Answers
Answer:
a) 5²/4². b) 4.2²/2.8²
This is your answer ☺️☺️
a. [tex]\frac{5}{4}[/tex]
b. [tex]\frac{3}{2}[/tex] or [tex]1\frac{1}{2}[/tex]
Steps:For a.)Apply radical rule: [tex]\sqrt[n]{\frac{a}{b} } =\frac{\sqrt[n]{a}}{\sqrt[n]{b} }[/tex], assuming [tex]a\geq 0,b\geq 0[/tex]= [tex]\frac{\sqrt{25} }{\sqrt{16} }[/tex][tex]\sqrt{16}=4[/tex]
[tex]\frac{\sqrt{25} }{4}[/tex]
[tex]\sqrt{25} =5[/tex]
[tex]=\frac{5}{4}[/tex]
For b.)[tex]\frac{\sqrt{18} }{\sqrt{8} }[/tex]Apply radical rule: [tex]\frac{\sqrt{a} }{\sqrt{b} } =\sqrt{\frac{a}{b} }[/tex]Which means[tex]\frac{\sqrt{18} }{\sqrt{8} }=\sqrt{\frac{18}{8} }[/tex][tex]=\sqrt{\frac{18}{8} }[/tex]
2. Cancel [tex]\frac{18}{8}[/tex]: [tex]\frac{9}{4}[/tex]
= [tex]\sqrt{\frac{9}{4} }[/tex]
Now apply the radical rule: [tex]\sqrt[n]{\frac{a}{b} } =\frac{\sqrt[n]{a} }{\sqrt[n]{b} }[/tex] assuming [tex]a\geq 0,b\geq 0[/tex]
= [tex]\frac{\sqrt{9} }{\sqrt{4} }[/tex][tex]\sqrt{4}=2[/tex]
[tex]=\frac{\sqrt{9} }{2}[/tex]
[tex]\sqrt{9}=3[/tex]
The final answer for b.) should be [tex]\frac{3}{2}[/tex]
Related Questions
Please help!
(Vieta's Formulas) Let [tex]r[/tex], [tex]s[/tex], and [tex]t[/tex] be solutions to the equation [tex]$2x^3 - 3x^2 + 4x - 1 = 0$[/tex]. Find [tex]$r^2+s^2+t^2$[/tex].
Please include an explanation as well :)
Answers
We are given the polynomial:
2x³ - 3x² + 4x - 1 = 0
We need to find the value of r² + s² + t² where r,s,t are the solutions.
Simplifying r² + s² + t²:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
[since a²+b²+c² = (a+b+c)² - 2(ab + bc + ca)]
Using the Vieta's formulae:
Above, we can see that in order to find the value of r² + s² + t², we need to find the value of the sum of solutions and sum of solutions taken 2 at a time.
Sum of roots:
We know that the Vieta's formula to find the sum of roots is:
Sum of roots = [tex]-\frac{b}{a}[/tex]
Where b and a are the coefficients from the general form: ax³ + bx² + cx - d
We notice that for the given equation, b = -3 ; a = 2
Sum of roots = [tex]-(\frac{-3}{2})[/tex]
Sum of roots = [tex]\frac{3}{2}[/tex]
Hence, the sum of roots (r + s + t) = 3/2
Sum of roots taken two at a time:
We know that the Vieta's formula to find the sum of roots taken 2 at a time is: Sum of roots taken 2 at a time = [tex]\frac{c}{a}[/tex]
Where c and a are the coefficients from the general form: ax³ + bx² + cx - d
for the given equation, c = 4 ; a = 2
Sum of roots taken 2 at a time = [tex]\frac{4}{2}[/tex]
Sum of roots taken 2 at a time = 2
Hence, the sum of roots taken 2 at a time (rs + st + rt) = 2
Finding the value of r² + s² + t²:
We proved before that:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
now that we know the values of (r + s + t) and (rs + st + rt), we can plug those values to get our answer
r² + s² + t² = ([tex]\frac{3}{2}[/tex])² - 2(2)
r² + s² + t² = ([tex]\frac{9}{4\\}[/tex]) - 4
r² + s² + t² = [tex]\frac{9 - 16}{4\\}[/tex]
r² + s² + t² = [tex]\frac{-7}{4}[/tex] = -1.75
Hence, the value of r² + s² + t² is -1.75
Solve the system.
y = 3x + 1
-x + 2y = -3
Answers
-3, -3
,........... .......
