Answers
Option B
[tex]3 x\sqrt{2} x[/tex] is the choice equivalent to [tex]\sqrt{6} x^{2} \cdot \sqrt{3} x[/tex]
Solution:
Step 1:
When we multiply two roots i.e. [tex]\sqrt{6} x^{2}[/tex] and [tex]\sqrt{3} x[/tex] the values are multiplied and still kept inside the root.
So [tex]\sqrt{6} x^{2}[/tex] × [tex]\sqrt{3} x[/tex] = [tex]\sqrt{6} x^{2} \times 3 x[/tex].
Step 2:
We then multiply the values in the root.
[tex]\sqrt{6} x^{2} \times 3 x[/tex] = [tex]\sqrt{18 x^{3}}[/tex]
Step 3;
We take the values out of the root by splitting up the value.
[tex]{18 x^{3}}[/tex] = [tex](9 \times 2)\left(x^{2} \times x\right)[/tex]
[tex]\sqrt{9}=3[/tex] and [tex]\sqrt{x^{2}}=x[/tex]
So [tex]\sqrt{18 x^{3}}[/tex] = [tex]\sqrt{9} \times 2 \times x^{2} \times x[/tex]
When we take values out of the root, we replace it with the square-rooted value on the outside.
[tex]\sqrt{18 x^{3}}[/tex] = [tex]3 x \sqrt{2 x}[/tex].
Thus option B is correct
Related Questions
If gasoline costs $47.86 for 12.5 gallons of gasoline, how much does it cost for 8 gallons?
Round your answer to the nearest cent.
Answers
Answer:
8 gallons of gasoline costs $30.63.
Step-by-step explanation:
Set up a proportion to solve for x, or the cost of 8 gallons of gasoline. The $47.86 goes on top of the first ratio, and 12.5 goes on top of the second. This is because the $47.86 is the cost of the 12.5 gallons of gasoline. Next, put x on the bottom of the first ratio and 8 on the bottom of the second ratio. This is because the amount of money you are trying to find, x, is the cost of the 8 gallons of gasoline. The proportion should look like this: [tex]\frac{47.86}{x} = \frac{12.5}{8}[/tex]
To solve the proportion, use cross multiplication. To do that, multiply 8 by 47.86 to get 382.88. Then, divide 382.88 by 12.5. The answer is 30.6304, so round to the nearest cent to get a total of $30.63.
I hope this helps! ☺
a line goes through the points. (3,-5) and (5,-1)
Answers
Answer:
9+10 equals 21
Step-by-step explanation:
Just bc im big brain
Which fraction can be expressed as a terminating decimal? 1/9, 3/11, 5/8, 2/3
Answers
Answer:
2/3 can be expressed as 0.6666666666666666666666 repeating
Step-by-step explanation:
Answer:
1/3 there is no 2/3
Step-by-step explanation:
Original Price: $125
Discount: ?
Sale Price: $81.25
Answers
Answer:
The discount is 43.75 dollars.
Step-by-step explanation:
125 - 81.25 = 43.75
Final answer:
The discount percentage applied to reduce the original price of $125 to the sale price of $81.25 is 35%.
Explanation:
A student is trying to find out the discount percentage that was applied to an item originally priced at $125 to have a final sale price of $81.25. To calculate the discount, one can use the formula: Discount percentage = ((Original Price - Sale Price) / Original Price) imes 100%. Applying this to the given values: ($125 - $81.25) / $125 imes 100% = $43.75 / $125 imes 100% = 35%. Thus, the discount percentage applied is 35%.
WHICH SENTENCE IDENTIFIES THE Y INTERCEPT AND ORDERED PAIR OF THE POINT ON THE GRAPH
Answers
The line intercepts the y axis at 2, so that is the y intercept.
The ordered pair is (1,3) because ordered pairs go (x,y)
a store had three baskets with an equal number of flower bouquets in each. customers purchased 8 bouquets from each basket, and there are now a total of 18 bouquets left. Write and solve an equation to find how many bouquets of flowers were initially in each basket.
Answers
Answer:
8
Step-by-step explanation:
18+8=26
26 / 3 = 8
8
hope this helped!
~ angilina
i was watching mineHUB in lesson and the Bluetooth was not on and everyone heard what should i do i have been sent out of class
Answers
Answer:
act like you dont care next time keep the volume down
Step-by-step explanation:
5x - 1= 3х + 9
Find x
Answers
Answer:
X=5
Step-by-step explanation:
[tex]5x - 1 = 3x + 9 \\ 5x - 3x = 9 + 1 \\ 2x = 10 \\ x = 5[/tex]
5x-1=3x+9
collect like terms
5x-3x=9+1
2x=10
divide both sides by 2
x=5
The manufacturer of cell phones spends $320 to make each cell phone and sells them for 440 . The manufacturer also has fixed costs each month of $11400 .
