equilateral (all sides are equal), isosceles (two sides of equal length), or scalene (no sides are of equal length). Without the measurements of the sides, we cannot determine the type of triangle FGH.
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Solve each system of equations algebraically.
How can coordinate proof be used to prove two lines are perpendicular?
Answer:
To prove that two lines are parallel, we find their slope and verify that those slopes are equal. Perpendicular lines are lines that create 90 degree angles where they intersect. We can prove that two lines are perpendicular by finding their slopes and verifying that the slopes are negative reciprocals of one another.
The product of slope of both line is -1.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
As, We determine the slopes of two lines and confirm that they are equal in order to demonstrate that the lines are parallel.
Lines that connect at 90 degree angles are said to be perpendicular.
By determining the slopes of two lines and confirming that the slopes are negative reciprocals of one another, we can demonstrate that the lines are perpendicular.
Hence, the product of slope of both line is -1.
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find the volume of the pyramid
Answer:
6
Step-by-step explanation:
To calculate the volume of this pyramid, you first need to find the volume of the triangular base. The formula for the area of a triangle is bh/2, where b is the length of the base and h is the length of the height. In this case, 3*4/2=6. Now, you need to multiply by the height of the pyramid and divide by 3 to get 6*3/3=6 cubic inches. Hope this helps!
Help looks like i forgot to read a ruler
Answer:
The answer might be A
Step-by-step explanation:
hope this helps
The blue line is the graph of y – 1 = x. Use the sliders to make the orange line represent 2x + y = –5. Examine the graph. What is the solution of the system of these two equations? Hint: Convert to slope-intercept form before using the sliders. The solution to the system is .
Answer(-2, -1)
Step-by-step explanation:
I guessed and got it right.
Answer:
-2, -1
Step-by-step explanation:
i did math
Andrea’s savings account has a balance of $3668. After 3 years, what will the amount of interest be at 4% compounded quarterly?
Answer: 10%
Step-by-step explanation:
Answer:
its $465.19 (D) incase anyone still needs it
Step-by-step explanation:
just do it
laura walks 3/5 mile to school each day. isaiah's walk to school is 3 times as long as lauras. how far does isaiah walk to school each day?
Answer:
[tex]\frac{9}{5}[/tex] miles.
Step-by-step explanation:
This problem requires you to multiply the length of Laura's walk by 3 to solve for Isaiah's walk to school.
[tex]\frac{3}{5}[/tex]×[tex]\frac{3}{1}[/tex]= [tex]\frac{9}{5}[/tex] miles.
If you draw 2 cards from a deck what is the probability you draw 2 jacks if no cards are replaced
Answer:
12/2652 = 0.452488688%
Step-by-step explanation:
So, there are 4 jacks out of 52 cards, the probablility of pulling a jack out the first time, is 4/52.
Now that you pulled out 1 jack, there are 51 cards left in the deck, and the chances that you pull out another jack, is 3/51.
Now you would multiply these 2 fractions together, to get 12/2652 = 0.452488688%
A person stands 303030 meters east of an intersection and watches a car driving away from the intersection to the north at 171717 meters per second. At a certain instant, the car is 161616 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
The rate change of the distance between the car and the person at that instant will be 15.69 meter.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
A person stands 30 meters east of an intersection and watches a car driving away from the intersection to the north at 17 meters per second.
At a certain instant, the car is 161616 meters from the intersection.
Now,
Let the distance of the car from the intersection and from the person be x and y at any time t respectively.
So, We can apply the Pythagoras theorem as;
y² = x² + 10²
y = √ x² + 10²
Differentiate with respect to t , we get;
[tex]\frac{dy}{dt} = \frac{1}{2\sqrt{x^2 + 100} } 2x \frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{1}{\sqrt{x^2 + 100} } x \frac{dx}{dt}[/tex]
Since, the person standing towards the intersection at 17 m/s.
dx/dt = 17
Hence, [tex]\frac{dy}{dt} = \frac{1}{\sqrt{x^2 + 100} } x *17[/tex]
At x = 16 meters
So, [tex]\frac{dy}{dt} = \frac{1}{\sqrt{24^2 + 100} } 24 *17[/tex]
[tex]\frac{dy}{dt} = 408 / \sqrt{676}[/tex]
[tex]\frac{dy}{dt} = 408 / 26[/tex]
[tex]\frac{dy}{dt} = 15.69[/tex]
Thus, The rate change of the distance between the car and the person at that instant will be 15.69 meter.
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What is the slope?
A) 3/7
B) 7/3
C) -3/7
D) -7/3
Answer:
B) 7/3
Step-by-step explanation:
To find the slope of a line using a graph, locate two points. In this example, the points are (0, -2) and (3, 5).
Then, find the distance between the two points. To do so in this example, find the difference between 0 and 3, and -2 and 5.
3 - 0 = 3
5 - (-2) = 7
Since we're dealing with slope, the answer will be in y/x form. 7 is the distance between the y-coordinates and 3 is the difference between the x-coordinates, the answer is 7/3.
Answer: 7/3
Step-by-step explanation:
Count how many spaces you are going up from the first point to the second point and how many spaces over to the point
8-10x=7+5X
4-10x=3+5x
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so
It's been a long time since you fell in love
You ain't coming out your shell, you really ain't been yourself
Tell me what must I do (do tell, my love)
'Cause luckily I'm good at reading
I wouldn't bug him, but he won't stop cheesin'
And we can dance all day around it
If you front then I'll be bouncing
If you want it scream and shout it, babe
Before I leave you dry
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so (yeah)
Let me check my chest, my breath right quick (ha)
He ain't never seen it in a dress like this (ah)
He ain't never even been impressed like this
Prolly why I got him quiet on the set like zip
Like it, love it, need it bad
Take it, own it, steal it, fast
Boy, stop playing, grab my az
Why you actin' like you shy?
Shut it, save it, keep it, pushin'
Why you beating 'round the bush?
And knowing you want all this woman
Never knock it 'til you try (yeah, yeah)
All of them betches hating I have you with me
All of my nigzas saying you mad committed
Realer than anybody you had, and pretty
All of that body-ody, the az and tizys
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so
Day to night to morning, keep with me in the moment
I'd let you had I known it, why don't you say so?
Didn't even notice, no punches left to roll with
You got to keep me focused, you want it, say so
Armando found the volume of the figure below by using the steps shown.
A rectangular prism with a length of 18 inches, width of 5 inches, and height of 8 inches. A triangular prism with a base of 18 inches and height of 6 inches. The prism has a height of 5 inches.
What mistake, if any, did Armando make?
Armando determined the volume correctly.
Armando used the wrong formula for the total volume.
Armando used the wrong dimensions for the triangular prism.
Armando did not apply the order of operations correctly.
Armando use the wrong demensions for the triangular prism?Answer:
Step-by-step explanation:
The mistake is Armando used the wrong dimensions for the triangular prism, the correct option is C.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
We are given that;
Height of pyramid= 6in
Dimensions of prism= 8*18*5
Now,
To find the area of the triangular base, he should have used:
A=21bh
A=21(18)(6)
A=54
Therefore, by the rectangular prism the answer will be Armando used the wrong dimensions for the triangular prism.
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What is the upper and lower bound?
Answer:
As shown in picture:
Original x = 360 - (59 + 108 + 81) = 112 deg
Upper bound of x (when all known elements are considered at lower bound)
U = 360 - (58 + 107 + 80) = 115 deg
Lower bound of x (when all known elements are considered at upper bound)
L = 360 - (60 + 109 + 82) = 109 deg
Hope this helps!
:)
Answer:
112 deg,115 deg , 108 deg
Step-by-step explanation:
i hope this helps you.
Evaluate the expression.
StartFraction 16.8 minus 1.2 squared over negative 4.3 + 3 (negative 0.7) EndFraction = StartFraction 16.8 minus 1.44 over negative 4.3 + (negative 2.1) EndFraction
Answer:
-2.4
Step-by-step explanation:
The solution to the given expression is -2.4.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}\\\\\frac{15.36}{-4.3-2.1} =\frac{15.36}{-4.3-2.1}\\\\\frac{15.36}{-6.4} =\frac{15.36}{-6.4}[/tex]
-2.4 = -2.4
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Complete Question:
Evaluate the expression.
[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}[/tex]
HELP PLEASE!!!
These are the cost and revenue functions for a line of 24-pound bags of dog food sold by a large distributor:
R(x) = -31.72x2 + 2,030x
C(x) = -126.96x + 26,391
The maximum profit of $ ____ can be made when the selling price of the dog food is set to $ ____ per bag.
Answer:
The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.
