*URGENT ALGEBRA 2* Anyone know these answers? Choices provided. Will award brainliest.
Answers
Question 1. Translate y = 2/x 3 units to the left and 4 units up.
Answer:
2
y = -------- + 4 <------- the fourth option
(x + 3)
Explanation:
1) Given function:
y = f(x) = 2 / x
2) Translatiing 3 units to the left is making f(x + 3), so that implies:
y = 2 / (x + 3)
3) Translating 4 units up is making f(x + 3) + 4, so that implies:
2
y = -------- + 4
(x + 3)
Which is the fourth option.
Question 2. simplify
t^2 + 2t - 24
----------------
t^2 - 36
Answer: fourth option
t - 4
------ , with t ≠ - 6 and t ≠ 6.
t + 6
Explanation:
1) Factor the numerator:
t^2 + 2t - 24 = (t + 6) (t - 4)
2) Factor the denominator:
t^2 - 36 = (t + 6) (t - 6)
3) Rewrite the fraction:
(t + 6) (t - 4)
-------------------
(t + 6) (t - 6)
4) Cancel the factor t + 6 which is in both numerator and denominator, which you can do only y t + 6 ≠ 0 => t ≠ -6.
t - 4
-------
t - 6
That is the simplified expression, with the restrictions that t ≠ - 6 and t ≠ 6, because the denominator cannot be 0.
Question 3. Find the product of:
x^2 + 7x + 10 x^2 - 3x - 18
------------------ * ---------------------
x + 3 x^2 + x - 2
Answer: the fhird option:
(x + 5) (x - 6)
------------------
x - 1
with x ≠ -3, x ≠ - 2, and x ≠ 1.
Explanation:
1) Factor x^2 + 7x + 10
x^2 + 7x + 10 = (x + 5) (x + 2)
2) Factor x^2 - 3x - 18
x^2 - 3x - 18 = (x - 6)(x + 3)
3) Factor x^2 + x - 2
x^2 + x - 2 = (x + 2) (x - 1)
4) Rewrite the given expression using the factors:
(x + 5) (x + 2) (x - 6) (x + 3)
--------------------------------------
(x + 3) (x + 2) (x - 1)
5) Cancel the factors that appear on both the numerator and denominator:
(x + 5) (x - 6)
------------------
x - 1
The restrictions are those values of x that make any factor that is or was in the denominator: x ≠ -3, x ≠ - 2, and x ≠ 1.
Question 4. Simplify the complex fraction:
n - 4
------------------
n^2 - 2n - 15
--------------------------
n + 1
-----------
n + 3
Answer: option 4.
n - 4
------------------
(n - 5) ( n + 3)
Explanation
1) Factor n^2 - 2n - 15
n^2 - 2n - 15 = (n - 5)(n + 3)
2) rewrite the expression:
n - 4
---------------------
(n - 5) ( n + 3)
----------------------------
n + 1
----------
n + 3
3) Convert (n + 1) / (n + 3) into its reciprocal (n + 3) / (n + 1), and multiply instead of dividing.
n - 4 n + 3
--------------------- * --------
(n - 5) ( n + 3) ( n + 1)
4) Cancel n + 3
n - 4
------------------
(n - 5) ( n + 3)
That is the simplest form.
Question 5. Find the difference
Answer: second choice
1 - n
--------
n + 4
Explanation:
1) given:
n^2 + 3n + 2 2n
----------------- - -------
n^2 + 6n + 8 n + 4
2) factor the two quadratic trinomials
n^2 + 3n + 2 = (n + 2) ( n + 1)
n^2 + 6n + 8 = (n + 4) (n + 2)
3) Rewrite the expression:
(n + 2) (n + 1) 2n
----------------------- - -------
(n + 4 ) (n + 2) n + 4
4) cancel the factor n + 2
n + 1 2n
----------- - --------
n + 4 n + 4
5) subract the fractions. They have the same denominator.
n + 1 - 2n 1 - n
--------------- = ----------
n + 4 n + 4
And that is the simples form.
Question 6. Problem
Irina paints 1 room in 9 hours
Paulo paints 1 room in 8 hours
How long working together?
Answer:
x / 9 + x / 8 = 1, x ≈ 4.24 hours
Explanation:
1) In the time x, Irina will paint x / 9 parts of the room
2) Paulo will paint (in the same time) x / 8 parts of the same room
3) The total painted is 1 room.