Answers
Answer:
x=95
Step-by-step explanation:
320x+11400=440x
320*95+11400=440*95
30,400+11,400=41,800
41,800=41,800
The manufacturer needs to sell approximately 95 cell phones to cover its fixed costs of $11,400 per month. The profit per month depends on the number of units sold, with a contribution margin of $120 per unit after covering variable costs.
To analyze the manufacturer's costs and profitability, we can break down the information provided:Cost to Make Each Cell Phone: $320 per unitSelling Price of Each Cell Phone: $440 per unitFixed Costs: $11,400 per monthFirst, let's calculate the variable cost per unit, which is the cost to make each cell phone:Variable Cost per Unit = Cost to Make Each Cell Phone = $320Now, we can calculate the contribution margin per unit, which is the amount each phone contributes to covering fixed costs and generating profit:Contribution Margin per Unit = Selling Price - Variable Cost per UnitContribution Margin per Unit = $440 - $320 = $120Next, calculate the break-even point in units, which is the number of units the manufacturer needs to sell to cover its fixed costs:Break-Even Point (in units) = Fixed Costs / Contribution Margin per UnitBreak-Even Point (in units) = $11,400 / $120 ≈ 95 unitsSo, the manufacturer needs to sell approximately 95 cell phones to cover its fixed costs.To determine the profit, we can calculate the profit per month after covering fixed costs:Profit per Month = (Selling Price - Variable Cost per Unit) * Number of Units Sold - Fixed CostsSuppose the manufacturer sells "X" cell phones per month. Then:Profit per Month = ($440 - $320) * X - $11,400Now, you can calculate the profit for any given number of cell phones sold.For more questions on profit -
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In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees. What is the measure of Angle A B C ? 36° 43° 72° 144°
Answers
Answer:
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.
Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees.
What is the measure of Angle A B C ?
36° *****
43°
72°
144°
Step-by-step explanation:
its 36°
Applying the central angle theorem, the measure of angle ABC is: a. 36°
What is the Central Angle Theorem?The central angle theorem states that the angle measure of a central angle equals the measure of the intercepted arc.Inscribed angle = half the intercepted arc.Given:
m∠ADC = (7x + 2)° (central angle)
measure of intercepted arc AC = (8x - 8)°
Therefore:
(7x + 2)° = (8x - 8)°
Solve for x7x + 2 = 8x - 8
8 + 2 = 8x - 7x
10 = x
x = 10
Thus:
m∠ABC is an inscribed angle = half of measure of intercepted arc AC
Therefore:m∠ABC = 1/2(8x - 8)°
Plug in the value of xm∠ABC = 1/2[8(10) - 8]
m∠ABC = 36°
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Identify the vertex of each graph. Tell whether it is a minimum or a maximum.
Answers
Answer: Minimum
Step-by-step explanation:
Answer:1,-6 minimum
Step-by-step explanation:Minimum vertex will look like a smiley face and a maximum will look somewhat like a frown. As for the vertex just follow the lines the x and y are on.
1 3/4+z= 2 2/3
Wat is z
Answers
Answer:
11/12 is Z
Step-by-step explanation:
Do you need the explanation?
The required value of z is 11/12 in the given equation.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The equation is given in the question as:
1 3/4 + z = 2 2/3
We have to determine the value of z in the given equation,
As per the question, we have
⇒ 1 3/4 + z = 2 2/3
Convert the mixed numbers into fractions,
⇒ 7/4 + z = 8/3
Rearrange the terms in the above equation,
⇒ z = 8/3 - 7/4
Take LCM in the term of fractions,
⇒ z = (32 - 21)/12
⇒ z = 11/12
Therefore, the required value of z is 11/12 in the given equation.
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Which best describes the graphs of the line that passes through (−12, 15) and (4, −5), and the line that passes through (−8, −9) and (16, 21)?
A)
They are parallel lines.
B)
They are vertical lines.
C)
They are perpendicular lines.
D)
They are intersecting lines.
Answers
Answer:
C) They are perpendicular lines.
Step-by-step explanation:
We first need to find the slope of the graph of the lines passing through these points using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The slope of the line that passes through (−12, 15) and (4, −5) is
[tex] m_{1} = \frac{ - 5 - 15}{4 - - 12} [/tex]
[tex]m_{1} = \frac{ - 20}{16} = - \frac{5}{4} [/tex]
The slope of the line going through (−8, −9) and (16, 21) is
[tex] m_{2} = \frac{21 - - 9}{16 - - 8} [/tex]
[tex] m_{2} = \frac{21 + 9}{16 + 8} [/tex]
[tex]m_{2} = \frac{30}{24} = \frac{5}{4} [/tex]
The product of the two slopes is
[tex]m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1[/tex]
Since
[tex]m_{1} \times m_{2} = - 1[/tex]
the two lines are perpendicular.
Answer:D) They are intersecting lines.
Step-by-step explanation: that other answer was wrong .
Three persons EB and C work together on a job and finish it finish it in 18 days if E and be working together can finish the job in 45 days find how long C working alone would take to complete it
Answers
Answer: 30 days
Step-by-step explanation:
Working together, E & B get 1/45 of the job done per day
Working alone, C gets 1/x of the job done per day
Working together, E, B, & C get 1/18 of the job done per day.
[tex]EB:\dfrac{1}{45}\qquad C: \dfrac{1}{x}\qquad EBC:\dfrac{1}{18}\\\\\\\\EB+C=EBC\\\\ \dfrac{1}{45}\ +\dfrac{1}{x}=\dfrac{1}{18}\\\\\\(45\cdot 18\cdot x)\bigg(\dfrac{1}{45}+\dfrac{1}{x}=\dfrac{1}{18}\bigg)\\\\\\.\qquad \qquad 18x+810=45x\\\\.\qquad \qquad \qquad 810=27x\\\\.\qquad\qquad \qquad \large\boxed{30=x}[/tex]
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value
of the function.
fx) = x2 - 6x + 5
Answers
Answer:
(3,-4)
Step-by-step explanation:
minimum is shown if you were to graph it,
i dont really know how else to explain it, its sorta self explanatory.. :)
Answer:
Since the leading coefficient of x^2 is positive. Therefore, it is a minimum.
The value of the minimum is: (3, -4)
0.009 times 0.07
show how you got the answer
Answers
Answer:
63/100000 or 0.000063
Step-by-step explanation:
0.009*0.07 is the same as 9/1000*7/100 which is 63/100000 when you multiply numerator with numerator and denominator with denominator.
So your answer is 63/100000 or 0.000063
what’s the relationship? linear, exponential, or neither?
Answers
Answer:
This relationship is linear
Step-by-step explanation:
As x goes up by 5, y goes up 3. Since this is a constant rate, this relationship is, therefore, linear
What is the angle of a triangle if one angle is 68 and the other is 52
Answers
Answer:
The last angle is 60 degrees
Step-by-step explanation:
All triangles add up to 180 degrees
Step 1: Make an equation
What is the angle of a triangle if one angle is 68 and the other is 52.
68 + 52 + x = 180
Step 2: Combine like terms
68 + 52 + x = 180
120 + x = 180
Step 3: Subtract 120 from both sides
120 + x - 120 = 180 - 120
x = 60
Answer: The last angle is 60 degrees
The sum of the angles in a triangle will be equal to 180°.
68 + 52 = 120°
180 - 120 = 60° (This is the 3rd angle)
Best of Luck!
Strawberries cost $2.14 per pound and Annie purchased 1.3 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
A. $2.78
B. $2.79
C. $27.82
D. $27.90
Answers
Answer:
A. $2.78
Step-by-step explanation:
You would multiply the cost per pound, $2.14, by the amount of pounds bought, 1.3. Then round to the nearest hundredth.
2.14 x 1.3 = 2.782
2.782 rounded to the nearest hundredth is $2.78
Answer:
I think it is 2.78 sorry if it’s not
Step-by-step explanation:
slope:
y-intercept:
equation:
Answers
y intercept= b
Equation: y=mx+b
We can conclude -
m = -A/B → unit rate of change of [y] with respect to [x].c = - C/A → the point where the graph cuts the [y] axis.Equation → y = mx + cWhat is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given is a straight line.
The equation of a straight line is written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Now, from this we get -
m = -A/B {Slope}
c = - C/A {y - intercept}
So, the equation will be -
y = mx + c
We can also calculate slope by -
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, we can write -
m = -A/B → unit rate of change of [y] with respect to [x].
c = - C/A → the point where the graph cuts the [y] axis.
Equation → y = mx + c
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What is the justification for step 1 in the solution process?
