Solve 6(x-3)=45
How do u do this?
Answer:
It is 6×x 6x-18=45
6x=45-18
=27
6x=27
27 divided by 6 = 4.5
A fast food restaurant estimates the cost of making hamburgers to be $2.05 per hamburger plus an ade
If $13,025 represents the total cost of making a hamburgers, which equation can be used to find the numb
O 13,025 = 2.05 + 2,000x
O 13,025 = 2.05€ + 2,000
O 13,025x = 2.05 + 2,000
O 13,025 (2.05 + 2,000)
Based on the total cost of making hamburgers, and the cost per hamburger the equation to find the number of hamburgers made is 13,025 = 2.05x + 2,000
How to find the number of hamburgers?The cost of a single hamburger is $2.05 and this is in addition to a fixed cost of $2,000 for fixed costs.
This means that the number of hamburgers x, can be found by the formula:
Total cost of hamburgers = Cost per hamburger x Number of hamburgers + Fixed costs
Using x and the given figures gives:
13,025 = 2.05x + 2,000
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Find an equation in the form y = ax²+bx+c for the parabola passing through the points.
(-4,-40), (-3,-13), (-2,4)
the formula for the parabola that passes through the points, y = ax2 + bx + c. The values of a, b, and c are -9, -19,32 respectively.
What exactly does parabola mean?The intersection of a right circular cone with a plane parallel to an element of the cone creates a plane curve, which is equivalent to a point moving so that its distance from a given point equals its distance from a fixed line.
based on the available facts;
Parabola fundamental: y = ax2 + bx + c
We can plug in three locations for (x, y) to get three equations at once.
(-4, -40): 40 = 4a - 2b + c {equation 1}
(-3, -13): -13 = 9a + 3b + c {equation 2}
(-2,4): 4 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = -40 {equation 1}
a - b + c = 4 {equation 3}
--------------------- subtract
3a - b = -44
9a + 3b + c = -13 {equation 2}
a - b + c = 4 {equation 3}
-------------------- subtract
8a + 4b = -17
We now have two equations with 2 unknowns we can use to find a, b
3a - b = -44 {equation 4}
8a + 4b = -4 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = -176
8a + 4b = -4
----------------- add
20a = -180
a = 180/20
a = -9
8a + 4b = -4
4b = -76
b = -19
Plug these 2 values into one of the original equations and solve for c
4 = a - b + c {equation 3}
4 = -9-19 + c
4 = -28 + c
4+28= c
c = 32
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Please help! What is the domain of the function shown in the graph below?
Answer:
[-2,infinitysymbol)
Step-by-step explanation:
If you have a graph to look at, the domain is like you are walking up and down the x-axis (which is actually not up/down but left/right) and you're stating where this graph exists.
If you walked all the way over to -10 and looked up or down, the graph just doesn't exist over there.
The graph exists from -2, including -2, so use the SQUARE bracket [.
On the right side there's an arrow on the graph so it keeps going forever. Thats infinitysymbol.
Always wrap a parenthesis ), around the infinity symbol.
Interval notation uses the [SQUARE] brackets or (parenthesis) and even though it looks like a point, its not. It means
[FromHere, ToHere) and answers the question, where is the graph?
The cross-section of a lean-to shelter is in the shape of a triangle. The base of the triangle is 66 feet more than twice its height. If the area of the triangle is 108108 square feet, determine the length of the base and the height of the triangle in feet
A triangle with an area of 108 square feet has a base length and height equal to 24 feet and 9 feet, respectively.
Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle.
A = 1/2bh
where b is the length of the base
h is the height
If the base of the triangle is 6 feet more than twice its height, then we have b = 6 + 2h.
A = 1/2bh
A = 1/2(6 + 2h)(h)
A = h^2 + 3h
If the area of the triangle is 108 square feet, then
A = h^2 + 3h
108 = h^2 + 3h
h^2 + 3h - 108 = 0
Getting the roots of the polynomial.
h^2 + 3h - 108 = 0
(h - 9)(h + 12) = 0
h = 9 ; h = -12
Since h must be a positive number, h = 9 feet.
Substitute the value of h in the equation for b.
b = 6 + 2h
b = 6 + 2(9)
b = 6 + 18
b = 24 feet
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The points (t,–4) and (2,–8) fall on a line with a slope of –2. What is the value of t?
The value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 as required in the task content is; 0.
What is the value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2?It follows from the task content that the value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 be determined.
Since, slope, m = (y2-y1) / (x2-x1)
Ultimately, the value of t can be determined as follows;
-2 = (-8-(-4))/(2-t)
-4 +2t = -4
2t = 0
t = 0.
