the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.
What is the area under the curve?The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.
The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.
The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve
2y = 4√x
Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x
so, 4√x + 4x = 8
or, √x + x = 2
or, √x = (2 - x)
or, x = (2 - x)²
or, x = x² - 4x + 4
or, x² - 5x + 4 = 0
or, ( x - 4) ( x - 1) = 0
or, x = 4, 1
when x = 4 then y = 2√4 = 4
when x = 1 then y = 2 √1 = 2
when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.
Thus, only intersection point is: (1,2)
This is the type (II) region.
So, integrate the region with respect to y.
Now, area =
= [tex]\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy[/tex]
= [tex]\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy[/tex]
= [tex]\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2[/tex]
= [tex]\frac{117}{12} - 6 + \frac{21}{4}[/tex]
= [tex]\frac{108}{12}[/tex]
= 9
Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.
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If 1.5 liters of washing up liquid is 2.70$ find the cost of 1 liter
The cost of one liter of washing up liquid would be = $1.8
What is liters?Liters is a variable that is can be used to denote the measurement of a liquid.
The quantity of the washing up liquid that was given= 1.5 liters.
The cost of 1.5 liters of washing up liquid =$2.70
If 1.5 L = 2.70
1 L = X
Make X the subject of formula;
X = 1× 2.70/1.5
X = $1.8
Therefore, the cost of one liter of washing up liquid would be = $1.8
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4. Find the lengths of the sides of a triangle with vertices: (0, 0), (5, 0), (5, 12). (1 point)
O5, 12, 12
O5, 5, 12
O5, 12, 5
O5, 12, 13
The lengths of the sides of the triangle are 5, 12, and 13.
So the correct option is the last one.
How to find the lengths of the sides?Remember that if we have two points (x₁, y₁) and (x₂, y₂), the distance between these two points is given by the formula:
d = √( (x₁ - x₂)² + (y₁ - y₂)²)
Here we know that the vertices of our triangle are the points:
(0, 0), (5, 0), (5, 12)
And we want to find the lengths of the sides.
We can get the length of the first side using the points (0, 0), (5, 0)
d₁ = √( (0 - 5)² + (0 - 0)²) = 5
The length of the second side is: (5, 0), (5, 12).
d₂ = √( (5 - 5)² + (0 - 12)²) = 12
The length of the third is side is given by the points (5, 12) and (0, 0)
d₃ = √( (5 - 0)² + (12 - 12)²)
d₃ = √(25 + 144) = 13
Then the correct option is the last one:
5, 12, 13.
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A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground. Find the height to which the ladder will reach the wall.
A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.
What is height?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.
From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.
let, h = height of ladder
Given that,
length of ladder = 12 ft
angle with the ground = 52°
As we know,
sinθ = h/12
or, sin (52°) = h/12
or, 0.7880 = h/12
or, h = 9.456 foot.
the height to which the ladder will reach the wall 9.456 foot.
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Hailey goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Hailey decides to leave a tip of 24% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Hailey paid.
The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .
What is business Mathematics?
Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.
According to Question:
let the the subtotal on the bill was xx dollars
A tax of 8% is added on bill then Bill becomes xx + 8% of xx
The of 8% on bill = (108/100)xx
Now the Final bill = xx + (108/100)xx
= (208/100)xx
Hailey decides to leave a tip of 24% on the entire bill (including the tax)
So the Total Amount = (208/100)xx + 24% of Final bills
⇒
24% of (208/100)xx = (208/100)(124/100)xx
The Total amount = (208/100)xx +(208/100)(124/100)xx
Let the Amount be A
hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx
⇒ A = (52/25)xx +(52/25)(31/25)xx
⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)
⇒ 625A = 1300xx + 1612xx
⇒ 625A = 2912xx
⇒ A = (2912/625)xx
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Write and equation of the line in slope-intercept form. (0,-2) (1,3)
Answer:
y=5x−2
I hope this helps!
A line passes through the point (6,-1) and is perpendicular to the line with the equation -2x + 3y = -6.
