You are given a total of $240 to buy either good X or good Y, which are priced at $6 and $10, respectively. Draw a budget line that expresses all combinations of the two goods that can be purchased with this budget. What happens to the initial budget line if the budget is reduced by 25%? What happens if the price of X doubles? What happens if the price of Y falls to 8?
Answers
6X + 10 Y = 240
Rewriting this in slope intercept form
10y = -6x+240
y = -6/10x + 240/10
y = -.6x + 24
We know that x and y cannot be less than 0
The y intercept is 24 and the x intercept ( where y=0) is 40
To find the x intercept let y = 0
0 = -.6x + 24
-24 = -.6x
-24/.6 = -.6x/-/6
40 =x
If the budget is reduced by 25%, that means 240 is 25% less or 75% of the original value
75% of 240 = .75*240 or 180
6x+10y = 180
10y = -6x+180
y = -.6x+18
The y intercept is 18 and the x intercept is 30
If the price of x doubles
6 will become 12
12x+10y = 240
10y = -12x + 240
y = -1.2x +24
The y intercept is 24 and the x intercept is 20
If the price of y falls to 8
6x+8y = 240
8y = -6x+240
y = -6/8x + 240/8
y = -.75x + 30
The y intercept is 30 and the x intercept is 40
Related Questions
In kickboxing, it is found that the pressure, p, needed to break a board varies inversely with the length of the board.If it takes 5 lbs of pressure to break a board that is 2 feet long, how long is the board that requires 18 lbs of pressureto break?
Answers
The pressure, p, needed to break a board varies inversely with the length of the board.
Formula for a inverse variation:
[tex]y=\frac{k}{x}[/tex]In the given situation the variable p is the dependent variable (y) and the variable l (length) is the independt variable (x).
Use the given data to find the value of the constant k:
[tex]k=y\cdot x[/tex]if it takes 5 lbs of pressure to break a board that is 2 feet long:
[tex]\begin{gathered} k=5\cdot2 \\ k=10 \end{gathered}[/tex]Using the value of k you get the next equation for the given varation:
[tex]p=\frac{10}{l}[/tex]How long is the board that requires 18 lbs of pressure to break?
Find l when p is 18:
[tex]18=\frac{10}{l}[/tex]solve l:
[tex]\begin{gathered} 18\cdot l=10 \\ l=\frac{10}{18} \\ \\ l=0.55 \end{gathered}[/tex]Then, the board that requires 18lbs of pressure to break has a length of 0.55 feetCalculate the following geometric sum. Round to three decimal places. (1.07)^18 + (1.07)^17 +...+ (1.07)^2 + (1.07) +1
Answers
Given:
[tex]a=(1.07)^{18};\text{ r=}\frac{1}{1.07}[/tex]The series power starts with 18 and ends in 0, n=19
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex][tex]S_{19}=\frac{(1.07)^{18}(1-(\frac{1}{1.07})^{19})}{1-\frac{1}{1.07}}[/tex][tex]S_{19}=\frac{(1.07)^{18}\lbrack1-0.2766\rbrack}{\frac{1.07-1}{1.07}}[/tex][tex]S_{19}=\frac{(1.07)^{18}\lbrack0.7234\rbrack}{\frac{0.07}{1.07}}[/tex][tex]S_{19}=(1.07)^{18}\lbrack0.7234\rbrack\times\frac{1.07}{0.07}[/tex][tex]S_{19}=(1.07)^{19}\lbrack10.3343\rbrack[/tex][tex]S_{19}=(3.6165)(10.3343)[/tex][tex]S_{19}=37.3709[/tex]If the area of the rhombus below is 273 m 2, and diagonal AC = 13 m, find the length of diagonal BD.
Answers
1) Since the area of a Rhombus is given by the product of their diagonals over 2. We can tell that:
[tex]\begin{gathered} A=\frac{AC\times BD}{2} \\ \\ 273=\frac{13BD}{2} \\ \\ 13BD=546 \\ \\ BD=\frac{546}{13} \\ \\ BD=42 \end{gathered}[/tex]2) Thus, we can tell that the length of BD is 42
The quadratic Function has a vertex at (3,4). The quadratic also goes through the point (7,12). Find the value using the information.y=a(x-h)^2+k
Answers
Given:
[tex]\begin{gathered} Vertex:(h,k)=(3,4) \\ Point:(x,y)=(7,12) \end{gathered}[/tex]The equation given is,
[tex]y=a(x-h)^2+k[/tex]Therefore,
[tex]\begin{gathered} 12=a(7-3)^2+4 \\ 12=a(4)^2+4 \\ 12=16a+4 \\ 12-4=16a \\ 8=16a \\ \frac{8}{16}=\frac{16a}{16} \\ \frac{1}{2}=a \\ \therefore a=\frac{1}{2} \end{gathered}[/tex]Hence,
[tex]a=\frac{1}{2}[/tex]The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone.
Answers
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Also, in this problem, x is the number of monthly minutes used and y is the total monthly payment of the Splint plan.
The slope can be found by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) is the given information, x1=280 min, y1=$178, x2=730 min and y2=$403.
Replace these values and solve for m:
[tex]\begin{gathered} m=\frac{403-178}{730-280}=\frac{225}{450} \\ \text{Simplify} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, replace m and one of the coordinates in the equation of the line and solve for b:
[tex]\begin{gathered} 178=\frac{1}{2}280+b \\ 178=140+b \\ b=178-140 \\ b=38 \end{gathered}[/tex]Thus, the equation is:
[tex]y=\frac{1}{2}x+38[/tex]b. The monthly cost, if 910 minutes are used, is:
[tex]\begin{gathered} y=\frac{1}{2}910+38 \\ y=455+38 \\ y=493 \end{gathered}[/tex]If 910 minutes are used, the total cost will be 493 dollars.
Express the following as a simple fraction involving positive exponents only
Answers
Recall that if x≠0, then:
[tex]\begin{gathered} x^{-m}=\frac{1}{x^m} \\ \text{where m is an integer.} \end{gathered}[/tex]Therefore:
[tex]2x^{-1}-5x^{-2}=\frac{2}{x}-\frac{5}{x^2}\text{.}[/tex]Now, if x≠0, notice that:
[tex]\frac{2}{x}=\frac{2x}{x^2}\text{.}[/tex]Then:
[tex]\begin{gathered} 2x^{-1}-5x^{-2}=\frac{2x}{x^2}-\frac{5}{x^2} \\ =\frac{2x-5}{x^2}\text{.} \end{gathered}[/tex]Answer:
[tex]\frac{2x-5}{x^2}\text{.}[/tex]At noon the temperature was 37°F. At 7 AM the temperature was 17°F colder. Thetemperature at 7PM was 4 Degrees Fahrenheit warmer than at 7 AM What was the temperature at7 PM?
Answers
Answer:
The temperature at 7 PM is:
[tex]24^{\circ}F[/tex]Explanation:
Given;
At noon the temperature was 37°F.
[tex]T_n=37^{\circ}F[/tex]At 7 AM the temperature was 17°F colder;
[tex]\begin{gathered} T_{AM}=(T_n-17)^{\circ^{}} \\ T_{AM}=(37-17)^{\circ} \\ T_{AM}=20^{\circ}F \end{gathered}[/tex]The temperature at 7PM was 4 Degrees Fahrenheit warmer than at 7 AM;
[tex]\begin{gathered} T_{PM}=T_{AM}+4 \\ T_{PM}=(20_{}+4)^{\circ}F \\ T_{PM}=24^{\circ}F \end{gathered}[/tex]The temperature at 7 PM is;
[tex]24^{\circ}F[/tex]
Notación científica el exponente se cambia como por ejemplo6.612x10-⁸ y me da6612.10-¹¹?esta bien la respuesta ?Scientific notationthe exponent is changed as for example6.612x10-⁸ and it gives me6612.10-¹¹?the answer is ok
Answers
Tenemos el siguiente número en notación científica:
[tex]6.612\times10^{-8}[/tex]En la notación científica, cada vez que movemos el punto decimal hacia la derecha, debemos restar una unidad al exponente del diez, es decir:
[tex]6612\times10^{-11}[/tex]Es equivalente, ya que movimos el decimal 3 espacios hacia la derecha, por lo tanto se le restan 3 unidade al exponente del 10, como el exponente era -8, entonces: -8 -3 = -11.
The ratio of oblong tables to round tables at a conference is 3:5. The total number of tables at the conference is 72. How many of each type are there? There are ? Oblong tables and ? Round tables. Solve for both question marks.
Answers
Since the ratio of the oblong tables to round tables is 3: 5
Since the total number of tables is 72
Let us find the sum of the ratios and equate it by 72
[tex]\begin{gathered} 3x+5x=72 \\ 8x=72 \end{gathered}[/tex]Let us divide both sides by 8 to find the value of x, which is the number of units in each type
[tex]\begin{gathered} \frac{8x}{8}=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Now multiply 9 by each term of the ratio to find the number of each type
[tex]\begin{gathered} 3\times9=27 \\ 5\times9=45 \end{gathered}[/tex]There are 27 oblong tables
There are 45 round tables
Challenge in a company, 90% of the workers are men. If 250 people work for the company who aren't men, how many workers are there in all? Use pencil and paper Show two different ways that you can solve this problem. There are workers in all. (Type a whole number)
Answers
1) Gathering the data
90% are men
250 people who aren't men, then they are women.
2) Since we have the percentage of men, and the number of women, we can find how many workers this way:
250 ---------------- 10%
x ----------------------100%
10x = 25000
x=2500 workers
2500- 250 = 2250 men
and 250 women.
Alternatively, we can find this another way, since we know that 250 corresponds to 10%
2500x0.9
a line passes through the points 2 -4 and 6 10 what is the equation of the line
Answers
We have a line passing through two points, we can employ the equation of a line in two-point form to obtain this line;
The equation is, for points
[tex](x_1,y_1)\&(x_2,y_2)[/tex]The equation of a line passing through both points is;
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]For the points (2, -4) and (6, 10), we have
[tex]\begin{gathered} \frac{10-(-4)}{6-2}=\frac{y-(-4)}{x-2} \\ \frac{14}{4}=\frac{y+4}{x-2} \\ \text{cross multiply, we have} \\ 4(y+4)=14(x-2)_{} \\ 4y+16=14x-28 \\ 4y=14x-16-28 \\ 4y=14x-44 \\ \text{Divide both sides by 2, to obtain} \\ 2y=7x-22 \\ y=\frac{7}{2}x-22 \end{gathered}[/tex]Therefore the equation of the line is y = (7/2)x - 22
What is the slope of the line created by this equation? y=7.3x+0
Answers
Given:
[tex]y=7.3x+0[/tex]Compare with the equation
[tex]y=mx+c[/tex][tex]\text{Slope(m)}=7.3[/tex]Answer:
The slope is 7.3
Step-by-step explanation:
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 7.3x +0
The slope is 7.3 and the y intercept is 0
12. Given: the circle at the right with centre A, the indicated perpendicular, and a radius of 5. The length of the horizontal segment labelled x is _______.
Answers
In general, if a diameter of a circle is perpendicular to a chord, then it bisects the chord.
On the other hand, consider the diagram below
Therefore, we can calculate x by means of the Pythagorean theorem, as shown below
[tex]\begin{gathered} radius^2=3^2+x^2 \\ \Rightarrow x^2=radius^2-3^2=5^2-3^2=25-9=16 \\ \Rightarrow x=4 \end{gathered}[/tex]Thus, the answer is x=4.In 3 days, a polar bear can eat up to 42.6 pounds of fish. What rate can relate the number of pounds of fish to the number of days by finding the unit rate.
Answers
ANSWER:
14.2 pounds per day
STEP-BY-STEP EXPLANATION:
The unit rate would be the quotient between the number of pounds and the number of days, just like this:
[tex]\frac{42.6}{3}=14.2\text{ pounds per day}[/tex]Which means that the polar bear eats 14.2 pounds per day
suppose the width of a certain rectangle is 3 inches more than 1/4 of its length. The perimeter of the rectangle is 66 inches. Find the length and width of the rectangle.
Answers
The length of the rectangle = 24 inches
The width of the rectangle = 9 inches
Explanations:Let the width of the rectangle be represented by w
Let the length of the rectangle be represented by l
The width is 3 inches more than 1/4 of the length
This can be written mathematically as:
[tex]w\text{ = }\frac{l}{4}+3\ldots\ldots\ldots\ldots\ldots\text{.}(1)[/tex]The perimeter, p = 66 inches
The perimeter of a rectangle is given by the formula:
p = 2(l + w)
66 = 2(l + w)
l + w = 66/2
l + w = 33
w = 33 - l...........................(2)
Substitute equation (2) into equation (1)
[tex]\begin{gathered} 33\text{ - l = }\frac{l}{4}+3 \\ \text{Mulitply through by 4} \\ 132\text{ - 4l }=\text{ l + 12} \\ l\text{ + 4l = 132 - 12} \\ 5l\text{ = }120 \\ l\text{ = }\frac{120}{5} \\ l\text{ = 24} \end{gathered}[/tex]Substitute l = 24 into equation (2)
w = 33 - l
w = 33 - 24
w = 9
The length of the rectangle = 24 inches
The width of the rectangle = 9 inches
solve the equation y:4x-7y=28
Answers
we have
4x-7y=28
Solve for y
that means -----> isolate the variable y
subtract 4x both sides
-7y=-4x+28
Divide by -7 both sides
y=(-4/7)x-28/7
y=(-4/7)x-4Part 2The perimeter of rectangle is equal to
P=2(L+W)
step 1
Find the perimeter of rectangle CARD
substitute the given values
P=2(2x-5+6x+10)
P=2(8x+5)
P=16x+10
step 2
Find the perimeter of rectangle BEST
P=2(10x+3+4x-7)
P=2(14x-4)
P=28x-8
step 3
find the difference
Difference=(16x+10)-(28x-8)
Difference=-12x+181.5.25ZEFG and ZGFH are a linear pair, mZEFG = 5n + 21, and mZGFH=4n + 15. What are m ZEFG and mZGFH?mZEFG=mZGFH = ”(Simplify your answers.)
Answers
Linear pairs of angles:
It means that they add to 180º.
In this question:
mZEFG = 5n + 21
mZGFH =4n + 15
Since they are linear:
mZEFT + mZGFH = 180
5n + 21 + 4n + 15 = 180
9n + 36 = 180
9n = 180 - 36
9n = 144
n = 144/9
n = 16
Now we have n, so we can find the measures of both angles.
mZEFG = 5n + 21 = 5*16 + 21 = 80 + 21 = 101
mZGFH =4n + 15 = 4*16 + 15 = 64 + 15 = 79
Answer:
mZEFG = 101, mZGFH = 79
-0.5a la 6 potencia es?
Answers
Respuesta:
0.015625
Explicacion paso-a-paso:
Quando la potencia es par, el resultado sera positivo.
0.5 puede ser escrito como 1/2
[tex](-0.5)^6=(\frac{1}{2})^6=\frac{1^6}{2^6}=\frac{1}{64}=0.015625[/tex]15. Ten bands are to perform at a weekend festival. How many different ways are there to schedule their appearances?
Answers
Given:
Number of bands performing = 10
Number of ways to schedule 'n' distinct objects = n!
Therefore, number of ways to schedule 10 performers is given by:
[tex]\begin{gathered} =10! \\ =10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \\ =3628800 \end{gathered}[/tex]Hence, the required number of ways are 3628800
A new car is purchased for $18,000 and over time its value depreciates by one halfevery 6 years. What is the value of the car 19 years after it was purchased, to thenearest hundred dollars?
Answers
We have the following:
We must pass the time from 19 years to periods of 6 years, as follows
[tex]\frac{19}{6}=3.17[/tex]That is, 19 years are 3.17 periods of 6 years
now, the formula to calculate the value of the car is
[tex]c=A\cdot(1-x)^n[/tex]Where A is the initial value, x is the depreciation and n is the time in periods of 6 years
Replacing:
[tex]c=18000\cdot(1-0.5)^{3.17}=1999.89[/tex]Therefore the value of the car would be approximately 1999.9 dollars
Answer: 2000
Step-by-step explanation:
the answer is 2000 after rounding up 1999.9
12. The seventh and eighth grade students are selling tickets to the talent show. The eighth grade studentshave sold fifteen more than twice the number of tickets that the seventh grade students have. If theysold 486 tickets altogether, how many did the eighth grade students sell?
Answers
If x is the number of tickets the seventh grade students sold, then you have:
tickets sold by seventh grade students = x
tickets sold by seventh grade students = x
I am thinking of two numbers the sum of the two is 10 and the difference is six
Answers
Hello! Let's write this numbers as x and y.
We know:
x + y = 10
x - y = 6
Solving using the method of elimination:
Now we just have to replace where's x by 8 in one of the equations, look:
So, the first number is 8 and the second number is 2.
Fill in the blanks below with the correct units.(a) A piece of paper is about 9 ?v wide.(b) A large horse weighs about 1 ?(c) A bucket holds about 5 ?of water.
Answers
a. A piece of paper is about 9 inches wide. (since a paper cannot be 9 feet 9 yards or 9 miles)
b. A large horse weighs about 1 ton (a horse can't have a weight of 1 ounce or 1 pound)
c. A bucket holds about 5 pints (5 gallons is too much for a bucket.)
Parallelogram QRST has vertices QC-4,2), R(-2,4), S(0,1), and I(-2.1). Draw and label the imageafter a counterclockwise rotation of 270° about the origin.
Answers
A counterclockwise rotation of 270 degrees about the origin is given by the rule:
[tex](x,y)\rightarrow(y,-x)[/tex]Apply the rotation to each point to find the new coordinates:
[tex]\begin{gathered} Q(-4,2)\rightarrow Q^{\prime}(2,4) \\ R(-2,4)\rightarrow R^{\prime}(4,2) \\ S(0,1)\rightarrow S^{\prime}(1,0) \\ T(-2,1)\rightarrow T^{\prime}(1,2) \end{gathered}[/tex]Plot Q', R', S', and T' on a coordinate plane and draw the rotated figure:
Which number line shows the solutions to a < 7? O A. -8 -6 -4 -2 0 2 4 6 8 OB. 8-6-4-20 2.26 8 O I c. -8 6 4 2 0 O D. 8 6 4 2 0 2 4 6
Answers
The correct option is C
The equation that represents this situation is:
y = x + 4
Explanation:Given that
x = original price
y = sale price
Since the sale price is $4 less than the original price, this means the original price can only be equal to the sale price if $4 is added to it.
We can write this as:
y = x + 4
The length of the wire is how many ft?Picture included below
Answers
We have a pole and a wire that will form a right triangle.
We can draw it like this:
We can then find the length of the wire (x), which is the hypotenuse of the triangle, using the Pythagorean theorem:
[tex]\begin{gathered} x^2=2^2+18^2 \\ x^2=4+324 \\ x^2=328 \\ x=\sqrt{328} \\ x\approx18.1\text{ }ft \end{gathered}[/tex]Answer: the length of the wire is 18.1 ft approximately.
14. Find the equation of the Plsssss help this is for algebra 1 20 points!!!!line containing the points (2,-2) and (4, 1).(A) 3x - 2y = 10[B] - 2x + 3y = -5(C) 3x - 2y = -5[D] - 2x + 3y = 10
Answers
The equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]where (x1,y1) is a point in the line and m is the slope.
In our case we have two points but we don't have the slope yet, to find it we need to remember that the slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, in our case:
[tex]\begin{gathered} m=\frac{1-(-2)}{4-2} \\ =\frac{1+2}{2} \\ =\frac{3}{2} \end{gathered}[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-1=\frac{3}{2}(x-4) \\ 2y-2=3x-12 \\ 3x-2y=-2+10 \\ 3x-2y=10 \end{gathered}[/tex]Therefore the answer is A.
Order 2/3, 3/7, 7/19 From least to greatest
Answers
Given:
The fractions are,
[tex]\frac{2}{3},\frac{3}{7},\frac{7}{19}[/tex]To order: From least to greatest.
Explanation:
Since the denominator is unequal
Let us find the LCM of 3, 7, and 19.
[tex]\begin{gathered} LCM=3\times7\times19 \\ =399 \end{gathered}[/tex]Let us make all the denominators 399.
[tex]\begin{gathered} \frac{2}{3}\times\frac{133}{133}=\frac{266}{399} \\ \frac{3}{7}\times\frac{57}{57}=\frac{171}{399} \\ \frac{7}{19}\times\frac{21}{21}=\frac{147}{399} \end{gathered}[/tex]Since,
[tex]147<171<266[/tex]Therefore, we can write
[tex]\frac{7}{19}\lt\frac{3}{7}\lt\frac{2}{3}[/tex]Therefore, the numbers from least to greatest is,
[tex]\frac{7}{19},\frac{3}{7},\frac{2}{3}[/tex]Final answer:
[tex]\frac{7}{19},\frac{3}{7},\frac{2}{3}[/tex]Question 20
of 50 Step 1 of 1
Samantha wants to buy a new minivan for $19,000. She has talked to the loan officer at her credit union and knows that they will loan her $11,000.
She must also pay $345 for a license fee and $1300 for taxes. What amount of cash will she need to buy the minivan?
Answers
Given
Samantha wants to buy a new minivan for $19,000.
She pay $345 for a license fee and $1300 for taxes.
loan officer give loan = $11,000.
Find
What amount of cash will she need to buy the minivan?
Explanation
Total amount she wants to buy the new minivan = $19,000 + $345 + $1300 = $ 20645
Loan officer agree to loan her of $ 11000
so , amount of cash will she need to buy = $ 20645 - $ 11000 = $9645
Final Answer
Hence , the amount of cash will she need to buy the minivan is $ 9645
A unit rate is a rate in which the unit in the denominator is:
Answers
Problem
A unit rate is a rate in which the unit in the denominator is:
Solution
the answer for this case would be one
And the reason is because by definition the unit rate ratio between two different units is a division with a denominator of one.