The two numbers that add up to 83 with a difference of 7 are 45 and 38. We can find these numbers by setting up a system of linear equations and solving for each variable.
To find the two numbers where the sum is 83 and the difference is 7, we can set up two equations based on the information provided:
Let the first number be x and the second number be y.The sum of the two numbers is x + y = 83.The difference of the two numbers is x - y = 7.To solve the system of equations, we can use the method of addition. Add the two equations together to eliminate the variable y:
(x + y) + (x - y) = 83 + 72x = 90x = 90 / 2x = 45With the value of x known, you can substitute it into the first equation to find y:
45 + y = 83y = 83 - 45y = 38Therefore, the two numbers are 45 and 38.
Jim is 2 years older than 3 times his little brother Tommy. Together their ages add up to 18. How old is each?
Final answer:
By setting up an equation based on the given information that Jim is 2 years older than 3 times Tommy's age and their combined ages are 18, we find that Tommy is 4 years old and Jim is 14 years old.
Explanation:
The question is about finding the ages of Jim and his younger brother Tommy given that Jim is 2 years older than 3 times Tommy's age and together their ages add up to 18. Let's denote Tommy's age as T years. Therefore, Jim's age would be 3T + 2 years. According to the problem, if we add both ages, the sum is 18. So, we can set up the following equation to find their ages:
T + (3T + 2) = 18
Simplifying this equation gives:
4T + 2 = 18
4T = 16
T = 4
Thus, Tommy is 4 years old. To find Jim's age, we substitute Tommy's age back into the equation for Jim's age:
Jim's age = 3(4) + 2 = 12 + 2 = 14
Therefore, Tommy is 4 years old, and Jim is 14 years old.
Simplify .
[tex]\sqrt{x} 18[/tex]
Answer:
[tex]3\sqrt{2} \sqrt{x}[/tex]
Let y=f(x) be the particular solution to the differential equation dy/dx=(x^2+1)/e^y with the initial condition f(1)=0. What is the value of f(2) ?
[tex]\( f(2) = \ln \left( \frac{14}{3} \right) \)[/tex]. You can calculate this value to get a numerical result.
To find the particular solution [tex]\( y = f(x) \)[/tex] to the given differential equation [tex]\( \frac{dy}{dx} = \frac{x^2 + 1}{e^y} \)[/tex] with the initial condition [tex]\( f(1) = 0 \)[/tex] and then evaluate [tex]\( f(2) \),[/tex] we can follow these steps:
1. Separate variables:
[tex]\[ e^y dy = (x^2 + 1) dx \][/tex]
2. Integrate both sides:
[tex]\[ \int e^y dy = \int (x^2 + 1) dx \][/tex]
[tex]\[ e^y = \frac{1}{3} x^3 + x + C \][/tex]
3. Apply the initial condition [tex]\( f(1) = 0 \):[/tex]
[tex]\[ e^0 = \frac{1}{3} (1)^3 + 1 + C \][/tex]
[tex]\[ 1 = \frac{1}{3} + 1 + C \][/tex]
[tex]\[ C = \frac{2}{3} \][/tex]
So, the particular solution is:
[tex]\[ e^y = \frac{1}{3} x^3 + x + \frac{2}{3} \][/tex]
4. Solve for y :
[tex]\[ y = \ln \left( \frac{1}{3} x^3 + x + \frac{2}{3} \right) \][/tex]
Now, we need to find f(2), which means finding the value of y when x = 2:
[tex]\[ y = \ln \left( \frac{1}{3} (2)^3 + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{8}{3} + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{14}{3} \right) \][/tex]
[tex]\lim_{x\to \infty} \frac{\sqrt{9x^{2} +x+1} -\sqrt{4x^{2} +2x+1} }{x+1}[/tex]
Answer:
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}\right)=1[/tex]
Step-by-step explanation:
Considering the expression
[tex]\lim _{x\to \infty \:}\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}[/tex]
Steps to solve
[tex]\lim _{x\to \infty \:}\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}[/tex]
