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.
3 0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x - 24 = 0
10 ft
(x + 2) ft
* x2 + 2x - 48 = 0
* x2 + (x + 2)2 = 100
xft
Not drawn to scale
Answers
The equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Solution:
From given,
Area of right triangle = 24 square feet
Also from given figure in question (attached below )
base = x and height = x + 2
The area of triangle is given by formula:
[tex]Area = \frac{1}{2} \times base \times height[/tex]
Substituting the values we get,
[tex]24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\[/tex]
Also, the above equation can be written as,
[tex]x^2 + (x+2)^2 =100[/tex]
Thus the equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Answer:
A, D, E
Step-by-step explanation:
From the answer above, but the letters to make it easier :)
Related Questions
A rectangular garden measuring 12 meter by 16 meter is to have a walkway installed around it with a width of x meters as shown below find the area of the walkway
Answers
Answer:
[tex]Area\ of\ walkway=4x^2+56x\ meter^2[/tex]
Step-by-step explanation:
[tex]Length\ of\ garden=16\ meters\\\\Width\ of\ garden=12\ meters\\\\Width\ of\ walkway=x\ meters\\\\Now\ Length\ of\ new\ rectangular=16+x+x\ \ \ \ \ (as\ x\ meter\ walkway\ increased\ both\ the\ sides)\\\\Now\ width\ of\ new\ rectangular=12+x+x\ \ \ \ \ (as\ x\ meter\ walkway\ increased\ both\ the\ sides)\\\\Area\ of\ walkway=Area\ of\ new\ rectangular-Area\ of\ rectangular\\\\Area\ of\ rectangle=length\times width\\\\Area\ of\ walkway=(16+2x)\times (12+2x)-16\times 12[/tex][tex]Area\ of\ walkway=16\times 12+2x\times 12+16\times 2x+2x\times 2x-16\times 12\\\\Area\ of\ walkway=4x^2+56x\ meter^2[/tex]
A regular hexagon is shown.
What is the measure of the radius, c, rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.
6 in.
10 in.
14 in.
24 in.
Answers
Answer:
14 in.
Step-by-step explanation:
well to start we have to know the relationships between angles, legs and the hypotenuse.
a: adjacent
o: opposite
h: hypotenuse
sin α = o/h
cos α= a/h
tan α = o/a
now as we know that the triangle that is formed has a right angle of 90 degrees, and two other angles that are 30 and 60 degrees.
We can know this by the properties of the hexagons
hexagon is formed by 6 equilateral triangles
equilateral triangles have 3 angles of 60 degrees
the triangle of the image is half of one of those triangles so it will have the upper angle of 30 and the other of 60
Now if we take the angle of 30 degrees and apply the following formula
sin α = o/h
cos 30 = a/h
0.866 = 12/h
h = 12/0.866
h = 13.8564
h = c
the nearest number is 14
Answer:14in on edg.
Step-by-step explanation:
please help..!!!!!!!
Answers
Answer:
E) (-4, -3)
Step-by-step explanation:
To use elimination, you need to have one variable in both equations that have the same coefficient. (The coefficient is the number attached to the variable). Both equations have "7y".
The way elimination works is by eliminating one of the variables first. Decide how (-7y) and (-7y) can cancel out and become 0. You can either add or subtract.
(-7y) - (-7y) Try subtracting
= (-7y) + 7y
= 0
Based on this, we should subtract the whole equations.
Set up the equations like normal subtraction. Then, subtract each of the terms that have the same variable.
. 4x - 7y = 5
- 9x - 7y = -15 Do 4x - 9x = -5x. -7y - (-7y) = 0. 5 - (-15) = 20.
. -5x - 0 = 20 "y" cancelled out
. -5x = 20 Isolate 'x'
. -5x/-5 = 20/-5 Divide both sides by -5
. x = -4 Solved x-coordinate
Substitute 'x' for -4 in any of the equations. Then simplify and isolate "y" to solve for the y-coordinate.
4x - 7y = 5
4(-4) - 7y = 5 Simplify the multiplication.
-16 - 7y = 5 Start isolating 'y' now
-16 + 16 - 7y = 5 + 16 Add 16 to both sides. Left side cancels out 16
-7y = 5 + 16 Solved right side by adding
-7y = 21
-7y/-7 = 21/-7 Divide both sides by -7
y = -3 Solved y-coordinate
Therefore the answer is (-4, -3).
PLEASE HELP ME WITH THIS QUICK 1. What is the measurement of PQ
Answers
Answer:
12.72 units
Step-by-step explanation:
Recall the mnemonics: SOHCAHTOA
We want to find PQ, which is opposite to the 58° angle.
So we use the sine ratio: SOH , which means Sine is Opposite/Hypotenuse
[tex] \sin(58 \degree) = \frac{PQ}{15} [/tex]
This implies that:
[tex]PQ = 15 \sin(58) [/tex]
We substitute the value for sin58° to get:
[tex]PQ = 15(0.848)[/tex]
PQ=12.72
how do you solve this system , y=1/2x-4 and y=-2x+1 by graphing
Answers
Answer:
x=2
y=-3
Step-by-step explanation:
we have
[tex]y=\frac{1}{2}x-4[/tex] ----> equation A
[tex]y=-2x+1[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations by graphing is the intersection point both lines.
using a graphing tool
The intersection point is (2,-3)
therefore
The solution is
x=2
y=-3
Simon makes 30 cakes he gives 1/5 of the cakes to Sali. He gives 10 percent of the 30 cakes to Jane what fraction of the 30 cakes does he have left?
Answers
Answer:
7/10
Step-by-step explanation:
0.1 = [tex]\frac{1}{10}[/tex]
1/5
30 × 1/10 = 3
30 × 1/5 = 6
6+3 = 9
30 - 9 = 21
21/30 simplified = 7/10
Answer:
7/10
Step-by-step explanation:
Total number of cakes made by Simon = 30 cakes.
Number of cakes gave to Sali =
1/5 Of total cakes = 1/5 x 30 = 6 cakes.
Number of the cakes gave to Jane = 10% of 30 cakes
10/100 as a decimal 0.10.
10% of 30 cakes = 0.10 times
30 = 3 cakes.
Total number of cakes left = Total cakes made - Cakes gave to Sali - Cakes gave to Jane
30-6-3 = 21
21 cakes left.
21/30 = 7/10
Convert 13200 feet into miles
Answers
Answer:
2.5 miles
Step-by-step explanation:
to do this, you must know that there is 5280 feet in one mile.
then divide 5280 feet into 13200
13200 ÷ 5280 = 2.5
13200 feet can be converted to miles by dividing the length in feet by the conversion factor of 5280, which represents the number of feet in a mile.
To convert feet to miles,
divide the length in feet by the conversion factor of 5280, as there are 5280 feet in a mile. By dividing 13200 feet by 5280, the results in 2.5 miles. This means that 13200 feet is equal to 2.5 miles in length.To convert 13200 feet to miles, divide 13200 by 5280.
[tex]13200 / 5280 = 2.5[/tex] miles.
13200 feet is equivalent to 2.5 miles
Therefore, 13200 feet is equivalent to 2.5 miles by dividing the length in feet by the conversion factor of 5280, which represents the number of feet in a mile.
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Find the missing side length of m.
Answers
Answer:
m=4
Step-by-step explanation:
Since we know that quadrilateral ABCD is similar to QRST, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
[tex]\frac{ST}{CD}=\frac{RS}{BC}\\\\\frac{6}{15} =\frac{m}{10}\\[/tex]
[tex]\frac{6*10}{15} =m\\m=60/15=4[/tex]
m=4
if a=10 and b=2,then a/b•b=
Answers
a=10 & b=2, according to this, 10/2=5, so now it's 5*2=10
the perimeter of a regular hexagon is represented by this expression 42x-24. the expression ______ represents the length of one side of the hexagon.
Answers
Yo sup??
let the lenght of one side of the hexagon be y
total perimeter=sum of lenght of all sides=6y
But
perimeter=42x-24
Therefore
6y=42x-24
y=7x-4
Hence the equation of one side is 7x-4
Hope this helps
The answer is 7x-4.
Hope this helped
Based on the graph below, what are the factors of the quadratic function?
Answers
it is the X+3 and (x+.2)
a pool manager balances the ph level of a pool. the price of a bucket of chlorine tablets is $90, and the price of a ph test kit is $11. the manager uses a coupon that applies a 40% discount to the total cost of the two items. how much money does the pool manager pay for each item?
Answers
The pool manager pays $54 for the chlorine tablets and $6.60 for the pH test kit.
Explanation:The pool manager pays $54 for the bucket of chlorine tablets and $6.60 for the pH test kit after applying the 40% discount.
To find the price of the chlorine tablets after the discount, we multiply $90 by 40% to get $36. Subtracting $36 from $90 gives us the final price of $54.To find the price of the pH test kit after the discount, we multiply $11 by 40% to get $4.40. Subtracting $4.40 from $11 gives us the final price of $6.60.Therefore, the pool manager pays $54 for the chlorine tablets and $6.60 for the pH test kit.
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The pool manager pays the cost of $54 for the chlorine tablets and $6.60 for the pH test kit.
Explanation:The calculation you're looking to perform is a simple example of a percentage discount on a sum of money. To figure out how much the pool manager pays for each item, you have to first calculate the total cost of the items. The total cost of both the bucket of chlorine tablets ($90) and the pH test kit ($11) is $101.
A 40% discount on the total cost is then calculated by taking 40% of $101, which is $40.40. This discount is subtracted from the total cost (101-40.40), leaving the pool manager to pay $60.60. To determine the cost of each item after the discount, we assume that the discount was applied equally to both items.
This means that the cost price for each the bucket of chlorine tablets and pH test kit, after the discount, would be $54 and $6.60 respectively.
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The two figures above are congruent. Find the measure of the angle that isn't labeled on either figure.
Answers
Answer:
I think it's 100
Step-by-step explanation:
133 + 86 + 41 = 260
360 - 260 = 100
What is 10 2/6 minus 7 3/6
Answers
Answer:
2 5/6
Step-by-step explanation:
10 2/6 - 7 3/6
10 - 7 = 3
2/6 - 3/6 = -1/6
3-1/6 = 2 5/6
If A and B are independent events, P(A and B) =
Answers
Answer:
If A and B are independent events, P(A and B) = P (A) * P (B)
Step-by-step explanation:
Let's recall that independent events means that when one event occurs, it has no impact or influence on the probability of another event occurring. Here’s an example. Let’s say that we have two events, A and B.
Event A : it rains in Seattle
Event B : the Super Bowl match is cancelled in Miami
The two events are independent; if it rains in Seattle, this will have no impact on the probability that the Super Bowl match is cancelled in Miami. Raining in Seattle and the cancellation of the Super Bowl are independent events, therefore:
P(A and B) = P (A) * P (B)
A flower pot’s base has six sides that are all the same length. Each side measures
x−6
units. The base’s perimeter is 78 units. what is the value of x?
Answers
Since we know there are 6 sides and each side has the length of x-6, we set up this equation and solve:
6(x-6)=78
x-6=13
x=19
So the value of x is 19, which means each side has a length of 13 units.
Hope this helped!
Jack has some marbles. He has ten more red marbles than blue marbles. He has fewer yellow marbles than blue marbles.
How many of each color marble could Jack have?
(This is the whole question)
Answers
A possible number of marbles for this situation is:
Red = 13
Blue = 3
Yellow = 2
How many of each color marble could Jack have?
Let's define the variables:
R = number of red marbles.
B = number of blue marbles.
Y = yellow marbles.
Then we can write:
R = B + 10
Y < B
So we have only these two conditions, now let's find possible values.
If we define B = 3, then:
R = 3 + 10 = 13
Y < 3
Then Y can be 2.
So a possible value is:
Red = 13
Blue = 3
Yellow = 2
Final answer:
The number of each color marble Jack has can be determined by setting the number of blue marbles as a variable. Red marbles are ten more than blue, and yellow marbles are fewer than blue. Specific combinations are possible as long as these conditions are met.
Explanation:
Jack has some marbles. He has ten more red marbles than blue marbles and fewer yellow marbles than blue marbles. To determine how many of each color marble Jack could have, consider blue marbles as the variable x. Then, the number of red marbles would be x + 10 and the number of yellow marbles would be less than x.
Here are a few possible combinations:
If Jack has 1 blue marble, he cannot have 10 more red marbles and fewer yellow marbles as this would result in a negative number of yellow marbles which is not possible.
If Jack has 2 blue marbles, then he would have 12 red marbles (x + 10), and potentially 1 yellow marble since it needs to be less than the number of blue marbles.
If Jack has 3 blue marbles, he would have 13 red marbles, and it could be 1 or 2 yellow marbles.
Thus, the compositions of marbles are dependent on the number of blue marbles Jack has. As long as the number of red marbles is ten more than blue and the yellow marbles are fewer than blue, the condition is satisfied.
A 17 minute telephone call from Boston to Chicago costs 2.38 what is the cost per minute?
Answers
Answer:
0.14
Step-by-step explanation:
As for 17-minute call = 2.38 cost
Thus per minute call which is 1 minute call is = 2.38/17 min
Therefore the answer is 0.14
$2.38 divided by 17 is 0.14
Kayla is running for charity. Her dad pledges to give her $0.50 per mile she runs. Her mom pledges to give her a flat donation of $5. How many miles will Kayla have to run to get the same donation from both parents?
Answers
Answer:
10 miles
Step-by-step explanation:
Let m represent the number of miles Kayla runs. We want to find m such that ...
0.50m = 5.00
Divide by the coefficient of m:
m = 5.00/0.50 = 10
Kayla has to run 10 miles to get the same donation from both parents.
Answer:
!0 miles
Step-by-step explanation:
i need help PLEASE!!!!
Answers
Answer:
OPTION A
OPTION B
OPTION D
Step-by-step explanation:
Given that a bag of apples cost 'a' dollars.
A bag of oranges cost 'a + 2' dollars.
Therefore, one bag each of apples and oranges should cost: a + a + 2 dollars.
Since, Dorie buys 5 bags of apples and Oranges, it would have costed her:
5(a + a + 2)
= 5(2a + 2)
= 10a + 10
Hence, OPTION A, B and D are the correct answers.
Write an equation in point-slope form for the line through the given point that has the given slope.
(5, –8); m = –3
Answers
Answer:
y=mx+b is the formula. So -8=-3x+5 would be the answer..
since (x,y) just substitute these numbers you have it into the formulas... Take y from (5,-8) and place it into y=mx+b. Next take the slope which is -3. And then since its a postive number we add are x from (x,y). -8=-3x+5. We also add x next to the slope (-3) becuase we are trying to solve for x. And we always put it next to the slope. Hope this helps!
Answer:
Step-by-step explanation:
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) you have : m=-3 and x_1 = 5 and y_1 = -8
an equation in the point-slope is : y +8 = m(x - 5)
How to write 2.751 in word from
Answers
Answer: Two and Seven hundred fifty one thousanths
Step-by-step explanation:
18
Andy flies from the UK to Japan.
His plane ticket costs £554.
Andy then flies from Japan to Australia.
His plane ticket costs 70 140 Japanese Yen.
The exchange rate is £1 = 140 Japanese Yen.
Leila flies from the UK to Australia.
Her plane ticket costs 1860 Australian dollars.
The exchange rate is 1 Australian dollar = £0.62.
Who pays more to fly from the UK to Australia, Andy or Leila?
You must show clearly how you get your answer.
Answers
Answer: Leia pays more to fly from the UK to Australia
Step-by-step explanation:
We have two persons, Andy and Leila; both travel from UK to Australia but in different ways:
For Andy:
-He first flies from UK to Japan and the cost of the ticket is [tex]\£ 554[/tex]
-Then he flies from Japan to Australia and the cost of the ticket is [tex]70140 Yen[/tex]
So, the cost of Andy's trip is:
[tex]\£ 554+70140 Yen[/tex] (1)
Taking into account that we have to use the same units to sum two quantities, we have to convert the Yens to [tex]\£[/tex]; knowing that [tex]\£ 1=140 Yen[/tex]:
[tex]70140 Yen \frac{\£ 1}{140 Yen}=\£501[/tex]
Then, (1) is rewritten as:
[tex]\£ 554+\£501=\£1055[/tex] (2) This is the total cost of Andy's trip
For Leila:
She flies directly from UK to Australia and the cost of her ticket is [tex]\$ 1860[/tex] (Australian dollars)
Taking into account that we have the price of Andy's trip in [tex]\£[/tex], we have to convert the Australian dollars to [tex]\£[/tex], in order to compare.
So, knowing that [tex]\$ 1=\£ 0.62[/tex] we have:
[tex]\$ 1860 \frac{\£ 0.62}{\$ 1}=\£1153.2[/tex] (3) This is the total cost of Leila's trip
Hence, comparing (2) and (3) we can see that Leila paid more to fly from UK to Australia.
How many solutions does this system of equations have?
y=-2x+2
2y+4x=4
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
look at picture
What is the perimeter of the 9-inch by 12-inch photo?
Answers
9+9+12+12.
24+18.
Answer? 42 inches
Answer:
The perimeter is 42 inches
Step-by-step explanation:
The perimeter is the sum of each side. So 9 + 9 + 12 + 12 = 42
You can also use the formula, w*2 + l*2 = P
Hope this helped! :)
Which expression is equivalent to 210d2 - 63d
Answers
Answer:
21d (10d - 3)
Step-by-step explanation:
Factor 21d out of 210d² - 63d
I don't know if this answered your question correctly, but that is how I would solve it.
The expression is equivalent to 210d² - 63d is 21d( 10d - 3).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 210d² - 63d
now, factorizing each term of expression
210d² = 2 x 3 x 5 x 7 x d x d
-63d = -3 x 3 x 3 x d
So, 210d² - 63d
= (2 x 3 x 5 x 7 x d x d) - (3 x 3 x 7 x d).
= 21d (2 x 5 x d - 3 )
= 21d( 10d - 3)
Hence, the equivalent expression is 21d( 10d - 3).
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*WILL GIVE BRAINLIEST*
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.
Which would you rather do?
Answers
Answer:
$50 and
$30
Step-by-step explanation:
Question 1. Principal = $500
Rate = 5%
Time = 2yesrs
Interest = PRT /100
= 500 x 5 x 2 /100
= 5000/100
= $50
Interest = PRT/100
Principal P =$500
Rate = 3%
Time = 2 years
Therefore, interest =
500 x 3 x 2 /100
= 3000/100
= $30
PLEASE HELP QUICK!!!!
Answers
Answer:
Step-by-step explanation:
ABC = 72 degrees
CBF = 108 degrees
DBE = 18 degrees
ADB = 90 degrees
which sum will be irrational?
a) 3+2
b) square root 19 + 7 over 2
c) 18 over 3 + 11 over 10,000 d) -6+(-3.251)
Answers
Option b) square root 19 + 7 over 2 will be an irrational sum because it includes the square root of a non-perfect square (19), which is an irrational number, added to a rational number (7/2).
The question asks which sum will be irrational. To determine this, we must look at each of the options:
a) 3+2 is the sum of two integers, which is also an integer, and thus a rational number.
b) square root 19 + 7 over 2 involves the square root of 19, which is an irrational number because 19 is not a perfect square. The sum of an irrational number and a rational number (7/2) is irrational.
c) 18 over 3 + 11 over 10,000 is the sum of two rational numbers, as both fractions can be simplified to a common form with integer numerators and denominators.
d) -6+(-3.251) is the sum of two rational numbers, since 3.251 can be expressed as a fraction.
The sum in option b will be irrational because it involves the sum of an irrational number, square root 19, and a rational number, 7/2. All the other sums are of rational numbers and will, therefore, also be rational.
JKL is a right triangle. JL = 10, KL = 8,
and JK = 6. What is cos L?
10
What is the answer
Answers
Answer:
[tex] \cos L = \dfrac{4}{5} [/tex]
Step-by-step explanation:
The right angle is angle K. KL and JK are legs. JL is the hypotenuse.
For angle L, KL is the adjacent leg.
In general, for acute angle A of a right triangle,
[tex] \cos A = \dfrac{adjacent~leg}{hypotenuse} [/tex]
In this case,
[tex] \cos L = \dfrac{adj~leg}{hyp} [/tex]
[tex] \cos L = \dfrac{KL}{JL} [/tex]
[tex] \cos L = \dfrac{8}{10} [/tex]
[tex] \cos L = \dfrac{4}{5} [/tex]