Answer:
Line v: y = x + 5
Step-by-step explanation:
Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:
[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]
The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:
[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]
Mr Agrawal has an electrical shop. he sold a tube light for rs 240 at 20% profit. find the cost price of tube light.
Answer:
192
Step-by-step explanation:
If 20% is the profit, then 80% is the cost.
.8 x 240 = 192
What is the domain of the following relation?
a. {-3, -1, 1, 4, 5}
b. {-5, 0, 2, 6}
c. {-3, -5, 0, 2, 4, 5, 6}
d. there is no domain
The domain of the relation in the diagram below is: a. {-3, -1, 1, 4, 5}.
What is the Domain of a Relation?A relation has a set of domain elements, which are all the inputs of the relation that are mapped to a set of range elements, which are all the corresponding outputs of the relation.
Given the relation as shown in the diagram that is attached below showing a mapping, the set of input values is {-3, -1, 1, 4, 5}, while the set of output values is {-5, 0, 2, 6}.
Therefore, {-3, -1, 1, 4, 5} is the domain of the relation because it is the set of all input values, while the range of the relation is {-5, 0, 2, 6}, because it is the set of all output values that corresponds to the input values.
The domain is therefore: a. {-3, -1, 1, 4, 5}.
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A dairy farmer wants to mix a 45% protein supplement and a standard 20% protein ration to make 2000 pounds of a high-grade 35% protein ration. How many pounds of each should he use?
The farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
From given information,
Type 1: 45 percent of protein in the supplement is x pounds
Type 2: 20 percent of the protein in the supplement is (2000 - x) pounds
Also Mixture A 35% of the protein in the supplement is 2000 pounds
According to the equation after removing the percentage sign we have
45x + 20(2000-x)= 35*2000
45x + 40000 - 20x = 70000
25x = 30000
x = 1200
Now for type 2 mixture we have
2000 - 1200 = 800 pounds
Therefore, the farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
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Use the graph of the following function (x) to find the value.
f(1)
From the graph of the given function , the value of f(1) = -1.
As given in the question,
From the graph of the given function,
Two coordinates from the graph are as follow:
( x₁ , y₁) = (1, -1)
( x₂ , y₂ ) = ( 0, -3 )
Equation of the line representing the function is given by:
(y - y₁) /(x-x₁) = ( y₂ -y₁)/ (x₂ -x₁)
⇒(y +1)/ (x-1) = (-3 +1)/ (0-1)
⇒ (y +1)/ (x-1) = 2
⇒y +1 = 2x -2
⇒ y = 2x -3
To get the value of x we have,
y = f(x)
⇒f(x) = 2x -3
⇒f(1) = 2(1) -3
⇒f(1) = -1
Therefore, from the graph of the given function , the value of f(1) = -1.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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(7x-7)
63°
(3x +45)
(9-4)
Find x and y
The value of x is 33 and y is 39.
What is parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.As, (7x- 7) = 3x+ 45 (corresponding angles)
4x = 52
x= 13
Now, 7x- 7 + w + 63 = 180 (linear pair)
w= 180- 147
w= 33 degree.
y-6 = 33 (Alternate interior angle)
y= 39
Hence, the value of x is 33 and y is 39.
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Determine when the function is positive, negative, increasing, or decreasing.
Then describe the end behavior of the function.
The function is positive and increasing from 0 to 2.5, at negative and decreasing from 0 to -2.5, respectively.
How to find returns to scale?
Returns to scale involves an increase in an output more than when all the inputs increase proportionately.
Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.
This shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.
In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.
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Find the y intercept and slope of the linear equation
0 = 4.5 - 2y + 4.8x
Find the measure of the exterior angle.
Answer:
x is 109°
hopefully this will help u
What is the slope of line KH if H(-4, 2) and K(2, -2)? Remember to reduce!
The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.
What is a slope?A mathematical word used to define a line's direction and steepness is its slope or gradient.
If a line is rising from left to right, it is growing. The slope is positive, or m>0
If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0
A line has zero slopes if it is horizontal. This function is constant.
The slope of a line is y - y₁ = m(x - x₁)
Slope m = (y₂ - y₁)/(x₂ - x₁)
m = (- 2 - 2)/(2 + 4)
m = - 4/6
m = - 2/3
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Question 8 (1 point)
The selling price of a widget is $15 and the fixed cost per month is $4,800. The variable cost per widget is $9. Calculate the
contribution margin rate.
0000
b
C
d
Question 8 of 20 | Page 8 of 20
40%
60%
30%
50%
The contribution margin rate is 40%.
What is contribution margin rate?
A company's contribution margin rate is the total revenue minus variable costs divided by the revenue.
First we need to determine the contribution margin in order to calculate the contribution margin rate. There are two approaches to determine the contribution margin.
Contribution Margin = Net Sales Revenue – Variable CostContribution Margin = Fixed Costs + Net IncomeContribution Margin = $15 - $9 = $6
The contribution margin is $6.
Now we will calculate the contribution margin rate using this formula,
Contribution Margin Rate = Contribution Margin [tex]/[/tex] Sales Revenue
Contribution Margin Rate = $6 / $15
= 0.4 * 100
= 40%.
Hence the contribution margin rate is 40%.
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Which graph has a slope of 4/5?
Use Figure 1 to evaluate each trigonometric function of angle A . The side adjacent to angle A has length 4 and the side opposite angle A has length 10.
The trigonometric ratios for angle A are measured below.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a right angled triangle as shown in the image attached.
The six trigonometric ratios are -
sin (A) = 10/√116
cos (A) = 4/√116
tan (A) = 10/4
cosec (A) = √116/10
sec (A) = √116/4
cot (A) = 4/10
Therefore, the trigonometric ratios for angle A are measured above.
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-8 What is 9.15 x 10°° written in standard form?
The value of the number 9.15 x 10° written in standard form is equal to 9.15.
As given in the question,
Given number is equal to :
9.15 x 10°
Given number 9.15 x 10° is written in standard form.
The value of the given number 9.15 x 10° written in standard form is given by:
9.15 x 10°
Here 10° = 1
Using property of number: Any number raise to zero is always equal to 1.
9.15 x 1
Using Multiplicative identity , number multiply to 1 remain number itself.
= 9.15
Therefore, the value of the number 9.15 x 10° written in standard form is equal to 9.15.
The complete question is:
What is the value of 9.15 x 10° written in standard form?
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Two buses leave a station at the same time and travel in opposite directions. On bus travels 17 km/h faster than the other. If the two buses are 836 kilometers apart after 4 hours, what is the rate of each bus
Step-by-step explanation:
speed = distance / time
to get distance, we have to multiply by time.
the speed the 2 busses are moving seat from each other is
x + (x + 17) = 2x + 17
x = the speed of one bus
x + 17 = the speed of the other bus.
so, after 4 hours the distance between them is
(2x + 17) × 4 = 836
2x + 17 = 209
2x = 192
x = 96 km/h
bus 1 travels at 96 km/h.
bus 2 travels at 96+17 = 113 km/h.
A shoe store is offering a series of markdowns for its customers due to its need for quick cash. The shoe store is offering the markdowns in the following order: 35%, 20%, and 10%. What would be the sale price of a pair of boots, if it originally costs $165.00?
The final price of the shoes after successive discounts is $77.22.
What is a discount?
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
Main Body:
Sale price = Original price - discount
The formula for successive discount is given by=
Cost price*(1 - discount₁/100)*(1 - discount₂/100)*(1 - discount₃/100)
Now calculating:
According to the question , Cost price = $165
sale price = 165*(1-0.35)*(1-0.20)*(1-0.10)
= 165*0.65*0.8*0.9
= $77.22
Hence the answer to sale price of the shoe would be $77.22
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You need more than 120 cups of iced tea but less than 180 cups of iced tea for a
picnic. Each batch of iced tea makes 30 cups. Which inequality represents the
number of batches b you need to make?
The required equation of inequality is 4 ≤ b ≤ 6
Given ; Cups of iced tea = 120 cups
and the cups of iced coffee should not be less than 180 cups
Thus this is a question of inequality
Each batch of iced tea makes = 30 cups
thus the required equation is
[tex]\frac{120}{30}[/tex] and this is less than the number of batches which is represented by b
thus the equation would be [tex]\frac{120}{30}[/tex] ≤ b
And it should be less than 180 cups of iced tea
thus the equation would be
b ≤ [tex]\frac{180}{30}[/tex]
Thus the required equation is :
[tex]\frac{120}{30}[/tex] ≤ b ≤ [tex]\frac{180}{30}[/tex]
On simplifying this we will get ;
4 ≤ b ≤ 6
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Ralph wants to join a travel soccer team, a discretionary expense. His parents tell him he must get a job to earn the money to cover the costs. Ralph now views this discretionary expense as an
essential expense since he must pay his parents back. The costs of the travel team are listed below.
Find the total cost of being on the team.
If Ralph takes a summer job and works 10 weeks over the summer, how much must be average each week to cover the travel team expenses?
If Ralph is paid at a flat rate of exactly q dollars each week, what is the standard deviation of the distribution of his 10 weekly paychecks?
The total cost to be in the team will be $1192. He must earn an average of $119.2 per week for 10 weeks. If Ralph is paid at a flat rate of exactly q dollars each week, so the standard deviation will $0.
What is total cost?Total cost is the sum of all expenditures made to produce a certain level of output; when this total cost is divided by the quantity produced, average or unit cost is discovered. The sum of the fixed and variable costs is the total cost. For instance, if a company has a fixed cost per unit of $30 and a variable cost per unit of $5 that increases as output increases, the total cost will be $35. Total cost is equal to the sum of all fixed and variable costs. Total Cost = (Average Fixed Cost + Average Variable Cost) x Number of Units is another way to express it. All of this had to do with the total cost formula, which is a crucial idea for figuring out the total cost of production.
Here,
The expenses of team is,
Uniform=$67.00
Registration=$50.00
Tournaments=$775.00
Travel =$300.00
Total cost=sum of all expense
=67+50+775+300
=$1192
Average cost=Total cost/number of weeks he worked
=1192/10
=$119.2
Deviation of distribution cost,
If Ralph is paid at a flat rate of exactly q dollars each week then there will be $0 deviation.
It will cost $1192 in total to join the team. For ten weeks, he must make an average of $119.2 per week. If Ralph receives a fixed weekly salary of exactly q dollars, the standard deviation will be zero.
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helppppppppppppppppppppppppp
Answer:
E
Step-by-step explanation:
I am a line & domain is -7
Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
What property did Bill use?
The addition property used by Bill in finding the actual December temperature is the commutative property of addition.
According to the question,
We have the following information:
Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.
The commutative property of addition means that if two numbers are added and their order is inversed then the result of addition will always be the same.
For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.
Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.
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What is an equation of a line, in point-slope form, that passes through (1, -7) and has a slope of -2/3?
O y-7= -2/3( x + 1)
Oy+7= -2/3(x - 1)
Oy+7=2/3(x + 1)
O y-7=2/3(x-1)
Answer:
second option
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (1, - 7 ) , then
y - (- 7) = - [tex]\frac{2}{3}[/tex] (x - 1) , that is
y + 7 = - [tex]\frac{2}{3}[/tex] (x - 1)
Simon invests $7000 into an account that earns 0.4% simple interest annually.
Which statement best describes the relationship between the number of years Simon has his money invested and the account balance in any year?
1:
The relationship is linear. His account increases each year by a constant value of $280.
2:The relationship is exponential. The ratio of his account balance any year to the previous year is 1.004.
3:The relationship is exponential. The ratio of his account balance any year to the previous year is 0.004.
4:The relationship is linear. His account increases each year by a constant value of $28.
The relationship is linear. His account increases each year by a constant value of $28.
The relationship between the number of years that Simon's money is invested and the account balance can be described as 4:The relationship is linear. His account increases each year by a constant value of $28.
How to find the relationship between variables?The simple interest due to Simon's account every year is:
= Simple interest rate x Amount invested
= 0.4% x 7, 000
= $28
This means that every year, Simon's account would increase by a value of $28.
This represents a linear relationship because in linear relationships, the value of the variables increases by a constant amount each year or period.
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Factor the given number 102 Input the number's prime factors in ascending order.
The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Derek's hourly rate is $10 and Charlie's hourly rate is $10.45, Charlie's earns $0.45 more per hour than Derek.
What is unit rate?A unit rate means a rate for one of something.
Given that, a graph which shows Derek's earning hourly, and Charlie earns $52.25 in 5 hours of work,
Derek's earns $10 for an hour
Charlie's earning for an hour = 52.25/ 5 = $10.45
Hence, Charlie's hourly rate is $10.45, and he earns $0.45 more per hour than Derek.
