Answer:
[tex]a=\frac{7}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a-1}{a-3}=\frac{a+1}{a-4}[/tex]
[tex](a-1)(a-4)=(a-3)(a+1)[/tex]
[tex]a^2-5a+4=a^2-2a-3[/tex]
[tex]-5a+4=-2a-3[/tex]
[tex]-3a+4=-3[/tex]
[tex]-3a=-7[/tex]
[tex]a=\frac{7}{3}[/tex]
From a hot-air balloon, Grayson measures a 29^{\circ} ∘ angle of depression to a landmark that’s 1004 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon’s vertical distance above the ground is 556 feet
The set up will form a right triangle.
Given the following parameters
Angle of depression = 29 degreesHorizontal distance = 1004 feetTo get the height above the ground, we will use the SOH CAH TOA identity as shown;
Opposite = h
Adjacent = 1004 feet
Tan theta = h/1004
Tan 29 = h/1004
h = 1004 tan 29
h = 1004(0.5543)
h = 556.52 feet
Hence the balloon’s vertical distance above the ground is 556 feet
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A city's population is increasing at a rate of 2% per year.
If this rate of growth remains the same and the population is 2 million in the year 2014, approximately how many people will there be after 20 years?
a.)
2.02 million
b.)
2.88 million
c.)
2.14 million
d.)
2.97 million
Based on the information the number of people that will there after 20 years is: d.) 2.97 million.
Using this formula
P(t) = Population ×(1+ rate)^t
Where:
Population=2 million
rate=2%
time=20 years
Let plug in the formula
P(t) = 2×(1+.02)^20
P(t) = 2×(1.02)^20
P(t) = 2×1.485947
P(t) = 2.97 million
Inconclusion the number of people that will there after 20 years is: d.) 2.97 million.
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clothing store sells t shirt in only three colors red blue green the colors are in the ratio of 3:4:5 if the store has a total of 60 how many blue t shirt
Answer:
Step-by-step explanation:
red/blue = 3/4 and you get blue/green = 4/5
= 60/4 = 15
you have 15 red shirts, 20 blue shirts, and 25 green shirts.
15/20 = 3/4
20/25 = 4/5
if you simplify 15/20, you will see that it is equivalent to 3/4
if you simplify 20/25, you will see that it is equivalent to 4/5.
a room that needs to be tiled is 12 1/2 feet wide by 14 feet long. tiles that mesure 2x2 are $0.79 per tile. Tiles that measure 3x3 are 1.25 per tile. which size tile should be used for this project to save the most money? How many tiles would be needed? How much would you spend on them? HELP PLEASE!
Answer:
Step-by-step explanation:
Area of the room is 12.5(14) = 175 ft²
2x2 tiles are 4 ft²
175 /4 = 43.75 tiles so 44 will be needed
44($0.79) = $34.76
3x3 tiles are 9ft²
175/9 = 19.4444... so 20 will be needed
20($1.25) = $25.00
the larger tiles will cost $9.24 less than the smaller tiles.
Obviously some of the tiles will need to be cut to fit as the length and width of the room are not always a uniform number of tiles for either side.
Suppose there is a 1.4 drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 52.8, what will be the temperature when the plane reaches an altitude of 11,000?
Answer:
37.4
Step-by-step explanation:
1.4 times 11 and subtract that from 52.8
1) Solve 3x 8-6. Graph the solution.
A)
B)
C)
D)
Answer: negative 2 arrow to the left
Step-by-step explanation:
2/8 and 1/2 write < or >
Answer:
0.5 > 0.25
Step-by-step explanation:
2/8 = 1/4 = 0.25
1/2 = 0.5
Answer:
<
Step-by-step explanation:
1/2 equals more than 2/8.
Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.
Find the quotient: 0.12)78.6.
PLEASEEEE HELP!DUE IN 1 HOUR! A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $3000 when sold. A ranch-style house requires $40,000 of capital and provides an $7000 profit. If the contractor has $3.8 million of capital on hand, how many houses of each type should she build for maximum profit?
Answer:
Step-by-step explanation:
A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $2000 when sold. A ranch-style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.2 million of capital on hand, how many houses of each type should she build for maximum profit?
? colonials
? ranches
For maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses. The maximum profit achievable is $740,000.
Let x be the number of colonial houses built.
Let y be the number of ranch-style houses built.
Now, we can set up the objective function, which represents the total profit:
Total Profit (P) = 3000x + 7000y
The total cost of the houses built cannot exceed the available capital, which is $3.8 million (or $3,800,000):
30,000x + 40,000y ≤ 3,800,000
The number of building lots used cannot exceed the total number of lots available, which is 100:
x + y ≤ 100
Also, we need to consider that the number of houses (x and y) must be non-negative:
x ≥ 0
y ≥ 0
Now, we have the linear programming model with the objective function and constraints.
We need to find the values of x and y that maximize the total profit (P).
Graph the feasible region determined by the constraints (x + y ≤ 100, x ≥ 0, y ≥ 0, 30,000x + 40,000y ≤ 3,800,000), and then evaluate the objective function (P = 3000x + 7000y) at each corner point of the feasible region to find the maximum profit.
The feasible region is a polygon with vertices at the following points:
(0, 0)
(0, 95) (Intersection of x = 0 and y = 95)
(80, 20) (Intersection of x = 80 and y = 20)
(100, 0) (Intersection of x = 100 and y = 0)
Now, evaluate the objective function (P) at each corner point:
(0, 0): P = 0
(0, 95): P = 665,000
(80, 20): P = 740,000
(100, 0): P = 300,000
The maximum profit of $740,000 occurs when the contractor builds 80 colonial houses and 20 ranch-style houses
Hence, for maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses.
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Volume of the pedestal box
Answer:
112 in.³
Step-by-step explanation:
This box is a combination of two rectangular prisms:
bottom - 9 in. by 2 in. by 4 in.
top - 5 in. by 2 in. by 4 in.
total volume = 9 in. × 2 in. × 4 in. + 5 in. × 2 in. × 4 in.
total volume = 112 in.³
Answer:
its 112
Step-by-step explanation:
first see how it looks like 2 boxes on top of each other, break it into major parts then multiply depth by wighth by highth
Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
Answer:
[tex]\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}[/tex]
Step-by-step explanation:
[tex]\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>[/tex]
Answer:
Step-by-step explanation:
-u-v = 6,-11
u-v = -10,-3
v-u = 10,3
n is m% of what?
It DEFINITELY a variable
what is y=2x+3 y=−3x+3
Step-by-step explanation:
equate the two equations
Can the sum of two palindromic numbers be another palindromic number?
Answer:
Every positive integer can be written as the sum of three palindromes, numbers that remain the same when their digits are reverse. For example, 389 = 11 + 55 + 323. This holds not just for base 10 but for any base b ≥ 5.
X- y = -7 slope intercept form
Answer:
[tex]y=x+7[/tex]
Step-by-step explanation:
Let's simply rearrange bringing y to the RHS, -7 to the LHS and reading right to left:
[tex]x+7=y \rightarrow y=x+7[/tex]
I need help asap! Pls :)
Answer:
x = 18
Step-by-step explanation:
An M&Ms factory produces 109,500,000 M&M’s every day. About 1/5 of its M&Ms are yellow. Find the number of yellow M&M’s produced at this factory
Answer:
It's not possible to answer precisely. About 1/5 of 109,500,000 is equal to about 109,500,000*.2 which is about 21,900,000.
Step-by-step explanation:
The first thing to note is that the amount of yellow M&Ms isn't precisely 1/5th. It's about 1/5th.
So, applying the math, 109,500,000 times 1 and divided by 5 = 21,900,000, but that's not the answer, because of the uncertainty.
The answer has to be "about 21,900,000."
You plant 9 rows of different bulbs in a garden. For each row, you use the rule, “onion, onion, garlic, flower.” How many garlic and flower bulbs do you plant altogether? How many bulbs do you use in all?
Answer:
18; 36
Step-by-step explanation:
If there's 9 rows of "onion, onion, garlic, flower", then you repeat this cycle 9 times.
onion, onion, garlic, flower(1)
onion, onion, garlic, flower(2)
onion, onion, garlic, flower(3)
onion, onion, garlic, flower(4)
onion, onion, garlic, flower(5)
onion, onion, garlic, flower(6)
onion, onion, garlic, flower(7)
onion, onion, garlic, flower(8)
onion, onion, garlic, flower(9)
Add up the garlic and flower bulbs, which equals 18. Then add up all of the bulbs, which is 36.
-hope it helps
Given f(x) = 21 - 1, complete the missing values in the table
Answer:
first one is f(x)=-5
second one is f(x)=7
third one is x=-3
4th one is x=0
5th one is f(x)=1
6th one is x=-4
Step-by-step explanation:
first one. plug in x as -2:
f(x)=2*-2-1=-4-1=-5
second one is the same way:
f(x)=4*2-1=8-1=7
third one is a different one:
2x-1=-7
2x=-6
x=-3
4th one is the same way:
2x-1=-1
2x=0
x=0
5th way is the same thing as previous:
f(x)=2*1-1=2-1=1
Finally, the 6th one is the same thing as the 4th one:
2x-1=-9
2x=-8
x=-4
Done!
An auditorium has 72 rows of seats. The first row contains 70 seats. As you move to the rear of the auditorium, each row has 2 more seats than the previous row. How many seats are in the 24 th row
The number of seats on the 24th row is 3220.
The number of chairs in the 24th row is a function of the rate at which the chairs increase and the number of rows. The formula that can be used to determine the number of seats on the 24th row is:
P x [r x (n - 1)]
Where:
P = number of seats on the first row = 72r = rate of growth of the seats = 2n = number of the row = 2470 x [2x (24 - 1)]
70 x (2 x 23)
= 70 x 46
= 3220
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Problem Guitars Galore
Johnny Inneger saved $100 to buy a guitar. Then he bought one for $80. Johnny lost patience learning to play it and decided to sell it to his friend Michael Michael had also saved $100 Michael really wanted the guitar, so he paid Johnny $90 for it. After johnny saw his favorite guitar player in a concert, he wanted to buy back the guitar. He bought it back from Michael for $95. Now Michael has offered Johnny 585 for the guitar. Johnny is deciding whether he will accept the offer. if he does will he have lost any money on the guitar? If so, how much?
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in the simplest form
3/4 divided by 3
Step-by-step explanation:
3/4 ÷ 3
recall that the inverse of division is multiplication
=3/4 x 1/3
=1/4
A credit card company charges an annual simple interest rate of 24%. in august, your purchases totaled $956. How much will you pay for interest, if you pay off that debt in 2 years 3 months?
Answer:
83
I know because I did this problem a few years ago
Lila earns 2,725,98 per month how much money does she have left after paying all these bills
Rent 1,250,00 groceries 325,78 electricity 55,27
Answer:
$1,094.93
Step-by-step explanation:
The income is how much money you make. You lose the money you spend. To find how much money you have left, just subtract the income with everything you spent.
This means the final answer is: 2725.98 - (1250.00 + 325.78 + 55.27) = $1,094.93
Pls help I’m failing do it on paper and put it in the answer box
Step-by-step explanation:
there is no mathematical problem to solve.
just follow the instructions as given.
this is an exercise for you to get a feeling about what is what. it is imperative that you do it.
there is really nothing to solve.
remember, that a positive slope means the line goes up (from left to right), and a negative slope means the line goes down (again from left to right).
and I am sure you know what vertical and horizontal means.
Answer this!
18 divides x
this makes no sense so maybe try something better
Victor buys5/8 kg of prawns each week. How many kilograms of prawns does he buy in 4 weeks?
Answer:
37/8
Step-by-step explanation:
5/8+32/8
5+32/8
37/8
There are 40 students in your class of which 23 are boys. What fraction of the students are girls?
Answer:17/23
Step-by-step explanation:
Answer: 17/40 of the students are girls.
Step-by-step explanation:
First, to find the number of girls in the class, we can subtract the number of boys (23) from the total number of students (40) to get:
40 - 23 = 17
There are 17 girls in the class.
Finally, to get the fraction of the girl students of the class, we can divide the number of girls (17) by the total number of students (40) to get:
17 ÷ 40 = [tex]\frac{17}{40}[/tex]
Since the fraction [tex]\frac{17}{40}[/tex] is already simplified, the final answer comes out to be [tex]\frac{17}{40}[/tex].
Convert 8 fluid ounces into milliliters. Round your answer to the nearest whole number.
Answer:
236.588 milliliters so the answer is 240
Step-by-step explanation:
for an approximate result, multiply the volume value by 29.574
Which statement below is TRUE about |-2| and |-5|?
|-5| is greater than |-2|
|-2| is greater than the |-5|
Neither statement is true
Answer:
|-5| is greater than |-2|
Step-by-step explanation:
the absolute value of -5, is 5, which is greater than the absolute value of -2, which is 2. Have a wonderful rest of your day! I hope this helps!