[tex]\mathrm{Divide\:by\:highest\:denominator\:power:}\:\frac{\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}}{1+\frac{1}{x}}[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}}{1+\frac{1}{x}}\right)[/tex]
[tex]\lim _{x\to a}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\lim _{x\to a}f\left(x\right)}{\lim _{x\to a}g\left(x\right)},\:\quad \lim _{x\to a}g\left(x\right)\ne 0[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\frac{\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)}{\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)}.....[1][/tex]
As
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)=1[/tex]
Solving
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)....[A][/tex]
[tex]\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)-\lim _{x\to \infty \:}\left(\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)[/tex]
Also
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)=3[/tex]
Solving
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)......[B][/tex]
[tex]\lim _{x\to a}\left[f\left(x\right)\right]^b=\left[\lim _{x\to a}f\left(x\right)\right]^b[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\sqrt{\lim _{x\to \infty \:}\left(9+\lim _{x\to \infty \:}\left(\frac{1}{x}+\lim _{x\to \infty \:}\left(\frac{1}{x^2}\right)\right)\right)}[/tex]
[tex]\lim _{x\to \infty \:}\left(9\right)=9[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{1}{x}\right)=0[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{1}{x^2}\right)=0[/tex]
So, Equation [B] becomes
⇒ [tex]\sqrt{9+0+0}[/tex]
⇒ [tex]3[/tex]
Similarly, we can find
[tex]\lim _{x\to \infty \:}\left(\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)=2[/tex]
So, Equation [A] becomes
⇒ [tex]3-2[/tex]
⇒ 1
Also
[tex]\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)=1[/tex]
Thus, equation becomes
[tex]\frac{\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)}{\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)}=\frac{1}{1}=1[/tex]
Therefore,
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}\right)=1[/tex]
Keywords: limit
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The square of m reduced by 49
Square of m reduced by 49 = m²- 49
Step-by-step explanation:
Let us consider the variable as m.
Square of m is given as m².
Reduction factor is 49.
So the expression for the square of m reduced by 49 is given as m²- 49.
1. What is the extraneous solution of √x−3 + x = 9?
2. If the volume of a cube is 108 ft^3, what is the side length? Keep your answer in radical form.
Can someone help with either of them? Thanks!
Answer:
1. x = 12
2. 3∛4 feet.
Step-by-step explanation:
1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.
Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)
⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]
Squaring both sides we get,
⇒ x - 3 = 81 - 18x + x²
⇒ x² - 19x + 84 = 0
⇒ x² - 12x - 7x + 84 = 0
⇒ (x - 12)(x - 7) = 0
⇒ x = 12 or 7.
Now, putting x = 12 in the equation (1) we get,
[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]
Again, putting x = 7 in the equation (1) we get,
[tex]\sqrt{7 - 3} + 7 = 9[/tex]
Therefore, x = 12 is an extraneous solution of this equation. (Answer)
2. The volume of a cube with side lengths a ft. is given to be 108 ft³.
So, a³ = 108
⇒ a = 3∛4 feet.
Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)
10 times a number, then add 20
Answer:
10x+20
Step-by-step explanation:
Answer: The equation is 10x+20
(x is a variable, not a multiplication symbol)
Step-by-step explanation:
10 times a number, that is unknown, plus 20.
x is the unknown number.
10x plus 20.
10x+20
Solve for x. Show your work. -1/2 x < -12
-1/2x < -12
Divide both sides by -1/2
Also because you are dividing by a negative number you need to reverse the inequality sign.
X > 24
Can someone find the total area of this poster
Answer: 1,360
Step-by-step explanation:
20 * 20 = 400
20 * 12 = 240
240 * 4 = 960
960 + 400 = 1,360
The graph of the equation x = y2 + 4 is symmetric with respect to which of the following?
a. the 3-axis
c. the line y = -x+ 4
b. the x-axis
d. the line y = x
Answer:
the graph of the equation will be symmetric about option b.) x axis
Step-by-step explanation:
i) the given equation is x = [tex]y^2[/tex] + 4
ii) therefore [tex]y^{2}[/tex] = x - 4
iii) the equation is that of a parabola with vertex at (4,0)
iv) the graph of the equation will be symmetric about option b.) x axis
and then you have to graph it but im stuck on graphing f(2) so please help
[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]
Solution:
Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]
Domain = {–1, 0, 1, 2, 3}
Substitute the given values in the function.
At x = –1,
[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]
[tex]=6 \times \frac{3}{2}[/tex]
= 9
[tex](x, f(x))=(-1, 9)[/tex]
At x = –0,
[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]
[tex](x, f(x))=(0,6)[/tex]
At x = 1,
[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]
[tex](x, f(x))=(1,4)[/tex]
At x = 2,
[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]
[tex]=\frac{24}{9}[/tex]
[tex]=2\frac{6}{9}[/tex] (Cancel the common terms)
[tex]=2\frac{2}{3}[/tex]
[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]
At x = 3,
[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]
[tex]=\frac{48}{27}[/tex] (Cancel the common terms)
[tex]=\frac{16}{9}[/tex]
[tex]=1\frac{7}{9}[/tex]
[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]
Plot the points in the graph.
The image of the graph is attached below.
Afon read pages in 30 minutes.
Find the number of minutes read per page and the number of pages read per minute.
I need help im bad at 7th grade math!!!!!!!!
Answer:
Therefore Afon can read 0.75 pages per minute.
Step-by-step explanation:
Afon read 22 1/2 pages in 30 minutes
Therefore Afon read 22.5 pages in 30 minutes.
Therefore the number of pages Afon can read in 1 minute
[tex]= \dfrac{22.5}{30} = \dfrac{45}{60} = \dfrac{9}{12} = \dfrac{3}{4} = 0.75 pages[/tex]
Therefore Afon can read 0.75 pages per minute.
It takes 1 1/4 minutes to fill a 3 gallon bucket at this rate how long will it take to fill a 50 gallon tub
It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.
Step-by-step explanation:
Time taken to fill 3 gallons bucket = [tex]1\frac{1}{4}=\frac{5}{4}\ minutes[/tex]
We have to find time required to fill 50 gallons tub.
3 gallons = [tex]\frac{5}{4}\ minutes[/tex]
1 gallon = [tex]\frac{5}{4}*\frac{1}{3}\ minutes[/tex]
1 gallon = [tex]\frac{5}{12}\ minutes[/tex]
To find the time required for 50 gallons;
50 gallons = 50 * Time per gallon
50 gallons = [tex]50*\frac{5}{12}[/tex]
50 gallons = [tex]\frac{250}{12}[/tex] = [tex]\frac{125}{6}[/tex]
50 gallons = [tex]20\frac{5}{6}\ minutes[/tex]
It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.
Keywords: fraction, division
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Final answer:
It takes approximately 20.83 minutes to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket, considering a constant rate of filling.
Explanation:
The question asks us to determine how long it will take to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket. To solve this, we can set up a proportion since the rates of gallons per minute will be the same for both the bucket and the tub.
First, let's convert the time from minutes to seconds to match the unit for seconds provided in the example. There are 60 seconds in a minute, so 1 1/4 minutes is equal to 75 seconds.
Now, we know it takes 75 seconds to fill 3 gallons. Let's calculate the number of seconds it takes to fill 1 gallon, and then we will use that rate to find out how many seconds it will take to fill 50 gallons.
We divide 75 seconds by 3 gallons, to get 25 seconds per gallon. Then we multiply this rate by 50 gallons to find the total time needed to fill the tub:
25 seconds/gallon × 50 gallons = 1250 seconds.
