An expression when written in either radical form or rational exponent form be rewritten to fit the other form as well.
When we write in different forms the Denominator defines as the Index and the Numerator defines as Power on the variable.
For Example:-We can write [tex]4^{\frac{2}{3}[/tex] as [tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]
Again, vice versa,
For example:-We can write [tex]\sqrt[5]{x^4}[/tex] as [tex]x^{\frac{4}{5}[/tex]
Therefore , we can written in other forms as well to fit .
Learn more about Numerator and Denominator here : https://brainly.com/question/10667435
To convert from radical form to rational exponent form, use [tex]\( \sqrt[n]{a} = a^{1/n} \),[/tex] and vice versa for conversion.
An expression written in radical form can be rewritten in rational exponent form and vice versa using the following conversions:
1. From Radical Form to Rational Exponent Form:
- For a radical expression [tex]\( \sqrt[n]{a} \), where \( n \)[/tex] is the index and [tex]\( a \)[/tex] is the radicand:
- The equivalent expression in rational exponent form is [tex]\( a^{1/n} \)[/tex].
2. From Rational Exponent Form to Radical Form:
- For an expression [tex]\( a^{m/n} \)[/tex], where [tex]\( a \)[/tex] is the base, [tex]\( m \)[/tex] is the numerator, and [tex]\( n \)[/tex] is the denominator:
- The equivalent expression in radical form is [tex]\( \sqrt[n]{a^m} \).[/tex]
These conversions allow us to switch between radical form and rational exponent form easily. It's important to remember that the index of the radical corresponds to the denominator of the rational exponent, and the exponent of the base corresponds to the numerator of the rational exponent.
carl is paid $10 plus $8 an hour he was paid $66 how many hours did he work?
The triangles below are similar. Find the value of x.
9
8
10.5
11
Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime
Solve for x.
x/2≥−4
x≥−8
x≥−2
x≤−2
x≤−8
Question 1: Describe how you would use the distributive property to simplify (39 x 5). Question 2: Your best friend tells you the solution of 375 = x - 28 is 347. Explain your best friend's error.
1) The data in the table below represents the pressure of the gas as the temperature changes. Plot a graph of the data, using the space below. Draw a trend line and calculate its slope. How are the variables related? What will he pressure of the gas be at 0C?
the graph looks like this
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
Answer:
The pressure of the gas 0°C is about 699.
Step-by-step explanation:
The given table of values is
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
The general form of a trend line is
[tex]y=a+bx[/tex]
where, b is slope and a is y-intercept.
[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]a=\overline{y}-b\overline{x}[/tex]
Using graphing calculator, we get
[tex]a=699.006826[/tex]
[tex]b=2.552218[/tex]
The equation of line of best bit is
[tex]y = 2.552218x + 699.006826[/tex]
where, y is pressure at x°C.
We need to find the pressure of the gas at 0°C.
Substitute x=0 in the above equation.
[tex]y = 2.552218(0) + 699.006826[/tex]
[tex]y =699.006826[/tex]
[tex]y \approx 699[/tex]
Therefore the pressure of the gas 0°C is about 699.
Math test assesment chapter 5 answer #9
1,119.85 is estimate to what number
Simplify
sqrt(3 + 2 sqrt 2) ...?
Answer:
[tex]1+\sqrt{2}[/tex]
Step-by-step explanation:
We have been given a radical expression [tex]\sqrt{3+2\sqrt{2}}[/tex]. We are asked to simplify the given expression.
We will add [tex](\sqrt{2})^2-2[/tex] to our given expression as after adding and subtracting same quantity the value of our expression will be same.
[tex]\sqrt{3+2\sqrt{2}+(\sqrt{2})^2-2}[/tex]
[tex]\sqrt{3-2+2\sqrt{2}+(\sqrt{2})^2}[/tex]
[tex]\sqrt{1+2\sqrt{2}+(\sqrt{2})^2}[/tex]
Using perfect square formula [tex](a+b)^2=a^2+2ab+b^2[/tex] we can rewrite our expression as:
[tex]\sqrt{1^2+2\sqrt{2}\cdot 1+(\sqrt{2})^2}[/tex]
[tex]\sqrt{(1+\sqrt{2})^2}[/tex]
Applying radical rule [tex]\sqrt[n]{x^n} =x[/tex], we will get,
[tex](1+\sqrt{2})^{\frac{2}{2}}=1+\sqrt{2}[/tex]
Therefore, the simplified form of our given expression would be [tex]1+\sqrt{2}[/tex].