8x + 15 = 11x + 2
Step 1: 8x = 11x − 13
A.
the division property of equality
B.
the addition property of equality
C.
the subtraction property of equality
D.
the multiplication property of equality
Answers
Answer:
C.
the subtraction property of equality
Step-by-step explanation:
Given
8x + 15 = 11x + 2
Subtract 15 from both sides of the equation
8x + 15 - 15 = 11x + 2 - 15
8x = 11x - 13
Answer:
the addition property of equality
Step-by-step explanation:
Compare step 1 with step 2 in the solution process:
step 1: -5x = -4x - 15
step 2: -x = -15
The variable was isolated on the left side of the equation by adding 4x to both sides. This is justified by the addition property of equality.
y = x -5x + 1 y= 3x - 2
is ( 3 , 8 ) a solution of the system ?
Answers
You are riding your bicycle. It takes you 9min to go 2.5 mi. If you continue traveling at the same rate, how long will it take you to go 7 mi?
Answers
Answer:
Step-by-step explanation:
To find out how many miles you are going per minute you would find the unit rate. The unit rate is 3.6
You are going at 3.6 minutes per mile.
So you would multiply 3.6 by 7 to get 25.2 minutes.
Which point approximates the square root of 15
Answers
Option B:
Point B approximates [tex]\sqrt{15}[/tex].
Solution:
Let us first find the approximate value of [tex]\sqrt{15}[/tex].
[tex]\sqrt{15}=3.87[/tex]
In the number line 3.87 lies between 3 and 4.
So that [tex]\sqrt{15}[/tex] lies between 3 and 4.
Look at the given number line.
Point B lies between 2 and 4.
Hence point B approximates [tex]\sqrt{15}[/tex].
Option B is the correct answer.
PLS HELP
What is the volume of the right rectangular prism shown?
A. 8 un3
B. 20 un3
C. 24 un3
D. 12 un3
Answers
Answer:
12 UN 3
Step-by-step explanation:
ok i hope this is right answer
I need help with this question
Answers
The answers are 15 guests, 7 tables, 24 guests, and 10 tables respectively.
Step-by-step explanation:
Step 1: Find relation between the number of tables and guests. Given that for every 6 guests, Maya uses 2 tables.2 tables ⇒ 6 guests
1 table ⇒ 6/2 = 3 guests
Step 2: Find number of guests for 5 tables.5 tables = 5 × 3 = 15 guests
Step 3: Find number of tables for 21 guests.Number of tables = 21/3 = 7 tables
Step 4: Find number of guests for 8 tables.Number of guests = 8 × 3 = 24 guests
Step 5: Find number of tables for 30 guests.Number of tables = 30/3 = 10 tables
find x and y?????????
Answers
Answer:
[tex]a)\\x=12\\y=12\sqrt{3}[/tex]
Step-by-step explanation:
The angle without a numerical value is 30°
Using the 30-60-90 rule:
x = a24 = 2ay = [tex]a\sqrt{2}[/tex]Since we know that 2a is the side with length 24
[tex]2a=24\\a=24/2\\a=12\\x=12[/tex]
To find y
[tex]y=a\sqrt{3}\\a=12\\y=12\sqrt{3}\\[/tex]
Jake swims a distance from one end of a 50 meter pool to the other end in 25 seconds. What is his average speed?
Answers
Answer:
2 meters/ second
Step-by-step explanation:
Speed is equal to distance divided by time
Speed = 50 meters / 25 seconds
= 2 meters/ second
What is the slope of the line that passes through the points (4, -2) and (24, -17)?
Write your answer in simplest form.
Answers
-3/4
EXPLANATION
rise over run.
(Rise is the y value)
From -2 to -17 is -15
From 4 to 24 is 20
Therefore the slops is -15/20
need help with 3x48 and 48x3
Answers
Answer:
144
Step-by-step explanation:
48×3= 144
48×3=144
to make it easier just add the number being multiplied the amount of times its being multiplied.
48+48+48=144
Both 3x48 and 48x3 yield the same result, which is 144, because multiplication is commutative.
Both expressions involve multiplying the numbers 3 and 48.
In the first expression, 3x48 means you're multiplying 3 by 48. This gives you 144, because 3 times 48 equals 144.
In the second expression, 48x3 means you're multiplying 48 by 3. This also gives you 144, because multiplication is commutative, which means the order of the numbers doesn't change the result. So, whether you multiply 3 by 48 or 48 by 3, you'll always get the same answer, which is 144.
So, to summarize:
3x48 = 144
48x3 = 144
Both expressions result in the same value of 144.
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