Step-by-step explanation:
Profit = Revenue - Cost
P(x) = R(x) -C(x)
= -31.72x^2 + 2,030x -( -126.96x + 26,391)
Distribute the minus sign
= -31.72x^2 + 2,030x+126.96x - 26,391
Combine like terms
= -31.72 x^2 + 2156.96 x - 26391
This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)
vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34
Evaluate P(x) at x=34 to determine the profit
P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391
-36668.32+73336.64-26391
10277.32
The maximum profit of $10,243.32 can be made when the selling price of the dog food is set to $947.17. per bag.
1. Define the profit function: Profit [tex](\( P(x) \))[/tex] is calculated by subtracting the cost function [tex](\( C(x) \))[/tex] from the revenue function [tex](\( R(x) \)):[/tex]
[tex]\[ P(x) = R(x) - C(x) \][/tex]
2. Substitute the given revenue and cost functions:
[tex]\[ R(x) = -31.72x^2 + 2,030x \][/tex]
[tex]\[ C(x) = -126.96x + 26,391 \][/tex]
3. Plug in the revenue and cost functions into the profit function:
[tex]\[ P(x) = (-31.72x^2 + 2,030x) - (-126.96x + 26,391) \][/tex]
[tex]\[ P(x) = -31.72x^2 + 2,156.96x - 26,391 \][/tex]
4. Find the x-coordinate of the vertex of the profit function:
The x-coordinate of the vertex is given by:
[tex]\[ x = \frac{-b}{2a} \][/tex]
where [tex]\( a = -31.72 \) and \( b = 2,156.96 \).[/tex]
[tex]\[ x = \frac{-2,156.96}{2*(-31.72)} \][/tex]
x ≈ 34
5. Calculate the maximum profit:
Substitute x ≈ 34 into the profit function:
P(34) ≈ [tex]-31.72(34)^2 + 2,156.96(34) - 26,391[/tex]
P(34) ≈ 10,243.32
6. Determine the selling price per bag that maximizes profit:
Plug x ≈ 34 into the revenue function to find the corresponding revenue:
[tex]\[ R(34)[/tex] ≈ [tex]-31.72(34)^2 + 2,030(34)[/tex]
[tex]\[ R(34)[/tex] ≈ [tex]32,183.68[/tex]
Divide the revenue by the quantity x ≈ 34 to find the selling price per bag:
[tex]\[ \text{Selling price per bag}[/tex] ≈ [tex]\frac{32,183.68}{34}[/tex] ≈ [tex]947.17[/tex]
So, the maximum profit is approximately $10,243.32, and the selling price per bag that maximizes profit is approximately $947.17.
Out of the 1,480 students in Gila Monster High School, 896 are girls. A total of 373 of the students made the honor roll. The number of girls who appeared on the honor roll was 5 less than twice the number of boys.
How many girls are in the honor roll
How many boys are in the honor roll
Answer:
There are 126 boys on the honor roll and 247 girls on the honor roll.
Step-by-step explanation:
Out of the 1,480 students in Gila Monster High School, a total of 373 of the students made the honor roll.
Let the number of girls that made the honor roll be g.
Let the number of boys that made the honor roll be b.
This means that:
b + g = 373_________________(1)
The number of girls who appeared on the honor roll was 5 less than twice the number of boys.
This means that:
g = 2b - 5___________________(2)
Let us insert (2) in (1):
b + (2b - 5) = 373
=> b + 2b - 5 = 373
3b = 373 + 5
3b = 378
=> b = 378 / 3 = 126
From (1):
b + g = 373
=> 126 + g = 373
g = 373 - 126
g = 247 girls
Therefore, there are 126 boys on the honor roll and 247 girls on the honor roll.
Which expression can be used to find the volume
of the rectangular prism in cubic centimeters?
The expression that can be used to find the volume of the rectangular prism is 20825 cm³.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The formula for the volume of a rectangular prism is given by:
V = A x h
where A is the area of the base and h is the height of the prism.
In this case,
The area of the base is given as 245 cm^2 and the height is given as 85 cm.
Therefore, we can substitute these values into the formula to get:
V = 245 x 85
Multiplying these values together, we get:
V = 20825 cm³
Therefore,
The expression that can be used to find the volume of the rectangular prism is 20825 cm³.
