[tex]\text{Given that,}\\\\x-\dfrac 3x = 7\\\\\\\textbf{i).}\\\\\\x^2 + \dfrac 9{x^2}\\\\\\=x^2 + \left(\dfrac 3 x \right)^2\\\\\\=\left(x- \dfrac 3x \right)^2 + 2 \cdot x \cdot \dfrac 3x\\\\\\=7^2 +6\\\\\\=55[/tex]
[tex]\textbf{ii)}\\\\~~~~~\left(x+\dfrac 3 x \right)^2 = \left( x - \dfrac 3x \right)^2+4 \cdot x \cdot \dfrac 3x\\\\\\\implies \left(x+\dfrac 3 x \right)^2 = 7^2 +12\\\\\\\implies \left(x+\dfrac 3 x \right)^2 =61\\\\\\\implies x+ \dfrac 3x = \pm\sqrt{61}\\\\\\[/tex]
[tex]\textbf{iii)}\\\\\\x^2 -\dfrac 9{x^2}\\\\\\=x^2 - \left(\dfrac 3{x} \right)^2\\\\\\=\left( x-\dfrac 3x \right)\left( x+\dfrac 3x \right)\\\\\\=7\sqrt{61}~~ \text{or}~~ -7\sqrt{61}[/tex]
please please please help me with these four questions! giving brainly!!
Answer:
Step-by-step explanation:
A: y=6n+ 4 When n =5
B: y=45-(9n+7) When n = 2
Answer:
A=34 B=20
Step-by-step explanation:
A: y=6(5)+4 (34)
B: y=45-(9(2)+7)
y= 45-(18+7)
y=45-25 (20)
can i have help with this
Answer:
help
Step-by-step explanation:
with what what is the question
If y varies directly with x and
y=15 when x is 9, what is x when
y=30?
Answer:
x = 18
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 15 when x = 9 , then
15 = 9x ( divide both sides by 9 )
[tex]\frac{15}{9}[/tex] = x , that is
x = [tex]\frac{5}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x ← equation of variation
when y = 30 , then
30 = [tex]\frac{5}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )
90 = 5x ( divide both sides by 5 )
18 = x
9. What is the vertex of the function? f(x) = 3x² - 8x + 10
Answer:
The vertex of the function is (1.333, 4.667)
Step-by-step explanation:
1. Calculate -b / 2a. This is the x-coordinate of the vertex.
2. simply plug -b / 2a into the equation for x and solve for y.
[tex]Y = 3x^{2} - 8x + 10\\Compare with the form of y = ax^{2} + bx + c\\So that means a = 3, b = -8, and c = 10.[/tex]
Calculate -b/2a:
[tex]X = -(-8)/2(3)[/tex]
[tex]X = 8/6[/tex]
This is equal to 1.33 recurring
Plug 8/6 for x and solve for y:
[tex]Y = 3x^{2} - 8x + 10[/tex]
[tex]Y = 3(\frac{8}{6})^{2} - 8(\frac{8}{6}) + 10[/tex]
[tex]Y = \frac{48}{9} - \frac{64}{6} + 10\\[/tex]
This is equal to 4.66 reccuring.
A school has 124 students who want to take a new computer class.
Each class can have a maximum of 18 students. Which inequality could
be used to determine how many classes, c, need to be scheduled so
that all students can take the class?
I need help with this question please-
Answer:
2) -1, 0, 1, 2, 3, 4
3) 78, -2 , 1
Step-by-step explanation:
2) Substitute the x into the equation.
3) Substitute the 9 as the x value into the function so ([tex]9^2[/tex]) -3 = 78 etc.
Evaluate -2x-2y when x = 2 and y=4
A cube with a cylindrical hole cut out of the middle is shown. The edge length of the cube is 36 feet, and the circle on the front face of the cube has a diameter of 4 feet. The volume of this figure is
46204 ft³
Explanation:
Volume of cube: length³ ⇒ 36³ ⇒ 46656 ft³
Volume of cylinder: πr²h ⇒ π(2)²(36) ⇒ 144π ⇒ 452.39 ft³
Volume of the figure: 46656 - 452.15 = 46203.61 ft³ ≈ 46204 ft³
For cube
Volume=side³V=36³V=46656ft³For cylinder
Area of base:-
π(4/2)²3.14(2)²4(3.14)12.56ft²Volume:-
Area of base×Height12.56(36)452.16ft³Volume of figure:-
46656-452.1646203.84ft³A circle with a 2-inch radius is translated a distance of 12 inches perpendicular to the plane it is in. If copies of the circle are left along the path of the translation, what three-dimensional figure is formed, and what equation can be used to represent its volume?
