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
There are only three correct equations for the area of the right triangle which are:
0.5(x)(x + 2) = 24x² + 2x - 48 = 0x² + (x + 2)² = 100.Area of a triangleThe area of a triangle is calculated by dividing the product of the base and height of the triangle.
base of the triangle = x
height of the triangle = x + 2
area of the triangle = 1/2(x)(x + 2)
so
1/2(x)(x + 2) = 24...(1)
1/2 is also 0.5, so the equation 0.5(x)(x + 2) = 24 is correct.
by cross multiplication, equation (1) becomes;
x(x + 2) = 48
x² + 2x = 48 {expand the left hand side}
x² + 2x - 48 = 0 {subtract 48 from both sides}
so the equation x² + 2x - 48 = 0 is correct.
Considering the last equation, x² + (x + 2)² = 100
x² + x² + 4x + 4 = 100
2x² + 4x = 100 - 4 {collect like terms}
2x² + 4x = 96 {divide through by 2}
x² + 2x = 48
x² + 2x - 48 = 0
so the equation x² + (x + 2)² = 100 is equivalent to the equation (1) and so is also correct.
Therefore, the equations 0.5(x)(x + 2) = 24, x² + 2x - 48 = 0, and x² + (x + 2)² = 100 are correct and can be used to find the length of sides for the right triangle.
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Related Questions
Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has three fertilizer types, two temperature zones, and five water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.
The University of Montana ski team has ten entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the ten team entrants achieve first, second, and third places?
There are 15 qualified applicants for 4 trainee positions in a fast-food management program. How many different groups of trainees can be selected?
Answers
Answer:
The University of Montana ski team has ten entrants in a men's downhill ski event. The coach would like the first, second,
Need help ASAP. Just solve what you can and make sure to tell me what is what.
100 POINTS
Answers
Answer:
9x3+5x2=37
8-(7-5)^2+8=12
10-3+5+5x4=32
ill solve rest in comments
9x3+5x2=37
8-(7-5)^2+8=12
10-3+5+5x4=32
(Total 3 marks)
10.
A plane flies 1400 kilometres in 2 hours 20 minutes.
Calculate the average speed, in km/h, of the plane.
km/h
(Total 3 marks)
Answers
Answer:
600 km/hour
Step-by-step explanation:
1400 km in 2 hrs & 20 mins (or 2.33 hours)
1400/2.33 = 600 km/hour
Find m
3x-6
8x+4
130
Answers
Answer:
<A = 30°
The steps are given in the pic. Hope it will help :)
The tape diagram represents an equation. w 1.3 2.7
Answers
Answer: 2/3
Step-by-step explanation:
Answer: w + 1.3 = 2.7
Step-by-step explanation: i did it in khan academy ∩(︶▽︶)∩ HOPE IT HELPS
PLEASE HELP The value of x in A is _, and the value of y in B is_.
Answers
1000003842638476238476+2837428734682764283746
Answers
Answer:
3.8374326e+21
Step-by-step explanation:
id.k goo.gle said this
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Round to the nearest tenth if necessary. Gender| 0-30| 30-60| 60-90| 90+ Male| 23|35|76|46 Female|31|42|46|16
Answers
Answer:
The expected frequency for the cell E2,2 is = 33
Step-by-step explanation:
The given data is
Gender | 0-30| 30-60| 60-90| 90+ Totals
Male | 23 | 35 | 76 | 46 180
Female | 31 | 42 | 46 | 16 135
Totals 54 77 122 62 315
The expected frequency for the cell E2,2 is :
Expected for the (30-60 box for females) = Total of (30-6)/ (total )* females
= ( 77/315)135= 33
Here p= 77/315 and n= 135
therefor X= pn = 33
χ²= (33-42)²/33= 2.455 ( for the single value of E2,2=33)
Expected for the (30-60 box for males) = Total of (30-6)/ (total )* males
= ( 77/315)180= 44
χ²= (44-42)²/44= 0.09
The critical region is χ² (0.05) 3 ≥ χ²= 11.34
Let the null and alternate hypothesis be
H0:the number of minutes spent online per day is not related to gender
against
Ha: the number of minutes spent online per day is related to gender
The single value of χ² for E2,2 = 2.45 is less than the critical value of 11.34.
3
What is the remainder when 2,308 is divided by
nine? Give your answer as a fraction.
Answers
Answer:
254 R 6
Step-by-step explanation:
Answer:
256 7/16
Step-by-step explanation:
2308/9 = 256 7/16
The value of a house wa shilling 600,000 in 2005.It increased by 25% in 2006 and 10% in 2007 but dropped by 15% in 2007 find its value in 2008
Answers
Given:
The value of a house is 600,000 in 2005.
It increased by 25% in 2006 and 10% in 2007 but dropped by 15% in 2007.
To find:
The value of the house in 2008.
Solution:
We have,
Value of house in 2005 = 600,000
It increased by 25% in 2006.
Value of house in 2006 = [tex]600,000+\dfrac{25}{100}600,000[/tex]
= [tex]600,000+150,000[/tex]
= [tex]750,000[/tex]
It increased by 10% in 2007
Value of house in 2007 = [tex]750,000+\dfrac{10}{100}750,000[/tex]
= [tex]750,000+75,000[/tex]
= [tex]825,000[/tex]
But it dropped by 15% in 2007.
Value of house in 2008 = [tex]825,000-\dfrac{15}{100}825,000[/tex]
= [tex]825,000-123,750[/tex]
= [tex]701,250[/tex]
Therefore, the value of the house in 2008 is 701,250.
Find the segment lengths
Answers
Answer:
y = 18
Step-by-step explanation:
[tex] \frac{21 + 7}{21} = \frac{y + 6}{y} [/tex]
[tex] \frac{28}{21} = \frac{y + 6}{y} [/tex]
Cross multiply
28*y = 21(y + 6)
28y = 21y + 126
28y - 21y = 126
7y = 126
y = 126/7
y = 18
(5 pts) It takes Jack 3 hours longer to write holiday cards than it takes Jill. Together, they can write them
in 2 hours. How long does it take each person to write the cards working alone?
Answers
Answer:
Jack needs 6 hours and Jill needs 3 hours.
Step-by-step explanation:
Let's define the variables:
X = rate at which Jack can write a holiday card.
Y = rate at which Jill can write a holiday card.
Each of them will need a given time to write a card, such that:
X*T = 1 card
We know that Jack needs 3 more hours to write a card than Jill, then Jill needs 3 hours less than Jack, so if Jack needs T hours, Jill will need T - 3 hours
Then we have the equation:
Y*(T - 3 hr) = 1 card
And we also know that when they work together, they need 2 hours, then:
(X + Y)*2 hr = 1 card.
So we have 3 equations:
X*T = 1 card
Y*(T - 3 hr) = 1 card
(X + Y)*2 hr = 1 card.
Now let's ignore the card part just for the equations, then we get:
X*T = 1
Y*(T - 3 hr) = 1
(X + Y)*2 hr = 1
To solve it, we first need to isolate one variable in one of the equations, let's isolate T in the first equation, we get:
T = 1/X
Now we can replace this in the second equation to get:
Y*((1/X) - 3hr) = 1
So now we have two equations:
(X + Y)*2 hr = 1
Y*((1/X) - 3hr) = 1
We need to do the same, isolate one variable in one of the equations, let's isolate Y in the above one:
Y*2hr = 1 - X*2hr
Y = (1 - X*2hr)/2hr
Now we can replace this in the other equation to get:
((1 - X)/2hr)*((1/X) - 3hr) = 1
Now we can solve this for X:
((1 - X)/2hr)*((1/X) - 3hr) = 1
(1 - X)*((1/X) - 3hr) = 2 hr
1/X - 3hr - X*2hr/X + X*2hr*3hr = 2hr
1/X - 3hr - 2hr + X*6hr^2 = 2hr
1/X + X*6hr^2 = 2hr + 3 hr + 2 hr = 7hr
1/X + X*6hr^2 = 7hr
Now we can multiply all by X to get:
X/X + X*(X*6hr^2) = 7hr*X
Now we have the quadratic equation:
(6hr^2)*X^2 - (7hr)*X + 1 = 0
We can find the solutions of this equation if we use the Bhaskara's formula, the solutions are:
[tex]X = \frac{-(-7hr) +- \sqrt{(-7hr)^2 - 4*(6hr^2)*1} }{2*6hr^2} = \frac{7hr +- 5hr}{12 hr^2}[/tex]
Then we have two solutions:
X = (7hr + 5hr)/12hr = 1 hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.167 card/hr
Then Jill's rate will be:
Y = (1 - X*2hr)/2hr = (1 - 1card/hr*2hr)/2hr = -0.5 card/hr
So we have a negative rate, this makes no sense, so we can discard this option. The other solution for X is:
X = (7hr - 5hr)/12hr = 0.166... hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.166... card/hr
If we have this, then the rate for Jill will be:
Y = Y = (1 - X*2hr)/2hr = (1 - 0.167card/hr*2hr)/2hr = 0.333 card/hr
Then we have:
X = 0.167 card/hr
If we use the first equation, we get:
(0.166... card/hr)*T = 1 card
T = 1 card/((0.166... card/hr)) = 6 hours
Then Jack needs 6 hours to write a card.
And we know that Jill needs 3 hours less than that, then Jill needs 3 hours.
helppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says that the evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero. The paper reports this as Professor McDaniel said that good researchers tend to be poor teachers, and vice versa. Which statement in plain language (i.e. without the word correlation) correctly explains the psychologist's meaning?
A)There is little connection between research productivity and teaching rating.
B) While bad researchers tend to be good teachers, there is no similar relationship between good researchers and bad teachers.
C) While good researchers tend to be bad teachers, there is no similar relationship between bad researchers and good teachers.
D) Good researchers tend to be bad teachers and bad researchers tend to be good teachers.
Answers
Answer:
The correct option is A.
Step-by-step explanation:
As the psychologist states that there is no correlation found between teaching ratings and research productivity of the same faculty member, meaning that there is no significant relationship between the two. The paper's report states quite the opposite, that there is an inverse correlation. The statement that explains what the psychologist says correctly is A. There is little connection between teaching rating and research productivity.
I hope this answer helps.
Pls help
Identify each angle pair as adjacent, vertical, or neither. Identify Structure Refer to the diagram at the right. Identify each angle pair as adjacent, vertical, or neither.
Answers
Answer:
angle 5 and angle 6 are adjacent angles, all adjacent means is directly next to each other, another example would be 6 and 1; 1 and 2; 2 and 3, etc
and example of vertical angles would be 6 and 3, they basically form an x, another example is 5 and 2, 1 and 4, etc
an examples of angles that would qualify as neither would be 1 and 3, they are not next to one another, thus they are not adjacent, and they do not form an x so they are not vertical, another example would be 5 and 3
Solve 5x + 34 = –2 + 7x for x.
Question 14 options:
A)
x = 12
B)
x = 18
C)
x = –16
D)
x = –24
Answers
Answer:
x = 18
Step-by-step explanation:
A collection agent earns a fixed amount for each call that he makes, as
shown in the graph below.
If the collection agent makes 11 calls, how much will he earn in total?
Answers
Answer:
The answer is $9.90
Step-by-step explanation:
help quick
Write the ratio as a fraction in lowest terms. Be sure to make necessary conversions:
12 feet to 15 inches
Answers
48/53
Steps
15 inches = 1.25 feet
Ratio = 12 : 1.25
Simplified = 9.6 : 1
9.6 + 1 = 10.6
9.6/10.6 = 48/53
Checking...
12 feet = 144 inches
Ratio = 144 : 15
144 + 15 = 159
144/159 = 48/53
Answer:
[tex] \frac{12}{15} [/tex]
Step-by-step explanation:
12:15
•=12[tex] \frac{12}{15} [/tex]What is the sum of 1 2 + 1 4 12+14? Use the fraction strip to help.
Answers
Answer:
6/8 or in simple terms, 3/4
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{1}{4} \\ = ( \frac{1}{4} + \frac{1}{4} ) + \frac{1}{4} \\ = ( \frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) \\ = ( \frac{2}{8} ) + ( \frac{2}{8} ) + ( \frac{2}{8} ) \\ = \frac{6}{8} \\ = \frac{2 \times 3}{2 \times 4} \\ = \frac{3}{4} [/tex]
The given operation of the two fractions can be found as 6/8. The correct option is (D).
What is a fraction?A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.
The number a is called as the numerator and b is the denominator.
The given expression is 1/2 + 1/4.
It can be solved using the strip given as below,
The number of 1/8 sections under 1/2 in the strip is 4.
And, the number of 1/8 sections under 1/4 in the strip is 2.
Then, the addition of the two fractions is equivalent to the total number of 1/8 sections under both of them.
It can be written in mathematical form as,
⇒ 1/2 + 1/4
⇒ 4 × 1/8 + 2 × 1/8
⇒ 6/8
Hence, the required sum of the given fractions can be evaluated as 6/8.
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Which equation has the steepest graph?
Answer Choices:
y = 2x + 4
y = -4x – 1
y = 1/2 x + 10
y = 5x + 2
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
in order to find if a line is steeper, you need to look at the slope
the greater the slope, the steeper the line will be
y = 2x + 4
y = -4x - 1
y = 1/2x + 10
y = 5x + 2
out of all of these options, y = 5x + 2 has the largest slope. this means that it is the steepest one.
Find the Area Please
Answers
This should be the correct answer
please help me thank you
Answers
Answer:
D) Perpendicular
Step-by-step explanation:
Red: 5y+4x=-30
Blue: y=5/4x-5
170
The following problems were in your worksheet on direct and inverse proportion. Reformulate the
relationships as algebraic expressions and remember to define the variables you use. You do not
have to solve the expressions.
5. The students in class usually drink a lot of water to help with their studies. I have found that
with five students in the class at least 30 litres of water is needed. How much water will be
needed when there are 30 students in the class?
Answers
Answer:
For s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.
Step-by-step explanation:
This question is solved by proportions, using rule of three.
I am going to say that:
s is the number of students.
l is the number of liters of water needed for s students.
I have found that with five students in the class at least 30 litres of water is needed.
This means that:
[tex]\frac{s}{l} = \frac{5}{30}[/tex]
[tex]5l = 30s[/tex]
[tex]l = \frac{30s}{5}[/tex]
[tex]l = 6s[/tex]
This means that for s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.
you work at a coffee house roasted coffee beans retain 3/5 of the initial weight approximately what percentage of the initial weight do they retain
Answers
Answer:
they retain 3/5 or 60% of their initial weight
Step-by-step explanation:
How would yoy simplify 4(5+x)
Answers
Answer:
4x + 20
Step-by-step explanation:
4(5 + x) = 4 * 5 + 4 * x = 20 + 4x = 4x + 20
Hope this helps you out! Cya
51 –
6.8 + 4.3/4
-0.8
Answers
Answer:
11.325
Step-by-step explanation:
Ce clasă ești sa văd daca te pot ajuta
Please please give answer , the numbers on the side are the options
Answers
Answer:
24 tiles (none of the options given is correct)
Step-by-step explanation:
Number of tiles required to floor the room = area of the room/area of 1 tile
Area of the room = 36m * 24m = 864 m²
Area of 1 tile = 6² = 36 m²
Number of times required = 864/36 = 24 tiles
3.5-5.5n-4n+8 help please
Answers
A server sees 90 customers over 6 hours. How many customers did they see in 1 hour? *
Answers
Answer:
They saw 15 customers per hour.
Step-by-step explanation:
Because its 90 divided by 6 basically
you have 60 oz of egg noodles. yiu need 5 oz to make one serving of chicken noodle soup. how maby servings can you make
Answers
Answer:
The answer is 12
Step-by-step explanation:
You have to divide 5 and 60 or you can multiply by 5 until you get to 60.
Answer:
12
Step-by-step explanation:
60/5=12