The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
Answers
The equation that is used to find the length of the legs of the triangle is
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0
The area of the triangle is 24 square feet.
We know that the area of a triangle is given by the formula
1/2 × base × height.
Now in the attached figure we can see that the length of the base is x feet
The height of the right-angled triangle is (x+2) feet.
So the area of the triangle will be:
area = 1/2 · (x) · (x+2)
or, area = 0.5x(x+2)
But the area of the triangle is 24 square feet. Therefore the Equation to find the legs will be 0.5x(x+2) = 24.
Now if we use the properties of Pythagoras theorem we can write the formula as
hypotenuse² = sum of squares of legs
10² = x² + (x+2)²
Therefore we get the second equation.
Now simplifying the above equation we get:
10² = x² + (x+2)²
or, 2x² + 4x - 96 = 0
or, x² + 2x - 48 = 0
This is the third option.
Therefore the required equation are:
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0 .
Disclaimer: The missing image of the triangle is attached below.
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Related Questions
The area of a children's rectangular playground is 1189 square meters. The length
is 12 meters longer than the width. Determine the length and width of the
playground.
Answers
Answer:
[tex]1+\sqrt{1190}[/tex] and [tex]\sqrt{1190}-11[/tex]
Step-by-step explanation:
Let the length in meters be [tex]l[/tex]. Then, the width is [tex]l-12[/tex].
[tex]l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=\frac{2 +\sqrt{(-2)^2-4(1)(-1189)}}{2(1)} \text{ } (l>0) \\ \\ l=1+\sqrt{1190} \\ \\ \implies l-12=\sqrt{1190}-11[/tex]
Find the greatest possible error for the given measurement
350 mi
a.0.5 mi
b. 5 mi
C.17.5 mi
D 175
Answers
Suppose that a timer for video game has a randomly determined length of time after which an enemy appears. the timer is programmed so that the enemy is equally likely to appear any time between .25 minutes and 2.75 minutes after the timer starts.
(a) Draw a density curve model this distribution of random numbers. Be sure to include scales on both axes.
(b) About what percent of the time will an enemy appear between 0.5 minutes and 2 minutes after the timer starts?
(c) Find the 20th percentile of this distribution.
Answers
Considering the uniform distribution, we have that:
a) The density curve is given by the image at the end of the answer.
b) The percentage of time in which an enemy will appear between 0.5 minutes and 2 minutes after the timer starts is of 60%.
c) The 20th percentile for the distribution is of 0.75 minutes.
What is the uniform probability distribution?The uniform probability distribution is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
In this problem, the bounds are given as follows:
a = 0.25, b = 2.75.
The height of the density curve is of:
f(x) = 1/(b - a).
Hence:
f(x) = 1/(2.75 - 0.25) = 0.4.
As shown by the image given at the end of the answer.
The probability that a measure is between two values is given by:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence, for item b:
P(0.5 < X < 2) = (2 - 0.5)/(2.75 - 0.25) = 0.6 = 60%.
The 20th percentile is the value of X for which:
X = a + 0.2(b - a).
Hence:
X = 0.25 + 0.2(2.75 - 0.25) = 0.75 minutes.
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5 (a) (b) Identify the nature of two stationary points for y=4x³ - 96x² +576x.
Answers
Answer: (0,0) (12,0)
Step-by-step explanation:
y=4x³-96x²+576x
Let y=0
Hence,
4x³-96x²+576x=0
Divide both parts of the equation by 4:
x³-24x²+144x=0
x(x²-24x+144x)=0
x=0
Thus, (0,0)
x²-24x+144=0
x²-2(x)(12)+12(12)=0
x²-2(x)(12)+12²=0
(x-12)²=0
x-12=0
x=12
Thus, (12,0)
bro please help. Im depressed because nobody will help me(true or false questions)
Answers
True - Jim Gyms initial value is 45 and Revolution Fitness is 50.
True- In 2 months Jim Gym would pay 75$ and Revolution Fitness would pay 75$ as well.
In 2005, 10.8 out of every 50 employees at a company were women. If there are 47,093 total company employees, estimate the number of women.
The number of women at the company is ___
Answers
Answer:
10,172 women
Step-by-step explanation:
47093 / 50 = 941.86
So 941.86 lots of 50 women
941.86 x 10.8 = 10172.088 women
rounded to 10,172 women
( can't have part of a person
which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answers
Answer:
first and third expressions
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex]
then
[tex]\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }[/tex]
= [tex]3^{\frac{4}{9}-\frac{2}{9} }[/tex] ← first expression
= [tex]3^{\frac{2}{9} }[/tex] ← third expression
Use the discriminant to determine the number of solutions to the quadratic equation
m² - 9m + 3 = 0.
Answers
Answer: 2 real solutions
Step-by-step explanation:
The discriminant is [tex](-9)^2 -4(1)(3)=69[/tex].
Since the discriminant is positive, there are 2 real solutions.
E
Solving a word problem using a system of linear equations of th...
QUESTION
ODD 03
Zachary
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is $25. For 2 pounds of walnuts
and 3 pounds of chocolate chips, the total cost is $11. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answers
As per the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
As given in the question,
Let us consider the cost of each pound of walnuts is equal to $x.
And cost of each pound of chocolate chips is equal to $y.
Now as per the given condition system of equation is given by,
4x + 8y = 25 __(1)
2x + 3y = 11 __-(2)
Multiply (2) by 2 and subtract it from (1) we get,
4x + 8y = 25
4x + 6y = 22
0x + 2y = 3
⇒y = $(3/2)
Substitute value of y in (1) to get the value of x,
4x + 8(3/2) = 25
⇒4x = 25-12
⇒x = $(13/4)
Therefore, for the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
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a group of climbers are at an altitude of at most 17,500 feet. They are on their way to the top of mount everest, which is at an altitude of 29,035 feet. How many more feet do they have left to climb?
PLEASE AASSAAPP
Answers
Answer: They have to climb 11,535 ft.
Step-by-step explanation:
To solve this equation, we need to do this equation:
29,035 ft - 17,500 ft.
29,035 ft - 17,500 ft = 11,535 ft.
help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
-1/6 x 12/5
you will get -2/5
$1.50; + 5%
Please show work :>
Answers
Answer:
0.075%
Step-by-step explanation:
Answer:
1.57500 US$
Step-by-step explanation:
You equation looked like this:
$1.50; + 5% so guugle thought something else it should be:
$1.50 + 5% without the " ; "
The ammount of 5% = 0.075
Since your adding the 5% or 0.075 it would be =
1.50 + 0.075 = 1.57500
y'all get it now?
The balance on a credit card, that charges a
28.5% APR interest rate, over a 1 month
period has a daily balance of $145. What is
the finance charge, on the average daily
balance, for this 1 month period?
28.5% = 0.285
Hint: Divide the decimal by 12 to get the monthly interest
rate. Do not round that answer. Take that answer and
multiply it to the average daily balance.
Finance charge = $[?]
Round to the nearest hundredth
Answers
The finance charge on the average daily balance for , this 1 month period is $3.45 .
In the question ,
it is given that ,
the daily balance over the period of 1 month = $145
The APR rate of interest = 28.5%
the monthly APR rate of interest = (28.5%)/12 = 2.375%
the finance charge for the 1 month period can be calculated using the formula .
finance charge = (daily average balance)×(monthly rate of interest)
Substituting the values , we get
finance charge = 145 × 2.375%
= 145 × 0.02375
= 3.44375
≈ 3.45
Therefore , The finance charge on the average daily balance for , this 1 month period is $3.45 .
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The mass, m , of a lorry is 6.58 tonnes truncated to 2 decimal places. Write the error interval for m in the form a ≤ m < b .
Answers
The error interval for m is 6.58 ≤ m < 6.59
What is truncation?Truncation is a process of dropping all decimal places after a certain point without rounding the number.
Given that, the mass, m, of the lorry is 6.58 tonnes truncated to 2 decimal places.
Since the number is truncated to two decimal places, the error interval is,
6.58 ≤ m < 6.59
Hence, the error interval for m is 6.58 ≤ m < 6.59.
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40 POINTS AND BRAINLIEST!! <3
Answers
Let’s solve the ratio:
5x+2x+3x=140
10x=140
x=14
3m - 14*5=70 canes.
2m - 14*2=28 canes.
2.5m - 14*3=42 canes.
In fractions what is the probability that a teenager selected at random is female and their favourite hobby is watching films
Answers
The probability that a teenager selected at random is female and their favourite hobby is watching films is 1/4.
What is probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From the information given, there is a total of 32 teenagers. Of those, 8 are female with a favorite hobby of watching films.
Therefore, the probability will be:
= Female who watch films / Total teenagers
= 8/32
= 1/4.
The probability is 1/4.
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Complete question
A group of teenagers is asked about their favorite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total
Male 9 2 3 14
Female 7 3 8 18
Total 16 5 11 32
Q6a. In fractions, what is the probability that a teenager selected at random is female and their favourite hobby is watching films? You can simplify this fraction if you wish.
7/15 + 9/15 + 4/15!!!!!!
Answers
Answer:
4/3 or 1.333333
Step-by-step explanation:
Use a compass and straight edge to create a line parallel to line AB through a point E that is not on line AB. First, draw a line from point E that crosses line AB, and label the intersection point C. Which step comes next?
- Set the compass point on A and draw an arc of any size across line .
- Move the compass point to the upper arc and mark off an arc, creating point D.
- Set the compass width to the width of the arc that crosses line .
- Place the point of the compass on C and draw an arc that crosses both lines.
Answers
Answer:
Step-by-step explanation:
The given steps describe constructing a parallel line using a compass and straightedge given line and a point E that is not on line .
Step 1: Draw a line through point E that intersects line , and label the point of intersection, C.
Step 2: Place the point of the compass on C and draw an arc that crosses both lines.
Step 3: Without adjusting the compass width, move the compass to point E and draw an arc that has a similar orientation to the first arc drawn.
Step 4: Set the compass width to where the lower arc crosses the two lines.
Step 5: Move the compass point to the upper arc on the intersection of the arc and line .
Step 6: Draw an arc so it intersects the bottom of the arc. Label the intersection D.
Step 7: Use a straightedge to connect points E and D to form the parallel line .
so the answer is Place the point of the compass on C and draw an arc that crosses both lines
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
I can be certain that my predicted value will match the actual value exactly.
Answers
With a correlation coefficient of 0, A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?A correlation coefficient measures the strength of the linear relationship between two variables.
Correlation coefficients usually range between -1 to 1, and they show how one variable moves in relation to another.
A positive correlation coefficient indicates that the two variables move uniformly in the same direction, while a negative correlation coefficient shows the opposite.
A zero correlation coefficient shows no linear relationship between the two variables.
Thus, if the correlation coefficient is 0, then Option A is correct.
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Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability
that the first card will be a spade, the second card will be a black card, and the third card will be a ten.
Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.
Given that,
A normal 52-card deck is used to randomly select three cards.
We have to find the probability that a spade, a black card, and a ten will be dealt as the first, second, and third cards, respectively.
Three cards are drawn with replacement from a standard deck so for the first one i.e heart , probability is (13/52)=0.25
for 2nd one i.e red it is (26/52)=0.5
for 3rd one i.e queen it is (4/52)=0.0769
thus, the answer is 0.25*0.5*0.0769=0.0096
Therefore, The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.
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Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally
Answers
Answer: $110 but that may be wrong
Step-by-step explanation:
can someone help please
Answers
Answer: 2%
Step-by-step explanation:
First, we know that the experimental value is 13.3, and the true value 13.6. After plugging in, we get |13.3 - 13.6| = -0.3 which is just 0.3 as it is the absolute value. Then, we divide it by 13.6 which brings us the equation 0.3/1.36 which rounds to 0.022. Continuing, we multiply it by 100 which gets our answer of 2.2. The nearest percent is 2, so our answer is 2 percent.
Perimeter of the rectangle is 136 units . Find vaule of z
4z+3. 3z+2
Answers
Then 4z+3+3z+2= 136
7z+3+2=136
7z+5=136
Then u move the +5 to the other side (but when u move it…. U have to change the + to a -)
Then it becomes 7z =136-5
7z= 131
Then divide 131 by 7
Z= 131/7
=18.7(round up to 3 significant figures)
You give tours on the Great Lakes and talk about points of interest.
Answers
The Great Lakes are the world's largest group of freshwater lakes by total area and second-largest by total volume.
What are the Great Lakes?The Great Lakes, also known as the Great Lakes of North America or the Laurentian Great Lakes are a series of large interconnected freshwater lakes with sea-like characteristics in North America's mid-east region that connect to the Atlantic Ocean via the Saint Lawrence River.
Superior, Michigan, Huron, Erie, and Ontario are the names of five lakes that are located on or near the Canada-United States border. Lakes Michigan and Huron are joined hydrologically at the Straits of Mackinac. The Great Lakes Waterway allows for modern water travel.
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In a telephone poll, 36 people said they like shopping and 7 people said they do not like shopping. What is the ratio of the number of people who do not like shopping to the total number of people polled?
Answers
Answer:
7:43 or [tex]\frac{7}{43}[/tex]
Step-by-step explanation:
The total is 43 7 + 36
Answer:
7:43
Step-by-step explanation:
36+7 = 43
43 is the total amount of people that were polled
those who don't like shopping are 7, as stated in the question
the ratio is 7:43
Roberto is applying for a mortgage. He has a monthly gross income of $3,500. The home he would like to buy has monthly payments for the following: $1,000 mortgage, $150 property taxes, $75 homeowners insurance premium, and $75 mortgage insurance premium. Roberto also has other monthly debts totaling $500 per month. Based on the Federal Housing Administration (FHA) total fixed payments-to-income ratio, would he qualify for the mortgage loan?
Answers
Based on the Federal Housing Administration's (FHA) total fixed payments-to-income ratio, Roberto would not qualify for the mortgage loan.
What is the fixed payments-to-income ratio?The Federal Housing Administration (FHA) allows 31% of a person's income to settle housing costs (as the front-end ratio) and 43% (as the back-end ratio) towards housing expenses and other long-term debt.
Monthly gross income = $3,500
Monthly payments for Housing:
Monthly mortgage = $1,000
Property taxes = $150
Homeowners insurance premium = $75
Mortgage insurance premium = $75
Total monthly housing costs = $1,300
Other monthly debts per month = $500
Total monthly payments = $1,800
Minimum front-end ratio = 31% = $1,085 ($3,500 x 31%)
Maximum back-end ratio = 43% = $1,505 ($3,500 x 43%)
Thus, using the FHA fixed payments-to-income ratio, Roberto would not qualify.
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The product of two consecutive integers is 110. Find the integers. Note: There are two sets of answers. The first set contains only positive answers and the second one contains only negative answers. Provide the answers in ascending order (smaller numbers first, greater numbers second)
Answers
Answer:
10 and 11
or
-11 and -10
Step-by-step explanation:
Which relation describes a function? What makes it a function?
Answers
{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.
Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:
Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.
The complete question is given below,
Which relation describes a function? What makes it a function?
A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.
B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.
C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.
D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.
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Binomial Distribution Assignment
A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. A carton
contains 12 bulbs.
-What is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective?
-What is the probability that at most 2 bulbs will be defective?
-What is the probability that at least 1 bulb will be defective?
-What is the probability that between 3 and 6 bulbs will be defective?
7
Answers
The binomial distribution is a parametric probability distribution with two parameters, X and B. For a large number of trials, n, binomial probability tends to follow a continuous normal probability distribution.
What is meant by binomial distribution?The binomial distribution is a type of probability distribution that models the likelihood of one of two outcomes given a set of parameters. It sums up the number of trials when each trial has the same chance of achieving a single outcome.
Therefore,
The following is the definition of the Binomial distribution's probability mass function:
P (X = x) = (n x)p x(1p)n x, where x = 0, 1, 2, 3,..., n
Given,
Probability of defective, p = 0.03
Number of bulbs, n = 144
(i) The required probability is P(X = 5).
P(X = 5) = (1445) 0.035(1 − 0.03)144 − 5
= 144151 × (144 − 5) 1 × 0.035(1 − 0.03)144 − 5 ≈ 0.169
Within a carton of 144 bulbs, there is a 0.169 percent chance that 5 of them will be defective.
(ii) The required probability is P(X>2).
P(X>2) = 1 − P(X≤2)
= 1 − P(X = 0) − P(X = 1) − P(X = 2)
= 1 − 144101 × (144 − 0)10.030
Then simplifying,
(1 − 0.03)144 − 0 − 14411 × (144 − 1) 10.031 (1 − 0.03)144 − 1 − 14412 × (144 − 2)10.032 (1 − 0.03)144 − 2
= 1 − 0.01245 − 0.0554 − 0.1226
= 0.810
There is a 0.810 percent chance that there will be more than two faulty bulbs in a carton of 144 bulbs.
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A motorboat travels 74 kilometers in 2 hours going upstream. It travels 110 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answers
The rate of the boat in still water is 45.5 km/hr and the rate of the current is 100.5 km/hr.
How to find speed?A motorboat travels 74 km in 2 hours going upstream.
Rate = Distance/time
Rate = 74 /2
Rate = 36 km/hr
It travels 110 km going downstream
Rate = Distance/time = 110/2
Rate = 55 km/hr
Equations:
Upstream: b-c = 36 km/hr
Downstrm: b+c = 55 km/hr
Add and solve for b
2b = 36 km/hr + 55 km/hr
2b = 91 km/hr
Divide both side by 2b
b = 91 km/hr /2
b = 45.5 km/hr (speed of the boat)
Solve for c
b+c = 55
45.5+ c = 55
c = 55 + 45.5
c = 100.5 km/hr (speed of the current)
Therefore 45.5 km/hr and 100.5 km/hr are the speed.
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