The given linear equation has only one solution i.e. x = 3/4
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Here,
On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and
Hence, the given linear equation has only one solution i.e. x = 3/4.
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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
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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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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which is the correct answer ????
The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.
According to the question,
We have the following two equations:
Equation 1: y = -5x+10
Equation 2: 2x+y = 7
Now, we will substitute the value of y from equation 1 in equation 2.
So, we have the following expression:
2x+(-5x+10) = 7
(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)
Hence, the correct option is B.
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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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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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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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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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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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Which graph has a slope of 4/5?
The ratio of 7th grade students to 8th grade students in a soccer league is 7:13, if there are 100 students in all ,how many are in 7th grade ?
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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What are the solutions to the equation 3k² + k-3=0?
Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as
a list of numbers, separated with commas. Example: 3.25,4.16
k=
Answer:
Step-by-step explanation:
Solution
Solve with the quadratic formula
3k2+k−3=0 : k=(−1+√376)/6 , k=(−1−√376 )/6 (Decimal: k=0.84712…, k=−1.18046…)- Answer
Steps
3k2+k−3=0
Solve with the quadratic formula
For a quadratic equation of the form ax^2+bx+c=0,
the solutions are x1, 2=(−b±√b^2−4ac)/2a where a=3, b=1, c=−3
Substituting we have
k1, 2= [(−1±√1^2−4· 3(−3)]/2· 3
Apply rule 1^a=1 , therefore 1^2=1
=√1+4· 3· 3=√1+36
√1^2−4· 3(−3)=√37
Therefore,
k1, 2=(−1±√37)/2· 3
k1, 2=(−1±√37)/6
Separate the solutions
k1=(−1+√37)/6
k2=(−1−√37)/6
The solutions to the quadratic equation are:
k=(−1+√37)/6 , k=(−1−√37)/6
k1=0.84712 k2=−1.18046
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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Factor the given number 102 Input the number's prime factors in ascending order.
-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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On December 12, Lowell Corporation accepted a $160,000, 120-day, non-interest-bearing note from Able.com. What is the maturity value of the note?
If On December 12, Lowell Corporation accepted a $160,000, 120-day, non-interest-bearing note from Able.com. the maturity value of the note is: $213,333.
How to find the maturity value of the note?Using this formula to find the maturity value of the note
Maturity value of the note = Principal + interest
Let plug in the formula
Maturity value of the note = $160,000 + ($160,000 × 120 /360)
Maturity value of the note = $160,000 + $53,333
Maturity value of the note = $213,333
Therefore the maturity value of the note is $213,333.
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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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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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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 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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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.
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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Find the y intercept and slope of the linear equation
0 = 4.5 - 2y + 4.8x
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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helppppppppppppppppppppppppp
Answer:
E
Step-by-step explanation:
I am a line & domain is -7
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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Find the measure of the exterior angle.
Answer:
x is 109°
hopefully this will help u
In how many ways can a committee of 5 men and 6 women be formed from a group of 8 men and 7 women?
By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:
392
In how many ways can the committee be formed?For a set of N elements, the number of different sets of K elements that can be formed is:
C(N, K) = N!/(K!*(N - K)!)
Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women
Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:
for men:
C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56
for women:
C(7, 6) = 7!/(6!*(7 - 6)!) = 7
Then the total number of different committees is:
C = 56*7 = 392
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There are 17 counters in a bag. The table shows the number of counters of each colour. Colour Number of Counters Red 7 What fraction of the counters are blue? Blue 2 Yellow 5 Green 3
Answer: 2/17 or 2 over 17
Step-by-step explanation:
