Solving a value mixture problem using a system of linear....
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $20 and same-day tickets cost $35. For one performance,
there were 60 tickets sold in all, and the total amount paid for them was $1500. How many tickets of each type were sold?
Number of advance tickets sold:
Number of same-day tickets sold:
The linear equation 20x + 35(60-x) = 1500 can be solved to find the number of tickets.
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its related terms in various languages may have somewhat different definitions; for example, in French, an equation is described as including one or more elements, but in English, an equation is any well-formed formula that includes two expressions linked by an equals sign.
Let the number of advance tickets sold = x
And then, the number of same-day tickets sold = 60 - x
Then, the equation formed is
20x + 35(60-x) = 1500
=> 20x + 2100 - 35x = 1500
=> -15x = 1500 - 2100
=> x = -600/ -15 = 40
Hence, the number of advance tickets sold = 40
And the number of same-day tickets sold = 60 - 40 = 20
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how do we do this one there three parts to it
Given the following question:
Part A:
Your answer is option B, you can find this by checking the values. We are given 107, 128, 163, 212, 275 if you check the values on the graph, you can see that they are exact. So, your answer is option B.
I will give brainliest and rate, if you do this right
Find the first derivative of the following:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \:1.) \: \: \: \frac{dy}{dx} = cot(x)[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \:2.) \: \: \frac{dy}{dx} = 2x \sdot {3}^{ {x}^{2} } \sdot ln(3) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We need to find derivative of the following functions
1.) y = ln(sin x)[tex]\qquad \tt \rightarrow \:y = ln(sin(x))[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (ln(sin(x)))[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{sin(x)} \sdot cos(x)[/tex]
[ by chain rule ]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = cot(x)[/tex]
[tex]\large{ 2.)\tt y = {3}^{{x}^{2}}} [/tex]
[tex]\qquad \tt \rightarrow \:y = {3}^{ {x}^{2} } [/tex]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} ( {3}^{ {x}^{2} } )[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = {3}^{ {x}^{2} } \sdot ln(3) \sdot(2x) \sdot(1)[/tex]
[tex] \displaystyle\qquad \tt \rightarrow \: \frac{dy}{dx} = 2x \sdot {3}^{ {x}^{2} } \sdot ln(3) [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The linear function y = 145 + 30x represents the cost y (in dollars) of an airline ticket after adding x checked
bags. At most 5 bags can be checked.
a. Interpret the terms and coefficient in the equation.
From the given parameters to determine the cost of the airline ticket, we can interpret that that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.
How to interpret Equation of a line in slope intercept form?
We are given the linear equation that represents the cost of an airline ticket after adding a number of checked bags as;
y = 145 + 30x
where;
y is the cost (in dollars) of an airline ticket after adding a number of checked bags
x is the number of checked bags
Thus, if there is a maximum of 5 bags that can be checked, then we have;
y = 145 + 30(5)
y = $295
This means that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.
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"A line goes through the points (1, -10) and (-3, -2). Write the equation of the line in slope-intercept form, then find the x-intercept of the line. Show your work algebraically for full credit."
Slope
[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]
Equation
[tex]y+10=-2(x-1)[/tex]
x-intercept
The x-intercept is when y=0.
[tex]10=-2(x-1)\\\\-5=x-1\\\\x=-4[/tex]
So, the x-intercept is (-4, 0).
HURRY Find all solutions to the equation x3 + 100x + 8x2 = –800.
–10, –8, 10
–10, 8, 10
8, –10i, 10i
–8, –10i, 10i
Answer:
-8, -10i, 10i
Step-by-step explanation:
x^3 + 8x^2 + 11x = -800
I just plugged it into my calculator
You need to purchase supplies for the trip. You have $1000 to spend.
Oxen: $40 each
Food: $0.20 per lb
Clothing: $10 per set.
Matt also charges 7% tax
Purchase at least 2 oxen, 500lbs of food, and 5 sets of clothing. You may want to purchase more.
Select the amount of items and find the total cost including tax.
The total cost of purchasing the minimum quantities for the trip, including sales tax of 7% is $246.10, while you can buy 4 times more.
What is a sales tax?A sales tax is a use or consumption tax, indirectly levied by the government on buyers of certain taxable items.
The seller collects the sales tax on behalf of the government.
Total amount to spend on supplies = $1,000
Items Cost Unit Units Total Units Total for more
Oxen: $40 each 2 $80 8 $320
Food: $0.20 per lb 500 100 2,000 400
Clothing: $10 per set 5 50 20 200
Total cost before tax $230 $920
7% sales tax $16.10 64.40
Total cost after tax $246.10 $984.40
Change = $15.60
Thus, with $1,000, you can purchase 4 times the above quantities and still have some change after paying the required sales tax.
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(A.) Given the one-to-one function f(x)= 7x - 2, find it's inverse function.
Which is f ^ -1(x)= 1/7x - 2/7
(B.) The graphs of f and f^ -1 are symmetric with respect to the line defined by
y = _______
The inverse function of one-to-one function f(x)= 7x - 2 is [tex]f^{-1}=\frac{x}{7}+\frac{2}{7}[/tex].
The graphs of f and [tex]f^{-1}[/tex] are symmetric with respect to the line defined by y = x.
Given that:-
f(x)= 7x - 2
Let f(x) = y
Hence,
[tex]f^{-1}(y)=x[/tex]
Hence, we can write,
y = 7x - 2
y + 2 = 7x
x = y/7 + 2/7
[tex]f^{-1}(y) = y/7 + 2/7[/tex]
Replacing y by x, we get,
[tex]f^{-1}(x) = x/7 + 2/7[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = x/7 + 2/7[/tex].
The graph of inverse is always the mirror image of the function's graph in the line y = x. It is because they're basically 100% similar but in reverse just like you in a mirror.
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Use a law of exponents to write (-3mn^5)^4 as a product of powers
The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]
Here we have to determine the sign for exponential or radical expression
(-3m[tex]n^{5}[/tex])^4
Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]
Similarly
(-3m[tex]n^{5}[/tex])^4
= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]
Now using the exponent power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get
= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]
Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].
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Solve the system of equations by multiplying. -3x +2y= 4 4x-13y=5
Answer:
x=-2 and y=-1Step-by-step explanation:
To find the value of x and y, isolate it on one side of the equation.
-3x+2y=4, 4x=13y=5
-3x+2y=4
[tex]\rightarrow \sf{x=-\dfrac{4-2y}{3}}[/tex]
Substitute.
[tex]\sf{4\left(-\dfrac{4-2y}{3}\right)-13y=5}[/tex]
Solve.
Use the distributive property.
A(B+C)=AB+AC
A(B-C)=AB-AC
[tex]\sf{=\dfrac{-16-31y}{3}=5}[/tex]
Isolate the term of y.
Multiply by 3 from both sides.
[tex]\sf{\dfrac{3\left(-16-31y\right)}{3}=5*3}[/tex]
Solve.
Multiply the numbers from left to right.
5*3=15
-16-31y=15
Add by 16 from both sides.
-16-31y+16=15+16
Solve.
15+16=31
-31y=31
Divide by -31 from both sides.
-31y/-31=31/-31
Solve.
y=-1
Substitute of y=-1.
[tex]\sf{x=-\dfrac{4-2\left(-1\right)}{3}}[/tex]
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract4-2(-1)
Do parentheses by multiply first.
2(-1)=-2
4-(-2)
4+2=6
-6/3
Divide.
-6/3=-2
x=-2
[tex]\Rightarrow \boxed{\sf{x=-2, \quad y=-1}}[/tex]
Therefore, the correct answer is x=-2, and y=-1.
I hope this helps, let me know if you have any questions.
Use the multiplier method to increase 88 by 14%
You must show your working.
Answer:
100.32
Step-by-step explanation:
You want 88 increased by 14% using the multiplier method.
MultiplierThe multiplier used to increase an amount by some fraction (p) of that amount is (1 +p). Here, the fraction is 14%, or 0.14. That means the multiplier is ...
multiplier = 1 +p
multiplier = 1 +0.14 = 1.14
The increased amount is then ...
88 × 1.14 = 100.32 . . . . . . . 88 increased by 14%
__
The actual work is done by a calculator, as shown in the attachment.
The net of a rectangular prism with a square base is shown. Use the net to find the surface area of the prism. Please help.
The value of surface area will be equal to 450 cm square. Thus, option B is the correct answer.
A rectangular prism may be defined as a 3-dimensional solid figure containing 6 faces and its base are in form of rectangle. The surface area may be given as the sum of all individual side areas. The prism given is like a cube and has 6 sides. The sides given are top - bottom, left - right and front - back. In the case given in the question we have top and bottom given as 5×5 squares, and the other 4 sides are equal 5×20 rectangles. So, we find the area as following
From top - bottom: 2× 5×5 = 50 cm²
From left - right: 2× 20×5 = 200 cm²
From front - back: 2× 20×5 = 200 cm²
Thus, in total the surface area will be given as = 200 + 200 + 50 = 450 cm².
