- 2a = - 20 | x (-)
2a = 20
a = 20 : 2
a = 10
Answer:
a=10
Step-by-step explanation:
-2a=-20
Divide -2 on each side. You should get a=10
Sarah inherited a sum of 1,539 dollars with an interest rate of 1% per year what is the accrued value after 5 years, 10 years, and 15 years. Show all work. any help would be great.
Answer:
See explanation
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest,
P = principal,
r = rate (as decimal),
t = time
In your case,
[tex]P=\$1,539\\ \\r=0.01[/tex]
If [tex]t_1=5[/tex] years, then
[tex]I_1=1,539\cdot 0.01\cdot 5=76.95[/tex] and the whole sum is [tex]\$1,539+\$76.95=\$1,615.95[/tex]
If [tex]t_2=10[/tex] years, then
[tex]I_2=1,539\cdot 0.01\cdot 10=153.9[/tex] and the whole sum is [tex]\$1,539+\$153.9=\$1,692.9[/tex]
If [tex]t_3=15[/tex] years, then
[tex]I_3=1,539\cdot 0.01\cdot 15=230.85[/tex] and the whole sum is [tex]\$1,539+\$230.85=\$1,769.85[/tex]
Brainliest!!!!!! Plz help !!!!
Using data for population in the District of Columbia, write an exponential model of the form a ∙ bx to estimate this population in the years after 2005.
A.) a ∙ bx = (550,521)(0.993)x
B.) a ∙ bx = (550,521)(0.990)x
C.) a ∙ bx = (550,521)(0.992)x
D.) a ∙ bx = (550,521)(0.991)x
Answer:
Its C Hope dis helps!!!
Step-by-step explanation:
Without the actual data, we cannot definitively decide the correct exponential model for the population of the District of Columbia. The options provided all share the same initial quantity, with different growth factors. To pick one, we would need data on the annual population growth or decline.
Explanation:The question is asking us to choose an exponential model of the form a ∙ bx that best represents the population of the District of Columbia for years after 2005. As we are not provided actual data on the population growth or decline, we can't definitively choose between the options. In this kind of model, a is the initial quantity (population in the year 2005), and b is the growth factor per the time period (in this case: annually). In all options provided we have the same initial quantity '550,521'. The difference is in the growth factors .993, .990, .992, and .991. Without the actual data, we cannot definitively pick one. However, if the population is declining each year, you'd expect the growth factor to be less than 1. In case if it's growing you'd expect it to be more than 1.
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1). 21 is what percent of 168. 4) what number is 62 percent of 50
2). What is 4 percent of 150. 5) 15 percent of 15 is what
3) 1 percent of 500 is what number 6) 40 percent of 25 is what number
1) 21 is 12.50% of 168.
2) 4% of 150 is 6.
3) 1% of 500 is 5.
4) 62% of 50 is 31.
5) 15% of 15 is 2.25
6) 40 percent of 25 is 10.
Step-by-step explanation:
1). 21 is what percent of 168.
Let,
x be the percent.
Therefore,
x% of 168 = 21
[tex]\frac{x}{100}*168=21[/tex]
[tex]1.68x=21[/tex]
Dividing both sides by 1.68
[tex]\frac{1.68x}{1.68}=\frac{21}{1.68}\\x=12.50[/tex]
21 is 12.50% of 168.
2). What is 4 percent of 150.
4% of 150 = [tex]\frac{4}{100}*150[/tex]
4% of 150 = [tex]\frac{600}{100} = 6[/tex]
4% of 150 is 6.
3) 1 percent of 500 is what number
1% of 500 = [tex]\frac{1}{100}*500[/tex]
1% of 500 is 5.
4) what number is 62 percent of 50
62% of 50 = [tex]\frac{62}{100}*50[/tex]
62% of 50 = [tex]0.62*50=31[/tex]
62% of 50 is 31.
5) 15 percent of 15 is what
15% of 15 = [tex]\frac{15}{100}*15[/tex]
15% of 15 = [tex]\frac{225}{100}=2.25[/tex]
15% of 15 is 2.25
6) 40 percent of 25 is what number
40% of 25 = [tex]\frac{40}{100}*25[/tex]
40% of 25 = [tex]\frac{1000}{100}=10[/tex]
40 percent of 25 is 10.
Keywords: percentage
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Which graph shows the result of dilating this figure by a factor 1/3 about the origin
Plot the vertices A'(-12, 9), B'(9, 3), and C'(6, -3) on the coordinate plane. Label them as A', B', and C', respectively.
To determine the coordinates of the dilated triangle A'B'C', we can follow these steps:
1. Find the coordinates of the original triangle's vertices: A(-4, 3), B(3, 3), and C(2, -1).
2. Dilate each vertex from the origin by a scale factor of 3. This means we will multiply the x and y coordinates of each vertex by 3.
- For vertex A: Multiply -4 by 3 to get -12 and multiply 3 by 3 to get 9. Therefore, the coordinates of A' are (-12, 9).
- For vertex B: Multiply 3 by 3 to get 9. The y-coordinate remains the same at 3. Therefore, the coordinates of B' are (9, 3).
- For vertex C: Multiply 2 by 3 to get 6 and multiply -1 by 3 to get -3. Therefore, the coordinates of C' are (6, -3).
3. Plot the vertices A'(-12, 9), B'(9, 3), and C'(6, -3) on the coordinate plane. Label them as A', B', and C', respectively.
Note: The original triangle ABC remains unchanged on the coordinate plane.
By following these steps, you will have successfully determined the coordinates of the dilated triangle A'B'C' and plotted it on the coordinate plane.
What is the percent of 47.382
Answer: 0.47382
Step-by-step explanation:
The percent of 47.382 is dividing the figure by 100%
47.382/100= 0.47382
What expression is equivalent to (3g)1/3
Answer:
g
Step-by-step explanation:
it asks u to multiply 3g and 1/3, going u one third of 3g, resulting in g
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answer:
8 and 5
Step-by-step explanation:
The sum of 8 and 5 implies
8 + 5 = 13
The difference between 8 and 5 implies:
8 - 5 = 3
Therefore, the sum of two numbers that gives 13 and their difference being 3 are 8 and 5.
Simplify 12x to the power of 7 y to the power of 3 divided by 6x to the power of 3 y
Answer:
2x⁴y²
Step-by-step explanation:
The question gives us the expression;
12x⁷y³ ÷ 6x³y
We are supposed to simplify the expression;
First we could divide the digits;
12 ÷ 6 = 2
Then we divide the like terms;
x⁷ ÷ x³
This means;
[tex]=\frac{x*x*x*x*x*x*x }{x*x*x}[/tex]
[tex]= x*x*x*x[/tex]
[tex]=x^4[/tex]
y³ ÷ y
That is;
[tex]=\frac{y*y*y}{y}[/tex]
[tex]=y*y[/tex]
[tex]=y^2[/tex]
Therefore, the simplified expression will be 2x⁴y²
In triangle DEF, DK is the angle bisector of angle EDF. If EK=2, FK=5, and DF=10, what is the length of DE?
Answer:
4 units
Step-by-step explanation:
In triangle DEF, DK is the angle bisector of angle EDF.
Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.
Hence,
[tex]\dfrac{DE}{DF}=\dfrac{EK}{KF}[/tex]
Thus,
[tex]\dfrac{DE}{10}=\dfrac{2}{5}\\ \\5DE=2\cdot 10\\ \\5DE=20\\ \\DE=4[/tex]
Raphael runs every day for a number of weeks. He runs for 35 days in a row. How many weeks did he run?
Answer:
2 weeks and 5 days
Step-by-step explanation:
Final answer:
Raphael ran for a total of 5 weeks, calculated by dividing the total number of days he ran (35 days) by the number of days in a week (7 days).
Explanation:
Raphael runs for 35 days in a row, and we need to calculate how many weeks he runs. A week consists of 7 days. To find out the number of weeks Raphael ran, we divided the total number of run days by the number of days in a week.
Number of weeks = Total run days / Days in a week = 35 / 7 = 5
Therefore, Raphael ran for 5 weeks, illustrating the duration of his consistent running routine in terms of weeks. This computation provides a clear understanding of the duration of Raphael's running streak in a familiar time frame, aiding in tracking and planning his exercise regimen.
In a direct proportion y = kx, the number k is called the constant of ______.
Answer:
Proportionality
Step-by-step explanation:
Write the ratio 36:56 in its lowest terms
help me on geometry??
Answer:
15. ∠ABE = 50°
16. ∠EBD = 10n - 19
Step-by-step explanation:
If [tex]$ \overline{\textbf{BE}} $[/tex] bisects ∠ABD then we have ∠ABE = ∠DBE
So, we will have: (6x + 2)° = (8x - 14)°
⇒ 6x + 2 = 8x - 14
⇒ 8x - 6x = 14 + 2
⇒ 2x =16
⇒ x = 8
∴ ∠ABE = 6(8) + 2
= 48 + 2
= 50°
∴∠ABE = 50°
16. If [tex]$ \overline{\textbf{BE}} $[/tex] bisects ∠ABD then ∠ABE + ∠EBD = ∠ABD
⇒(12n - 8) + ∠EBD = (22n - 11)
⇒ ∠EBD = 22n - 11 - 12n + 8
⇒ ∠EBD = 10n - 3
Hence, the answer.
A number added to its reciprocal is 2 9/10. Find the number and show your work.
Answer:
[tex]\displaystyle x=\frac{5}{2}, x=\frac{2}{5}[/tex]
Step-by-step explanation:
Quadratic Equations
The quadratic equation has the following general form
[tex]ax^2+bx+c=0[/tex]
It can be solved by several methods, including the well-known quadratic formula
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The question requires us to find a number that added with its reciprocal results 2 9/10. If x is the required number
[tex]\displaystyle x+\frac{1}{x}=2\ \frac{9}{10}=\frac{29}{10}[/tex]
Operating
[tex]\displaystyle \frac{x^2+1}{x}=\frac{29}{10}[/tex]
Rearranging
[tex]10(x^2+1)=29x[/tex]
[tex]10x^2-29x+10=0[/tex]
Comparing with the general quadratic equation, we have
[tex]a=10,\ b=-29,\ c=10[/tex]
Using the formula
[tex]\displaystyle x=\frac{29\pm \sqrt{(-29)^2-4(10)(10)}}{2(10)}[/tex]
[tex]\displaystyle x=\frac{29\pm \sqrt{441}}{20}=\frac{29\pm 21}{20}[/tex]
It gives us two possible solutions
[tex]\displaystyle \boxed{x=\frac{5}{2}, x=\frac{2}{5}}[/tex]
Both are valid solutions since
[tex]\displaystyle \frac{5}{2}+\frac{2}{5}=\frac{29}{10}[/tex]
Find midpoint (-6, 3) (4,-3)
Step-by-step explanation:
Given points are (-6,3) and (4,-3)
[tex]x_1=-6 ,[/tex] [tex]y_1=3[/tex] , [tex]x_2= 4[/tex] and [tex]y_2 = -3[/tex]
Coordinate of mid point [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
[tex]=(\frac{-6+4}{2} ,\frac{3+(-3)}{2})[/tex]
=(1,0)
In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year? (Round your answer to the nearest cent.)
Answer:
$3.34
Step-by-step explanation:
$1.39 x 2.4 = $3.336
Answer:
next year the cost of bread will rise to $3.34
Erica and her sister Laura are making baby blankets to sell at a boutique. Erica has already completed 10 blankets and can finish 6 more blankets per day. Laura has already completed 6 blankets and can finish 10 more blankets per day. At some point, they will have completed the same number of blankets. How many blankets will each woman have made? How long will that take?
Answer:
Laura and Erica will both have made 16 blankets in one more day.
Step-by-step explanation:
i) Erica has made 10 blankets already.
ii) Erica can make 6 blankets more per day
iii) Laura has completed 6 blankets already
iv) Laura can complete 10 more blankets per day.
v) Let x be the number of days to the point when they will have completed the same number of blankets
vi) Therefore the number of blankets that Erica makes till x days is = to the number of blankets that Laura makes till x days
vi) therefore 10 + 6x = 6 + 10x ⇒ 4x = 4 ⇒ x = 1 day
vii) Therefore Laura and Erica will both have made 16 blankets in one more day.
Joshua’s annual salary from eagle fork mining is $3400. What percent of Joshua‘s monthly salary is used for monthly apartment rent of $105
How to solve 7+3=4+_
Answer: 7+3=4+6
Step-by-step explanation: 7+3=10 and so does 4+6
What is the true solution to the equation below
Answer:
C I think
Step-by-step explanation:
yeyeye
Answer:
[tex]x_{1}[/tex] = 1, [tex]x_{2}[/tex] = 4, so your answer is C
Step-by-step explanation:
-610 minus positive 185
Answer: -425
Step-by-step explanation:
Is 57 a prime number
For 57 to be a prime number, it would have been required that 57 has only two divisors, i.e., itself and 1. However, 57 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 57 = 3 x 19, where 3 and 19 are both prime numbers.
Answer: No
Step-by-step explanation: For 57 to be a prime number, it would have been required that 57 has only 2 divisors, ie itself and 1. How ever 57 is a semiprime because it is the product of a two non- necessarily distinct prime numbers. inderd, 57= 3×19, where 3 and 19 are prime numbers.
What is the x-intercept of
x + 9y = 1
People leaving a movie theater were asked to name their favorite type of movie. The circle graph shows the percent of people surveyed who preferred each type of movie.
Of the people surveyed, 27 said that science fiction is their favorite type.
How many people were surveyed in all?
Enter your answer in the box.
A pie chart depicting movie genres. Comedy is at 33 percent, Action is at 19 percent, Adventure is at 13 percent, Drama is at 10 percent, Suspense is at 7 percent, and Science Fiction is at 18 percent.
Answer:
The number of persons surveyed leaving a movie theater is 150.
Step-by-step explanation:
Science fiction 18% or 0.18 = 27 persons surveyed.
Total of persons surveyed = 2,700/18
Total of persons surveyed = 150
The number of persons surveyed leaving a movie theater is 150.
Answer:
150 people were surveyed.
6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent?
After 28 years, there will be approximately $48,505.29 in the account.
To calculate the amount of money that will be in the account after 28 years with an annual interest rate of 8.25%, we can use the formula for compound interest:
[tex]\[ A = P \times (1 + r)^n \][/tex]
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money), which is $6700 in this case.
- r is the annual interest rate (in decimal form), which is 8.25% or 0.0825.
- n is the number of years, which is 28 in this case.
Plugging in the values into the formula:
[tex]\[ A = 6700 \times (1 + 0.0825)^{28} \][/tex]
Calculating the value:
[tex]\[ A = 6700 \times (1.0825)^{28} \][/tex]
[tex]\[ A \approx 6700 \times 7.2417 \][/tex]
[tex]\[ A \approx 48,505.29 \][/tex]
5x=7y, X+7Y=21 how do u solve this by elemination
Answer:
The values are [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])
Step-by-step explanation:
Given equations are [tex]5x=7y\hfill (1)[/tex] and
[tex]x+7y=21\hfill (2)[/tex]
To solve the given equations by elimination method:
Equation (1) can be written as [tex]5x-7y=0\hfill (3)[/tex] and
Now multiply the equation (2) into 5 we get
[tex]5x+35y=105\hfill (4)[/tex]
Subtracting equations (3) and (4) we get
[tex]5x-7y=0[/tex]
[tex]5x+35y=105[/tex]
_________________
-42y=-105
[tex]y=\frac{105}{42}[/tex]
Therefore [tex]y=\frac{5}{2}[/tex]
Substitute the value [tex]y=\frac{5}{2}[/tex] in equation (1) we get
[tex]5x=7\times \frac{5}{2}[/tex]
[tex]5x=\frac{35}{2}[/tex]
[tex]x=\frac{35}{2\times 5}[/tex]
[tex]x=\frac{7}{2}[/tex]
Therefore [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])
I NEED HELP ON THIS QUESTION ASAP
Answer:
(2.5, -.25)
Step-by-step explanation:
I'm not positive that I know exactly what they want on this one....but since you specifically asked me to look at your other question, I tried.
See pic.
What is the length of HL ?
Answer:
21
Step-by-step explanation:
You know the length of JK 12
you also know the length of GF 2.5*12=30
HL is a mid segment because it cuts both legs it intersects in half.
Using the rule saying that the mid segment is half the bases added up we can figure out that HL = (12+30)/2 = 21
Answer:
21
Step-by-step explanation:
Find attached the solution
Describe how to solve the inequality 3x+4<13 using algebra tiles
The solution is x < 3.
Solution:
The given expression is 3x + 4 < 13.
To solve the given inequality.
3x + 4 < 13
Subtract 4 tiles on both sides of the inequality.
⇒ 3x + 4 – 4 < 13 – 4
⇒ 3x < 9
Divide by 3 tiles on both sides of the inequality.
⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ x < 3
Hence the solution is x < 3.
Final answer:
To solve the inequality using algebra tiles, represent 3x+4 with tiles on one side and 13 units on the other, remove 4 units from both sides to get 3x < 9 and then divide the remaining 9 units into 3 groups to find x < 3.
Explanation:
To solve the inequality 3x+4<13 using algebra tiles, we follow these steps:
Start by representing the inequality with algebra tiles. Place 3 x-tiles (each representing 'x') and 4 unit tiles (each representing '1') on one side of a mat to model the expression 3x+4.
On the other side, place 13 unit tiles to represent the number 13.
To isolate the variable x, we need to remove the same number of unit tiles from each side. Remove 4 unit tiles from each side of the mat, which corresponds to Subtracting 4 from both sides of the inequality.
After removal, the inequality on the mat now shows 3x tiles on one side and 9 unit tiles on the other, representing the inequality 3x < 9.
Lastly, to find the value of one x-tile, divide the remaining unit tiles into 3 equal groups. Since there are 9 units left, each group will consist of 3 unit tiles, indicating that each x-tile is less than 3. This gives us the final inequality x < 3.
From this process, we've determined that for the original inequality 3x+4<13, the solution is x<3.
What are fractions greater than 1/2 but less than one
We know that 1/2 as a decimal is 0.5. Any decimal/fraction between 0.5 and 1 will be correct. For Example, 0.75 is greater than 0.5 but less then 1. 0.75 as a fraction is 3/4.
Best of Luck!