The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true?
A. The sum of the areas of Square N and Square L is equal to the area of Square K.
B. The sum of the areas of Square N and Square L is greater than the area of Square K.
C. The sum of the areas of Square N and Square K is equal to the area of Square L.
D. The sum of the areas of Square N and Square K is less than the area of Square L.
Answers
Answer: C
Step-by-step explanation: Because I said soooaiahi
Joey earns a weekly salary of $325 plus a commission on his total sales. Last week his sales were $2950, and he earned a total of $915. What was his commission rate?
Answers
Answer:
Commission rate is 20%.
Step-by-step explanation:
Joey's weekly salary is $325
Plus a commission on his total sales.
Let commission is x% on his total sales.
So, we can set up equation for the given information as
325+x%(2950)= 915
Solve this equation for x%.
Subtract both sides 325
x%(2950) =590
Divide both sides by 2950
x%=0.2
We know x% means it is [tex]\frac{x}{100}[/tex]
So, [tex]\frac{x}{100} =0.2[/tex]
Multiply both sides by 100
x=20%.
So, commission rate is 20%
A bookcase is to have 5 shelves including the top. The height of the bookcase is to be 3 feet more than the width and only 20 feet of lumber is available. Use an equation to determine the width and height of the bookcase?
Answers
Answer:
The width and height is 1.375 and 4.375 respectively
Step-by-step explanation:
The computation of the width and height of the book case is shown below:
Let the width be w
And, the height be h
So, the following equations should be made
5w+3h=20 ......(i)
h = w + 3......(2)
Now
put the value of h in equation (1)
5w + 3(w + 3) = 20
5w + 3w + 9 = 20
8w = 20-9
8w = 11
w = 11 ÷ 8
= 1.375
And, the height would be
= 1.375 + 3
= 4.375
-2.5 x 3 = with shown work pls
Answers
Answer:
7.5
Step-by-step explanation:
-2.5 x 3 = 7.5
Answer:-7.5
Step-by-step explanation:
(−2.5)(3)
=−7.5
I need this answer ASAP! Please help!
A ladder is leaning against a building. The ladder forms an angle of 77° with the ground. The distance from the base of the ladder to the base of the building is 8 feet.
Answers
Answer:
Step-by-step explanation:
sin77=h/8
h=8sin77
h=8(0.9744)
h=7.7952ft
How do you solve for x in the equation (2x - 3)/5 = (x + 1)/6?
Answers
Answer:
x= 23 /7
Step-by-step explanation:
Explaination:
(2x-3)/5=(x+1)/6 -> add 3 on both sides
2x /5=(x+4)/6 -> subtract x from both sides
x/5=4/6 -> divide 4 by 6
x/5= 2/3 -> multiply by 5 on both sides
x= 10/3 ~ 3.33333
Does the rule y = −2 · 2x represent a linear or an exponential function?
Exponential
Answers
Write the equation of the line shown on the graph in slope-intercept form.
Remember Slope-Intercept Form is y=mx+b
Answers
Answer:
[tex]y = x -3[/tex]
Step-by-step explanation:
1) First, find the slope by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. We can see that the two points marked on the line are (0, -3) and (3,0). So, substitute the x and y values of those points into the formula and solve:
[tex]m = \frac{(0)-(-3)}{(3)-(0)} \\m = \frac{0+3}{3-0} \\m = \frac{3}{3} \\m=1[/tex]
So, the slope is 1.
2) Slope-intercept form is represented by the formula [tex]y = mx+b[/tex]. Substitute values for [tex]m[/tex] and [tex]b[/tex] in order to write an equation.
Substitute 1 for [tex]m[/tex] since it represents the slope. Substitute -3 for [tex]b[/tex] since it represents the y-intercept. (Remember that the y-intercept is the point at which the line intersects the y-axis. So, by looking at the graph provided, we can see that (0,-3) is the y-intercept without doing any calculations.) This gives the following answer:
[tex]y = x -3[/tex]
If x=−5, what is the value of 7−x(2x+1)?
Answers
Answjnweijfbiqwerf
Step-by-step explanation:
Can someone please help????
