Answers
Answer:
Y = -1/2X +4
Step-by-step explanation:
x1 y1 x2 y2
2 3 0 4
(Y2-Y1) (4)-(3)= 1 ΔY 1
(X2-X1) (0)-(2)= -2 ΔX -2
slope= - 1/2
B= 4
Y =-0.5X +4
Related Questions
Danny Metzger's parents invested $1600 when he was born. This money is to be used for Danny's college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19. Find the amount that will be available each year, if money is worth 7%, compounded annually. (Round your answer to the nearest cent.)
Answers
Answer:
[tex]\begin{array}{ccl}Year&&End \ of \ year \ balance\\1&&\$4,483.18\\2&& \$3,088.68\\3&&\$1,596.57\\4&&0\end{array}[/tex]
Step-by-step explanation:
The initial amount invested, P = $1,600
Danny's age at which the amount, A, is to be used for his college, t = 19 years
The number of equal annual payments, m, to be withdrawn from the amount = 4
The compound interest on the account, r = 7% = 0.07
Let, A, represent the amount at the year the annual withdrawals starts to be made, we have;
[tex]A = P \times \left(1+\dfrac{r}{n} \right)^{n \times t}[/tex]
n = The number of times the interest is applied annually = 1
Therefore;
[tex]A = 1,600 \times \left(1+\dfrac{0.07}{1} \right)^{1 \times 19} \approx 5,786.444[/tex]
The amount, m, is withdrawn at start of Danny's first year in college to give the amount in the account = A - m
The amount in the account at the end of the first year with compound interest, r = (A - m)×(1 + r)¹ = (A - m)×(1 + r)
At the stat of the second year, the second withdrawal is made to give the starting amount = (A - m)×(1 + r) - m
The amount in the account at the end of the second year = ((A - m)×(1 + r) - m)×(1 + r)
At the start of the third year, the amount in the account = ((A - m)×(1 + r) - m)×(1 + r) - m
At the end of the third year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r)
At the start of the forth year, the last yearly installment is withdrawn from the account and we have 0 balance in the account.
Therefore, on the fourth year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) - m = 0
(A - m)×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ - m×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ = m×(1 + r)³ + m×(1 + r)² + m×(1 + r) + m = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
A×(1 + r)³ = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
m = A×(1 + r)³/((1 + r)³ + (1 + r)² + (1 + r) + 1)
∴ m = 5,786.444×(1 + 0.07)³/((1 + 0.07)³ + (1 + 0.07)² + (1 + 0.07) + 1) ≈ 1,596.56
The amount withdrawn annually, m ≈ $1,596.56
The amount in the account at the end of the each year is given as follows;
First year = (A - m)×(1 + r) = (5,786.444 - 1,596.56)×(1 + 0.07) ≈ 4,483.17588
Second year = ((A - m)×(1 + r) - m)×(1 + r) = ((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) = 3,088.68
Third year = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) = (((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) - 1,596.56) × (1 + 0.07) = 1,596.57
At the end of the first year, we have $4,483.17588
At the end of the second year, we have $3,088.68
At the end of the third year, we have $1,596.57
At the end of the fourth year, we have 0
Let f(x) = x2 − 1 and g(x) = 3x. Find gf and state its domain
Answers
Step-by-step explanation:
here's the answer to your question
Answer:
[tex]g(x) \times f(x) = 3{x}^{3} -3x[/tex]
X exists for all real numbers.
Y exists for all real numbers.
Peter plays basketball. In one game, he needs to score at least 38 points to have a
season high of 1,200 points. He scores x number of 2 pointers and y number of 3
pointers and meets his goal of at least 38 points.
Using the variables given, write an inequality describing this scenario.
