Solve each equation. Identify the solutions as rational or irrational numbers.
Answers
[tex]\textbf{a)}\\\\~~~~~~~x(3x-4)=5\\\\\implies 3x^2 -4x = 5\\\\\implies 3x^2 -4x=5\\\\\implies x^2 - \dfrac 43 x = \dfrac 53\\ \\\implies x^2 - 2\cdot \dfrac 23 \cdot x + \left( \dfrac 23 \right)^2 - \left( \dfrac 23 \right)^2 = \dfrac 53\\\\\implies \left(x-\dfrac 23 \right)^2 = \dfrac 53 + \dfrac 49\\\\\implies \left(x-\dfrac 23 \right)^2= \dfrac{19}{9}\\\\\implies x- \dfrac 23 = \pm\dfrac{\sqrt{19}}3\\\\\implies x=\dfrac 23 \pm\dfrac{\sqrt{19}}3\\\\[/tex]
[tex]\text{The solutions are irrational.}\\\\\\\textbf{b)}\\\\~~~~~~~(3x-2)^2 = \dfrac 14\\\\\implies 3x -2 = \pm \dfrac 12\\\\\implies 3x = 2\pm \dfrac 12\\\\\implies x = \dfrac 23 \pm \dfrac 16\\\\ \implies x = \dfrac 56 ,~~ x =\dfrac 12 \\ \\\text{The solutions are rational .}[/tex]
Related Questions
Just answer the question RN im in a rush
Answers
Answer:
https://brainly.com/question/27407610
Step-by-step explanation:
Find the GCF of 60, 96, and 156.
Answers
Answer:
GCF = 12
for the values 60, 96, 156
Step-by-step explanation:
Solution by Factorization:
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
Then the greatest common factor is 12.
pls explain why and how the answer u got is proportional
Answers
Answer:
A
Step-by-step explanation:
This is because to find out if a table is proportional you have to do y divided by x. Whatever table has the same answer on all of the table sections when you divide y by x, that is proportional.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**
Answers
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z.
How to apply logarithms on a exponential function
Logarithms are the reciprocal of exponential functions. In this question we must apply logarithms and its properties to obtain a linear-like expression in the following lines. The logarithm properties are summarized below:
㏒ₐ (b/c) = ㏒ₐ b - ㏒ₐ c (1)
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c (2)
㏒ₐ bⁿ = n · ㏒ₐ b (3)
a) To obtain the corresponding logarithmic function we apply logarithms on both sides of the expression:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶ (4)
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. [tex]\blacksquare[/tex]
b) The expanded logaritmic form of (4) consists in the addition and subtraction of logarithms of non-power numbers, whose formed could be found, if possible, by logarithm properties:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶
㏒ 12³ = ㏒ x⁴ + ㏒ y³ + ㏒ z⁶
3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z
The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z. [tex]\blacksquare[/tex]
To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/24211708
GIVING BRAINLIEST TO THE PERSON THAT CAN EXPLAIN THIS THE BEST (:
Answers
Answer:
25π-24
Step-by-step explanation:
from the figure,
radius of the circle(r)=diameter of the circle(d)/2
=10/2
=5
Area of the circle(A)=πr^2
=π5^2
=25π
Again,
base of the right angle triangle(b)=6
perpendicular of right angle triangle(p)=8
we also know,
the area of right angle triangle = 1/2*base*height
=1/2*6*8
=1/2*48
=48/2
=24
Now, Area of the shaded region=Area of circle - Area of right angle triangle (given in the figure)
Area of shaded region= 25π -24
Find the slant height?
Answers
Answer:
59.94
Step-by-step explanation:
Slant height = √(height)² + (1/2 base)²
Sh = √53² + 28²Sh = √2809 + 784Sh = 59.94In this figure, 12.2% of the area is painted blue.
How much of the area is painted blue?
