Answer:
therefore for direct variation that will include the point (4, 16) is y = 4x
Step-by-step explanation:
i) for direct variation we can say that y = k [tex]\times[/tex] x
ii) substituting the given values of x and y into the equation in i) we get
16 = k [tex]\times[/tex] 4
Therefore k = [tex]\frac{16}{4}[/tex] = 4
iii) therefore for direct variation that will include the point (4, 16) is y = 4x
The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle?
The area of the rectangle is 300 square inches, calculated by multiplying the length (20 inches) by the width (15 inches).
To find the area of the rectangle, we can use the formula for the area of a rectangle, which is [tex]\( \text{length} \times \text{width} \).[/tex] However, we need to find the length of the rectangle first.
We are given that the width of the rectangle is 15 inches. Let's denote the length of the rectangle as [tex]\( l \).[/tex]
We know that the diagonal of a rectangle forms a right triangle with the length and width of the rectangle. Therefore, we can use the Pythagorean theorem to find the length of the rectangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides (the length and the width).
So, we have:
[tex]\[ l^2 + 15^2 = 25^2 \][/tex]
Solving for[tex]\( l \):\[ l^2 = 25^2 - 15^2 \]\[ l^2 = 625 - 225 \]\[ l^2 = 400 \][/tex]
Taking the square root of both sides:
[tex]\[ l = \sqrt{400} \]\[ l = 20 \][/tex]
Now that we have found the length of the rectangle to be 20 inches, we can calculate the area:
[tex]\[ \text{Area} = \text{length} \times \text{width} \]\[ \text{Area} = 20 \times 15 \]\[ \text{Area} = 300 \, \text{square inches} \][/tex]
So, the area of the rectangle is 300 square inches.
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 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
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]
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]
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.
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
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
Write the ratio 36:56 in its lowest terms
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:
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.
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.
Type the correct answer in the box
c = cost of food/med for cats
d = cost of food/med for dog
y = total cost/spent
What you know:
y = 6c + d [has 6 cats and 1 dog]
c = 2/3d - 5 [cost for cat is 5 less than 2/3 cost for dog]
y = $195
y = 6c + d
Substitute/plug in what you know, plug in (2/3d - 5) for c and 195 for y
195 = 6(2/3d - 5) + d Distribute/multiply 6 into (2/3d - 5)
195 = 4d - 30 + d Combine like terms
195 = 5d - 30 Add 30 on both sides of the equation
225 = 5d Divide 5 on both sides
$45 = d
disjoint subsets A and B of a universal set U, except assume that n(U)=120, n(A)=45, and n(B)=50.
Then n(A′∪B)=
Answer:
n (A' U B ) = 75
Step-by-step explanation:
Here, given : n(U)=120, n(A)=45, and n(B)=50
As we know:
n (A ' U B) = n(A) − n (A∩B) ... (1)
Here, n(A) = 45
So, n( A') = n(U) - n(A) = 120 - 45 = 75
⇒ n(A') = 75
Now, as given A and B are disjoint sets.
⇒ n (A ∩ B) = Ф
So, (A' U B ) = A'
So, n (A' U B ) =n( A') = 75
⇒ n (A' U B ) = 75
help me on geometry??
Answer:
15. ∠ABE = 50°
16. ∠EBD = 10n - 19
Step-by-step explanation:
If [tex]$ \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.
whats the area of 3,0 3,9 8,9 8,0 in units
Answer:2
Step-by-step explanation:
What does 22 divided by 3 plus 1 equal?
Answer:
8.33
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:
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
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.
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.
-610 minus positive 185
Answer: -425
Step-by-step explanation:
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 a direct proportion y = kx, the number k is called the constant of ______.
Answer:
Proportionality
Step-by-step explanation:
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.
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.
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]
A circle with circumference 6 has an arc with a 20 central angle,
What is the length of the arc?
Answer:
0.3 units
Step-by-step explanation:
The ratio of the length of the arc to the circumference of the circle is proportional to the ratio of the central angle to the sum of angle in a circle.
[tex]\frac{l}{6}=\frac{20}{360}[/tex]
This implies that:
[tex]l=\frac{20}{360}*6[/tex]
This simplifies to: [tex]l=\frac{20}{60}[/tex]
[tex]l=\frac{1}{3}=0.3 units[/tex]
Since the circumference of this circle is 6 units, the length of the arc formed is equal to 0.33 units
Given the following data:
Circumference = 6 units.
Central angle = 20°
How to calculate the length of the arc.Mathematically, if you want to determine the length of the arc formed by a circle, you will divide the angle subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle as follows:
20/360 × 6 = 0.33 units.
Read more on circumference here: brainly.com/question/14478195
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.
How to solve 7+3=4+_
Answer: 7+3=4+6
Step-by-step explanation: 7+3=10 and so does 4+6