Answers
Answer:
your answer is the third one
Step-by-step explanation:
Answer:
its 4
Step-by-step explanation:
What is 2x+7y=28 in slope intercept form
Answers
Answer:
y = -2/7x + 4
25 POINTS IF YOU ANSWER THIS AND PLEASE TELL ME WHAT K IS!!
Answers
9514 1404 393
Answer:
k = 2
Step-by-step explanation:
Find a coordinate of a point and its image. k is the ratio of those.
Here, it is easy to use the y-coordinate of J and J'.
Jy = -1
J'y = -2
k = J'y/Jy = -2/-1 = 2
The scale factor k is 2.
A polygon on a coordinate grid was transformed using the rule (x,y) -> (x-4,y-3). Which of these describes this transformation?
A: a translation 4 units to the left and 3 units down
B: a translation 4 units to the right and 3 units down
C: a translation 4 units to the left and 3 units up
D: a translation 4 units to the right and 3 units up
Answers
Explanation:
someone please help me ASAP!!!!!!!
Answers
Answer:
the change in x is 1, the change in y is 4, the slope is 1/4
Step-by-step explanation:
the time increases by one minutes as the temperature increases by 4 degrees. therefore, every one minutes the temperature increases by four degrees. 1/4
Answer:
1, 4 and 4
Step-by-step explanation:
x = 10-9 = 1
y = 64-60 = 4
Rate of change = temperture / time
= 4/1
= 4.
x
4
4x + 10x+4
a (2n+1)
Answers
Answer:
1st =14x+4
2nd =2an+a
Step-by-step explanation:
1st Let's simplify step-by-step.
4x+10x+4
Combine Like Terms:
=4x+10x+4
=(4x+10x)+(4)
=14x+4
2nd
a(2n+1)
=(a)(2n+1)
=(a)(2n)+(a)(1)
=2an+a
Hope this helps :)
PLS BRAINLIEST
The mean heigh of American Males is 69.5 inches. The height of the 43 male presidents have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the 43 presidents as a simple random sample, determine if there is evidence to suggest that the US presidents are taller than the average American male. Use the a= 0.05 level of significance.
Answers
Answer:
There is sufficient statistical evidence to suggest that the US presidents are taller than the average American male
Step-by-step explanation:
The given parameters are;
The mean height of American Males, μ = 69.5 inches
The mean height of 43 male presidents, [tex]\overline x[/tex] = 70.78
The standard deviation, s = 2.77 inches
The number of male presidents = 43
The null hypothesis; H₀ μ = [tex]\overline x[/tex]
The alternative hypothesis; Hₐ μ ≠ [tex]\overline x[/tex]
The significance level, α = 0.05
The t test for the sample with unknown population standard deviation is given as follows;
[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{70.78-69.5 }{\dfrac{2.77 }{\sqrt{43}}} \approx 3.0302[/tex]
The degrees of freedom, df = n - 1 = 43 - 1 = 42
The critical 't' value = 2.0181
Therefore, given that the t test value is larger than the critical-t, we reject the null hypothesis, therefore, there is sufficient statistical evidence to suggest that the US presidents are taller than the average American male
what is the surface area of this rectangle prison of 6 9 4
Answers
Answer:
You need to be specific on which is the length, height and width. Making the most basic assumption I would have to assume the answer is 228
Step-by-step explanation:
Formula for the surface area of a rectangular prism is A=2(wl+hl+hw)
A = 2 x (9 x 6 + 4 x 6 + 4 x 9)
A = 2 x (54 + 24 + 36)
A = 2 (114)
A = 228
WILL GIVE BRAINLIEST!
Two angles of a triangle measure 45° and 87°. Find the measure of the third angle, in degrees. (Enter an exact number.)
°
Answers
Answer:
48
Step-by-step explanation:
All the angles of a triangle add up to 180
180-45-87=48
Hope this helps! If it did, please mark it brainliest!
P.S. Make sure not to fall for the link scams ;)
What is the slope of the equation: y = - 5x -6
Answers
Answer:
-5
Step-by-step explanation:
The slope is always the coefficient of x, and the coefficient of x here is negative 5.
Please help and show your work!!
Factor the following
[tex]3x^{2} -4x-7[/tex]
Answers
Answer:
[tex] \sf \huge \boxed{ \boxed{(3x - 7)(x + 1)}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:factoringPEMDASlet's solve:[tex] \sf \: rewrite \: - 4x \: as \: 3x - 7 x: \\ \sf {3x}^{2} + 3x - 7x - 7[/tex][tex] \sf factor \: out \: 3x: \\ \sf3x( x + 1) - 7x - 7[/tex][tex] \sf factor \: out \: - 7: \\ \sf3x( x + 1) - 7(x + 1)[/tex][tex] \sf \: group : \\ (3x - 7)(x + 1)[/tex]and we are done!
Explanation:
1.) Use the sum-pruduct pattern
3x^2-4x-7
3x^2+3x-7x -7
Common factor from two pairs
3x^2 +3x-7x-7
3x(x+1) - 7(x+1
Rewrite in factored form
3x(x+1) - 7(x+1)
(3x-7) (x+1)
Answer:
(3x-7)(x+1) I know we both have the same answer18x^2-8=0 I have to factor it but I’m not sure how to! Please help!
Answers
Answer:
hope it helps...........
Answer:
[tex]x=-2/3, 2/3[/tex]
Step-by-step explanation:
Kareem received $50 during his birthday. In addition, he saves $10 each week. Which equation can help find w, the number of weeks it will take Kareem to save a total of $200?
Answers
then to solve-
subtract 50 from both sides so now it’s 10w=150
then divide the 10 from both sides to get w alone
and you should get w=15
Answer: 50+10w=200 w=15
Step-by-step explanation:
So we know that Kareem starts off with $50 and every week he gains an additional $10 so as many weeks it takes to get $150 in addition to the $50 he already has to get $200. so $50+$10w=$200 where w represents the number of weeks it takes until the sum is 200
81^5 = 3x pls help edg 2021
Answers
Answer:
if you have a calculator...
Step-by-step explanation:
take 85 to the 5th power and then divide that by 3.
Answer:
20
Step-by-step explanation:
correct on edge
An advertising company is curious about the impact the lengths of their television advertisements have on viewers' feelings about a product. They showed advertisements of different lengths to a group of volunteers and asked the volunteers to rate how positive they felt about the product on a scale of 111 to 101010. Their data is shown in the table below.
Avg. product rating/ 6.0/ 7.0/ 5.0/ 3.0/ 2.5
Ad length (seconds) 30/ 45/ 60/ 75/ 90
Answers
Answer:
Graph C
Step-by-step explanation:
Khan Academy
The correct graph that represents the given data effectively would be:
Graph C
The given data offers the average ratings of the product and the length of their advertisements in seconds.The third graph most effectively shows the data as it contains provided variables on the appropriate axis i.e. ad length on the x-axis and the average rating on the y-axis. The other graphs fail to represent the explanatory variable and the other variable effectively.Thus, 'graph C' in the scatter plot format is the correct answer.
Learn more about "Data" here:
brainly.com/question/16348111
At a party, James notices that 15 pitchers of lemonade are filled to the same level, but not to the top. He combines all the lemonade to fill six whole pitchers. What fraction of each of the 15 pitchers was full?
Answers
Answer:
1/6th of them
Step-by-step explanation:
If m = (3x-1) and n = (3x+1),sjow that x² = mn+1 by 9
Answers
Step-by-step explanation:
[tex] {x}^{2} = \frac{mn + 1}{9} [/tex]
[tex](3x - 1)(3x + 1)[/tex]
[tex]9 {x}^{2} - 1[/tex]
[tex] {x}^{2} = \frac{9 {x}^{2 } - 1 + 1 } {9} [/tex]
[tex] {x}^{2} = \frac{9 {x}^{2} }{9} [/tex]
[tex] {x}^{2} = {x}^{2} [/tex]
So this identity is true.
Consuelo won the lottery. He can receive $100,000 or $3 on day 1, $9 on day 2, $27 on day 3... etc for 30 days. Which option will give Consuelo the most money?
how would I solve this? I'm not sure what to do on this question, don't give me the answer, just kinda tell me what to do
Answers
Answer:
ordü use uuuuuv bûsh!!!!!!!!!!
Evaluate using P E M D A S 2 x 3 + 4
Answers
Step-by-step explanation:
We would do multiplication first, because of order of operations.
2x3=6
Now we add.
6+4=10
hope it helps! :3
Then 6+4
Equals =10