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26% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answer:
a) p(X =2) = 0.261
b) P(x>2) = 0.566
c) P(2<x<5) = 0.334
Step-by-step explanation:
Given 24% of U.S. adults say they are more likely to make purchases during a sales tax holiday
Probability 0f U.S. adults say they are more likely to make purchases during a sales tax holiday (p) = 0.24
n = 10
By using Poisson distribution
mean number of make purchases during a sales tax holiday
λ = np = 10 X 0.24 = 2.4
a)
The probability of getting exactly '2'
The probability
b) The probability of getting more than '2'
= 0.090 + 0.2177+0.261 = 0.566
P(x>2) = 0.566
c) The probability of getting between two and five
P( 2<x<5) = P(x=3)+p(x=4) =P(2<x<5) = 0.2090 + 0.125 = 0.334
hope this helps
PLEASE HELP ASAP!!! Write the expression as a power and evaluate it.
8•2^7
Answer:
1024
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
, then
8 × [tex]2^{7}[/tex]
= 2³ × [tex]2^{7}[/tex]
= [tex]2^{(3+7)}[/tex]
= [tex]2^{10}[/tex]
= 1024
Differentiate the function with respect to x.
The differentiation of the given function is [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex].
In the given question we have to differentiate the given function with respect to x.
The given function is f(x)= [tex]tan(x^4)\cdot(3x^3+2)[/tex].
We have to differentiate the given function so we differentiate using the Product Rule.
The Product Rule of Differentiation is
d/dx[h(x)g(x)]=h(x) d/dx g(x)+g(x) d/dx h(x)
In the given function the value of
h(x) = [tex]tan(x^4)[/tex] and g(x) = [tex](3x^3+2)[/tex]
So;
f'(x)= [tex]tan(x^4)[/tex]d/dx [tex](3x^3+2)[/tex] + [tex](3x^3+2)[/tex] d/dx [tex]tan(x^4)[/tex]............(1)
We firstly find the value of d/dx [tex](3x^3+2)[/tex] and d/dx [tex]tan(x^4)[/tex].
We firstly find the value of d/dx [tex](3x^3+2)[/tex]
As we know that d/dx of x^n =nx^(n-1) and d/dx a=0
So;
d/dx [tex](3x^3+2)[/tex]= 3 d/dx [tex]x^3[/tex]+d/dx 2
d/dx [tex](3x^3+2)[/tex]=3(3[tex]x^2[/tex])+0
d/dx [tex](3x^3+2)[/tex]=9[tex]x^2[/tex]
Now finding the value of d/dx tan([tex]x^4[/tex])
d/dx [tex]tan(x^4)[/tex] = d/dx [tex]tan(x^4)[/tex] d/dx [tex]x^4[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]sec^2(x^4)\cdot(4x^3)[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]4x^3sec^2(x^4)[/tex]
Now putting the values of differentiation in equation 1
f'(x)= [tex]tan(x^4)\cdot9x^2[/tex] + [tex](3x^3+2)\cdot4x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]3x^3\cdot4x^3sec^2(x^4)+2\cdot4x^3sec^2(x^4)[/tex]
Simplifying
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{3+3}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
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When Max was a puppy, he weighted 5 1/2 pounds. At his 1-year check-up with the vet, Max weighted 15.8 pounds. How much weight did Max gain between the time he was a puppy and his 1-year check-up?
Max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
When Max was a puppy, he weighted [tex]5\frac{1}{2}[/tex] pounds
At his 1-year check-up with the vet, Max weighted 15.8 pounds
We need to find the weight did Max gain between the time he was a puppy and his 1-year check-up.
To find this we need to find the difference when Max was a puppy and after one year check up.
Difference is nothing but subtracting one value from another value.
Let us convert mixed fraction [tex]5\frac{1}{2}[/tex] pounds to improper.
[tex]5\frac{1}{2}[/tex] =11/2=5.5
Now subtract 15.8-5.5
10.3 pounds.
Hence, max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.
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how much is 1191 less than 1111
Answer: If you mean how much is 1111 less than 1191, then your answer is
80.
Step-by-step explanation: 1191 - 1111 = 80.
You pick a card at random.
5678
What is P(not divisor of 45)?
Write your answer as a percentage.
%
As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.
What is meant by percentage?A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct.," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement. Percentage = (Original number/Another number) x 100 is the formula for calculating the percentage of one number from another. A percentage is a value or ratio that represents a fraction of 100 in mathematics. Percentage means one hundred percent. There are no units in it. A percentage is a number that tells us how much out of 100 we are talking about, and it can also be written as a decimal or a fraction - three for the price of one.Therefore,
45/5 = 9
45/6 = 7.5
45/7 = 6.42
45/8 = 5.62
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