Finally, to convert seconds back to minutes, we divide 1250 seconds by 60:
1250 seconds ÷ 60 seconds/minute = 20 5/6 minutes or approximately 20.83 minutes.
So, it takes approximately 20.83 minutes to fill a 50 gallon tub at the given rate.
Estimate by rounding the largest number to hundreds and then multiplying.
691 x 4 is approximately
Answer:
approximately 2,800
Step-by-step explanation:
you would round 691 to 700 then multiply by 4
Answer:
2,800
Step-by-step explanation:
In saying "largest number," I believe the question means that you should round 691 up to 700 (nearest hundreds). Multiple 700 by 4, and you will get 2,800! Hope this helps! :)
Solve for N , I can’t get this , I’ll give brainliest to who gets it!!!
Answer:
55
Step-by-step explanation:
The two shortest sides added up need to be longer then the longest angle so 48 + 55 = 103>73
- Write the linear function for the line that passes through the point (3, 7) and has a slope of 2.
Answer:
lool at the picture shown
which plane is closer to the base of the airplane tower? explain. The distance for Plane A, to the nearest tenth, is ____ kilometers. The distance for Plane B, to the nearest tenth, is _____ kilometers. help!!
Answer:
Plane B is closer.
The distance for Plane A is 7.9 km.
The distance for Plane B is 7.4 km.
Step-by-step explanation:
To find the distance to the tower, altitude must be converted to kilometers. Each 1000 ft is 0.3048 km, so the heights of the planes are ...
-- Plane A: (20 thousand ft)*(0.3048 km/thousand ft) = 6.096 km
-- Plane B: (8 thousand ft)*(0.3048 km/thousand ft) = 2.4384 km
The Pythagorean theorem can be used to find the distance from each plane to the tower:
-- distance = √((ground distance)² + (height)²)
-- Plane A distance = √(5² +6.096²) ≈ √62.16 ≈ 7.9 . . . km
-- Plane B distance = √(7² +2.4384²) ≈ √54.95 ≈ 7.4 . . . km
The distance for Plane B is shorter, so Plane B is closer to the tower.
Copy the problems onto your paper, mark the givens and prove the statements asked.
Given ∠E ≅ ∠T, M − midpoint of TE Prove: MI ≅ MR
MI ≅ MR proved by using ASA postulate of congruence
Step-by-step explanation:
Let us revise the cases of congruence
SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ∵ M is the mid-point of TE
∴ MT = ME
In Δs TMI and EMR
∵ ∠T ≅ ∠E ⇒ given
∵ ∠TMI ≅ EMR ⇒ vertical opposite angles
∵ MT = ME ⇒ proved
∴ Δ TMI ≅ ΔEMR by ASA postulate of congruence
- From congruence, corresponding sides are equal
∴ MI ≅ MR
MI ≅ MR proved by using ASA postulate of congruence
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The question is about a geometry proof related to congruent angles and midpoints, but additional information is needed to provide a specific solution.
Explanation:The question appears to be a geometry proof involving congruent angles and midpoints. The goal is to prove that two line segments MI and MR are congruent given ∠E ≅ ∠T, and M is the midpoint of TE.
To prove this, one would need to provide more information about the points I and R, such as their positions relative to point E, T, and M.
Without this additional information, it is difficult to give a specific proof. However, typical proof strategies might involve showing that triangles EMI and TMR are congruent by Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS) postulates, depending on the position of points I and R.
In the triangle below, what is the sine of 30°?
Answer:
There's no picture. Is it D.√3 / 2
Step-by-step explanation:
Subtracting 1 from which digit in the number 12,345 will decrease the value of the number by 1,000
There are 26 students in Mrs. Augello’s math class. The number of boys is three less than the number of girls. Write a system of equations that represents the number of boys and girls.
Answer:
[tex]b+g=26[/tex]
[tex]b=g-3[/tex]
Step-by-step explanation:
Let the number of boys be reprented by [tex]b[/tex]
Let the number of girls be represented by [tex]g\\[/tex]
↓ Total number of boys + girls must be 26
[tex]b+g=26[/tex]
↓ Number of boys is 3 less than the number of girls
[tex]b=g-3[/tex]
The system of equations that represents the number of boys and girls are [tex]x+y=26[/tex] and [tex]x = y-3[/tex] and this can be determined by forming the linear equation.
Given :
There are 26 students in Mrs. Augello’s math class. The number of boys is three less than the number of girls.The following steps can be used in order to determine the system of equations that represents the number of boys and girls:
Step 1 - Let the total number of boys be 'x' and the total number of girls be 'y'.
Step 2 - So, the linear equation that represents the total number of students in Mrs. Augello's math class is:
[tex]x+y=26[/tex] --- (1)
Step 3 - The linear equation that represents the situation "number of boys is three less than the number of girls" is:
[tex]x = y-3[/tex] --- (2)
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A 25-foot flag pole casts a shadow of 40 feet. What is the approximate height from the top of the flag pole to the top of the shadow? 45 47 65
Answer:45
Step-by-step explanation:
it is 45
Step-by-step explanation:
Can someone please answer this question please answer it correctly and show work please
Answer:
42) 122.72 square inches
43) 212.83 additional feet of fabric
Step-by-step explanation:
42)
Diameter = [tex]12\frac{1}{2}[/tex] = 12.5 inches
Radius = (1/2) * Diameter = (1/2) * 12.5 = 6.25 inches
The formula for calculating the area of a circle is π * Radius²
π * Radius²
Substitute radius and pi into formula
3.14159265359 * 6.25²
Solve exponent
3.14159265359 * 39.0625
Multiply
122.7184630309
Round to the nearest hundredth
122.72 square inches
43) Clarissa needs 500 feet of fabric
She has these pieces
3 pieces of fabric that are each 18 yards long
1 piece of fabric that is [tex]16\frac{1}{2}[/tex] yards long
1 piece of fabric that is [tex]75\frac{2}{3}[/tex] feet long
Convert all yard measurements to feet and all fractions to decimals
(1 yard = 3 feet)
3 pieces of fabric that are each 54 feet long
1 piece of fabric that is 49.5 yards long
1 piece of fabric that is 75.67 feet long
Add all lengths
3(54) + 49.5 + 75.67
162 + 49.5 + 75.67 = 287.17
Subtract from 500 to find missing length
500 - 287.17 = 212.83
212.83 additional feet of fabric
Hope this helps :)
Find the cube root of 3357
Mrs.Lohens made curtains for her children’s bedrooms. She used 4 3/4 yards of fabric for Nickys room and 6 5/8 yards for Linda’s room. How much fabric did she use in all?
Answer:
[tex]11\frac{3}{8}\ yd[/tex]
Step-by-step explanation:
we know that
To find out the total yards of fabric used, add up the yards of fabric used for Nickys' room and the yards of fabric used for Linda's room
so
[tex]4\frac{3}{4}+6\frac{5}{8}[/tex]
Convert mixed number to an improper fraction
[tex]4\frac{3}{4}\ yd=4+\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}\ yd[/tex]
[tex]6\frac{5}{8}\ yd=6+\frac{5}{8}=\frac{6*8+5}{8}=\frac{53}{8}\ yd[/tex]
Adds the fractions
[tex]\frac{19}{4}+\frac{53}{8}=\frac{2*19+53}{8}= \frac{91}{8}\ yd[/tex]
Convert to mixed number
[tex]\frac{91}{8}\ yd= \frac{88}{8}+ \frac{3}{8}= 11\frac{3}{8}\ yd[/tex]
3x^3 - 2y^-6x^2y^2+xy for x=2/3 and y=1/2
To evaluate the expression[tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) for \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\),[/tex]let's substitute these values into the expression:
[tex]\[3\left(\frac{2}{3}\right)^3 - \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 + \frac{2}{3} \times \frac{1}{2}\][/tex]
Let's simplify this step by step.