So the equation is:
x / 9 + x / 8 = 1
4) The solution of that equation is:
[8x + 9x ] / (9*8) = 1
=> 8x + 9x = 72
=> 17x = 72
=> x = 72 / 17
=> x ≈ 4.24 hours
Related Questions
PLEASE FULL ANSWERS! need all the help I can get
Answers
The question is What happens at 4 -- exactly.
The function at x =4 is determined by 2 * x or 2*4 = 8
But look what happens to the top and bottom functions when you get infinitely close to x = 4. You could let x = 3.99999 to see what happens to the top function
g(x) = x - 2 when x is less than 4. So ...
Put in g(3.99999) = x - 2
g(3.99999) = 3.99999 - 2 = 1.99999 which rounds to 2. That's nowheres near 8.
We have already shown that at this point this is going to be discontinuous. 2 does not equal 8. But just for fun, we should try the bottom function
Suppose x = 3.99999 again.
then g(3.99999) = sqrt(3.99999) which is almost 2. there's no way that will work.
You buy a new laptop for
$299.99
$299.99
.
The sales tax is
6%
6%
.
What is the total cost for the laptop including the sales tax?
Answers
[tex]1 + \frac{tax}{100} [/tex]
So in this case we have to multiply by
[tex]1 + \frac{6}{100} = 1.06[/tex]
Therefore the price including tax is
[tex]299.99 \times 1.06 = 317.99[/tex]
Hence, $317.99
HELP!
Jeff volunteers his time by working at an animal shelter. Each year he works for a total of 240 hours. So far this year, he has worked 97 hours. Which equation will solve for how many more hours (h) Jeff will volunteer for?
A) 97 = 240 + h
B) 97 = 240h
C) 240 = 97 + h
D) 240 = 97 - h
A survey asked a group of students to choose their favorite type of sport from the choices of soccer, softball, basketball, and others. The results of the survey are shown in the graph.
Based on the graph, how many students in a class of 84 students would be expected to choose a sport other than soccer, softball, or basketball as their favorite type of sport?
A) 3
B) 12
C) 24
D) 72
You're the banker at HappyBank.com. Identify the two borrowers you would MOST likely offer a loan based on their credit scores.
A) F. Lutts and B. Parker
B) F. Lutts and K. Teller
C) A. Fulbright and K. Teller
D) A. Fulbright and B. Parker
What is the prime factorization of 240?
A) 23 · 3 · 5
B) 23 · 5 · 7
C) 24 · 3 · 5
D) 24 · 3 · 7
Answers
240 = 97 + h
For the second question, there is no graph so I cannot answer it.
3rd question: no image, can't answer.
4th question:
Use a factor tree:
240
/ \
10*24
/\ /\
5*2 *8*3
/ / /\ \
5 * 2 *4*2 *3
/ / /\ \ \
5 * 2 *2*2 * 2 * 3
Starting with the smallest factor and using exponents we have
[tex]2^4*3*5[/tex]
C is the correct choice.
Given that Jeff volunteers his time by working at an animal shelter, and each year he works for a total of 240 hours, and so far this year, he has worked 97 hours, to determine which equation will solve for how many more hours (h ) Jeff will volunteer for, the following calculation must be performed:
240 - 97 = h 240 = 97 + h
Therefore, C is the correct choice.
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I'M OFFERING 10 POINTS (More Than What It's Worth) AND BRAINLIEST ANSWER PLEASE SHOW ALL OF YOUR WORK. Thanks In Advance Guys
Answers
What is the degree of the polynomial a4 + b3 - 2ab + c?
Answers
The variables of the polynomial are:
variable 1: a
variable 2: b
The degree of the polynomial, in this case, is given by the term of the polynomial that has the highest exponent.
We then have the following polynomial:
[tex]a ^ 4 + b ^ 3 - 2ab + c [/tex]
The term with the greatest exponent is:
[tex]a ^ 4 [/tex]
Therefore, the polynomial is of degree 4.
Answer:
The polynomial is of degree 4.
The degree of any given polynomial is said to be the highest power in the exponent of variables given in the polynomial.
For example, quadratic equations like (4x² + 4x + 1) have degree 2.
Here given polynomial is (a⁴ + b³ - 2a·b + c), this polynomial is a multivariable expression.