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If the straight line that passes through (2, 1) and (5, 7) is drawn accurately,
it passes through the point (20, y).
What number does y stand for?
The point (x, 21) lies on the same line.
What number does x stand for?
Here, use this to help you: https://www.map.mathshell.org/download.php?fileid=1676
[(2,0)((-1, 3){(1,0)[(-1, -3)(0, 2)[(-3,-1)]Line 1Line 2Point of Intersection(0, 2). (-5, -3)(0,5). (-5, -5)(-2, 1), (-3,-1)(0, 2), (2,0)(4,-2), (1,1)(4,2), (0, -2)(2,-2), (0, 2)(2, 1), (3, 2)ResetNext
Line (0, 2), (-5, -3) ---> y = x + 2
Line (0, 5), (-5, -5) ---> y = 2x + 5
Point of intersection ---> we need to equate both equations:
[tex]x+2=2x+5\Rightarrow-5+2=2x-x\Rightarrow-3=x[/tex]If x = -3 ---> y = -3 + 2 ---> y = -1
The point of intersection in this case is (-3, -1) (the last one, from left to right).
Second caseLine (-2, 1), (-3, -1) ---> y = 2x + 5
Line (0, 2), (2, 0) ---> y = -x + 2
Equating both equations to find the intersection point:
[tex]2x+5=-x+2\Rightarrow2x+x=2-5\Rightarrow3x=-3\Rightarrow x=-1[/tex]If x = -1, then y = -(-1) + 2 ---> y = 1 + 2 ---> y = 3
The point of intersection is (-1, 3) (the second one, from left to right).
Third caseLine (4, -2), (1, 1) ---> y = -x +2
Line (4, 2), (0, -2) ---> y = x - 2
Then, we have ---> intersection point:
[tex]-x+2=x-2\Rightarrow2+2=x+x\Rightarrow4=2x\Rightarrow x=2[/tex]Using the second equation to find y ---> y = 2 -2 ---> y = 0
The point of intersection is (2, 0) (the first point, from left to right).
Fourth caseLine (2, -2) (0, 2) ---> y = -2x + 2
Line (2, 1), (3, 2) ---> y = x - 1
Then, we have:
[tex]-2x+2=x-1\Rightarrow1+2=x+2x\Rightarrow3=3x\Rightarrow x=1[/tex]Using the second equation to find y ---> y = 1 - 1 ---> y = 0
The point of intesection is (1, 0) ( the third point, from left to right).
If x = 2 and y=-3, then xy^2 =
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
-xy^2 =
Let x=2 and y = -3
-(2) (-3)^2
-2 (9)
-18
Answer:
18.
Step-by-step explanation:
(2)(-3)^2
Parentheses first. There's nothing to do so, the exponent is next. -3^2 is 9. 9 * 2 = 18.
Hope this helps! :)
PLS HELP I NEED IT
The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 6 centimeters. The company has decided that a washer whose actual circumference is in the interval 5.8
Solving the circumference function, we have that:
The corresponding interval for diameters of the washers is 1.85 ≤ d ≤ 1.97.
What is the interval of possible values for the diameter?The circumference of a circle of diameter d is given by:
C = 3.14d.
As stated in the problem.
The interval of circumference values is:
5.8 ≤ C ≤ 6.2.
Hence the lowest possible value for the diameter is given by:
3.14d = 5.8
d = 5.8/3.14
d = 1.85.
The highest possible value for the diameter is given by:
3.14d = 6.2
d = 6.2/3.14
d = 1.97.
Then the compound inequality that completes the given sentence is:
1.85 ≤ d ≤ 1.97.
What is the missing information?The interval for the circumference values is given by:
5.8 ≤ C ≤ 6.2.
We have to complete the following sentence with the compound inequality:
The corresponding interval for diameters of the washers is
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Together, Luke and James have never eaten more than 16 pieces of pizza at one time.Which equation describes y, the total number of pieces that Luke has eaten at one time givenx, the number of pieces that James has eaten?a. y <_16-x b. y>_16-x c. y=16-x d. not here
y ≤ 16 - x (option A)
Explanation:let the total number of pieces Luke ate at a time = y
Let the total number of pieces James ate at a time = x
They have never eaten more than 16 pices of pizza
This is written as:
maximum 16 : ≤ 16
number of pieces Luke ate at a time + total number of pieces James ate at a time ≤ 16
y + x ≤ 16
rewritting to make y subject of formula:
y ≤ 16 - x (option A)
Increased from __ hours to ___ hours
The level of ibuprofen in the patients bloodstream increased from 0 hours to 2 hours.
