Answer:
y-intercept = (0,0)
x-intercepts (0,0), (-2, 0)
Step-by-step explanation:
For y-intercept
If you think about a graph, when does the graph intercept/hit y. What is your value for x. Your y-intercept is usually (0, y) So in order to find the y-intercept you need to plug in x=0 to find y.
Equation:
y=16x²+32x substitute x=0
y=16(0)²+32(0)
y=0
y-intercept = (0,0)
For x-intercept
When you have an x intercept it looks like (x, 0), so you must solve for x when y=0
Because this is a quadratic equation(parabola), you will get 2 x-intercepts.
y=16x²+32x
0=16x²+32x > In order to solver for x, you must factor but in this case
you can take out the greatest common factor (GCF) =16x
0=16x(x +2) >Typically when you factor you get 2 parentheses and set
each parenthesis equal to 0, but instead we've pulled
an x on the outside. When there is an x outside you set
the outside equal to 0 as well as the parenthesis to
solve for x.
16x = 0 (x+2)=0
x=0 x= -2
x-intercepts (0,0), (-2, 0)
Find the area of the triangle with vertices A(-3, 2), B(1, - 2). and C(1, 3).
Answer:
10 units squared
Step-by-step explanation:
Main steps
Step 1. Identify which leg to use as a base
Step 2. Calculate the base length
Step 3. Calculate the height
Step 4. Calculate the area
Step 1. Identify which leg to use as a base
We are given that the shape is a triangle. The formula for the area of a triangle is [tex]A_{triangle}=\frac{1}{2}bh[/tex] where b is the "base" of a triangle, and h is the "height".
One common misconception is that the base must be at the bottom (although it is easy to think of it that way). Rotating the shape, any of the three sides could be at the bottom, and thus any of the three sides could be the base.
The "height" of the triangle depends on which leg is being used as a base. The height for a given base is always the shortest distance from the vertex opposite the base to the line that contains the base. This shortest distance always ends up being the line segment that is perpendicular to the base.
In this case, since side BC is along the gridlines, it will be easiest to use side BC as the base, because the perpendicular line for the height will be along gridlines. The height is the distance from A to the side BC (which is a line segment between (-3,2) and (1,2)).
Step 2. Calculate the base length
The base length is the distance between the two endpoints of the line segment. The distance formula is [tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using Point B as Point 1, and Point C as Point 2:
[tex]D=\sqrt{((1)-(1))^2+((3)-(-2))^2}[/tex]
[tex]D=\sqrt{(0)^2+(5)^2}[/tex]
[tex]D=\sqrt{0+25}[/tex]
[tex]D=\sqrt{25}[/tex]
[tex]D=5[/tex] units
So the base length is 5 units
b=5 units
Since these point are on a graph, it can be verified by counting the squares between the two points, however if work needs to be shown, the Distance formula is the "work".
Step 3. Calculate the height
The "height" for the base from step 2 is a line segment between (-3,2) and (1,2). This distance can again be found using the distance formula:
Using Point A as Point 1, and the point (1,2) on BC as Point 2:
[tex]D=\sqrt{((-3)-(1))^2+((2)-(2))^2}[/tex]
[tex]D=\sqrt{(-4)^2+(0)^2}[/tex]
[tex]D=\sqrt{16+0}[/tex]
[tex]D=\sqrt{16}[/tex]
[tex]D=4[/tex] units
So the height for the base from Step 2 is 4 units.
h=4 units
Again, these point are on a graph, so this answer can be verified by counting the squares between the two points.
Step 4. Calculate the area
Using the formula for the area of a triangle discussed in Step 1, the area can be calculated:
[tex]A_{triangle}=\frac{1}{2}(5~\text{units})(4~\text{units})[/tex]
[tex]A_{triangle}=10 \text{ units}^2[/tex]
PLS HELP
During a 90-minute school play, the main character was on stage 80% of the time. What amount of time in minutes was the main character on stage?
88. 9 minutes
112. 5 minutes
80 minutes
72 minutes
Answer: He was on stage for exactly 80 minutes
Step-by-step explanation: Because it can't be 72 because that would be 70% of the time just like 88.9 that's 88.9% of the time and 112.5 will be to much so the correct answer is C 80 minutes.
Use the distributive property to write an equivalent expression.
3(7 p - 3 q + 9)
Answer:
27p - 9q + 27
Step-by-step explanation:
3(7p - 3q + 9) ← multiply each term in the parenthesis by the 3
= 21p - 9q + 27
On a coordinate plane, a triangle has points F (3, 4), D (5, negative 3), and E (1, negative 2).
What are the coordinates of the image of vertex D after a reflection across the x-axis?
(5, 3)
(–5, –3)
(–3, 5)
(3, –5)
Answer:
(5, 3)
Step-by-step explanation:
Since we are reflecting by the x-axis, the x-cooridnate would stay the same.
Vertex D is 3 units dow from the x-axis. By reflecting in using the x=0 reference,the y-coordinate would be a positivo 3 now.
Answer:
D. (3, -5) on edge
Step-by-step explanation:
Picture below⬇️, tried two answers and got me wrong… hope I helped :)
Work out(−3)2−3×(2×54)÷112
Answer:
-249/28
Step-by-step explanation:
express in simplified exponential notation.
x^3 •x^5=
The simplified exponential notation of the given expression is x⁸.
Given that, simplified exponential notation, x³·x⁵,
x³·x⁵ we need to simplify it,
We know that,
mᵃ × mᵇ = mᵃ⁺ᵇ
x³·x⁵ = x³⁺⁵
x³·x⁵ = x⁸
Hence, the simplified exponential notation of the given expression is x⁸.
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PUZZLE#2 can you find the slope and type the correct code?
We can write the slope of the line mathematically as -
m = (y₂ - y₁)/(x₂ - x₁)
or
m = dy/dx
The general equation of a straight line is -
y = mx + c
Here, {c} is the {y} - intercept & {m} is the slope of the line. It also denotes the unit rate. Unit rate is the rate at which the value of {y} changes per unit change in the value of {x}. We can write the slope of the line mathematically as -
m = (y₂ - y₁)/(x₂ - x₁)
or
m = dy/dx
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An inequality is shown.
Answer: 24
Step-by-step explanation:
For inequalities, you would solve for x like you would if it were an equal sign but keep the sign in middle. The only thing that changes the sign is if you multiply or divide by a negative, then the sign flips(this is not so in this case.
[tex]\sqrt{x}[/tex]<5 square both sides to get rid of square root
x<5²
x<25 x is less than 25; it cannot be = to 25 so the largest integer it can be is 24
in a group of 32 children, 25% have blue eyes. how many children do not have blue eyes?
Answer: 24 children
Step-by-step explanation:
Answer:
Step-by-step explanation:
So if 25% have blue eyes, 75% do not.
100% - 25% = 75%
What is 75% of 32?
Change 75% to a decimal by movinf g the decimal two places to the left.
and multiply.
32 × .75 = 24
This is how to calculate the solution.
Please help!!!
What is a 3 sided polygon called?
Answer: A three sided polygon is a triangle.
Step-by-step explanation:
Types of these include: isosceles, equilateral, scalene, obtuse, acute, and right triangles. Example:
which of the following are true statements? i. based on careful use of control groups, experiments can often indicate cause-and-effect relationships. ii. while observational studies may suggest relationships, great care must be taken in concluding that there is cause and effect because of the lack of control over lurking variables. iii. a complete census is the only way to establish a cause-and-effect relationship absolutely
Based on control groups, experiments indicate cause-and-effect relationships. While observational studies, great care must be taken in concluding cause and effect. Correct options are i and ii.
Statement i is a true statement. Experiments are designed to test causal relationships between variables by manipulating one variable while keeping all others constant, allowing researchers to establish cause-and-effect relationships with greater certainty.
The use of control groups allows researchers to isolate the effects of the independent variable from other potential confounding variables.
Statement ii is also a true statement. Observational studies are more prone to the influence of lurking variables that cannot be controlled for, which makes it more difficult to establish a cause-and-effect relationship between variables.
However, careful analysis and the use of statistical methods can help control for the influence of some lurking variables and provide evidence to support a causal relationship.
Statement iii is a false statement. While a complete census can provide comprehensive information about a population, it does not necessarily establish cause-and-effect relationships absolutely.
Causality is typically established through well-designed experiments or observational studies that carefully control for confounding variables, and it is rare for any single study to establish causal relationships with absolute certainty.
Instead, scientific evidence is accumulated over time through multiple studies that support the same conclusion, and even then, there is always some degree of uncertainty and potential for alternative explanations.
Correct options are i and ii.
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local county officials have heard reports that a service station is allowing cars 20 years and older with known violations to pass their annual safety inspection. from administrative data, they know 30% of all cars 20 years and older do not pass their annual safety inspection. to test their theory about the service station, they request records from the most recent 150 inspections of cars of this type, finding 30 of the 150 had been rejected. let p be the true rate of cars 20 years and older that do not pass their annual safety inspection from this service station. what are the implied null and alternative hypotheses local county officials are testing?
The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤ 30%.
The alternative hypothesis implied that cars 20 years or older do not pass safety inspection > 30%
The local county officials are testing a hypothesis about the proportion of cars 20 years.
And older that do not pass their annual safety inspection at the service station.
The null hypothesis and alternative hypothesis can be stated as follows,
Null hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤ 30%.
Alternative hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.
The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.
And that the rejection rate of 30% is consistent .
With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.
The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.
And that the rejection rate is lower than the true rate of cars 20 years .
And older that do not pass their annual safety inspection at the service station.
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In Figure NOPR above, segments NR and OP are parallel, and segments NO and RP are parallel.
Pair each set of equations with the corresponding transformation of figure NOPR to figure N'O'P'R'.
Picture Below
The transformations on their most likely corresponding equations are;
1. O'P' lies on x = 3; N'R' lies on x = 6.
Clockwise rotation of 180° about the origin and then a reflection over the x-axis2. O'P' lies on y = -3; N'P' lies on y = -6.
Reflection over the y-axis and then reflect over the x-axis3.
P'R' lies on y = -2, and O'N' lies on y = -6.
Counterclockwise rotation of 90° about the origin
How do you identify transformation?To identify transformations, we have to be conversant with various rules of transformation. When we reflect over the x or y-axis, the signs of the coordinates for x or y are supposed to change to negative.
However, Any transformation that happens such that the coordinates of the equation are both positive means that the image is on the first quatrain of the graph, which is the right and upper side of the x-axis.
If the rectangle is at the second quatrain, and it is rotated 180° degrees, it means that it still maintains its upright position. and when it is reflected back through the x-axis, it still maintains its upright position.
If the rectangle is rotated 90° counterclockwise, it bends and therefore the coordinates change.
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A water park has pools, slides, and rides that, in total, make use of 8.7 x 105 gallons
of water. They plan to add a ride that would make use of an additional 7.8 x 10³
gallons of water. Use scientific notation to express the total gallons of water made use
of in the park after the new ride is installed.
Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
The form of the container the water is contained in affects how much water is contained inside. You must know the length, breadth, and depth of a square or rectangular vessel in order to calculate its volume using the volume equation V=L*W*D, where L stands for length, W for width, and D for depth. The volume equation in this case reads: V= (r²)Dπ, where r stands for the radius, D for depth, and, or pi, is a constant value that is typically rounded to 3.14. To perform the same volume calculation for a circular vessel, you must know the vessel's depth and diameter or radius.
Given, the water park has water which is 8.6*10⁵ gallons.
We know that 10⁵ = 100000
Thus, 8.6*10⁵ = 860000
The new ride would use an additional 9.1*10⁴ gallons.
Again, 10⁴ = 10000
Thus, 9.1*10⁴ = 91000
Total water that would be required now is equal to the sum of the original water volume and the volume required by the new ride
= (860000+91000) gallons
= 951000 gallons
= 9.51*10⁵ gallons
Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
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2. a. The total cost of 60 apples and 100 eggs is €108,000.00. The cost of 72 apples is the same as that of 30 eggs. Find how much 12 apples and 20 eggs will cost.
In art class students are mixing blue and red paint to make purple paint. Madelyn mixes 3 cups of blue paint and 10 cups of red paint. Arturo mixes 1 cup of blue paint and 4 cups of red paint. Whose purple paint will be redder?
Answer:
To compare the purple paints that Madelyn and Arturo made, you need to find the ratio of red to blue in each mixture. You can do this by dividing the amount of red paint by the amount of blue paint.
For Madelyn, the ratio of red to blue is:
10 / 3 = 3.33
For Arturo, the ratio of red to blue is:
4 / 1 = 4
Since Arturo has a higher ratio of red to blue, his purple paint will be redder than Madelyn’s.
The area of a circle is 25π square units. Find th
e circumference of it in terms of π or a unit number
Answer:
10π
Step-by-step explanation:
A=25π
25π=πr^2
25=r^2
5=r
C=2πr
=2π5
=10π
If the odds on a bet are 13:1 against, what is the probability of winning? Express your answer as a fraction.
If the odds on a bet are 13:1 against, then the probability of winning can be found using the formula:
probability of winning = 1 / (odds against + 1)
Substituting the given values, we get:
probability of winning = 1 / (13 + 1) = 1/14
Therefore, the probability of winning is 1/14 as a fraction.
The graph shows g(x), which is a translation of
f(x) = = x². Write the function rule for g(x).
-10 -8 -6 -4
-2
104
-8-
-6-
-4-
2-
0
-2-
-4-
-6
-8-
-10₂
2
4
6
8
Write your answer in the form a(x − h)² + k,
where a, h, and k are integers or simplified
fractions.
g(x) =?
The function rule for g(x) is f(x) = (x - 5)² + 0.
How to determine the function rule?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.Since the parent function is represented by f(x) = x², a function rule for g(x) is given by;
f(x) = a(x − h)² + k
f(x) = 1(x - 5)² + 0.
f(x) = (x - 5)² + 0.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Mrs. Singh bought 9 folders and 9 notebooks. the cost of each folder was $2.50. each notebook cost $4.00 Write two equivalent expressions and then find the total cost.
a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:
2.50x4.00y.b) The total cost of the purchase by Mrs. Singh is $58.50.
What are algebraic expressions?Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).
The unit cost of folders = $2.50
The unit cost of notebooks = $4.00
The number of folders bought = 9
The number of notebooks bought = 9
Let the number of folders bought = x
Let the number of notebooks bought = y
Expressions of the Costs:Folders: 2.50x
Notebooks: 4.00y
Total Costs:Folders: 2.50x = $22.50 ($2.50 x 9)
Notebooks: 4.00y = $36.00 ($4 x 9)
Total costs = $58.50
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While grocery shopping, Dylan bought
some apples for $3.50. He also bought
some grapes that cost $1.25 more than
the apples. The combined cost of the
grapes and apples made up 20% of his
total grocery bill. What was the total
amount of Dylan's grocery bill in dollars
and cents?
Answer:
Dylan's grocery bill was $41.25.
Step-by-step explanation:
Let's call the cost of the grapes "g".
We know that the grapes cost $1.25 more than the apples, so we can write:
g = 3.50 + 1.25 = 4.75
The combined cost of the grapes and apples is 20% of Dylan's total grocery bill, so we can write:
3.50 + 4.75 = 0.20x
where x is the total grocery bill.
We can solve for x by simplifying the equation:
8.25 = 0.20x
x = 8.25 / 0.20
x = 41.25
Therefore, the total amount of Dylan's grocery bill was $41.25.
Answer:
Dylan's total grocery bill was $41.25
Step-by-step explanation:
Let the cost of the apples be a. Then, the cost of the grapes is a + 1.25, since the grapes cost $1.25 more than the apples.
The combined cost of the apples and grapes is a + (a + 1.25) = 2a + 1.25.
We know that the combined cost of the apples and grapes is 20% of Dylan's total grocery bill, so we can set up the following equation:
2a + 1.25 = 0.2x
where x is the total cost of Dylan's grocery bill.
To solve for x, we can isolate x on one side of the equation:
2a + 1.25 = 0.2x
2a = 0.2x - 1.25
a = 0.1x - 0.625
We also know that the cost of the apples is $3.50, so we can set up another equation:
a = 3.5
Substituting this into the equation we just found:
3.5 = 0.1x - 0.625
4.125 = 0.1x
x = 41.25
Therefore, Dylan's total grocery bill was $41.25.
suppose i have an organization that has 60 members, i'm going to pick one person at random to be the president, another person to be the vice president, and a third person to be the treasurer. how many ways can this be done?
There are 205,320 ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer from a group of 60 members.
The number of ways to select the president from the 60 members is 60, since any one of the 60 members can be chosen.
Once the president has been chosen, there are only 59 members left to choose from for the vice president. Therefore, there are 59 ways to select the vice president.
Similarly, after the president and vice president have been chosen, there are only 58 members left to choose from for the treasurer. Therefore, there are 58 ways to select the treasurer.
Using the multiplication principle of counting, the total number of ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer is
60 x 59 x 58 = 205,320
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the team wins .73 of their games. if they play 10 games, what is the probability that they win nine games?
Thus, the probability that the team wins nine games out of 10 is approximately 0.2365, or about 23.65%.
To solve this problem, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the total number of trials (games played)
- k is the number of successes (games won)
- p is the probability of success in one trial (winning a game)
- (n choose k) is the binomial coefficient, which can be calculated as n! / (k! * (n - k)!)
In this case, n = 10, p = 0.73, and k = 9. So we have:
P(X = 9) = (10 choose 9) * 0.73^9 * (1 - 0.73)^(10 - 9)
P(X = 9) = 10 * 0.73^9 * 0.27^1
P(X = 9) = 0.2365
Therefore, the probability that the team wins nine games out of 10 is approximately 0.2365, or about 23.65%.
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6.
ind
ke
12Tom earns $100 to start a painting
job and $35 per hour to complete it.
All jobs he accepts earn him at least
$500. If h represents the number of
hours spent painting, which inequality
describes Tom's situation?
A. 100 + 35h > 500
B. 100 + 35h ≥ 500
C. 100 + 35h < 500
D. 100 + 35h ≤ 500
The inequality to represent Tom's situation is 100 + 35h ≥ 500.
How to find the solve inequality?Tom earns $100 to start a painting job and $35 per hour to complete it. All
jobs he accepts earn him at least $500.
h represents the number of hours spent painting . Therefore, the inequality that represent Tom's situation is as follows:
Therefore,
100 + 35h ≥ 500
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If you arranged the cubes on the floor to make a square would the square fit in your classroom? What would it’s dimensions be? Explain your reasoning
The squares may or may not fit in the classroom, depending on the dimensions
Would the square fit in the classroom?The number of cubes is given as
Cubes = 1000000
The area of a square is
Area = Length^2
In this case, the number of cubes is the area
So, we have
Length^2 = 1000000
Take the square root of both sides
Length = 1000
This means that the dimensions would be 1000 by 1000
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I'm a number between 17 and 25 i'm a multpile of 3 6 is not mynfactor
The number that fits the given criteria is 21.
The number 21 is between 17 and 25, and it is a multiple of 3. It is not a multiple of 6 because it is not divisible evenly by 6.
The factors of 21 are 1, 3, 7, and 21. Since 6 is not one of its factors, 21 satisfies the given conditions.
To find the answer, we first identify the range of numbers given, which is between 17 and 25.
Next, we look for a number within this range that is a multiple of 3. Multiples of 3 are numbers that can be divided evenly by 3 without leaving a remainder.
Among the numbers in the given range, only 21 satisfies this condition. Lastly, we check if the number is a multiple of 6. A multiple of 6 is a number that can be divided evenly by 6 without leaving a remainder.
Since 21 cannot be divided evenly by 6, it does not meet this criterion. Therefore, 21 is the number that fits all the given conditions.
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The managers of an airline analyzed a random sample of flights and found that 95% of the flights arrived on time. The airline has 480 flights scheduled for next week. What is the BEST estimate of the number of these flights that will NOT arrive on time?
Answer:
456
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
The two lines shown below are perpendicular. If the slope of the red line is 1/2 what is the slope of the green line?
Answer:
B) -2
Step-by-step explanation:
When perpendicular lines accur to find the translated line just flip the numerator and denominator and making the reciprocals negitive
the life of light bulbs is distributed normally. the standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for between 557 and 561 hours. round your answer to four decimal places.
The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%
Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:
z = (x - μ) / σ
where x is the bulb lifetime we're fascinated by
, μ is the cruel(mean) lifetime,
and σ is the standard deviation.
For 557 hours:
z1 = (557 - 530) / 15 = 1.8
For 561 hours:
z2 = (561 - 530) / 15 = 2.07
Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:
P(z1 < Z < z2) = P(1.8 < Z < 2.07)
This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.
Employing a standard ordinary dispersion table or a calculator, we discover:
P(1.8 < Z < 2.07) ≈ 0.0382
Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places).
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Classes
BIG IDEAS MATH
# 5
The side lengths of a triangle are 15, 20, and x. What values of x make the triangle a right triangle?
Right angle: x =
What values of x make the triangle an acute triangle?
and
Acute angle:
What values of x make the triangle an obtuse triangle?
Obtuse angle:
Previous
The values of x make the triangle a right triangle is 25
What values of x make the triangle a right triangle?Given that
Legs = 15 and 20
For a right triangle, we have
x^2 = 15^2 + 20^2
So, we have
x^2 = 625
This gives
x = 25
What values of x make the triangle an acute triangle?In this case, the value of x would be less than 25 calculated above
What values of x make the triangle an obtuse triangle?In this case, the value of x would be greater than 25 calculated above
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