Answer:
-16
Step-by-step explanation:
1. multiply the minus sign on both sides now we have 4x=-64
2. divide 4 on both sides
You're done! x=-16
Given △
PQR, drag the correct side lengths to complete the table.
Right triangle P Q R has R as its right angle. A segment is drawn from R to S on side P Q. Angle P S R is a right angle.
PQ and PSPS and QSQR and QSPQ and QSPR and QS
Side Lengths Geometric Mean
RS
PR
QR
The correct side lengths to complete the table are RS: Geometric mean of PR and QR, PR: Geometric mean of RS and QR and QR: Geometric mean of PR and RS.
What is Geometric?Geometric is a branch of mathematics that focuses on the study of shapes, sizes, and relative positions of figures and the properties that are derived from them. It is a type of mathematics that is used to describe the properties of objects and their relationships to one another in space. Geometry is also used to describe the movement of objects in space.
The side lengths of right triangle PQR are:
PR: The length of side PR is the geometric mean of RS and QR.
QR: The length of side QR is the geometric mean of PR and RS.
RS: The length of side RS is the geometric mean of PR and QR.
PQ: The length of side PQ is the hypotenuse of the right triangle PQR.
PS: The length of side PS is the hypotenuse of the right triangle PSR.
QS: The length of side QS is the hypotenuse of the right triangle QSR.
Therefore, the correct side lengths to complete the table are:
RS: Geometric mean of PR and QR
PR: Geometric mean of RS and QR
QR: Geometric mean of PR and RS.
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Arun has x pennies and y nickels. He has no less than 20 coins worth a maximum of $0.40 combined. Solve this system of inequalities graphically and determine one possible solution.
One possible solution of this system is Arun has 5 nickels and 15 pennies.
Define system of linear inequalitiesOne or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system.
From the question;x+y≥20
0.05x+0.01y≤0.40
x≥0
y≥0
Inequality: y≥20-x
Inequality: y≥5x-40
x≥0
y≥0
The solution set satisfying the inequality is shown in black area above when x=5 and y=15
So, Arun has 5 nickels and 15 pennies.
Graph of the system of inequalities is attached below.
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please help!! i have no idea how to do this.
hi!
first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.
on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.
then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.
do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.
i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)
next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.
continue down the table. it is the same with x=-2.
next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(
continue down the table and keep doing that!
next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.
next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).
the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.
i hope this was helpful! :)
The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
Answer:
The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
Step-by-step explanation:
The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
There are 140 cars in a parking lot bob looks at 15 cars and finds out that 2 of those cars in the parking lot are gray colored?
Answer:
Step-by-step explanation:
about 18.7
Answer:
18.7
Step-by-step explanation:
2 gray cars / 15 cars = x gray cars / 140 cars
Solving for x, we get:
x = 2 gray cars * 140 cars / 15 cars
x = 18.67 gray cars
Can someone please teach me how to find out if this linear, quadratic, or exponential?
First we find the difference of y values. Then Find the difference of the differences. If the difference of the differences is a constant then the data represents a quadratic function.
find the diffrence. enter your answerin simplest terms usingthe slash (/) as a fraction bar
3/4 - 1/3
Answer:
5/12
Step-by-step explanation:
3/4 - 1/3
We need to use the common denominator of 12
3/4 * 3/3 = 9/12
1/3 * 4/4 = 4/12
9/12 - 4/12 = 5/12
will the signs be reversed each time in algebraic expansion?
That note about "both signs have been reversed" only applies to the example on the right side, where –4 was distributed into the expression in parentheses.
Notice on the left example, the signs were not reversed.
When you distribute a negative number, that's when the signs will reverse. Since you're distributing a negative number, you'll be multiplying each term in parentheses by a negative number and that negative is what reverses the sign on every term.
So, yes all of the signs will be reversed each time you distribute a negative number into the parentheses, but not if you distribute a positive number.
PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS !
Answer:13)2,4,6,8
14)x=3
Step-by-step explanation:
13) you should make it equal to numbers inside bracket {}.
for example,
1.-6x+11=-37
-6x=-37-11=-48
x=8
2.-6x+11=-25
-6x=-36
x=6
3.-6x+11=-13
-6x=-24
x=4
4.-6x+11=-1
-6x=-12
x=2
14)f(x)=13
f(x)=3x+4=13
3x=9
x=3
Use the graphs of f and g to find (f+g)(−2).