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Write an equation parallel to y=3x−1 and goes through the point (-2, -13)
Answer:
y=3x-7
Step-by-step explanation:
we use the equation of the line:
y=mx+b
if the line is parallel, then the slope(m) of the line stays the same:
y=3x+b
we then substitute the ordered pair into the equation and solve for b:
-13 = 3(-2)+b
-13 = -6+b
-13+6 = b
-7 = b
now we substitute the b value into the original equation and the answer:
y=3x-7
Hope this helps :)
Determine whether each pair of functions are inverse functions. Picture attached.
Answer:
The correct answer is B.
how can we tell if a fraction 3/2 is equal to the square root of 2
The fraction 3/2 and square root of 2 are not equivalent because their decimal approximations (1.5 and about 1.41 respectively) are not the same.
Explanation:To determine if a fraction like 3/2 is equal to the square root of 2, we would need to compare their decimal values.
First, divide 3 by 2 to get the decimal value for the fraction, which is 1.5.
For the square root of 2, we can use a calculator and find that its approximate decimal value is 1.41.
Therefore, since 1.5 is not equal to 1.41, the fraction 3/2 is not equivalent to the square root of 2.
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The fraction 3/2 is not equal to the square root of 2. By comparing the values directly or using fractional exponents, we can see that squaring 3/2 gives us 9/4, which is not equal to 2, and numerically the square root of 2 is approximately 1.414.
To determine if the fraction 3/2 is equal to the square root of 2, we can compare them directly or convert them into the same format. Recall that fractional exponents serve as another way to represent roots. Specifically, an exponent of 1/2 equates to taking the square root of a number. Thus, [tex](3/2)^{2}[/tex] would equal 3/2 multiplied by itself, which is 9/4, and that is not equal to 2. Therefore, 3/2 is not the square root of 2. We can also numerically evaluate the square root of 2, which is approximately 1.414, and see that it does not equal 3/2, which is 1.5.
Another consideration is that the square root of any number x can be expressed as [tex]x^{1/2}[/tex]. For instance, [tex](\sqrt{2})^2[/tex] = 2 because [tex](2^{1/2})^2[/tex] equals [tex]2^{1/2 * 2}[/tex] = 2. When we do this with 3/2, we would have [tex](3/2)^{1/2} * (3/2)^{1/2}[/tex] = 3/2, which does not satisfy the equation for the square root of 2. Therefore, 3/2 is not equal to the square root of 2.
Omar wants to use a graph to solve the equation below.
log Subscript 6 Baseline x = log Subscript 2 Baseline (x + 4)
Which system of equations should Omar use?
y 1 = StartFraction log 6 Over x EndFraction , y 2 = StartFraction log 2 Over x + 4 EndFraction
y 1 = StartFraction log x Over log 6 EndFraction, y 2 = StartFraction log x + 4 Over log 2 EndFraction
y 1 = StartFraction log 6 Over log 2 EndFraction, y 2 = StartFraction log x Over log (x + 4) EndFraction
y 1 = StartFraction log x Over log 6 EndFraction, y 2 = StartFraction log (x + 4) Over log 2 EndFraction
Answer:
D. y 1 = StartFraction log x Over log 6 EndFraction, y 2 = StartFraction log (x + 4) Over log 2 EndFraction
Step-by-step explanation:
Omar should use the system of equations y₁ = logx/log6, and y₂ = log(x+4)/log2 option second is correct.
What is a logarithm?
It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have a log equation:
log₆x = log₂(x + 4)
As we know:
logₐᵇ = log(b)/log(a)
After applying the above property:
logx/log6 = log(x+4)/log2
y₁ = logx/log6
y₂ = log(x+4)/log2
Thus, Omar should use the system of equations y₁ = logx/log6, and y₂ = log(x+4)/log2 option second is correct.
Learn more about the Logarithm here:
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Convert 12 1/2% into a decimal (It isn't 12.50)
Convert 12 1/2% into a fraction (It isn't 25/2)
Answer:
0.125 and 1/8
Step-by-step explanation:
To convert a percentage to a decimal, divide by 100 to move 2 decimal places to the left.
12.50% / 100 = 0.125
To convert a percentage into a fraction, rewrite the decimal number you got and put it over 1. Multiply the numerator and denominator by 1000 to move 3 decimal places to the right and get your fraction.
[tex]\frac{0.125}{1}[/tex] · [tex]\frac{1000}{1000}[/tex] = 125/1000
Divide the numerator and denominator by the GCF, 125, to get your simplified fraction.
125/125 = 1
1000/125 = 8
125/1000 = 1/8