What is ibuprofen?
Ibuprofen is an example of an NSAID that is used to relieve pain, fever, and inflammation. This includes menstruation pain, migraines, and rheumatoid arthritis. Additionally, it can be applied to seal off a premature infant's patent ductus arteriosus. It can be given orally or intravenously. After an hour, it usually begins to function.
In the graph that is attached, the y-axis represents the concentration of ibuprofen in the patient's bloodstream, and the x-axis represents the number of hours since ibuprofen was last consumed.
As we can see from the graph, the curve increases from a time of 0 hours, which corresponds to 0 mg of ibuprofen, to a time of 2 hours, which corresponds to 400 mg of ibuprofen.
The curve starts to descend after that point. We will settle for the first assertion because increase is what we are interested in.
Thus, we may conclude that the increase in ibuprofen level occurred between 0 and 2 hours.
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What is the greatest number of sweets that
can be bought with $2 if each sweet costs
30 cents?
Answer:
6 sweets
Step-by-step explanation:
add 30 until you are going over
A study of the squirrel population in Center City Park showed that, on average, the squirrels live to be 6.5
years old. The lifespans of the squirrels may vary by as much as 1 year. What is the range of ages (in years)
to which the squirrels live?
The most appropriate choice for linear inequation will be given by-
The range of ages to which the squirrels live is 5 to 8 years
What is Linear Inequation?
Linear Inequation involves comparision between two values with the help of <, >, [tex]\leq , \geq[/tex]
.
Here,
Let the range of ages (in years) to which the squirrels live be [tex]x[/tex] years
The lifespans of the squirrels may vary by as much as 1 year.
By the problem,
[tex]|x - 6.5|\leq 1.5\\-1.5 \leq x - 6.5 \leq 1.5\\x - 6.5\geq -1.5[/tex]and [tex]x-6.5\leq 1.5[/tex]
[tex]x \geq 6.5-1.5[/tex] and [tex]x \leq 6.5 + 1.5\\[/tex]
[tex]x \geq 5[/tex] and [tex]x \leq 8[/tex]
The range of ages to which the squirrels live is 5 to 8 years
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Are these right? Geometry by the way, someone please help
With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.
It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°
What is a rigid transformation?A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.
Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.
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A car travels a distance of 100km for 1h38min45sec.a)Round off the time to the nearest 1/4 hour b)Use the rounded time to find the average speed for the journey
Answer: 57.14 km/hr
Step-by-step explanation: if an hour is divided into quarters it will be in increments of 15 minutes, since one hour is 60 minutes. 60 minutes divided by 5 is 15 minutes.
So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.
this is 1 hour + 3/4 hour = 1 3/4 hour. This is same as 1.75 hour
3/4 is .75
speed divided by the time will give the average speed.
100km/1.75hours = 57.14 km/per hour
Answer:
(a) 1 hour 45 min
(b) 57.1 km/h (nearest tenth)
Step-by-step explanation:
Given information:
Distance = 100 kmTime = 1 h 38 min 45 sec[tex]\large\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Part (a)[tex]\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}[/tex]
Therefore, the nearest ¹/₄ hours either side of the given time is:
1 hour 30 min1 hour 45 min1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.
1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.
Therefore, the nearest ¹/₄ hour to the given time is:
1 hour 45 min.Part (b)1 hour 45 min = 1.75 min (in decimal form)
Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:
[tex]\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}[/tex]
What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the two points is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
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Byron jogs home from a park at an average speed of 6mi / h After half an hour he is 4 miles from home . What is an equation , in point - slope form, that represents Byron's distance from home , y, after hours?
A. y-6=-4(x-1/2)
B. y-4=-6(x-1/2)
C. y-1/2=-6(x-4)
D. y-4=6(x+1/2)
An equation, in point-slope form, that represents Byron's distance from home, y, after hours is: B. y - 4 = 6(x - 1/2).
What is the point-slope form?The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.
Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following data:
Average speed (slope), m = 6 mi/h.
Point, y = 4.
Point, x = 1/2
Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 4 = 6(x - 1/2)
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You went to an action figure shop to buy a figure of your favorite anime character. The purchase price was $20, and the selling price was $30. You gave the shop owner $100, but the owner didn't have any change. So he went to the neighboring shop, got change for $100, and gave you $70. Unfortunately, the neighboring shop owner found out that the 100-dollar bill given to him was fake, so he went to the action figure shop and got back his change of $100. Now the question is, how much did the owner of the action figure store lose in total?
