The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which gives the value as [tex]300(1.04)^6[/tex]
Explanation:The explicit formula that can be used to find the account's balance at the beginning of year 6 is:
[tex]B = P(1 + r/n)^(nt)[/tex]
Where:
B is the balance after a certain number of yearsP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times that interest is compounded per yeart is the number of yearsIn this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:
[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]
[tex]B = 300(1 + 0.04)^6[/tex]
[tex]B = 300(1.04)^6[/tex]
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Which of the following Best describes the function -x^4+1
a)The degree of the function is even so the ends of the graph continue in opposite directions. Because the leading coefficient is positive the left side of the graph continues down the coordinate plane and the right side continues upward.
b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward
c) The degree of the function is even so the ends of the graph continue in opposite directions. because the leading coefficient is negative the left side of the graph continues up the coordinate plane and the right side continues downward
d) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is positive the left side of the graph continues of the coordinate plane and the right side also continues upward.
ANSWER
b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward
EXPLANATION
The given polynomial function is
[tex]f(x) = - {x}^{4} + 1[/tex]
The degree of this function is even which is 4.
The function extends in the same direction at both ends.
In other words both ends continue in the same direction.
Since the coefficient of the leading term is negative, the graph extends to negative infinity at both ends.
The correct answer is B
given that ABCD is a rhombus, what is the value of x?
Answer:
D. 18Step-by-step explanation:
We know:
1. Diagonals of a rhombus are perpendicular.
2. Diagonals divide the rhombus on four congruent right triangles.
3. The sum of measures of acute angles in a right triangle is equal 90°.
Angles CAD and ACB are alternate angles. Therefore they are congruent:
m∠DAC = m∠ACB ⇒ m∠ACB = x°.
From 3. we have the equation:
(5x - 18) + x = 90
(5x + x) - 18 = 90 add 18 to both sides
6x = 108 divide both sides by 6
x = 18
Answer:
Option D
Step-by-step explanation:
In any Rhombus the diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.
So,
5x-18+x+90=180 ( Angles of a triangle add to 180 degrees)
Simplifying like terms:
6x+72=180
Subtracting 72 both sides :
6x= 108
Dividing by 6 both sides:
x=18.
Option D is correct.
given that (-7,1) is on the graph of f(x), find the corresponding point for the function 3f(x)
Answer:
(-7,3)
Step-by-step explanation:
Given that point (-7,1) is on the graph of f(x), means that
[tex]f(-7)=1[/tex]
To find the corresponding point for the function y=3f(x), you have to find the value of the function at x=-7.
Substitute x=-7 into the function's expression:
[tex]y=3f(-7)[/tex]
Since f(-7)=1, we have that
[tex]y=3\cdot 1=3[/tex]
Hence, the corresponding point has coordinates (-7,3)
To find the corresponding point for the function 3f(x), multiply the y-coordinate of the given point by 3.
Explanation:To find the corresponding point for the function 3f(x), we need to multiply the y-coordinate of the given point by 3.
Given that (-7,1) is on the graph of f(x), we multiply the y-coordinate by 3 to get (1*3) = 3.
Therefore, the corresponding point for the function 3f(x) is (-7,3).
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Evaluate the following expression.
2 cubed
A.) 69
B.) 27
C.) 5
D.) 8
Answer:
D) 8
Step-by-step explanation:
2^3 means 2 times itself 3 times:
2*2*2
2*2 is 4 so:
4*2
4*2 is 8 so the answer is D, 8!
D) 8
What's the equation defining?Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. example, 2 + 4 + 5 = 11 is an equation.
Do equations always contain terms?When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters
2^3 means 2 times itself 3 times:
2*2*2
2*2 is 4 so:
4*2
4*2 = 8
so the option is D, 8
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find the missing side
Answer:
[tex]x=15.56[/tex]
Step-by-step explanation:
We can use the law of sines here. However, we will first need to solve for the missing angle.
The interior angles of a triangle add up to 180.
Therefore,
[tex]35+90+x=180[/tex]
where [tex]x[/tex] is the missing angle.
