Hello, I am unsure how to get to the answer, can you include a sign chart as well for the second derivative thank you.
Answers
We want to find the intervals of concavity of the function;
[tex]y=-x^4+8x^2-4[/tex]We start by taking the second derivatives;
[tex]\begin{gathered} y^{\prime}=-4x^3+16x \\ y^{\prime}^{\prime}=-12x^2+16 \end{gathered}[/tex]When a function is concave up, the second derivative is positive, thus; we seek the intervals where;
[tex]\begin{gathered} -12x^2+16>0 \\ -12x^2>-16 \\ x^2<\frac{16}{12} \\ x^2<\frac{4}{3} \\ x<\pm\sqrt{\frac{4}{3}} \end{gathered}[/tex]Let's find the points of inflection, this is where the second derivative is zero;
[tex]\begin{gathered} -12x^2+16=0 \\ -12x^2=-16 \\ x^2=\frac{16}{12}=\frac{4}{3} \\ x=\pm\frac{4}{3} \end{gathered}[/tex]The y values will be;
[tex]\begin{gathered} -(\frac{4}{3})^4+8(\frac{4}{3})^2-4=\frac{44}{9} \\ -(-\frac{4}{3})^4+8(-\frac{4}{3})^2-4=\frac{44}{9} \end{gathered}[/tex]Thus, the answers are;
[tex]\begin{gathered} Concave\text{ }up:(-\sqrt{\frac{4}{3}},\sqrt{\frac{4}{3}}) \\ Inflection\text{ }points:(-\sqrt{\frac{4}{3}},\frac{44}{9}),(\sqrt{\frac{4}{3}},\frac{44}{9}) \end{gathered}[/tex]Thus the answer is option D;
This is a sign chart for the second derivative;
Related Questions
Find the value of k in the data set so that f (x) is a linear function.
Answers
The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]so
step 1
Find out the slope m
we take two points from the table
(2,3) and (5,9)
[tex]\begin{gathered} m=\frac{9-3}{5-2} \\ \\ m=\frac{6}{3} \\ \\ m=2 \end{gathered}[/tex]step 2
Find out the value of b
we have
m=2
point (2,3)
substitute and solve for b
[tex]\begin{gathered} 3=2(2)+b \\ 3=4+b \\ b=-1 \end{gathered}[/tex]The linear equation is
[tex]f(x)=2x-1[/tex]step 3
Find out the value of k
For x=-2
[tex]\begin{gathered} f(x)=2(-2)-1 \\ f(x)=-4-1 \\ f(x)=-5 \end{gathered}[/tex]therefore
The value of k=-5A triangular prism has base edges 3 cm ,6 cm, and 7 cm long . it's lateral area is 272 cm2. what is the highest of the prism ?The height of the prism is _cm. (simplify your answer .)
Answers
ANSWER
h = 17cm
EXPLANATION
The lateral area is the sum of the areas of the non-triangular faces - which are rec
Dion features Great Dane 62 cups of draw water Creek has a new bag with 160 cups of dog food beyond will pick up more dog food at the pet store in 2 1/2 weeks will the new bag of food last until then
Answers
The bag contains 160 cups of feed.
If the dog eats 62 cups of feed per week, we can calculate how many weeks of feed does the bag contain by dividing 160 by 62:
[tex]\#\text{weeks}=\frac{160\text{ cups}}{62\text{ cups/week}}\approx2.58\text{ weeks}[/tex]As she will be picking more feed in 2 1/2 = 2.5 weeks, and as 2.58 > 2.5, we know that the bag of feed will last until then.
Answer: Yes, it will last 2.58 weeks, that is greater than 2 1/2 weeks.
PART A: Solve both linear equations for y = mx + b form. (2 points) y = -2x + 3 2x + 2y = 4
Answers
Answer:
(1, 1)
Explanation;
Given the simultaneous equation:
y = -2x + 3 ..... 1
2x + 2y = 4 ...... 2
Substitute equation 1 into 2;
2x+2y = 4
2x+2(-2x+3) = 4
Expand
2x-4x+6 = 4
-2x + 6 = 4
-2x = 4 - 6
-2x = -2
Divide both sides by -2
-2x/-2 = -2/-2
x = 1
Substituting x = 1 into equation 1;
From 1:
y = -2x + 3
y = -2(1) + 3
y = -2 + 3
y = 1
Hence the solution to the system of equation is (1, 1)
45 points!!!!