What is the result of isolating y2 in the equation below?
(x - 2)^2 + y2 = 64
A. y2 = -x2 + 4x + 60
B. y2 = -x2 + 4x + 4
C. y2 = 64 - x2
D. y2 = x2 + 4x + 60
Answer with explanation:
The given equation which represents a circle having center at, (2,0) and radius =8 is,
[tex](x - 2)^2 + y^2 = 64\\\\y^2=64 - (x-2)^2\\\\y^2=64 - (x^2-4 x +4)\\\\ y^2=64 -x^2+4 x-4\\\\y^2=60+4 x-x^2[/tex]
Result of isolating y² in the equation below, gives
Option A
[tex]y^2=60+4 x-x^2[/tex]
what is 999 divided by 3
jill sold half her comic books then bought 16 more she now has 36 how many did she start with? help me plz ...?
The function c(x)=35x+75 r
If the repair took 5 hours, the total cost would be $250.
To find the total cost if the repair took 5 hours, we need to evaluate the function[tex]\(C(x)\) at \(x = 5\).[/tex]
Given that [tex]\(C(x) = 35x + 75\),[/tex] we substitute [tex]\(x = 5\)[/tex] into the function:
[tex]\[C(5) = 35 \times 5 + 75\]\[C(5) = 175 + 75\]\[C(5) = 250\][/tex]
So, if the repair took 5 hours, the total cost would be $250.
Complete correct question:
The function C(x) = 35x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace our alternator, where x is the number of hours of labor. What would be the total cost if the repair took 5 hours?
What is the converse of the following true conditional? If the converse is true, rewrite the statements as a bioconditional. If either is false, give a counter example. If two lines are parallel, they do not intersect
The converse of the statement 'If two lines are parallel, they do not intersect' is 'If two lines do not intersect, they are parallel', which is false. A counterexample to this converse is skew lines that do not intersect but are not parallel. Thus, we can't write both statements as a biconditional
Explanation:The subject of your question is regarding conditional statements and their converses in mathematics. A conditional statement is often expressed in the form: 'If p, then q', where p is a hypothesis and q is a conclusion. The converse of a conditional statement switches the hypothesis and the conclusion, i.e., 'If q, then p'.
In the context of your question, the conditional statement given is 'If two lines are parallel, they do not intersect'. The converse of this statement is 'If two lines do not intersect, they are parallel'. However, this converse is not true. A counterexample can be two lines that do not intersect but are not parallel because they are skew lines, which exist in three dimensions and do not lie in the same plane. Thus, the statements can't be written as a biconditional as one is not a valid conditional.
Learn more about Converse of a Conditional Statement here:https://brainly.com/question/2386083
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Which is the largest religion in india? zoroastrianism hinduism daoism judaism?
Will calculators or computers be needed to perform some calculations?
Answer:
yes
Step-by-step explanation:
When performing certain statistical calculations, finding roots, or working with powers, calculators or computers are necessary for the calculations; otherwise, more traditional methods will be sufficient.
Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?
painter was hired to design and draw a mural for a new restaurant. before he can design the mural, he needs to know the are of the wall. the restaurant manager informs the painter that the mural wall is 6-√2 feet tall by 12-√2 feet wide. what is the total area of the mural wall? (recall that the area of a rectangle is the width multiplied by the length)
a. 70-18√2 square feet
b. 74-18√2 square feet
c. 74-6√2 square feet
d. 74+18√2 square feet ...?
Glenn has a beginning balance of $840 in his checking account. He has a deposit of $375 and withdraws $250 from the ATM. If the ATM fee is $3, what is his new balance?
$718
$212
$962
$572
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15?
There are 35 students going to the zoo each vans can hold 6 students how many vans are needed
ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack what is the total amount cloth ,in yards ryan use to make all 6 backpacks
Answer:
Ryan use 4. 50 yards of cloth to make 6 backpack.
Step-by-step explanation:
Given : ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack.
To find : what is the total amount cloth ,in yards ryan use to make all 6 backpacks.
Solution : We have given that
Ryan make a backpack to use = [tex]\frac{3}{4}[/tex] of a cloth.
Ryan make such 6 backpack = [tex]6*\frac{3}{4}[/tex]
= [tex]\frac{18}{4}[/tex] .
= 4. 50 yards.
Therefore, Ryan use 4. 50 yards of cloth to make 6 backpack.
Write the function in slope-intercept form. Then graph the function.
2x - 5y = -6
Marcus solved for x in the quadratic equation x2 – 10x + 25 = 0.
Answer:
Option 1,3 and 4 are correct.
Step-by-step explanation:
Given is a quadratic equation
[tex]x^2-10x+25=0[/tex]
Marcus used quadratic formula to solve this
The correct use of formula is
[tex]\frac{-b+/\sqrt{b^2-4ac} }{2a}[/tex]
for the quadratic equation [tex]ax^2+bx+c=0[/tex]
Comparing we have a =1, b =-10: c=25
The student should have substituted -10 for b but he wrong did only 10
II option is wrong since 2 is substituted correctly
III option is right -4ac i.e. the product x 4 must have been subtracted
IV option is right since repeated root is there so only one solution
Ariel wants to write 8 entries for her blog. After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents Ariel's remaining entries?
graph of line going through (0, 0) with a slope of 1.5
graph of line going through (0, 2) with a slope of 2
graph of line going through (0, 8) with a slope of 1.5
graph of line going through (0, 3) with a slope of 3
Answer:
Graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
Step-by-step explanation:
Ariel wants to write 8 entries for her blog.
After 2 hours, she has 5 entries left. [tex](x_1,y_1)=(2,5)[/tex]
After 4 hours, she has 2 entries left. [tex](x_2,y_2)=(4,2)[/tex]
So, now using two point slope form:
[tex]y-y_1=m(x-x_1)[/tex] ---1
where [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
So , substituting the given points we get the equation that represents the given situation .
[tex]m = \frac{2-5}{4-2}[/tex]
[tex]m = \frac{-3}{2}[/tex]
[tex]m = -1.5[/tex]
Now,
[tex]y-5 = -1.5(x-2)[/tex]
[tex]y-5 = -1.5x+3[/tex]
Thus the slope of the given situation is 1.5
Now at x = 0
[tex]y-5 = -1.5*0+3[/tex]
[tex]y=8[/tex]
So, at 0 hour 8 entries left .
So, graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles.
To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance.
Within a specific stretch spanning 5 miles, the roadway inclines approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.
Trigonometric principles aid in determining the elevation gained by the highway over this distance.
Given:
An angle of ascent (θ) of 6 degrees and a horizontal distance (adjacent side) of 5 miles, our objective is to ascertain the vertical distance (opposite side).
Utilizing the tangent function in trigonometry:
[tex]\[ \tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}} \][/tex]
[tex]\[ \tan(6^\circ) = \frac{{\text{{height}}}}{{5}} \][/tex]
The calculation for the height is:
height = 5 × tan(6°)
Plugging in the values:
height ≈ 5 × 0.1051
height ≈ 0.5255 miles
To convert this to feet (1 mile = 5280 feet):
height ≈ 0.5255 × 5280
height ≈ 2771.64 feet
Thus, within this 5-mile segment, the roadway ascends approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.
Work out tan(19pi/4) without a calculator
Please help 3 questions will Upvote
1.Write the equation of a line with a slope of 3 and a y-intercept of 1.
y = x + 3
y = 3x + 1
3x + y = 1
x + 3y = 1
2.Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form.
y – 1 = 2(x – 3)
y – 3 = 2(x – 1)
x – 1 = 2(y – 3)
x – 3 = 2(y – 1)
3.Write the equation of the line that passes through (–2, 6) and (2, 14) in slope-intercept form.
y = 2x – 2
y = 2x + 10
y = 0.5x + 7
y = 0.5x – 4
What is 7/50 in decimal form?
what is the area of a park that is 100 yards square?