Using the graph the value of the function (f + g)(-2) = 5
What are graphs?A graph is a diagrammatic representation of a function
Since we have the graphs of the function f(x) and g(x), we desire to find (f + g)(-2). We proceed as follows.
First, we note that (f + g)(x) = f(x) + g(x)
Now, we need to find (f + g)(-2) = f(-2) + g(-2)
So, we use the graph to find these values.
From the graph
f(-2) = 2 and g(-2) = 3
So, substituting the values of the variables into the equation, we have that
(f + g)(-2) = f(-2) + g(-2)
= 2 + 3
= 5
So, (f + g)(-2) = 5
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What is you answer and how many solutions for the following 3r- 9=3(r + 3)
Answer:
0
Step-by-step explanation:
3r-9=3(r+3)
3r-9=3r+9
collect like terms
3r-3r=9-9
r=0
Answer:
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identify how many solutions are possible for r.}[/tex]
[tex]\textsf{First, we should simplify the given equation.}[/tex]
[tex]\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}[/tex]
[tex]\textsf{values \underline{inside} the parentheses.}[/tex]
[tex]\textsf{Let's begin simplifying the equation.}[/tex]
[tex]\large\underline{\textsf{Simplify.}}[/tex]
[tex]\mathtt{3r-9=3(r+3)}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{3r-9=(3 \times r)+(3 \times 3)}[/tex]
[tex]\mathtt{3r-9=3r+9}[/tex]
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
[tex]\large\underline{\textsf{Why?:}}[/tex]
[tex]\textsf{Any value that is substituted into r will \underline{never} make the equation true.}[/tex]
How to solve this equation
g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .
what is functiοn ?A functiοn is a mathematical fοrmula that gives each input value in a set an individual οutput value. Tο put it anοther way, a functiοn is a cοnnectiοn between twο sets where each element in the first set (referred tο as the dοmain). There are several methοds tο express a functiοn, including with a graph, a table οf values, οr a fοrmula. Mοst frequently, a fοrmula οr equatiοn is used tο represent a functiοn.
We need tο sοlve fοr x in terms οf g in οrder tο derive the inverse functiοn g-1(x) οf g(x) = lοg(x + 1). (x).
We can expοnentiate bοth sides by starting with g(x) = lοg(x + 1) and using the definitiοn οf lοgarithms:
G(x) = lοg(x + 1) = e(x)
[tex]e^{(g(x))} = x + 1[/tex]
Hence, by taking away 1 frοm bοth sides, we can isοlate x:
[tex]x = e^{(g(x))} - 1[/tex]
Inverse functiοn g-1(x) is thus:
[tex]g-1(x) = e^x - 1[/tex]
Hence, g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .
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A large university accepts 70% of the students who apply.
Answer: 3,500
Step-by-step explanation: 70% of 20,000 is 14,000 25% of 14,000 is 3,500
Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $550 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $5,000 and never have to pay annual membership dues.
Obviously, the lifetime membership isn’t a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it’s a great deal. Suppose that the appropriate annual interest rate is 7.5%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $550 in annual membership dues? (Note: Round your answer up to the nearest year.)
21 years
18 years
14 years
12 years
In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4.5% annual interest rate, what is its value as of 2018 (392 years later)?
$987,122,447.84
$635,647,030.80
$859,993,041.68
$747,820,036.24
Answer:
For the lifetime membership to be cheaper than paying $550 in annual membership dues, we need to calculate the present value of the lifetime membership and compare it to the present value of the stream of annual payments.
The present value of the lifetime membership can be calculated using the formula for the present value of a lump sum:
PV = FV / (1 + r)^n
where FV is the future value (which is the cost of the lifetime membership today, $5,000), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
The present value of the stream of annual payments can be calculated using the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where A is the annual payment ($550), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
We need to find the minimum number of years for which the present value of the lifetime membership is less than the present value of the stream of annual payments. We can do this by setting the two present values equal to each other and solving for n:
5000 / (1 + 0.075)^n = 550 * [(1 - (1 + 0.075)^-n) / 0.075]
Solving this equation gives n ≈ 18.7 years. Rounded up to the nearest year, this means that Lloyd must remain a member of the ADLA for at least 19 years for the lifetime membership to be cheaper than paying $550 in annual membership dues.
Therefore, the answer is 19 years.
For the second question, we can use the formula for the future value of a lump sum:
FV = PV * (1 + r)^n
where PV is the present value ($24), r is the annual interest rate (4.5%), and n is the number of years (392).
Substituting the given values, we get:
FV = 24 * (1 + 0.045)^392
FV ≈ $859,993,041.68
Therefore, the value of the $24 purchase price as of 2018 is approximately $859,993,041.68.
How do you determine which trigonometric function to use to solve a problem?
Answer: I would use tan or cot
Step-by-step explanation:
Consider a home mortgage of 200,000 at six APR of 9% for 20 years. Of the total payment over the term of the loan x% is paid toward the principal and x% is paid toward the interest.
The tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.
Tο sοlve this prοblem, we need tο use the fοrmula fοr a fixed-rate mοrtgage payment:
[tex]P = (Pv \times r) / (1 - (1 + r)^{(-n))[/tex]
Where:
Pv = present value οf the mοrtgage (in this case, $200,000)
r = mοnthly interest rate (APR divided by 12)
n = tοtal number οf payments (20 years × 12 mοnths per year = 240)
First, we need tο find the mοnthly interest rate:
r = 9% / 12 = 0.0075
Next, we can plug in the values and simplify the fοrmula:
[tex]P = (200,000\times 0.0075) / (1 - (1 + 0.0075)^{(-240))[/tex]
P ≈ $1,734.84
Therefοre, the mοnthly payment οn the mοrtgage is apprοximately $1,734.84.
Tο determine the percentage οf the payment that gοes tοward principal and interest, we need tο lοοk at the amοrtizatiοn schedule fοr the mοrtgage. This will shοw hοw much οf each payment gοes tοward principal and interest οver time.
Using an οnline amοrtizatiοn calculatοr, we can see that οver the 20-year term οf the mοrtgage, apprοximately 44% οf the tοtal payments gο tοward principal and 56% gο tοward interest.
Therefοre, οf the tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.
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Find the length of the missing side for this
right triangle.
12
9
Step-by-step explanation:
therefore 9 x 9+12
81+144
225/2
15
How do you find the distance between the points shown? (C: 6, -4) and (D: 6, -8)
A. Subtract the distance between each point and the x-axis
B. Add the distance between each point and the x-axis
C. Subtract the distance between each point and the y-axis
D. Add the distance between each point and the y-axis
Therefore , the solution of the given problem of expressions comes out to be it is 4 units between locations C and D.
What does a expression actually mean?Calculations like arbitrary division, joining, multiplication variable and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.
Here,
We can apply the distance calculation to determine the separation between two points:
=> distance= √((x2 - x1)² + y2 - y1)²)
where the coordinates for the two points are (x1, y1) and (x2, y2).
This formula allows us to determine the separation between points
C (6, -4) and D (6, -8) as follows:
=> distance = √[(6 - 6)^2 + (-8 - (-4))^2]
=> distance = √[0^2 + (-4)^2]
=> distance = √[16]
=> distance = 4
As a result, it is 4 units between locations C and D. Both of the available answer options are incorrect.
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the value of y varies jointly with x and the square of z, and y=90 when x=5 and z=3. find the equation represents this relationship
Answer:
Step-by-step explanation:
If y varies jointly with x and the square of z, we can express this relationship as:
y = kx z^2
where k is the constant of variation. To find the value of k, we can use the given information that y = 90 when x = 5 and z = 3:
90 = k(5)(3)^2
Simplifying, we get:
90 = 45k
Dividing both sides by 45, we get:
k = 2
Now we can substitute this value of k into our equation to get:
y = 2xz^2
Therefore, the equation that represents the relationship between y, x, and z is:
y = 2xz^2
HELP LIKE FR I SRSLY DK
Answer: whole = 45; part = 15%
Step-by-step explanation:
The part ( a.k.a the fraction) is the percentage.
15% can be expressed as 15/100 = 3/20.
The whole is 45.
Hope this helps! :)
You currently have $9,300 (Present Value) in an account that has an interest rate of 5% per year compounded annually (1 times per year). You want to withdraw all your money when it reaches $15,810 (Future Value). In how many years will you be able to withdraw all your money?
EASY MATH POINTS!
Answer from the screenshot.
Therefore, the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
What is rate of change of linear function?The rate of change of a linear function is the slope of the line, which represents the rate at which the output (dependent variable) changes with respect to the input (independent variable).
A line's slope is calculated by dividing the difference in y-coordinates between any two locations on the line by the difference in x-coordinates. Geometrically, the slope is the tangent of the angle that the line makes with the x-axis.
Here in the graph we have x and y values find out the slope,
To calculate the slope of a line from two points (x1, y1) and (x2, y2), we use the formula:
[tex]Slope =\frac{(y2 - y1)}{(x2 - x1)}[/tex] = 4 (for every two points)
So, the line is linear and the rate of change of this linear function is 4/1, which means that for every 1 lb increase in the x-coordinate, the y-coordinate (the output) increases by $4.
Therefor the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
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4.586 to the nearest cm
Answer:
See below.
Step-by-step explanation:
We are asked to round 4.586 cm to the nearest cm.
What is Rounding?
Rounding is a simple method used to change a number, and all of the numbers behind it to 0. Rounding is similar to an approximation, in order to show you how I should give you an example.
Example:
Round 459 to the hundreds place.
The hundreds place is where the 4 is. We should look at the 5.
Requirements necessary are that 5 needs to be greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 500.
Rounding is an approximation because it's close to the actual number, in other words, inexact.
Let's use the example as a guide for our problem now.
4.586 to the nearest cm (ones place)
The ones place is the 4. We should look at the 5.
5 is greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 5.000 cm.
Our final answer is 5.000 cm.
Rueben’s chocolate bar is 41% cocoa. If the weight of the chocolate bar is 67 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth
The weight of cocoa in Rueben’s chocolate bar is found as 27.47 grams.
Explain about the percentage of the number?Several fields employ percentage. It frequently appears in accounting and finance-related topics including taxation, sales, earnings, and interest rates. The grades of the pupils were expressed in a number of schools and institutions using percentages. Percentages are used to express probabilities, nutritional information, and download times.Percentage of cocoa in Rueben’s chocolate bar = 41%.
Weight of the chocolate bar = 67 grams.
Grams of cocoa in chocolate bar = 0.41*67
Grams of cocoa in chocolate bar = 27.47 grams
Thus, weight of cocoa in Rueben’s chocolate bar is found as 27.47 grams.
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A bald eagle also eats 400g of food per day.It eats fish, as well as seal carcasses that have washed up on the beach. A seal eats fish fish eating fish with 1.0 microgram per gram of DDE in their tissue. The DDE builds up in the seal's body so that the seal has 2.0 micrograms per DDE in its tissue. If the bald eagle eats 200g of seal, how much DDE does the bald eagle consume in one day.
The bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.
First, we need tο calculate the amοunt οf DDE in the 200g οf seal that the bald eagle eats:
What dοes DDE stability mean?If a delay differential equatiοn (DDE) equilibrium is lοcally asymptοtically stable fοr all delays, it is said tο be tοtally stable. We οutline standards fοr DDEs with discrete time delays' absοlute stability.
Calculate the amοunt οf DDE in 1 gram οf fish:
1.0 micrοgram οf DDE per gram οf fish
Calculate the amοunt οf fish the seal eats tο accumulate 2.0 micrοgrams οf DDE in its tissue:
2.0 micrοgrams οf DDE per gram οf seal / 1.0 micrοgram οf DDE per gram οf fish = 2.0 grams οf fish per gram οf seal
Calculate the amοunt οf seal that the bald eagle eats:
200g οf seal
Calculate the amοunt οf fish the bald eagle cοnsumes frοm the 200g οf seal:
200g οf seal * (1 gram οf fish / 2.0 grams οf fish per gram οf seal) = 100g οf fish
Calculate the amοunt οf DDE the bald eagle cοnsumes frοm the fish it ate frοm the seal:
100g οf fish * 1.0 micrοgram οf DDE per gram οf fish = 100 micrοgrams οf DDE
Therefοre, the bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.
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Help pleaseee can you tell me the the answers in order please
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued
The answer if subpart are as follows :-
A) To find the annual rate of change between 1991 and 2000, we need to use the formula for exponential decay, which is:
V(t) = V(0) * e raise to the power (-rt)
Where V(t) is the value of the car at time t, V(0) is the initial value of the car, r is the annual rate of change (as a decimal), and e is the mathematical constant 2.71828...
Plugging in the values we have:
V(2000) = $12,000
V(1991) = $45,000
t = 9 years
$12,000 = $45,000 * e raise to the power (-r * 9)
Dividing both sides by $45,000 and taking the natural logarithm of both sides gives:
ln(0.26667) = -9r
Solving for r:
r = ln(0.26667) / (-9) = 0.1356
So the annual rate of change between 1991 and 2000 is 0.1356, which represents a decrease in value of 13.56% per year.
B) To express the answer from part A in percentage form, we need to multiply by 100 and round to two decimal places:
r = 0.1356 * 100 = 13.56%
C) If we assume that the car value continues to drop by the same percentage as it did between 1991 and 2000, we can use the same formula as before to find the value of the car in 2003:
V(2003) = V(2000) * e raise to the power (-r * 3)
Plugging in the values we have:
r = 0.1356
V(2000) = $12,000
V(2003) = $12,000 * e raise to the power (-0.1356 * 3) = $6,044.48
So the value of the car in 2003 would be approximately $6,044.48, rounded to the nearest 50 dollars as requested.
In summary, the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued. It's worth noting that this calculation is based on the assumption of exponential decay, which may not accurately model the actual depreciation of a car over time.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
(a) The derivative of the function, dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
(b) The equation of the tangent line to the curve at (1, 1) is y = (-779/9)x + 778/9.
What is the derivative of the function?To find dy/dx, we differentiate both sides of the equation with respect to x using the chain rule and product rule as necessary:
d/dx (57x⁷) + d/dx (10x³⁸y) + d/dx (y⁹) = d/dx (68)
Simplifying each term using the power rule and the chain rule where appropriate, we get:
399x⁶ + 380x³⁷y + 9y⁸(dy/dx) = 0
Now, solving for dy/dx, we get:
dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
To find the equation of the tangent line to the curve at (1, 1), we first need to evaluate dy/dx at that point. Plugging in x = 1 and y = 1 into the expression for dy/dx, we get:
dy/dx = (-399 - 380) / 9 = -779/9
Now we can use the point-slope form of the equation of a line to find the tangent line. The point-slope form is:
y - y1 = m(x - x1)
where;
m is the slope and (x1, y1) is the point.Plugging in m = -779/9, x1 = 1, and y1 = 1, we get:
y - 1 = (-779/9)(x - 1)
Simplifying, we get:
y = (-779/9)x + 778/9
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timmy has 3,000 miles on his car. he drives 38 miles each day. write a linear model to represent the situation
Answer:
38
Step-by-step explanation:
Let x represent the number of days Timmy has been driving his car since he had 3,000 miles on it. Then, his total mileage can be represented as:
Total mileage = 3,000 + (38 × x)
This is a linear model, because the relationship between the total mileage and the number of days driven is a straight line with a constant slope of 38. The y-intercept of this line is 3,000, which represents the initial mileage on Timmy's car. The slope of 38 indicates that the car is being driven 38 miles further each day, which corresponds to the rate of change in the total mileage.
What is the value of x in a triangle with one side being (4x-4) and the other side being 30
The value for the x in the triangle with sides (4x - 4) and 30 is obtained as x > 6.8.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Assume that the side length 30 is the greatest of the 3 sides.
Using this fact, we can write an inequality based on the lengths of the sides in the given triangle -
(4x - 4) + x > 30
Simplifying this inequality, we get -
4x + x - 4 > 30
Adding x on LHS, we get -
5x > 34
Dividing both sides by 5, we get -
x > 6.8
Therefore, the value of x is greater than 6.8.
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A cereal box advertises that it contains 20% more. It now contains 18.48 ounces. What was the original cereal box amount?
Answer:
If the new cereal box contains 20% more than the original cereal box, then the original cereal box contained 100% - 20% = 80% of the new cereal box.
Let X be the original cereal box amount in ounces, then we can set up the following equation:
X + 0.20X = 18.48
Simplifying and solving for X:
1.20X = 18.48
X = 15.40
Therefore, the original cereal box amount was 15.40 ounces.