1.22 cm²
3.05 cm²
4.27 cm²
5.49 cm²
Answers
The area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
What is the Area of a Triangle and Square?Area of triangle = 1/2(b)(h)Area of Square = s²The figure is composed of a triangle and a square. Find the area of the figure.
Area of the figure = 1/2(b)(h) + s² = 1/2(5)(4) + 5² = 35 cm²
12.2% of the area of the figure = 12.2/100 × 35 = 4.27 cm²
Therefore, the area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
Learn more about area of square and triangle on:
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Calculate the perimeter of the triangle
below.
24cm
32cm
Answers
So, s = 16.
One side is 15.
Let the second side be x.
So, the third side = 32 - 15 - x = 17 - x.
Area = 24 cm^2
So, 24^2 = s(s - 15)(s - x)(s - 17 + x)
So, 576 = 16(16 - 15)(16 - x)(16 - 17 + x)
So, 576 = 16*1(16 - x)( - 1 + x)
So, 576/16 = (16 - x)( - 1 + x)
So, 36 = - 16 + 17x - x^2
So, x^2 - 17x + 52 = 0
So, (x - 13)(x - 4) = 0
So, x = 13 or x = 4
So, the lengths of the remaining two sides are 4 cm and 13 cm.
how many days are in 3 weeks??
Answers
Answer:
21
Step-by-step explanation:
because 7 day or in a week so 7 time 3 = 21
Answer:
21
Step-by-step explanation:
Becasue there are 7 days in a week, So use and time 7x3 and you will get 21 multiplication.
During geometry class, students are told that δtsr ≅ δusv. marcus states that δtsr is mapped to δusv by performing a rotation about point s. sam states that δtsr is mapped to δusv by a reflection across the line that goes through point s. determine if either student is correct. marcus is correct. sam is correct. both students are correct. neither student is correct.
Answers
Transformation involves changing the position of a shape through translation, dilation, rotation and reflection.Marcus's claim is correct.
What is transformation?A process by which one figure, expression, or function is converted into another one of similar value.
The triangles are given as: ΔTSR and ΔUSV
By comparison, we can see that point S is on both triangles, and this point on both triangles corresponds.
So, to map ΔTSR to ΔUSV, then ΔTSR must be rotated about point S to ΔUSV or rotate ΔUSV about point S to ΔTSR.
Hence, Marcus is correct, and Sam is not.
Read more about transformation at:
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Answer:
A. Marcus is correct.
Credits to the guy above! :))
A bag contains 4 red, 4 blue, 4green, and 4 yellow marbles. A marbles is randomly pulled from the bag and replaced seven times. The table shows the outcome of the experiment. Which marble color’s observed frequency is closest to its expected frequency?
Answers
Answer:i think that there would not be a frequency because their is an equal chance of anycolr being pulled
Step-by-step explanation:
please get this righttt!
Answers
Answer:
5/9
Step-by-step explanation:
this is the answer kinda not explainable so yeah
Put the following items in order from most expensive to least expensive. item base price change direction blender $29.73 9% markdown hat $14.16 77% markup ink $20.17 27% markup heater $28.46 22% markdown a. blender, heater, ink, hat b. blender, ink, hat, heater c. ink, hat, blender, heater d. ink, heater, blender, hat please select the best answer from the choices provided a b c d
Answers
Leonard runs a pet-sitting service. He charges $20 per day, which includes three walks and two feedings. He charges $5 for each extra walk. Which expression describes how much Leonard would charge for a single day of pet sitting with w extra walks?
Answers
y = 5w +20
its 5$ for every walk.
No matter what, it starts at 20 so that is our Y intercept.
Therefore, we make the eqaution using what we know.
y = 5w + 20
340 to nearest hundred
Answers
Answer:
300 - hope this helped :)
Step-by-step explanation:
340 to the nearest hundred
is 300 since thats the closest
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). which represents g(x)? g(x) = (x 9)2 4 g(x) = (x 9)2 − 4 g(x) = (x − 4)2 9 g(x) = (x 4)2 9
Answers
A function assigns values of one set to another. The function that will represent g(x) is g(x)=(x-4)²+9.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As it is given to us that we need to move the graph of the function 9 units up and 4 units towards the right. Therefore, the function that will represent the new location of the graph can be written as,
[tex]g(x) = (x-4)^2+9[/tex]
Hence, the function that will represent g(x) is g(x)=(x-4)²+9.
Learn more about Function:
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Answer:
Option C. g(x) = (x - 4)² + 9
Step-by-step explanation:
The given function is f(x) = x². Following transformations have been done to get the new function as followed
for 9 units up
The parent function f(x) will become as g(x) = x² + 9
then 4 units shifted to the right
Then the new function becomes g(x) = (x - 4)² + 9
A space ship travels at 8 2 miles per hour and traveled for 81 8 hours.
Select the answer that represents how many miles the space ship traveled.
Answers
Answer:
D
Step-by-step explanation:
8^2 m/hr * 8^18 hr = 8^(2+18) = 8^20 miles
What is the completely factored form of the expression 16x2 8x 32? 4(4x2 2x 8) 4(12x2 4x 28) 8(2x2 x 4) 8x(8x2 x 24)
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The factored form of the expression 16x²+8x+32 is 8(2x²+x+4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The completely factored form of the expression can be written as,
[tex]16x^2+8x+32\\\\=8(2x^2+x+4)[/tex]
Thus, the factored form of the expression 16x²+8x+32 is 8(2x²+x+4).
Learn more about Expression:
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What is the common denominator of 2/5 and 3/10
Answers
Answer:
Answer:
10
Step-by-step explanation:
3/10~3/10
2/5
5x2=10
2x2=4
2/5=4/*10*
write 0.004 as a fraction in words.
Answers
Step-by-step explanation:
0.004 as a fraction is 1/250
one over two hundred and fifty
Answer:
one over Two hundred and fifty
Step-by-step explanation:
As we can see the 4 is 2 zeros away from the decimal point. This means that 4 must be in the thousandths place.
Therefore our answer is four thousandths.
Remember that we it is behind the decimal point, it becomes ths at the end.
To change this into a fraction we should get 4/1000 by taking the words literally.
Dividing both sides by 4 gives us 1/250
1/250 in words is one over Two hundred and fifty
I guess
Brainliest if helped
How many outfits can be made from five shirts three pairs of pants and two pairs of shoes?
Answers
Answer:
3*5*2=30
He can make 30 outfits.
Step-by-step explanation:
3*5*2=30
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By what factor were the dimensions of the pentagon multiplied?
12. 5
625
5
50
Answers
5
reason is because if you’re pentagon has lines of 5 then the area would be 25
4x^2- 4x-1=0 i need the awnser
Answers
Answer:
See below
Step-by-step explanation:
Do you know how to use the Quadratic Formula with
a = 4 b = -4 c = -1
results in x = 1/2 +- sqrt(2) / 2
PLEASE HELP URGENT
Maggie is walking her dog. She walks 2/3 mile in 7/10 of an hour. At this same rate, what distances can she walk? Select all that apply.
5/7 mile in 3/4 of an hour
7/10 mike in 2/3 of an hour
10/3 miles in 1 1/2 hours
32/21 miles in 1 3/5 hours
5/3 mikes in 1 9/10 hours
Answers
We want to find the mile per hour rate (mi/hr).
That is 2/3 divided by 7/10
Which is 2/3 times 10/7
Numerator is 20
Denominator is 21
So 20/21 miles per hour. .95238009…
Convert each answer (flipping the second fraction since it is division)
5/7 times 4/3 is 20/21
7/10 times 3/2 is 21/20
10/3 divided by 1.5 hours which is 3/2.