[tex]35+90+x=180[/tex]
[tex]x+125=180[/tex]
[tex]x=55[/tex]
So the missing angle is 55 degrees.
Now we can use the law of sines to set up a proportion.
[tex]\frac{19}{sin(90)}=\frac{x}{sin(55)}[/tex]
Now simplify the equation.
[tex]x=15.56[/tex]
Rounded to the nearest hundredth.
Answer:
x ≈ 19.6
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{19}[/tex]
Multiply both sides by 19
19 × cos35° = x, hence
x ≈ 19.6 ( to 1 dec. place )
Find the four-digit number which has the remainder of 112 when divided by 131, and the remainder of 98 when divided by 132.
[tex]n[/tex] - 4-digit number
[tex]q[/tex] - quotient
[tex]131q+112=n\\132q+98=n\\\\131q+112=132q+98\\q=14\\\\131\cdot14+112=n\\\boxed{n=1946}[/tex]
The four-digit number which has the remainder of 112 when divided by 131 is 1946.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, number which has the remainder of 112 when divided by 131.
Let n be the number and q be the quotient.
We know that, Dividend = Divisor × Quotient + Remainder
Now, n=131×q+112 ------(i)
The remainder of 98 when divided by 132.
That is, n=132×q+98 ------(ii)
From equation (i) and (ii), we get
131×q+112=132×q+98
131q+112=132q+98
132q-131q=112-98
q=14
Substitute q=14 in equation (i), we get
n=131×14+112
n=1946
Therefore, the four digit number is 1946.
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3(x - 4) + 5 - x= 2x - 7
how many solutions are there to this equation?
Answer:
The equation has infinity solutions
Step-by-step explanation:
3( x - 4 ) + 5 - x = 2 x - 7
⇒ Expand brackets
3 x - 12 + 5 - x = 2 x - 7
⇒ Simplify
2 x - 7 = 2 x - 7
Joan had a garden 10.1 m long and 4.2 m wide. She decides to fence it in to keep out the deer. The dimensions of the fence are 11.2 m long and 5.0 m wide. What is the area between the fence and the garden?
Answer:
14.08 m
Step-by-step explanation:
Start by finding the area of the fence and the area of the garden. Garden- 10.1*4.2=42.42 Fence-11.3*5=56.5
Now subtract the two values. 56.5-42.42=14.08
NEED MAJOR HELP ONLY ONE CHANCE LEFT !!! Which degree would it be ???
Answer:
104
Step-by-step explanation:
< MON = 180 - 104 = 76
This is an isosceles triangle.
There fore < OMN = 76
< LMN = 180 -76 = 104
The sum of three consecutive integers is 45. What are the integers
Divide 45 by 3 ( the quantity of consecutive numbers) This will give you the middle number, then use the number higher and lower.
45/3 = 15
14 + 15 + 16 = 45
The 3 numbers are 14, 15 and 16
If set D is not the empty set but is a subset of set E, then which of the following is true? D ∩ E = D D ∩ E = E D ∩ E = ∅
Answer:
D intersect E=D (the first one you have)
Step-by-step explanation:
D is a subset of E
That means all the elements in D are also in E
So the intersection of D and E is D.
The first thing you wrote is correct, that is, D intersect E=D is right
Answer:
[tex]D\cap E[/tex]=D
Step-by-step explanation:
We are given that D is not empty set but D is a subset of set E.
We have to find the true statement.
[tex]D\neq \phi[/tex]
D is a subset of set E
Therefore,[tex]D\subset E\neq \phi[/tex]
Intersection: It is the set of common elements of two sets.
Therefore,[tex]D\cap E[/tex]=D
Because E contains all elements of D .
Hence, Option A is true.
Simplify the expression by combining like terms.
4y+7x- 2y+4x
Hello!
Answer:
[tex]\boxed{2y+11x}[/tex]
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
First, you switch sides. *Group like terms*
[tex]4y-2y+7x+4x[/tex]
Then, you add the similar to elements. You can also add the numbers from left to right.
[tex]4y-2y=2y[/tex]
[tex]2y+7x+4x[/tex]
[tex]7x+4x=11x[/tex]
[tex]\boxed{2y+11x}\checkmark[/tex], is the correct answer.
Hope this helps!
Have a nice day! :)
Answer:
2y + 11x
Step-by-step explanation:
Simplify the expression 4y+7x- 2y+4x
To simplify any expression, combine the like terms by adding or subtracting
To simplify 4y+7x- 2y+4x, combine the like terms
combine 4y and -2y, = 2y and
combine 7x and 4x = 11x
2y + 11x
solve the equations. log(2x-3)=log(3-x)-2
[tex] log(2x - 3) = log(3 - x) - 2 \\[/tex]
Answer:
1.59
Step-by-step explanation:
log (2x-3)= log (3-x) -2
log (2x-3)/(3-x) =-2
If we remove log,
2x-3/(3-x) = e^-2
2x-3= 3e^-2 -xe^-2
2x+ xe^-2 = 3e^-2+3
x(2+e^-2) = 3( e^-2+1)
If you use calculator you will get answer nearly equal to 1.59.
Fiona solved the equation shown 1/2-1/3(6x-3)=-13/2 what is the missing step of her solution
Answer:
Simplify by combining like terms, she combined 1/2 and 1 which equals 3/2. Your answer is A.
Step-by-step explanation:
The missing step in Fiona's solution to the equation 1/2 - 1/3(6x - 3) = -13/2 was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2.
Explanation:To find the missing step of Fiona's solution, we first need to simplify the equation. The given equation is 1/2 - 1/3(6x - 3) = -13/2. The missing step may be the distribution of the 1/3 onto the (6x - 3). This leads to 1/2 - (2x - 1) = -13/2.
Following this, we need to remove the fraction on the left side of the equation by multiplying the entire equation by 2. This gives 1 - (4x - 2) = -13. Finally, simplifying this further gives us -4x = -16, and solving for x we get x = 4.
Therefore, Fiona's missing step was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2 to get rid of fractions.
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Last year, a total of 26 inches of rain fell in Center City. This year, experts predict rainfall in Center City will increase by 15% over last year's total.
How many more inches of rain are predicted to fall in Center City this year than last year?
Multiply last years rainfall by the percent of increase.
26 inches x 0.15 = 3.9 inches more.
Round the answer as needed.
First, we need to find 15% of last years total rainfall to estimate next years. To do this, multiply last years rain by the decimal form of 15%.
26*.15=3.9
There will be 3.9 more inches of rain predicted to fall next year.
Hope this helps!
PLEASE HELP! BRAINIEST WILL BE MARK IF RIGHT!
Answer:
X int : 5
Y int : 15
Step-by-step explanation:
y=15
-
3x=15
3/3 15/3
x=5
Answer:
y-intercept=15 and x-intercept = 5
Step-by-step explanation:
We have the following equation:
3x + y = 15.
To find the x-intercept and y-intercept we have to do the following:
1. To find the y-intercept we need to make x=0, and solve for 'y' as follows:
3x + y = 15 ⇒ 3(0) + y = 15 ⇒ y=15
2. To find the x-intercept we need to make y=0, and solve for 'x' as follows:
3x + y = 15 ⇒ 3x + (0) = 15 ⇒ 3x = 15 ⇒ x=5
Therefore, the y-intercept=15 and x-intercept = 5
Factor the expression.
125x^3+512
Answer:
its (5x+8)(25x^2-40x+64
Step-by-step explanation:cuz
What type of triangle can a right triangle be?
scalene
acute
obtuse
isosceles
Answer:
acute
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
acute and obtuse
Step-by-step explanation:
In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene. In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. Please mark me as branliest. Thank you :3
Which number is larger, 9.1 or √81 ? Explain
for 15 pts!!!! ASAP I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Can someone help ...
Find the missing variable for a parallelogram:
A = LaTeX: 32in^2 32 i n 2
h =
b = 6.3 in
(1in=2.54cm)
Answer:
Height of parallelogram = 5.07 inches
Step-by-step explanation:
We are given Area of Parallelogram = 32 in^2
Height of Parallelogram = ?
Base of Parallelogram = 6.3 in
The formula to find the Area of Parallelogram is:
Area of Parallelogram = Base * Height
32 = 6.3 * Height
=> Height = 32/6.3
=> Height = 5.07 inches
So, height of parallelogram = 5.07 inches
The missing variable for this parallelogram is the height, which is 5.08 inches.
Further explanationWe begin with the formula for the area of a parallelogram:
A = bh, where A represents the area, b represents the base and h represents the height.We plug in all given information. We know the area, 32 in², and we know the base, 6.3 in:
32 = 6.3hNext we solve for our variable, h. Since 6.3 and h are beside each other, we know they have been multiplied. To cancel this, we will divide both sides by 6.3:
[tex]\frac{32}{6.3} = \frac{6.3h}{6.3}\\ \\5.079=h\\\\5.08 \approx h[/tex]This means that the missing variable, the height, is approximately 5.08 inches.
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Keywords: missing variables, missing measurements, area of parallelogram, missing side of parallelogram
What is the equation of the line that is perpendicular to the given line and passes through the point (2,6)?
Answer:
x=2
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is its greatest possible value for width?
Answer:
Step-by-step explanation:
Perimeter= 2L+2W. If L=3W(three times the width) then 2(3W)+2W=112. Or 6W+2W=112 which is equal to 8W=112. To solve for the width, divide both sides by 8 and find 112/8=14, therefore W=14.
Answer:
14 cm
Step-by-step explanation:
Given the length is 3 times the width
If each width is denoted by W, then each length is L = 3W
Perimeter (add up all lengths and widths),
= L + L + W + W
= 3W + 3W + W + W
= 8W
Given that the max perimeter is 112cm
hence 8W = 112,
W = 14 cm at most
A car salesman earns a 20% commission on every car that he sells. Approximately what commission would he make if he sold a car for $9,895?
First you are going to multiply the number by the percent. 9,895 x 20= 197,900.
Now divide the answer by 100. 197,900 / 100= 1,979.
This means the car salesman should make 1,979 from the car sale.
Remember, multiply the number by the percent, then divide that answer by 100.
I hope this helps! :)
if my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this?
Answer:
[tex]5x\leq30[/tex]
Step-by-step explanation:
Let
x -----> the number of ice cream
we know that
[tex]5x\leq30[/tex]
Solve for x
Divide by 5 both sides
[tex]x\leq30/5[/tex]
[tex]x\leq 6\ ice\ cream[/tex]
therefore
The maximum number of ice cream is 6
Determine if each set of ordered pairs represents a function.
(2,3), (6,-5), (-1,3)
Answer:
yes
Step-by-step explanation:
You can perform the "line test." If it is a function, there will not be two x's of the same value. In this case, x is 2,6,-1. No number repeats, thus making a function.
Answer:
Function:
(7, -4) (0, 9), (2, -2)
(-6, 5), (-5,6), (8,2)
(2, 3), (6, -5), (-1,3)
Not a Function:
(1, 9), (-3, -2), (1, -4)
(0, 3), (0, 7), (4, 0)
Step-by-step explanation:
I got it right on edge lol
also none of the other answers for this question on here are right
A=4(14-1)
———- +7
3(6)-5
Answer:
Im boutta fail my final
Step-by-step explanation:
1 like= 1 prayer
match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5
Answer:
k(x) = (3g + 5h)(x) ⇒ (1)
k(x) = (5h - 3g)(x) ⇒ (3)
k(x) = (h - g)(x) ⇒ (2)
k(x) = (g + h)(x) ⇒ (4)
k(x) = (5g + 3h)(x) ⇒ (5)
k(x) = (3h - 5g)(x) ⇒ (6)
Step-by-step explanation:
* To solve this problem we will substitute h(x) and g(x) in k(x) in the
right column to find the corresponding function formula in the
left column
∵ h(x) = 5 - 3x
∵ g(x) = -3^x + 5
- Lets start with the right column
# k(x) = (3g + 5h)(x)
∵ g(x) = -3^x + 5
∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]
- Lets simplify 3 × -3^x
take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)
∴ -3(3 × 3^x) = -(3^x+1)
∴ 3g(x) = -3^x+1 + 15
∵ h(x) = 5 - 3x
∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x
- Now substitute 3g(x) and 5h(x) in k(x)
∵ k(x) = (3g + 5h)(x)
∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify
∴ k(x) = 40 - 3^x+1 - 15x
∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)
* k(x) = (3g + 5h)(x) ⇒ (1)
# k(x) = (5h - 3g)(x)
∵ 5h(x) = 25 - 15x
∵ 3g(x) = -3^x+1 + 15
∵ k(x) = (5h - 3g)(x)
∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify
∴ k(x) = 10 + 3^x+1 - 15x
∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)
* k(x) = (5h - 3g)(x) ⇒ (3)
# k(x) = (h - g)(x)
∵ h(x) = 5 - 3x
∵ g(x) = -3^x + 5
∵ k(x) = (h - g)(x)
∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify
∴ k(x) = 3^x - 3x
∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)
* k(x) = (h - g)(x) ⇒ (2)
# k(x) = (g + h)(x)
∵ h(x) = 5 - 3x
∵ g(x) = -3^x + 5
∵ k(x) = (g + h)(x)
∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify
∴ k(x) = 10 - 3^x - 3x
∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)
* k(x) = (g + h)(x) ⇒ (4)
# k(x) = (5g + 3h)(x)
∵ g(x) = -3^x + 5
∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25
∴ 5g(x) = -5(3^x) + 25
∵ h(x) = 5 - 3x
∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x
- Now substitute 5g(x) and 3h(x) in k(x)
∵ k(x) = (5g + 3h)(x)
∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify
∴ k(x) = 40 - 5(3^x) - 9x
∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)
* k(x) = (5g + 3h)(x) ⇒ (5)
# k(x) = (3h - 5g)(x)
∵ 3h(x) = 15 - 9x
∵ 5g(x) = -5(3^x) + 25
∵ k(x) = (3h - 5g)(x)
∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify
∴ k(x) = 5(3^x) - 9x - 10
∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)
* k(x) = (3h - 5g)(x) ⇒ (6)
PLEASE HELP!!!! Type the correct answer in each box.
The graph that correctly represents the inequality 2x > 50 is graph
. The graph that correctly represents the inequality x + 6 < 32 is graph
Answer:
the first one is graph c and the second, graph b.
Step-by-step explanation:
They are both linear inequalities, so for both, you have to solve for x first. For the first one, since x is basically multiplied to 2 (2x), you have to divide both sides to get x by itself, and you get x>25. The graph has to have an opened circle, and the arrow should go to the right because all the numbers greater than 25 can be x. For the second one, you have to subtract 6 to both sides to get x by itself which then leaves you with ×<26. This one should also be an opened circle, and is going to the left, because all the numbers less than 26 can be x.
Answer:
first box c second box b
Step-by-step explanation:
Which equation describes this line?
Answer:
B. [tex]y-9=2(x-1)[/tex]
Step-by-step explanation:
We have been given graph of a line on coordinate plane. We are asked to find the equation of our given line.
First of all, we will find slope of our line using points [tex](-2,3)\text{ and }(1,9)[/tex] in slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{9-3}{1-(-2)}[/tex]
[tex]m=\frac{6}{1+2}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
We can see that our given equations are in point-slope form of equation: [tex](y-y_1)=m(x-x_1)[/tex], where,
m = Slope,
[tex](x_1,y_1)[/tex] = Coordinates of point on line.
We can get two equations of our line in point-slope form as:
[tex](y-3)=2(x--2)[/tex]
[tex](y-3)=2(x+2)[/tex] or
[tex](y-9)=2(x-1)[/tex]
Upon looking at our given choices, we can see that option B is the correct choice.