For each triangle shown below, determine whether you would use the Law of Sines or Law of Cosines to find angle x, and explain how you know which Law to use. Then find angle x to the nearest tenth.
NOTE: The perimeter of ABC-31
Answers
Given:
The figure of a triangle.
The perimeter of the triangle ABC is 31.
To find:
The value of x in the given triangle.
Solution:
Three sides of the triangle ABC are AB, BC, AC are their measures are [tex]3b-4,2b+1,b+10[/tex] respectively.
The perimeter of the triangle ABC is 31.
[tex]AB+BC+AC=31[/tex]
[tex](3b-4)+(2b+1)+(b+10)=31[/tex]
[tex]6b+7=31[/tex]
Subtract 7 from both sides.
[tex]6b=31-7[/tex]
[tex]6b=24[/tex]
[tex]b=\dfrac{24}{6}[/tex]
[tex]b=4[/tex]
Now, the measures of the sides are:
[tex]AB=3b-4[/tex]
[tex]AB=3(4)-4[/tex]
[tex]AB=12-4[/tex]
[tex]AB=8[/tex]
[tex]BC=2b+1[/tex]
[tex]BC=2(4)+1[/tex]
[tex]BC=8+1[/tex]
[tex]BC=9[/tex]
And,
[tex]AC=b+10[/tex]
[tex]AC=4+10[/tex]
[tex]AC=14[/tex]
Using the law of cosines, we get
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
[tex]\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}[/tex]
[tex]\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}[/tex]
[tex]\cos A=\dfrac{179}{224}[/tex]
Using calculator, we get
[tex]\cos A=0.7991[/tex]
[tex]A=\cos ^{-1}(0.7991)[/tex]
[tex]x=36.9558^\circ[/tex]
[tex]x\approx 37.0^\circ[/tex]
Therefore, the value of x is 37.0 degrees.
Related Questions
As an estimation we are told 5 miles is 8 km. Convert 17.8 km to miles.
Answers
Answer:
17.8km = 11.125 miles
Step-by-step explanation:
From 5 miles = 8km, we can form the ratio km:miles as 8 : 5.
We want to put the ratio in the form 1 : n, which gives us 1 : 0.625 (we divide both 8 and 5 by 8 to get this form).
Now, using the ratio km:miles as 1:0.625, we have to multiply both 1 and 0.625 by 17.8 to gain the ratio 17.8 : n, therefore giving us the ratio 17.8 : 11.125.
Hence, 17.8km = 11.125 miles
Answer:
11.125 miles
Step-by-step explanation:
Proportions:
5 miles ⇒ 8 km
A miles ⇒ 17.8 km
A = 17.8km*5miles/8miles
A = 11.125 miles
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Answer:
The point is inside. I used Desmos and it showed this.
aand (-4,2) can be placed inside the circle.
Step-by-step explanation:
40 pointsanad brainliest for this, it's really important!
Answers
Step-by-step explanation:
C = 6 n + 4,500
the set up cost is represented by the initial value of the function, which is $4,500.
the ongoing cost of materials and labor is represented by the rate of change of the function, which is $6 per bottle.
ILL GIVE BRAINLIEST PLZ ANSWER
Answers
Answer:
-6
Step-by-step explanation:
y = -6x - 5
The equation is put in slope intercept form
( y = mx + b )
Where m = slope and b = y intercept
-6 is in the spot of "m"
Meaning that the slope would be -6
Answer:
slope is -6
Step-by-step explanation:
y = mx+b
m is slope :)
b is the point, where the line intersects the y axis
Maths Assignment
4-a^2
Answers
Answer:
(2-a)^2
(2+a) (2-a)...
Answer:
Step-by-step explanation:
Use the identity: a² - b² = (a+ b)(a - b)
4 - a² = 2² - a² {Here a = 2 and b = a}
= (2 +a) (2 - a)
In a class of 55 students, 15 students like Math but not English and 18 students liked English but not Math. If 5 students did not like both, how many students liked both subjects? Represent the above information in a Venn-diagram.
Answers
Hope this helps! Please consider marking me the Brainliest, it’s not necessary, but very much appreciated. Have a great day!
A cubical house can hold 4096m of air .find the height of the house
Answers
Answer:
16 m
Step-by-step explanation:
V = [tex]s^{3}[/tex]
4096 = [tex]s^{3}[/tex]
cube root of 4096 = 16
y = 2 3 x − 5 y = −2x + 3 On a coordinate plane, 2 lines intersect at (negative 3, negative 3). She determined that the solution is (–3, –3). Is she correct? If not, explain why.
Answers
Given:
The two equations are:
[tex]y=\dfrac{2}{3}x-5[/tex]
[tex]y=-2x+3[/tex]
To find:
Whether (-3,-3) is a solution of the given equation or not.
Solution:
Table of values for [tex]y=\dfrac{2}{3}x-5[/tex],
x y
0 -5
7.5 0
Plot the points (0,-5) and (7.5,0) on a coordinate plane and connect them by a straight line.
Table of values for [tex]y=-2x+3[/tex],
x y
0 3
1.5 0
Plot the points (0,3) and (1.5,0) on a coordinate plane and connect them by a straight line.
From the below graph, it is clear that the graphs of both lines intersect each other at (3,-3). So, the solution of given equations is (3,-3) instead of (-3,-3).
Therefore, she is incorrect because the correct solution is (3,-3).
solve for:− 5 − 6 ≤ 8 − 8 − (show your work)
Answers
Answer:
hope it helps.
stay safe healthy and happy...Can someone help me with this math homework please!
Answers
Answer:
1st, 2nd and 6th options
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] - x + [tex]\frac{1}{6}[/tex] = 6x ( multiply through by 6 to clear the fractions )
4 - 6x + 1 = 36x ← option 1 will have the same solution set
----------------------------------------------------------------------
Adding the 2 fractions on the left side gives
[tex]\frac{4}{6}[/tex] +[tex]\frac{1}{6}[/tex] - x = 6x , that is
[tex]\frac{5}{6}[/tex] - x = 6x ← option 2 will have the same solution set
------------------------------------------------------------------------
From
4 - 6x + 1 = 36x ( add 6x to both sides )
5 = 42x ← option 6 will have the same solution set
At the farmers' market, Lillian bought 5/12 of a pound of string beans and 1/12 of a pound of lima beans. How many more pounds of string beans did Lillian purchase?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
1/3 more pounds of string beans.
Step-by-step explanation:
Amount of string beans: 5/12 of a lbs(pound)
Amount of lima beans: 1/12 of a lbs
Amount of string beans - Amount of lima beans = 5/12-1/12 =4/12 which simplifies down to 1/3.
The sum of a number and nine is fifteen
Write an equation to represent the sentence
Answers
Answer:
x+9=15
Step-by-step explanation:
a number plus 9 is fifteen
let x represent the unknown number
x+9=15
:) ur welcome
hope this helped
Aimee wants to cut a piece of ribbon that is 5 1/4 meters long into lengths that are 1 1/8 meters long. How many full pieces can she cut?
Answers
Answer:
Four pieces.
Step-by-step explanation:
If Aimee has a piece of ribbon that is 5 1/4, or 5 2/8 meters long, then you will want to divide that main part into smaller parts of the other length.
1 1/8 meters multiplied by 1 is 1 1/8 meters. This still fits. 1 1/8 meters multiplied by 2 is 2 1/4 meters. This still fits. 1 1/8 meters multiplied by 3 is 3 3/8 meters, which still fits. 1 1/8 meters multiplied by 4 is 4 1/2 meters, which still fits. However, once you reach 5, or 5 5/8 total, then that is over the size of the whole.
So, four full pieces can be cut.
What is the value of the following function when x = 0?
у = -5
y = -2
y = -1
y = 0
Answers
Answer:
y = - 2
Step-by-step explanation:
x = 0 lies on the y- axis
The only point on the y- axis where the function crosses is y = - 2
Then when x = 0, y = - 2
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right
Answers
So the interior angle would still be 135
A girl walked 6km from her house to a market and discovered that she had covered 4/5 of the distance to the market how far is the market from her house
Answers
Answer: [tex]7.5\ km[/tex]
Step-by-step explanation:
Given
Girl has traveled 6 km from her house
She has covered [tex]\frac{4}{5}[/tex] of the distance
Suppose the total distance is x
[tex]\therefore 6=\dfrac{4x}{5}\\\\\Rightarrow x=\dfrac{30}{4}\\\\\Rightarrow x=\dfrac{15}{2}\ \text{km}\\\\\Rightarrow x=7.5\ \text{km}[/tex]
What is the value of X?
3
4
6
8
Answers
Answer:
The answer is 4
Step-by-step explanation:
please help a and b
Answers
Answer:
a=144.15
median=157.5
Problem: Construct a triangle with interior angle measures of 60° and 60°. Let one of the side lengths be 10. What are the lengths of the other sides?
Answers
Answer:
10 and 10
Step-by-step explanation:
This is because of the triangle having all sides with the same angle. This is a equilateral triangle
Use the drop-down menus to describe the key aspects of the function
f(x) = –x2 – 2x – 1.
Answers
Answer:
Step-by-step explanation:
Given function is,
f(x) = -x² - 2x - 1
= -(x² + 2x + 1)
= -(x + 2)²
Comparing this equation with the vertex form of a quadratic function,
f(x) = a(x - h)² + k
Here, (h, k) is the vertex.
Vertex of the function is (-2, 0)
Leading coefficient of the function = -1
Therefore, parabola will open downwards.
Function will be increasing in the interval (-∞, -2).
Function will be decreasing in the interval (-2, -∞).
Domain of the function → (-∞, ∞)
Range of the function → (-∞, 0]
Answer:
Step-by-step explanation:
edge
Class 3 question ,pls help
Answers
Answer:
bigger number minus larger number plus 1
430-421 = 9 + 1 = 10
573 - 567 = 6+1 = 7
898 - 890 = 8+ 1 = 9
Step-by-step explanation:
The table below shows how much Joe earns, y, after working x hours.
Joe’s Earnings
Hours worked
Money earned
4
$30
10
$75
12
$90
22
$165
The relationship between money earned and hours worked is linear. Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). How do the two slopes compare?
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the x-axis.
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the y-axis.
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.
The slope between (4, 30) and (12, 90) is less because 4 is a factor of 12 and 30 is a factor of 90.
Answers
Answer: Given : Joe’s Earnings and hour worked
The relationship between money earned and hours worked is linear.
Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75).
To Find : How do the two slopes compare?
Solution:
Hours worked Money earned
4 $30
10 $75
12 $90
22 $165
slope between (4, 30) and (12, 90),
= (90 - 30)/(12 - 4)
= 60/8
= 15/2
slope between (4, 30) and (10, 75)
= (75 - 30)/(10-4)
= 45/6
= 15/2
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.
Both Slopes are same.
i hope this helped and have a nice day/night
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same. The correct answer is the third option.
The slope between two points (x₁,y₁) and (x₂, y₂) on a straight line is given by (y₂ - y₁)/(x₂ -x₁ ).
Let's calculate the slopes:
The slope between (4, 30) and (12, 90):
Slope = (90 - 30) / (12 - 4)
= 60 / 8
= 7.5
The slope between (4, 30) and (10, 75):
Slope = (75 - 30) / (10 - 4)
= 45 / 6
= 7.5
As we can see, the slopes between the two sets of ordered pairs are the same.
Thus, the slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.
Hence, the correct answer is the third option.
Learn more about the slope of the line here:
brainly.com/question/14511992
#SPJ7
PLEASE HELP ASAP!!!
solve for the given variable and show your work. 3a-12b=30. solve for b.
Answers
Answer:
b=(-10-a)/4
First factor out the common number:3
Then divide both sides by 3
Then simplify 30/3 to 10
Then subtract a to get your answer
What is the value of y?
Answers
180 = 2y + 70
180 - 70 = 2y
110 = 2y
y = 110/2
y = 55
the sum of triangle is 180:
[tex]y + 40 + y + 30 = 180 \\ 2y + 70 = 180 \\ 2y = 180 - 70 \\ 2y = 110 \\ y = \frac{110}{2} \\ y = 55[/tex]
Please solve the question attached:
Answers
Answer:
magnitude is 4.5 lb, and the direction is given by the angle 250°.
Step-by-step explanation:
We can see that the magnitude is 4.5lb (it is already written in the graph, the "distance" between R and T).
To find the angle, remember that the angle is measured counterclockwise from the positive x-axis.
We can see that the angle, measured clockwise, is 110°
And the angle of a complete revolution is 360°
The sum of the angle measured clockwise and the angle measured counterclockwise should be equal to 360°
Then the angle, measured counterclockwise is given by:
360° - 110° = 250°
Then the magnitude is 4.5lb, and the direction is given by the angle 250°.
8/m - b/n simplified
Answers
Answer:
[see below]
Step-by-step explanation:
[tex]\frac{8}{m}-\frac{b}{n}\\\\\rightarrow \text{Adjust based on LCM}\\\text{LCM: } mn\\\\\frac{8n}{mn}-\frac{bm}{mn}\\\\\boxed{\frac{8n-mb}{mn}}[/tex]
Hope this helps.
Find the last digit of the number 41875 * so that it is divisible by 18.
Answers
Answer: 2.
Step-by-step explanation:
if you were to divide 418752 by 18 you would get a clear (without decimal) number, that would equal 23264
3 years later a mother will be 4 times as
old as her son. 3 years ago ,the mother age was two times as old as her son age will be 8 years hence. What are their present ages?
Answers
Answer:
33 and 6 yearsStep-by-step explanation:
Mother's age = mSon's age = s3 years later:
m + 3 = 4(s + 3) ⇒ m = 4s + 12 - 3 = 4s + 93 years ago:
m - 3 = 2(s + 8) ⇒ m = 2s + 18 + 3 = 2s + 21Solve for s by substitution:
4s + 9 = 2s + 212s = 12s = 6Find the value of m:
m = 4*6 + 9 = 33Mother is 33 and son is 6
Please help me ASAP!!!
Answers
Answer:
[tex]108 in^{2}[/tex]
Step-by-step explanation:
[tex]===========================================[/tex]
Formulas:
Area of a rectangle/square:
[tex]A=lw[/tex]
Area of a triangle:
[tex]A=bh\frac{1}{2}[/tex]
[tex]===========================================[/tex]
To find the square, length*width. Both the length and width are 6, so the area of the square is 36 in.
The triangles all have a base of 6 and a height of 6. So, 36 divided by 2 or multiplied by [tex]\frac{1}{2}[/tex]
You would get 18 in.
There are 4 triangles, so multiply 18 by 4. 72 in.
Add up 36 and 72.
The answer is 108.
[tex]===========================================[/tex]
[tex]108 in^{2}[/tex]
Help me please
I will mark you as brainliest
Answers
Answer:
In picture
Step-by-step explanation:
Brainliest please~
[tex](0,3)[/tex] and [tex](1,-2)[/tex]
Equation: (refer the image below)
Slope:
[tex]m=\frac{3+2}{0-1}[/tex]
[tex]m=-5[/tex]
Equation:
[tex]y=5x-b[/tex]
[tex]3=b[/tex]
Substitute (0,3)
Point: [tex](1,-2)[/tex]