Answer: A
Step-by-step explanation:
Before we find the equation of the perpendicular line, we have to find the slope of the original line.
The slope-intercept form of the equation is y=mx+b, so let's change that.
[tex]-2x+3y=-6[/tex] [add both sides by 2x]
[tex]3y=2x-6[/tex] [divide both sides by 3]
[tex]y=\frac{2}{3} x-2[/tex]
This gives slope as [tex]\frac{2}{3}[/tex].
There are 2 things for us to do to find the slope of a perpendicular line.
1. reciprocal
2. change sign
Let's apply those rules.
1. [tex]\frac{3}{2}[/tex]
2. [tex]-\frac{3}{2}[/tex]
Now, we can find the perpendicular lines by plugging in our new point.
[tex]y=-\frac{3}{2} x+b[/tex] [plug in x and y]
[tex]-1=-\frac{3}{2}(6)+b[/tex] [multiply]
[tex]-1=-9+b[/tex] [add both sides by 9]
[tex]b=8[/tex]
Now we can plug in for our slope-intercept equation.
[tex]y=-\frac{3}{2} x+8[/tex]
Since answers are in standard form, we have to manipulate it.
[tex]y=-\frac{3}{2} x+8[/tex] [add both sides by [tex]\frac{3}{2} x[/tex]]
[tex]\frac{3}{2}x+y=8[/tex] [multiply both sides by 2]
[tex]3x+2y=16[/tex]
Therefore, our final answer is A.
Solve for x
O4
O5
O-10
O12
Answer:
x = 5
Step-by-step explanation:
Firstly, we know that corresponding angles are the same. So we can say that 25x + 5 = 26x
Let’s simplify this equation:
25x + 5 =26x
-25x -25x
5 = x
Therefore, x = 5.
If f(x) = 3x-1 and g(x) = x^2+2, what is (f ° g)(x)?
Answer:
(f ○ g)(x) = 3x² + 5
Step-by-step explanation:
substitute x = g(x) into f(x) , that is
(f ○ g)(x)
= f(g(x))
= f(x² + 2)
= 3(x² + 2) - 1
= 3x² + 6 - 1
= 3x² + 5
Graph Y= -1/4 x + 6.
The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = -(1/4)x + 6
Convert the equation into intercept form, then we have
y = -(1/4)x + 6
4y = - x + 24
x + 4y = 24
x / 24 + y / 6 = 1
The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.
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Please help! Division of Polynomials, Find the quotient and remainder.
First:
Quotient: [tex]2x^{2} -11x+58[/tex]
Remainder: [tex]-294[/tex]
Second:
Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]
Remainder: [tex]422[/tex]
Third:
Quotient: [tex]2x-3[/tex]
Remainder: [tex]12[/tex]
Frank gets a Lamborghini for Christmas from Bill Nye for $225,000. Frank crashes the Lamborghini and survives. But his car is damaged. His repairs will cost 55% of the original price, but 30% of the price is covered by insurance. How much money does Frank owe?
Answer: Frank has to pay 56,250 dollars
Step-by-step explanation: If Frank's repair costs 55% of the original price, that means he'll have to pay 123,750 dollars because 55% of 225,000 is 123,750. But he doesn't have to pay that amount because the car insurance is paying 30% of 225,000 which is 67,500 dollars. So the car insurance is paying 67,500 dollars out of the 123,750 dollars in damage. So you'll have the subtract 123,750 by 67,500 which is 56,250 dollars.
If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air
Answer:
Step-by-step explanation:
I am not super sure about this one
write the equation of a parabola whose vertex is (-3,4) and passes through: (2,8). Put in vertex form.
The equation of the parabola that has a vertex (-3,4) and passes through (2,8) is 25y = 4x² + 24x + 13.
What is parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the DirectX and focus, respectively.