If triangles ABC and ADE are similar in this diagram, what is the length of the pond?
The pond is ? ft long.
Answers
Answer:
a
Step-by-step explanation:
ans. 87.25 ft
(solution shown in picture)
BRAINLIEST Look at the image for the problem, round to the nearest hundredth if possible.
Answers
You plan on retiring in 43 years. You expect the IRA to have an APR of 5.3%, compounded monthly. How much money will you have when you retire? Use $265.35 as the monthly amount.
Answers
Number of years is 43 years
rate per anum is 5.3%
Principal is $265.35
n is 12 month
t is 43 years
Using a compound interest formula
[tex]A=P(1+\frac{r}{100n})^{nt}[/tex][tex]A=265.35(1+\frac{5.3}{12\times100})^{12\times43}[/tex][tex]A=265.35(1+0.004417)^{516}[/tex][tex]\begin{gathered} A=265.35(1.004417)^{516} \\ =265.35\times9.71968511 \\ =2579.12 \end{gathered}[/tex]Hence, I will have $2579.12 when I retire
A group of biologists is surveying the mice population in a forest. The equatio n=75 times 3t gives the total number of mice, n, t years after the survey began. What does the number 3 mean in the situationA: the common difference B: The total populationC: the common ratioD: the slope
Answers
A linear function is given by the expression:
y=mx+b,
since 3 is the coefficient of the variable of interest we can say that's the slope.
Hancox Homes is a popular construction company that builds affordable housing. When the company first started, they sold 1 home the first month, 3 homes the second month, 9 homes the third month, and 27 homes the fourth month. DESCRIBE THE PATTERN THEN REPRESENT THE SEQUENCE AS A NUMERIC SEQUENCE AND A TABLE OF VALUE
Answers
The pattern is given below
1, 3, 9, 27
We can clearly see that the terms are indeed the powers of 3
i.e
[tex]\begin{gathered} 3^0\text{ = 1} \\ 3^1\text{ = 3} \\ 3^2\text{ = 9} \\ 3^3\text{ =27} \end{gathered}[/tex]looking closely at the sequence generated, we can show that it follows the geometric sequence as
[tex]r\text{ = }\frac{T_2}{T_1}\text{ = }\frac{T_3}{T_2}\text{ = }\frac{T_{n+1}}{T_n}[/tex]Thus, the common ratio r equals
[tex]r\text{ = }\frac{3}{1}\text{ = }\frac{9}{3}\text{ = }\frac{27}{9}\text{ = 3}[/tex]for any two consecutive numbers in the sequence
Hence, we can express the sequence as a numeric sequence thus:
[tex]\begin{gathered} \text{Recall that T}_n=ar^{n-1} \\ T_n=(1)(3)^{n-1} \\ T_n=3^{n-1} \end{gathered}[/tex]We can also create a table of values to show that this sequence follows the geometric sequence
a blind state test is over and a new favorite juice flavor has been selected. The new flavor received 5 votes for every vote received by the original flavor. the new flavor received 705 votes. how many votes did the original flavor receive?
Answers
Let the number of votes received by the original flavor be x and let the votes received by the new flavor be y:
Since, for every vote received by the original flavor, 5 votes are received by the new flavor. It follows that the number of votes received by the new flavor is 5 times the number of votes received by the original flavor. That is:
[tex]y=5x[/tex]Substitute the number of votes y=705 votes for the new flavor into the equation and solve for x:
[tex]\begin{gathered} 705=5x \\ \text{Swap the sides of the equation:} \\ \Rightarrow5x=705 \\ \Rightarrow\frac{5x}{5}=\frac{705}{5} \\ \Rightarrow x=141\text{ votes} \end{gathered}[/tex]Hence, the number of votes the original flavor receive
Find the value of each variable in the circle to the right . The dot represents the center of the circle . a= (Simplify your answer . Do not include the degree symbol in your answer .)
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Given that the triangle is formed by the diameter of the triangle, we can deduct that angle b is 90°.
[tex]b=90[/tex]Then, we use the inscribed angle theorem to get
[tex]a=\frac{1}{2}\cdot109=54.5[/tex]Then, we use the interior angles theorem (triangle) to find the third acute angle
[tex]\begin{gathered} a+b+x=180 \\ 54.5+90+x=180 \\ x=180-90-54.5 \\ x=35.5 \end{gathered}[/tex]Now, we find arc c
[tex]\begin{gathered} x=\frac{1}{2}\cdot c \\ 35.5=\frac{1}{2}\cdot c \\ c=2\cdot35.5 \\ c=71 \end{gathered}[/tex]Hence, a = 54.5, b = 90, and c = 71.hello I seem to be having some difficulty with this problem and need some help thank you
Answers
Solution
Given that
The Parker's are saving up to go for a family vacation in 3 years
Number of year, n, is 3 years.
They invested $3100 into an account
Principal, P, is $3100
Annual interest rate of 1.36% compounded monthly
a) To find the amount, A, the Parker's account after 3 years, the formula is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where
[tex]\begin{gathered} r=\frac{1.36}{100}=0.0136 \\ t=12 \end{gathered}[/tex]Substitute the variables into the formula above
[tex]\begin{gathered} A=3100(1+\frac{0.0136}{12})^{3\times12} \\ A=3100(1+\frac{0.0136}{12})^{36}=\text{ \$3229.02} \\ A=\text{ \$3229.02 \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the amount in the Parker's account after 3 years is $3,229.02 (nearest cent)
b) To find the interest, I, earned on the Parker's investment, the formula is
[tex]I=A-P[/tex]Where
[tex]\begin{gathered} A=\text{ \$3229.02} \\ P=\text{ \$3100} \end{gathered}[/tex]Substitute the values into the formula to find the interest above
[tex]\begin{gathered} I=A-P \\ I=3229.02-3100=\text{ \$129.02} \\ I=\text{ \$129.02} \end{gathered}[/tex]Hence, the interest, I, earned on the Parker's investment is $129.02 (nearest cent)
Given sine of theta equals square root of three/ two determine three possible angles for theta on the domain of [0, infinity)
Answers
Answer:
60°, 120°, and 420°.
Explanation:
Given:
[tex]\sin\theta=\frac{\sqrt{3}}{2}[/tex]Take the arcsin of both sides:
[tex]\begin{gathered} \theta=\arcsin(\frac{\sqrt{3}}{2}) \\ \theta=60\degree+360(n)\text{ or }\theta=120\degree+360(n),\theta\in[0,\infty) \end{gathered}[/tex]Therefore, three possible angles for θ on the domain of [0, ∞) are:
[tex]\begin{gathered} \theta=60\degree \\ \theta=120\operatorname{\degree} \\ \theta=60\operatorname{\degree}+360\degree=420\degree \end{gathered}[/tex]Three possible angles are 60°, 120°, and 420°.
Consider the following graph of two functions.(8.9(-2)Step 3 of 4: Find (8 (-2)Enable Zoom/Pan8(x) = 3x - 1101MA10-510-5f(x) = x + 3
Answers
Given:
Two functions are given
[tex]\begin{gathered} f(x)=x+3 \\ g(x)=-3x-1 \end{gathered}[/tex]Required:
We have to find (g.f)(-2)
Explanation:
to find (g.f)(-2) first we have to find the (g.f)(x)
to find (g.f)(x) we have to put value of f(x) as x in g
[tex]g(f)(x)=-3(x+3)-1=-3x-9-1=-3x-10[/tex]now put the value of x-2
[tex]g(f)(-2)=-3(-2)-10=6-10=-4[/tex]Final answer:
[tex](g.f)(-2)=-4[/tex]for given equations
The function is decreasing on the interval (-0, 0)and increasing on the interval (0, 0).The function is increasing on the interval (-0,0)and decreasing on the interval (0, ).The function is increasing on the interval (-00, 0).The function is decreasing on the interval(-0, 0).
Answers
D; The function is decreasing in the interval;
[tex](-\infty,\infty)[/tex]Here, we want to interpret the given rate of change of the function
From what we have, coming from negative infinity, we can see that there is a decrease in the rate of change of the function. As we move closer to zero, we can see a decrease in the range value of the function
Now, moving away from zero, we can see that there is a continuous decrease as we move towards positive infinity. We can therefore conclude that there is a continuous decrease from the point x = 0 towards the point x = positive infinity
So, the correct choice here is that the function is decreasing in the interval negative infinity to positive infinity
What is the possible postulate or theorem to be used?
Answers
Solution
For this case we need to select the possible postulate inorder that the two triangles are similar so we can use:
d. AAS
Since we have two congruent angles and one equivalent side
From 1965 to 2000, twice as many people immigrated to the United States from the Philippines as from Vietnam. The total number of immigrants from these two countries was 2,100,000. How many people came to the United States from each country?
Answers
Data:
• Twice as many people immigrated from the Philippines as from Vietnam.
,• People immigrated from Vietnam ( ,V ,)
,• People immigrated from Philipines (, P ,)
Procedure:
0. We have to build two equations based on the information provided:
[tex]P=2V[/tex][tex]V+P=2,100,000[/tex]2. Replacing the first equation in the second, we get the following equation:
[tex]V+2V=2,100,000[/tex][tex]3V=2,100,000[/tex][tex]V=\frac{2,100,000}{3}[/tex][tex]V=700,000[/tex]3. Then, we replace this value in the first equation:
[tex]P=2V[/tex][tex]P=2\cdot700,000[/tex][tex]P=1,400,000[/tex]Answer:
• People immigrated from Vietnam = 700,000
,• People immigrated from Philipines = 1,400,000
Help these are all parts of one question just find the answers for them and in your answer label it like part A part B part C part D please and thank you. 1. The 30% discount on a $49 dollhouse2.the 20% tip on a $8 sandwich3. the total cost of a $112.75 meal with a 20% tip4. the price paid for a $15 shirt after a 45% discount
Answers
The 30% discount refers to 30% of 49 less. So, let's find 30% of 49.
[tex]0.30\cdot49=14.7[/tex]The discount is $14.7. To find the final price, we subtract
[tex]49-14.7=34.30[/tex]The final price, after the discount, is $34.30.
PART B.20% tip on an $8 sandwich means we have to find 20% of 8.
[tex]0.20\cdot8=1.6[/tex]The tip is $1.6.
PART C.First, we find the 20% of 112.75.
[tex]0.20\cdot112.75=22.55[/tex]Then, we add the tip to the cost.
[tex]112.75+22.55=135.30[/tex]The final price is $135.30.
PART D.First, we find 45% of 15.
[tex]0.45\cdot15=6.75[/tex]Then, we subtract the discount from the price
[tex]15-6.75=8.25[/tex]The price paid was $8.25.
Find the area of the shaded region given the radius of each circle is 4. Answer in exact form is preferred.
Answers
In each circle, we have a sector that subtends an angle of 270 deg at the center, with a radius of 4
We can obtain the area of each sector as :
[tex]\begin{gathered} \text{Area of sector = }\frac{\theta}{360^0}\text{ }\times\text{ }\pi r^2 \\ =\text{ }\frac{270^0}{360^0}\text{ }\times\text{ }\pi\text{ }\times4^2 \\ =\text{ 37.7 square units} \end{gathered}[/tex]Given that there are 4 of such sectors, we have:
[tex]\begin{gathered} \text{Area of shaded region = 4 }\times\text{ 37.7} \\ =\text{ }150.8\text{ square units} \\ =\text{ 151 square units} \end{gathered}[/tex]Answer = 151 square units
use the elimination method to solve the system of equations write your answer as ordered pair
Answers
Solution:
Given the system of equations below;
[tex]\begin{gathered} 4x+6y=24...(1) \\ 4x-y=10...(2) \end{gathered}[/tex]Applying the elimination method
Eliminating the variable x by subtracting equation (2) from (1)
[tex]\begin{gathered} 4x+6y-(4x-y)=24-10 \\ 4x+6y-4x+y=14 \\ Collect\text{ like terms} \\ 4x-4x+6y+y=14 \\ 7y=14 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7y}{7}=\frac{14}{7} \\ y=2 \end{gathered}[/tex]Substituting 2 for y into equation (2) to find the value of x
[tex]\begin{gathered} 4x-y=10 \\ 4x-2=10 \\ Collect\text{ like terms} \\ 4x=10+2 \\ 4x=12 \\ Divide\text{ both sides by 4} \\ \frac{4x}{4}=\frac{12}{4} \\ x=3 \end{gathered}[/tex]The solution to the system of equations in ordered pair is
[tex](3,2)[/tex]To check the solution
A standard number cube is tossed. Find the probability of getting P(greater than 2 or less than 4).1/215/66
Answers
The probability of getting P(greater than 2 or less than 4) is given by
[tex]\begin{gathered} P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(greater than 2 AND less than 4)} \\ \text{which is equal to} \\ P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(3)} \end{gathered}[/tex]because the a number greater than 2 and less than 4 is 3.
Since the cube has 6 faces, the probability of getting one face is 1/6, then we have
[tex]\begin{gathered} \text{P(greater than 2)}=P(3)+P(4)+P(5)+P(6) \\ \text{P(greater than 2)}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ \text{P(greater than 2)}=\frac{4}{6} \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} P(\text{less than 4)}=P(3)+P(2)+P(1) \\ P(\text{less than 4)}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ P(\text{less than 4)}=\frac{3}{6} \end{gathered}[/tex]since P(3)= 1/6, we have
[tex]\begin{gathered} P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(3)} \\ P(\text{greater than 2 OR less than 4)=}\frac{4}{6}+\frac{3}{6}-\frac{1}{6} \end{gathered}[/tex]which gives
[tex]P(\text{greater than 2 OR less than 4)=}\frac{7-1}{6}=\frac{6}{6}=1[/tex]Therefore, the answer is 1.
Please solve this question for me Note: the value of p=2
Answers
Given:
[tex]\sum_{n\mathop{=}1}^{\infty}\frac{(np)^{-2}}{\frac{2}{n^2}+\frac{3}{n}+1}[/tex]Find-:
Find the formula for n partial sum, and determine whether the series converges or diverges.
Explanation-:
The value is:
[tex]\begin{gathered} =\sum_{n\mathop{=}1}^{\infty}\frac{(np)^{-2}}{\frac{2}{n^2}+\frac{3}{n}+1} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2p^2(\frac{1}{n^2}+\frac{3}{n}+1)} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{p^2(\frac{n^2}{n^2}+\frac{3n^2}{n}+n^2)} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{p^2(1+3n+n^2)} \end{gathered}[/tex]So, the value is,
[tex]=\frac{1}{p^2}\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2+3n+1}[/tex]Apply telescoping series
[tex]\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2+3n+1}=\frac{1}{2}[/tex]The value is:
[tex]\begin{gathered} =\frac{1}{p^2}\times\frac{1}{2} \\ \\ =\frac{1}{2p^2} \end{gathered}[/tex]It is a series of converges.
[tex]\begin{gathered} =\frac{1}{2p^2} \\ \\ =\frac{1}{2(2)^2} \\ \\ =\frac{1}{2\times4} \\ \\ =\frac{1}{8} \end{gathered}[/tex]Is it necessary to perform the horizontal line test when finding the inverse of every function? Why or why not?
Answers
The function has an inverse if it is a one-to-one function
We use the horizontal line test to check if the function is a one-to-one function or not
Then it is necessary to use the horizontal line test because if the function is not a one-to-one function there is no inverse to it
The answer is
Yes it is necessary
what is the explicit formula for this sequence-15, -18, -21, -24,...
Answers
Answer: The explicit formula for the following sequence is:
[tex]-15,-18,-21,-24[/tex]According to the pattern in the sequence, the explicit formula is as follows:
[tex]\begin{gathered} a_n=-15-3(n-1) \\ \\ a_n=-15-3n+3 \\ \\ a_n=-12-3n \\ \\ \therefore\rightarrow \\ \\ a_n=-12-3n=-15+(n-1)(-3) \\ \\ a_n=-15+(n-1)(-3) \end{gathered}[/tex]Therefore the answer is Option(2).
A research study asked 1749 homeowners how many bedrooms were in their homes. The results are shown in the table below. What is the probability that a homeowner chosen at random has 3 bedrooms? # of bedrooms # of homeowners12 or less. 4903. 5774. 4555 ot more. 227Answers:13%26%28%33%
Answers
Probability that a homeowner chosen at random has 3 bedrooms:
[tex]\begin{gathered} P(3\text{ bedrooms)=}\frac{\#homeowners\text{ with 3 bedrooms}}{\#\text{total homeowners}} \\ \\ P(3\text{ bedrooms)=}\frac{577}{490+577+455+227}=\frac{577}{1749}\approx0.33 \end{gathered}[/tex]Multiply the probability by 100 to get it in %:
[tex]0.33\cdot100=33[/tex]Then, the probability that a homeowner chosen at random has 3 bedrooms is 33%In 2019, there were 143 teen drivers killed; total fatalities (deaths) were 3,754. What is the % of teen driver deaths?
Answers
3.81%
1) Since the total number of casualties was 3,754 we can find the percentage of 143 teens setting a proportion
3754 -------- 100%
143 ------------ x
Cross multiplying we have
3754x = 14300
x=14300/3754
x=3.809
x≈ 3.81%
2) So the percentage of teen driver deaths was in 2019, 3.81% of all fatalities.
32. Find the equation of the line that matches thefollowing data table:Xy491661A. y = -x + 10B. y = x +9C. y = -3x + 3D. y = 3x + 9
Answers
ANSWER
A. y = -1/4x + 10
EXPLANATION
We have to find the equation of the line in slope-intercept form,
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this case, only two points are given, so the slope of the line is,
[tex]m=\frac{6-9}{16-4}=\frac{-3}{12}=-\frac{1}{4}[/tex]So, for now, the equation is,
[tex]y=-\frac{1}{4}x+b[/tex]To find the y-intercept, b, replace x and y with one of the points,
[tex]9=-\frac{1}{4}(4)+b[/tex]And solve for b,
[tex]9=-1+b\text{ }\Rightarrow\text{ }b=9+1=10[/tex]Hence, the equation of the line is y = -1/4x + 10.
Compute the probability of tossing a six-sided die and getting an even number
Answers
sixe sided die so number of possible outcome is=6
And a die with even number is (2,4,6)
so number of favorable outcome is:3
then probability is:
[tex]\begin{gathered} \text{probability}=\frac{favorable-outcom\text{ }}{\text{total outcom}} \\ =\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]so probability is half.
car averages 15 miles per gallon of gas in city driving and 20 miles per gallon in highway driving. At these rates, how many gallons of gas will the car use on a 600 mile trip if 4/5 of the trip is highway driving and the rest is city driving
Answers
We have the average rate of fuel consumption for both city and highway.
Driving in the city, the car can travel 15 miles per gallon, while on highway it can travel 20 miles per gallon.
Alternatively, we can say that driving in the city, the car consumes 1/15 gallons per each mile traveled, while on highway it consumes 1/20 gallons per each mile travelled:
[tex]\begin{gathered} \text{Fuel consumption:} \\ \text{City: }\frac{1}{15}\text{gal}/\text{mile} \\ \text{Highway: }\frac{1}{20}\text{gal}/\text{mile} \end{gathered}[/tex]Expressing the fuel consumption that way will allow us to calculate easier the total amount of fuel consumed later.
The car will travel 600 miles. 4/5 of that trip will be on highway, therefore the remaining 1/5 will be in the city.
With this information, we can calculate exactly how many miles are traveled on highway and how many in the city:
[tex]\text{Miles on highway}=\frac{4}{5}\cdot600=\frac{2400}{5}=480\text{miles}[/tex][tex]\text{Miles on city}=\frac{1}{5}\cdot600=\frac{600}{5}=120\text{miles}[/tex]Then, from those 600 miles traveled, 480 will be on highway while 120 will be on city.
If the travels 120 miles on the city, and it consumes 1/15 gallons per each mile travelled, we can calculate the amount of fuel used in the city as follows:
[tex]120\text{miles}\cdot\frac{1}{15}\frac{\text{gallons}}{\text{mile}}=8\text{gallons}[/tex]While travelling 120 miles in the city, the car will consume 8 gallons.
Similarly, for the amount of fuel used while on the highway:
[tex]480\text{miles}\cdot\frac{1}{20}\frac{\text{gallons}}{\text{mile}}=24\text{gallons}[/tex]While travelling 480 miles in the city, the car will consume 24 gallons.
Now we know the number of gallons the car used each part of the trip. The total amount used for the whole trip is just the sum of them:
[tex]\text{Total fuel consumed}=8\text{gallons}+24\text{gallons}=32\text{gallons}[/tex]The car will use 32 gallons on its 600-mile trip.
Solve the following system by graphing. What isthe solution?1.) (2, 1)2.) (1, 2)3.) (-1, 2)4.) (2, -1)
Answers
EXPLANATION:
To correctly solve the system of equations, we must follow the following steps:
-We must use a method that allows us to match one of the variables.
-We must first find the value of the variable x and finally we must replace that value in the equations to find y.
The exercise is as follows:
[tex]\begin{gathered} y=-4x-2;\text{ y=2x+4} \\ \text{ y=y} \\ -4x-2=2x+4 \\ -4x-2x=\text{ 2+4} \\ -6x=6 \\ x=\frac{6}{-6} \\ x=-1 \end{gathered}[/tex]Now we must replace value of x in both equations: