(12x)^1/2 in radical form
Answer: [tex]\sqrt{12x}[/tex]
Step-by-step explanation:
Tim and Jessica plan to rent a camper van for a vacation. The van costs $183 per day.
The rental includes 120 miles for free and then charges $0.39 per mile.
The total price Tim and Jessica paid to rent the camper van is $598.74. Write an
equation that models the cost of the van rental in terms of miles traveled, m.
Create an equation
The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .
What is the equation that represents the cost?The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
The general form of linear equations is: y = a + bx
Where:
a = intercept
b = slope
The form of the equation that models the cost is:
Total cost = cost of renting the van + [cost per mile x (m - 120 miles)
$598.74 = $183 + [$0.39 x (m - 120)
$598.74 = $183 + $0.39m - 46.80
$598.74 = 136.20 + $0.39m
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it was 5 degrees above zero in the morning. By afternoon the temperature rose 27 degrees. How warm was it?
It was 33 degrees warm in the afternoon
How to determine how warm it was?From the question, we have the following parameters that can be used in our computation:
In the morning = 5 degrees above zero
Afternoon = Rise of 27 degrees
The degree of warmth in the afternoon is then calculated as
Degree of warmth = Temperature In the morning + Rise of the temperature
Substitute the known values in the above equation, so, we have the following representation
Degree of warmth = 5 + 27
Evaluate the sum
Degree of warmth = 33
Hence, the temperature is 33 degrees
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Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units
Can you find the measure of the indicated angle and type the correct code? Please remember to type in ALL CAPS with no spaces,
Answer:
hey I need this answer and puzzle 4 and 5 you got these things?
Step-by-step explanation:
please
The measure of angles A, B , C and D°are 36°, 63°, 71° and 111° respectively
How to determine the measure of the indicated angle?
To find the measure of angles of A, B, C and D, you need to apply some of the angle geometry concepts as follows:
1. m<A
(x+24)° and A = 3x
Since alternate angles are equal, thus:
3x° = (x+24)°
3x -x = 24
2x = 24
x =24/2 = 12
Also, A = 3x = 3(12) = 36°
2. m<B
B = 10x-27 and 7x
Since corresponding angles are equal, thus:
10x -27 = 7x
10x -7x = 27
3x = 27
x = 27/3 = 9
Also, B = 10x -27 = 10(9) -27 = 90-27 = 63°
3. m<C
C = (5x+1)° and (6x-13)°
Since corresponding angles are equal, thus:
(5x+1)° = (6x-13)°
6x -5x = 13+1
x = 14
Also, C = 5x+1 = 5(14) + 1 = 70+1 = 71°
4. m<D
(6x+3)° and D = (4x+39)°
Since alternate angles are equal, thus:
6x+3 = 4x+39
6x-4x = 39-3
2x=36
x = 36/2 =18
Also, D = 4x+39 = 4(18) + 39 = 72+39 = 111°
Therefore, the m<A = 36°, m<B = 63°, m<C = 71° and m<D =111°. Since B, A, H and E correspond to m<A, m<B, m<C and m<D respectively, so type BAHE in the answer box
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A carpet installer measures three rectangular bedrooms for new carpeting how much carpet is needed for the three bedrooms bedroom a 3.1 m x 3.1 m bedroom be 2.9 m x 3.2 m bedroom c2.5 m x 3.4 m
The 27.4 m² of carpet is needed for three bedrooms.
Firstly we will calculate the area of each room.
Area of bedroom a = 3.1 × 3.1
Area of bedroom a = 9.61 m²
Area of bedroom b = 2.9 × 3.2
Performing multiplication on Right Hand Side of the equation
Area of bedroom b = 9.29 m²
Area of bedroom c = 2.5 × 3.4
Area of bedroom c = 8.5 m²
Total area of all the rooms = 9.61 + 9.29 + 8.5
Performing addition on Right Hand Side of the equation
Total area of all the rooms = 27.4 m²
Hence, 27.4 m² carpet is required for three bedrooms.
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3409.1 in exponential form
3409.1 In exponential form is 3.4091 * 10^3
What is exponential form?Writing a number in exponential form is a way of writing numbers using base and exponents
Scientific notations is among the ways numbers appears in exponential forms
using scientific notation we have
= 3409.1
converting to fractions
= 34091 / 10
applying the scientific notation
= 3.4091 / 10 * 10000
eliminating the fraction by dividing by 10
= 3.4091 * 1000
applying exponential notation
= 3.4091 * 10^3
rewriting gives
= 3.4091 E+3
In scientific notation 10^3 is E+3 and it is called kilo and can be represented as k
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need halp with the ques answer pls
The value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10
From the given number line
The value of A = 7.51
The number line is defined as the straight line that consist of integers in equal intervals. We can also says that the number line is the pictorial representation of numbers on a horizontal line.
The rounding of a number is defined as a number is make it simple by keeping its value intact but closer to the next number. The closer to tenth, hundredth, thousand etc.
The value of A = 7.51
Rounding the rounder to nearest tenth = 10
Rounding the number to nearest hundredth = 0
Hence, the value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10.
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1 trillion = 1,000 billion
There are about 40 trillion cells in the human body.
Each cell consists of about 100 trillion atoms.
About how many atoms are there in the human body altogether?
Give your answer in standard form.
The number of atoms in standard form is 4 × 10²⁵ atoms
What is standard form?Standard form is number written in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer
How to find how many atoms are there in the human body altogether in standard form?Since there are about 40 trillion cells in the human body. and each cell consists of about 100 trillion atoms, we have that
40 trillion cells = 40 trillion × 1 cell
Also, 1 cell = 100 trillion atoms.
So, 40 trillion × 1 cell = 40 trillion × 100 trillion atoms.
Now, we know that 1 trillion = 1000 billion
So, Number of atoms = 40 trillion × 100 trillion atoms
= 40 × trillion × 100 × 1 trillion atoms.
= 40 × 1000 billion × 100 × 1000 billion atoms.
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
We know that 1 billion = 1000000000
So,
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
= 40 × 1000 × 100 × 1000 × 1000000000 × 1000000000 atoms
= 40000000000000000000000000
= 4 × 10000000000000000000000000
= 4 × 10²⁵ atoms
So, the number of atoms in standard form is 4 × 10²⁵ atoms
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A shopkeeper buys a dress for 40$ she sells it for 48$
Workout the percentage increase in the price of the dress.
Please help now
i need help like immediately
1/4 (8x+4)=2x-4
Answer: the statement is false
Step-by-step explanation:
y= 3x + a / 2x -5
express x in terms of a and y
The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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One-third of a number decreased by six equals eight. What is the number?
Answer:
42
Step-by-step explanation:
6+8=14x3=42
42/3=14-6=8
Y+2=1/4 x in standard form
Answer:
-[tex]\frac{1}{4}x[/tex] + y = -2
Step-by-step explanation:
Standard form: Ax + By = C
y + 2 = [tex]\frac{1}{4} x[/tex]
Rearrange terms:
1. Subtract 2 from both sides
y = [tex]\frac{1}{4} x[/tex] - 2
2. Subtract [tex]\frac{1}{4} x[/tex] from both sides
-[tex]\frac{1}{4}x[/tex] + y = -2
a cashier cannot tell the difference between cilantro and parsley. customers would only buy either cilantro or parsley. he knows that 20% of his customers prefer parsley. these customers will buy parsley 40% of the time when shopping. otherwise, they wouldn't buy either herb. 40% of his customers prefer cilantro and will buy cilantro 15% of the time when shopping. otherwise, they wouldn't buy either herb. the other 40% of his customers don't prefer, and thus don't buy, either herb. given the next customer buys one of the two herbs, what is the probability it is parsley?
Probability that customer buy parsley given buy any of two herb
= 0.5714
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Parsley ( 0.4 , 0.6 )
buy = B ∩ P = 0.08
Don't buy = DB ∩ P = 0.12
Cilantro = ( 0.15 , 0.85 )
buy = B ∩ C = 0.06
Don't buy = DB ∩ C = 0.34
Don't buy anything = DB = 0.4
P( Buy anything ) = P(B∩P) + P( B ∩ C )
= 0.08 + 0.06 = 0.14
Now, P( P/B) = P( P ∩ B)/P(B)
= 0.08/0.14 = 4/7 = 0.5714
Hence, probability that customer buy parsley given buy any of two herb
= 0.5714
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Consider the line y=-3/4x-9.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 2).
Find the equation of the line that is parallel to this line and passes through the point (-4, 2).
Equation of perpendicular line:
Equation of parallel line:
Answer:
Equation of Perpendicular Line: 4x-3y=22
Equation of parallel line:3x+4y+4=
how do u solve these simultaneous equations
y=3x+5
y=4x^2+x
The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).
What is the solution to the simultaneous equations?It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.
Given: y = 3x + 5 and y = 4x² + x.
Therefore, since y = y; it follows that the equation which holds true is;
3x + 5 = 4x² + x
4x² - 2x - 5 = 0.
Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;
x = 1.4 OR x = -0.9.
Therefore, the corresponding values of y are;
y = 3(1.4) + 5 = 9.2
OR
y = 3(-0.9) + 5 = 2.3
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Fahima buys
2 packets of bread rolls costing £1.50 for each packet
1 bottle of ketchup costing £1.60
3 packets of sausages
Fahima pays with a £10 note
she gets 30p change
fahmia works out that one packet of sausages costs £2.30
is fahima right?
you must show how you get you answer
very stuck please help
The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
In the question ,
it is given that
the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .
the slope is = (5 -(-2))/(-8 -6)
= 7/(-14)
= -1/2
so , the slope of the required line is = 2 .
The equation of the line passing through the point (3,1) with slope 2 is
(y - 1) = 2*(x-3)
y -1 = 2x - 6
y = 2x - 6 + 1
y = 2x - 5
the equation of line is y [tex]=[/tex] 2x - 5
the perpendicular slope is = 2
the y intercept is -5 .
Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
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-12a + -5b - 12c + 6a - 8b - (-4)
Answer:
-6a -13b - 12c + 4
Step-by-step explanation:
-12a + -5b - 12c + 6a - 8b - (-4)
-12a + -5b - 12c + 6a - 8b + 4 [a "- -" = +]
(-12a + 6a) -(5b -8b) - 12c + 4 [Group like terms.]
-6a -13b - 12c + 4
1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
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Please help me with this question
state: how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
Define confidence interval.In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.
Given,
Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)
The normal distribution's standard deviation, s = 3000 pounds
95% confidence interval
N = 20 observations were made.
Mean = 30,800
Margin of error :
z₇ × √3000².20
±1.314.8079
Confidence interval
= Mean + Margin of error
= 30,800 ±1.314.8079
= 29,485.192 , 32,114.8
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
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solve the inequality 2b + 5 <_ 30
The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5
What are inequalities?Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to
The symbols include
less thangreater thanless than or equal to greater than or equal toIn the problem given the symbol used is less than or equal to and the equation is solved by
2b + 5 ≤ 30
2b + 5 - 5 ≤ 30 - 5
2b ≤ 25
dividing through by 2
2b / 2 ≤ 30 / 2
b ≤ 12.5
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20-foot extension ladder set base six feet from house How far up will ladder reach?
The top of the 20-foot ladder used for painting will be 19 feet up from the base of the house
How to determine how high up the house the ladder will goinformation given in the question
Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder
he sets the base of the ladder six feet from the house
adjacent = 6 feet from the house
opposite = how far up will the top of the ladder reach = ?
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = adjacent² + opposite²
substituting the values into the equation
let x be thow far up will the top of the ladder reach
20² = 6² + x²
400 = 36 + x²
400 - 36 = x²
x² = 364
x = √364
x = 19.08
The ladder Brain borrowed will go 19 feet high
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complete question
Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?
Tyler bought a bowling ball for $80. Sales tax is 7%. What is the total cost of the bowling ball?
Answer:
Step-by-step explanation:
first multiply
80* 7% you can also do it as 80* (7/100)
=5.6
then,
add 80 and the ans of 80* (7/100)
80+5.6= 85.6
Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86
What is the y-intercept for x^3+8x^2+11x-20? How many zeros are their in the graph?
Solve for the value of v.
123°
(2v+1)°
Step-by-step explanation:
the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.
so,
123 = 2v + 1
2v = 122
v = 61
olumide plays the piano and guitar.for every 5 min of piano practice,he spends 8 min practicing guitar.how many minutes will olumide practice piano if he spends 64 minutes practicing guitar?
Answer:
Olumide will practice 40 minutes of playing the piano
Step-by-step explanation:
Olumide practices piano and guitar in the ratio of 5:8
64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.
5 x 8 = 40 minutes of piano practice
