D. 2x -3y = 18
Step-by-step explanation:Multiply by 3, then rearrange.
... y = 2/3x -6
... 3y = 2x -18 . . . . . multiply by 3
... 0 = 2x -3y -18 . . . subtract 3y
... 18 = 2x -3y . . . . . add 18
... 2x - 3y - 18 . . . . . swap sides to match the form of the answers
Convert theta= 3pi/4 to rectangular form.
A. y= -1
B. y= 1
C. y= x
D. y= -x
E. x= -1
[tex]\theta=\dfrac{3\pi}{4}=\pi-\dfrac{\pi}{4}\\\\y=\tan\theta x\\\\y=\left(\tan\dfrac{3\pi}{4}\right)x\\\\y=\left(\tan\left(\pi-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(\tan\left(-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(-\tan\dfrac{\pi}{4}\right)x\\\\y=-1x\\\\\boxed{y=-x}\to\boxed{D.}[/tex]
Answer:
If you are doing it on edge it is x+y=0
Step-by-step explanation:
x+y=0 when you solve for y it equals -x( y=-x)
What isn't the volume of the cylinder below? Radius 8 height 3
Answer: The volume is 603.19, so whichever answer doesn't equal that.
Step-by-step explanation:
V= πr^2h
V= π(8)^2(3)
V= 603.19
Volume = 192πunits³
Work is provided in the image attached.
Math true or false
Septima investing money into two different accounts at the same time. the system of inequalities represent the balance of each account where x represents the number of years the money has been invested.
Math! Please help! Please explain your answers.
Answer:
FalseFalseTrueStep-by-step explanation:
Since the given expression represents the account balance, the initial amount (when x=0) is $500 in Account A, and $100 in Account B. (Less money was invested in account B.)
The growth rate of each account is $1.03 per year.* (The growth rate ($/year) is identical for each account.)
The total of the initial amounts invested is $500 +100 = $600.
_____
* Comment on growth rate
Since the account balance is shown as greater than or equal to the given expression, there appears to be the possibility that adjustments are made to the account balance by some means other than the growth predicted by this inequality. For example, if the balance in Account A is $900 at the end of 1 year, the inequality will still be true, but the extra $398.97 will be in addition to the $1.03 growth predicted by this expression.
This means we really cannot say what the growth rates of the accounts might be, except that it is a minimum of $1.03 per year in each account.
_____
Comment on the expressions
More usually, we would expect to see an account balance have the equation a = 400·1.03^x. That is, the interest rate would be 3% and it would be compounded annually. The expression 400 + 1.03x is very unusual in this situation.
A plant has a initial height of 1 inch and grows at a constant rate of 3 inches each month. A second plant that also grows at a constant rate has an initial height of 4 inches and is 28 inches taller after 1 year. After how many months are the plant the same height?
Answer: that would be 3 months.
Step-by-step explanation:
An apartment complex offers 15 apartments with a view of the river, 8 with two bedrooms, and 6 that have both selections. How many only have a view of the river?
Answer:
9
Step-by-step explanation:
Otf the 15 that have a view of the river, 6 have both selections.
The remaining 9 only have a view of the river.
Ralph wants to purchase a renters insurance policy for his new apartment. His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment. Below is a list of items Ralph made of the items he has in his apartment that he would like to be insured with his policy. What will Ralph’s annual renters insurance premium be? Ralph's Stuff Value TV $150 VCR $60 DVD Player $100 Stereo $80 Sofa $200 Entertainment Center $100 Microwave $40 Coffee Maker $20 Computer $850 Bicycle $200 Coin Collection $600 Pictures/Posters $175 a. $17.88 b. $35.48 c. $214.58 d. $425.65 Please select the best answer from the choices provided A B C D Mark this and return
Answer:
d. $425.65
Step-by-step explanation:
The total value of Ralph's stuff is ...
... 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175 = 2575
The premium is 16.53% of that, so is ...
... 0.1653 × 2575 = 425.65
Answer:
The insurance company charges an annual premium of $425.65 .
Option (d) is correct .
Step-by-step explanation:
As given
Ralph wants to purchase a renters insurance policy for his new apartment.
His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment.
Total amount of the items he owns and is keeping in his apartment = TV cost + VCR cost + DVD Player cost + Stereo cost + Sofa cost + Entertainment centre cost + Microwave cost + Coffee Maker cost + Computer cost + Bicycle cost + Coin Collection cost + Pictures/Posters cost
Putting all the values in the above
Total amount of the items he owns and is keeping in his apartment = $150 + $60 +$100 + $ 80 + $200 + $100 + $40 + $20 + $850 + $ 200 + $ 600 + $ 175
Total amount of the items he owns and is keeping in his apartment = $ 2575
16.53 % is written in the decimal form .
[tex]= \frac{16.53}{100}[/tex]
= 0.1653
Insurance company charges an annual premium = 0.1653 × Total amount of the items he owns and is keeping in his apartment .
= 0.1653 × 2575
= $ 425.65 (Approx)
Therefore the insurance company charges an annual premium of $425.65 .
Option (d) is correct .
A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. What is the value of x?
Final answer:
To find the value of x in a rectangle with a length of 4 inches, set up the equation 2(4 + x) = 4x and solve for x. The value of x is 4 inches.
Explanation:
To find the value of x, we need to set up an equation using the given information. The perimeter of a rectangle is equal to twice the length plus twice the width. The area of a rectangle is equal to the length times the width. So, we can set up the equation: 2(4 + x) = 4x. Next, solve the equation for x:
8 + 2x = 4x
8 = 4x - 2x
8 = 2x
4 = x
Therefore, the value of x is 4 inches.
help please !!!
What is the recursive rule for an=−3n+1 ?
an=
a1=
To find a1, put 1 in the given equation and evaluate.
... a1 = -3·1 +1
... a1 = -2
Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...
... a[n] = a[n-1] - 3
Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
(−1, 2)
(1, 1)
(0, 0)
(4,−25)
(1, 1), (4, -25)
Step-by-step explanation:You can evaluate the function to see.
f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2
f(1) = -3^(1-1) +2 = -1 +2 = 1
f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0
f(4) = -3^(4 -1) +2 = -27 +2 = -25
_____
Or, you can graph the points and the curve.
Answer:
(1, 1), (4, -25)
Step-by-step explanation:
How much of the 8% solution should we use to make 100g of a 3% solution?
This is all I have don't ask me any questions I don't know anything else about this
Answer:
37.5 g
Step-by-step explanation:
The final solution will contain 3% × 100 g = 3 g of solute. This amount of solute will be found in w grams of 8% solution, where ...
... 3 = 0.08 × w
... 3/0.08 = w = 37.5 . . . . . grams of 8% solution
Answer:
37.5 grams
Step-by-step explanation:
;)
Can someone pls help me find the lowest common denominator of
x³y⁴
Step-by-step explanation:The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...
x³ · yx · y⁴Find the highest power of each of the factors, and multiply those together.
The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...
... x³y⁴
_____
Then the two fractions are ...
... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)
The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining 1 3/4 miles to the lookout. The trail the hikers will use to return from the lookout is 1/2 mile shorter than the trail they will use to go to the lookout. Each hiker will bring 1/4 gallon of water for each mile to and from the lookout. Determine the total distance, in miles, each hiker will hike? and Determine the total number of gallons of water each hiker will bring ?
Answer:
7 miles1 3/4 gallonsStep-by-step explanation:
The distance to the lookout is the sum of distances before and after the rest stop:
... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi
The distance from the lookout is 1/2 mile shorter, so is ...
... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi
Then the total hike is ...
... total distance = "to" distance + "from" distance
... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi
... total distance = 7 mi
The water each hiker will bring is ...
... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal
Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.
First, we need to determine the total distance each hiker will travel:
Initial hike to rest: 2 milesRemaining hike to the lookout: 1 3/4 miles or 1.75 milesTotal distance to the lookout: 2 + 1.75 = 3.75 milesThe return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:
Return trail distance: 3.75 - 0.5 = 3.25 milesSumming up the distances:
Total hiking distance: 3.75 + 3.25 = 7 milesCalculating Total Water Needed:
Each hiker brings 1/4 gallon of water per mile:
Total miles hiked: 7 milesWater needed per mile: 1/4 gallonTotal water needed: 7 * 1/4 = 1.75 gallonsThus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.
The diameter of a hydrogen atom 0.000000000106 meter. write this diameter in scientific notation
The Diameter of Hydrogen Atom in Scientific Notation is :
✿ 1.06 × 10⁻¹⁰ Meters
Answer:
1.06 x 10-10 mStep-by-step explanation: I just solve it.
The table shows formulas for the recommended heart rates during exercise for a person who is "a" years old. Write and solve a compound inequality to determine the heart rate range for a 16 year old person.
Answer:
102 ≤ heart rate ≤ 183.6
Step-by-step explanation:
... lower limit ≤ heart rate ≤ upper limit
Put 16 where "a" is and do the arithmetic.
... lower limit = 0.5(220 -16) = 102
... upper limit = 0.9(220 -16) = 183.6
Then the inequality is ...
... 102 ≤ heart rate ≤ 183.6
_____
Comment on the problem
There is nothing to "solve" here. One only needs to evaluate the limits.
In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.
Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.
The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).
For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.
Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.
For more such questions on Compound Inequality, click on:
https://brainly.com/question/31904612
#SPJ2
suppose y varies directly with x. if y= 24 when x = 4, what is y when x = 9?
Answer: y=54
Step-by-step explanation: so 24/4 is 6 soooo 9*6=54 ez
Answer:
y =54
Step-by-step explanation:
We can use the equation y =kx
If we know y and x we can solve fork
24 = k*4
24/4 = k
6 =k
y = 6x
Substitute in 9
y =6*9
y =54
please help me asap!
Answer:
d 31 degrees
Step-by-step explanation:
We can use the formula
<C = 1/2 (arc AE - arc BD)
Let substitute in what we know
ARC AE = 120
ARC BD = 58
<C = 1/2 (120 - 58)
<c = 1/2(62)
<c = 31
A jetski rental company charges a $50 deposit, plus $25 per hour to rent a jetski. This can be represented by the formula T = 25h + 50, where T is the total cost, and h is the number of hours rented. If the deposited is changed to $40 and the hourly rate is changed to $35, how much more money will the company make on a hour of rental?
Answer:
None, the answer will be the same
Step-by-step explanation:
Ming is given the following function and asked to find b. f(x)=15(b)x If f(4) = 1215, what is one possible value of b?
Step-by-step explanation:
f(x) = 15(b)x
f(4) = 1215
15(b)4 = 1215
(15)(4)b = 1215
60b = 1215
60b / 60 = 1215 / 60
b = 20.25
Check the answer
15 * 20.25 * 4 = 1215
Answer:
3
Step-by-step explanation:
if you did this on prepworks its 3.
1215=15(b)4
121515=(b)4
81=b4
92=b4
(32)2=b4
34=b4
b = ±3
In an airplane 35% of the passengers are children they’re 140 children on the airplane how many passengers are on the airplane
Answer:
there are 49 passengers
Step-by-step explanation: 35%=0.35
0.35*140= 49
Barney works as a car salesman and earns $175 for every car that he sells. He has fixed expenses of $3100 every month. He has laid out his projected variable expenses as well as his projected car sales for the first 6 months of next year.
. EXPENSES VARIABLE CARS SOLD
january 2,600 32
feb 3,200 36
march 1,600 26
may 800 22
which month will barney sell enough cars to pay for all his monthly expenses ?
feb
Step-by-step explanation:When the number of cars needed to be sold to meet fixed plus variable expenses is subtracted from the number of cars projected to be sold, the result is negative for all months listed except February. In that month, Barney covers is expenses.
We have computed ...
... (expected car sales) - (needed car sales)
where ...
... (needed car sales) = (variable expenses + fixed expenses)/(income per car sold)
For January, this calculation gives ...
... 32 - (2600 +3100)/175 = 32 -32.571 = -0.571
That is, Barney does not project he will sell enough cars to pay his January expenses.
In February, the result is 0, which means he will sell enough cars in February to pay all his monthly expenses.
Three hundred people were asked to choose their favorite of the following ice cream flavors: vanilla, chocolate, or strawberry. Which of the following fractions is the best estimate for the number of people that chose vanilla?
1/3 1/4 1/10 1/2
Answer:
I believe it would still be considered 1/2
Step-by-step explanation:
Answer:
1/2Step-by-step explanation:
the average temperature in Alaska in January is -9°F in February it is -16°F which month has the coldest temperature
Answer:
February
Step-by-step explanation:
February is colder by 7°F
-9 - 7 = -16
~
Answer:February
Step-by-step explanation:
If you see the number line below -16 is more far than -9
-------------------------------------------------------------------------------------------------
' ' '
-16 -9 0
I forgot how to this can someone help please
Answer:
1728
Step-by-step explanation:
You could write it like this
5.4 * 10^5 * 3.2 * 10^-3
You could do this by multiplying the numbers first
5.4 * 3.2 = 17.28
Now work with the powers of 10
10^5 * 10^-3 = 10^(5 - 3) = 10^2
10^2 = 100
So the answer is 17.28 * 100 = 1728
Write 2^100 as an exponent with a base of 32.
Answer:
2 is a factor 5 times
Step-by-step explanation:
2 x 2 x 2 x 2 x 2 =32
Find the discriminant and determine how many solutions the equation has and if they are imaginary or real. Please show all work.
y = 4x^2 - 5x + 1
Answer:
as discriminant = 9, it has two real solutions.
Step-by-step explanation:
for eqn ax^2 + bx + c, discriminant = b^2 - 4ac
y = 4x^2 - 5x + 1
discriminant = (-5)^2 - 4(4)(1)
= 25 - 16
= 9
as discriminant > 0, it has two real solutions.
Answer:
Discriminant = 9 and the equation has two real solutions
Step-by-step explanation:
For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.
If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.
In this case, y = 4x^2 - 5x + 1.
So its discriminant = -5^2 - 4*4*1
= 9 so it has two real solutions.
Which inequality represents the graph shown below?
Answer:
2<x<∞
Step-by-step explanation:
The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.
The arrow goes to positive infinity. Which gives us our upper or left bound.
Answer:
r>(greater than or equal to)2.5
Step-by-step explanation:
What is one method to find the measure of angle B?
Answer:
A is the right one
Step-by-step explanation:
it is right on edge
We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
BCD is a right angle triangle
We have to find the angle B from the triangle
BD is the hypotenuse which is √89
DC is the opposite side of angle B
We can find angle B by using sine function.
Or we can find the length of BC by using pythagorean theorem
then find the tanB function
tanB=8/BC
Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ2
△ABC @ △DEF. Find the measures of the given angles or the lengths of the given sides
BC = 3z + 2, EF = z + 6
Answer:
BC = EF = 8
Step-by-step explanation:
Assuming you mean BC ≅ EF, then ...
... 3z +2 = z +6
... 2z = 4 . . . . . . . . add -2-z
... z = 2 . . . . . . . . . divide by 2
BC = EF = 2+6 = 8
The question is about finding the measures of given sides and angles in similar triangles. By setting up a proportion between the given sides BC and EF, we can solve for the variable 'z'. This 'z' can then be used to find the sides and angles of the triangles.
Explanation:In the case of the problem, we're dealing with the concept of similar triangles in geometry. Since △ABC is similar to △DEF, this means that the corresponding sides are in proportion, and corresponding angles are equal.
Given that BC = 3z + 2 and EF = z + 6, we can write a proportion: BC/EF = 3z+2 / z+6, because the lengths of the corresponding sides of these two similar triangles should be in ratio.
Then you can solve this equation for the variable 'z', which will give us the values for sides BC and EF. If necessary, you can also find the measure of the angles using the values of 'z'.
Learn more about Similar triangles here:https://brainly.com/question/32489731
#SPJ2
If GF is a midsegment of CDE, find CD.
A. 3.4
B. 6.8
C. 13.6
D. 14
Answer:
C
Step-by-step explanation:
Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}[/tex]
We can now cross multiply and solve for CD:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}[/tex]
Since GF is a midsegment of CDE, CD is double of CF. So we can write:
[tex]CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0[/tex]
By using quadratic formula [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:
[tex]\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2[/tex]
Since the expression for CD is [tex]\frac{15x^2+16x+3.2}{2x+3}[/tex] , we plug in [tex]x=2[/tex] into this expression to find value of CD:
[tex]\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6[/tex]
The correct answer is C
Answer:
C. 13.6
Step-by-step explanation:
We have been given that GF is a mid-segment of CDE.
Since we know that mid-segment of a triangle is half the length of its parallel side.
We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:
[tex]GF=\frac{1}{2}ED[/tex]
Let us substitute given value of GF and ED to find our x.
[tex]2x+3=\frac{1}{2}(5x+4)[/tex]
Multiply both sides of equation by 2.
[tex]2*(2x+3)=2*\frac{1}{2}(5x+4)[/tex]
[tex]2*(2x+3)=5x+4[/tex]
[tex]4x+6=5x+4[/tex]
[tex]6=5x+4-4x[/tex]
[tex]6=x+4[/tex]
[tex]6-4=x[/tex]
[tex]2=x[/tex]
We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.
[tex]\frac{CF}{GF}=\frac{CD}{ED}[/tex]
Substitute given values.
[tex]\frac{3x+0.8}{2x+3}=\frac{CD}{5x+4}[/tex]
Upon substituting x=2 in our equation we will get,
[tex]\frac{3*2+0.8}{2*2+3}=\frac{CD}{5*2+4}[/tex]
Let us simplify our equation.
[tex]\frac{6+0.8}{4+3}=\frac{CD}{10+4}[/tex]
[tex]\frac{6.8}{7}=\frac{CD}{14}[/tex]
[tex]14*\frac{6.8}{7}=CD[/tex]
[tex]2*6.8=CD[/tex]
[tex]13.6=CD[/tex]
Therefore, CD equals 13.6 and option C is the correct choice.
As a promotion, a clothing store draws the name of one of its customers each week. The prize is a coupon for the store. If the winner is not present at the drawing, he or she cannot claim the prize, and the amount of the coupon increases for the following week's drawing. The function f(x) = 20 (1.2)^x gives the amount of the coupon in dollars after x weeks of the prize going unclaimed. {{ x is the exponent on (1.2). }}
(A) What is the percent increase each week?
(B) What is the original amount of the coupon? (the initial value)
(C) What is the amount of the coupon after 2 weeks of the prize going unclaimed?
(D) After how many weeks of the prize going unclaimed will the amount of the coupon be greater than $100?
The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.