Therefore, the value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 as required in the task content is; 0.
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A scientific report says that the proportion of the population that is left-handed is
0.10 with a margin of error of 0.02.
a. Is 0.07 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
b. Is 0.087 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
c. Is 0.128 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
A) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
B) 0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is
left-handed.
C) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
How to Interpret Confidence Interval?
We are given that;
Population that is left-handed = 0.10
Margin of error =0.02.
A) Confidence interval = 0.07 ± 0.02
CL = (0.05, 0.09)
0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
b) Confidence interval = 0.087 ± 0.02
CL = (0.067, 0.107)
0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is
left-handed.
c) Confidence interval = 0.128 ± 0.02
CL = (0.108, 0.148)
0.1 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
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Draw a scatter plot and find the line of best fit for each set of data. (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396)
The scatter plot is shown in attached images and the line of best fit for the data set is y=24.6607x+24.7637.
The given data set is (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396).
Plot the points on a coordinate plane.
Calculate the mean of the x -values and the y -values.
[tex]\begin{aligned}\bar{X}&=\frac{3+5+7+9+11+13+15}{7}\\ &=\frac{63}{7} \text{ or } 9\\ \bar{Y}&=\frac{100+150+195+244+296+346+396}{7}\\ &=\frac{1727}{7}\text{ or }246.71\end[/tex]
Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get
[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=112[/tex]
and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=2762[/tex]
Calculate the slope.
[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{2762}{112}\\ &=24.6607\end[/tex]
Calculate the y -intercept.
Use the formula to compute the y -intercept.
[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=246.71-(24.6607\times 9)\\ &=246.71-221.9463\\ &=24.7637\end[/tex]
Use the slope and y -intercept to form to find the equation of the line of best fit.
The slope of the line is 24.6607 and the y -intercept is 24.7637 .
Therefore, the equation is y=24.6607x+24.7637.
Draw the line on the scatter plot.
Hence, the scatter plot is shown in attached image and the line of best fit for given data set (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396) is y=24.6607x+24.7637.
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The slope of line a is 5. The slope of line b is 1/5 . Which statement is true
The lines are parallel.
The lines are neither perpendicular nor parallel.
The lines are perpendicular.
The statement is true that the lines are neither perpendicular nor parallel.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Slope tells how vertical a line is thus more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
The Slope of parallel lines are same, similarly Slopes of perpendicular lines are negative reciprocal of each other.
Parallel lines have the same slope beacuse the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
If there are two lines perpendicular to each other, then their slopes are negative reciprocal of each other meaning if one line's slope is 'a', then its perpendicular line's slope would be -1/a
We have been given that the slope of line a is 5 and the slope of line b is 1/5.
The statement is true that the lines are neither perpendicular nor parallel.
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6x-3y=21
what would be the answer and how would i solve this
Answer:
x= 7+y/2
The slope is 2
Step-by-step explanation:
Pilar paid $2.40 for 2 cans of dog food at the pet store. leo visited the same pet store and spent $3.60 on 3 cans of dog food. write an equation to represent the proportional relationship between cans of dog food, x, and total cost, y.
Answer:
y = 1.2x
Step-by-step explanation:
The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is
y = 1.2x
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
Pilar:
Cost of 2 cans of dog food = $2,40
We can write this as an equation:
2 = 2.40 ____(1)
Leo:
Cost of 3 cans of dog food = $3.60
We can write this as an equation:
3 = 3.60 ____(2)
From (1) and (2) we get,
The cost of dog food y is proportional to 1.2 of the cans of dog food x.
y = 1.2x
Thus,
The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is
y = 1.2x
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PLS PLS HELP OMG PLSS
The time that Natasha will be able to finish the last piece of equipment will be 8.15 pm
How to calculate the time?It should be noted that the following information can be deduced based on the information given:
Steeper = 18 minutes
Treadmill = 25 minutes
Rower = 27 minutes
Bike = 1 hour 5 minutes = 65 minutes
Total minutes = 18 + 25 + 27 + 65 = 135 minutes = 2 hours 15 minutes
It should be noted that there's an interval of 5 minutes between each equipment. The time for all the equipment will be:
= 5 × 3 = 15 minutes
Therefore since the starting time is 5.45 pm, the ending period will be:
= 5.45 + 15 minutes + 2 hours 15 minutes
= 8.15 pm
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Suppose the cost of an item is c. First, the cost is discounted by 30%. Then sales tax of 6.5% is added to the sales price. Write an algebraic expression for the final cost of the item using the variable c.
