The simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
We need to solve given radical expressions.
1) √216k⁴
= √216 × √k⁴
= √(6 × 36) × √(k²)²
= 6√6 × k²
= 6√6k²
2) √28x³y³
= √(7 * 4) × √x³ × √y³
= 2√7 * x√x * y√y
= 2√7 * xy√(xy)
3) √192n³
= √(64 × 3) * √n³
= 8√3 * n√n
= 8n√(3n)
4)∛40n²
= ∛(8 × 5) * ∛n²
= ∛2³ * ∛5 * ∛n²
= 2∛n²n^(2/3)
5) ∛216x³
= ∛216 * ∛x³
= ∛6³ * ∛x³
= 6 * x
= 6x
6) ⁴√128x⁶y⁸
= ⁴√128 * ⁴√x⁶ * ⁴√y⁸
= ⁴√(16 × 8) * x(⁴√x²) * y(⁴√y²)
= 2 * 8^(1/4) * xy (x²y²)^(1/4)
= 2xy8^(1/4)√xy
7) √252a³b^4
= √(36 × 7) * √a³ * √b^4
= 6√7 * a√a * b²
= 6ab²√(7a)
Therefore, the simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
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Is (–4, 10) a solution to the equation 10 – 5x = y? Explain your answer.
A line passes through the point (10,2) and has a slope of -3/2
Write an equation in point-slope form for this line
Answer:
y=-1,5x+17
Step-by-step explanation:
(10,2) => x=10, y=2
a - slope
a=-1,5
y=ax+b -linear equation
2=(-1,5)*10+b
2=-15+b
b=17
y=-1,5x+17
Mrs. Ryder estimates that 18 people will attend an open house. A total of 30 people actually attend the open house. What is the percent error of Mrs. Ryder’s estimate?
PLEASE HELP!!
Ryan will drive his car in spain. the speedometer in the car shows the speed in miles per hour only. he will be driving on a road with a speed limit of 100 kilometres per hour. ryan uses this rule to find this speed in miles per hour.
Answer:
the conversion factor
Step-by-step explanation:
Calculate 70/cos 20° round to 1 decimal place.
The answer of this 70/cos 20° round to 1 decimal place is 74.5
To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.
From the simple calculator we can find the value of cos 20° which is 0.9397.
Now we use this value to solve the above equation.
70/cos 20°;
70/0.9397;
74.491.
written that we have to round of the value to first decimal place, so the answer will become 74.5
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suppose that for a particular family of t-distributions that t2 has 2 degrees of freedom (df) and t9 has 9 degrees of freedom. what would you anticipate happening to tdf as the df increase?
The critical t-distribution values converge to the critical z-distribution values as a particular family of t-distributions that t2 has 2 degrees of freedom (df) and t9 has 9 degrees of freedom.
What is degree of freedom?The maximum number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom, also known as numerical freedom of variance, are the maximum number of logically independent values that can be present in sample data. Degrees of freedom are frequently brought up when discussing various mathematical hypothesis testing techniques, like the chi-square.
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4√42+6√75 simplified
6 + 12(X + 3) = 7X + 30 + 6X
Answer:
x = 12
Step-by-step explanation:
Given equation,
→ 6 + 12(x + 3) = 7x + 30 + 6x
Now the value of x will be,
→ 6 + 12(x + 3) = 7x + 30 + 6x
→ 6 + 12x + 36 = 7x + 30 + 6x
→ 12x + 42 = 13x + 30
→ 13x + 30 = 12x + 42
→ 13x - 12x = 42 - 30
→ [ x = 12 ]
Hence, the value of x is 12.
e) (3x + 2x)(3x + 4xy + 2)
Answer:
20xy^2 + 15x^2 + 10x
Step-by-step explanation:
Movie ticket cot $8 for regular admiion and $5 for tudent. For a particular movie, 48 ticket are old and the amount collected for the ticket wa $300. Find the number of ticket old to tudent. Find the number of ticket old at regular price. Set up a ytem of 2 equation with 2 variable to olve thi problem
The number of tickets sold at a regular price is 20.
The linear equation:
an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Let x be the number of regular admission and y be the number of students.
The first statement is 48 tickets are sold. By this we get the first equation:
x + y = 48 ----------(1)
The second statement is the total collection for the ticket is $300. Form this we get the second equation:
8x + 5y = 300 --------(2)
Multiplying the equation by 5 we have:
5x + 5y = 240 --------(3)
Now subtracting equation (3) from (2) we get:
3x = 60
x = 20
Therefore we get that the ticket sold at regular price is 20.
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Line segment XY is located at X(2, 6) and Y(4,8). If the line segments is dilated by a scale factor of 2 with a center of dilation of T(0, 0). What are the coordinates of X’?
You can graph it below.
A. (7, 8)
B. (7, 15)
C. (-4, 14)
D. (4, 12)
The coordinates of X’ is (4,12)
What is dilation?Dilation means changing the size of an object without changing its shape.