Given:
The vertex = (-3, 4) and the point = (2, 8)
Write the equation using the standard form given below,
[tex]y = a (x - h)^2 + k[/tex]
y = a[x - (-3)]² + 4
y = a(x + 3)² + 4
Now put the coordinates,
8 = a (2 + 3)² + 4
8 = 25a + 4
a = 4 / 25
Put the value of a in the above equation,
y = 4/25 × (x + 3)² + 4
25y = 4 (x² + 9 +6x) + 100
25y = 4x² + 36 +24x + 100
25y = 4x² + 24x + 13
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How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6
Sam passed the marker of 483 miles, in 6 hours.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135
Simplifying the above expression gives the mile marker
M = 483 miles
Thus, the required miles are 483.
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if a point is characterized as having both a nonzero x and y coordinate and oppositely signed coordinates, then the point must be in which of the labeled quadrants in the standard xy coordinate plane?
The labeled quadrants in the standard xy coordinate plane is Quadrant II
What is Quadrants?
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Concept:
The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.
The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).
The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.
The labeled quadrants in the standard xy coordinate plane is Quadrant II
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Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question
Answer:
10 years old
Step-by-step explanation:
an irs auditor randomly selects 3 tax returns from59returns of which7contain errors. what is the probabilitythat she selects none of those containing errors?
Therefore , the probability that she selects none of those containing errors is 0.6798.
What does probability really mean?Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.
Here,
Number of ways of selecting 3 returns out of 59 is C(59,3).
Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).
The probability that she selects none of those containing errors is
P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798
Therefore , the probability that she selects none of those containing errors is 0.6798.
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Juan borrowed $2000 for 1 year and
paid 15% interest. How much
interest did he pay in a year?
Answer:At the rate of 15% the amount of interest on $2000
Step-by-step explanation:
simple amount= Principle(1+rt)
where r= rate of inetrest
t= time
principal is initial amount
therefore, amount=2000(1+15*1)
Amount = $2,300.00
Interest = Amount - Principal = $300.00
Answer:
Step-by-step explanation:
Interest = Principle * Rate * Time /100
Principle = $2000
Rate = 15 %
Time = 1 year
I = 2000 * 15 * 1/100
I = 300
Juan has to pay $300 in a year
Please help, I will give u 20 points and I will choose u as the brainlyest answer. ( only if you get it right)
The missing factor for A in the model is 3/4
The missing factor for B in the model is 1/5The factor pair is 3/20How to determine the missing factor for A?From the question, we have the following parameters that can be used in our computation:
Length of column A = 4
Shaded region in column A = 3
This means that
The missing factor = Shaded region/Length of column A
Substitute the known values in the above equation, so, we have the following representation
The missing factor, A = 3/4
How to determine the missing factor for B?Here, we have
Length of column B = 5
Shaded region in column B = 1
This means that
The missing factor = Shaded region/Length of column B
Substitute the known values in the above equation, so, we have the following representation
The missing factor, B = 1/5
The factor pairIn (a) and (b), we have
The missing factor, A = 3/4
The missing factor, B = 1/5
So, we have
Pair = 3/4 * 1/5
Evaluate
Pair = 3/20
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What does y equal, in this picture with 30 60 90 triangles?
The value of y= 5.49≈ 5.5cm
What is 30-60-90 traingle?
The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.
By 30-60-90 triangle rule,
Side across 60° angle = x
Hypotenuse side = 2x= 15
Side across 30° angle = x√3
By solving,
2x= 15
x= 7.5cm
So side across 60° angle= 7.5 cm
Side across 30° angle = 7.5×√3
= 7.5× 1.732= 12.99≈ 13cm
As the figure given us square so,
13= 7.5+y
y= 13-7.5
y= 5.5 cm
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Inequality
x + y > 11
.05x + .10y < .95
the inequality model will be x+2y<19
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
x + y > 11
.05x + .10y < .95
by multiplying 20 in inequality we get x+2y<19
Hence, the inequality model will be x+2y<19
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You have a party of four that requested separate checks. The table's checks were for $35, $28, $42, and $22. With tips you collect $144 from the table. Tips of over 15% indicate the service is good. Did tipping indicate good service at this table?.
The tipping didn't indicate good service at this table.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both
Since the table's checks were for $35, $28, $42, and $22. The total cost will be:
= $35 + $28 + $42 + $22
= $127
A tip of 15% will give a value of:
= $127 + (15% × $127)
= $46
Since With tips you collect $144 from the table, this is not a good service.
