A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the first two fence posts at (6, 0) and at (0, 25). The final fence post is on the property line at x = 30. Find the point where the trainer can place the final fence post.
Answer:
[tex]C = (30,500)[/tex]
Step-by-step explanation:
Given
[tex]Area = 1800ft^2[/tex]
[tex]A = (6,0)[/tex]
[tex]B = (0,25)[/tex]
[tex]C(x,y) = (30,y)[/tex]
Required
Determine the coordinates of C
The area of triangle is calculated as thus:
[tex]Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}[/tex]
This gives:
[tex]1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(0- 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(-25)|}{2}[/tex]
[tex]1800= \frac{|150 - 6y -750 |}{2}[/tex]
[tex]1800= \frac{|150 -750- 6y |}{2}[/tex]
[tex]1800= \frac{|-600- 6y |}{2}[/tex]
Multiply through by 2
[tex]2 * 1800= |-600- 6y|[/tex]
[tex]3600= |-600- 6y|[/tex]
[tex]3600= |-(600+ 6y)|[/tex]
[tex]3600= 600+ 6y[/tex]
Solve for 6y
[tex]6y = 3600 - 600[/tex]
[tex]6y = 3000[/tex]
Solve for y
[tex]y = 3000/6[/tex]
[tex]y = 500[/tex]
Hence:
The point is:
[tex]C = (30,500)[/tex]
Johnny will work 15 hours a week during the 36 week school year, and 40 hours a
week the other 16 weeks of the year. If he makes 9 dollars per hour before taxes
and plans to save half of the money, how much will he have saved for the entire
year?
answer choices:
a- $4,248
b- $5,310
c- $10,620
d- $1,944
which answer is right
Which graph represents a proportional relationship?
2. Find the domain and range of the function: *
1 point
f (x)=
3(x + 2)2 +7
212
Domain is all reals, range is y greater than or equal to 7
Domain is all reals, range is y less than or equal to 7
Domain is all reals, range is all reals
Domain is x greater than or equal to 7. range is all reals
Domain is x less than or equal to 7, range is all reals
3.
I think the correct answer would be :
Domain is all Reals , Range is all Reals.
Peter is saving money to buy an MP3 Player. After one month, he has $50. After two months he has $85. After three months, he has $120. He plans to keep saving at the same rate. How long will it take Peter to save enough money to buy an MP3 Player that costs $295?
Answer:
9 months
Step-by-step explanation:
peter is saving 35 dollars per month.
295=35x
295/35=8.42 which is less than 295
9 is an approximate answer
35*9 equals 315, which is enough to pay 295 and have 20 dollars left over
Solve and Simplify -3-7/8
Answer:-1.25
Step-by-step explanation: First you add -3 and -7 it is -10/8 then you devide -10/8 and it is -1.25
Enter the value of 7 + (-3) - 3 - 7
Answer:
-6
Step-by-step explanation:
Simplify: 7 - 3 - 3 - 77 - 3 - 3 - 7 = -6I hope this helps!
Answer:
-3
Step-by-step explanation:
Select a true statement *
15 points
To convert a Unit Rate into another, we have to add or subtract a Unit Ratio to the original Unit Rate.
To convert a Unit Rate into another, we have to multiply the original Unit Rate by one or two Unit Ratios.
To convert a Unit Rate into another, we have to obtain a denominator different than one.
It is no possible to convert a Unit Rate into another.
Answer: To convert a Unit Rate into another, we have to multiply the original Unit Rate by one or two Unit Ratios.
Step-by-step explanation:
Unit rates are usually convertible to other units using multiplication and division attributes to ensure equivalence depending on preference or units being converted. Once the ratio or proportion between the two units (original and target) have been obtained, the original Unit is multiplied by the ratio of the two units to obtain the target unit rate. This way both units are equivalent to each other.
Identify all the numbered angles that are congruent to the given angle.
Justify your answers.
Answer/Step-by-step explanation:
The reasons for the stated numbered angles that are congruent to the given angles are written in the parentheses as follows:
7. <7 ≅ 65° (alternate interior angles)
<4 ≅ 65° (corresponding angles)
<1 ≅ 65° (vertical angles)
8. <4 ≅ 51° (alternate interior angles)
<5 ≅ 51° (corresponding angles)
<7 ≅ 51° (vertical angles)
9. <1 ≅ 120° (corresponding angles)
<3 ≅ 120° (alternate angles)
solve for x 3x+10 3x -28 will mark brainest answers are 1. 33 2. 34 3. 35 4. 36 ty so much 1 left godbless
Answer:
1. x = 33Step-by-step explanation:
3x+10 + 3x -28 = 180
3x + 3x = 180 + 28 - 10
6x = 198
x = 198/6
x = 33
Answer:
33
Step-by-step explanation:
By the same side interior angle theorem, we can find that 3x + 10 and 3x - 28 are supplementary. Knowing this, we can make the equation:
(3x + 10) + (3x - 28) = 180
Now we can solve for x. Combine like terms.
6x - 18 = 180
Add 18 from both sides.
6x = 198
Divide both sides by 6.
x = 33
So the value of x would be 33.
I hope you find my answer and explanation to be helpful. Happy studying.
If x2 = 20, what is the value of x?
Answer:
10
Step-by-step explanation:
20/2=10 so x=10
Answer:
10
Step-by-step explanation:
The home that you want to purchase requires that you pay 3 points towards a $225,600 loan. Determine the cost of the home after the 3 points have been applied.
a.$225,600
c.$230,112
b.$227,856
d.$232,368
Answer:
D
Step-by-step explanation:
Comment above.
Mr. Jones has to invest in three types of stocks, low-risk, medium-risk, and high-risk. He invests according to three principles. The amount invested in low-risk stocks will be at most more than the amount invested in medium-risk stocks. At least will be invested in low- and medium-risk stocks. No more than will be invested in medium- and high-risk stocks. The expected yields are % for low-risk stocks, % for medium-risk stocks, and % for high-risk stocks. How much money should Mr. Jones invest in each type of stock to maximize his total expected yield?
Answer:
Since the numbers are missing, I looked for a similar question:
Mr. Jones has $9000 to invest in three types of stocks: low-risk, medium-risk and high-risk. He invests according to the following rules: the amount invested in low-risk stocks will be at most $1000 more than the amount invested in medium-risk stocks. At least $7000 will be invested in a combination of low- and medium-risk stocks. No more than $7000 will be invested in a combination of medium- and high-risk stocks. The expected annual returns are 6% for low-risk stocks, 7% for medium-risk stocks, and 8% for high-risk stocks. How much should he invest in each type of stock to maximize his total expected yield?
let:
L = low risk stocks
M = medium risk stocks
H = high risk stocks
maximize 0.06L + 0.07M + 0.08H
L + M + H ≤ 9000
L ≥ M + 1000
L + M ≥ 7000
M + H ≤ 7000
using solver, the optimal solution = 4,000L + 3,000M + 2,000H , which yields a maximum profit = $610
Mr. Jones should invest $4,000 in low risk stocks, $3,000 in medium risk stocks and $2,000 in high risk stocks.
HELP!!!
The first two steps of a proof of the Pythagorean theorem are shown. What is the
next step?
a а
a а
b
Step 1
Step 2
A. Rearrange pieces to form a square with side length a + b.
B. Form an outer square that has squares with areas of a2 and b2 inside it.
O C. Move up the sides labeled c.
D. Rotate both triangles to form a square with side length c.
Answer:D
Step-by-step explanation:
I got you!
How i do this yall..?
Solve for nn by simplifying both sides of the equation, then isolating the variable.
n=4, −2
Answer:
We know that a modulus gives us the absolute value of a number
Hence, this modulus will give a positive value, regardless of the actual value in the modulus
| -1 + n | = 3
(-1 + n) or (1 - n) = 3 -------------------This tells us that either one of the values will give us the same answer
-1 + n = 3 or 1 - n = 3
n = 4 or n = -2
What number is not an integer
3407, 6.729, 0, -46
Answer:
6.729
Step-by-step explanation:
Integers only include plsitive and negative numbers and zero. 6.729 is a number alright but it is a fractional or decimal number.
There are 11 frogs at the pond. There are 5 frogs in the water. The rest are in the mud. How many frogs are in the mud?
Answer:
This is easy math. 11-5=6. Six frogs are in the water.
Step-by-step explanation:
11 represents the whole of frogs, and 5 represents the frogs in the water.
Who can help me with this
A: How many total hours were worked this week?
Answer- 14 hours were worked this week
B: How many overtime hours were worked?
Answer- 36 overtime hours were worked
I hope this helps you out!!
Answer:
A. 41 hours were worked the whole week
Partial credit
00:00
Selma buys 10 juice boxes. She wants to give 2 juice boxes to each friend.
Part A
Which expressions can Selma use to figure out how many friends can get juice boxes? Choose all that apply
A.
10 - 2
B. 0 + 2. 2 + 24 + 2. 6 + 2
10 - 2
D
10 X 2
E. 10 - 2.8 - 2.6 -2.4 - 2.2 - 2
00:00
Part B
Solve the problem. How many friends can get juice boxes?
Enter you answer in the box
Answer:
A
Step-by-step explanation:
you will figure out how many friends can get juice boxes if you do 10-2 and you keep going until you have 0 left
The ordered pairs below represent a relation. Is the relation a function? (4,6) (5,6) (6,7) (7,8)
Answer:
no because two inputs have the same outputs
Step-by-step explanation:
is there a way you guys can show me how to graph this equation? if not something will do
Answer:
you can use an online graphing calculator
Step-by-step explanation:
Use the link in the screenshot
btw, the line after the word calculator is the cursor, so don't put anything after the word calculator.
If the second term in a geometric sequence is -8 and the common ratio is 2, what is the value of the third term?
-4
-10
-16
Answer:-16
Step-by-step explanation:
what is 56897712937e+ - (-73618260) ??
Your answer is 1.54737637e11
Answer:
154737637418
Step-by-step explanation:
Give an example of two events that are not mutually exclusive.
Answer: in the case of rolling a die the event of getting an 'odd-face' and the event of getting 'less than 4' are not mutually exclusive and they are also known as compatible event. The event of getting an 'odd-face' and the event of getting 'less than 4' occur when we get either 1 or 3.
Step-by-step explanation:
also turning ur body (left and right)
Evaluate the function.
f(x) = -x^2+ 7x - 13
Find f(-3)
what is the steps to this problem.
2(3b-2)=2(2b+12)
Answer:
14
Step-by-step explanation:
Step 1:
2 ( 3b - 2 ) = 2 ( 2b + 12 ) Equation
Step 2:
6b - 4 = 4b + 24 Multiply
Step 3:
6b = 4b + 28 Add 4 on both sides
Step 4:
2b = 28 Subtract 4b on both sides
Step 5:
b = 28 ÷ 2 Divide
Answer:
b = 14
Hope This Helps :)
f(x) = 3x + 2
What is f(5)?
Hello!
f(x) = 3x + 2
Since you are provided with f(5), we will replace every "x" in the equation with the number 5.
f(5) = 3(5) + 2
f(5) = 15 + 2
f(5) = 17
I hope this helps you! Have a great day!
- Mal
Find the error and and the correct answer
Answer:
Error: Multiplied both sides by 3/4 instead of 4/3.
Solution: x = 16
Step-by-step explanation:
The error is that you multiplied both sides by [tex]\frac{3}{4}[/tex] instead of dividing both sides by [tex]\frac{3}{4}[/tex].
This is an error because:
[tex]\frac{3}{4} *\frac{3}{4} x\neq x[/tex]
Actually:
[tex]\frac{3}{4} *\frac{3}{4} x=\frac{9}{16} x[/tex]
What you want to do instead is divide both sides by [tex]\frac{3}{4}[/tex]. Remember, dividing both sides by [tex]\frac{3}{4}[/tex] would be the same as multiplying both sides by [tex]\frac{4}{3}[/tex].
Now, lets find the correct answer:
[tex]\frac{3}{4}x=12[/tex]
Multiply both sides by 4/3.
x = 16
So the correct answer would be x = 16.
I hope this helps. Happy studying.
Find the midpoint of the segment with the following endpoints.
(-6, 4) and (-1,-6)
Answer:
(−7 / 2, −1)
Step-by-step explanation:
Shanti is making prize bags for her friends. She will use a total of 32 toys and 40 erasers in the prize box. What is the greatest number of prize bags Shanti can make if she wants each bad to have the same number of toys in the same number of erasers? The greatest number of prize bags Shanti can make is ?