Answers
I am currently on mobile, but the > should have a solid line beneath. I know that 2x + 3y needs to be greater than or equal to 38, since if he scores less than 38 points he won’t meet his season high of 1,200.
match the property to its correct name
A} additive inverse property
B} multiplicative inverse property
C} commutative property of multiplication
D} multiplicative identity
E} commutative property of complement
F} ascending property of multiplication
G} distributive property
H} associative property of multiplication
I} additive identification property
J} zero property
{1} x+(y-z)=(x+y)+z
2} (pq) * 1 = pq
3} (5x)y-5(xy)
4} a+5b = 5b + a
5} a+0=a
6} gh - hg
7} 8 + (-8)=0
8} x * 0 = 0
9} 5 * (1/5)=1
10} 2(a+h)=2a * 2b
Answers
Additive inverse and multiplicative inverse are mathematics function which creates net impact of an equation as zero.
The correct names are matched with their respective properties.
A. 7. 8 + [-8] = 0
B. 9. 5 * [1/5] = 0
C. 4. a + 5b = 5b + a
D. 2. [pq] * 1 = pq
E. 6. gh - hg
F. 3. [5x] y-5 [xy]
G. 10. 2 [a + b] = 2a * 2b
I. 5. a + 0 = a
J. 8. x* 0 = 0
Additive inverse property is when the net result from addition is zero.
Multiplicative inverse property is the equation which gives answer zero when two variables are multiplied.
Learn more at https://brainly.com/question/24325325
8tbsp. 2tsp.
x 15
_________
Answers
what is the ratio of the surface area to the volume of a cube with sides length 5
Answers
Answer:
6 : 5
Step-by-step explanation:
Volume of a cube = s^3
5^3 = 125
Surface area of a cube = 6s^2
6(5^2) = 6(25) = 150
150 : 125
30 : 25
6 : 5
Instructions: Find the missing segment in the image below.
Triangle with a missing segment.
Answers
Answer:
x=44
Step-by-step explanation:
20/x=30/22+x
20x+440=30x
440=10x
x=44
simplify (-216mtn square)/(8mn)
Answers
Answer:
-27tn
Step-by-step explanation:
Use KIO (keep, inverse, opposite) then divide.
in a right triangle the two sides are 10 and 5. find all possible values for the third side.
hint: there are two possibilities
Answers
Answer:
1. about 11.18
2. about 8.66
Step-by-step explanation:
1. 5^2 + 10^2= 125
square root of 125 equals about 11.18
2. 10^2-5^2=75
square root of 75 equals about 8.66
i really need help with this since it’s practice for my midterms
Answers
Answer:
It is D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Evaluate the fractions inside the absolute value
2 [tex]\frac{5}{6}[/tex] + [tex]\frac{7}{4}[/tex] ( change mixed number to improper fraction )
= [tex]\frac{17}{6}[/tex] + [tex]\frac{7}{4}[/tex] ( the LCM of 6 and 4 is 12 ) , then
= [tex]\frac{17(2)}{6(2)}[/tex] + [tex]\frac{7(3)}{4(3)}[/tex]
= [tex]\frac{34}{12}[/tex] + [tex]\frac{21}{12}[/tex] ( add the numerators, leaving the common denominator )
= [tex]\frac{55}{12}[/tex]
= 4 [tex]\frac{7}{12}[/tex] → D
Please help me find the area of this figure! Thanks!!
Answers
Answer:
Step-by-step explanation:
Figure consists of three parts; one Triangle , one rectangle and a square.
Triangle:
Base = b = 13+9 = 22 cm
height = 16 cm
[tex]Area \ of \ triangle = \frac{1}{2}* b*h\\\\= \frac{1}{2}*22*16\\\\= 11 *16\\\\= 176 \ cm^{2}[/tex]
Rectangle 1:
length = 14 cm
Width = 4 cm
Area of R1 = length * width = 14 * 4 = 56 cm²
Area of Square R2:
side = 8 cm
Area of square = side * side = 8 * 8 = 64 cm²
Area of shaded region = 176 + 56 + 64 = 296 cm²
Help ! With step by step solution
Answers
Answer:
the correct answer is C
Step-by-step explanation:
first step you change the x and y powers to the square root(showing in the pic).
second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...
Convert the angle 0 = 310° to radians. Express your answer exactly.
Answers
Answer:
5.425
Step-by-step explanation:
310° = 310° × π ÷ 180°
= 310° × 3.142 ÷ 180°
= 310° × 0.0175
= 5.425
Answer:
[tex]\frac{31\pi }{18}[/tex]Step-by-step explanation:
i got it right on khan[tex]\frac{31\pi }{18}[/tex]
Which of the following is a solution of y + x < -5?
(-2, -3)
(-4, -2)
(-3, -2)
(-1, -3)
Answers
The answer is (-4, -2)
-2 + -4 < -5
-6 < -5
Hope this helps!
Answer:
(- 4, - 2 )
Step-by-step explanation:
Substitute the coordinate value into the left side of the inequality and compare the value obtained to the right side
(- 2 , - 3 )
- 3 - 2 = - 5 = - 5 ← not a solution
(- 4, - 2 )
- 2 - 4 = - 6 < - 5 ← solution
(- 3, - 2 )
- 2 - 3 = - 5 ← not a solution
(- 1, - 3 )
- 3 - 1 = - 4 > - 5 ← not a solution
shop sells shirts. In
January they reduce the
price of all their £50 shirts
by 50%. In February they
decide to increase the price
of all their shirts by 50%. In
March they decide to
reduce the price of their
shirts by 50% again. What is
the cost of a shirt in March?
Answers
The shirts cost £25 in January
50% more of £25 = £12.5
The shirts cost £37.5 in February
50% off of £37.5 = £18.75
A shirt in March cost £18.75
PLSSSS I NEED HELP PLS HELP MEEE IM FAILING Pythagorean theorem
Answers
South would be straight down (leg 1 of the triangle) and east would be right from that point (leg 2 of the triangle). Therefore, we are looking for the hypotenuse of the triangle.
Pythagorean Theorem: a^2 + b^2 = c^2
6^2 + 5^2 = c^2
36 + 25 = c^2
61 = c^2
c = sqrt(61)
c = 7.8 miles
Hope this helps!
Which could be the graph of f(x) = |x - h| + k if h and k are both positive?
Answers
Answer:
The first option would be your answer. The graph should be positive due to the modulus.
The first option is good.
Hope it helped!
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:
A)
A = (45,000)e–0.02t
B)
A = 45,000 + e–0.02t
C)
A = (45,000)e0.02t
D)
A = 45,000 + e0.02t
Answers
Answer:
Step-by-step explanation:
The general form of this equation is
[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.
Therefore, filling in:
[tex]A=45000e^{-.02t[/tex]
Help me solve this please!
Answers
Answer Should be 45
Answered by Gauthmath must click thanks and mark brainliest
Three adults are picked at random from those with a mass of 70 kg or less.
Calculate the probability that one of them has a mass of 35 kg or less and the other two each have a
mass greater than 35 kg.
Answers
in 16 years, Marissa will be five times older than she is today. How old is she?
Answers
Answer:
4
Step-by-step explanation:
1 5
2 10
3 15
4 20
i wrote it out
x+16=5x
16=4x
4=x
Marissa is currently four years old.
What is algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.
Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
Let's represent Marissa's current age "x".
According to the given question, in 16 years she will be five times older than she is today, which we can express as:
x + 16 = 5x
Solving for x, we can subtract x from both sides:
16 = 4x
Dividing both sides by 4, we get:
x = 4
Therefore, Marissa is currently 4 years old.
To learn more about the Algebra link is given below.
brainly.com/question/953809
#SPJ6
if 2x+20 and 3x+20 makes a straight angke find value of x
Answers
Answer:
x = 28
Step-by-step explanation:
The sum of the angles in a straight angle = 180°
Sum the angles and equate to 180
2x + 20 + 3x + 20 = 180
5x + 40 = 180 ( subtract 40 from both sides )
5x = 140 ( divide both sides by 5 )
x = 28
2. Your school building casts a shadow 25 feet long. You are 6 feet tall and cast a shadow 18 inches long. Find the height of the school building in feet
Answers
Answer:
Height of school building = 100 feet
Step-by-step explanation:
Given;
Shadow of school building = 25 feet
Height of individual = 6 feet
Shadow of individual = 18 inches = 1.5 feet
Find:
Height of school building
Computation:
Height of individual / Shadow of individual = Height of school building / Shadow of school building
6 / 1.5 = Height of school building / 25
Height of school building = 25 x 4
Height of school building = 100 feet
The hardware store sells green buckets, which hold 7 liters of water, and white buckets, which hold 1 liter. Austin bought 8 buckets. His buckets will hold 38 liters in total. How many of each type of bucket did Austin buy?
? green buckets
? white buckets
Answers
Answer: 5 green buckets and 3 white buckets
Step-by-step explanation: each green bucket is 7 liters so if Austin buys 5 of them that'll equal 35 liters already. And each white bucket is 1 liter so if he buys 3 of those that'll get him to 38
Please help me please and thank you
Answers
Answer:
3x² + 2x - 9 = 0
Step-by-step explanation:
Standard form of a quadratic: ax² + bx + c
Move all terms to one side of the equation:
[tex]3x^2-9=-2x\\3x^2-9+2x=-2x+2x\\3x^2+2x-9=0[/tex]
help with this pls geometry!!
Answers
Answer:
548
Step-by-step explanation:
First, the sides:
7 × 12 = 84
84 × 2 = 168
7 × 10 = 70
70 × 2 = 140
10 × 12 = 120
120 × 2 = 240
Add:
168 + 140 + 240
^ ^
308 + 240
548
Hope this helped.
Answer:
The surface area of the rectangular prism is 548[tex]ft^{2}[/tex]
Step-by-step explanation:
To find the surface area of the rectangular prism you need to use the formula
A=2(wl+hl+hw)
Answer to question commented:
The surface area of the other rectangular prism is 430[tex]ft^{2}[/tex]
Hope this helps!
Solve the simultaneous equation, will give out brainliest answer
a=bcd
a+b=cd
a+b+c=d
a+b+c+d=1
Answers
Answer:
a=1/2,b=-1,c=-1 and d=1/2
Am I right please?
Answer:
a = 1/42; b = 1/7; c = 1/3; d = 1/2
Step-by-step explanation:
a = bcd
a + b = cd
a + b + c = d
a + b + c + d = 1
d + d = 1
2d = 1
d = 1/2
2a = bc
2a + 2b = c
2a + 2b + 2c = 1
bc + 2b = c
bc + 2b - c = 0
bc + 2b + 2c = 1
-3c = -1
c = 1/3
a + b = cd
a + b = 1/6
a = bcd
a = b(1/3)(1/2)
a = 1/6 b
1/6 b + b = 1/6
7/6 b = 1/6
b = 6/42
b = 1/7
a = 1/6 b
a = 1/6 * 1/7
a = 1/42
2. Sum of two numbers = 16
Difference of the numbers = 6
Find the numbers.
What is their product?
Answers
There product is 55
Answer:
Step-by-step explanation:
let the numbers be x and y.
x+y=16
x-y=6
add
2x=22
x=22/2=11
11+x=16
x=16-11=5
product xy=11×5=55
Myles has calculated that 1/2 a box of tile will cover 1/6 of his kitchen floor. How many boxes of tile will he need to cover the entire kitchen?
Answers
Answer: He need 3 boxes.
Step-by-step explanation:
Every 1/6 of his floor needs 1/2 of the tile box.Split his floor into 6 parts, each part needing 1/2 of the tile box:
[tex]6*\frac{1}{2} =\frac{6}{2} =3[/tex]
Or you can add 1/2 six times for each 1/6 of the floor:
[tex]\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} =\frac{6}{2}=3[/tex]
is (4, 4) a solution of the graphed system of inequalities?
answers are
A) Yes
B) No
Answers
Answer: A) Yes
If (4, 4) lies within the double-shaded area that covers the solution set of both inequalities, then it's a solution.
It does, therefore, it's a solution to the system of inequalities.