Answer:
See below
Step-by-step explanation:
This will create a cylinder volume = 1/2 pi r^2 h = 1/2 pi 4 * 12
= 24 pi = 75.398 in^3
Answer:
Step-by-step explanation:
1=10^0 into logarithmic form
Answer:
[tex]0 = log_{10} 1[/tex]
Step-by-step explanation:
Base for the exponent and for the logarithm are the same!
10^0 is the exponential form where 10 is the base and 0 the exponent
[tex]log_{10} 1[/tex] is the logarithm form where 10 is the base
To solve [tex]log_{10} 1 =[/tex] ask the question :
To what power should I raise the base 10 to obtain the number 1 ?
The answer to the power 0 therefore
[tex]log_{10} 1 = 0[/tex]
[tex]1 = 10^{0} -is-the- exponential -form\\0 = log_{10} 1 - is -the -logarithmic -form[/tex]
Please help i will give brainly
Answer:
C
Step-by-step explanation:
Multiplying the sequence by 2 gives us the next term. Therefore it has to be the formula a1 x r^n-1. If we substitute the values it would end up as the answer C
Answer:
The correct answer would be option C; 12 x 2ⁿ⁻¹
Step-by-step explanation:
You can check this using any number
since n is the term number we can check it;
let's say we have to find out the answer to the third term number, so we will substitute the n by 3 in the equation from option C and solve
term = 12 x 2ⁿ⁻¹
term = 12 x 2 ³ ⁻¹
term = 12 x 2 ²
term = 12 x 4
term = 48
The term does match the third number in the series given above and hence the equation works!
Hope this helps!
Use the quadratic formula to solve for x.
PLEASE HELP ASAP ON MY MATH!!
Answer:
Area of shaded region=41 square feet
Area of non shaded region= 87 square feet
Step-by-step explanation:
As, Shaded area is made of different shapes including two rectangles and one triangle
So,
Area of shaded region,
[tex]=(8\times2)+(10\times 1)+(\frac{1}{2}\times 3\times10)\\\\ =16+10+15=41 \quad \text{square feet}[/tex]
Area of non shaded region=total area of rectangular region-Shaded region
[tex]=(16\times 8)-(41)\\=128-41\\=87 \quad \text{square feet}[/tex]
Answer:
( 16 × 8 )-40
128 -40
=87 square feet
Manny saves coins in a jar. He counts his dimes and has $16. How many dimes does Manny have?
• 1 hour = 60 minutes
• 1 kilometer = 1000 meters
• 1 mile = 1.6 kilometers
Calvin biked 24 miles in 2 hours. What is his approximate
average speed in meters per minute?
1 mile = 1.6 kilometers so 24*1.6 = 38.4
24 miles = 38.4 kilometers
1 kilometer = 1000 meters so 38.4*1000 = 38,400 meters
38.4 kilometers = 38,400 meters
1 hour = 60 minutes so 2*60 = 120
2 hours = 120 minutes
To calculate meters per minute, divide.
38,400 / 120 = 320
So that means that Calvin's approximate speed is 320 meters per minute.
hello thee please solve my question
Find the value of x and y
If
5x+10y=55
4x-12y=10
Answer:
It is attached
Step-by-step explanation:
What is the volume of a rectangular prism that is 1 1/2 inches by 2 1/4 inches by 4 inches? SHow your reasoning.
Answer:
27/2 in^3 or 13.5 in^3 as a mixed fraction
Step-by-step explanation:
V=whl
Simplify the following:
(1 + 1/2) (2 + 1/4)×4
Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:
(2/2 + 1/2) (2 + 1/4)×4
2/2 + 1/2 = (2 + 1)/2:
((2 + 1)/2) (2 + 1/4)×4
2 + 1 = 3:
3/2 (2 + 1/4)×4
Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:
(3×4)/2 ((4×2)/4 + 1/4)
4×2 = 8:
(3 (8/4 + 1/4)×4)/2
8/4 + 1/4 = (8 + 1)/4:
(3×4)/2 ((8 + 1)/4)
8 + 1 = 9:
3/2×9/4×4
3/2×9/4×4 = (3×9×4)/(2×4):
(3×9×4)/(2×4)
(3×9×4)/(2×4) = 4/4×(3×9)/2 = (3×9)/2:
(3×9)/2
3×9 = 27:
Answer: 27/2 or 13.5 as a mixed fraction
Andy said that any shape with more than three sides or angles has the same number of lines of symmetry. Is this true or false?
Step-by-step explanation:
How do I solve and what is the answer
Answer:
Step-by-step explanation:
the 2nd and 4th answers look good. the 1st answer is correct as well.
To solve this look at the x axis and y axis, the x axis is in inches, the y axis is in pounds. So you know that as the distance increase per inch, the force in pounds is increasing too.
so the force applied is going up, 0.73 pounds , for each inch of travel ( or stretch) of the spring.
A television and DVD player cost a total of $984. The cost of the television is three times the cost of the DVD player. Find the cost of each item
Answer:
Step-by-step explanation:
so the dvd player is 984 dollars so now we multiply it by three and our total would be 2,952
for a sample size of 115 and a population parameter of 0.1, what is the standard error of the sampling distribution? round your answer to three decimal places.
Which of the following statements are true about the given rational equation? check all of the boxes that apply. 4 x 6 1 x2 = x 10 x3 6x2 x = 1 is a solution. x = 0 is a solution. x = –1 is a solution. x = –6 is a solution.
We can actually see that the statements that are true are:
A. x = 1 is a solution.
C. x = –1 is a solution.
What is rational equation?Rational equation is actually known as an equation that contains at least one fraction. The denominator and numerator are known to be polynomials.
We can see then that:
[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{x + 10}{ {x}^{3} + 6 {x}^{2} } [/tex]
It's clear that: x ≠ 0 and x ≠ -6.
Looking for the LCM of the left hand side, we will have:
[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{4 {x}^{2 } + (x + 6)}{(x + 6) {x}^{2} } [/tex]
So, we will see that left hand side and right hand side are equal.
[tex]4 {x}^{2} + x + 6 = x + 10[/tex]
[tex]4 {x}^{2} = 10 - 6[/tex]
[tex]4 {x}^{2} = 4[/tex]
[tex] {x}^{2} = 1[/tex]
[tex] x = 1[/tex]
or
[tex]x = - 1[/tex]
So, we can see that options A and C are correct.
Learn more about rational equation on https://brainly.com/question/11611235
Answer:
-1 and 1 or A and C
Step-by-step explanation:
Heather wrote an inequality that compared the morning temperature, in degrees fahrenheit, of two different cities. Choose all of the inequalities
heather wrote an inequality that compared the morning temperature, in degrees fahrenheit, of two different cities.
choose all of the inequalities that heather could have written.
da.
2-3
b. 2 < -10 c. 4 >-20
d. -5 -3
foy
e. -8 < -15
The inequalities that Heather could have written to compare the temperatures will be:
B. 2 < -10
C. 4 >-20
E. -8 < -15
What is inequality?It should be noted that inequality us the relation between two expressions that aren't equal.
Therefore, the inequalities that Heather could have written to compare the temperatures will be: 2 < -10, 4 >-20,and -8 < -15.
Learn more about inequalities on:
https://brainly.com/question/24372553
factor the polynomial
72a^5b^3c - 32a^3b^2c^2
Answer:
8a³b²c(9a²b - 4c)
Step-by-step explanation:
The GCF of 72 and 32 is 8.
72a^5b^3c - 32a^3b^2c^2 = 8a³b²c(9a²b - 4c)
If you work 40 hours in a week and make $800. How much will you make if
you work 60 hours?
Answer:
1,200
Step-by-step explanation:
Divide 800 by 40
Then take that answer which is 20 and multiply it by 60
Then you get 1,200
50 points
enter the value of c when the expression 21.2x + c is equivalent to 5.3(4x - 2.6).
Answer:
c = -13.78.
Step-by-step explanation:
21.2x + c ≡ 5.3(4x - 2.6)
21.2x + c ≡ 21.2x - 13.78
Equating constant terms:
c = -13.78.
Answer:
13.78
Step-by-step explanation:
21.2x + c = 5.3(4x - 2.6)
open the bracket
21.2x + c = 21.2x - 13.78
collect like terms
c + 13.78 = 21.2x - 21.2x
c + 13.78 = 0
c = -13.78
Which shows the terms of the series? 4 12 48 192 4 12 36 3 12 48 192 3 12 48
The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
What is summation?In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.
Now we have a given term
[tex]\sum_{n=1}^{4} 3(4)^{n-1}[/tex]
By solving the above term;
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}[/tex]
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3[/tex]
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192[/tex]
Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
To know more about Summation follow
https://brainly.com/question/2767605
Answer:
1. 3 + 12 +48 + 192
2. 255 edge
Step-by-step explanation:
What is the rate of change and y intercept
5 is the awsterstdysytghujfhds
3x squared =118. Solve the equation. Round to the nearest hundredth if necessary.
Answer:
3.62
Step-by-step explanation:
118 square rooted is 10.86
10.86/3 = 3.62
Answer:
[tex]x=\pm6.27\: \textsf{(nearest hundredth)}[/tex]
Step-by-step explanation:
Given equation:
[tex]3x^2=118[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x^2}{3}=\dfrac{118}{3}[/tex]
[tex]\implies x^2=\dfrac{118}{3}[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{\dfrac{118}{3}}[/tex]
[tex]\implies x=\pm\sqrt{\dfrac{118}{3}}[/tex]
[tex]\implies x=\pm6.27\: \textsf{(nearest hundredth)}[/tex]