Determine which statement is incorrect and explain why it is incorrect.
You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.
The hypotenuse is the longest side in a right triangle.
You can solve for the unknown angle of any right triangle, if you know the lengths any two sides, by using inverse trigonometric functions.
If you are given a right triangle and you know that one angle is 30 degrees, then the other angle must be 60 degrees..
Answers
The incorrect statement is that You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Pythagoras theorem is only applied for right angled triangles.
There is hypotenuse which is the longest side for only right angled triangles. So we cannot find the length of the third side of any triangle using the Pythagorean theorem.
Hence the statement that you can solve for any triangle's unknown side using the Pythagorean theorem is incorrect.
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Related Questions
2 1/2 yards into inches
Answers
1 yard = 36 inches
2 1/2 yards x 36 = 90 inches
Answer: 90 inches
There were 470 people at a play. The admission price was $3 for adults and $1 for children.
The admission receipts were $910. How many adults and how many children attended?
Answers
Answer:
220 adults and 250 children
Step-by-step explanation:
we require to set up 2 equations and solve simultaneously.
let a be the number of adults and c the number of children , then
a + c = 470 → (1) based on number of people
3a + c = 910 → (2) based on ticket sales
subtract (1) from (2) term by term to eliminate c
(3a - a) + (c - c) = 910 - 470
2a + 0 = 440
2a = 440 ( divide both sides by 2 )
a = 220
substitute a = 220 into (1) and solve for c
220 + c = 470 ( subtract 220 from both sides )
c = 250
that is 220 adults and 250 children attended
Find the value of x. You may assume triangle ABC is similar to triangle STU.
(click on the photo to make it better quality) PLEASE HELP!!!
Answers
By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.
In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.
Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:
angle BAC = angle STU
4x = 100
To find the value of x, we divide both sides of the equation by 4:
x = 100/4
x = 25
Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.
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What is the slope of line k?
Answers
Answer: Slope: 2/3
Step-by-step explanation:
2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answers
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
Dylan and Eric were the lead scorers in a basketball game. Dylan scored p points in the second period of the game. Eric scored as many points as Dylan in the same period of the game. a) Write an expression for Eric's score in terms of p. points b) If Dylan scored 18 points in the second period, how many points did Eric score?
Answers
I think the answers 3048_&8_9_)_)_
the 7th grade fundraiser gives away a large container of gumballs to the student who is closest to guessing the correct number of gumballs in the container noticing that the container is a cube. Sally decides to count the number of gumballs along the length of one side if Sally get 729 gumballs how many gumballs did she count along one side of the container
Answers
If the container is a cube, every side is a square, so the length and the width are the same.
To get the number of gumballs based on the number of gumballs in one side, we can use the following equation
\(TotalGumballs=x^3\)Where x is the number of gumballs along one side. So, replacing the total by 729 and solving for x, we get:
\(\begin{gathered} 729=x^3 \\ \sqrt[3]{729}=x \\ 9=x \end{gathered}\)Answer: She counts 9 gumballs along one side of the container
Can somebody please help me and tell me what the error is!! PLEASE I NEED HELP ELSE I WILL FAIL MY CLASS AND GO TO SUMMER SCHOOL SO PLESE HELP ME!
Answers
Answer:
I think that is enlargement
Step-by-step explanation:
i like helping out people oh by the way i'm new will you be my friend
Research has shown that approximately 1 woman in 500 Carrie’s a mutation of particular gene. About 48% of women with this mutation develop colon cancer find the probability that a randomly selected woman will carry the mutation of this gene and will develop colon cancer
Answers
Let's denote the probability of carrying the gene mutation as P(M) and the probability of developing colon cancer given the gene mutation as P(C|M). Given the information provided, P(M) can be calculated as 1 in 500, which is equivalent to 1/500.
The probability of developing colon cancer given the gene mutation is stated as 48%, which can be expressed as 0.48.
