Answer: y = -3x + 8
Step-by-step explanation:
The formula for finding equation of line when two points are given is :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 1
[tex]x_{2}[/tex] = -2
[tex]y_{1}[/tex] = 5
[tex]y_{2}[/tex] = 14
Substituting the values , we have
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{14-5}{-2-1}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{9}{-3}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{-3}{1}[/tex]
y-5 = -3(x-1)
y -5 = -3x + 3
writing the equation in slope - intercept form , we will make y the subject of the formula:
y = -3x + 3 + 5
y = -3x + 8
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.
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]
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]
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
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.
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]
If c (x) = StartFraction 5 Over x minus 2 EndFraction and d(x) = x + 3, what is the domain of (cd)(x)?
all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3
Answer:
The domain of the function (cd)(x) will be all real values of x except x = 2.
Step-by-step explanation:
The two functions are [tex]c(x) = \frac{5}{x - 2}[/tex] and d(x) = x + 3
So, (cd)(x) = [tex](\frac{5}{x - 2})(x + 3) = \frac{5(x + 3)}{x - 2}[/tex]
Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.
Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)
Answer:
the answer is b on edg2020
Step-by-step explanation:
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.
How to solve 7+3=4+_
Answer: 7+3=4+6
Step-by-step explanation: 7+3=10 and so does 4+6
In a direct proportion y = kx, the number k is called the constant of ______.
Answer:
Proportionality
Step-by-step explanation:
Before he went shopping, Andy had $28. After he cashed a check, he had more than $75. What is the amount of the check Andy cashed?
Answer:
$47
Step-by-step explanation:
Andy's initial amount was $28.
The question is on subtraction. It is meant to understand your capacity on worded form of subtraction.
After Andy cashed the cheque, his amoussou rose from $28 to $75.
Therefore, to know the amount on the cheque we subtract the initial amount from the total amount.
$75 - $28 = $47
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.
Write the ratio 36:56 in its lowest terms
I need to know this answer
Answer:
r = 7
Step-by-step explanation:
Given
r + 15 = 4r - 6 ( subtract 4r from both sides )
- 3r + 15 = - 6 ( subtract 15 from both sides )
- 3r = - 21 ( divide both sides by - 3 )
r = 7
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
whats the area of 3,0 3,9 8,9 8,0 in units
Answer:2
Step-by-step explanation:
-610 minus positive 185
Answer: -425
Step-by-step explanation:
An inscribed angle of circle T has a measure of 36°. Determine the measure of the intercepted arc?
A. 72
B. 6
C. 36
D. 18
Answer:
A
Step-by-step explanation:
An inscribed angle of circle T has a measure of 36°.
The cantral angle subtended on the same arc as this inscribed angle has the measure twice greater than inscribed angle, so the measure of the central angle is
[tex]36^{\circ}\cdot 2=72^{\circ}[/tex]
The measure of the intercepted arc (at which angles are subtended) is the same as the measure of the central angle, so correct option is option A
Answer:
a is the answer
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.
disjoint subsets A and B of a universal set U, except assume that n(U)=120, n(A)=45, and n(B)=50.
Then n(A′∪B)=
Answer:
n (A' U B ) = 75
Step-by-step explanation:
Here, given : n(U)=120, n(A)=45, and n(B)=50
As we know:
n (A ' U B) = n(A) − n (A∩B) ... (1)
Here, n(A) = 45
So, n( A') = n(U) - n(A) = 120 - 45 = 75
⇒ n(A') = 75
Now, as given A and B are disjoint sets.
⇒ n (A ∩ B) = Ф
So, (A' U B ) = A'
So, n (A' U B ) =n( A') = 75
⇒ n (A' U B ) = 75
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 $3.34
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answer:
8 and 5
Step-by-step explanation:
The sum of 8 and 5 implies
8 + 5 = 13
The difference between 8 and 5 implies:
8 - 5 = 3
Therefore, the sum of two numbers that gives 13 and their difference being 3 are 8 and 5.
Sarah inherited a sum of 1,539 dollars with an interest rate of 1% per year what is the accrued value after 5 years, 10 years, and 15 years. Show all work. any help would be great.
Answer:
See explanation
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest,
P = principal,
r = rate (as decimal),
t = time
In your case,
[tex]P=\$1,539\\ \\r=0.01[/tex]
If [tex]t_1=5[/tex] years, then
[tex]I_1=1,539\cdot 0.01\cdot 5=76.95[/tex] and the whole sum is [tex]\$1,539+\$76.95=\$1,615.95[/tex]
If [tex]t_2=10[/tex] years, then
[tex]I_2=1,539\cdot 0.01\cdot 10=153.9[/tex] and the whole sum is [tex]\$1,539+\$153.9=\$1,692.9[/tex]
If [tex]t_3=15[/tex] years, then
[tex]I_3=1,539\cdot 0.01\cdot 15=230.85[/tex] and the whole sum is [tex]\$1,539+\$230.85=\$1,769.85[/tex]
What expression is equivalent to (3g)1/3
Answer:
g
Step-by-step explanation:
it asks u to multiply 3g and 1/3, going u one third of 3g, resulting in g
help me on geometry??
Answer:
15. ∠ABE = 50°
16. ∠EBD = 10n - 19
Step-by-step explanation:
If [tex]$ \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.
Which equation can be simplified to find the inverse of y = x2 – 7? x = y squared minus one-seventh StartFraction 1 Over x EndFraction = y squared minus 7 x = y2 – 7 –x = y2 – 7
Answer:
x = y^2 – 7
Step-by-step explanation:
The first step in finding the inverse of y = f(x) can be to write the equation x = f(y). The equation shown above is such an equation.
Answer:
[tex]x= y^2-7[/tex]
Step-by-step explanation:
We have been given an equation [tex]y=x^2-7[/tex]. We are asked to determine that which equation can be simplified to find the inverse of our given equation.
We know that to find inverse of an equation, the x and y-values are interchanged.
Let us interchange x and y values for our given equation.
[tex]x= y^2-7[/tex]
Therefore, the equation [tex]x= y^2-7[/tex] can be simplified to find the inverse of our given equation.
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:
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.
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.
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
Learn more about percentage at:
brainly.com/question/10081622brainly.com/question/10341324#LearnwithBrainly