Using a system of equations, the amounts invested in each fund are given as follows:
Growth: $2,000.Income: $2,000.Market: $2,000.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested into the growth fund.Variable y: amount invested into the income fund.Variable z: amount invested into the market fund.The teacher invested 5000, hence:
x + y + z = 5000.
After a year, the amount was of $5,450, hence, considering the return rates:
1.12x + 1.08y + 1.05z = 5450.
The teacher invested twice as much in the income fund as in the money market fund, hence:
y = 2z.
Then, replacing y = 2z in the first two equations:
x + 3z = 5000 -> x = 5000 - 3z.1.12x + 3.21z = 5450.Replacing the first equation into the second.
1.12(5000 - 3z) + 3.21z = 5450.
0.15z = 150
z = 150/0.15
z = 1000.
Hence:
y = 2z = 2000.x = 5000 - 3z = 2000.The amounts invested in each fund are given as follows:
Growth: $2,000.Income: $2,000.Market: $2,000.More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
A quadrilateral has a perimeter of 12 and all of the side lengths are odd integers. What is the probability that the quadrilateral is a rhombus?
A quadrilateral has a perimeter of 12 and all of the side lengths are odd integer then the probability that the quadrilateral is a rhombus is 1/4.
What is perimeter ?If the midpoints of a rhombus with 12-inch sides are connected, a quadrilateral is created. A square with a 12-inch diagonal would be the quadrilateral that is constructed.
A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.
All four side lengths must be added up in order to determine the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to accomplish this task efficiently.
To learn more about perimeter from the given link:
brainly.com/question/6465134
#SPJ4
Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q →
The true statements are
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → qHow to determine the true statement?The original statement is given as:
If a number is negative, the additive inverse is positive
This can be represented as
If p, then q
i.e. if p → q
So, (a) is correct
For the inverse, we simply negate the hypothesis and the conclusion
i.e. if ¬p → ¬q ----(b) is correct
For the converse, we simply switch the hypothesis and the conclusion
i.e. if q → p ----(e) is correct
Hence, the true statements are (a), (b) and (e)
Read more about conditional statements at:
https://brainly.com/question/4421013
#SPJ1
Use log₅ 2 ≈ 0.43 and log₅7 ≈ 1.21 and the properties of logarithms to approximate log₅ √14 without using a calculator.
[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82
The property of logarithms log ab = log a + log b , log a/b = log a - log b
[tex]log_{5} 2[/tex] ≈ 0.43
[tex]log_{5} 7[/tex] ≈ 1.21
We need to find,
[tex]log_{5} \sqrt{14}[/tex]
= 1/2[tex]log_{5} 14[/tex]
= 1/2[tex]log_{5} 2*7[/tex] ( log ab = log a + log b)
= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])
=1/2( 0.43 + 1.21)
= 1/2 × 1.64
= 0.82
Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82
To know more about the logarithms refer to the link given below:
https://brainly.com/question/12049968
#SPJ4
Please help i am not sure how to do this
Given that the zeros of a quadratic function are -2 and 8, what is the standard form of the quadratic function?
Using quadratic equation, The equation for given value of zeros is equation is x² - 6x - 16 = 0.
What is a quadratic equation?f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form. The three graphs in the image below are all parabolas.
The following must be true if those are the 0s:
-2 + 2 = 0
8 - 8 = 0
We would thus get the following equation if we were to include them in a quadratic-based one:
(x + 2)(x - 8) = 0
x² - 8x + 2x - 16 = 0
FOIL
Roughly speaking, x² - 6x - 16 = 0
To learn more about quadratic equation from given link
https://brainly.com/question/1214333
#SPJ1
Answer:
f(x) = x2 − 6x − 16
Step-by-step explanation:
Write the zeros as solutions of two equations.
x = −2 x = 8
x + 2 = 0 x − 8 = 0 Rewrite each equation so that it equals 0.
Find the product of the two binomials.
(x + 2)(x − 8) = x2 − 8x + 2x − 16 Multiply.
= x2 − 6x − 16 Simplify.
Rewrite the equation in function notation.
f(x) = x2 − 6x − 16
Therefore, the quadratic function with zeros of −2 and 8 is f(x) = x2 − 6x − 16.
susie and friends rent 3 life jackets and a boat. the life jacket rents for $5.00 each. the boat rents for $25.00 per hour. the total cost is $115. what is an equation that can be written to be present this situation? explain your steps.
PLEASE HELP!!
The equation that can be written to represent this situation is 15 + 25h = 115.
How to illustrate the equation?Let the number of hours be represented by h.
The equation will be:
(3 × 5) + (25 × h) = 115
15+ 25h = 115
It should be noted that 15 represents the cost of jackets
Therefore, the equation that can be written to represent this situation is 15 + 25h = 115.