The owner loses the figure and the $70 that gives back, so the total amount he loses is $90.
How much did the owner of the action figure store lose in total?
We know that the owner initially has a figure whose price is $20, and he sells it for $30.
Then, he sells it for a $100 bill, so he gives $70 back.
The problem is that the $100 bill was fake, so at this point the total amount that he loses is:
The value of the action figure (which is $20) plus the $70 that he gives back.
Adding these two we get:
$20 + $70 = $90
The owner loses $90 in total.
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What is the area of the figure? The figure is not drawn to scale.thank you ! :)
Solution
- The formula for finding the area of a triangle is given below:
[tex]\begin{gathered} A=\frac{1}{2}\times b\times h \\ where, \\ b=\text{ The base of the triangle} \\ h=\text{ The perpendicular height} \end{gathered}[/tex]- We have been given:
[tex]\begin{gathered} b=5.4cm \\ h=2cm \end{gathered}[/tex]- Therefore, we can find the area as follows:
[tex]\begin{gathered} A=\frac{1}{2}\times2cm\times5.4cm \\ \\ \therefore A=5.4cm^2 \end{gathered}[/tex]Final Answer
The area is 5.4cm²
what is the domain of x^2-4 ?
A shipping company charges 18.95 for a large package and a small one for 9.75. What is the best estimate Of the cost to ship 5 large packs and 3 small packages
The best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.
What is the best estimate?
Best estimate means an income, expense, or circumstance prediction based on past amounts of income and expenses and known factual information concerning future circumstances which affect eligibility, expenses to be incurred; or income to be received in the benefit month.
Given that
Shipping company charges 18.95 for a large package.
Shipping company charges 9.75 for a small package.
For 5 large packs shipping company charges = 5 × 18.95 = 94.75
For 3 small packs shipping company charges = 3 × 9.75 = 29.25
Therefore, the best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.
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Given a || b , and c is not parallel to a or b, which statements must be true? a 1/2 3 / 4 Select each correct answer b . 5/6 7/8 mZ2 = m_7 9/10 C m27 = m_10 11 / 12 mZ8 = m29 m24 = m28
m∠2 = m∠7
and
m∠4 = m∠8
Both are correct answers and should be ticked
Here, we want to select which of the statements must be correct based on the diagram given
a) m∠2 = m∠7
This is correct
m∠2 = m∠3 as they are vertically opposite angles
However, m∠3 = m∠7 as they are vertically opposite angles
b) m∠7 = m∠10
We cannot compare the relationship between b and c as the pair are not parallel lines
c) m∠8 = m∠9
This is not correct also as the pair of lines are not parallel
d) m∠4 = m∠8
These two are corresponding angles, so they are congruent and thus equal in value
Answer this Graph based Question I will make you brailiest and provide you 50 points. And also explain the (vii) Question..
Answer:
(i) -2, (ii) Attached, (iii) x = - 1, (iv) y=6 maximum, y= - 2 minimum, (v) x = 0.723, (vi) y = - 3, (vii) y = - 1
Step-by-step explanation:
GivenFunction y = (x + 1)² - 3(i) Find the value of y when x = - 2
y = (- 2 + 1)² - 3 = (-1)² - 3 = 1 - 3 = - 2(ii) See the graph attached
(iii) The axis of symmetry is the vertical line passing through the vertex, which is x + 1 = 0 or x = - 1.
This is also reflected on the attached graph.
(iv) From the graph it is visible that in the given interval the function is decreasing, so the value at x = - 4 is the maximum and the value at x = - 2 is minimum:
y(-4) = (-4 + 1)² - 3 = 9 - 3 = 6 maximumy(-2) = (-2 + 1)² - 3 = 1 - 3 = - 2 minimumThese two points too are given on the same graph.
(v) There ate two x-intercepts, the one on the right is the larger one.
It is (0.732, 0), marked on the graph.
(vi) This function is the standard form of the given:
(x + 1)² - 3 = x² + 2x + 1 - 3 = x² + 2x - 2With the positive leading coefficient of 1, it has a minimum value but no maximum. The minimum of this function is at its vertex, which is (- 1, 3) as per graph.
(vii) The function y = x² + 2x is the translation of the given function up by two units.
So its minimum value is 2 units greater:
(-1, - 3+2) = (-1, -1)