Final answer:
To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.
Explanation:
To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.
Triangle Inequality Theorem:
Take the two known sides of the triangle.
Add the lengths of the two sides together.
Subtract the sum from the total perimeter of the triangle.
Law of Cosines:
Label the two known sides as 'a' and 'b', and the angle between them as 'C'.
Use the formula c² = a² + b² - 2abcos(C) to find the square of the third side.
Take the square root of the result to find the length of the third side.
Does anyone know anything about The Distributive property? Please help!
5 out of 8 bags of m&ms had exactly 32 pieces in them. How many bags out of 40 should have exactly 32 pieces
Have you found a positive o negative correlation between the independent and dependent variables
Write the equation of the perpendicular bisector of RS. Point R is located at (–1, 3), and point S is located at (3, 1).
Find d: ??? Ft. Plz help idk this question
What is the exact value of cos 30° ?
Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.
Side AB will be the hypotenuse.
cos 60° = AC / AB -------[ cos 60° = 1/2]
So, AB = 2 AC -------------------------------(1)
Apply Pythagorean Theorem to find BC
AB² = BC² + AC²
4 AC² = BC² + AC²
So, BC = √3 AC ------------------------(2)
Now, we shall find the value of cos 30°
cos 30° = CB / AB
or, = √3 AC / 2 AC -------using equations (1) and (2)
So, cos 30° = √3 / 2
Hence, the exact value of
Since ∠A = 2∠B. So, cos 30° will be √3 / 2
The answer is √3 / 2
Simon invested $1,550 at 6.5% simple interest. He earned $302.25 in interest after t years. What is the value of t?
Answer:
Marco deposited $500 in a savings account earning 4% simple interest over 5 years.
What was the total amount of interest earned at the end of 5 years?
$40
$50
$100
$200
Step-by-step explanation:
Trains on the line reached an average speed of 125 miles per hour. Approximately, what is this speed in kilometers per hour?
Please help me with this
List the following stocks and bonds in order from lowest default risk to highest default risk.
A. foreign government bond, common stock, preferred stock
B. foreign government bond, preferred stock, common stock
C. common stock, preferred stock, foreign government bond
D. preferred stock, common stock, foreign government bond
What happened to the cat who swallowed a ball of yarn?
At a local baseball game there are 3 hot dog vendors. collectively the vendors sold 1,700 hot dogs. if vendor a sold 456, vendor b sold 607, and vendor c sold 637, what percentage of the total did each vendor sell? (round to the nearest percent.) a) 26 percent, 40 percent, 44 percent b) 45 percent, 37 percent, 18 percent c) 27 percent, 36 percent, 37 percent d) 30 percent, 35 percent, 35 percent
A child is standing at point c and flying a kite located at point a, 25 ft above the ground. as the child lets out more string, the kite rises to a point b, directly above point
a. if the angle of elevation changes from 50º to 65º, how much higher to the nearest foot, is the kite than it was initially?
Final answer:
To calculate the height increase of the kite, we can use trigonometry and the formula tan(angle) = h / distance. By plugging in the values, we find that the kite is approximately 25 * tan(65º) ft higher than it was initially.
Explanation:
To find how much higher the kite is than it was initially, we need to determine the difference in height between points a and b. Since point b is directly above point a, the difference in height can be calculated using trigonometry.
We can use the tangent of the angle of elevation to find the height increase. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height increase (h) and the adjacent side is the distance between points a and c. We can use the formula tan(angle) = h / distance to solve for h.
Given that the angle changes from 50º to 65º, we can calculate the height increase as follows:
tan(65º) = h / distance
Solving for h:
h = tan(65º) * distance
Plugging in the values:
h = tan(65º) * distance
h ≈ tan(65º) * 25 ft
Rounding to the nearest foot, the kite is approximately 25 * tan(65º) ft higher than it was initially.
Which transformation of Figure A results in Figure A'?
a reflection across the y-axis
a reflection across the x-axis
a clockwise rotation of 90° about the origin
a translation 12 units right and 2 units down.
Answer:
A translation 12 units right and 2 units down.
Step-by-step explanation:
Given : Figure A and figure A'.
To find : Which transformation of Figure A results in Figure A'.
Solution : We have given that
Parent Triangle A with coordinates ( -6 ,-3) ; ( -4 ,-5) ; ( -8 , - 4)
Transformed triangle with coordinates ( 6 ,-5) ; ( 8 ,-7) ; ( 4 , - 6)
We can see from the coordinates
( -6 +12 ,-3-2) = ( 6 ,-5)
( -4+ 12 ,-5 -2) = ( 8 ,-7)
( -8 + 12 , - 4 -2) = ( 4 , - 6).
Therefore, A translation 12 units right and 2 units down.
Bart can paint one house in 3 hours. ann can paint one house in 5 hours. how long would it take bart & ann to paint one house if they worked together?
The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?
6.50
Hope this helps.
Add. Express your answer in lowest terms. 8 3/10 + 7 2/15
To add 8 3/10 and 7 2/15, we need to find a common denominator. The sum is 15 1/15.
Explanation:To add 8 3/10 and 7 2/15, we need to find a common denominator. The least common multiple of 10 and 15 is 30. So we convert both fractions to have a denominator of 30: 8 3/10 = 8 9/30 and 7 2/15 = 7 4/30. Now we can add the whole numbers and the fractions separately:
8 + 7 = 159/30 + 4/30 = 13/30Combining the results, the sum is 15 13/30. To express the answer in lowest terms, we can simplify the fraction: 13 and 30 are both divisible by 13, so dividing both by 13 gives us 1 and 2/30. Therefore, the final answer is 15 2/30, which can be further simplified to 15 1/15.
Is quadrilateral JKLM the result of a dilation of quadrilateral ABCD by a scale factor of 2? Why or why not? Yes, because sides JK and ML are twice as long as sides AB and DC. Yes, because both figures are parallelograms, so corresponding sides are parallel. No, because sides JK and ML are not twice as long as sides AB and DC. No, because sides JM and KL have different slopes from sides AD and BC.
Answer:
(d) No, because sides JM and KL have different slopes from sides AD and BC
Step-by-step explanation:
You want to know if quadrilateral JKLM is a dilation of ABCD by a factor of 2, and why or why not.
DilationDilation multiplies the distance of each point on the figure from the center of dilation by the scale factor. Dilation by a scale factor of 2 will move JKLM twice as far from the origin as ABCD. This preserves slopes and angles, but changes lengths by the scale factor.
In the given figure, ABCD is 2 units wide and 2 units high. If JKLM is a dilation by a factor of 2, it will be 4 units wide and 4 units high.
JKLM is 5 units high, so is not a dilation. JK and ML are twice as long as AB and DC, so choice C is not an appropriate explanation.
Sides JM and KL have different slopes from sides AD and BC, choice D.
__
Additional comment
The slopes of JM and KL are 5/2. The slopes of AD and BC are 2/1, a different value.
Answer: D
Step-by-step explanation:
What is the value of x?
jack paid $2.60 sales tax on a $52 pair of shoes that he purchased. how much sales tax will his friend pay if his friend purhases a $28 shirt?
A spinner is divided into 5 equal sections numbered 1 to 5. The theoretical probability of the spinner stopping on 3 is 20%. Which of the following is most likely the number of 3's spun in 10,000 spins?
A. 3358
B. 1243
C. 2589
D. 2067
ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.
Out of 100 students, how many should weigh between 64 and 96 pounds?
Consider a single spin on the spinner shown below. Which events are mutually exclusive? Check all that apply.
landing on an unshaded portion and landing on 2
landing on a shaded portion and landing on 3
landing on a shaded portion and landing on an even number
landing on an unshaded portion and landing on a number greater than 3
landing on a shaded portion and landing on an unshaded portion
Answer:
Options A, B and E represent mutually exclusive events.
Step-by-step explanation:
Two events are mutually exclusive that can not happen at a same time.
Now let us look at our options and find which statements represent mutually exclusive events.
A. We can see that landing on an unshaded portion and landing on 2 are mutually exclusive events as unshaded portion contains 3 and 4 and 2 lies on shaded portion.
B. Landing on a shaded portion and landing on 3 is also mutually exclusive as 3 lies on unshaded portion.
C. Landing on a shaded portion and landing on an even number can happen at the same time as 2 is an even number and it lies on shaded portion.
D. Landing on an unshaded portion and landing on a number greater than 3 can happen at the same time as 4 in greater than 3 and it lies on unshaded portion.
E. Landing on a shaded portion and landing on an unshaded portion are mutually exclusive events as spinner can be either in shaded portion or in unshaded portion.
Therefore, Options A, B and E are our correct choices.
Answer:
A, B, E
Step-by-step explanation:
I just did it on edge and got it right
At the local grocer, the prices for apples are the following: 9 ounces for $1.89 or 1 pound for $2.49. How much will you save per pound, by buying the least expensive? Round to the nearest cent.
A.) $0.87
B.) $0.10
C.) $0.60
D.) $0.21
Answer: Option 'A' is correct.
Explanation:
Cost of 9 ounces of apples = $1.89
Cost of 1 ounce of apple is given by
[tex]\frac{1.89}{9}=\$0.21[/tex]
Now, if he bought 1 pound of apple,
Cost of 1 pound of apple = $2.49
Cost of 16 ounces = $2.49
(∵ 1 pound = 16 ounces)
Cost of 1 ounce of apple is given by
[tex]\frac{2.49}{16}=\$0.156[/tex]
So, Second option is the least expensive if he bought 1 pound of apple for $2.49
Then, he will save which is given by
[tex]0.21-0.156=0.054\times 16=$0.87\ per pound[/tex]
Hence, option 'A' is correct.
Final answer:
You will save $0.87 per pound by purchasing apples at the price per pound rate ($2.49) compared to the 9-ounce rate ($1.89 for 9 ounces), with the savings calculated by converting the 9-ounce price to a per pound rate and comparing it to the given per pound price.
Explanation:
To determine how much you will save per pound by buying the least expensive option for apples, first convert the price for 9 ounces into the equivalent price per pound. Since there are 16 ounces in a pound, you need to calculate the price per ounce and then multiply by 16 for the pound equivalence. The price per ounce for the first option is $1.89/9 ounces = $0.21 per ounce. Hence, the price per pound would be $0.21 per ounce × 16 ounces/pound = $3.36 per pound.
Now compare the price per pound of both options. The specified price per pound is $2.49, and the calculated price per pound for the 9-ounce option is $3.36. The savings per pound when buying the least expensive option ($2.49 per pound) would be $3.36 - $2.49 = $0.87 per pound, rounded to the nearest cent.
Therefore, the correct answer is (A) $0.87.
Share out £80 between Tom and jerry in the ratio 3:2
Will give brainliest! How many distinct triangles can be made? I think I have to first find the measure of length b and then compare measure a with b and h to find the answer. Please help me out on how to find measure length b
The line graphed below passes through the points (-2, 0) and (0, -3). Use the slope formula to calculate the slope between the given points. Verify the slope by counting the rise over the run on the graph.
Answer:
The answer is -4/5
Step-by-step explanation:
It just is. The test said so.
If the area is 72 and the perimeter is 34, what are it's dimensions
Lynh manages a small company with 12 employees. He offers profit sharing where 5% of profits at end of year is distributed evenly to the employees. Each employee earned $2,300 in profit sharing in 2013. What was the total profit?
We need to find the total profit of Lynh Mangoes. It is given that the 5 % of profit to be distributed equally between 12 employees.
Profit received by each employee = $ 2,300
Total profit received by 12 employees = $ 2,300 × Profit received by each employee
Total profit received by 12 employees = $ 27,600
It is given that 5 % to be distributed.
Thus, 5 % of total profit = $ 27,600
Total profit = $ 27,600 ÷ 5 %
Total profit = $ 552,000
the amount that results when $4000 is compounded at 6% annually over seven years