To find the probability of both events occurring, we multiply P(M) and P(C|M):
P(M and C) = P(M) * P(C|M) = (1/500) * 0.48
Therefore, the probability that a randomly selected woman will carry the mutation of this gene and develop colon cancer is (1/500) * 0.48, which can be calculated as a decimal or percentage based on your preference.
Determine which expression is equivalent to 15a + 6. (5 points)
a
3(5a + 6)
b
3(5a + 2)
c
5(3a + 6)
d
5(3a + 2)
Question 2 (5 points)
(03.01 LC)
Excellence Middle School charges $6.25 for students from all grade levels to attend the school dance. If s represents the number of seventh grade students who came to the dance and g represents the number of eighth grade students at the dance, which expression best represents the total money collected for attending the dance. (5 points)
a
6.25s + g
b
6.25(s + g)
c
13.50(s + g)
d
13.50s + g
Question 3 (5 points)
(03.01 LC)
Ken and Paul have been mowing lawns to earn extra money. Their jobs earn $65 per week. Ken worked for x weeks and earned an extra $18. Paul worked for y weeks. From the expressions below, select one that determines the total amount that Ken and Paul earned mowing lawns. ? (5 points)
a
83x + 65y
b
65x − 18 + 65y
c
60x + 83y
d
65x + 18 + 65y
Question 4 (5 points)
(03.02 MC)
Michelle and her friends wondered who had the most pop albums in their music collection. She recorded the information below:
Music Collection Survey
Name Number of Pop Albums Total Number of Albums in the collection
Michelle 33 60
Sasha 36 78
Kat 40 89
Monica 24 59
Based on the survey, which friend had the greatest percentage of pop albums? (5 points)
a
Michelle
b
Sasha
c
Kat
d
Monica
Question 5 (5 points)
(03.02 MC)
Lynne was wondering which game was more popular so she aksed her friend which they liked to play more, FortNite or Among Us. She found that of the 80 people who responded, 0.55 of them preferred FortNite, and 30% of them preferred Among Us. How many more of her friends prefer FortNite than Among Us? (5 points)
a
30
b
20
c
44.45
d
5
Question 6 (5 points)
(03.02 MC)
Hulk, Iron Man, Thor, and Captain America together clean out evil from 60 cities. Hulk cleaned up 0.25 of the cities, Iron Man cleaned up 12 of the 60 cities, Thor cleaned 35% of the cities, and Captain America cleaned up the the remaining cities. Who cleaned up the most cities? (5 points)
a
Hulk
b
Iron Man
c
Thor
d
Captain America
Question 7 (5 points)
(03.04 MC)
Solve for x: (5 points)
a
12
b
−12
c
-35
d
35
Question 8 (5 points)
(03.04 MC)
Clark Kent needs to buy some new glasses. He has $70 to spend and the glasses that he wants only costs $30. He wants to spend the remainder of his money on new capes. Each cape costs $8. Which inequality represents the number of capes he can purchase? (5 points)
a
x ≥ 5
b
x ≤ 11
c
x ≤ 5
d
x ≥ 11
Question 9 (5 points)
(03.04 LC)
Find the equation that can represent the situation if the sum of two numbers is 32. We also know that the greater number is 5 more than the smaller number. (5 points)
a
x + (x + 5) = 32
b
x − (x + 5) = 32
c
x(x + 5) = 32
d
x(x − 5) = 32
Question 10 (5 points)
(03.05 MC)
SpongeBob needs $44 to buy a new pair of rectangle pants. He has already been able to save $9 and plans to work as a cook where he can earn $7 per hour. Which inequality shows the minimum number of hours, n, that SpongeBob will have to work as a cook to earn enough to buy the rectangle pants? (5 points)
a
9 + 7n ≤ 44, so n ≤ 5
b
9 + 7n ≥ 44, so n ≥ 5
c
7n ≥ 44 + 9, so n ≥ 7.8
d
7n ≤ 44 + 9, so n ≤ 7.8
Question 11 (5 points)
(03.05 MC)
Jesse sells clothes in the Yee Haw! Western Clothing store and earns $40 per day. She earns an extra $5 for each lasso she sells. If Jesse wants to earn at least $70 per day, which inequality shows the minimum number of lasso, n, that she would need to sell? (5 points)
a
40 + 5n ≤ 70, so n ≤ 6
b
40 + 5n ≥ 70, so n ≥ 25
c
40 + 5n ≤ 70, so n ≤ 25
d
40 + 5n ≥ 70, so n ≥ 6
Question 12 (5 points)
(03.05 MC)
Defne was looking online and saw some some cakes that looked delicious. Each cake costs $10.01 and has a shipping cost of $9.96 per order. If Defne wants to spend no more than $50 for the cakes, which inequality shows the maximum number of cakes, c, Defne can buy?(5 points)
a
9.96p − 10.01p ≤ 50, so p ≤ 1
b
9.96p + 10.01p ≤ 50, so p ≤ 2
c
9.96 − 10.01p ≤ 50, so p ≤ 3
d
9.96 + 10.01p ≤ 50, so p ≤ 4
I NEED HELP (ASAP)
Answers
Answer:
1. \(Expression: 3(5a + 2)\)
2. \(Total\ charges = 6.25(s+g)\)
3. \(Total = 65x + 18 + 65y\)
4. Michelle
5. 20 friends
6. Thor
8. \(x\leq 5\)
9. \(x + x + 5 = 32\)
10. \(7n + 9 \leq 44\) so: \(n \leq 5\)
11. \(40 + 5n \leq 70\) So: \(n \leq 6\)
12. \(10.01 p + 9.96 \leq 50\) so \(p \leq 4\)
Step-by-step explanation:
1. Given
\(Expression: 15a + 6\)
Required
Determine the equivalent expression
\(Expression: 15a + 6\)
Expand:
\(Expression: 3 * 5a + 3 * 2\)
Factorize:
\(Expression: 3(5a + 2)\)
Hence, the equivalent expression of the given expression is \(3(5a + 2)\)
2.
Given
\(Charges = \$6.25\)
s = seventh grade students
g = eight grade students
Required
Determine the total charges
First, we need to calculate the total number of charges:
\(Total=s+g\)
\(Total\ charges = Charges * Total\)
\(Total\ charges = 6.25(s+g)\)
3. Given
Ken
\(Duration = x\ weeks\)
\(Extra\ Earnings = \$18\)
\(Weekly\ Earnings = \$65\)
Paul
\(Weekly\ Earnings = \$65\)
\(Duration = y\ weeks\)
Ken's total charges is:
\(Weekly\ Earnings * Duration + Extra\ Earnings\)
\(65 * x + 18\)
\(65x + 18\)
Paul's total charges is:
\(Weekly\ Earnings * Duration\)
\(65 * y\)
\(65 y\)
\(Total = Ken + Paul\)
\(Total = 65x + 18 + 65y\)
4.
To calculate the percentage, we simply divided the number of pop albums by the total number of albums.
For Michelle.
\(\%Pop = \frac{33}{60} * 100\%\)
\(\%Pop = \frac{3300\%}{60}\)
\(\%Pop = 55\%\)
For Sasha
\(\%Pop = \frac{36}{78} * 100\%\)
\(\%Pop = \frac{3600\%}{78}\)
\(\%Pop = 46.2\%\)
For Kat:
\(\%Pop = \frac{40}{89} * 100\%\)
\(\%Pop = \frac{4000\%}{89}\)
\(\%Pop = 44.9\%\)
For Monica:
\(\%Pop = \frac{24}{59} * 100\%\)
\(\%Pop = \frac{2400\%}{59}\)
\(\%Pop = 40.7\%\)
From the calculation above, Michelle has the highest percentage of Pop music
5.
\(People = 80\)
\(Fortnite = 0.55\)
\(Among\ Us = 30\%\)
Required
Determine number of friends that prefer fortnite more than among us
First, we need to calculate the number of people that prefer Fortnite.
\(Fortnite = 0.55 * 80\)
\(Fortnite = 44\)
Next, we need to calculate the number of people that prefer Among Us.
\(Among\ Us = 30\% * 80\)
\(Among\ Us = 24\)
The difference is:
\(Difference = 44 - 24\)
\(Difference = 20\)
Hence, 20 more people preferred Fortnite to Among Us
6.
\(Hulk = 0.25\)
\(Iron\ Man = 12\)
\(Thor = 35\%\)
Captain America cleaned the rest
\(Total = 60\)
Number of cities by each is:
\(Hulk = 0.25 * 60\)
\(Hulk = 15\)
\(Iron\ Man = 12\)
\(Thor = 35\%\)
\(Thor = 35\% * 60\)
\(Thor = 21\)
\(Captain\ America = 60 - 15 -12 - 21\)
\(Captain\ America = 12\)
By comparison, Thor cleaned the highest number of cities
7. This question is not clear
\(Total = \$70\)
\(Glass = \$30\)
\(Each\ Cape = \$8\)
Let the number of cape be x.
We have that:
\(8 * x + 30 \leq 70\)
\(8 x +\leq 70 - 30\)
\(8 x +\leq 40\)
\(x\leq 5\)
9.
Let the first number be x and the second be y
\(x + y = 32\)
\(y = x + 5\)
Substitute x + 5 for y in the first equation
\(x + x + 5 = 32\)
10.
\(Savings = \$9\)
Earnings = $7 per hous
Total = $44
The inequality is:
\(7 * n + 9 \leq 44\)
\(7n + 9 \leq 44\)
\(7n \leq 44 - 9\)
\(7n \leq 35\)
\(n \leq 5\)
11.
Earnings = $40
Extra = $5 per lasso
Total Earnings = At least $70 daily
The inequality is:
\(40 + 5n \leq 70\)
\(5n \leq 70 - 40\)
\(5n \leq 30\)
\(n \leq 6\)
12.
\(Each\ Cake = \$0.01\)
\(Shipping = \$9.96\) per order
\(Available = \$50\) --- maximum
The inequality is:
\(10.01 * p + 9.96 \leq 50\)
\(10.01 p + 9.96 \leq 50\)
\(10.01 p \leq 50 - 9.96\)
\(10.01 p \leq 40.04\)
\(p \leq 4\)
Given two points (2, 7) and (1, -2) on a line, calculate the slope of the line.
A. slope 7
B. slope 8
C. slope 9
D. slope 10
Answers
Answer:
Step-by-step explanation:
Slope of line passing through (2, 7) and (1, -2) = (-2-7)/(1-2) = 9
Choose the best selection for the
quadrilateral with vertices at the
following points:
(-3,0), (-3,-3), (0,-3), (0,0)
Hint: Start by graphing the points.
Distance Formula: d = √(x2-x₁)² + (Y2 − ₁)²
A. Trapezoid
C. Rectangle
B. Rhombus
D. Square
Answers
Answer:
D. Square
Step-by-step explanation:
You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).
GraphA graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.
The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.
The figure is all of a rectangle, rhombus, and square.
The most specific name for the figure is Square.
__
Additional comment
A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.
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While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd. The actual number of cattle in the herd was 600.
What was the percent of error, rounded to the nearest percent?
15%
20%
25%
30%
Answers
The solution is, the percent of error, rounded to the nearest percent is 25%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
now, we have to find the percent of error, rounded to the nearest percent.
so, we get,
Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
so, error = 750 - 600
= 150
so, we get,
the percent of error = 150 * 100 / 600
= 25%
Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.
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please help me !!!!
Answers
9514 1404 393
Answer:
(a) 260 square centimeters
Step-by-step explanation:
The figure consists of a 10 cm square and four congruent triangles with base 10 cm and height 8 cm. Using the formulas for the area of a square and a triangle, the total area is ...
area = square area + 4 × triangle area
area = s² + 4×(1/2bh) = (10 cm)²+ 2(10 cm)(8 cm) = (100 +160) cm²
area = 260 cm²
Match the picture with the definition. PLEASE HELP!!
16 pts!
Answers
Answer: bottom is 135° and 45°
top is intersecting and thats all ik
Step-by-step explanation:
use the web and pictures from the web to help.
Please help!!!! Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and the top right angle is angle 2. Arc R Q is 53 degrees and arc S T is 47 degrees. Angle 1 intersepts arc R Q. Angle 2 intersepts arc R S. What are the measures of angles 1 and 2?
m∠1 = °
m∠2 = °
Answers
Answers: angle 1 =50 and angle 2 =130
Step-by-step explanation: on edgen
Plz help Plz help
Ella played a math game and had the five cards shown.
7 0 -4 -10
Her score was the sum of the numbers on these five cards. What was Ella’s score?
3
⊝
23
−5
⊝
Not here
Answers
Answer:
-7 (Not here)
Step-by-step explanation:
1. A negative plus a negative equals a negative/ a negative minus a positive equals a negative so: -10 -4 = -14
2. -14 + 7 = -7 so your answer is -7 and it's not an answer choice so you would select "Not here"
Convert.
_____seconds = 15 minutes 19 seconds
Answers
Answer: 919 seconds in 15 minutes and 19 seconds
Step-by-step explanation:
60 x 15 = 900
900 + 19 = 919
3(×+2)=3×-6 I got 0 is that right or wrong
Answers
Answer:
Step-by-step explanation:
3(x + 2) = 3x - 6
3x - 6 = 3x - 6
Subtract 6 from both sides of the equation. Then you will get 3x = 3x - 12. Now subtract 3x from both sides of the equation. Leaving you with 0 = -12. So I guess it’s correct?
4. Suppose 600 students were surveyed regarding their GPAs. The average GPA was found to be 2.75. Using a confidence level of 90%, what is the margin of error if the standard deviation is 0.45
?
4.73%
2.97%
9.5%
All changes saved
14.04%
Answers
Answer:4. Suppose 600 students were surveyed regarding their GPAs. The average GPA was found to be 2.75. Using a confidence level of 90%, what is the margin of error if the standard deviation is 0.45
?
4.73%
2.97%
9.5%
All changes saved
14.04%
Step-by-step explanation:
There are 4 ounces of
lime juice in 52 ounces
of punch. How much
lime juice is needed for
130 ounces of punch?
Answers
There are 4 ounces of lime juice in 52 ounces of punch, let represent the number of ounces of lime juice in 130 ounces of punch, there are 1690 ounces of the lime juice in 130 ounces of punch.
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified.
'Ounce' is also used in the following other contexts:
A unit of the force is the ounce-force (see below).
A unit of the volume is the fluid ounce.
A multitude of distinct ounces measuring mass or volume have been employed historically by various trades at various times and in various countries.
Since,
Ounces of the lime juice=4
Ounces of the punch=52
Ounce needed for 1 punch=52÷4=13
Ounces needed for 130 ounces of the punch=13×130=1690
Therefore, the ounces of the lime juice needed for 130 ounces of punch=1690.
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what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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a farmer has two types of milk, one that is 28% butterfat and another that is 16% butterfat. how many gallons of each should be combined to create a 60-gallon mixture that is 22.5% butterfat?
Answers
30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.
Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,
⇒ x + y = 60 ⇒ x = 60 - y ----(1),
Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,
⇒ 28% of x + 16% of y = 22% of 60
⇒ 0.28x + 0.16y = 0.22 × 60
⇒ 0.28x + 0.16y = 13.2
⇒ 28x + 16y = 1320
⇒ 14x + 8y = 660
From equation (1),
14(60-y) + 8y = 660
840 - 14y + 8y = 660
6y = 180
y = 30
Again from equation (1),
x = 60 - y
= 60 - 30
= 30
Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%
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How to Evaluate 5/9 x 8
Answers
Answer:
4 4/9
Step-by-step explanation:
First, you have to set it up: 5/9 times 8/1
We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.
Next, Multiply.
5/9x8/1=40/9 as an inproper fraction
As a proper fraction, it is written as 4 4/9
find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
Answers
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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The number of adults who attend a music festival, measured in hundreds of people, is represented by the function a(d)=−0.3d2+3d+10, where d is the number of days since the festival opened.
The number of teenagers who attend the same music festival, measured in hundreds of people, is represented by the function t(d)=−0.2d2+4d+12, where d is the number of days since the festival opened.
What function, f(d) , can be used to determine how many more teenagers than adults attend the festival on any day?
f(d)=−0.1d2+d+22
f(d)=0.1d2+d+2
f(d)=−0.1d2+7d+2
f(d)=0.1d2+7d+2
Answers
Answer:
f(d)=0.1d^2+d+2
Step-by-step explanation:
t(d)=−0.2d2+4d+12
a(d)=−0.3d2+3d+10
how many more teenagers than adults attend the festival on any day?
==>
f(d) = t(d) - a(d)
=0.1d^2+d+2
Esfandairi Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.18 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life. The project is estimated to generate $1,730,000 in annual sales, with costs of $640,000. The project requires an initial investment in net working capital of $290,000, and the fixed asset will have a market value of $240,000 at the end of the project.
a. If the tax rate is 24 percent, what is the project’s Year 0 net cash flow? Year 1? Year 2? Year 3? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, e.g., 1,234,567.)
b.
If the required return is 12 percent, what is the project's NPV? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Answers
Answer:
a
Step-by-step explanation:
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The net present value of the project is $0.15 million.
What is the net present value?Net present value is the present value of after-tax cash flows from an investment less the amount invested.
hee, we have,
The first step is to determine the cash flow of the project.
Cash flow = (sales - cost - depreciation) × (1 - tax) + depreciation
Depreciation = (cost of the asset ) / useful life
Depreciation = $2.18 million / 3
Depreciation = 0.727 million
Cash flow = (1.645 - 0.61 - 0.727) x (1 - 0.21) + 0.727 = $0.97 million
Net present value = -2.18 million + 0.97 / 1.12 + 0.97 / 1.12² + 0.97 / 1.12³
= $0.15 million
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4.
Jaiden earned $84 last week. Peter earned only $12. Jaiden’s earnings are how many times greater than Peter’s? Choose the answer that has the correct equation AND the correct solution to the equation.
12x = 84; x = 7 times more
12 + x = 84; x = 72 times more
84x = 12; x = 7 times more
12x = 84; x = 9 times more
PREVIOUS
Answers
Answer:
i belive the answer is B
Step-by-step explanation:
Answer: A
Step-by-step explanation:
84 divided by 12 is 7
x/5= 5, solve for x
Answers
The given equation is:
\(\frac{x}{5}=\text{ 5}\)\(\frac{x}{5}=\frac{5}{1}\)The next step is to do a cross multiplication\(x\text{ }\times1\text{ = 5}\times5\)\(x\text{ = 25}\)How do you convert x^2+4x+2 in vertex form?
Please explain how you do it.
Answers
Answer:
(-2,-2)
Step-by-step explanation:
Answer:
f(x)=(x+2)2−3 or (x−(−2)2−3
Step-by-step explanation:
Vertex form of equation is
f(x)=a(x−h)2+k
Here, we have f(x)=x2+4x+1, hence we have a=1. So for converting to this form, we complete the square using
(x+a)2=x2+2ax+a2 for which we have to identify a and then add and subtract a2. Hence,