The Algebraic expression for the final cost of the item using the variable c is 0.7455c
The cost of the item is c
Algebraic expression after discounting the cost by 30%
c - 30%of c
c- 0.3c
0.7c
Now, Algebraic expression after the application of 6.5% of sales tax
0.7c + 6.5%of 0.7c
0.7c +0.065(.7c)
0.7c +0.0455c
0.74.55c
Hence, 0.7455c is the algebraic expression for the final cost of the item using the variable c.
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
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The total cost (in cents) of x+2 markers is x³+5 x²+2 x-8
a. Write an expression that models the cost of each marker.
An expression that models the cost of each marker, when the cost of x + 2 markers is x³ + 5 x² + 2 x - 8, is x² + 3 x - 4
Given,
Total number of markers = x + 2
The total cost of markers = x³ + 5 x² + 2 x - 8
An expression to model the cost of each marker can be found by dividing the total cost of markers by the total number of markers.
This implies, the expression can be given as :
(x³ + 5 x² + 2 x - 8) / (x + 2)
x² + 3 x - 4
_______________
x + 2 | x³ + 5 x² + 2 x - 8
x³ + 2 x²
________________
3 x² + 2 x
3 x² + 6 x
________________
- 4 x - 8
- 4 x - 8
_________________
0
The quotient of this division is the expression that the cost of each marker.
Therefore, An expression that models the cost of each marker when the cost of x + 2 markers is taken into account. x³ + 5 x² + 2 x - 8, is x² + 3 x - 4
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Given f(x) = x + 9, write the new function if the y-intercept is decreased by three unit.
Answer:
f(x) = x + 6
Step-by-step explanation:
if the y-intercept is decreased by 3 units in the slope formula where b is the y-intercept, then the answer is x + 6
pls help asap no rush tho
Answer:
32.4! or 9 with the square root of 13!
Step-by-step explanation:
You have to add the outside numbers and keep 13 the same. Then proceed answer that getting 32.4.
Hopefully this answered your question have a nice day! :D
help, please, begging you
Hank's pickup can travel 75 miles on5 gallons of gas. How many gallons will Hank's pickup need to travel 60 miles?
The answer is 4
Step-by-step explanation:
Answer:
4 gallons
Step-by-step explanation:
75/5=15
This means that per gallon gives 15 miles.
15*4=60
1 gallon x 4 = 4 gallons.
Answer = 4 gallons
Hope this helps :)
name 3 fractions between 2/8 and 3/8
Answer:
1/3, 2/7, and 3/10
Step-by-step explanation:
2/8 = 0.25
3/8= 0.375
1/3=0.333333
2/7=0.28571
3/10=0.3
Julia decides to purchase the BLT stock, which pays a dividend. What will the 1.2% dividend on her $1,000 investment be?
What are the costs of this investment?
Select the correct answer from each drop-down menu.
Julia will receive $
She will have to pay
in dividends each year.
to buy the stock.
on that income. An additional cost of this investment includes
Answer:Julia will receive $12 she will have to pay TAXES on that income.An additional cost of this investment includes A BROKER FEE to buy a stock
Step-by-step explanation:
Which expression is a factor of this polynomial?
X^3+2x^2-9x-18
-
9x 18
-
OA.
(x + 1)
OB. (x + 2)
OC. (x-6)
OD. (x - 2)
The factor is the solution of zeros of the equation and x + 2 making it zero therefore x + 2 will be the solution of the given polynomial so option (B) will be correct.
What are the roots of an equation?Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.
Given the polynomial,
x³ + 2x² - 9x - 18
A factor is consist of a solution of zeros of any polynomial.
For example;
x² + 5x + 6 = 0
x(x + 2) + 3(x + 2) = 0
(x + 3)(x + 2) = 0
Here x + 3 and x + 2 are factor and solution is x = -3 and -2
Similarly,
x³ + 2x² - 9x - 18 = 0
The factor must be the solution to this.
By cross-checking option
Option (A) x + 1 = 0 → x = -1
Keeping x = -1
(-1)³ + 2(-1)² - 9(-1) - 18 = -8 ≠ 0 so it is not the factor.
Option (B) (x + 2) = 0 → x = -2
(-2)³ + 2(-2)² - 9(-2) - 18
-8 + 8 + 18 - 18 = 0 = 0 so it will be factor of the polynomial.
Hence " x + 2 will be the solution of the given polynomial".
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The formula for the Ideal Gas Law is P V=n R T , where P is the pressure in kilopascals ( kPA), V is the volume in liters (L), T is the temperature in Kelvin (K), n is the number of moles of gas, and R=8.314 is the universal gas constant.
a. Write an equation to find the volume in terms of P, n, R , and T .
The equation to find the volume in terms of P, n, R , and T is:
[tex]V=\frac{n R T}{P}[/tex]
What is Ideal Gas Law?The ideal gas law is the general gas equation. It is a good approximation to find behavior of gases under different conditions. This law says that the product of pressure in the atmosphere and volume is equal to product of moles and temperature. We generally use an equation to define these relations.
Equation of ideal gas law
P V=n R T
where,
P = pressure measured in atmosphere
V = volume measured in liters
n = number of moles present in gas
T = temperature
R = gas constant
Ideal gas equation shows several direct and indirect variations between the different elements , such as in the equation pressure (P) shows direct variation with n and T , and inverse variation with volume (V).
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Simplify. 3 √18 +2√72
The rationalized expression in general term is given by: 21√2
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
3 √18 +2√72, in this expression we have no values in the denominator, so we must only decompose the square root to reduce the term without altering its value.
√18 = √2×3×3 = √2√3² = 3√2√72 = √2×2×2×3×3 = √2³×3² = 3×2√2 = 6√23√18 +2√72
3×3√2 + 2×6√2
9√2 + 12√2
21√2
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please help me I'm running out of time!!
Answer:
The answer is hotdog you can cook the hotdog and eat it
Please explain thank u
Answer:
x = 6
Step-by-step explanation:
multiply by 6 the whole equation to eliminate fractions and convert the coefficients and independent numbers to integers:
[tex]4x-1=3x+5[/tex]
[tex]4x-3x=5+1[/tex]
[tex]x=6[/tex]
Hope this helps
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
In the equation:
[tex] \frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6} [/tex]
Multiply both sides of the equation by the common denominator which is 6
[tex] \frac{2 \times 6}{3} x - \frac{1 \times 6}{6 } = \frac{1 \times 6}{2} x + \frac{5 \times 6}{6} [/tex]
[tex] ⟹ \frac{12}{3} x - \frac{6}{6} = \frac{6}{2} x + \frac{30}{6} [/tex]
Reduce the fraction
[tex]4x - 1 = 3x + 5[/tex]
Now, collect like terms to find the value of x
[tex]4x - 3x = 5 + 1[/tex]
Therefore:
[tex]x = 6[/tex]
I hope this helpswhat is the gcf of 16 and 48
Answer:
16
Step-by-step explanation:
The GCF of two non-zero integers, x(16) and y(48), is the greatest positive integer m(16) that divides both x(16) and y(48) without any remainder.
Answer:16
Step-by-step explanation: i did this question on a test before
v=
5.7+67v= -9.3+65v
Step-by-step explanation:
let's write it a little bit nicer
5.7 + 67v = -9.3 + 65v | subtract 65v on both sides
5.7 + 2v = -9.3 | subtract 5.7 on both sides
2v = -9.3 - 5.7 = -15 | divide both sides by 2
v = -7.5
Write each equation in logarithmic form.
243=3⁵
The logarithmic form of the equation is [tex]log_{3}243=5[/tex] .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log x The logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e. The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation 243 = 3⁵ .
Taking log on both sides , we get
[tex]log(243) =log3^5[/tex] ..(1)
Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get
[tex]log(243) =5log3[/tex]
On rearranging the above equation , we get
[tex]\frac{log243}{log3} =5[/tex] ..(2)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\
[tex]\frac{log243}{log3}[/tex] can be written as [tex]log_{3}243[/tex] using property
Putting in equation (2) , we get
[tex]log_{3}243=5[/tex]
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The locations of a house, market, and library from a right triangle as shown in the diagram
There are √34 miles between the house and the library
How to determine how many miles is the house from the library?The given parameters are
Distance between house and market, x = 3 miles
Distance between market and library, y = 5 miles
The number of miles between the house and the library is calculated as
Distance = √x² + y²
Substitute the known values in the above equation
So, we have
Distance = √3² + 5²
Evaluate the exponents in the above equation
So, we have
Distance = √9 + 25
Evaluate the sum in the above equation
So, we have
Distance = √34
Hence, there are √34 miles between the house and the library
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A standard die is rolled. Find the probability that the number rolled is less than 2
======================================================
Explanation:
E = event space = {1}
The event space is the set of things we want to happen. There's only one outcome and it's the "1" (since it's smaller than 2)
S = sample space = {1,2,3,4,5,6}
There are 6 items in the sample space.
Divide the two counts to get the fraction 1/6 which is the probability of rolling a result less than 2. In other words, the probability of landing on "1" is 1/6 since there's one face with that label out of 6 faces total.
Side note: 1/6 = 0.1667 = 16.67% approximately