Given that, Line segment XY is located at X(2, 6) and Y(4,8). If the line segments are dilated by a scale factor of 2 with a centre of dilation of
T(0,0).
The rule for a figure dilated by a scale factor k with a centre of dilation (a, b) is;
(x, y) → (k(x-a) + a, k(y-b) + b)
The line segment is dilated by a scale factor of 2 with a centre of dilation of T(0,0)
According to the rule,
(x, y) → (2(x-0) + 0, 2(y-0) + 0)
(x, y) → 2x + 2y
The coordinates of X' are (2, 6)
X(2, 6) → (2*2, 2*6)
X(2, 6) → (4, 12)
Hence, The coordinates of X’ is (4,12)
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The points (-1 14) and (2 r) lie on a line with slope -2. Find the missing coordinate r.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{14})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{r}) \hspace{5em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{14}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{-2} \\\\\\ \cfrac{r-14}{2+1}=-2\implies \cfrac{r-14}{3}=-2\implies r-14=-6\implies r=8[/tex]
name each part below using 14(x)^13
a. base?
b.power?
c.exponent?
d.coefficient?
In 14x¹³ , x¹³ is exponent with base x , power 13 and 14 as coefficient
Exponent is a method of expressing large numbers in terms of powers.
It means when a number is multiplied by itself many times we can express expressed it in exponent form .
The symbol used for representing the exponent is "^" .This symbol is known as carrot
Base is that number that is being multiplied.
tells how many times that number is multiplied.
In the given question,
14x¹³
Base = x
because x is multiplied 13 times
so, Power = 13
Exponent = x¹³
Coefficient = 14
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Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.
Answer:
7.8
Step-by-step explanation:
You want the distance between P(8, 2) and Q(3, 8).
Distance between pointsThe distance between points is given by the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((3 -8)² +(8 -2)²) = √((-5)² +6²) = √61
d ≈ 7.8
The distance between points P and Q is about 7.8 units.
__
Additional comment
You will notice that the desired distance is the length of the hypotenuse of a right triangle with legs that are 5 and 6. The Pythagorean theorem tells you that length is √(5² +6²) = √61, as above. The distance formula is based on the Pythagorean theorem.
You can find the relevant triangle leg lengths by counting grid squares on the graph. Of course, the distance formula does the same thing by subtracting coordinate values.
Write the equation for the logarithmic function that has the following transformation from the parent logarithmic function. The function will have a base of 10. You will not have to write the 10. It is assumed.
shifted 3 units left
vertical compression by a factor of 2
reflected across the y-axis
shifted down 5 units
please help
The equation for the logarithmic function that has the following transformation from the parent logarithmic function. The other factors are mentioned in the answer below.
What is a logarithmic function?An essential tool for arithmetic calculations is the logarithmic function. John Napier, a Scottish mathematician, physicist, and astronomer, made the discovery of logarithms in the 16th century. It has a wide range of uses in complex scientific and astronomical calculations. Exponential functions and logarithmic curves are closely related, and the latter is thought of as the inverse of the former.
Parent function is y = log x
1. Shifted 3 units left,
y = log (x+3)
2. The vertical compression by a factor of 2,
y = 2 log(x+3)
3. Reflection across the y-axis,
y = 2 log(-x+3)
4. Shifting down by 5 units,
y = 2 log(-x+3)-5
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
From the given exponential function y = 7.1(1.03)ˣ, the amount produced in 2006 was approximately 7.8 billion pounds and the estimated amount in 2014 will be approximately 9.8 billion pounds
Exponential FunctionAn exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
In the function given;
y = 7.1(1.03)ˣ
x = number of years after 2003a) What is the estimated number in 2006
x in 2006 = 3
x = 3
Insert the values into the formula above;
y = 7.1(1.03)³
y = 7.76 ≅ 7.8 billion pounds
b)
The cheese produced in 2014
x in 2014 = 11
Insert in the value and solve
y = 7.1(1.03)¹¹
y = 9.83 ≅ 9.8 billion pounds
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Please help me! I have 15 minutes of the test left
Answer:
(0,15) The time it take to fill the ball with air
Step-by-step explanation:
On edge 2022
Play cues with the dimensions shown reign algebraic expression that Jackson can use to find the total volume in cubic inches of the two bins for any value of I then find the total volume of the bins
when I equals four
Select all the values of x that make the equation |3x + 4| − 9 = 0 true.
A. 1 2/3
B. −1 2/3
C. 4 1/3
D. −4 1/3
E. 5 2/3
F. −5 2/3
Answer:
A and D
Step-by-step explanation:
|3x + 4| − 9 = 0
|3x + 4| = 9
3x+4 = 9 v 3x+4 = -9
3x=5 v 3x=-13
x=⁵/₃ v x=-¹³/₃
x=1 ²/₃ v x=-4¹/₃
what is \left \{ {{7x-9y=-30} \atop {-3x-6y=3}} \right using substitution
Answer:
[tex]x=-2\frac{9}{23} , y=\frac{16}{23 }[/tex]
Step-by-step explanation:
7x - 9y = -30 ------ equation (1)
-3x - 6y = 3 ------ equation (2)
From equation (2),
3x + 6y = -3
x + 2y = -1
∴ x = -2y - 1 ------ equation (3)
Substitute equation (3) into equation (1):
7(-2y - 1) - 9y = -30
-14y - 14 - 9y = -30
-23y = -16
23y = 16
∴ y = [tex]\frac{16}{23}[/tex]
Substitute y = [tex]\frac{16}{23}[/tex] into equation (3):
x = -2([tex]\frac{16}{23}[/tex]) - 1
= -[tex]\frac{32}{23}[/tex] - 1
= -[tex]\frac{55}{23}[/tex] = -[tex]2\frac{9}{23}[/tex]
b. Find the zeros of the function D(k) and make a sketch of its graph.
HELP I DONT UNDERSTAND
What value of n in the expression below would make it a
perfect square trinomial?
x² −14x + n
Answer:
n = 49
Step-by-step explanation:
49 has a factor of -7 which can also add up to -14
Eg : -7(-7) = 49, -7 + (-7) = -14
49
x²-14x+49=(x-7)²
An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial.
It is of the form (ax2 + bx + c).
Real numbers a, b, and c are present here, and a ≠0.
The given equation is x2 + 14x + c
To find the value of c
We can take half of the linear coefficient and square it
14/2 = 7
72 = 49
Therefore, the value of c is 49.
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292500 to the nearest 1000
Answer:
293,000.
Step-by-step explanation:
Just round to the nearest thousandth, and add 500 since you originally had 292,500.
Answer:
Step-by-step explanation:
292500 to the nearest 1000 is 293000.
Connie says an expression for the phrase "10 more
than the square of a number" is x2 + 10. Sharon says
it is 10x². Who is correct? Explain.
Answer:
Connie - [tex]x^{2} + 10[/tex]
Step-by-step explanation:
10 more means that you are adding ten to the square of x
e.) if the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour explain ?
pa help plsss with explanation
If the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour it is not possible.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
if the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour
Time = 2 hours
Distance = speed x time
Distance(for car ) = (65)(2) = 130 km
Distance(for bus ) = (75)(2) = 150 km
Total distance = 130 + 150 = 280 km
But the distance between car and bus is 350 km.
Thus, if the car's speed is 65 kilometers per hour if it possible that the bus speed 75 kilometers per hour it is not possible.
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a prescription calls for 50 g of a 10% ointment the pharmacist only has a 5% ointment and the pure ingredient available how much of the 5% ointment and the pure ingredient are needed to compound the prescription
25 g of 5% ointment and the pure ingredient are needed to compound the prescription.
A ratio is a comparison of two or more numbers that indicates their relative sizes. When two or more ratios are multiplied termwise, the resulting ratio is known as a compound ratio. The first quantity in the ratio is known as the antecedent, and the second quantity is known as the consequent.
For example, the compound ratio of two ratios, a:b and m:n, is am: bn.
Given,
Prescription requirement 50g for 10% ointment
but pharmacist has 5% ointment and pure ingredient
then to compound the prescription pharmacist needs x g
calculation:-
[tex]50 : 10 :: x : 5\\\\\frac{50}{10}=\frac{x}{5}\\\\5=\frac{x}{5}\\\\x=25[/tex]
Thus, required quantity of ointment and pure ingredient is 25 g.
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perfect square number is closer to 11
Answer:
9
Step-by-step explanation:
3 x 3 = 9
4 x 4 = 16
16 - 11 = 5
11 - 9 = 2
2 is less than 5 which makes it closer to 11.
Answer:
Ans = 9
Step-by-step explanation:
3 x 3 =9
4 x 4 =16
2 x 2 =4
what is X?
NOTE: Angles not necessarily drawn to scale.
Answer:
x=60
Step-by-step explanation:
180 = 100 + 20 + x
180 = 120 + x
-x = 120 - 180
-x = -60
x = 60
Answer: bro you gotta figure dis out
Step-by-step explanation:hhahahahahahahahahahaahahhaha
Rasheed has two and three-fourths cups of berries. He uses four-sixths of a cup of berries to make a milkshake. He then uses one-half of a cup of berries. After he makes his milkshake and muffins, how many cups of berries will Rasheed have left?
A. four-eighteenths cups
B. sixteen twenty-fourths cups
C. one and five twenty-fourths cups
D. one and seven-twelfths cups
For the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that, Rasheed has two and three-fourths cups of berries. He uses four-sixths of a cup of berries to make a milkshake. He then uses one-half of a cup of berries.
The number of cups of berries will Rasheed has left is found by subtracting the total used amount from the total amount,
=2 3/4-(4/6+1/2)
=11/4-(4/6+1/2)
=11/4 - 7/6
=19/12
=1 7/12
1.58
Thus, for the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.
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