I hope I am reading the problem right: The price of a mountain bike increased by 20% in the past year. The value is $150. What was the value of the mountain bike last year?
Let's simplify this. One year, there was this radical mountain bike that used to have an unsaid price, x. That year, that price of x increased by 20% more than it was before, or 120% times the original value. Because of that, it's now $150.
We can equation this.
1.20x = 150
x = 150/1.2
x = 125
The bike, I believe, cost $125 last year. Hope this helps!
Final answer:
To find the value of the mountain bike last year, we can use the concept of percentage increase and decrease.
Explanation:
To find the value of the mountain bike last year, we can use the concept of percentage increase and decrease. If the price of the bike increases by 20%, then the current value is 120% of the previous value.
To find the previous value, we can set up an equation: 120% of the previous value is equal to $150. Mathematically, this can be written as 1.2x = 150, where x is the previous value.
Solving the equation, we divide both sides by 1.2 to isolate x: x = $125. Therefore, the value of the mountain bike last year was $125.
I know that: the first term of the sequence is -2, and the fifth term is - 1/8 . What is the 2nd term, 3rd term 4th term do you know?
Solution
Here the first term = -2
5th term = -1/8
Now we have to find the common ratio (r)
Fifth term A5 = -1/8
-1/8 =[tex]a_{1} r^{4}[/tex]
Here [tex]a_{1} = -2[/tex]
Plug in [tex]a_{1} = -2[/tex] in the fifth term and find the value of r.
-1/8 = -2[tex]r^{4}[/tex]
[tex]r^{4} = \frac{-1/8}{-2}[/tex]
[tex]r^{4} = \frac{1}{16}[/tex]
Taking 4th root, we get
r = [tex]\frac{1}{2}[/tex]
Now let's find the second term.
[tex]a_{2} =[/tex] first term *r = -2 *1/2 = -1
2nd term = -1
3rd term = second term * 1/2 = -1 * 1/2 = -1/2
4th term = 3rd term *r = -1/2 *1/2 = -1/4
Thank you :)
The 2nd term is -1 , the 3rd term is [tex]\( -\frac{1}{2} \)[/tex], and the 4th term is [tex]\( -\frac{1}{4} \)[/tex].
To find the 2nd, 3rd, and 4th terms of the sequence, we need to determine the common ratio of the sequence since the given terms suggest it is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Let's denote the first term of the sequence as [tex]\( a_1 \)[/tex] and the common ratio as r. The n-th term of a geometric sequence can be found using the formula:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
Given:
[tex]\[ a_1 = -2 \] \[ a_5 = -\frac{1}{8} \][/tex]
We can use the fifth term to find the common ratio r by plugging in the values into the formula for the n-th term:
[tex]\[ a_5 = a_1 \cdot r^{(5-1)} \] \[ -\frac{1}{8} = -2 \cdot r^4 \] \[ r^4 = \frac{-2}{-8} \] \[ r^4 = \frac{1}{4} \] \[ r = \pm\sqrt[4]{\frac{1}{4}} \] \[ r = \pm\frac{1}{2} \][/tex]
Since we are dealing with a sequence where the terms are decreasing in absolute value and changing sign (from negative to positive), we choose the positive value for r:
[tex]\[ r = \frac{1}{2} \][/tex]
Now we can find the 2nd, 3rd, and 4th terms:
[tex]\[ a_2 = a_1 \cdot r^{(2-1)} = -2 \cdot \left(\frac{1}{2}\right)^1 = -1 \] \[ a_3 = a_1 \cdot r^{(3-1)} = -2 \cdot \left(\frac{1}{2}\right)^2 = -\frac{1}{2} \] \[ a_4 = a_1 \cdot r^{(4-1)} = -2 \cdot \left(\frac{1}{2}\right)^3 = -\frac{1}{4} \][/tex]
The final answer is:
[tex]\[ a_2 = -1, \quad a_3 = -\frac{1}{2}, \quad a_4 = -\frac{1}{4} \][/tex]
estimate 771 divided by 3.6
Final answer:
To estimate the division of 771 by 3.6, round 3.6 to 4 and divide 771 by 4 to get an approximate result of 192.75.
Explanation:
To estimate 771 divided by 3.6, we can round 3.6 to the nearest whole number, which is 4. The estimation calculation would then be 771 ÷ 4. Dividing 771 by 4 can be done by breaking down 771 into 760 + 11. Now, 760 ÷ 4 equals 190, and 11 ÷ 4 is approximately 2.75. Adding these two results, we get an estimated total of 192.75. Therefore, the estimated result of 771 ÷ 3.6 is approximately 192.75.
what is the midpoint of the horizontal line segment graphed below (-2,3) (10,3)
The midpoint of the given line segment with endpoints (-2, 3) and (10, 3) is (4, 3). Thus, the option B is correct.
To determine the midpoint of a line segment, we can use the midpoint formula.
The midpoint formula states that the midpoint coordinates of a line segment with endpoints [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are given by:
[tex]Midpoint = (\dfrac{(x_1 + x_2)} {2}, \dfrac{(y_1 + y_2)} { 2})[/tex]
As per the question, the endpoints of the line segment are (-2, 3) and (10, 3).
Using the given midpoint formula:
Midpoint = ((-2 + 10) / 2, (3 + 3) / 2)
Midpoint = (8 / 2, 6 / 2)
Midpoint = (4, 3)
Therefore, the midpoint of the line segment with endpoints (-2, 3) and (10, 3) is (4, 3).
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Keisha solved the following equation: 4x − 2x + 8 = 6(x + 4) Step Work Justification 1 2x + 8 = 6(x + 4) Combine like terms 2 2x + 8 = 6x + 24 Associative property of multiplication 3 −4x + 8 = 24 Subtraction property of equality 4 −4x = 16 Addition property of equality 5 x = −4 Division property of equality
4x - 2x + 8 = 6(x + 4) Given
(4x - 2x) + 8 = 6(x + 4)
2x + 8 = 6(x + 4) Combine like terms
2x + 8 = (6)(x) + (6)(4)
2x + 8 = 6x + 24 Distributive Property
2x - 6x + 8 = 6x - 6x + 24
-4x + 8 = 24 Subtraction Property of Equality
-4x + 8 - 8 = 24 - 8
-4x = 16 Subtraction Property of Equality
-4x : (-4) = 16 : (-4)
x = -4 Division Property of Equality
What is the solution of the equation when solved over complex numbers? x^2+27=0
the solution of the equation x²+27 = 0 is 3√3 i
What are real and imaginary roots ?
A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.
In other words real roots can be represented in a number line where as imaginary roots can not.
In order to determine the simplification, we have to know the rule of the imaginary numbers.
The imaginary numbers are the same than real numbers, but they add just one term more, which is :
√-1 = i
So, to implicate this term, we have to use the rules of the roots:
given equation is :
x²+27 = 0
solving for x by Subtracting 27 from both sides
x²+27 -27 = -27
x² = -27
To remove square root , take square root on both sides
√x² = √-27
x = √-27
The value of √-1 is 'i' therefore,
x = i√27
x =3√3 i
Therefore, The solution of the equation x²+27 = 0 is 3√3 i
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Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(x+6)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?
SHOW ALL WORK
Given dimensions of a rectangular garden are:
length = 2(x+6) feet
width = 3.5x feet
using the distributive property on length we get, length = 2x+12
Perimeter of a rectangle is 2(length+width)
So, P = 2(2x+12+3.5x)
Solving it we get,
P = 2(5.5x +12) ..............adding like terms
P = [tex](2\times5.5)+(2\times12)[/tex] .............multiplying and adding
P = 11x+24
So, perimeter is 11x+24 feet. This value of fencing will be needed.
Twenty-seven is the product of three and a number
It’s the product of three and nine.
A certain triangle has 30 angle and 60 angle which much be a true statement about the triangle
Answer:
D
Step-by-step explanation:
The longest side is twice as long as the shortest side because lets suppose I have a triangle that has vertices with angles 30 and 60, the last one has to be 90 because the total is 180 degrees. Now for a 30 60 triangle, if the hypotenuse has a length of 2, the following ratios will hold true for the other two sides. The side that shares the 90 degrees and 60 degrees corners will be of length 1 and the side that shares the 30 degrees and 90 degrees corners (vertices) will be of length sqrt(3). This is true all the time. In this case the correct answer is that the longest side is twice as long as the shortest side because the longest side is the hypotenuse with length 2 and the shortest side will be the one that shares the 90 degrees and 60 degrees corners and is of length 1.
Answer:
A
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!
What is an equation of the line that is parallel to y=3x−8 and passes through (1, 8) ?
Im pretty sure its y = 3x - 17
Which operation is NOT closed for polynomials?
A) add a trinomial to a trinomial
B) divide a binomial by a trinomial
C) multiply a binomial by a binomial
D) subtract a binomial from a trinomial
Answer:
Option B is the correct choice.
Step-by-step explanation:
Since we know that polynomials are closed under addition, subtraction and multiplication but not under division because division of two polynomials is not necessarily a polynomial.
Dividing a binomial by a trinomial will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.
Therefore, option B is the correct choice.
How would u do -6-(-1)=
The answer would be -5 because:
-6-(-1)
Keep Change Flip
-6 + 1
Different signs Subtract..so the answer would be 5 but then you add the negative to it because -6 is greater than the positive 1
put the following decimals in order from least to greatest 4.08; 4.3; 4.803; 4.038
Answer:
4.038 < 4.08 < 4.3 < 4.803
Step-by-step explanation:
We are given four decimal numbers and we have to arrange them in increasing order:
The numbers are 4.08, 4.3, 4.803, 4.038
The expanded form of these decimal numbers are:
[tex]4.08 = 4 + \displaystyle\frac{8}{100}[/tex]
[tex]4.3 = 4 + \displaystyle\frac{3}{10}[/tex]
[tex]4.803 = 4 + \displaystyle\frac{8}{10} + \displaystyle\frac{3}{1000}[/tex]
[tex]4.038 = 4 + \displaystyle\frac{3}{100} + \displaystyle\frac{8}{1000}[/tex]
Thus, the increasing order is:
4.038 < 4.08 < 4.3 < 4.803
Compare 4 x 10^6 and 2 x 10^7.
A) 2 x 10^7 is 7 times larger than 4 x 10^6
B) 2 x 10^7 is 6 times larger than 4 x 10^6
C) 2 x 10^7 is 5 times larger than 4 x 10^6
D) 2 x 10^7 is 3 times larger than 4 x 10^6
Answer:
C. [tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]
Step-by-step explanation:
We want to compare [tex]4\times 10^6[/tex] and [tex]2\times 10^7[/tex].
In order to determine how many times
[tex]2\times 10^7[/tex]
is larger than
[tex]4\times 10^6[/tex],
we need to divide [tex]2\times 10^7[/tex] by [tex]4\times 10^6[/tex] to obtain;
[tex]\frac{2\times 10^7}{4\times 10^6} =\frac{10}{2} =5[/tex]
Therefore we can see that;
[tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]
The correct answer is C.
I need help with those two questions.but it says to rename the numbers so yeah
Rachel earns $21 per day for 22a-22d select true or false for each statement
22a. False
22b. True
22c. True
22d. False
For each scenario, we multiply Rachel's daily earnings ($21) by the number of days worked to find her total earnings.
In 22a, Rachel earns 21 × 20 = $420, not $421 as stated.
In 22b, Rachel indeed earns 21 × 15 = $315, making the statement true.
Similarly, in 22c, Rachel earns 21 × 13 = $273, confirming the statement as true.
However, in 22d, Rachel's earnings for 13 days amount to 21 × 13 = $273, not $250, rendering the statement false.
Therefore, the true statements are 22b and 22c, while 22a and 22d are false.
Complete Question:
Write the equation of the line in slope intercept form that passes through the points (-1,1) and (2,13)
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, 1) and (2, 13). Substitute:
[tex]m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4[/tex]
Therefore the equation of a line is
[tex]y=4x+b[/tex]
Put the coordinates of the point (2, 13) to the equation of a line:
[tex]13=4(2)+b[/tex]
[tex]13=8+b[/tex] subtract 8 from both sides
[tex]5=b\to b=5[/tex]
Answer: y = 4x + 5A function follows the rule y = -75 - 5 x . When the function's output is 25, the equation is 25 = -75 - 5 x . What is the function input when the output is 25? 20 -20 10 -10
Answer: C. -20
Hope this helps!! Please mark me brainliest??
PLEASE HELP ITS REALLY EASY
12*7 = 84
84 Pumpkin Plants
The variable, usually on the x-axis, which is used to predict y-values, is called the ____ variable. It is also sometimes called the explanatory variable.
Answer: Independent variable
Step-by-step explanation:
The variable usually on the x-axis, which is used to predict y-values, is called the Independent variable.
Discussion:
In most mathematical relations including linear programming problems; we usually have a combination of two variables namely;
Dependent andIndependent variableThe variable whose value determines the value of other variables is termed the independent variable and is usually plotted on the x-axis.
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Britt has 4 full boxes plus 12 extra CDs, and Jim has 3 full boxes and 5 extra CDs. If the number of CDs in each box is represented by c, Write an expression that shows the total number of CDs that Britt and Jim have.
This is actually quite easy.
Britt=4c+12 because 4 boxes and 12 extra
Jim=3c+5 because 3 boxes and 5 extra
Final answer:
The total number of CDs that Britt and Jim have is represented by the expression 7c + 17, where c is the number of CDs in each full box.
Explanation:
The total number of CDs that Britt and Jim have can be expressed using the variable c, which represents the number of CDs in each full box. Britt has 4 full boxes and 12 extra CDs, so her total is given by the expression 4c + 12. Jim has 3 full boxes plus 5 extra CDs, so his total is 3c + 5. To find the combined total number of CDs for both Britt and Jim, we add their individual totals:
Total CDs = Britt's CDs + Jim's CDs
Total CDs = (4c + 12) + (3c + 5)
By combining like terms, we get:
Total CDs = 7c + 17
This expression represents the total number of CDs that Britt and Jim have together in terms of c, the number of CDs per box.
I need this today ASAP!!!!
-4 1/2 + 1/3
The answer of this expression is - 4 1/6
A chain 5 links long is joined to a chain 7 links long. How many links long is the resulting chain
12 links long because 5 + 7 = 12
I really need help on this one
definition of parallelogram
∠2
∠3
transitive property of congruence
he coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .
What is the perimeter of the polygon?
Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
Answer: The perimeter is 17.52
Step-by-step explanation:
1. You can plot the points, as you can see in the graph attached.
2. As you can see in the graph, the points are:
[tex]A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)[/tex]
And the lenghts AB and EA are:
[tex]AB=5[/tex]
[tex]EA=2[/tex]
3. To find the other lenghts, you can apply the formula for calculate the distance between two points:
[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
4. Thefore, you have:
[tex]BC=\sqrt{(2-(-2))^{2}+(4-3)^{2}}=4.12\\CD=\sqrt{(2-3)^{2}+(4-1)^{2}}=3.16\\DE=\sqrt{(3-0)^{2}+(1-(-2))^{2}}=4.24[/tex]
5. The perimeter is:
[tex]P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52[/tex]
The perimeter of the polygon is 18.64 units.
Explanation:To find the perimeter of a polygon, we need to sum the lengths of all its sides. Let's calculate the distance between each consecutive pair of vertices and add them up.
The distance between (-2, -2) and (-2, 3) is 5 units.
The distance between (-2, 3) and (2, 4) is 4.24 units (rounded to the nearest tenth).
The distance between (2, 4) and (3, 1) is 3.16 units (rounded to the nearest tenth).
The distance between (3, 1) and (0, -2) is 4.24 units (rounded to the nearest tenth).
The distance between (0, -2) and (-2, -2) is 2 units.
Adding up these distances, the perimeter of the polygon is 5 + 4.24 + 3.16 + 4.24 + 2 = 18.64 units (rounded to the nearest tenth).
what the missing number
the answer is -4
hope it helpsss
5^-4 is 5 to power of negative 4
Two Algebra Questions! Help!
1) Divide 8x4 – 6x3 + 7x2 – 11x +10 by 2x – 1 using long division. Show all work. Then explain if 2x – 1 is a factor of the dividend.
2) Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely. Show all work for finding the factors. Sketch the graph by hand, use the graph below, label at least 6 points on the graph. State the factors and the roots. (Hint: two of your factors will be complex
ANSWER TO QUESTION 1
Check attachment for long division.
From our long division we can write the following;
[tex]\frac{8x^4-6x^3+7x^2-11x+10}{2x-1} =4x^3-x^2+3x-4+\frac{6}{2x-1}[/tex]
Since the polynomial
[tex]8x^4-6x^3+7x^2-11x+10[/tex] leaves a non zero remainder of [tex]6[/tex] when divided by [tex]2x-1[/tex], we conclude that [tex]2x-1[/tex] not a factor of the dividend,
ANSWER TO QUESTION 2
We want to factor
[tex]f(x)=x^4+x^3-8x^2+6x+36[/tex]
The possible rational roots are;
[tex]\pm1, \pm 2,\pm 3, \pm 4,\pm 6,\pm 9, \pm18, \pm 36[/tex]
We found
[tex]f(-2)=(-2)^4+(-2)^3-8(-2)^2+6(-2)+36[/tex]
[tex]f(-2)=16+-8-32+-12+36[/tex]
[tex]f(-2)=-36+36[/tex]
[tex]f(-2)=0[/tex]
and
[tex]f(-3)=(-3)^4+(-3)^3-8(-3)^2+6(-3)+36[/tex]
[tex]f(-3)=81-27-72-18+36[/tex]
[tex]f(-3)=-36+36[/tex]
[tex]f(-3)=0[/tex].
This means that [tex](x+2)[/tex] and [tex](x+3)[/tex] are factors of the polynomial.
This also means that
[tex](x+2)(x+3)=x^2+5x+6[/tex] is also a factor of the polynomial
So we apply long division to obtain the remaining factors as shown in the attachment.
[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x^2-4x+6)[/tex]
We factor further to obtain;
[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x-(2-\sqrt{2}i))(x-(2+\sqrt{2}i))[/tex]
A building company used 24 workers to prepare a building site. The site measured 30 acres and the work was completed in 10 days.
a) The company is asked to prepare another site measuring 45 acres. The company must complete the work on the new site in 12 days. How many extra workers must they use if they are to meet the deadline?
b) What assumption have you made in your calculations? How does this affect your answers?
Answer:
30 workers are required.
Step-by-step explanation:
If the site measured 30 acres and was completed in 10 days, then it can be said that on average [tex]\frac{30}{10} = 3\frac{acres}{day}[/tex] were made.
Then, 24 workers completed 3 acres / day.
Then, [tex]\frac{24.workers}{\frac{3acres}{day}} = \frac{8..Workers * days}{acre}[/tex]
8 workers can complete 1 acre per day
Now to know how many workers are needed to complete 45 acres in 12 days, we multiply:
[tex]8\frac{Workers * days}{acre}*\frac{45}{12} \frac{acres}{days} = 30.workers[/tex].
Finally, 30 workers are required.
To solve this problem it was assumed that everyone worked at the same pace, which may not be true, the fact that some work at a slower or faster pace than another could alter the result, causing them to finish less or more acres by day.
What is. 15% of 35 plz answer thank u
Fifteen of thirty-five is 5.25
it would be 5.25 because how to do a percent of something is to change it to a decimal. 15% = .15 so .15 x 35 = 5.25 :) hope this helps
what are the solutions of the inequality (x-3)(x+5)<=0
Assuming that the inequality you were going for was a ≤, set both polynomials less than or equal to 0.
x - 3 ≤ 0
x + 5 ≤ 0
For the first equation add 3 to both sides of the inequality. For the second, subtract 5 from both sides.
x ≤ 3
x ≤ - 5
These would be your solutions I guess, however, if you want to expand upon that, your actual answer is (- ∞, - 5] because if you were to plot these two inequalities on a number line, that is where the overlap would occur.
PLEASE HELP ASAP!!! GIVING 20 POINTS AND BRAINLIEST!!!!
If one gallon is the same amount as 16 cups, how many cups equal 2.5 gallons? (Only input whole numbers.)
Answer: 40 cups
If you have 2.5 gallons and need to convert it to cups, you first need to know how these two units of liquid volume compare to each other in size.
There are 16 customary cups in one gallon. To find how many cups are in 2.5 gallons, you'd multiply 2.5 (the number of gallons you have) by 16 (the number of cups in one gallon).
2.5 x 16 equals 40. This tells you that 2.5 gallons is equivalent to 40 cups
Question: If one gallon is the same amount as 16 cups, how many cups equal 2.5 gallons? (Only input whole numbers.)
Explantion: 16(number of cups per gallon)×2.5(amount of gallons)
The equation would be [tex]16*2.5[/tex] and that equals 40.
Answer: 40 cups