The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 3x + 5 and g(x) = x2.
Find f(x) • g(x).
A: 3x2 + 5
B: 3x3 + 5x2
C: x2 − 3x − 5
D: 3x3 + 3x2 + 5
Plsssss help its for a test
Answer:
3 x³ + 5x²
Step-by-step explanation:
that is the procedure above
write two inequalities to compare -2 and -18
Step-by-step explanation:
here's the answer to your question
how do I simplify when there are fractions on fractions
Answer: y/y+x
Step-by-step explanation: Reduce the fraction at the bottom (1 - x/y) (1 + x/y) = 1 + x/y = simplify and you get y/y+x
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 This money is to be used for Danny's college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19.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.)
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The number of equal annual payments, m, to be withdrawn from the amount = 4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The amount, m, is withdrawn at start of Danny's first year in college to give the amount in the account = A - m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At the start of the forth year, the last yearly installment is withdrawn from the account and we have 0 balance in the account.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
what is the rule for the reflection
Step-by-step explanation:
We reflect We triangle across both axis so the x and y values will both switch.
Our triangle is originally in the second quadrant but then go to the 4the after we reflect it.
Second Quadrant are
^;8+1—](
in 16 years, Marissa will be five times older than she is today. How old is she?
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.
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Two angles are a linear pair. The measure of one angle is 10 more than 25% of the other. Find the measures of both angles.
Answer:
Linear pairs add up to 180°
1st angle = x
2nd angle = x+24 (24° more than the first)
The equation would be
1st angle + second angle = 180 Subbing in the expressions we came up with:
x+x+24 = 180
if 2x+20 and 3x+20 makes a straight angke find value of x
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
Please answer correctly and you will receive a crown and brainliest.
Answer:
See explanation
Step-by-step explanation:
Chevy Malibu hybrid = 6.8
Ford mustang = 9.6
Nissan Pathfinder = 10.8
Toyota Corolla = 6.3
1. Chevy Malibu hybrid to Toyota Corolla = 6.8 to 6.3
= 6.8 : 6.3
= 6.8 / 6.3
2. Nissan Pathfinder to Ford mustang = 10.8 to 9.6
= 10.8 : 9.6
= 10.8 / 9.6
= 2.7 / 2.4
3. Toyota Corolla to Nissan Pathfinder = 6.3 to 10.8
= 6.3 : 10.8
= 6.3 / 10.8
4. Ford mustang to Chevy Malibu hybrid = 9.6 to 6.8
= 9.6 : 6.8
= 9.6 / 6.8
= 2.4 / 1.7
Giving brainliest! Graph and solve the inequality y≤2|x+2|-7
Show the vertex, whether it’s a dotted or solid line, and axis of symmetry, also where the graph should be filled in!
Answer:
hope this helps u......
Answer:
Step-by-step explanation:
I don't know why the graphs I have been putting in look like that. simpler way of putting it is the line is where the red and black meet. if that makes sense. I'm sorry if is doesn't. I hope this helps tho.
Please help me find the area of this figure! Thanks!!
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
Is 5 a prime number
Answer:
yes
Step-by-step explanation:
A prime number is only divisible by 1 and itself in terms of natural numbers
5 is only divisible by 1 and 5 so it is a prime number
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
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
What is an equation of the line that passes through the points (0, 8) and (-8, -4)?
Answer:
y = 1.2x + 2
Step-by-step explanation:
slope = (8 - 2)/(5 - 0) = 6/5y-intercept = (0, 2)y = (6/5)x + 2y = 1.2x + 2
Answer:
y=1.5x +8
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
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]
Which of the following is a solution of y + x < -5?
(-2, -3)
(-4, -2)
(-3, -2)
(-1, -3)
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
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.
PLSSSS I NEED HELP PLS HELP MEEE IM FAILING Pythagorean theorem
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!
⁴⁄₇ × ²⁄₃
Click the picture so that you can see the whole question
Answer:
8/21
Step-by-step explanation:
just multiply the numerator and denominator
Which equation matches the graph shown?
Answer:
f(x) = -(x+2)(x-1)
Step-by-step explanation:
We know the zeros are at 1 and -2
f(x) = a *(x-b1)(x-b2) where b1 and b2 are the zeros and a is a constant
f(x) =a(x-1)(x- -2)
f(x) =a(x-1)(x+2)
We know that a must be negative since the parabola opens down so
The only choice is choice D where a = -1
f(x) = -(x+2)(x-1)
construct a 2 ×2 Matrix whose elements aij are given by a ij = i+j
[tex]★ \sf\pink{Need \: Required \: Answer}[/tex]
Answer:
the required matrix is can be given as
Convert the angle 0 = 310° to radians. Express your answer exactly.
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]
Help ! With step by step solution
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...
What is the area of the triangle in the diagram?
Answer:
l think the answer is =C for this area of triangle
Let f(x) = x2 − 1 and g(x) = 3x. Find gf and state its domain
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.
Which could be the graph of f(x) = |x - h| + k if h and k are both positive?
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:
is (4, 4) a solution of the graphed system of inequalities?
answers are
A) Yes
B) No
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.
(Will give brainliest)
A candy company claims that their bags of jellybeans have a mean weight of 9.45 oz. 125 randomly chosen bags of jellybeans were sampled, and it was discovered that their mean weight was 9.68 oz, with a standard deviation of 1.23 oz. Test this hypothesis using a 99% confidence level.
A- Reject the null hypothesis. There is not enough evidence to oppose the company's claim.
B- Reject the null hypothesis. There is enough evidence to oppose the company's claim.
C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
D- Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.
Answer: C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Note: I'm not sure this is correct o_O
I used a graphing calculator and calculated the t-interval of the jellybean sample using a 99% confidence level:
tInterval 9.68,1.23,125,0.99
It resulted in 9.68 ± 0.287805.
Therefore, we're 99% confident that the weight number of jellybeans would lie between 9.3922 oz and 9.9678 oz.
A weight of 9.45 oz lies within this range, therefore, it is possible that the candy company's claim is true.
Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Mean weight was 9.68 oz
standard deviation of 1.23 oz
n=125
µₙ=9.68
σₙ=1.23/√125
=0.11
Confidence level 99%
z=2.58
-z<x-µₙ/σₙ<z
9.68-2.58(0.11)<x<9.68+2.58(0.11)
9.3962<x<9.9638
9.45 is between this range
Fail to reject the null hypothesis. There is not enough evidence to oppose the companys claim.
Hence, Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
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simplify (-216mtn square)/(8mn)
Answer:
-27tn
Step-by-step explanation:
Use KIO (keep, inverse, opposite) then divide.
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
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.
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