The length of each sides of the right triangle are as follows:
short leg = 27 ftlong leg = 90 fthypotenuse = 94 ftHow to find the sides of a right triangle?The shape of the city lot is a right triangle.
The hypotenuse side is 4 ft longer than one of the other side.
The perimeter of the lot is 440 ft.
Therefore, using Pythagoras theorem,
let
x = the other side
y = the second leg
x² + y² = (x + 4)²
x² + y² = (x + 4)(x + 4)
x² + y² = x² + 4x + 4x + 16
x² + y² = x² + 8x + 16
y² = 8x + 16
Hence,
x + x + 4 + y = 440
2x + y + 4 = 440
2x + y = 436
2x + y = 436
y = 436 - 2x
y² = 8x + 16
(436 - 2x)(436 - 2x) = 8x + 16
190096 - 872x - 872x - 4x² = 8x + 16
190096 - 1744x - 4x² = 8x + 16
4x² + 1752x -190080 = 0
4(x² + 438x - 47520) = 0
x² + 438x - 47520 = 0
Therefore,
x = 90 and x = - 528
Therefore, the hypotenuse side is 94 ft.
94² - 90² = y²
y = √8836 - 8100
y = √736
y = 27.1293199325
y = 27 ft
Therefore, the short leg, long leg and hypotenuse are 27 ft, 90 ft and 94 ft.
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Solve the equation P(x) = 8.
Answer:
Step-by-step explanation:
If 6 -x = 12, what is x - 6?
Answer: x - 6 = -12
Step-by-step explanation: first, we'll solve for x in 6 - x = 12. We'll isolate the variable by subtracting 6 from both sides, which gives us -x = 6. Now we'll divide both sides by -1 to get x and we will get -6 = x. So for the expression, we'll sub in the value we got for x from the equation, -6. -6 - 6 = -12.
Answer:
-12
Step-by-step explanation:
If one of the points that this relationship passes through is (,)=(300,10), find the
proportionality constant for this relationship. Round your answer to 3 decimal places.
Answer:
.033
Step-by-step explanation:
When there is a proportional relationship the constant of proportionality is y/x and in this case that would be 10/300 and that would be .033 rounded to three decimal places.
Subtract. Write your answer as a decimal.
5.5−8.1=
The solution of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex] which is a negative integer in decimal form.
The numbers of the number line are called integers. They include positive numbers, zero, and negative numbers.
Zero is neither considered a negative nor a positive number.
[tex]5.5\\[/tex] is a positive number and a smaller number when compared from [tex]8.1[/tex].
When a smaller number is subtracted from a larger number it results in subtraction with a negative sign.
[tex]5.5 - 8.1 \\= -2.6[/tex]
The subtraction of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex].
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ASAP pls help .....
11 Points
Answer:
0.008 3repeating
Step-by-step explanation:
18
You buy 8 gallons of gasoline and pay $23.20.
a.) Write an equation to represent this situation.
28
So
b.) Find the price of one gallon of gasoline.
I need help with this please
Answer: m<ABC = 45 degrees, m<DBC = 36 degrees
Step-by-step explanation:
set both equations equal to 81 because they add up to form one angle:
5x + 6 + 9x - 9 = 81
Combine like terms
14x - 3 = 81
Add three to both sides
14x = 84
Divide by 14 to find x
x = 6
To find the angles:
Measurement of angle ABC:
9(6) - 9 = 45 degrees
Take the original angle of 81 and subtract the angle you just found to find the remaining angle:
81 - 45 = 36
Therefore, the angle of DBC is 36 degrees
The graph below defines a function f (x). Find f (2).
3
N
7
s
4
m
14
-2 +
771 ?
1
2345
How can u do the 5th problem
Answer:
3/4 of 5. It equals 3 3/4.
Step-by-step explanation:
The question asks for 3/4 of 5 cups of milk.
Steve and Jenna go door-to-door selling chocolate bars. Steve sells 23 chocolate
bars and Jenna sells 12 chocolate bars. Together they collect $210. How should
they divide the money so that each person gets a fair share?
Answer:
Steve: $138.00
Jenna: $72.00
Step-by-step explanation:
Steve:
[tex]\frac{23}{35}[/tex] x 210 = 138
Jenna:
[tex]\frac{12}{35}[/tex] x 210 = 72
I'm not really sure what this means, but i'll do what i think is right!
Answer:
Steve: $138
Jenna: $72
Step-by-step explanation:
If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.
To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.
hope this helps!
The weight of an organ, an adult males has a bell shaped distribution with a mean of 320 g and a standard deviation of 45 g use the empirical rule to determine the following
A. About 95% of organs will be between what weights?
B. What percentage of organs weighs between 185 grams in 455 grams?
C. What percentage of organs weighs less than 185 grams or more than 455 grams?
D. What percentage of organs weighs between 275 grams in 410 grams?
1-7: MathXL for School: Practice & Problem Solving
Challenge You buy 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears. What is your total bill?
Grocery Store Prices
Item
Apples
Peaches
Pears
Cost
$0.99 per pound
$1.09 per pound
$1.19 per pound
Your total bill is:
(Round to the nearest cent as needed.)
The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
In the given question
The price of 1 pound apple = $0.99
The price of 1 pound Peaches = $1.09
The price of 1 pound Pears = $1.19
Total pounds of apples bought = 3.18 pounds
price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)
=3.18*0.99
=$3.15 ...(i)
Total pounds of Peaches bought = 1.45 pounds
price of 1.45 pounds of peaches = 1.45*1.09
= $1.59 ...(ii)
Total pounds of Pears bought = 1.71 pounds
price of 1.71 pounds of pears = 1.71*1.19
= $2.04 ...(iii)
Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.
Substituting the values from equation (i),(ii)and (iii) we get ,
Total bill = $3.15 + $1.59 + $2.04
= $6.78
Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
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How would this graph look please help
The inequality graph of the system of inequalities is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine how the inequality graph would look like?The system of inequalities is given as
-2x + 3y < 9
x^2 - y <= 10
4x + y > 3
In the above system of inequalities, there are two linear inequalities and a parabola inequality
The inequality symbols in the linear inequalities are opposite
This means that the region between both lines would be shaded
Also, for the parabola; the upper part would be shaded.
This is so because when y is made the subject of the formula, the symbol becomes >=
Using the above as a guide, the inequality graph of the system of inequalities is graph (a)
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Michael drove from point A to point B at 15 miles
per hour and immediately returned by the same
route at 30 miles per hour. What was his average
speed, in miles per hour, for the entire trip?
E. 20
F. 22.5
G. 24
H.25
Answer:
E
Step-by-step explanation:
Say the distance is 'd'
time for going = d/15
time for returning = d/30
average speed = total distance / ( total time)
= 2d / ( d/15 + d/30 )
solve for average speed = 20 mi/hr
Write the number name and expanded form for the number of driver ants that could be in two colonies.
Up to 22000 000 driver ants can live in a single colony
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
How to write a number in expanded form?
To write the number name and expanded form for the number of driver ants that could be in two colonies.
Given that Up to 22,000,000 driver of ants can live in a single colony
Now, from number expressions, we know that;
1, 000, 000 = 1 million
Thus number name is;
22,000,000= 22 million
Expanded form of 22,000,000 = 20,000,000 + 2,000,000
Thus, we conclude that;
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
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(Scientific Notation LC)
WILL MARK BRAINLEIST ONLY IF CORECCT!
!Rewrite 2,290,000 in scientific notation.
2.29 x 10−6
2.29 x 10−4
2.29 x 104
2.29 x 106
2,290,000 in scientific notation is 2.29 x 10⁶.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.
Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.
Now the given number is,
2,290,000
To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.
So, factorizing 2,290,000 we get,
2,290,000 = 229 x 10,000
Now converting 10,000 into multiples of 10
Since, 10,000 = 10 x 10 x 10 x 10
So, 2,290,000 can be written as,
2,290,000 = 229 x 10 x 10 x 10 x 10
Multiplying and divide 229 by 100 we get,
2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100
Rearranging we get,
2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)
Since, (229 x 100) / 100 = 2.29 x 100
2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)
And 100 = 10 x 10
Therefore we get,
2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10
Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶
Therefore we get,
⇒ 2,290,000 = 2.29 x 10⁶
this is the required scientific notation of 2,290,000 .
Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.
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Express 55 mph in kilometers per hour. Round to the nearest hundredth.
The normal cruising speed of a certain airplane is about 250 m/sec. What is this speed in miles per hour? Round to a whole number.
Answer:
900,000 mph
Step-by-step explanation:
I am assuming the m in he problems is standing for miles.
250m/sec x 60 sec/min x 60min/hour The sec cross out and the minutes cross out and you are left with miles be hour.
(x-j) (5x + k) = 0
How do i find x from this equation
Answer:
x = 5j-k
Step-by-step explanation:
(x-j) (5x+k) = 0
(x-j) * (5x+k) = 0
x - 5j + k = 0
x + k = 5j
x = 5j - k
help with 5,6,&7 please!! will mark as brailylist
mous this mobail phonffyuuyy
For what value of x does 3^2x = g^3x-4?
1
2
3
4
The value of x will be 2. So, Option B is correct for the equation [tex]3^{2x} = 9^{3x - 4}[/tex]
In the given question, the equation is [tex]3^{2x} = 9^{3x + 4}[/tex], we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,
=> [tex]3^{2x} = 9^{3x -4}[/tex] => [tex]3^{2x} = 3^{2(3x - 4)}[/tex]
We know according to the property of exponents if [tex]x^{m} = x^{n}[/tex], then m = n.
Similarly, in this equation the base of both RHS and LHS are the same, We get
=> 2x = 2(3x - 4)
=> 2x = 6x - 8 => 4x = 8
=> x = 2
We get value of x = 2.
Hence the value of x for this equation will be 2 and option B is correct.
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What is the result of
36 over 9 + 6?
Answer: 10
Step-by-step explanation:
First you can re-order = 36/9 + 6
36/9=4
Then add 4+6
It equals 10
You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner. How much should you charge per ticket if you expect 50 people to attend? (Round your answer to the nearest cent.)
Answer:
$13
Step-by-step explanation:
For 50 people it will cost you 150 + 50(10) or 500
150 +500 = 650 Divide that among 50 people and you get a cost of $13 a person.
Line AL is a perpendicular bisector of segment CM. Which of the following are true
Triangle ABC is an isosceles right triangle.
Because of A(-8,7) B(-4,2) C(1,6)
So AB=√[-8-(-4)]²+(7-2)²
=√41
BC=√(-4-1)²+(2-6)²
=√42
AC=√(-8-1)²+(7-6)²
=√82
AB=BC
AB²+BC²=AC²
So triangle ABC is an isosceles right triangle.
What is isosceles right triangle?
An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
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Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. Is she correct?
Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect
How to illustrate the information?From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.
Let's add (-3) + (-4)
It should be noted that the addition is equal to -7.
It should be noted that this doesn't corelate with what Luciana said.
Therefore, she is incorrect. It's only correct for positive numbers.
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For the given functions f and g, find the requested function.
Answer:
its 1
Step-by-step explanation:
i just know
Which is a solution of 2x+6>12? x>0 x>3 x>−1 x>5
Answer:
x>3
Step-by-step explanation:
2x+6-6 > 12-6 ditch the 6
2x/2 > 6/2 divide by 2
x>3
A group of people were asked if they had run a red light in the last year. The number of people that
responded yes is 397 and no is 159. Find the probability that if a person is chosen at random, he/she has
run a red light in the last year. Round to two decimal places.
Question Help:
If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.So, to find the probability:
P = number of favorable terms/number of total termsFavorable terms = 397Total number of terms = 397 + 159 = 556Apply values in the formula:
P = 397/556P = 0.714028On rounding off, P = 71%.Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
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A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?
A.150 feet
B.178 feet
C. 191 feet
D.212 feet
A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).
As given in the question,
Area of the square field = 22,500square feet
Let 'a' be the side and 'd' be the diagonal length of the square
a² =22,500
⇒a =150 foot
Using Pythagoras theorem
d² =a² +a²
⇒d² = 2(150)²
⇒d² =45000
⇒d =212.13
≈ 212 nearest foot (approximately)
Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with area of 22,500 square feet as given.
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Solve
31320= x + (.08x)
Answer:
Step-by-step explanation:
31320=x+0.08x
31320=1.08x
swap the sides
1.08x=31320
Divide by 1.08
x=29000