△ABC meets the given criteria:
• The perimeter of △ABC is 50 units.
• Only two of the sides have the same length.
• The third side is 16 units long, given in the diagram.
Part A (2 points):
What are the coordinates of point C that
will meet the criteria for △ABC ?
(6.25, 8) b. (8, 6.25) c. (8, 15) d. (15, 8)
Part B (3 points):
Point C is placed at (12,16) and point B is moved along the x-axis.
△ABC is still an isosceles triangle and point A is still at the origin.
What is the new perimeter of △ABC ?
Answers
The new perimeter of △ABC can be either 44.31 units or 52.99 units, depending on the location of point B.
What is isosceles triangle ?
An isosceles triangle is a triangle in which at least two sides have the same length. This means that two of the angles opposite the equal sides are also equal. The third side, which is opposite the unique angle, is called the base of the triangle. The altitude from the apex of the triangle to the base divides the base into two equal parts, and also bisects the apex angle, which is the angle between the two equal sides.
According to the question :
Part A:
Since two sides have the same length, we can assume that they have length x. Therefore, the third side must have length 50 - 2x - 16 = 34 - 2x. Since only two sides have the same length, we know that x is not equal to 16/2 = 8. So we have two equations:
x + x + (34 - 2x) = 50 (perimeter equation)
x ≠ 8 (condition for only two sides having the same length)
Solving the first equation for x, we get:
2x + 34 - 2x = 50
2x = 16
x = 8
This is a contradiction with the condition that x ≠ 8. Therefore, there is no point C that satisfies all the given criteria.
Answer: None of the above.
Part B:
Since △ABC is still an isosceles triangle, we know that the new length of side AB is equal to the original length of side AC, which is 16 units. Let the new x-coordinate of point B be b. Then the coordinates of points B and C are (b, 0) and (12, 16), respectively. Using the distance formula, we can find the length of side BC:
\(BC = \sqrt{(b - 12)^2 + 16^2}\)
Since the triangle is isosceles, we have:
AB = BC
\(16 = \sqrt{(b - 12)^2 + 16^2}\)
Squaring both sides and simplifying, we get:
\((b - 12)^2 = 144 - 16^2\)
\(b^2 - 24b + 128 = 0\)
(b - 4)(b - 20) = 0
Therefore, the possible x-coordinates of point B are 4 and 20. The new perimeter of △ABC is:
16 + AB + BC = 16 + 16 + BC
= 32 + BC
When B is at (4, 0), we have:
\(BC = \sqrt{(4 - 12)^2 + 16^2} = \sqrt{128} = 8\sqrt{2}\)
So the new perimeter is:
\(32 + 8\sqrt{2} \approx 44.31\)
When B is at (20, 0), we have:
\(BC = \sqrt{(20 - 12)^2 + 16^2} = 4\sqrt{10}\)
So the new perimeter is:
\(32 + 4\sqrt{10} \approx 52.99\)
Answer: The new perimeter of △ABC can be either 44.31 units or 52.99 units, depending on the location of point B.
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Related Questions
Kaj goes out to lunch. The bill, before tax and tip, was $17.35. A sales tax of 4% was added on. Kaj tipped 22% on the amount after the sales tax was added. How much tip did she leave? Round to the nearest cent.
Answers
1.04 *17.35=18.044
1.22*18.044=(rounded) 22.01
Think of (*) as “of” (example below)
So 1.04 (4%) OF $17.35 is $18.04
if it takes 24 minutes to walk 2 miles how long would it take to walk 6 miles
Answers
Step-by-step explanation:
24min= 2miles
? 6miles
it will be 6×24min÷2= 72minutes or 1hr 12min
Given: ABC is a right triangle
Prove: A^2 + b^2 =c^2
A = addition property of equality
B = Pythagorean theorem
C = Pieces of right triangles similarity theorem
D = cross product property
Answers
Answer: B
Step-by-step explanation:
You cannot use what you are trying to prove as a justification.
a towing vessel 25 meters in length is pushing barges ahead. how many white masthead lights is the vessel required to show at night?
Answers
A 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.
Define the term towing vessel?A commercial vessel that is pulling, pushing, hauling aboard, or any mixture of pulling, pressing, or hauling alongside, is referred to as a towing vessel.
Masthead light refers to a white light that is positioned over the fore and aft centerlines of the vessel.Showing an uninterrupted beam of light over a horizon arc of 225 degrees and fixed so that the light can be seen from directly in front of the beam to 22.5 degrees behind the beam.Along both side of the vessel, with the exception that on a vessel less than 12 meters in length, the masthead light must be positioned as closely as is practical to the fore .Thus, a 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.
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1. WILL GIVE BRAINLIST TO BEST ANSWER
Based on the data what would be the expected test score for a student that studies for 80
Answers
Answer:
90/100
Step-by-step explanation:
if you look at the graph on the bottom part it tells you the study time if you line it the left side which says the test score. so if they studied for 80 mins they are expected to have the score of between 85 and 90.
I need help.. evaluate the expression. Write the answer in simplest form
Answers
Answer:
Please check your question again
Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Use exact numbers.
y=y=y, equals
Answers
Answer:
y = 1/2 x -2
Step-by-step explanation:
rise/run from (-6, -5) to (-4, -4) = 1/2
(rise 1, run 2)
meaning that slope (m) = 1/2
we can now rewrite our points in y=mx + b formatting:
y = mx + b
-5 = (1/2)(-6) + b
-4 = (1/2)(-4)+b
now, let's solve for b
-5 = (1/2)(-6) + b
-5 = -3 + b
-2 = b
-4 = (1/2)(-4)+b
-4 = -2 + b
-2 = b
So, the equation for our line is y = \(\frac{1}{2}\) x- 2
hope this helps!! have a lovely day :)
Answer: y = 1/2x - 2
Step-by-step explanation: it’s right on khan academy (picture for proof)
Camilla's employer pays 90% of the total cost of her family's health insurance
plan, while Camilla pays the rest. If the total cost of the plan increases from
$850 per month to $950 per month, how much more will Camilla have to pay
each month?
A. $90
O B. $10
O C. $100
D. $9
Answers
Answer:
B. $10
Step-by-step explanation:
Camila's employer pays 90% of the total cost of her family's health insurance
plan
Therefore, Camilla pays only 10%
If the total cost of the plan increases from $850 per month to $950 per month, how much more will Camilla have to pay
each month?
Amount of health insurance Camilla pays at $850 per month = 10% of $850
= 0.1 * $850
= $85
Amount of health insurance Camilla pays at $950 per month = 10% of $950
= 0.1 * $950
= $95
Amount Camilla pays more = $95 - $85
= $10
B. $10
100,650 greater than 100,557 true or false
Answers
Answer:
True.
Step-by-step explanation:
100,650 is 93 digits greater than 100,557.
In ANOVA, which of the following is not affected by whether or not the population means are equal? between-samples estimate of o 2 within-samples estimate of o 2 None of these alternatives is correct.
Answers
In Analysis of variance, X (bar) is not affected by whether or not the population means are equal.
Analysis of variance is a statistical method for examining differences in means. It consists of a number of statistical models and the accompanying estimating techniques (such as the "variation" within and between groups). Ronald Fisher, a statistician, created Analysis of variance. The rule of total variance, on which the Analysis of variance is based, divides the observed variance in a given variable into components owing to various causes of variation.
ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the Analysis of variance is employed to determine whether two or more means differ from one another.
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Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time. What errors did the coach make? Check all that apply.
Answers
A) He used an incorrect time ratio converting hours to minutes.
c) He used an incorrect distance ratio converting miles to feet.
D) He incorrectly concluded that she is not running fast enough.
E) He cannot determine her average rate in miles per hour after only 15 minutes. Option A , C , D, E.
The coach made the following errors in his analysis:
A) He used an incorrect time ratio converting hours to minutes.
The coach converted the time of 15 minutes to hours, which is incorrect. To convert minutes to hours, we divide by 60. So, 15 minutes is equivalent to 15/60 = 0.25 hours. However, since the coach used an incorrect time ratio, this error affected his subsequent calculations.
C) He used an incorrect distance ratio converting miles to feet.
The coach likely used an incorrect conversion ratio when converting miles to feet. The correct conversion factor is 1 mile = 5280 feet. If the coach used an incorrect ratio, it would lead to an inaccurate conversion from miles to feet.
D) He incorrectly concluded that she is not running fast enough.
Due to the errors in the conversion of time and distance, the coach's calculation of Aliza's speed in feet per second is likely incorrect. Therefore, his conclusion that she is not running fast enough to exceed her fastest time is invalid since it is based on faulty calculations.
E) He cannot determine her average rate in miles per hour after only 15 minutes.
The coach determined Aliza's average rate in miles per hour based on her performance over 15 minutes. However, using the average rate over this short duration to draw conclusions about her overall performance is not accurate. It is insufficient to determine her average rate over a race or compare it to her fastest time.
To make an accurate assessment, the coach should re-evaluate the calculations by using the correct conversion factors and consider a more significant time interval to determine Aliza's average rate in miles per hour.
Option A , C, D, E are corrrect.
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Please help me I have been stuck for a while now
Answers
a wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
Answers
1.5 half lives times 5730 years per half life is 6590 years.
What is meant by Fraction?Fraction: A number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Fraction still left equals 0.5n, where n is the total number of half lives that have already passed.
Fraction left = 0.45, thus you have 0.45 = 0.5n and by figuring out n, you get,
n = log 0.5 + log 0.45
-0.347 = -0.301n
Half lives for n = 1.15 have passed.
1.5 half lives times 5730 years per half life is 6590 years.
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6590 years are equal to 1.5 half lives times 5730 years per half life.
What does "fraction" mean?
A fraction is a number that is expressed as a quotient by dividing the numerator by the denominator. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Where n is the total number of half lives that have already occurred, the fraction of time left is equal to 0.5n.
Fraction left = 0.45, thus you have 0.45 = 0.5n and by figuring out n, you get,
n = log 0.5 + log 0.45
-0.347 = -0.301n
Half lives for n = 1.15 have passed.
1.5 half lives times 5730 years per half life is 6590 years.
PLSSS HELP!!!!
NEED HELP ASAP.....
I HAVE TIME LIMIT
READY TO GIVE 25 POINTS
AND BRAINLIEST
Suhana walks 30 minutes to her school everyday. Her father who is a farmer decides to buy her a bicycle.
He has a cow and a buffalo on his farm. The two animals had cost him Rs 1800 and Rs 2400 respectively. Selling the cow will fetch him a profit of 10% whereas on the buffalo he will suffer a loss of 5%
He decides to sell his buffalo. The next day, he goes to the market and completes the deal.
The bicycle which costs Rs 900 is sold by the shopkeeper for Rs 1008.
Suhana’s father deposits Rs 1200 of the remaining amount in the bank at 9% p.a. for 3yrs.
Suhana is grateful to her father and works very hard as she realizes the
sacrifices her parents make for her.
What is the amount the farmer will receive at the end of 3 years??
Answers
Answer:
i think you need apply the compound interest
Write the standard form of the equation of a circle that contains the point (-10,-12) and has center (6,-8)
Answers
Equation of circle: (x-6)²+(y+8)²=272, with center (6,-8) and radius 16.49.
Equation of circle with given center and point?To find the standard form of the equation circle that contains the point (-10,-12) and has center (6,-8), we can use the distance formula between the center and the given point. The distance between the center and the given point is equal to the radius of the circle. Once we find the radius, we can use the standard form equation of a circle to write the equation.
Find the radius of the circle.The distance formula between the center (6,-8) and the given point (-10,-12) is given by:
radius = \(√[(x2 - x1)² + (y2 - y1)²]\)
radius = \(√[(6 - (-10))² + (-8 - (-12))²]\)
radius = \(√[(16)² + (4)²\)]
radius = √(272)
radius = 16.49 (rounded to two decimal places)
Write the standard form equation of the circle.The standard form equation of a circle with center (h,k) and radius r is given by:
\(( - h)² + (y - k)² = r²\)
Substituting the values of h, k, and r, we get:
\((x - 6)² + (y - (-8))² = 16.49²\)
Simplifying and expanding, we get:
\((x - 6)² + (y + 8)² = 272\)
Therefore, the standard form of the equation of the circle that contains the point (-10,-12) and has center (6,-8) is (x - 6)² + (y + 8)² = 272.
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the slope of x/3 + y/-6 =1 ?
Answers
Statistics question
Walmart claims that their checkout scanners correctly price 98.9% of the items sold. How many items would you expect to buy, on average, to find one that scans incorrectly? Round your answer up to the next integer
a) 2
b) 91
c) 99
d) 500
e) 989
Answers
Answer:
(b) 91
Step-by-step explanation:
The probability of an item scanning correctly is 98.9%, so the probability of an item scanning incorrectly is 1 - 98.9% = 1.1%.
The expected number of items to buy to find one that scans incorrectly is 1 / 1.1% = 91. This means that you would expect to buy 91 items on average to find one that scans incorrectly.
Rounding up to the next integer, the answer is 92. Therefore, the correct answer is (b) 91.
The ratio of boys to girls in a classroom is 3:5. If there are 80 students in a class, how many of them are girls
Answers
The classroom has 50 girls. The solution was achieved by adding the ratio values (3+5) to get the total parts, dividing the total students by this value to find the value of each part, and then multiplying this by the number of parts for girls.
Explanation:The subject of this question is a problem in Mathematics that deals with ratios and proportions. Specifically, the ratio of boys to girls in a classroom of students. The ratio given is 3:5, which means for every 3 boys, there are 5 girls. In a classroom with 80 students, we first need to calculate the total parts of this ratio by adding 3 (boys) and 5 (girls), which gives us a total of 8 parts. Having done that, we can now determine the value of a single part by dividing the total number of students (80) by the total parts (8). This gives us 10 students per part. To find out the number of girls, we multiply the number of parts for girls (5) by the number of students per part we computed (10), which equals 50. Therefore, in this classroom, there are 50 girls.
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benji keeps track of the number of frisbee golf holes on which he makes par or better. the table shows the number of holes benji has played during his round so far. if the ratio of holes with par or better to total holes played is equal to 0.4, on how many of the holes has benji made par or better?
Answers
Benji made par or better on 7 holes in his round so far.
the ratio of holes with par or better to total holes played is equal to 0.4. We need to determine on how many of the holes Benji has made par or better. Table that shows the number of holes Benji has played during his round so far is shown below: Number of holes played in round so far Holes played 6 12 18Number of holes with par or better Number of holes played
2x 6 0.4
The ratio of the number of holes with par or better to the total number of holes played is 0.4.So, (Number of holes with par or better) /
(Number of holes played) = 0.4
Number of holes with par or better
/ (6 + 12 + 18) = 0.42x / 36 = 0.4
Cross-multiplying the above equation, we get,
2x = 0.4 x 36 = 14.4Dividing by 2 on both sides, we get x = 7.2
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Find the missing length of the triangle. 6.5 mm 2.5 mm b The missing length is millimeters.
Answers
In order to determine the value of the missing length b, use the Pithagorean theorem, given by:
h² = a² + b²
where:
h = 6.5 mm
a = 2.5 mm
solve the previous equation for b, as follow:
b = √(h² - a²)
b = √(6.5² - 2.5²)mm
b = √36 mm
b = 6 mm
Hence, the value of the missing length is 6 mm
Jeanne makes hair bows to sell at the craft fair. Each bow requires 1.5 feet of ribbon. At the fabric store, ribbon is sold by the foot. If Jeanne wants to make 84 bows, how many feet of ribbon must she buy
Answers
Answer:
126
Step-by-step explanation:
That might be the answer sorry if im wrong
Use three unit multipliers to convert 5280ft to meters
Answers
The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.
As per the given,5280ft
It is known that 1 ft = 12 inches.
5280ft = 5280 x 12 inches
It is known that 1 inch = 2.54 cm
5280 x 12 inches = 5280 x 12 x 2.54 cm
It is known that 1 cm = 0.01 meter
5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter
⇒ 1609.344 meters
Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".
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Use the numbers on the conveyer belt to complete the equation
18 x ————- = 9 x————-
Answers
Step-by-step explanation:
I think...
18×9=9×18
hope it helps
1/3x^2-5=7 what is x
Answers
Answer:
x= 6
Step-by-step explanation:
\(\frac{1}{3}x^{2}-5=7\\\)
Add 5 to both sides
\(\frac{1}{3}x^{2}-5+5=7+5\\\\\frac{1}{3}x^{2}=12\\\)
Multiply both sides by 3
\(3*\frac{1}{3}x^{2}=12*3\\\\x^{2}=36\\\)
x² = 6*6
Take square root,
√x² =√6*6
x = 6
The goals in a hockey rink are 6 feet wide. A hockey player is standing 25 feet directly in front of the left side of one of the goals.
a) what is the maximum angle at which the player can shoot the puck to make it in the goal?
b) if the player skates forward 5 feet, how wide of a range of angles can the player shoot the puck to make it in the goal?
c) describe what happens to the maximum angle as the player gets closer to the goal
Answers
The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
a)
The given condition makes a right-angle triangle as shown below,
The tan function,
tanθ = 6/25
θ = 14.50°
b)
When a player is 5 feet closer means (20 feet far)
tanθ = 6/20
θ = 16.70°
c)
As the player gets closer the angle becomes more and more.
Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".
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There are 3 yellow, 3 green, and 3 red pens in a jar. Each day Michelle selects a pen without looking, uses the pen, and then replaces it in the jar. Over 14 days she selects a red pen 6 times. Compare the theoretical and experimental probabilities of this experiment.
(Hint: Calculate the theoretical probability and experimental probability
separately)
Answers
Experimental Probability: she picks the red pen 6/14 times
So the experimental is 1-2 times more than predicted via theoretical probability
I need help with this please
Answers
The segment AB is a radius and the notation is ↔ AB
Writing the notation with the term that best describes the segment ABFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we can see that
The segment AB goes from the center of the circle to a point on the circle
A line that goes from the center of the circle to a point on the circle is the radius of the circle
This means that the segment AB is a radius and the notation is ↔ AB
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i need help with this ASAP
Answers
Answer:
a) 2.5x + 5 b) $5
Step-by-step explanation:
We know that the rate is 2.50 an hour, and she parked for 4 hours. Multiply 2.5 by 4 to get 10. This means that she spent 10 out of 15 of her dollars on the rate, meaning the initial fee was 5 dollars.
Answer:
a. y = 2.5x + 5
b. $5
Step-by-step explanation:
y = mx + b
m = slope is the fee per hour
b = y-intercept is the fixed fee
y = 2.5x + b
We know that she paid $15 for 4 hours, so we have point (4, 15). We now replace x and y in the equation with 4 and 15, respectively, and solve for b.
15 = 2.5(4) + b
15 = 10 + b
b = 5
a. The equation is:
y = 2.5x + 5
b. The initial fee is $5
Write an equation and solve for the value of x (please show work)
Answers
Answer:
\(7x-11+5x-1=180\\12x-12=180\\12x=192\\\boxed{x=16}\)
Answer:
x=16
Step-by-step explanation:
The two angles form a straight line so they add to 180
7x-11 + 5x-1 = 180
Combine like terms
12x -12 =180
Add 12 to each side
12x-12 +12 =180+12
12x = 192
Divide each side by 12
12x/12 =192/12
x=16
A cat adoption facility takes in an average of 5 cats per day. The facility has to keep their cat occupancy below 300. Currently, the facility has 255 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take in cats?
Answers
Answer:
They can take in cats for 9 more days before they reach capacity.
Step-by-step explanation:
The easiest way to do this lol:
Subtract 255 from 300 to get 45. Since 45 is divisible by 5 which is the average amount of cats they can take per day, count by 5 with your fingers until you reach the number five. How many fingers are you holding up? Nine. Tadaaa.