[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$550\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &6 \end{cases} \\\\\\ A=550e^{0.03\cdot 6}\implies A=550e^{0.18}\implies A\approx 658.47[/tex]
state the restrictions on the domain of the equation.
Answer: Choice E
[tex]x \ne -4, -1[/tex]
This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]
======================================================
Reason:
If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.
x+4 = -4+4 = 0
Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.
Any other x value is valid.
Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.
solve for y: -32y^2 -24y = 0
Answer:
y = 0 , y = - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
- 32y² - 24y = 0 ← factor out - 8y from each term
- 8y(4y + 3) = 0 equate each factor to zero and solve for y
- 8y = 0 ⇒ y = 0
4y + 3 = 0 ⇒ 4y = - 3 ⇒ y = - [tex]\frac{3}{4}[/tex]
A safe's lock has a three number combination. The
numbers on the safe lock are 0 - 9. How many
combinations are possible if no number may be used
more than once?
Answer:
720 combinationsStep-by-step explanation:
Each number has initially 10 options.
If one option used for the first number then the second number has one less, 9 options. Similarly, the third number has one less number of options than the second number, 8 options.
Total number of combinations is
10*9*8 = 720I’m just trying to check my math, I got 159
Wellington city engineers are designing two parallel roads by the International Polo Club to help with traffic flow during tournaments.
Answer:
159°
Step-by-step explanation:
Angle 21° and <4 are supplementary angles!
21 + x = 180
x = 159°
Hope this helps!
The measure of angle ∠4 is 159.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
From the figure,
The angle opposite to 21° and ∠4 sum is 180.
This means,
Angles on the same side.
Now,
Opposite angles are equal.
So,
21 + ∠4 = 180
∠4 = 180 - 21
∠4 = 159
Thus,
The measure of angle ∠4 is 159.
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6. Find the H.C.F. of: (a) a² + 2ab + b2-c?, b? + 2bc + ? - a and c? +2ac + a-b? +
Answer:
- (a + b)^2
- (b + c)^2
- (a - b + c) (a + b + c)
The answer is given in the photos below (for verification),
I hope my answer helps you.
the ratio of the 6th and 8th term of an ap is 7:9. find the ratio between the sum of its first 10 terms to sum of its first 20 terms
Step-by-step explanation:
Tn = a + (n-1)d
where a is the first term, d is the common difference and n is the nth term
For the 6th term: T6 = a + (6-1)d
= a + 5d
For the 8th term: T8 = a + (8-1)d
= a + 7d
From the question (a + 5d)/(a + 7d) = 7/9
From the Equation above, we can say that;
a + 5d = 7......1
a + 7d = 9.....2
Solving equations 1 & 2 simultaneously, we have that a = 2 and d = 1
Sn = n/2[2a + (n-1)d]
where Sn is the sum of nth terms, n is the nth term, a is the first term and d is the common difference.
By substituting the values gotten into this equation. You would be able to find the ration between the sum of the first 10 terms to the sum of the first 20 terms
Answer:
see analysis for detailed explanation
A summer camp had
440
campers register this year. This is a
10
%
increase over the number registered last year.
Part A
The equation below relates
440
and
c
,
the number of campers registered last year. Complete the equation by entering a number in the
□
.
Enter only a whole number or decimal.
c
=
440
Part B
Enter a number in the
□
to show how many campers,
c
,
were registered last year.
campers
The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10
The number of campers last year is 400.
What are percentages?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.
How many campers attended last year?The number of campers last year = number of campers this year / (1 + percentage increase)
440 / 1.1 = 400
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Which equation has a vertex at (3, –2) and directrix of y = 0?
y + 2 = StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = 8 (x minus 3) squared
y + 2 = negative StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = negative 8 (x minus 3) squared
Answer: C
Answer:
The square below represents one whole.
What percent is represented by the shaded area?
The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?vvvvStep-by-step explanation:
7. What is the area of the white border?
8 cm
2 cm
9 cm
15 cm
What is the area of the white border
Answer:
119 cm^2
Step-by-step explanation:
To find the area of the white border, simply find the area of the outside rectangle and subtract the middle(dark) rectangle's area from that value.
White rectangle: 15x9 = 135
Dark rectangle: 8x2 = 16
135 - 16 = 119 cm^2
The unit is squared when finding the area of a two dimensional figure.
I need help please help me
i need help 9th grade math
Answer:
g(x) = 4x + 5
Step-by-step explanation:
f(x) + g(x) = 10x + 7 , then
6x + 2 + g(x) = 10x + 7 ← subtract 6x + 2 from both sides
g(x) = 10x + 7 - 6x - 2 ← collect like terms
g(x) = 4x + 5
Let's find
(f+g)(x)=f(x)+g(x)10x+7=6x+2+g(x)g(x)=10x-6x+7-2g(x)=4x+5Option D
Jack has $15,000 to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of 8%, compound continuously, and the other third in a regular savings account at 6% simple interest, how much does Jack earn after one year?
Based on the amounts that Jack invested into the different investment vehicles, the amount Jack earns a year would be $1,132.87.
How much does Jack earn from the high-yield savings account?The amount invested is:
= 2 / 3 x 15,000
= $10,000
Amount after a year:
= Amount x e ^ (rate x time)
= 10,000 x e ⁰.⁰⁸ ˣ ¹
= $10,832.87
How much does Jack make from the regular savings account?Amount invested:
= 1/3 x 15,000
= $5,000
Amount after a year:
= 5,000 x (1 + 6%)
= $5,300
How much did Jack earn in a year:= (10,832.87 + 5,300) - 15,000
= $1,132.87
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Find out more on continious compounding at https://brainly.com/question/3932907.
What information must you know about a triangle in order to use the Pythagorean Theorem to find the length of a missing side?
In order to use the Pythagorean Theorem, you must know the length or lengths of
Choose...
of the triangle and know that the measure of one of the angles is
Choose...
.
Answer: your obviously going to need to use the method a2+b2=c2
Try to calculate the radius if not given to you.
Step-by-step explanation:
In order to use the Pythagorean Theorem, you must know the lengths of at least 2 sides (any 2 sides, but it has to be 2.) of the triangle and know that the measure of one of the angles is 90 degrees.
HELPPPPPPPPPPPPPP ASAP
Answer:
Use the formula of Range Large-Small Data
I think it will help you.
Choose all lengths that are equal to
3 yards 16 inches.
A.
124 in.
B.
4 yd 4 in.
C.
3 yd 1 1/2 ft
D.
2 yd 52 in.
E.
10 ft 4 in.
(15 points)
Answer: The answer you would be looking for is A. D. E.
Step-by-step explanation:
I hope i helped and can i have brainliest please <3
The average rate of change for a function is greater from x = 110 x=2 than from x=2 to x=3. What type of function could it be? Select all that apply
Аlinear
Bquadratic
Cexponential
Answer:
The type of function is cexponential and Alinear
Marcel made an error when he used the distributive property to write an equivalent expression. which sentence describes the error? 32x−16====(8x⋅4)−(8⋅2)8x(4−2)8x(2)16x clear check both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses. 8x(2) does not equal 16x. 32x does not equal 8x⋅4. 32x and 16 have no factors in common
Answer:
I think he made a mistake in the first one
Step-by-step explanation:
Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
The expression is:
= 32x - 16
= 8x(4) - 2(8)
= 8(4x - 2)
The error is "both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses"
Thus, Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.
Learn more about the distributive property here:
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which function does the graph represent
a: f(x)=-0.5(x+4)^2-5
b: f(x)=0.5(x+4)^2-5
c: f(x)=0.5(x-4)^2-5
d:f(x)=-0.5(x-4)^2-5
Answer:
C: f(x) = 0.5(x-4)^2-5
Step-by-step explanation:
I graphed each function on Desmos, and matched it up with option C:
Answer:
the answer is C
Step-by-step explanation:
c: f(x)=0.5(x-4)^2-5
Which expression is equivalent to
Answer:
First option
Step-by-step explanation:
The expression can be simplified to:
[tex]\frac{8g^{15} }{64h^6}[/tex] = [tex]\frac{g^{15} }{8h^{6} }[/tex]
You can't simplify this further since the indices if you think about it is g 15 times or h 6 times so you can't simply them further.
For 100 points!!!
Three times a number, plus nine, equals negative two times the same number, plus forty-four. The number is?
Answer:
4A - 8 = 3A + 4
Step-by-step explanation:
Answer:
31/5
Step-by-step explanation:
3x+9=-2x+40
when you solve the equation, you get 31/5!
Please mark as brainliest if you can. Hope this helps!
(3.6×10−5)÷(9×10−7) in Standard Form
Answer: 31/83 (decimal form 0.373494)
Step-by-step explanation:
If the distance between A(x,3) and B(4.3) is 16 units, find the value of x.
Answer:
[tex] - 12[/tex]
Step-by-step explanation:
[tex]x1 = x \: \: y1 = 3 \\ x2 = 4 \: \: y2 = 3 \\ distance \: betwen \: two \: points = \sqrt{(x2 - x1) {}^{2} +( y2 - y1) {}^{2} } \\ 16= \sqrt{(4 - x) {}^{2} + (3 - 3) {}^{2} } \\ 16 = \sqrt{(4 - x) {}^{2} + 0} \\ 16 = \sqrt{(4 - x) {}^{2} } \\ 16 = 4 - x \\ 16 - 4 = - x \\ 12 = - x \\ x = - 12[/tex]
fing the midpoint of A(1-4) and B(-2;-7)
Find f(-2) for (x) = 3 . 2^x
O A. -36
O B. -12
O c.1/36
O D. 3/4
[tex]\sf f(x) = 3 \ * \ 2^x[/tex]
insert x = -2
[tex]\sf f(-2) = 3 \ * \ 2^{-2}[/tex]
[tex]\sf f(-2) = 3 \ * \ \dfrac{1}{4}[/tex]
[tex]\sf f(-2) = \dfrac{3}{4}[/tex]
option D. 3/4 will be the correct answer.
[tex]\\ \rm\Rrightarrow f(x)=3.2^x[/tex]
Put -2[tex]\\ \rm\Rrightarrow f(-2)[/tex]
[tex]\\ \rm\Rrightarrow 3.2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 3(1/4)[/tex]
[tex]\\ \rm\Rrightarrow 3/4[/tex]
HELP PLSSS - WILL MARK BRAINLIEST
Select the correct answer
which situation is best modeled by a nonlinear function with time as the independent variable?
A. The value of a gift card that decreases by three dollars each month
B. The value of a $20 bill
C. The value of a collectible baseball card that increases by constant factor of 1.1, or by 10%, each year
D. The value of an investment that increases by two dollars each week
Answer: Most likely it is A
Step-by-step explanation:
Although it should be B, because a non linear function doesn't have a rate of change. I already looked up this question many times so we know It's NOT C.
The best modeled by a nonlinear function with time as the independent variable is:
The value of a collectible baseball card that increases by a constant factor of 1.1, or by 10%, each year.
A nonlinear function is one that does not follow a straight line.
In this case, t
A) describes a linear function since the value of the gift card decreases by a fixed amount each month, resulting in a straight-line relationship.
B) describes a constant value, which is a special case of a linear function where there is no change over time.
C) The value of the collectible baseball card increases by a constant factor of 1.1 each year, which results in exponential growth. This behavior is best modeled by a nonlinear function.
D) describes a linear function since the value of the investment increases by a fixed amount each week, resulting in a straight-line relationship.
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100 PTS!! If line segment AB is dilated with a scale factor 3/2, what is the length of the new line segment A’B’?
A)7.5cm
B)15cm
C)20cm
D)30cm
Length of AB is not given so insufficient info provided
Let's see how to solve then
Scale factor is 3/2 means 3/2 is multiplied with AB to form A'B'
If length of AB is n the. then length of A'B' is 3n/2
The line graphed below has a slope of ____.
To find the slope, we must have two points
--> Two points: (-3,1) and (-1, -5)
The slope's formula is --> [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) --> (-3,1)(x2, y2) --> (-1, -5)So the slope = [tex]\frac{-5-1}{-1--3} =\frac{-6}{2} =-3[/tex]
The line graphed below has a slope of -3
Hope that helped!
PLEASE HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
k²= 6²+5²
k²= 36+25
k²= 61
k= V61
k=7.81
Selim walked 1/12 of a mile to the coffee shop in 712 of a mile to the dry cleaners how far apart is the coffee shop from the dry cleaners grid your answer NOTE: grid your answer as a fraction not a mixed number
Answer:
6/12 of a mile
Step-by-step explanation:
7/12-1/12=16/12
Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
Slope, m =
y-intercept, b =
Answer:
y = 5x + 3
Step-by-step explanation:
If the slope is 5 and the y-intercept is 3, we can substitute the value of the variables into the formula.
y = mx + b
y = (5)x + 3
y = 5x + 3
I hope this helps!