It is clearly visible that the highest power in the exponent of its variables is 4.
So, the degree of the given polynomial is 4.
which of the binomials below is a factor of this trinomial
5x^2+14x-3
a. x-3
b. x+3
c. 5x+3
d. 5x-3
Answers
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
[tex]5x^2+14x-3[/tex]
As we know "Split the middle term":
[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]
Since it is quadratic equation so, it has 2 roots.
So, the roots are (x+3) and (5x-1).
Hence, Option 'B' is correct.
A histogram is being made for the following list of data. 78, 92, 98, 87, 86, 72, 92, 81, 86, 92 If the length of each interval is going to be 6, how many bars will there be on the histogram? 4 5 6 7
Answers
Therefore, the range is 98-72 = 26
The bars, 26/6
= 4.33
≈ 5 (to accommodate all the values)
Thus the number of bars will be 5.
the greatest common factor of −27x2yz5 + 15x3z3
Answers
−27x2yz5 + 15x3z3
we know that
27-------------> 3³
15-------------> 3*5
z^5-----------> z² * z³
x³------------> x² * x
substituting in the original expression
−27x2yz5 + 15x3z3---------->[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]
[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]-------> [3*x² *z³]*{[-3² *y*z²]+[5*x]}
the greatest common factor is [3*x² *z³]
Rachel invested $15,000 in a nine-year CD giving 8.5% interest, but needed to withdraw $4,000 after two years. If the CD's penalty for withdrawal was six months' worth of interest on the amount withdrawn, how much money did Rachel have when the CD reached maturity, not including the amount she withdrew? Round answer to the nearest whole dollar.
a.
$19,925
b.
$8,795
c.
$19,795
d.
$12,965
Answers
Answer:
Option a ) $19,925
Step-by-step explanation:
$15,000 was invested for 9 years and then $4,000 was withdrawn after 2 years.
So, $11,000 was invested for entire 9 years and $4,000 was invested for 2 years.
Interest on $11,000 for 9 years @ 8.5 % = 11,000 X 9 X 8.5 % = $8,415
Interest on $4,000 for 2 years @ 8.5 % = 4,000 X 2 X 8.5 % = $680
Penalty for withdrawing $4,000 = 4000 X 8.5 % X 0.5 = $170
Total amount that Rachel will get on maturity = $11,000 + total interest - penalty = $11,000 + $8,415 + $680 - $170 = $19,925
Hope it helps.
Thank you !!
Please help me out asap!!! Thanks :)
Answers
Henry lives in Mississippi, which has a sales tax of 7%. He just bought a bed whose full price was $1600, but he got 30% off, because the store was having a sale. What was the total amount that Henry paid?
A.) $1120.00
B.) $1198.40
C.) $1934.40
D.) $1712.00
Answers
Answer:
B.) $1198.40
Step-by-step explanation:
Given,
The original price of the bed = $ 1600,
Since, in sale, he got 30 % off,
The price of bed in sale = The original price of the bed - 30 % of the original price of the bed
[tex]= 1600 - 30\% \text{ of } 1600[/tex]
[tex]=1600-\frac{30\times 1600}{100}[/tex]
[tex]=1600-\frac{48000}{100}[/tex]
[tex]=1600-480=\$ 1120[/tex]
Also, there is a sales tax of 7 % ,
Thus, the final price of the bed = The price of bed in sale + 7 % of the price of bed in sale
[tex]=1120+\frac{7\times 1120}{100}[/tex]
[tex]=1120+\frac{7840}{100}[/tex]
[tex]=1120+78.40=\$1198.40[/tex]
Hence, he paid $ 1198.40.
in y=16500-1500x what is the rate of change
Answers
Final answer:
The rate of change in the linear equation y=16500-1500x is -1500, indicating that y decreases by 1500 for each increase in x by one unit. This represents the slope of the line and shows a direct relationship between x and y in a regression line context.
Explanation:
In the equation y=16500-1500x, the rate of change is represented by the coefficient of x, which is -1500. This means that for each unit increase in x, the value of y decreases by 1500. Contrary to the provided reference which mistakenly lists the slope as -105,000/1, the actual rate of change in this linear equation is -1500. Such linear equations are often used to describe a regression line, which showcases the average relationship between the variables x and y in a scatter diagram.
The slope of a line in a linear equation like this one is crucial for understanding how changes in one variable affect another. This linear model is straightforward and does not change across different values of x, unlike in nonlinear models where the rate of change can vary.
Help I can't find anyone who knows the answer to this! I will fan and medal to the first person who can answer it!
A scientist sets up an experiment to see how colored lights affect the height of plant growth. He grows one group of plants in full sunlight, one group under red lights, one group under blue lights, and one group under green lights. All the plants are exactly that same type and all receive an equal intensity of life. At the end of the experiment he measures all the plants.
What is the independent and dependent variable in this equation?
(A) the color of the light
(B) the height of the plant
(C) sunlight
(D) The intensity of the light
Answers
Dependent variable-the variable that is observed or measured.
Answer:
Independent variable is the color of the light Dependent variable is the height of the plant
Elisa took out payday loan for $500 due in 2 weeks that charged an $80 fee. What is the periodic interest rate of the loan?
Answers
Draw the translation of LM along the vector (4, -5)
Answers
[tex] \binom{0}{ - 2} [/tex]
A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. (a) Write a function representing the rebound height for each bounce. (b) Graph the function. (c) After how many bounces would a new softball rebound less than 1 inch?
f(x) = 25(0.4)x; 6 bounces.
f(x) = 0.4(25)x; 6 bounces.
f(x) = 25(0.4)x; 4 bounces.
f(x) = 0.4(25)x; 4 bounces.
Answers
f(0) be the original height f(0)=25 in
then:
f(x)=f(0)(0.40)^x
since f(0)=25
f(x)=25(0.40)^x
the number of bounces that it will take for rebound to be less than 1 will be:
25(0.4)^x<1
this can be written as:
0.4^x<0.04
introducing natural logs we get:
xln0.4<ln0.04
x(-1.39794)<(-0.39794)
x>(-0.39794)/(-1.39794)
x>3.513~4
A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.
Answers
cos(t)=-15/17
tan(t)=-8/15
sec(t)=-17/15
csc(t)=17/8
cot(t)=-15/8
Point P is on the unit circle U. The values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
Given:
From the given figure, the coordinate of point P is [tex](-\dfrac{15}{17}, \dfrac{8}{17})[/tex].
The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be [tex](x,y)\equiv (cos\theta, sin\theta)[/tex].
By comparing the given coordinate with the general expression, the value sine and cosine function will be,
[tex]sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}[/tex]
Now, the other trigonometric functions will be,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}[/tex]
Therefore, the values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
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If carpet cost$5 per square yard, what would it cost to carpet a room that is 5 yards wide and 22 yards long?
Answers
So it’s 550
solve each equation 2/3 (m - 6)=3
Answers
2/3(m-6)= 3
2/3m-4=3
2/3m= 7
m= 10.5
We can check it.
2/3(10.5-6)= 3
7-4=3
3=3
I hope this helps!
~kaikers
multiply 2 by everything in fraction; keep same denominator for everything in parentheses
(2*m)/3 - (2*6)/3= 3
2m/3 - 12/3= 3
simplify 12/3= 4
2m/3 - 4= 3
Multiply everything by 3 to eliminate fraction
(3)(2m/3) - (3)(4)= (3)(3)
2m - 12= 9
add 12 to both sides
2m= 21
divide both sides by 2
m= 10.5
Check:
2/3(m-6)=3
2/3(10.5-6)= 3
2/3(4.5)= 3
(2*4.5)/3= 3
9/3= 3
3= 3
Hope this helps! :)
The point of intersection of the lines has an e-coordinate of?
Answers
.. y = k -x
.. 2x +3(k -x) = k +1
.. -x +3k = k +1 . . . . . collect terms
.. 2k -1 -x = 0 . . . . . . subtract k+1
.. 2k -1 = x . . . . . . . . .add x
The 3rd selection is appropriate.
HELP PLEASE
Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy. What is Daniel’s annual premium? Use the table. (table in attachment) $611.20 $728.00 $1268.80 $1652.80
Kara, a 25-year-old female, bought a $50,000, 10-year life insurance policy through her employer. Kara is paid semimonthly. How much is deducted from each of her paychecks for life insurance? Use the table below. $4.81 $5.21 $6.25 $6.77
Answers
Answer:
1) Option B- $728
2) Kara's annual premium is $62.5.
Step-by-step explanation:
1) Given : Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy.
To find : What is Daniel's annual premium?
Solution :
In the table given,
Annual premium is per $1000 of coverage.
Daniel's life insurance policy buy is $160,000
Annual premium per $1000 coverage Daniel buy at $160
37 year old male 10 year cost is $4.55
(marked in the attached table below)
Daniel's annual premium is [tex]4.55\times 160[/tex]
[tex]=\frac{455}{100}\times 160[/tex]
[tex]=728[/tex]
Daniel's annual premium is $728
Therefore, Option B is correct.
2) Given : Kara, a 25-year-old female, bought a $50,000, 10-year life insurance policy through her employer. Kara is paid semimonthly.
To find : How much is deducted from each of her paychecks for life insurance?
Solution :
In the table given,
Annual premium is per $1000 of coverage.
Kara's life insurance policy buy is $50,000
Annual premium per $1000 coverage Kara buy at $50
25 year old female 10 year cost is $2.50
(marked in the attached table below)
Kara is paid semimonthly
So, cost is[tex]\frac{2.50}{2}=1.25[/tex]
Kara's annual premium is [tex]1.25\times 50[/tex]
[tex]=\frac{1.25}{100}\times 50[/tex]
[tex]=62.5[/tex]
Kara's annual premium is $62.5.
Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97, how much of his first payment went toward note reduction(reducing principal)? Show your work.
Answers
Answer:
$66.97 is his first payment went toward reduction.
Step-by-step explanation:
Given : Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97.
To find : How much of his first payment went toward note reduction(reducing principal)?
Solution :
First we find the interest of 1 month on a loan of $85,000 at 7.2% interest.
[tex]I=85000\times \frac{7.2}{12\times 100}[/tex]
[tex]I=85000\times 0.006[/tex]
[tex]I=510[/tex]
Interest of 1 month is $510.
Monthly payment = $576.97
Now, first payment or reducing principal is given by
F= monthly payment - interest of 1 month
F=$576.97- $510
F=$66.97
Therefore, $66.97 is his first payment went toward reduction.
I need help fast. Identify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.
Answers
The apothem (a), radius (r), and perimeter (p) of a regular figure are defined as follows: the apothem is the perpendicular distance from the center of the figure to one of its sides, the radius is the distance from the center of the figure to any point on its circumference, and the perimeter is the total length of all its sides.
Explanation:The apothem (a) of a regular figure is the perpendicular distance from the center of the figure to one of its sides.
The radius (r) of a regular figure is the distance from the center of the figure to any point on its circumference.
The perimeter (p) of a regular figure is the total length of all its sides.
The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
Please answer quickly!
Answers
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
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.
In this problem, the changes are given as follows:
Shift down of 5 units, hence y -> y - 5.Shift left of 4 units, hence x -> x + 4.Hence the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
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The equation of the graph \\sqrt[3]{x} shifted down by 5 units and to the left by 4 units is \\sqrt[3]{x + 4} - 5.
Explanation:The transformation of the graph of y = \\sqrt[3]{x} down by 5 units and to the left by 4 units is represented by the function y = \\sqrt[3]{x + 4} - 5. When a graph is shifted to the left by 'a' units, we replace 'x' in the equation with (x + a). Similarly, when a graph is shifted down by 'b' units, we subtract 'b' from the function, resulting in f(x) - b. Therefore, incorporating both transformations into the original function, we get y = \\sqrt[3]{x + 4} - 5.
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PLEASE HELP!!!
The areas of a figure and its transformed image are the same. Which transformation could NOT have been applied to the original figure to create the image?
A. Rotation of 90
B. Reflection across a horizontal line
C. Dilation by a scale factor of 0.5
D. Translation down 4 and then right 1
Answers
The transformation that could NOT have been applied to the original figure to create an image with the same area is:
C. Dilation by a scale factor of 0.5.
To determine which transformation could NOT have been applied to the original figure to create the image with the same area, let's analyze each option:
A. Rotation of 90 degrees: When a figure is rotated by 90 degrees, the area remains the same.
This transformation is possible.
B. Reflection across a horizontal line: A reflection across a horizontal line (a horizontal flip) preserves the area of the figure.
This transformation is possible.
C. Dilation by a scale factor of 0.5: Dilation involves scaling a figure by a certain factor.
If a figure is dilated by a scale factor of 0.5, both its length and width are reduced to half, which means the area is reduced to one-fourth of the original area.
