Factor this polynomial expression.
15x^2- 2x - 8
O A. (5x + 4)(3x - 2)
O B. (5x - 4)(3x+2)
O C. (5x + 2)(3x - 4)
O D. (5x-2)(3x+4)
Answer:
B. (5x - 4)(3x + 2)
Step-by-step explanation:
Factor the following:
[tex] \longrightarrow [/tex] 15x² - 2x - 8
The coefficient of x² is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12.
So,
[tex] \longrightarrow [/tex] 15x² + (10 - 12)x - 8
[tex] \longrightarrow [/tex] 15x² + 10x - 12x - 8
[tex] \longrightarrow [/tex] 5x(3x + 2) - 4(3x + 2)
[tex] \longrightarrow [/tex] (5x - 4)(3x + 2)
Evaluate each value expression for the given value of x: 11 + x, x=12
Answer:
The value of 11+x at x=12 will be 23.
Step-by-step explanation:
Given the expression
[tex]11 + x[/tex]As we have to evaluate the expression at x=12
so substitute the value x=12 in the expression
[tex]11 + x[/tex]
[tex]=11+12[/tex]
[tex]=23[/tex]
Therefore, the value of 11+x at x=12 will be 23.
Find the equation of the line. Use the exact numbers.
Equation: y = _____ x _____
Tell whether the equation is linear. If so, enter the equation in standard form and give the values of A,B, and C.
1. y = 4x +9
2. 5x =6y - 2
Answer:
1. A=1, B=4, C=9
2.A=5 B=6, C=-2
You are deciding whether to buy a car for $ or to accept a lease agreement. The lease entails a $ fee plus monthly payments of $ for months. Under the lease agreement, you are responsible for service on the car and insurance. At the end of the lease, you may purchase the car for $. Complete parts a through c below.
Answer:
a. The correct option is C. No, because you will probably have to pay for service and insurance with either plan.
b. The correct option is A.Yes, the total cost of the car at the end of the lease is $47,400.
c. The correct option is D. Not all of the money is needed up front and you have years to decide if you want to buy the car.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore given as follows:
You are deciding whether to buy a car for $21,000 or to accept a lease agreement. The lease entails a $800 fee plus monthly payments of $250 for 48 months. Under the lease agreement, you are responsible for service on the car and insurance. At the end of the lease, you may purchase the car for $9000. Complete parts a through c below.
a. Should the cost of service and insurance determine which option you choose?
A. Yes, because you probably don't have to pay for services when you buy the car.
B. No, because it is cheaper to lease the car than to buy it.
C. No, because you will probably have to pay for service and insurance with either plan.
D. Yes, because you get a discount on your insurance when you lease the car.
b. Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the outset?
A.Yes, the total cost of the car at the end of the lease is $___ (fill in the blank)
B. No, the total cost of the car at the end of the lease is $___(fill in the blank)
c. What are some possible advantages of leasing the car?
A. You can sell the car whenever you want and you can make money on the car when you sell it.
B. The insurance costs less and you get a service discount.
C. You can give the car back whenever you want and you can get a new car whenever you want.
D. Not all of the money is needed up front and you have years to decide if you want to buy the car.
The explanation of the answer is now provided as follows:
a. Should the cost of service and insurance determine which option you choose?
No matter the option, wither buy or lease, that is chosen, the car will still have to be serviced and the insurance cost will have to be paid for. Therefore, the cost of service and insurance should not determine which option to choose.
Therefore, the correct option is C. No, because you will probably have to pay for service and insurance with either plan.
b. Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the outset?
From part a above, it is stated that the cost of service and insurance should not determine which option to choose. Therefore, the cost of service and insurance should not be included in calculating the total cost of purchasing the car at the end of the lease agreement.
This implies the only relevant costs to use in calculating the total cost of purchasing the car at the end of the lease agreement are the $800 monthly fee and the $9,000 cost of purchase at the end of the lease.
Therefore, the total cost of purchasing the car at the end of the lease agreement can be calculated as follows:
Total lease cost = (Monthly fee * Number of months) + Cost of Purchase = ($800 * 48) + $9,000 = $38,400 + $9,000 = $47,400
Therefore, the correct option is A.Yes, the total cost of the car at the end of the lease is $47,400.
c. What are some possible advantages of leasing the car?
Under a lease agreement, there is no need to pay all the money required to buy an item at once. The leasing of an item also enables one to examine the item in details to decide whether to buy it or not at the end of the lease agreement.
Based on the explanation above, the correct option is D. Not all of the money is needed up front and you have years to decide if you want to buy the car.
Twice as many students go to the park than to the theater. Five more students go to the theater than to the museum. If 16 students go to the park, how many students go to the museum?
Answer:
3 students
Step-by-step explanation:
Twice as many students go to the park than to the theater :
Let number who go the theater = t
Number who goes to park = 2t
5 more students go to the theater than to the museum
Number who goes to museum = t - 5
If number of students who goes to park = 16
How many students goes to the museum :
2t = 16
t = 16/2
t = 8
Number who goes to museum = t - 5
t - 5 = 8 - 5 = 3
Hence, number of students who goes to the museum = 3
What is the maximum number of intersection points a hyperbola and a parabola could have?
4 intersection points
A 450 gallon tank full of water is draining at a rate of 20 gallons per minute. We can represent the situation with the equation:
y
=
450
−
20
x
y
=
450
-
20
x
where x is the number of minutes that have passed by, and y is the amount of water in the tank. How long will it take for the tank to have 200 gallons?
A.
12.5 minutes
B.
32.5 minutes
C.
2.15 minutes
D.
20 minutes
Replace y with 200 ( amount of water in the tank) and solve for x:
200 = 450 -20x
Subtract 450 from both sides:
-250 = -20x
Divide both sides by-20:
X = 12.5
The answer is A. 12.5 minutes
pls help and it’s not 66
Answer:
15
Step-by-step explanation:
120=8x-10
130=8x
15=x
Answer:
x=15
sorry that should be right now tho
escribi los rsultados de cada cálculo como una exprecion decimal.
a)5+1/10+4/100=
b)1+5/10+7/100+5/1.000=
c)3/10+4/1.000=
POR FA NECESITO AYUDA ES PARA HOY
Answer:
a) 257/50 or 5.14
b) 657/100 or 6.57
c) 43/10 or 4.3
Step-by-step explanation:
Espero que esto ayude y que tengas un gran día! :)Jonathan increased his rate of walking by 25% at halfway to his destination and therefore arrived half an hour earlier than was planned. How long did it take for Jonathan walk to his destination?O
Answer:
1.67 hours
Step-by-step explanation:
Let the original speed of Jonathan = [tex]x[/tex] units/hr
Let the original time taken by Jonathan = [tex]y[/tex] hours
Let the distance = [tex]D[/tex] units
Formula for distance is given as:
[tex]Distance = Speed \times Time[/tex]
Given that half the distance is covered by original speed.
[tex]\Rightarrow \dfrac{D}{2} = \dfrac{x}{2}\times \dfrac{y}{2}\\\Rightarrow D = \dfrac{xy}{2} ..... (1)[/tex]
Half the distance is covered by increasing the rate by 25%.
i.e. increased speed:
[tex]\dfrac{5}{4}x\ units/hr[/tex]
Hence, Time taken:
[tex]\dfrac{y}{2}-\dfrac{1}{2}[/tex]
Distance traveled is half of the total distance:
[tex]\Rightarrow \dfrac{D}{2} = \dfrac{5x}{4}\times (\dfrac{y}{2}-\dfrac{1}{2})\\\Rightarrow D = \dfrac{5x}{2}\times (\dfrac{y}{2}-\dfrac{1}{2}) .... (2)[/tex]
Dividing (1) by (2):
[tex]\dfrac{xy\times 4}{2\times 5x(y-1)} = 1\\\Rightarrow 2y=5y-5\\\Rightarrow 3y=5\\\Rightarrow y =1.67\ hours[/tex]
Which of the following number lines represents the solution to the compound inequality 2x+ 9 <3 or -3x +4<(or equal to) -11 ?
Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
please help im very confused :)
also make sure to include the statements and reasonings as shown in the screenshot!
Answer:
See Below.
Step-by-step explanation:
1) Given:
[tex]3x+2y+7=5x+3y+10[/tex]
2) Subtraction Property of Equality (subtract 2y from both sides):
[tex]3x+7=5x+y+10[/tex]
3) Subtraction Property of Equality (subtract 5x from both sides):
[tex]-2x+7=y+10[/tex]
4) Subtraction Property of Equality (subtract 10 from both sides):
[tex]-2x-3=y[/tex]
5) Symmetric Property:
[tex]y=-2x-3[/tex]
6) Slope-intercept form:
[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]
7) Substitution:
[tex]m=-2[/tex]
what is the answer to (x+3)^2 +(y-6)^2
Answer:
1the answer is 1! hope this helps.
The answer is x^2+ y^2-27
2/3 of a number is 20 less than the original number. Find the original number
Answer:
60
Step-by-step explanation:
Let the original number be x.
According to the question we can write as (2/3)x+20x
On rearranging x−(2/3)x=20
Now taking the L.C.M od 1 and 3 is 3
(3x−2x)/3=20
x/3=20
Again by transposing x=60
So the original number is 60
Answer:
60
Step-by-step explanation:
Let the number be x
2/3 x = x -20
20 =x -2/3x
1/3 x =20
60 = x.
Jake has $100 dollars in his wallet. He spends $15 at Tastee Sub and $10 at Wawa. As he is walking home, Jake finds a $20 bill on the ground. Then Brandon comes along and borrows $40 from jake. That night jake decided to do some chores at home and earns $35. How much does jake end up with at the end of the day
Answer: $75
Step-by-step explanation:
Did you ever get the answer
Answer:
Confusion
Step-by-step explanation:
If point C is between points A and B, then AC+ blank = AB.
Answer:
AC+CB=AB
Step-by-step explanation:
Let's see.... If you are a visual learner this could help.
[tex]A----------C---------------B[/tex]
So you can see that C is right in between them so the distance between AC and the distance between CB would equal the whole line AB. So if you add AC and CB you would get AB.
jsjsjwjwjwjwjqjqjjqkqkakajajajajajjajaj
Answer:
csgrerhhhrsdShuavkilrqadccddvny
Step-by-step explanation:
Here is a map of an island with cities A, B and C
not tryna be rude but theres no map
Step-by-step explanation:
a) The three figures are 480 km, 240 km, and 300 km.
b) Kenzi has driven 60 km further than Jafar.
We have,
a)
The three figures bearing B from A are:
1 cm = 200 km
This means,
AB = 2.4 cm
So,
2.4 x 200 = 480 km
And,
BC has two parts:
1.2 cm and 1.5 cm
1.2 cm x 200 km = 240 km
1.5 x 200 km = 300 km
The three figures are 480 km, 240 km, and 300 km.
Now,
Jafar distance.
= AB
= 480 km
Kenzi distance.
= BC
= 240 km + 300 km
= 540 km
The difference between the distance driven.
= 540 km - 480 km
= 60 km
This means,
Kenzi has driven 60 km further than Jafar.
Thus,
The three figures are 480 km, 240 km, and 300 km.
Kenzi has driven 60 km further than Jafar.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ4
A medium-sized (4-pound) sugar pumpkin should yield around 1½ cups of mashed pumpkin. So, if a 4-pound pumpkin will yield about 1.5 cups of mashed pumpkin (pumpkin puree), how many cups of pumpkin puree will Steve Geddes' 2,528-pound pumpkin yield?
Answer: 948
Step-by-step explanation:
From the question, we are informed that 4-pound pumpkin will yield about 1.5 cups of mashed pumpkin (pumpkin puree).
Therefore, the number of cups of pumpkin puree that Steve Geddes' 2,528-pound pumpkin will yield will be:
= (2528/4) × 1.5
= 632 × 1.5
= 948 cups of pumpkin puree
if f(x) = 6x, what is f(3)
Answer:
f(x)=18
Step-by-step explanation:
When it gives you f(3), it is basically telling you that you need to plug in 3 for x. Doing so would give you f(3)=6(3) and you can multiply 6 and 3 together to get 18.
Suppose a Pony Express rider was paid $168 for 14 weeks of work.
If he was paid the same amount each week, how much was he paid for one week of work?
Solve 6w – 2 ≤ 10 for w.
Answer:
w greater than 2
Step-by-step explanation:
What is the value of the expression 2106÷162? What is the value of the expression 2106÷162? What is the value of the expression 2106÷162?
Answer:
13
Step-by-step explanation:
The value of the expression of 2106÷162 can be calculated as follows
= 2106÷162
= 13
Hence the value of the expression 2106 ÷ 162 is 13
. Express the balance sheets in common-size percents. (Do not round intermediate calculations and round your final percentage answers to 1 decimal place.)
Full question attached
Answer attached
Answer and Step-by-step explanation:
We are asked to find the percentage of each asset or liability in total assets and liabilities. To find percentage of each asset or liability in the balance sheet, we divide the asset or liability's value(from each year in the balance sheet) by total assets and liabilities for that year and multiply by 100:
A town has a population of 2000 and grows at 4% every year. What will be the population after 15 years, to the nearest whole number? I just need the correct answer
Answer:
3200
Step-by-step explanation:
growth = current population + rate * time
= 2000 * .04 * 15
= 1200
original population + growth = total
2000 + 1200 = 3200
It takes Ryan 1 5 of an hour to bike from home to school. His biking speed is 10 mph.
How far apart are his school and his house?
Answer:
2
Step-by-step explanation:
1/5*10
Use the Pythagorean Theorem to find the length of the sides "d" and "f." Explain your answer.
Answer:
f = 10·√3/3 ≈ 5.774
d = 5·√3/3 ≈ 2.887
Step-by-step explanation:
The given parameters are;
The angles opposite the 90°, right angle, = 60° and 30°
The length of the leg opposite the 60° angle = 5
Therefore, by Pythagorean Theorem, we have;
f² = d² + 5²
However, by trigonometry, we have;
sin(θ) = Opposite/Hypotenuse
For the angle of the triangle, θ = 30°, we have;
sin(30°) = d/f = 0.5
∴ d = f × 0.5 = 0.5·f
Substituting the value of d in the equation given by Pythagorean Theorem, we have;
f² = (0.5·f)² + 5² = 0.25·f² + 5²
f² = 0.25·f² + 5²
f² - 0.25·f² = 5²
0.75·f² = 5²
f² = 5²/0.75 = 100/3
f = 10/√3 = 10·√3/3
f = 10·√3/3
d = f × 0.5 = 10·√3/3 × 0.5 = 5·√3/3
d = 5·√3/3.
jack is paid £1800 a month. he spends half his money on rent. he spends the rest on food, bills and savings in the ratio 4:3:2 how much does he spend on bills?
Answer:
£300.
Step-by-step explanation:
He has £900 left after paying rent.
The fraction he spends on bills = 3(4+3+2)
= 3/9
= 1/3.
So he spends 900 * 1/3 = £300 on bills.