[tex]3a(2 + a) \\ 3 \times 5(2 + 5 ) \\ 15(7) \\ 150[/tex]
Find the value of x. Helpp Pleasee!
When you have a 90-degree angle in a triangle, what happens to the law of cosines? What formula does it "turn in to"?
Answer:
Pythagorean Theorem
Step-by-step explanation:
a² + b² = c²
The sum of the square of the hypotenuse is equal to the sum of the squares of the sides of the right triangle.
When you have a 90-degree angle in a triangle, the Law of Cosines simplifies to the Pythagorean theorem: c² = a² + b².
When you have a 90-degree angle in a triangle, it means that the triangle is a right triangle.
In a right triangle, one of the angles is exactly 90 degrees, and the side opposite to this right angle is called the hypotenuse.
The Pythagorean theorem relates the lengths of the sides of a right triangle and is a special case of the Law of Cosines.
The Law of Cosines is given by:
c² = a² + b² - 2abcos(C)
Where:
c is the length of the side opposite angle C.
a and b are the lengths of the other two sides.
C is the angle opposite side c.
Now, when you have a right triangle and C is the right angle (90 degrees), the cosine of the right angle becomes zero.
This is because the cosine of 90 degrees is 0.
Therefore, the Law of Cosines simplifies to:
c² = a² + b² - 2abcos(90°)
c² = a² + b²
Hence, c² = a² + b² is the well-known formula for the Pythagorean theorem, which relates the squares of the lengths of the two shorter sides (legs) of a right triangle to the square of the length of the hypotenuse.
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Vance wants to construct a circle tangent to all three sides of the acute, scalene triangle LMN using the following steps.
He will draw altitudes from vertex L and vertex M, and mark their intersection point as O.
He will draw the perpendicular from point O to side MN, and mark the intersection point as P.
He will draw the circle centered at point O which will pass through point P.
Which part of Vance's plan requires revision?
A.
Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.
B.
Vance should have found the intersection of two perpendicular bisectors of triangle LMN instead of two altitudes.
C.
Vance should have constructed all three altitudes instead of only constructing two altitudes.
D.
Vance should have used the compass to draw a circle through point N instead of point P.
The part that needs revision in the construction of the tangent to the triangle is C. Vance should have constructed all three altitudes instead of only constructing two altitudes.
What is a triangle?A triangle simply means a polygon that has three sides. Also, a triangle has there's edges as well as vertices.
In this case, in order to construct a circle tangent to all three sides of the acute, scalene triangle LMN, it should be noted that the three altitudes have to be taken into consideration.
This wasn't the case in the step given by Vance as only two altitudes were considered. Therefore, this should be the change that is required.
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Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1. 5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score? 69. 2 75. 6 90. 8 97. 2.
The expected score that Joe can obtain provided the probability of the left-out questions being correct as per the given situation is 90.8.
Points secured by Joe by answering correctly = 12*6 = 72
What is probability?Probability is the conversion of possibilities or occurrences in numbers.
Now, the probability of a correct guess in the questions in which Joe eliminated 2 choices = 1/3
So, the possible marks of Joe in those 4 questions = 1/3*4*6=8
Probability of correct guess in remaining 9 random guesses= 1/5
So, the possible marks that Joe can score in those 9 random guesses = 1/5*9*6 = 10.8
Therefore, the expected score of Joe = 72+8+10.8 = 90.8
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A taxi cab company charges an initial fee of $4 and then $5 per mile for a ride. Use the equation c = 5x + 4 to complete the table
Answer:
Plug in the number of miles for x and solve for c- this will be your total number.
Step-by-step explanation:
Plug in the values you need for your table and solve for c.
The height of three students in the class are given below. Order the students from shortest to tallest.
Answer:
Janis, Carl, Catherine
Step-by-step explanation:
janis=1.666
carl=1.7
catherine=2.333
please help i’ll mark
Answer:
c = 0.50(0.48)(1525)
Step-by-step explanation:
If 52% of the students are female, then
100% - 52% = 48% of the students are male
48% = 48/100 = 0.48
To find the number of students who are male:
⇒ total number of students x 0.48 = 0.48 x 1525
Half = 50% = 50/100 = 0.50
⇒ half of the male students = 0.50 x 0.48 x 1525
Solution: c = 0.50(0.48)(1525)
A lawn sprinkler sprays water in a circular area of grass. The diameter of the circular area of grass is 15 ft. What is the area that this sprinkler sprays with water?
Answer:
56.25[tex]\pi[/tex]ft² or 176.715 ft²... it depends of if you round or not
Step-by-step explanation:
area = πr², r=7.5, 7.5*7.5=56.25
8 divided by 0.61 show me how you solved it
Compare. Select<,>,=.
13 gal ? 55qt
Answer:
13 gal < 55 quarts
Step-by-step explanation:
There are approx 4 quarts in 1 gallon
Therefore, 13 gallons = 13 x 4 = 52 quarts
52 < 55
So 13 gal < 55 quarts
-1/6 - ( -3/5)
write answer in simplest form
Answer:
13/30
Step-by-step explanation:
Amy now earns $9.50 per hour. This is 125% of
what she earned last year. What did she earn per
hour last year?
answer:
$9.50 = 125% * (last years hourly wage)
$9.50 = 1.25*X
9.50/1.25 = X
$7.60 = X
she earned $7.60 per hour last year!
Does acute isosceles exist?
Yes Or no..
Answer:
YES
Step-by-step explanation:
isoceles triangles CAN be acute in real.
Just try to look at an isoceles triangle, if there is one angle that is obtuse, then there HAS to be an angle that is acute.
Thanks!
Answer:
Yes, acute isosceles triangles exist.
Step-by-step explanation:
two six sided dice are rolled and the two dice equals 7. what is the probability that one die is a 3
Let us solve the problem step by step.
here we have rolled two dice. So total no. of possible outcomes will be 6^2=36. These are (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).
Now, among these cases the cases where the sum is seven for (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) i.e. there are 6 cases.
Now, it is time to calculate the probability.
The required probability is,
p = (No. of cases favorable for the event)/(Total no. of cases)
=6/36 = 1/6
Therefore your answer is 1/6.If two six-sided dice are rolled and the two dice are equal. The probability that one die is a 3 will be 6.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that, two six-sided dice are rolled and the two dice equal 7.
If two dice are rolled. The total no. of possible outcomes will be,
= 6²
=36
The total outcomes are,
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).
If the desired outcome is their sum which is 7. All the possible cases are 6,
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
The required probability is,
p(sum=7) = (No. of cases favorable for the event)/(Total no. of cases)
p(sum=7)=6/36
p(sum=7)= 1/6
Thus, if two six-sided dice are rolled and the two dice are equal. The probability that one die is a 3 will be 6.
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Can someone help me understand what this means
Need help I have been stuck on this for a while
Answer:
sqrt25
Step-by-step explanation:
Step-By-Step explanation
Volume(rectangular prism) = lhw (length x width x height)
Since length x width is to find the base area, it mean length x width = 72 square inches.
=> Height = 288 : 72 = 4 inches.
Why did Marie Antoinette need to marry the French family?
33/9 but put the remainder as a fraction, also i need the solution
Answer:
3 2/3
Step-by-step explanation:
33/9 as a fraction you divide 33 by 9 and get 3 as a whole number and 6/9 then simplify 6/9 by 3 and get 2/3
Answer:
33/9 but put the remainder as a fraction, also i need the solution
Step-by-step explanation:
3. Mr Chen's salary was $2800. He spent $1500 and gave the rest equally to each of his 3 daughters and 2 sons. How much did each daughter receive? Ans:
Answer:
$260 each
Step-by-step explanation:
Combined, Mr. Chen as 5 children. 2800-1500 = 1300. 1300/5 = $260 per child.
In circle T, what is the value of x?
x = 19°
x = 20°
x = 24°
x = 29°
Check the picture below.
Answer:
(a) x° = 19°
Step-by-step explanation:
A triangle inscribed in a semicircle is a right triangle. That means the acute angles in the triangle are complementary:
x° = 90° -71° = 19°
Two friends at a restaurant each order a fruit drink. The available flavors are watermelon, orange, or mango. Write an organized list using the format to represent the sample space of the friends' fruit drinks.
Answer: A
Step-by-step explanation:
(Friend 1, Friend 2)
Friend 1 = x
Friend 2 = y
(x, y) variables are substitution for the flavors
So it cant be C or D
B doesn't have all the possible solutions
y= 5-3x
y= -3x+4
solution or no solution
Answer:
no solution
Step-by-step explanation:
y = 5 - 3x → (1)
y = - 3x + 4 → (2)
substitute y = - 3x + 4 into (1)
- 3x + 4 = 5 - 3x ( subtract 4 from both sides )
- 3x = 1 - 3x ( add 3x to both sides )
0 = 1 ← not possible
this indicates the system has no solutions
The straight line joining points A(p,3) and B(1,-1) has length 5, workout the value of p
Answer:
d^2 = <y2-y1>^2 + <x2 -x1) ^2
so
p =4
the cost of cab fare is $12.00 write and solve an equation to show the total with a 13% tip add
Answer:
13.56$
To write an equation, we need to think about what this is asking us. It's asking us to take a number and increase the total % to be 113% of the original number. This looks something like
[tex]y = 1.13x[/tex]
Where y is amount with a tip and x is amount before a tip. To calculate for 12 dollars, we plug 12 into x and it comes out as 13.56 dollars
Hope it helps!
Which graph represents the given function?
Answer: it’s b
bye don’t have a good day have a great day
Step-by-step explanation:
find the marked angles in each of the following. where a point O is given it is the centre of the circle.
Simplify -12x + 5x.
-17 x
-7
-7 x
Answer:
-7x
Step-by-step explanation:
==> -12x + 5x.
==> -12+5xx
==> -7x
Answer:
-7x
Step-by-step explanation:
−12x+5x
Combine Like Terms:
=−12x+5x
=(−12x+5x)
=−7x
Combining like terms - Combining like terms will simplify a math problem and is also the proper form for writing a polynomial. To combine like terms, just add the coefficients of each like term.
How do I solve this?
Answer:The solution is in the attached file
Step-by-step explanation:
Solution:
Note that:
Slope of line = 4Given point: (1, 13)Point slope form formula: y - y₁ = m(x - x₁)Use the formula to obtain the equation of the line.
y - y₁ = m(x - x₁)=> y - 13 = 4(x - 1)=> y - 13 = 4x - 4=> y = 4x - 4 + 13=> y = 4x + 9The equation of the line is y = 4x + 9.
PLEASE HELP ASAP I NEED THIS TO PASS 20 POINTS 5 STARS
1)By the Triangle Inequality Theorem which set of side lengths could create a triangle?A) 5, 10, 4B) 5, 7, 13C) 7, 9, 3D) 10, 4, 5
Answer:
C
Step-by-step explanation:
The answer is C because it is the only one where any combination of 2 sides will add up to be greater than the other sides.
Answer:
Step-by-step explanation:
A is not possible, because 5 + 4 < 10 (doesn't satisfly inequality.)
B is also not possible => 5 + 7 < 13 (doesn't satisfy inequality.)
D is also not possible => 4 + 5 < 10 (doesn't satisfy inequality)
So, the answer is C, cause the sum of 2 sides is always more than the other one.
Need answers for 9,11,15,17,26,36
