C. The alternative form of the law of cosines
When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using the alternative form of the law of cosines.
Explanation;From the law of cosines, given that a, b and c are the edges of a triangle and A, B and C are the corresponding interior angles of the the triangle.Then; a² = b² + c² − 2 bc cos A, or b² = a² + c² − 2 bc cos B, or c² = a² +b ² − 2 bc cos CTherefore; when given all the sides or edges of the triangle;
we can use the law of cosines to find one angle, then we use the law of cosines again to find the second angle, and finally,we use the point that angles in a triangle add up to 180 to get the third angle;The slope of the line below is –4. Use the coordinates of the labeled point to find a point-slope equation of the line.
A. y – 9 = 4(x + 4)
B. y + 9 = –4(x – 4)
C. y – 9 = –4(x + 4)
D. y + 9 = 4(x – 4)
Answer: y+9=-4(x-4)
Step-by-step explanation:
A P E X
Ken drew a pair of intersecting rays and marked the angle between them.
Which of these statements best compares the pair of intersecting rays with the angle?
-The rays and the angle have two endpoints each.
-The rays and the angle have their lines extending in opposite directions.
-The rays have a number of points lying on them and the angle has only one point lying on it.
-The rays extend infinitely and the angle is made by the rays which have a common endpoint.
...?
Answer:
-The rays extend infinitely and the angle is made by the rays which have a common endpoint.
Step-by-step explanation:
A ray starts from one point and extends in one direction forever.
An angle is the space between two intersecting lines at or close to the point where they meet. In this case two rays intersect each other at one point
Joe builds a toy house in the shape of a rectangular prism. If he paints each of its faces with a different color of paint, how many colors will he require?
4
5
6
8
12+5x-8=12x-10
Help me solve it step by step
The solution to -35x = -105 is -3.
True
False
The solution to 2x - 5 = 27 is also a solution of which of the following equations?
3 + 5x = 58
3x - 2 = 31
2x + 3 = 35
27 - 2x = 5
three kids named ricky, bobby, and terry have a total of 68 tech decks. Ricky has 8 more than bobby. terry has triple the number bobby has how many tech decks does each kid have?
Final answer:
Bobby has 12 tech decks, Ricky has 20 tech decks, and Terry has 36 tech decks.
Explanation:
Let's represent the number of tech decks each child has using variables.
Let's say Bobby has x tech decks. Since Ricky has 8 more tech decks than Bobby, Ricky has x + 8 tech decks. Terry has triple the number of tech decks that Bobby has, so Terry has 3x tech decks.
Now, we can set up an equation to represent the total number of tech decks:
x + x + 8 + 3x = 68
5x + 8 = 68
5x = 60
x = 12
So, Bobby has 12 tech decks, Ricky has 12 + 8 = 20 tech decks, and Terry has 3 * 12 = 36 tech decks.
an antenna is on top of an 80 foot building, 12 feet from the edge. from a point 60 feet from the base of the building,the angle from ground level to the top of the antenna is 68 degrees. find the height of the antenna to the nearest foot
The decimal of 2 quarters, 1 dime, and 4 pennies
How do you do long divison with 2 digits?
Jerome walked 2/3 mile in the morning and 11/12 mile in the evning. How many miles did he walk in all?
A.)19/24
B.)7/12
C.)1 and 7/12
D.)1 and 1/3
What is the tan of 30 degrees
Answer:
The value of tan 30 degrees is 0.57736.
Step-by-step explanation:
Tan 30 degrees in radical form is = [tex]\frac{1}{\sqrt{3} }[/tex]
We know [tex]\sqrt{3}[/tex] = 1.732
So, tan 30 degrees = [tex]\frac{1}{1.732}[/tex]
= 0.57736
The answer is 0.57736.
Please find attached the exact value reference triangle .
The required value of tan 30 degrees is 1/[tex]\sqrt{3}[/tex].
Given the trigonometric function tan 30 degrees.
The tangent of 30 degrees, written as tan(30°), can be evaluated without a calculator by using the trigonometric properties of special angles.
In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
For a 30°- 60°- 90° right triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, and the side adjacent to the 30-degree angle is equal to the length of the hypotenuse multiplied by
[tex]\sqrt{3}[/tex]/2.
In a 30°-60°-90° triangle, the tangent of 30 degrees is given by:
tan(30°) = (opposite side) / (adjacent side)
tan(30°) = (1/2) / ([tex]\sqrt{3}[/tex]/2)
tan(30°) = 1/[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]/3.
tan (30°) = [tex]\sqrt{3}[/tex]/3
Multiply both numerator and denominator by [tex]\sqrt{3}[/tex] gives,
tan(30°) = 3/3[tex]\sqrt{3}[/tex].
Divide both numerator and denominator by 3 gives,
tan(30°) = 1/[tex]\sqrt{3}[/tex].
Therefore, the tangent of 30 degrees is 1/[tex]\sqrt{3}[/tex].
Hence, the required value of tan 30 degrees is 1/[tex]\sqrt{3}[/tex].
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I have 28 toys that are solar 2/7 of them are Disney characters how many solar toys are Disney characters
Final answer:
To find out how many solar toys are Disney characters, multiply the total number of toys by the fraction of toys that are Disney characters.
Explanation:
To find out how many solar toys are Disney characters, we need to multiply the total number of toys by the fraction of toys that are Disney characters. In this case, 2/7 of the toys are Disney characters. So, we can calculate:
Number of solar Disney toys = Total number of solar toys × Fraction of Disney toys
Number of solar Disney toys = 28 × 2/7 = 8
Therefore, there are 8 solar toys that are Disney characters.
Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years?
Answer:
The answer is 44,237.
Step-by-step explanation:
50000×0.96×0.96×0.96
=44236.8
when rounded to the nearest dollar it is 44,237.
The total amount of money that your mother distributes to you and your two siblings if she gives each person x dollars
15 meters or 15 yards
sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0
Which description best describes the graph?
Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing
Answer:
linear increasing
Step-by-step explanation:
A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?
Find the area of the blue sector of the circle. Round to the nearest hundredth.
A)4.19 cm2
B)6.22 cm2
C)8.31 cm2
D)9.67 cm2 ...?
Answer:
A) 4.19 cm^2
Step-by-step explanation:
Megan is trying to remember her password for her computer. All she can remember is that it is 2 letters followed by 3 digits.
How many possible combinations are there for Megan's password?
A. 1,560
B. 1,676
C. 468,000
D. 492,804
E. 676,000
The number of permutations possible is 468000.
What is permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
The first two places are occupied by letters.
The last 3 places are occupied by numbers.
The permutation for the first 2 places is: [tex]26P_2[/tex]
The permutation for the last 3 places is: [tex]10P_3[/tex]
The total permutation is:
[tex]26P_2 \times 10P_3\\\\=468000[/tex]
Hence the correct option is option C.
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if 2 people bring 3 pies each and then 3 more people show up, how much pie will each person get?
HELP I BEG OF YOU!!!!!!!!!!!
In which figure is DE\\BC ? figure 1 figure 2 figure 3 figure 4
In Figure 4, in the triangle ΔABC, DE is parallel to BC, i.e., DE||BC.
A triangle is one of the most basic geometric figures, having 3 sides, 3 angles, and 3 vertices.
By the theorem of the triangle, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. Let's check the theorem holds for which triangle in the given figures.
Figure 1:
[tex]\frac{AD}{BD} = \frac{6}{15} =\frac{2}{5}[/tex]
[tex]\frac{AE}{CE} = \frac{6.6}{17.5} =\frac{66}{175}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 2:
[tex]\frac{AD}{BD} = \frac{5}{12}[/tex]
[tex]\frac{AE}{CE} = \frac{6}{15} =\frac{2}{5}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 3:
[tex]\frac{AD}{BD} = \frac{4}{12} =\frac{1}{3}[/tex]
[tex]\frac{AE}{CE} = \frac{5}{16}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 4 :
[tex]\frac{AD}{BD} = \frac{5.5}{15}[/tex]
[tex]= \frac{55}{150}\\ = \frac{11}{30}[/tex]
[tex]\frac{AE}{CE} = \frac{6.6}{18}[/tex]
[tex]=\frac{66}{180}\\ =\frac{11}{30}[/tex]
Since, [tex]\frac{AD}{BD} = \frac{AE}{CE}[/tex],
Therefore, in triangle ABC, DE is parallel to BC, i.e., DE||BC.
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What is the value of the function at x = 3?
Answer:
this goes to jaden rashid, jaden your all grown up now and so is ur cat, u will always be a legend
Step-by-step explanation:
the answer is 5
Julia ran 7000 meters, while carol ran 4 kilometers. who ran farther?
Deserts advance linearly, in easily mappable patterns.
True
False
This answer is false.
What is 1.3 repeating as a fraction?
Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like reading mystery stories, the number of students at the library who liked mystery stories was _____. (only put numeric values, no other symbols)
You are making small pizzas. you have 12 cups of flour. each pizza crust requires 3/4 cup of flour. how many pizza crusts can you make?