The value of f(12) which represents the amount of interest he will receive after 12 months is; $120.
Evidently, the sequence is an arithmetic progression;
As such, we must evaluate the common difference, d as follows;
d = f(2) - f(1)d = 20 - 10d = $10.The first term, a = $10
Therefore; From the nth term formula for an arithmetic progression;
f(12) = $10 + 11 ($10)f(12) = $10 + $110f(12) = $120Read more:
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How to say 12079 two different ways using hundred, tens, and ones
The number 12079 could be said two ways in terms of hundreds, tens, and ones. It can be 'twelve thousand, seventy-nine' or 'one hundred and twenty hundred, seven tens and nine ones'
Explanation:The number 12079 can be said in two different ways using hundred, tens and ones. First, you could say it as 'twelve thousand, seventy-nine.' This is because 12 is the thousands component (consisting of hundreds and thousands), and 79 is the ones and tens components. Secondly, you could say it as 'one hundred and twenty hundred, seven tens and nine ones'
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What is the slope of the line shown below?
A conjecture and the paragraph proof used to prove the conjecture are shown.
Given: E is the midpoint of segment D F. Prove: 2 D E equals D F. A segment DF is horizontal with endpoints D and F. E is the midpoint of the segment.
Drag an expression or statement to each box to complete the proof.
Answer:
1. DF (option 3)
2. segment addition postulate
3. segment congruence postulate
4. DF (option 5)
Answer with explanation:
Given: E is the mid point of DF.
Prove: 2 DE=D F
Proof with explanation:
It is given that [tex]\Bar{DE}[/tex] is mid point of [tex]\Bar{DF}[/tex].
1.→
So, [tex]\Bar{DE}\cong\Bar{DF}[/tex]
-------------------------By Definition of mid point
2.→ DE=E F----------------Segment Congruence Postulate
3.→DE+E F=D F ----------------Segment Addition Postulate
4.→DE+DE=D F-------------By Substitution
5.→Simplifying gives
2 DE=D F
What is 673.983 rounded to the nearest hundredth
I believe it would be 673.98
I hope this helps :)
673.983 rounded to the nearest hundredth is 673.98, as the third decimal digit (3) is less than 5.
To round the number 673.983 to the nearest hundredth, we need to look at the third decimal place, which is in the thousandths place. If this digit is 5 or greater, we round up. If it is less than 5, we keep the second decimal place as it is. In the case of 673.983, the third decimal digit is a 3, which is less than 5. Therefore, the number rounded to the nearest hundredth is 673.98.
the area of a quadrilateral is 8.4 square feet. find two decimals that give a product close to 8.4
Answer:
2.81 and 0.3 are two decimals that give a product of 8.43 which is close to 8.4
Step-by-step explanation:
let consider a decimal number 0.3
now consider another decimal number 2.81
now if we multiply these two numbers then we get 8.43 which is also a decimal number and it is close to 8.4.
Answer:
Hence the approximate values are 2.91 and 2.89
Step-by-step explanation:
The area of a quadrilateral is expressed as
A=L*B
Where L=length
B=breadth or width
I. e assuming it has two of its sides equal
Say given area is
A=L*B=8.4 square feet
Let's take the square root of the area A=2.898
=2.89
Approximately
L= 2.9 feet
Let's us divide the area by L to get B
8.4/2.9= 2.91
y = 4x – 10 y = 2 What is the solution to the system of equations?
ANSWER
The solution is
[tex](3,2)[/tex]
EXPLANATION
We were given the equations
[tex]y=4x-10--(1)[/tex]
and
[tex]y=2----equation (2)[/tex]
This is a simultaneous equation in [tex]x[/tex] and [tex]x[/tex].
But the coefficient of [tex]x[/tex] in the second equation is zero. that is why it seems to be absent.
We solve these two equations simultaneously
by putting [tex]y=2[/tex] in to equation (1).
Tis gives;
[tex]2=4x-10[/tex]
We add 10 to both sides to get;
[tex]12=4x[/tex]
we divide through by 4 to get
[tex]3=x[/tex]
Hence the solution for the system is [tex](3,2)[/tex]
Answer:
(3, 2)
Step-by-step explanation:
Two investments totaling $58,500 produce an annual income of $3795. One investment yields 5% per year, while the other yields 7% per year. How much is invested at each rate?
Total investment is =$58500
Annual income produced = $3795
Rate of one investment = 5%
Rate of second investment = 7%
Let the amount invested at 5% be = x
Then, amount invested at 7% rate will be = [tex]58500-x[/tex]
The equation becomes:
5%x + 7%(58500-x) = 3795
= 0.05x + 0.07(58500-x) = 3795
0.05x + 4095 - 0.07x = 3795
0.02x = 300
x = 15000
Hence, the amount invested at 5% is = $15000
Amount invested at 7% = 58500-15000 = $43500
i need to remember how to solve this problem
1 + 4x = -5 + 7x
1st step: you need to move 4x to the right and -5 to the left so that all the x's are in one place. 4x will be negative and -5 will be positive when you move them. So it will be:
1+5=7x-4x
2nd step:
3x=6
3rd step: you need to divide both sides into 3, because it is the common divisor.
x=2
To sum up:1 + 4x = -5+7x
7x - 4x = 1 + 5
3x = 6
x = 2You can try to memorize the summary. However, it is better to understand the solution as a whole.
Please help will give brainliest
A conjecture and the flowchart proof used to prove the conjecture are shown.
Given: Measure of angle D E G equals 51 degrees. Measure of angle G E F equals 39 degrees. Prove: Triangle D E F is a right triangle. Art: A right angle triangle D E F. Angle D E F is a right angle. Point G is on segment D F, and segment E G is drawn.
Drag an expression or phrase to each box to complete the proof.
box number one: given
box number two: angle addition postulate
box number three: 51 degrees + 39 degrees = m DEF
box number four: 90 degrees = m DEF
box number five: DEF is a right angle
box number six: definition of a right triangle
just took the test and these are the correct answers, hope i helped :)
Solution:
Given : ∠ D E G= 51°, ∠GEF=39°
To prove: Δ D E F is a right triangle.
Proof:
A right angle triangle D E F.
∠ D E F =90°.
Point G is on segment D F, and segment E G is drawn.
Now, taking ∠DEG and ∠GEF into consideration,
∠DEG=51° and ∠GEF=39°→→(Given)
∠DEG + ∠GEF =
∠DEF=51° + 39°
∠DEF=90°,showing Triangle D E F is a right triangle.
How many students practiced the piano more then 3 hours a week
The number of students that practice the piano more than 3 hours a week is 6
From the dot plot (see attachment), we have the following highlights
3 students practice the piano for 4 hours2 students practice the piano for 5 hours1 student practices the piano for 6 hoursNext, we add the total number of students
[tex]Total = 3 + 2 +1[/tex]
[tex]Total = 6[/tex]
Hence, the number of students that practice the piano more than 3 hours a week is 6
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The probability of something can be expressed as a decimal or as a percent. We know that the probability of something happening can not be below 0% or above 100%. Background information: To turn a percent into a decimal (or an integer depending on the number you are working with), you move the decimal two places to the left. For example: 56% would be 0.56 If probability has to be between 0% - 100%, between what two integers does probability have to be after you convert from a percent to an integer? *
Answer: The probability lies between 0 and 1
Step-by-step explanation:
As from the given information probability of an event lies between 0% to 100% .
To convert percent into integer or fraction we have to divide it by 100
[tex] 0\%= \frac{0}{100} = 0 [/tex]
And
[tex] 100\% = \frac{100}{100} = 1 [/tex]
From the above the probability of an event lie between integers 0 to 1.
I'd really appreciate it if anyone could help! :)
Which graph represents a function?
The graphs will be below the question.
C (third graph, the parabola); To find if it is a function or not draw a vertical line on the graph. If the vertical line could never intercept the figure more than once anywhere on the graph then it is a function.
From left to right of the pictures it's the 3rd photo. It's the 3rd photo because it passes the vertical line test witch means if a vertical line was drawn within the middle of the graph it would only pass through one line and not two. The other ones would pass through two lines instead of one. I hope this helped you!
A rectangle has perimeter 78 cm and length 34 cm. What is its? width?
The perimeter of a rectangle is twice the sum of the dimensions:
[tex] 2p = 2(w+l) [/tex]
We know two of the three unkowns, so we can solve for w:
[tex] 78 = 2(w+34) \iff 78 = 2w+68 \iff 10=2w \iff w=5 [/tex]
The sum of four consecutive even integers is 300.
integer 1: x
integer 2: x + 2
integer 3: x + 4
integer 4: x + 6
integer 1 + integer 2 + integer 3 + integer 4 = sum
x + x + 2 + x + 4 + x + 6 = 300
4x + 12 = 300
4x = 288
x = 72
Answer: 72, 74, 76, 78
Aurora has a cell phone plan that charges
$65
for phone service plus
$12
for each gigabyte of data used each month. If her bill for September is
$113,
how many gigabytes of data did she use in September?
Aurora used 4 gigabytes of data in September.
Explanation:To determine how many gigabytes of data Aurora used in September, we need to subtract the fixed phone service charge from her total bill. The difference will represent the additional charges for the data usage. Let's say she used x gigabytes. The equation for her bill can be written as: 65 + 12x = 113. To solve for x, we can subtract 65 from both sides and then divide both sides by 12 to isolate x. Solving this equation, we find that x = 4. So, Aurora used 4 gigabytes of data in September.
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The product of x and the sum of 6 and 8 times the square of x
"·" - product
"+" - sum
x² - square of x
Answer: x · (6 + 8 · x²) = x(6 + 8x²)
The expression "the product of x and the sum of 6 and 8 times the square of x" can be written as [tex]\( x \cdot (6 + 8x^2) \)[/tex].
The mathematical expression "the product of x and the sum of 6 and 8 times the square of x" is represented as [tex]\( x \cdot (6 + 8x^2) \)[/tex]. To simplify, distribute x into the parentheses, yielding 6x + 8x^3. This expression captures the specified operation, where x is multiplied by the sum of 6 and 8 times the square of x.
It is essential to follow the order of operations, ensuring that the square of x is calculated first, then multiplied by 8, and finally added to 6 before multiplying the result by x. This expression forms the algebraic representation of the described mathematical operation.
Write as a decimal . Tell whether the decimal terminates or repeats. 7/9
The fraction 7/9 converts to the decimal 0.77777778, which is a repeating decimal as the digit '7' repeats infinitely.
To convert the fraction 7/9 to a decimal, divide 7 by 9. So, when you divide 7 by 9, the answer you get is 0.77777778. This decimal does not terminate (come to an end after a specific number of decimal spaces), instead it repeats. Specifically, the digit '7' repeats indefinitely, so we can say its a repeating decimal.
As an example, if you consider 1/2, when you divide 1 by 2 it gives 0.5, which is a decimal that terminates. However, in our case - when we divided 7 by 9 it gave us 0.77777778 which repeats, hence it is a repeating decimal, not a terminating decimal. This is the key difference between repeating and terminating decimals.
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solve for x in the equation is x^2-4x-9=29
Step 1. Move all terms to one side
[tex]x^2-4x-9-29=0[/tex]
Step 2. Simplify [tex]x^2-4x-9-29[/tex] to [tex]x^2-4x-38[/tex]
[tex]x^2-4x-38=0[/tex]
Step 3. Use the Quadratic Formula
[tex]x=\frac{4+2\sqrt{42} }{2} ,\frac{4-2\sqrt{42} }{2 }[/tex]
Step 4. Simplify solutions
[tex]x = 2 \sqrt{42,} 2-\sqrt{42}[/tex]
Let's solve your equation step-by-step.
[tex]x^{2}[/tex]−4x−9=29
Step 1: Subtract 29 from both sides.
[tex]x^{2}[/tex]−4x−9−29=29−29
[tex]x^{2}[/tex]−4x−38=0
Step 2: Use quadratic formula with a=1, b=-4, c=-38.
[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]x=\frac{-(-4)+-\sqrt({-4})^{2} -4(1)(-38)}{2(1)}[/tex]
[tex]x=\frac{4-+\sqrt{168}}{2}[/tex]
Answer:
[tex]x=2+\sqrt{42}[/tex] or x = -2 [tex]\sqrt{42}[/tex]
Henry can write 5 pages of his novel in 3 hours. At this rate how many pages can Henry write in 8 hours? Please help!
Divide 5 pages by 3 hours to fins how many pages he wrote in 1 hour:
5 pages / 3 hours = 1 2/3 pages per hour.
Multiply 1 2/3 pages per hour by total hours to find total pages.:
1 2/3 x 8 = 13 1/3 pages (13.33)
Please help 20 points. Explain.
We can write this line in y-intercept form, and then solve to convert it to standard form.
Y = mx + b
m = slope
b = y-intercept
Y = -1/4x - 2 is the slope-intercept form of the equation.
Now, we can convert this to standard form.
Add 2 to both sides.
y + 2 = -1/4x
Subtract y from both sides.
-1/4x - y = 2
Multiply all terms by -4.
x + 4y = -8 (This is your answer.)
A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 16 and three fourths bushels each day. Represent the total change in the number of bushels she has for sale after 5 days.
To find the total change in the number of bushels the farmer has for sale after 5 days, multiply the average number of bushels sold per day by the number of days.
Explanation:To find the total change in the number of bushels the farmer has for sale after 5 days, we need to multiply the average number of bushels sold per day by the number of days.
The average number of bushels sold per day is 16 and three fourths, which can be written as 16.75.
Multiplying 16.75 by 5 gives us the total change in bushels after 5 days, which is 83.75 bushels.
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6. Which type of angle pair are LSM and OSN?
A. Adjacent angles
B. Linear pair
C. Complementary angles
D. Vertical angles
7. Which of the following statements are false?
A. LSM and MSN are adjacent angles
B. LSM and MSN form a linear pair of angles
C. LSM and MSN are vertical angles
D. M
8. Which angle is supplementary to LSM?
A. OSN
B. SLM
C. LMS
D. MSN
6. These angles are vertical angles, so D. is the correct answer!
7. These angles are not vertical angles, although I don't know what D. is....
8. D) MSN is the correct answer
a^2-2ab-6by+ay
Factor the expression
Factor a^2−2ab−6by+3ay
a^2−2ab+3ay−6by
=(a−2b)(a+3y)
Answer:
(a−2b)(a+3y)
the factored expression is:
a(a + y) - 2b(a + 3y)
We can factor the expression [tex]a^2-2ab-6by+ay[/tex] using a combination of grouping and factoring by difference of squares:
We can group the terms based on common factors:
[tex](a^2 + ay) - (2ab + 6by)[/tex]
In the first group, a is the common factor: a(a + y)
In the second group, 2b is the common factor: 2b(a + 3y)
Then we combine the terms
a(a + y) - 2b(a + 3y)
Therefore, the factored expression is:
a(a + y) - 2b(a + 3y)
4-5 of the money collected from a fundraiser was dived equally among 8 grades.What fraction of money did each grade receive
If you are just dividing percent's, then each grade would have 12.5 percent.
Evaluate
12x−3y
12x−3y
when
x=−
1
4
x=−14
and
y=3
y=3
.
12x - 3y
Put the values of x = -14 and y = 3 to the expression:
12(-14) - 3(3) = -168 - 9 = -177
A 13.5-gasoline tank is 4 / 5 full how many gallons will it take to fill the tank
Y=1/2x + 3/4
Select all of the points that are contained in the graph of the equation. There may be more than one.
(0, 1/2)
(0, 3/4)
(3/4, 0)
(3/4, 1/2)
(1/2, 1)
to test the points, substitute the x-coordinate into the equation and if the value of y equals the y-coordinate then the point lies on the graph
(0, [tex]\frac{1}{2}[/tex]) → y = 0 + [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]
(0 , [tex]\frac{3}{4}[/tex]) → y = [tex]\frac{3}{4}[/tex] ← on graph
([tex]\frac{3}{4}[/tex], 0) → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ 0
([tex]\frac{3}{4}[/tex],[tex]\frac{1}{2}[/tex] → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]
([tex]\frac{1}{2}[/tex], 1) → y = [tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 1 ← on graph
the points (0, [tex]\frac{3}{4}[/tex]) and ([tex]\frac{1}{2}[/tex], 1) are on the graph
The points that are contained in the graph of the straight line y = (1/2)x + 3/4 are (0,3/4) and (1/2,1).
What is an equation?An equation describes that both sides of the variables and constants are in different forms but they are equal.
To determine if each given point is contained in the graph of the equation Y = (1/2)x + 3/4 we will put the values of x in the equation and determine the corresponding value of y.
When x = 0, y = (3/4).
When x = (3/4), y = 9/8.
When x = 1/2, y = 1.
So, the points that are contained in the graph Y = (1/2)x + 3/4 are (0,3/4), (1/2,1).
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Twelve skateboards have 48 wheels. What is the value of the ratio of skateboards to wheels, in simplest form?
ratio = 12 : 48 = 1 : 4 = [tex]\frac{1}{4}[/tex] as a fraction in simplest form
Yolanda spends 8 1/2 hour per month playing soccer how many hrs does she play in a year
Please anyone help me