Answer:
[tex]\large\boxed{1.\ \dfrac{1}{x}=5+2\sqrt6}\\\boxed{2.\ \dfrac{x-1}{x}=-4-2\sqrt6}\\\boxed{3.\ \dfrac{x+1}{x}=6+2\sqrt6}[/tex]
Step-by-step explanation:
[tex]x=5-2\sqrt6\\\\1.\\\\\dfrac{1}{x}=\dfrac{1}{5-2\sqrt6}=\dfrac{1}{5-2\sqrt6}\cdot\dfrac{5+2\sqrt6}{5+2\sqrt6}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{5+2\sqrt6}{5^2-(2\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-2^2(\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-(4)(6)}=\dfrac{5+2\sqrt6}{25-24}\\\\=\dfrac{5+2\sqrt6}{1}=5+2\sqrt6\\\\2.\\\\\dfrac{x-1}{x}=\dfrac{x}{x}-\dfrac{1}{x}=1-\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x-1}{x}=1-(5+2\sqrt6)=1-5-2\sqrt6=-4-2\sqrt6[/tex]
[tex]3.\\\\\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x+1}{x}=1+5+2\sqrt6=6+2\sqrt6[/tex]
What is the solution for in (3x-5)=in11+2?
a. x=8
b. x=9
c. x=-3
d. x=7
Answer:
x = 3.133
Step-by-step explanation:
I'm going to take a chance and assume that you meant "ln 11," not "in11."
If I'm right, then we have:
3x-5 = ln 11 + 2.
Adding 5 to both sides yields
3x = ln 11 + 2 + 5, or ln 11 + 7. Since ln 11 = 2.398,
3x = 2.398 + 7, or 3x = 9.398, and so
x = 3.133.
If this is not what you expected, please ensure that you have copied down the original problem accurately. Thank you.
Say your car doesn’t run on straight gasoline and you have to mix the oil with gas together in a specific ratio of 2.4 fl oz of oil for every gallon of gasoline. If you have 1.5 gallons of gas, how much oil should you add?
Answer:
3.6 fl oz
Step- by-step explanation:
Well if one gallon equal 2.4 fl oz that would mean that half of a gallon would be half of that amount. Half of that amount would be 1.2 fl oz. we have now found how much a full gallon needs and how much half a gallon need. Now we add these 2 numbers. 2.4 fl oz + 1.2 fl oz = 3.6 fl oz.
Please give me Brainliest.
Final answer:
To get the correct oil mix for 1.5 gallons of gasoline at a ratio of 2.4 fl oz of oil per gallon, you should add 3.6 fl oz of oil.
Explanation:
To calculate the amount of oil needed for 1.5 gallons of gasoline with a mix ratio of 2.4 fl oz of oil per gallon, you follow these steps:
Determine the amount of oil needed for one gallon of gas, which is 2.4 fl oz.
Multiply this amount by the total gallons of gas. In this case, 2.4 fl oz x 1.5 gallons.
The calculation will be 2.4 fl oz/gallon x 1.5 gallons = 3.6 fl oz of oil.
Therefore, you should add 3.6 fl oz of oil to 1.5 gallons of gasoline to achieve the correct mix ratio.
Thanks, to everyone asking questions and giving answers. I finished my adult diploma today and a lot of it came from all of your help. The first two people to comment ANYTHING can have all of my remaining points, and may they get you to where you need to be. I will post more than one of these to distribute my points accordingly.
Brainliest to whoever has the best joke.
Answer:
congrats
Step-by-step explanation:
Find the missing triangle. Leave answer in simplest radical form. Also please explain clearly.
Answer:
Pythagorean Theorem
hypotenuse^2 = side^2 + side^2
16^2 = 7^2 + side ^ 2
256 - 49 = side^2
side x = sq root (207)
207 = 9 * 23 Therefore,
side x = 3 * sq root (23)
answer is A
Step-by-step explanation:
how many nickels does it take to make $4.85
Answer is:
37 nickels
Answer:
it takes 97 nickels
Step-by-step explanation:
4.85÷0.05=97
HELP! What type of association does the graph show between x and y? (5 points)
A graph shows scale on x axis and y axis from 0 to 12 at increments of 1. Dots are made at ordered pairs 1, 1 and 2, 1.1 and 3, 1.3 and 4, 1.7 and 5, 2 and 6, 2.5 and 7, 3.1 and 8, 4.2 and 9, 6 and 10, 10.
Select one:
a. Linear positive association
b. Nonlinear positive association
c. Linear negative association
d. Nonlinear negative association
The dots do not form a straight line, there is a small curve.
The dots do move up and to the right which makes it a positive curve.
The answer would be B. nonlinear positive association.
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Answer:
The test contains 10 three-point questions and 14 five-point questions
Step-by-step explanation:
Given equations are:
[tex]x+y = 24\\and\\3x+5y=100[/tex]
From 2nd equation we can deduce that x represents number of 3-point questions and y represents number of 5-point questions.
Using the substitution method:
From x+y = 24
y= 24-x
Putting this valu of y in 3x+5y=100
[tex]3x+5(24-x) = 100\\3x + 120 - 5x = 100\\-2x+120=100\\-2x = 100-120\\-2x = -20\\\frac{-2x}{-2} = \frac{-20}{-2}\\ x = 10\\Putting\ the\ value\ of\ x\ in\ x+y=24\\10+y=24\\y = 24-10\\y = 14[/tex]
Hence, the correct answer is:
The test contains 10 three-point questions and 14 five-point questions..
A rectangular prism has a length of 2 1/4 feet, a width of 6 feet, and a height of 3 1/2 feet.
What is the volume of the prism?
Enter your answer in the box.
ft³
For this case we have by definition, that the area of a rectangular prism is given by:
[tex]V = A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex] is the area of the base
h: It's the height
Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:
length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]
width: 6
Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]
So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]
Finally, the volume is given by:
[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]
Answer:
[tex]47.25 \ ft ^ 3[/tex]
ANSWER
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
EXPLANATION
The formula for calculating the volume of a rectangular prism is
[tex]Volume = l \times b \times h[/tex]
Where
[tex]l = 2 \frac{1}{4} ft[/tex]
is the length of the rectangular box,
[tex]w = 6ft[/tex]
is the width and
[tex]h = 3 \frac{1}{2} ft[/tex]
is the height of the rectangular prism.
We plug in the given dimensions into the formula to get:
[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]
Convert the mixed numbers to improper fraction to get:
[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]
Multiply out to get
[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]
Or
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
There are 1,379 souvenir paperweights that need to be packed in boxes. Each box will hold 15 paperweights. How many boxes will be needed?
92 boxes
1379/15=91.93 but u need a full box so 92
Answer:
92
Step-by-step explanation:
Given:
Number of Paperweights = 1,379
Number of Paperweights that each box can hold = 15
Number of boxes needed = 1379 ÷ 15 = 91.933 boxes
Because 0.933 of a box is of no use to anyone, we simply round this number up to the next whole box and just have the last box partially full.
This gives us 92 boxes.
Which graph represents the linear function below? y-4= (4/3)(x-2)
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y-4=(4/3)(x-2)[/tex]
This is the equation of a line into point slope form
The point is (2.4)
The slope is m=4/3
To plot the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
For x=0
y-4=(4/3)(0-2)
y=(-8/3)+4
y=4/3
The x-intercept is the value of x when the value of y is equal to zero
0-4=(4/3)(x-2)
-4=(4/3)x-(8/3)
Multiply by 3 both sides
-12=4x-8
4x=8-12
x=-1
we have the points
(2,4), (0,4/3),(-1,0)
Plot the line
Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.
see the attached figure
Sone for x and y
2x -y = 11
3x – 2y=6
Select one
a. (16.-21)
b. (4, -3)
c. (-3,4)
d. (16,21)
Answer:
d
Step-by-step explanation:
Given the 2 equations
2x - y = 11 → (1)
3x - 2y = 6 → (2)
Multiply (1) by - 2 and adding will eliminate y
- 4x + 2y = - 22 → (3)
Add (2) and (3) term by term
(3x - 4x) + (- 2y + 2y) = (6 - 22)
- x = - 16 ( multiply both sides by - 1 )
x = 16
Substitute x = 16 into (1) or (2) for corresponding value of y
(1) : 32 - y = 11 ( subtract 32 from both sides )
- y = - 21 ( multiply both sides by - 1 )
y = 21
Solution is (16, 21 ) → d
Answer:
It's d. (16,21).
Step-by-step explanation:
2x - y = 11 .............(1)
3x – 2y = 6...........(2)
Multiply the first equation by -2:
-4x + 2y = -22.......(3)
Adding (2) + (3):
-x = -16
x = 16.
Substitute for x in equation (1):
2(16) - y = 11
-y = 11-32 = -21
y = 21.
What is the slope of a line that is perpendicular to the line represented by the equation x – y = 8?
Answer:
-1
Step-by-step explanation:
Given equation of line is:
x - y = 8
In order to find the slope of other line we have to convert the given equation in standard form
So,
-y = -x + 8
Multiplying the equation with -1
y = x - 8
The co-efficient of x is the slope of the line.
Here the co-efficient is 1 so the slop of line is 1.
We know that the producct of slopes of perpendicular lines is -1.
Let m2 be the slope of the other line then
1 * m2 = -1
m2 = -1
So the slope of line perpendicular to line x-y = 8 will be: -1 ..
please help... I really need this.
Answer:
[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]
Step-by-step explanation:
The division problem given to us is [tex](4x^3-3x^2+5x+6)\div (x+6)[/tex].
To perform the synthetic division, we write out the coefficient of the polynomial. We set the linear factor to zero and solve for x, this becomes our divisor. That is [tex]x+6=0\implies x=-6[/tex].
We carry out the synthetic division as shown in the attachment.
The result of the synthetic division is 4 -27 167 -996
The first three terms are the coefficients of the quotient and the last term is the remainder.
Therefore the quotient is [tex]q(x)=4x^2-27x+167[/tex] and the remainder is [tex]r(x)=-996[/tex].
The dividend, the quotient and the divisor are written as
[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]
The correct answer is A
6. Simplify:
(1) (37 - (-8)]+[11 - (-30)]
Plz answer
Answer:
86
Step-by-step explanation:
Since something minus a negative is just adding, we get 37-(-8)=37+8 or 45. We can do the same with 11-(-30) which is 11+30 or 41. So 45+41=86
Answer:
86.
Step-by-step explanation:
Work out the 'inner' parentheses first:
(37 - (-8)] + [11 - (-30)]
= (37 + 8) + (11 + 30)
Now the outer parentheses:
= 45 + 41
= 86.
which is the graph of g(x)=[x+3]?
The graph of the equation y = x + 3 is a straight line with a slope of 1 and a y-intercept of 3. This means that for every increase of 1 in x, y increases by 1 and the line crosses the y-axis at y = 3.
Explanation:
The student is asking for the graph of the function g(x)=[x+3]. Please note, the symbol '[' and ']' is usually used to denote the greatest integer function or floor function, but since the context is not very clear, I'll assume that this is a simple linear function y = x + 3.
In such case, the graph of y = x + 3 is a **straight line** with a **slope** of 1 and a y-**intercept** of 3. Remember, the ^ slope is the change in y for every increase of 1 in x, and in this equation, for every increase of 1 in x, y increases by 1 . The intercept is simply where the line crosses the y-axis, and in this case it's at y = 3.
Learn more about Linear Function here:
https://brainly.com/question/31353350
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Does every line have a slope and a Y intercept
Answer:
Yes
Every straight line can be represented by an equation: y = mx + b.
m=slope
b=y-intercept
(www.math.com/school/subject2/lessons/S2U4L2GL.html)
The product of three consecutive numbers is 990. What is the sum you f the 3 whole numbers?
Answer:
20
Step-by-step explanation:
If the three numbers are x, x+1, and x+2, then:
x (x+1) (x+2) = 990
x (x² + 3x + 2) = 990
x³ + 3x² + 2x - 990 = 0
(x - 9) (x² + 12x + 110) = 0
Since x must be a whole number, x = 9. You can also use simple trial and error to find that the three numbers are 9, 10, 11.
The sum is:
9 + 10 + 11 = 20
10 points i need help i need to finish in 1 hour
how much does it cost to buy 3 drinks
Answer:
4.50
Step-by-step explanation:
3 divided by 2 is 1.5, which is equivalent to $1.50. So each drink cost 1.50. 1.50 x 3 = 4.50.
Classify the following triangle based on its angle measures.
A) Obtuse
B)Acute
C)right
D)equiangular
Answer:
A) Obtuse
Step-by-step explanation:
It is Obtuse due to the angle 115° being in the Triangle. This rules out Acute since the middle angle is not less than 90°. It is not Equiangular since all three angles are not equal. Furthermore it is not a right triangle either since there is no 90° angles. Making it Obtuse.
To classify a triangle based on angle measures, we need to know the specific angles. Triangles can be obtuse, acute, right, or equiangular, and each type has its own unique properties used in various applications across different fields.
Explanation:To classify the following triangle based on its angle measures, we must first understand the definitions of different types of triangles. A triangle can be classified as:
Obtuse: One angle is greater than 90 degrees.Acute: All angles are less than 90 degrees.Right: One angle is exactly 90 degrees.Equiangular: All angles are equal, and each measure 60 degrees since the sum of the angles in any triangle is 180 degrees.Considering these definitions, the seeking student must provide the angle measures of their specific triangle to accurately classify it.
Why Make These Distinctions?Making distinctions between different types of triangles is crucial because each classification has unique properties that are important in various fields such as mathematics, engineering, architecture, and physics. These properties assist in solving problems and understanding the world around us.
For instance, an obtuse triangle may be used in special construction scenarios, while right triangles are essential in trigonometry and geometry, appearing frequently in real-life applications like building and navigation.
Learn more about Triangle Classification here:https://brainly.com/question/4028542
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What is the length of QR?
Answer:
C
Step-by-step explanation:
Since the triangle is right with hypotenuse QR
Use Pythagoras' identity to solve for QR
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
QR² = 8² + (8[tex]\sqrt{3}[/tex] )²
= 64 + 192
= 256 ( take the square root of both sides )
QR = [tex]\sqrt{256}[/tex] = 16
Final answer:
The length of QR is approximately 2.25 units. Since qr and qs are similar, the length of QR is also approximately 2.25 units.
Explanation:
The length of QR can be determined based on the given information about the vectors near S, R, and T. The vectors near S start at about 6 units away, while vectors near R and T start at about 4 units. Using the equation qr|d² = qs|D², we can find that as|¶R = D² / d² = 36 / 16 = 2.25. Since qr and qs are similar, the length of QR is also approximately 2.25 units.
79+(-42 divide 6)- -24 the answer is 96 show me how u got it
79+(-42/6)-(-24)
first use -42 divide by 6
79 + (-7) - (-24)
then open all the parentheses
79 - 7 + 24
and use 79 minus 7
72 +24
add them together
96
That's how to get it.
Answer:
Step-by-step explanation:
79+(-42 divide 6)- -24
The first step is division
79+(-7)- -24
Then we add and subtract from left to right
72 --24
72+24
96
help me plzzzzzzzzz
Answer:
Whats the question?
Step-by-step explanation:
The table below represents how Marco feels about chocolate candy bars.
Answer:
The satisfaction level gained when a customer consumes a product is total utility.It calculated by finding the total sum of utility from consumption.
Marginal utility is the rate of change of total utility and quantity consumed.
Here you apply the expression, Marginal utility=change in total utility/change in quantity consumed
Let, Marginal utility=MU
Total utility=TU
Quantity consumed=QC
Then MU=ΔTU ÷Δ QC
Given the table
Chocolate Candy Bars Total Utility(utils) Marginal Utility(utils)
0 0 -
1 25 x
2 y 17
3 54 z
4 a b
5 66 4
6 c -1
Here you have assigned the missing areas with letter, hence finding the real values of the letters;
Apply MU=ΔTU÷ΔQC
[tex]1.17=\frac{y-25}{1}\\\\17=y-25\\\\y=17+25=42\\\\\\2.x=\frac{25-0}{1} \\\\x=25-0=25\\\\\\3.z=\frac{54-42}{1} \\\\z=54-42=12\\\\\\4.\frac{66-a}{1} =4\\\\66-a=4\\\\66-4=a\\a=62\\\\5.b=\frac{62-54}{1} =8\\\\\\6.\frac{c-66}{1} =-1\\\\\\c-66=-1\\\\c=-1+66=65[/tex]
Answers
y=42,x=25,z=12,a=62,b=8,c=65
Replace the letters with the real numbers in filling the table.
Are these fractions equivalent or nonequivalent?
xy/4y x/4
Answer:
They are equivalent
Step-by-step explanation:
x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent
Let y = safe load in pounds and x = length in feet of a horizontal beam. A constant of proportionality k exists such that y=k/x . y varies inversely as x. Determine the constant k for a beam with y = 2,000 pounds and x = 15 feet. a. 133.3 b. 3,000 c. 30,000
Answer:
Option c. 30,000
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
y ----> safe load in pounds
x ----> length in feet of a horizontal beam
we have
For [tex]x=15\ feet, y=2,000\ pounds[/tex]
Remember that
[tex]k=y*x[/tex]
substitute
[tex]k=2,000*15=30,000[/tex]
Each leg of a 45°-45°-90° triangle measures 12 cm.
What is the length of the hypotenuse?
4
45°
45°
6 cm
62 cm
12 cm
12 cm
12 cm
12V3 cm
Answer:
12 sqrt(2)
Step-by-step explanation:
Givens
a = 12 cm
b = 12 cm
c = ??
The triangle is isosceles with 1 right angle and 2 45 degree angles.
Formula
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
c^2 = 144 * 2
c = sqrt(144) * sqrt(2)
c = 12 * sqrt(2)
The answer isn't there. 12*sqrt(2) is the correct answer, 12sqrt(3).
Was this just a typo of some kind.
Let f(x) = 8x and g(x) = x - 3. What's
the smallest number that is in the domain of
fog?
Answer:
The smallest number that is in the domain of fog is 3
Step-by-step explanation:
f(x) = [tex]\sqrt{8x}[/tex] (as corrected in comments)
g(x) = x-3
we need to find fog = f(g(x))
For finding f(g(x)) we put the value of g(x) inside the f(x)
f(g(x))=[tex]\sqrt{8(x-3)}[/tex]
The domain of this function is x ≥ 3
because if value of x is less than 3 than the result would be negative and we know √f(x) ≥ 0
So, the smallest number that is in the domain of fog is 3
4.
Find the geometric mean of 4 and 12.
24
8
The geometric mean of two numbers is the square root of their product.
sqrt{4 • 12}
sqrt{48}
sqrt{16} •sqrt{3}
4•sqrt{3}.
The geometric mean of 4 and 12 is
4•sqrt{3}.
Factor.
8x2y2 – 4x2y – 12xy
4(8x2y2 – x – 12xy)
4(2xy – 4x2y – 12xy)
4x2y2(2xy – xy –3)
4xy(2xy – x – 3)
Answer:
4xy[2xy - x - 3]
Step-by-step explanation:
When finding the Greatest Common Factor [GCF], along with the coefficient, you have to factor out the least degree term possible, which in this case is 4xy. This is because although all terms have y and x, their degrees are not all similar, so we have to go with 4xy.
the system of equatios is solved using the linear combination method
1/2x4y=8 -2(1/2x+4y=8) -x-8y=-16
3x+24y - 12 1/3(3x+24y= 12) x+8y=4
0=-12
what does 0 = -12 mean regarding the solution to the system?
Answer: There are no solutions to the system because the equations represent parallel lines.
The value 0 = -12 indicates an inconsistent system with no solution.
0 = -12 means that the system of equations is inconsistent, and there is no solution. In this case, the equations represent parallel lines that never intersect, hence no common solution exists.