So 10/3 times 2/3 is 20/9
32/21 divided by 1 3/5 hours which is 5/5 plus 3/5 (add to get 8/5)
So 32/21 times 5/8 is 160/168
5/3 times 10/9 is 50/27
In order of answers
20/21
21/20
20/9
160/168
50/27
Original was 20/21 which is less than 1 (21/21)
So yes to 20/21
So no to 21/20, 20/9, 50/27
To see if 160/168 works simplify.
160/168 gives 80/84 gives 40/42 gives 20/21 when dividing by 2.
So 160/168 works.
So yes to
5/7 mile in 3/4 of an hour
32/21 miles in 1 3/5 hours
So no to
7/10 mile in 2/3 of an hour
10/3 miles in 1 1/2 hours
5/3 miles in 1 9/10 hours
Please mark as the best!
A rectangle has vertices (–1, 1), (–4, 1), (–1, 3), and (–4, 3). If the rectangle is reflected over the y-axis, what algebraic rule can be used to find each of the new vertices?
Select one:
A. (x,y)→(−x,−y)
B. (x,y)→(–y,–x)
C. (x,y)→(y,−x)
D. (x,y)→(−x,y)
Answers
Answer:
D. (x,y)→(−x,y)
Step-by-step explanation:
Reflecting OVER the Y axis means it will end up on the other side of the Y axis line. The Y coordinates remain unchanged while the X coordinates invert. Attaching a crude diagram to help you picture it.
Can anyone help me with my homework
Answers
Answer:
Below in bold.
Step-by-step explanation:
When x = -3, y = -(-3) - 2 = 3-2 = 1.
When x = 0, y = -0 - 2 = -2.
When x = 4, y = -4 - 2 = -6.
To draw the graph plot the 3 points and you should be able to draw a straight line through them.
Answer:
The first y value with -3, is 1.
The second y value with 0, is -2.
The third y value with 4, is -6.
A graph is shown below.
Step-by-step explanation:
It states that the rule is y = -x-2. So all we do is plug in the values shown in the table.
y = -(-3)-2
y = 1
The first point of intersection is at (-3,1)
y = -(0)-2
y = -2
The second point of intersection is at (0,-2)
y = -(4)-2
y = -6
The third point of intersection is at (4,-6)
So now, we plot the points, and draw a line connecting them all.
A perfect square is a number that is the square of a whole number. For example, 25 is a perfect square because it is the square of 5: 5 × 5 = 25. How many perfect squares are greater than 0 but less than 1000?
Answers
Perfect squares are squares of integers and since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000
What are perfect squares?A perfect square is a number that is the square of a whole number. For instance, 36 is a perfect square being the square of 6.
Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324... 961.
Since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000.
Learn more on perfect square here: https://brainly.com/question/26119721
Answer:
Since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000.
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Answers
An angle on a straight line is 180 degrees
⇒ this angel is made up of two angles with measures
⇒ 'x-7' and '57'
⇒ when these two angles are added up they are equal to the larger
angle that is 180 degrees in measure
Let's set up a mathematical equation based on the information and deduction:
[tex](x-7)+57=180\\x-7+57 = 180\\x + 50=180\\x = 130[/tex]
Answer: The value of x is 130
Hope that helps!
The baseball team in your community is playing for the championship. They will play seven games against the opposing team.
a. If the probability for your team to win is 74%, what is the probability for the other team to win?
b. Is this a binomial distribution? Why or why not?
c. What is the probability that your team will win 4 of the 7 games?
Answers
Answer:
a. 26%
b. It's a binomial distribution because the competition will only have two outcomes, win or lose.
c. 4/7 or 57%
Step-by-step explanation:
Hope this helps :)
For problem 8, find the area of the shaded region. The polygon is a regular polygon. please show work.
Answers
Answer:
34.7791 [unit²].
Step-by-step explanation:
1) area of the circle is:
πr²;
2) area of the regular polygon is:
6*r²√3*0.25=1.5√3r²;
3) the required area:
πr²-1.5√3r²=r²(π-1.5*√3)=64*(3.1415-1.5*1.7321)=34.7791