1. [tex]\(3\left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9}\)[/tex]
2. [tex]\(- \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 = - 2 \times 2^6 \times \frac{1}{3^2} \times \frac{1}{2^2} = - 2 \times 64 \times \frac{1}{9} \times \frac{1}{4} = - \frac{128}{9}\)[/tex]
3 .[tex]\(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\)[/tex]
Now, let's add these results together:
[tex]\[\frac{8}{9} - \frac{128}{9} + \frac{1}{3} = \frac{8 - 128 + 3}{9} = \frac{-117}{9} = -\frac{13}{3}\][/tex]
So, [tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) evaluated at \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\) is \(-\frac{13}{3}\).[/tex]
Please help I'm a little confused!
Eight is less than or equal to the quotient of a number and negative four.
I will have "x" represent the unknown number, or you could use a "?", doesn't matter.
[tex]8\leq \frac{x}{-4}[/tex] [8 is less than or equal to (≤) the quotient (÷) of a number and -4, so the number is being divided by -4]
If you need to solve this, you need to isolate/get the variable "x" by itself in the inequality:
[tex]8\leq \frac{x}{-4}[/tex] Multiply -4 on both sides to get rid of the fraction and get "x" by itself
[tex](-4)8\geq \frac{x}{-4} (-4)[/tex] When you multiply/divide by a negative number, you flip the sign (< >)
-32 ≥ x [-32 is greater than or equal to x, or x is less than or equal to -32]
Which statement describes the graph of f(x) = x² - 6x + 9 ?
a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)
Answer:
About
step 1 highlight numbers
step 2 do ctrl+f
step 3 type in 9
ENJOY
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Step-by-step explanation:
You can buy popcorn at the village theater in small, medium, or large sizes. The popcorn can be buttered or plain. If all of the choices are equally likely, what is the probability that a customer chooses a medium size with butter?Explain how you got your answer.
Answer:
1/6
Step-by-step explanation:
Divide using polynomial long division
(x^2+x-17)/(x-4)
The solution for (x^2+x-17) / (x-4) is (x + 5) + 3/(x-4)
Step-by-step explanation:
The given polynomial is (x^2+x-17) divided by (x-4)
Steps for long division method :
check the polynomial is written in descending order of power (x^3, x^2, and so on).To make the first term zero, multiply the divisor with one power lesser than the first term. For eg. To divide x^2, multiply the divisor with x.Subtract and bring down the next term.The above two steps are repeated until the last term gets divided.The term remaining after the last subtract step is the remainder. The final answer must be written in quotient and remainder as a fraction with the divisor.Using long division method :
x + 5
x-4 | x^2 + x - 17
(-)(x^2 - 4x)
5x - 17
(-)(5x -20)
3
The quotient is (x+5).
The remainder is 3.
The solution is written in the form of quotient + remainder/ divisor
∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3/(x-4)
Final answer:
To divide (x²+x-17) by (x-4) using polynomial long division, divide the highest order term of the dividend by the highest order term of the divisor, multiply the divisor by the result, subtract the result from the dividend, and repeat until there are no more terms or the remainder has lower degree. The quotient is x+5 and the remainder is -3.
Explanation:
To divide (x²+x-17) by (x-4) using polynomial long division:
Write the dividend (x²+x-17) and the divisor (x-4) in the division format.
Divide the highest order term of the dividend (x²) by the highest order term of the divisor (x). The result is x.
Multiply the entire divisor (x-4) by the result from step 2 (x) and write the result below the dividend.
Subtract the result from step 3 from the dividend.
Repeat steps 2-4 until there are no more terms to bring down or the degree of the remainder is less than the degree of the divisor.
The final quotient is x+5 and the remainder is -3.