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2. The basic advertising package has a value of $1,000
and the premium package has a value of $2,500. The
goal of the agency is to sell more than $60,000 worth
of small-business advertising packages.
If you know that exactly 10 premium packages were
sold, what can you say about the number of basic
packages the agency needs to sell to meet its goal?
1000b + 2500p = 60,000
1000b + 2500(10) = 60,000
1000b + 25000 = 60,000
1000b = 35,000
b = 35
they need to sell 35 basic packages to reach their goal of 60,000 dollars
if two cities lie on different tectonic plates, and those plates are moving so that the cities are approaching each other, how many years will it take for the two cities to be situated adjacent to each other? los angeles is 630 km south of san francisco. the plate under los angeles is moving north about 36 mm per year relative to the plate under san francisco. given this average rate of plate movement, how long will it take for los angeles to be located next to san francisco? show your work.
It will take about 18 million years for Los Angles to be located next to san Francisco.
The distance traveled is 630km (380 miles), and the net distance moves is 36mm per year.
We can use this formula to determine the answer :
Time = distance/rate
630 km = 630,000 m = 630, 000,000 mm
Time = 630,000,000 mm/ 36mm/year = 17,500,000 year
We could also put these dimensional relationship together as follows and then cancel units that occur in both the numerator and the denominator .
We are left with an answer in number of years:
630 km × [tex]\frac{1000m}{1km 1m}[/tex] × [tex]\frac{1000mm 1 year}{36mm}[/tex] = 17,500,000 year
Hence, It will take about 18 million years for Los Angles to be located next to san Francisco.
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a restaurant is introducing a new gluten-free recipe for the topping in its baked zucchini recipe. the chef will continue to use this topping if less than 8% of her customers complain about the new taste. using a random sample of customers, she conducts a hypothesis test with h0: the complaint rate is 8%, and ha: the complaint rate is less than 8%. what is a type i error and its consequence in this context?
By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.
What does testing your hypotheses mean?
To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.
First, a hazy assumption about the parameter or distribution is made.
What is hypothesis testing, and how can it be used?
A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.
The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.
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(URGENT!!) In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.
Responses
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ
The equivalent ratios to tan F = EL/ EF = OS/OJ
Similar triangles:Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.
All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.
Given that
△FEL∼△JOS
That means △FEL and △JOS are similar triangles
As we know tan θ = Opposite side / Adjacent side
From the triangle △FEL,
=> tan F = EL/EF
By the given information,
The similar triangle's corresponding sides will have the same ratio
=> EL/ EF = OS/OJ
Therefore
The equivalent ratios to tan F = EL/ EF = OS/OJ
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2/5 divided by 3/8 as a fraction
If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?
Answer:
1/2
Step-by-step explanation:
Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.
Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.
Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6
3/6=1/2
Miguel’s Skate Shop is having a sale on skateboards. The original price for its Extreme Skateboard is $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard?
The required percent decrease in the price of the skateboard is 40%.
What is the percentage?
A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here, we have
Original price = $84.50
sale price = $50.70
Percent decrease = 84.50-50.70/84.50 × 100 = 40%
Hence, the required percent decrease in the price of the skateboard is 40%.
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Which of the following represents the least value?
1/3 of 1,212
1/5 of 1,212
25% of 1,212
30% of 1,212
Answer:
1/5 of 1,212
Step-by-step explanation:
Note that 25% = 1/4 and 30% = 3/10.
The least value is achieved when we take the smallest fraction, which is 1/5.
Answer:
1/5 of 1212 is the smallest value
Step-by-step explanation:
if we convert 25% to a fraction we have 1/4
if we convert 30% to a fraction we have 3/10
now we convert each of the four fractions into equivalent fractions using lowest common denominator of 60
1/3 = 20/60
1/5 = 12/60
1/4 = 15/60
3/10 = 18/60
the smallest fraction is 12/60, or 1/5
therefore 1/5 of 1212 is the smallest value