This transformation is not possible because it changes the area.
D. Translation down 4 and then right 1: A translation moves a figure without changing its size or shape. A translation down 4 and then right 1 would not change the area of the figure, as it simply shifts the figure's position.
This transformation is possible.
So, the transformation that could NOT have been applied to the original figure to create an image with the same area is:
C. Dilation by a scale factor of 0.5
Dilation by a scale factor of 0.5 would change the area, making it incompatible with the condition that the areas of the original figure and its image are the same.
For similar question on transformation.
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prove that root 7 is irrational by the method of contradiction
Answers
Let assume that [tex]\sqrt7[/tex] is a rational number. Therefore it can be expressed as a fraction [tex]\dfrac{a}{b}[/tex] where[tex]a,b\in\mathbb{Z}[/tex] and [tex]\text{gcd}(a,b)=1[/tex].
[tex]\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2[/tex]
This means that [tex]a^2[/tex] is divisible by 7, and therefore also [tex]a[/tex] is divisible by 7.
So, [tex]a=7k[/tex] where [tex]k\in\mathbb{Z}[/tex]
[tex](7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2[/tex]
Analogically to [tex]a^2=7b^2[/tex] ------- [tex]b^2[/tex] is divisible by 7 and therefore so is [tex]b[/tex].
But if both numbers [tex]a[/tex] and [tex]b[/tex] are divisible by 7, then [tex]\text{gcd}(a,b)=7[/tex] which contradicts our earlier assumption that [tex]\text{gcd}(a,b)=1[/tex].
Therefore [tex]\sqrt7[/tex] is an irrational number.
Final answer:
To prove that √7 is irrational, we assume the opposite and show that it leads to a contradiction. We start by assuming that √7 is rational and can be expressed as a fraction. By squaring both sides of the equation and simplifying, we get an equation that leads to p and q being divisible by 7, which contradicts our initial assumption. Therefore, √7 must be irrational.
Explanation:
To prove that √7 is irrational using the method of contradiction, we assume the opposite, which is that √7 is rational. This means that it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. We can then square both sides of the equation (√7)² = (p/q)² and simplify to get the equation 7 = p²/q². Rearranging, we have p²= 7q².
From this equation, we can deduce that p² is divisible by 7, which means p must also be divisible by 7. Let's represent p as 7r, where r is another integer. Substituting back into the equation, we get (7r)² = 7q², which simplifies to 49r² = 7q². Dividing both sides by 7, we have 7r² = q². This implies that q² is also divisible by 7, so q must also be divisible by 7.
However, if both p and q are divisible by 7, this contradicts our initial assumption that p/q has no common factors other than 1. Therefore, our assumption that √7 is rational must be false, and hence √7 is irrational.
Match each as a Compound (C) or Element (E)
Cu
HCI
CCI4
Co
HI
CH4
Answers
HCI compound?
CCI4 compound
Co compound ?
HI compound
CH4 compound
For the data in the table, tell whether y varies directly with x . If it does, write an equation for the direct variation
X | Y
________
2 . -6.6
3 . -9.9
4 . -13.2
5 . -16.5
A. yes;y=-1/3x
B. yes;y=x - 3.3
C. no
D. yes; y = –3.3x
Answers
The behavior is linear.
The slope of the line will be:
m = (y2-y1) / (x2-x1)
The equation of the line will be.
y-yo = m (x-xo)
Where,
(xo, yo): Any point in the table.
The equation of the line in this case is:
y = -3.3x
Answer:
D. yes; y = -3.3x
Answer: D. yes; y = –3.3x
Step-by-step explanation:
Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?
A. 1/2
B. -1/2
C. -2
D. 2
Answers
If the slope of line p is 2, then the slope of line q is -1/2.
The correct answer is letter B, -1/2.
Answer:
- 1/2
Step-by-step explanation:
I just did it
[7.07] Choose the correct product of (6x + 2)2.
36x2 − 4
36x2 + 4
36x2 − 24x + 4
36x2 + 24x + 4
Answers
36x^2 + 24x + 4
Explanation:
The perfect square has the following general formula:
(a + b)^2 = a^2 + 2ab + b^2
Now, we will expand the given perfect square based on the above general formula:
(6x + 2)^2 = (6x)^2 + 2(6x*2) + (2)^2
= 36x^2 + 24x + 4
Hope this helps :)