Answer:
Since [tex]AB \neq BC \neq AC[/tex] and [tex]\cos B = 0[/tex], we conclude that given triangle is a right-angled and scalene.
Step-by-step explanation:
First, we determine the lengths of sides [tex]AB[/tex], [tex]BC[/tex] and [tex]AC[/tex] by the Equation of the Line Segment, which is based on the Pythagorean Theorem:
Line segment AB
[tex]AB = \sqrt{(4-1)^{2}+ (4-1)^{2}}[/tex]
[tex]AB = 3\sqrt{2}[/tex]
Line segment BC
[tex]BC = \sqrt{(6-4)^{2}+(2-4)^{2}}[/tex]
[tex]BC = 2\sqrt{2}[/tex]
Line segment AC
[tex]AC = \sqrt{(6-1)^{2}+(2-1)^{2}}[/tex]
[tex]AC = \sqrt{26}[/tex]
And the angles are found by means of the Law of Cosine:, where acute angles exist when [tex]0 < \cos \theta < 1[/tex], whereas obtuse angles exist for [tex]-1 < \cos \theta < 0[/tex].
Angle A
[tex]BC^{2} = AB^{2} + AC^{2} - 2\cdot AB\cdot AC \cdot \cos A[/tex] (1)
[tex]\cos A = \frac{BC^{2}-AB^{2}-AC^{2}}{-2\cdot AB\cdot AC}[/tex]
[tex]\cos A = \frac{8-18-26}{-2\dot (3\sqrt{2})\cdot (\sqrt{26})}[/tex]
[tex]\cos A = 0.832[/tex]
Angle B
[tex]AC^{2} = AB^{2} + BC^{2} - 2\cdot AB\cdot BC\cdot \cos B[/tex] (2)
[tex]\cos B = \frac{AC^{2}-AB^{2}-BC^{2}}{-2\cdot AB\cdot BC}[/tex]
[tex]\cos B = \frac{26-18-8}{-2\cdot (3\sqrt{2})\cdot (2\sqrt{2})}[/tex]
[tex]\cos B = 0[/tex]
Angle C
[tex]AB^{2} = AC^{2}+BC^{2}-2\cdot AC\cdot BC\cdot \cos C[/tex] (3)
[tex]\cos C = \frac{AB^{2}-AC^{2}-BC^{2}}{-2\cdot AC\cdot BC}[/tex]
[tex]\cos C = \frac{18 -26-8}{-2\cdot (\sqrt{26})\cdot (2\sqrt{2})}[/tex]
[tex]\cos C = 0.555[/tex]
Since [tex]AB \neq BC \neq AC[/tex] and [tex]\cos B = 0[/tex], we conclude that given triangle is a right-angled and scalene.
CHRIS
For the field trip this year, use the given information to determine the total
cost for each student and for all 30 students. Transportation costs have
already been paid.
For every 5 students, it would cost:
• $36.25 for admission to the museum, and
• $31.50 for lunch.
What is the total cost, in dollars, for admission and lunch for each student?
What is the total cost, in dollars, for admission and lunch for all 30 students?
1 Student: $
30 Students: $
Answer:
30 students: $346.5
1 student: $11.55
Step-by-step explanation:
It would cost a total of $57.75 every 5 student so just multiply by 6 to get your amount for 30 students. Then divide by 30 to get the amount per student.
Janice needs 3 gallons of lemonade for a party. She has 4 quarts, 6 pints, and 4 cups of lemonade already made. How many more cups does she need.
By what percent will the number changed if": it was doubled
Answer:
what number
Step-by-step explanation:
it took samatha 325 minutes to cook an 18 lb turkey.How many minutes per pound did it take to cook the turkey ?
Answer:
Below.
Step-by-step explanation:
325/18
= 18.055... minutes
= 18 minutes to nearest minute.
PLSSS HELP ILL GIVE BRAINLIEST TO THE RIGHT ANSWER
Answer:
56
Step-by-step explanation:
The simplest way to do this is to divide 3 by 21 to get 7. This means that it takes $7 to buy one T-shirt. If you multiple 8 X 7, you get 56. This mean that the correct answer is A. $56.00
Hope it helped and have a great day :)
find the measure of angle R
Answer:
R=(180-100)/2=40.
Step-by-step explanation:
Answer. Answer: (1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40.
10 POINTS!!!!!!! write an equation for a line that goes through the point (-3,-4) and has a slope on -2
Thats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya Lungs
make q the subject of 4p=5q-2
Answer:
5q = 4p + 2
Step-by-step explanation:
4p = 5q - 2
4p + 2 = 5q - 2 + 2
5q = 4p + 2
Can someone help me with 17 20 and especially 21
Only reply if your seriously trying to help me it would be really appreciate
What is the slope of AB?
Can anyone help me ??
Answer:
1/2
Step-by-step explanation:
Point A is (2, 3)
Point B is (6, 5)
To get the slope of a line, first select any two points on that line.
Then, take the difference of the y values, and divide it by the difference of the x values. This is also known as the change in y over the change in x, or rise over run.
[tex]\frac{3-5}{2-6} =\frac{-2}{-4} =\frac{1}{2}[/tex]
1/2 is the slope.
On Claudia's birthday, her parents open a savings account and deposit SS. They also deposit $50 each
year after that on her birthday. The account eams interest at an annual rate of 7% compounded annually
Caudia will make no withdrawals from the account for at least 15 years Complete the table to find how
much Caudla will have in her account at the end of the fifth year. Then compare this amount to the
$290.10 that would be in her account if she had received 5% interest.
What is the volume of a rectangular prism with the length of 4.5 ft, the width of 3.5 ft, and the height of 5.5 ft?
Answer:
The volume would be 86.63 feet squared
Hope this helps!
Mark me brainliest if I'm right :)
Which equation represents the line with slope – 2 that
passes through the point (-4, -5)?
Answer:
D. y+5 = -2(x+4)
Step-by-step explanation:
[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]
The equation above is point-slope form where x1 and y1 both are the point that the graph passes through ane m is slope as usual.
We are given the point (-4,-5) and slope of -2. We substitute these values in.
[tex] \large{y - ( - 5) = - 2(x - ( - 4))} \\ \large{y + 5 = - 2(x + 4)}[/tex]
Seventy-five percent, or 15, of the students in
Emily's homeroom class are going on a field trip. Two thirds, or 12, of the
students in Santiago's homeroom class are going on the field trip. Which
class has more students? Justify your answer.
Factor the expression completely.
15x2-5x - 10
15x2-5x - 10 =
Answer:
x=8
Step-by-step explanation:
30-5x-10
-5x+30-10
-5x+40
-5x= -40
divide both sides by -5
-5x/-5= -40/-5
x=8
find the value of x
50 points for all 5 questions.
Step-by-step explanation:
we have
5x+4=2x+9
5x-2x=9+4
3x=13
x=13/3
Answer:
x = 13/3
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ 2x + 9 = 5x - 4
Then the value of x will be,
→ 2x + 9 = 5x - 4
→ 2x - 5x = -4 - 9
→ -3x = -13
→ x = (-13)/(-3)
→ [ x = 13/3 ]
Hence, the value of x is 13/3.
What is the total surface area of a dog food can which has a diameter of 5 inches and a height of 7
inches?
Answer:
35.................
what is this equation factored
49x²-1
Find the value of y for the given value of x. y=x/3+5;x=6
Answer: Y= 7, X= 6
Step-by-step explanation:
2x – 5x + 16 = –3(x – 6)
Answer:
0=2
There are no solutions
Step-by-step explanation:
Answer:
2x – 5x + 16 = – 3(x – 6)
-3x + 16 = - 3x + 18
-3x + 3x + 16 = 18
16 = 18
Thus, This is a False Equation
-TheUnknownScientist
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
turtles are vulnerable. so A is your correct answer
Step-by-step explanation:
3x + y = -4
3x - 4y = 6
Answer:
(-1, -2) or x=-1 y=-2
Step-by-step explanation:
3x+y=-4 (1)
3x-4y=6 (2)
i used the first equation to subtract the second this cancels out the x
and you are left with:
5y=-10
y=-2
plug this back in:
2x+(-2)=-4
2x-2=-4
add 2 to both sides:
2x=-2
x=-1
I NEED HELP BADLY PLEASE
Answer:
m(DE) = 90°
Step-by-step explanation:
Since both circles are equal, therefore, their radius would be equal too.
m<S = 180 - right angle (angles on a straight line)
m<S = 180 - 90 = 90°
m<R = m<S (congruent triangles)
m<R = 90°
m<R = m(DE) (central angle = intercepted arc based on the central angle theorem)
Substitute
90° = m(DE)
m(DE) = 90°
Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y=-x+1
y=-2x+ 5
The black trapezoid is a dilation of the green trapezoid. What is the scale factor of the dilation?
A) 1/5
B) 1/3
C) 3
D) 5
============================================================
Explanation:
We're told that "The black trapezoid is a dilation of the green trapezoid". This means the black trapezoid is the image, while the green one is the preimage. In other words, the green is the "before" and the black is the "after". The mapping is [tex]\text{green} \to \text{black}[/tex] because of the ordering [tex]\text{preimage} \to \text{image}[/tex]
Since the green figure (preimage) is larger than the black figure (image), the scale factor must be some value k such that 0 < k < 1. That narrows the answer choices between A and B.
Focus on the green trapezoid. The bottom left corner is at (-10,0). The bottom right corner is at (5,0). The distance between these two points is 15 units.
Using the same idea, the distance along the bottom edge of the black trapezoid is 3 units. We can count out the spaces along the bottom, or we can note the two bottom corners are at (-2,0) and (1,0).
------------------------------
So far we found:
The bottom edge of the green trapezoid is 15 unitsThe bottom edge of the black trapezoid is 3 unitsThese two edges correspond to one another. We divide the values to get the scale factor. We divide the image length over its corresponding preimage length.
scale factor = (image length)/(preimage length)
scale factor = 3/15
scale factor = 1/5
What is the length of side AB of the triangle?
3
5
Square root of 6
Square root of 13
Answer:
√13
Step-by-step explanation:
Distance formula
√(4-2)²+(5-2)² = 2²+3² = √4+9 = √13
You are a life saver if you help me figure out this problem step by step. I swear my math teacher is trying to make me fail:(
A cylinder has a height of 7 yards and a radius of 14 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The answer to the nearest hundredth, the volume of the cylinder is approximately 4309.28 cubic yards.
To calculate the volume of a cylinder, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Radius (r) = 14 yards
Height (h) = 7 yards
Approximation of π = 3.14
Substituting these values into the formula, we have:
[tex]V = 3.14 \times(14^{2} )\times 7[/tex]
First, let's calculate the value of (14²):
[tex]14^{2} = 14 \times 14 = 196[/tex]
Now, substitute the values back into the formula:
[tex]V = 3.14 \times 196 \times 7[/tex]
Next, perform the calculations:
[tex]V = 3.14 \times 1372[/tex]
V ≈ 4309.28
For similar question on cylinder.
https://brainly.com/question/30858645
#SPJ11
A bowl has 2 blue candies and 3 red candies inside it.
The tree diagram shows that the first event tells us the probability of choosing each blue and red candy.
The second event describes the probability of choosing an additional blue and a red candy.
Find the value of x and y
Answer:
[tex]x = \frac{1}{4} [/tex]
[tex]y = \frac{2}{4} [/tex]
. In Paige's class, 13 of the 20 students were born in Texas. Based in the
information, if there are
8010 students at the school, how many students could
be expected to have been
born in Texas?
A.600 students
B.480 students
C.520 students
D.560 students
Answer:
Road shimmer
Wiggling the vision
Heat heat waves
I'm swimming in a mirror
Road shimmer
Wiggling the vision
Heat heat waves
I'm swimming in a
Sometimes, all I think about is you
Late nights in the middle of June
Heat waves been faking me out
Can't make you happier now
Sometimes, all I think about is you
Late nights in the middle of June
Heat waves been faking me out
Can't make you happier now
Usually I put
Something on TV
So we never think
About you and me
But today I see
Our reflections
Clearly in Hollywood
Laying on the screen
You just need a better life than this
You need something I can never give
Fake water all across the road
It's gone now the night has come but
Sometimes, all I think about is you
Late nights in the middle of June
Heat waves been faking me out…
Answer:490
Step-by-step explanation: