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 can be used to find the lengths of the legs of the given triangle is (A) 0.5(x)(x + 2) = 24.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the area of the triangle:
1/2 × base × heightSo, the height is (x+2) ft and the base is x ft.Now, use the formula and values to solve the equation:
24 = 1/2 × x × (x+2)24 = 0.5(x) (x + 2)Therefore, the equation that can be used to find the lengths of the legs of the given triangle is (A) 0.5(x)(x + 2) = 24.
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Correct question:
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
A. 0.5(x)(x + 2) = 24
B. x(x + 2) = 24
C. x2 + 2x – 24 = 0
D. x2 + 2x – 48 = 0
E. x2 + (x + 2)2 = 100
Related Questions
Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
–3 > x ≥ –1
–3 < x ≤ –1
–3 ≤ x < –1
–3 ≤ x > –1
Answers
Step-by-step explanation:
an open (empty) point means the point itself is not included.
a closed (filled) point means the point itself is included.
the x values going from -3 (not included) to -1 (included) means
-3 < x <= -1
so, the second answer is correct.
how to i find the decimal for 3√2 on a calculator its suppose to be 4.242 what do i put in what are the steps i can't figure it out.
Answers
Step-by-step explanation:
3√2 means 3 times the square root of 2.
Enter 2. Press the square root key to get square root of 2.
You should see 1.4142135
Now multiply by 3.
You should get 4.2426405
Find the length of side x in simplest radical form
with a rational denominator.
30⁰
X
4
60°
Answers
The value of measure of x in the triangle is,
⇒ x = 4√3 units
We have to given that,
A triangle is shown in image.
Now, WE can formulate by trigonometry formula we get;
⇒ tan 30° = Opposite / Base
⇒ tan 30° = 4 / x
⇒ 1/√3 = 4/x
⇒ x = 4√3 units
Thus, The value of measure of x in the triangle is,
⇒ x = 4√3 units
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of the company's
A company receives 1.5% commission on the sale price of each house sold. For each house he sells, James earns
commission. James sells a house for $205,000. How much money will James earn?
Answers
Answer:
$1,025
Step-by-step explanation:
(205000)(.015)/3 = 1025
James will receive or earn $1,025
22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.
A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.
B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.
C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
Answers
From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
What is meant by percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.
Given,
Amount of coffee in A bag of ground coffee = 11 ounces
Number of bags = 250 bags
Number of bags which contain 10.9 ounces of coffee = 50
The percentage of bags which contain 10.9 ounces of coffee
= (50/250) × 100 = 20%
This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.
Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
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Divide: 7 5/6 ÷ 2/3 need help
Answers
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.
Step 1: Convert the mixed number to an improper fraction:
7 5/6 = (6 * 7 + 5) / 6 = 47/6
Step 2: Multiply the improper fraction by the reciprocal of the fraction:
47/6 ÷ 2/3 = 47/6 * 3/2
Step 3: Simplify the fraction if possible:
47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12
Step 4: Simplify the fraction further, if necessary:
141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4
Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.
What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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Based on the pattern, what are the next two terms of the sequence?
Answers
Answer:
33 , 39
Step-by-step explanation:
given
9 , 15 , 21 , 27
there is a common difference between consecutive terms, that is
15 - 9 = 21 - 15 = 27 - 21 = 6
to obtain terms in the sequence add 6 to the preceding term
27 + 6 = 33
33 + 6 = 39
the next two terms are 33 and 39
15-9=6
21-15=6
27-21=6
That means we are adding 6 at every step. Therefore the next two elements must be
27+6=33 and 33+6=39
If a pound of rice flour costs $12, how many ounces can be bought for $6.90?
Answers
Answer:
9.2 ounce
Step-by-step explanation:
To do this, we divide $12 by 16 ounces, because there are 16 ounces in a pound:
12/16 = 0.75
Now, we need to find how many ounces can be bought for $4.80. To do this, we divide 6.90 by 0.75
=9.2 ounce
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. Health Club B charges a $30 sign-up fee and $40 per month. The graph below represents what Health Club A charges.
PPPLEASE HELLLLLLLLP I WILL GIVE BRAINLYYYYYYYYYYYYYY
Answers
Health club B costs $70 each month more than Health club A.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Health Club B charges a $30 sign-up fee and $40 per month. The graph below represents what Health Club A charges.
Now, Equation of line is,
For Health club B;
⇒ y = 40x + 30
For Health Club A;
⇒ y - 121 = (333 - 121) / (6 - 2) (x - 2)
⇒ y - 121 = 212/4 (x - 2)
⇒ y - 121 = 53 (x - 2)
⇒ y - 121 = 53x - 106
⇒ y = 53x - 106 + 121
⇒ y = 53x + 15
For each month,
Cost For Health club B;
⇒ y = 40x + 30
⇒ y = 40 + 30
⇒ y = $70
Cost For Health Club A;
⇒ y = 53x + 15
⇒ y = 53 + 15
⇒ y = $68
Thus, Health club B costs $70 each month more than health club A.
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Truman's father is designing a toy car ramp for him. His dad determined that the measure of angle x needs to be increased by 20
What is the measure of the new angle?
Answers
Answer:
20°
Step-by-step explanation:
Solution,
Here,
→(x+20°)+160°=180°[Sum of a straight line is 180°]
→x=180°-180°
→x=0°
Again,
→x+20°
→0°+20°
→20°
Answer:
I have the same problem as you and it told me that it’s 40
Step-by-step explanation:
simplify 4y(4y-4)-4(-4y+5+4y2)
Answers
Thank me later
A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
A 13.4 feet
B 14.6 feet
C 16.5 feet
D 18.0 feet
Answers
Answer:
A
Step-by-step explanation:
linda Put $610 in a savings account that pays 1.2% interest each year. Enrique puts $590 in a high-yield account that pays 3.9% interest each year.
PART A: After one year who has more money? How much more?
PART B: After a second year who has more money? How much more?
Answers
PART A: Linda has $4.41 more than Enrique after one year.
PART B: Enrique has $12.10 more than Linda after the second year.
PART A: After one year, we can calculate the amount of money each person has in their respective accounts.
For Linda's account:
Principal amount = $610
Interest rate = 1.2%
\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)
\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)
For Enrique's account:
Principal amount = $590
Interest rate = 3.9%
\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)
Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91
Comparing the two amounts, after one year Linda has more money.
The difference in the amount is:
$617.32 - $612.91 = $4.41
Therefore, Linda has $4.41 more than Enrique after one year.
PART B: After a second year, we need to calculate the amounts again.
For Linda's account:
Principal amount = $617.32
Interest rate = 1.2%
\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)
Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73
For Enrique's account:
Principal amount = $612.91
Interest rate = 3.9%
\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)
Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83
Comparing the two amounts, after the second year Enrique has more money.
The difference in the amount is:
$636.83 - $624.73 = $12.10
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If the Federal Reserve decreases the reserve rate from 6% to 4%, how does this affect the amount of money that would result because of fractional-reserve banking from an initial deposit into a bank of $15,000?
A.
It increases the amount by $250,000.
B.
It increases the amount by $125,000.
C.
It decreases the amount by $125,000.
D.
It decreases the amount by $250,000.
Answers
The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.
When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.
In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.
When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.
The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.
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-7x - 4y = -4 find the slope and y intercept of the line
Answers
Answer:
The slope is -7/4 and the y intercept is 1
Step-by-step explanation:
-7x - 4y = -4
Put the equation in slope intercept form and solve for y
y = mx+b where m is the slope and b is the y intercept
Add 7x to each side
-7x - 4y+7x =+7x -4
- 4y =7x -4
Divide by -4
-4y/-4 = 7x/-4 -4/-4
y = -7/4 x +1
The slope is -7/4 and the y intercept is 1
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
Answers
Answer:
f^-1 (-15) = -6
f^-1(4) + f(9) = 0
Step-by-step explanation:
f^-1 (-15) =
Look where the output is -15 and find the x value ( x=-6)
Since where are using the inverse function, the input becomes the output and the output and the output becomes the input
f^-1 (-15) = -6
f^-1 (4) = -11 (inverse function)
f(9) = 11 ( regular function)
f^-1(4) + f(9) = -11+11 = 0
14r + 12s / 4s - 10s
Answers
please help me asap
Answers
8. the lcd is 42 because it’s the smallest number that 6 and 7 are both factors of. the lcd is the bottom of the fraction
to make the denominator of (4/7) 42, we will multiply the top and bottom by 6 and we get (24/42)
to make the denominator of (3/6) 42, we will multiply the top and bottom by 7 and we get (21/42)
these two numbers now have the same denominator so we subtract them
24/42 - 21/42 = 3/42 which simplifies to 1/14
9. since these fractions already have a common denominator, we will make them mixed fractions
-5(2/7) as a mixed fraction. first multiply 5*7 which is 35. now add 2 which is 37. our mixed fraction is -37/7
-1(5/7) as a mixed fraction. multiple 1*7 which is 7. now add 5 which is 12. our mixed fraction is -12/7
now subtract (-37/7) - (12/7) and we get -49/7 which simplifies to -7
Graph both lines and plot the point of intersection of the system. -x+y=1 and 2x+y=10
Answers
The point of intersection of the system of equations is (3, 4) and this is plotted in the graph shown below.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In conclusion, the coordinate (3, 4) is the point of intersection of the given system of equations.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
Answers
The probability that it is raining if the flight has been delayed is 0.07, or 7%.
How to calculate the probabilityWe can use the following formula to calculate the probability that it is raining if the flight has been delayed:
P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)
We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):
= 0.07 * 0.18
= 0.0126.
Substituting these values into the formula, we get:
P(Rain|Delayed) = 0.0126 / 0.18 = 0.07
Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.
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Look at the pattern shown below.
2, 4, 16, 256 ...
What is f(n+ 1) in terms of f(n), where n represents the position of a term in this pattern?
A. (F(n))^2
B. 2(f(n))
C. (F(n)-1)^2
D. 2(f(n)-1)
Answers
Answer: (a)
Step-by-step explanation:
Given
The pattern is 2, 4, 16, 256...
From the pattern, we can see that the next term is square of the previous i.e.
\(\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2\)\(\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2\)
So, for the \(n^{th}\) term, the function is \(f(n)\)
For the next term, it is \(f(n+1)\)
So,
\(\Rightarrow f(n+1)=[f(n)]^2\)
Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Answers
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answers
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
two poles are 80 meters and 60 meters tall. Their bases are located at a distance of 90 meters. A grounding wire needs to connect the top of the poles with each other and the ground. At what point should we connect the wire with the ground if we wanted to use the least amount of wire?
Answers
It needs to do that route I guess. But I don't understand the last question well.
хSelect answersThe temperature the next morning is -7 °C, and Soren goes outskating. His mom calls to him and says, "The temperature haschanged by 5 °C since this morning, and it will change by 5 moredegrees by this afternoon! Soren doesn't want to skate if it getsabove 0 °C, but he doesn't know whether his mom was talkingabout the temperature going up or downWhich of these are possible temperatures that it could be thisafternoon? Select all that apply.
Answers
Thus, the final temertaure is 3 degree C.
Lines AB and CD are parallel. If the measure of angle W equals 124 degrees, what is the measure of angle X?
Answers
Answer:
56 degrees
Step-by-step explanation:
They are supplementary, so they add to 180. 180 - 124 = 56.
Answer:
56 degrees
Step-by-step explanation:
They are supplementary, so they add to 180. 180 - 124 = 56.
The measure of the angle is 17 times greater than its supplement.
Answers
Answer: supplement <17
Step-by-step explanation:
1. 17 is greater
2. supplement is smaller
100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!
Answers
Answer:
Yes; TSU ~ PJM
Step-by-step explanation:
Because the angle in between the sides are the same, we can see if each corresponding side is proportional to each other. If they are, then they are similar. (This is SAS similarity theorem)
First we can divide 10 by 15 and see if 14 divided by 21 is the same:
10/15 = 0.6666....
14/21 = 0.6666....
Yes, the two triangles are similar
Answer:
Δ STU \(\bold{\sim}\) ΔPJM similar
Step-by-step explanation:
Similar triangles are two or more triangles that have the same shape, but their sides are in proportion. In other words, if you divide the length of any side of one triangle by the corresponding side of another triangle, you will get the same number.
For Question:
In Δ STU and ΔPJM
TS:US =10:14=5:7
PJ: JM=15:21= 5:7
Since the length of any side of one triangle is by the corresponding side of another triangle, you will get the same number.
Therefore,
Δ STU \(\bold{\sim}\) ΔPJM is similar.
Hence Proved:
What unknown number makes
this equation true?
356 + 4 = 300 +