Learn more about equations on:
brainly.com/question/13763238
#SPJ1
The equation that can be written to be present this situation is 115 = 25x + 15
How to use equation to represent a situation?Susie and friends rent 3 life jackets and a boat.
The life jacket rents for $5.00 each.
The boat rents for $25.00 per hour.
The total cost is $115.
The equation that can be written to be present this situation is as follows:
The equations should be linear.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, the equations is as follows;
y = 25x + 15
115 = 25x + 15
where
x = number of hours you rent the boat.
learn more on equation here: https://brainly.com/question/3085237
#SPJ1
I need this answered please
y=mx+c, where m is slope. Here x=-2, x-intercept at (x,y)=(-2,0)
and there is no y intercept.
What is slope intercept form?y=mx+c, where m is slope.
The x-intercept is the value of x when y=0.
Since x=-2 for all values of y
it follows that x=-2 when y=0.
The y-intercept is the value of y when x=0 (or alternately the solution point of the form 90,y)). since x neq 0 not matter what value is assigned to y, no such point exists (graphically x=-2 is a vertical line parallel to, and therefore never intersecting, the Y-axis).
Therefore x-intercept at (x,y) is (-2,0) and there is no y intercept.
To learn more on Slope intercept form visit:
https://brainly.com/question/20786109
#SPJ1
If x=-3, then 4x²-7x+5=
A 2
B 14
C 20
D 42
E 62
The value of the polynomial at the point [tex]x=a[/tex], just replace [tex]x[/tex] with [tex]a[/tex] in the polynomial equation.
Verify the following equation:
[tex]=4x^{2} -7x+5[/tex]
The given solution:
[tex]x=-3[/tex]
[tex]4x^{2} -7x+5[/tex]
Find the equation:
[tex]4x^{2} -7x+5[/tex]
[tex]4(-3x)^{2} -7(-3)+5[/tex]
[tex]=4(9)+21+5[/tex]
[tex]=36+26[/tex]
[tex]=62[/tex]
Therefore,The option E [tex]62[/tex] is the correct answer
To learn more about the equation refer:
https://brainly.in/question/26920712
#SPJ4
Suppose that e and f are two events and that p(e and f)=0.1 and p(e)=0.2. what is p(f|e)?
The Probability of P(F/E) is 0.5 .
Baye's Theorem helps in finding the conditional probability probability of an event A given that event B has already occurred.
For Example : The probability of event A given that event B has already occurred is denoted by P(A/B) and is calculated by
[tex]P(A/B)=\frac{P(A.and.B) }{P(B)}[/tex]
It is given in the question that
P(E and F)=0.1 and
P(E)=0.2
Using Baye's Theorem ,we get
[tex]P(F/E)=\frac{P(F .and .E)}{P(E)}[/tex]
Substituting the values ,we get
[tex]P(F/E)=\frac{0.1}{0.2}\\ \\ =\frac{1}{2} \\ \\ =0.5[/tex]
Therefore , the probability of P(F/E) is 0.5 .
Learn more about Probability here https://brainly.com/question/17764757
#SPJ4
Multiply (4.12 × 10^−9)(8.3 × 10^15). Write the final answer in scientific notation.
34.196 × 10^−134
3.4196 × 10^7
3.4196 × 10^−135
34.196 × 10^6
The product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
How to evaluate the product in scientific notation?The product expression is given as
(4.12 × 10^−9)(8.3 × 10^15)
Rewrite properly as
(4.12 × 10^−9)(8.3 × 10^15) = (4.12 × 10^−9) * (8.3 × 10^15)
Evaluate the product of 4.12 and 8.3 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^−9 × 10^15
Evaluate the product of 10^−9 and 10^15 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^6
Rewrite the expression as
(4.12 × 10^−9)(8.3 × 10^15) = 3.4196 * 10^7
Hence, the product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
Read more about scientific notation a
https://brainly.com/question/27862246
#SPJ1
Answer:
Its B. 3.4196 x 10^7
Step-by-step explanation:
This is correct answer :))
Can someone help me! I have turned this is twice already and I am still getting it wrong. Write the numbers in decreasing order. 1.¯3, − 8/5, √13, π, −0.7
I keep saying the correct answer is √13, π, - 8/5, 1.¯3, -0.7
HOW IS THIS WRONG?!
The answer in ascending order is -8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]
What is ascending order?
Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Count how many digits are in each number. The number with the fewest digits is the smallest.
The numbers arranged in ascending order are
-8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]
To know more about ascending order arrangements, click on the link
https://brainly.com/question/20681445
#SPJ1
Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
Answer: i believe your answer is 21x=100
Step-by-step explanation: hope this helps
How do you solve for x?
Answer: x=60/13
Step-by-step explanation:
The smaller triangle has the same proportions as the bigger triangle.
Hence, 13/12=5/x
13/12=5/x
13 * x/12=5
13x=5*12
13x=60
x=60/13
Find the missing term of each arithmetic sequence.14,..., 28, ...........
The missing terms of the given arithmetic sequence AP are 14, 21, 28, 35.
What exactly is arithmetic progression?An arithmetic progression (AP) is a sequence with the same distinctions between each successive term.
Each term (apart from the first) in an arithmetic progression is derived by adding a specific number to the term before the first one.For the initial term 'a' of an AP as well as the common difference 'd,' the very next arithmetic progression equations are frequently used to solve different AP problems.An AP's most common difference 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1. nth term of an AP: an = a + (n - 1) dThe sum of an AP's n terms is: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the AP's final term.Now, in response to the question;
The arithmetic sequence.14,..., 28, ............
There are total 4 terms in the series.
Let the initial term is 'a₁' is given as 14.
Let the second term is 'a₂'.
Let the third term be 'a₃' which is given as 28.
Ans, the let the fourth term is represented as 'a₄'.
As, we know that in the AP, the difference of the two consecutive terms is equal and called as common difference.
Thus,
d = a₂ - a₁ ........(equation 1)
d = a₃ - a₂ .......(equation 2)
Thus, equating the two equation;
a₂ - a₁ = a₃ - a₂
Substituting the values;
a₂ - 14 = 28 - a₂
Simplifying the equation;
2a₂ = 28 + 14
2a₂ = 42
a₂ = 21.
Put the obtained value in equation 1 and find d.
d = a₂ - a₁
d = 21 - 14
d = 7
Now, estimate a₄.
a₄ = a₃ + d
a₄ = 28 + 7
a₄ = 35
Therefore, the complete arithmetic sequence is 14, 21, 28, 35.
To know more about the arithmetic sequence, here
https://brainly.com/question/6561461
#SPJ4
(2x -1){2} = (x+1){2}
Answer:
X = 2
Step-by-step explanation:
4x-2 = 2x+2 multiply the brackets on both sides
4x-2x = 2+2 bring thes x's to one side & the constants to another side
2x = 4 simplify
X = 4÷2 divide
x = 2
What does it mean to have a measure of center?
Answer:
It's a single number used to describe a set of numeric data.
Solve each equation. Check each solution. 1/3x =-2
Find a₁ for each arithmetic series.Evaluate S₁₀ for the series x+(x+y)+(x+2 y)+ . . . . .
The sum of the first 10 terms of the arithmetic series x+(x+y)+(x+2 y)+ . . . . . is S(10) = 10x+45y
The given arithmetic series:
x+(x+y)+(x+2 y)+ . . . . .
Notice that:
a(1) = x
a(2) = x+y
a(3) = x+2y
We can find the common difference:
d = a(2) - a(1)
= (x+y) - x = y
Recall the formula for the nth term of an arithmetic series:
a(n) = a(1) + (n - 1) . d
Substitute n = 10, a(1) = x, and d = y into the formula:
a(10) = x + (10 - 1)y
a(10) = x+9y
Use the sum formula:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [x + (x+9y)]
S(10) = 5 .(2x+9y)
S(10) = 10x+45y
Learn more about arithmetic series here:
https://brainly.com/question/11994891
#SPJ4
I NEED HELP WITH THIS MATH PROBLEM !!
An equation that relates T to N can be written as T = 750 + 560N.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).
How to write an equation relating T to N.Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:
T = A + B
Substituting the given parameters into the formula, we have;
T = (750 + 165N) + 395N
T = 750 + 165N + 395N
T = 750 + 560N.
Read more on function here: https://brainly.com/question/19537858
#SPJ1
Complete Question:
Ann and her husband are each starting a saving plan. Ann will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+165N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.
Simplify your answer as much as possible.
Which expression is equivalent to rm ÷ rn? (4 points)
rm − n
rm + n
rm ⋅ n
rm ÷ n
By applying the exponent rule of division, the equivalent expression to [tex]r^m \div r^n[/tex] is: A. [tex]r^{m - n}[/tex].
How to Determine Equivalent Expressions?Given the expression, [tex]r^m \div r^n[/tex], we can find the expression that is equivalent to it by rewriting the expression as shown below:
r^m ÷ r^n
According to the exponent rule of division, if we are to divide two bases together that have the same same base but different exponents, what we only need to do is to subtract their powers.
We would apply this same rule in this given problem.
Applying the exponents rule of division, we would subtract the powers:
r^m ÷ r^n = r^(m - n)
Therefore, by applying the exponent rule of division, the equivalent expression to [tex]r^m \div r^n[/tex] is: A. [tex]r^{m - n}[/tex].
Learn more about the exponent rule of division on:
https://brainly.com/question/2263967
#SPJ1
y varies directly with x . Explain your answer.If x is divided by 7 , what happens to y ?
The required value of y also gets divided by 7.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with other quantity, then we have a relation, y = kx
Now, find k for, some fixed value of x and y
Further, calculate y when x is divided by 7. In a general case, y will also be divided by 7 as both x and y varies directly.
Hence, the value of y also gets divided by 7.
To learn more about the constant of proportion, visit the link:
https://brainly.com/question/24868934
#SPJ4
What does the point (6,2) represent?
The volume of a cylinder is 770cm³. It has a height of 5cm. Find its radius.
The radius of a cylinder having height of 5cm and volume 770 cm³ is 7 cm.
Volume of a cylinder is the space occupied by it in a three - dimensional space.
Volume of a cylinder is calculated using the formula:
[tex]V = \pi r^{2} h[/tex]
[tex]r = \sqrt{\frac{V}{\pi h} }[/tex]
where r is the radius of the base of the cylinder.
is a constant having value 3.14
h is the height of the cylinder. It is the perpendicular height from the base.
According to the given condition,
V = 770 cm³ and h = 5 cm.
Substituting these values in the equation above,
∴ r = 7 cm
To learn more about volume of a cone, refer to this link:
brainly.com/question/1984638
#SPJ4
HELPPPP PLEASE I GOT 5 mins before it’s dueee .
Answer:
Jajajjajjajj
Step-by-step explanation:
What is the value of f(−1) when f(x)= 2 x + 2?
if f(x)=2x+2
and f(x)= -1
2(-1) +2
-2 + 2 =0
the value would be 0
Can you help me identify angle d?
Answer:
yes I need help
Step-by-step explanation:
I don't understand it very well.
With the information given, can you prove that this quadrilateral is a parallelogram?
Yes or No
PLEASE HELP
Answer:
yes
Step-by-step explanation:
there are two sets of parrelell line
i might have spelled it wrong
The parallelogram is ABCD with the sides AD parallel to BC
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the figure be represented as ABCD
Now , the sides AD and BC are parallel to each other
And , from the figure , we can say that the sides AB is parallel to CD
Therefore , the figure ABCD is a parallelogram
And , opposite sides of a parallelogram are parallel
Hence , the figure ABCD is a parallelogram
To learn more about parallelogram click :
https://brainly.com/question/23488153
#SPJ2
A number is divided by 6 and then the quotient is added to 12.The result is 4.Find the number
Answer:
So the number is -48
Step-by-step explanation:
Lets say that the number is x
(x /6)+12=4
x/6=-8
x=-48
6x+4<6 (x-9) solve the inequality
Answer:
No solutionsStep-by-step explanation:
6x + 4 < 6(x - 9) Distribute6x + 4 < 6x - 54 6x - 6x < - 54 - 4 Collect like terms0 < - 58 FalseFalse inequality, so no solutions.
What is the expression and value of "six less than nine times the sum of a number and eight" when n = 5? 9 (n 8) minus 6; when n = 5, the value is 111. 6 minus 9 (n 8); when n = 5, the value is 111. 9 (n) 8 minus 6; when n = 5, the value is 47. 6 minus 9 (n) 8; when n = 5, the value is 47.
The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.
Firstly forming the expression using given information, starting the end of sentence. Breaking sentence into parts as follows -
1. the sum of a number and eight
2. nine times the sum of a number and eight
3. six less than nine times the sum of a number and eight
Let the number be n.
So, equation according to 1. Sum = (n + 8)
Equation according to 2. 9(n + 8)
Equation according to 3. 9(n + 8) - 6
So, the expression is 9(n + 8) - 6
Now, keeping the value of n as 5 and finding the value of expression.
Value = 9(5 + 8 ) - 6
Firstly solving the bracket
Value = 9 × 13 - 6
Performing multiplication
Value = 117 - 6
Performing subtraction
Value = 111
Hence, the expression and value is A. 9(n+8)-6, when n=5, the value is 111
Learn more about solving expression -
brainly.com/question/29114
#SPJ4
The complete question is -
What is the expression and value of “six less than nine times the sum of a number and eight” when n = 5
A.9(n+8)-6, when n=5, the value is 111
B. 6-9(n+8), when n = 5, the value is 111
C. 9(n)+8-6, when n = 5 the value is 47
D.6-9(n), when n = 5, the value is 47
Answer:
The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.
Step-by-step explanation:
