Answer:
The possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.
Step-by-step explanation:
From statement we know that [tex]AB = 2\cdot BC[/tex]. By Analytical Geometry, we use the equation of a line segment, which is an application of the Pythagorean Theorem:
[tex]AB = 2\cdot BC[/tex]
[tex]\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}} = 2\cdot \sqrt{(x_{C}-x_{B})^{2}+(y_{C}-y_{B})^{2}}[/tex] (1)
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex], [tex]x_{C}[/tex] - x-Coordinates of points A, B and C.
[tex]y_{A}, y_{B}, y_{C}[/tex] - y-Coordinates of points A, B and C.
[tex](x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2} = 4\cdot (x_{C}-x_{B})^{2}+4\cdot (y_{C}-y_{B})^{2}[/tex]
Then, we expand and simplify the expression above:
[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} +x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot (x_{C}^{2}-2\cdot x_{C}\cdot x_{B}+x_{B}^{2})+4\cdot (y_{C}^{2}-2\cdot y_{C}\cdot y_{B}+y_{B}^{2})[/tex]
[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} + x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot x_{A}^{2}-8\cdot x_{C}\cdot x_{B}+4\cdot x_{B}^{2}+4\cdot y_{C}^{2}-8\cdot y_{C}\cdot y_{B}+4\cdot y_{B}^{2}[/tex]
If we know that [tex]x_{A} = 5[/tex], [tex]y_{A} = 6[/tex], [tex]x_{B} = 1[/tex], [tex]y_{B} = b[/tex], [tex]x_{C} = 1[/tex] and [tex]y_{C} = -3[/tex], then we have the following expression:
[tex]1 -10 +25 +b^{2} -12\cdot b+36 = 100 -8 +4 +36+24\cdot b +4\cdot b^{2}[/tex]
[tex]b^{2}-12\cdot b +52 = 4\cdot b^{2}+24\cdot b +132[/tex]
[tex]3\cdot b^{2}+36\cdot b +80 = 0[/tex]
This is a second order polynomial, which means the existence of two possible real solutions. By Quadratic Formula, we have the following y-coordinates for point B:
[tex]b_{1} \approx -2.944[/tex], [tex]b_{2} \approx -9.055[/tex]
In consequence, the possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.
A coffee shop recently sold 10 drinks, including 4 mochas. What is the experimental
probability that the next drink sold will be a mocha?
Simplify your answer and write it as a fraction or whole number.
P(mocha) =
Submit
Work it out
Not feeling ready yet? These can help:
Answer:
2/5
Step-by-step explanation:
IXl answer
The experimental probability that the next drink sold will be a mocha is 2/5.
Number of mochas =4
Total drinks =10
What is probability?Probability is the quantification of possibilities.
P(event) = Favorable outcomes/ Total outcomes
P(mocha) = 4/10
P(mocha) =2/5 =0.4 or 40%
Thus, the experimental probability that the next drink sold will be a mocha is 2/5.
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example of a 400 word essay which choosing a college
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Answer: 4/18
Step-by-step explanation:
The ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Let's suppose the x out of 18 can be written as 0.22222222
x/18 = 0.22222222
x = 3.999999 ≈ 4
It means 4/18 can be written as 0.22222222
Thus, the ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
Learn more about the ratio here:
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15 FT
-
12 FT
16 FT
9 FT
What is the Volume:
What is the Total Surface Area:
Answer:
28 ft
Step-by-step explanation:
i used my fingers
Which figures can have all of the properties shown below?
2 pairs of parallel sides
Sides that are perpendicular
Opposite sides that are equal
square, pentagon, rectangle
trapezoid, triangle, square
quadrilateral, square, rectangle
rectangle, hexagon, square
Answer:
Quadrilateral, square, rectangle
Step-by-step explanation:
An object have parallel sides if the sides have the same distance apart and they never meet.
Quadrilaterals usually have parallel sides
Polygons including triangles and pentagons do not have parallel sides
the sides of a quadrilateral are also perpendicular. the sides form a 90 degree angle with each other
Opposite sides of a quadrilateral are usually equal. For example, the opposite lengths of a rectangle are equal. the four sides of a square are equal
Help pls this is my first question on here and I need help with this pls. I will give you the brainliest and a thanks!! :)) Can you do 1 and 4 thanks!! :)))
Answer:
1. 18.85in
4. 25.13m
Step-by-step explanation:
I got you
So to find the circumference of any circle we use the equation 2pi(r)
2(3.1415)(3)= 18.85in for the first one because radius is half of the diameter which is 6 so half of 6 is 3
For 4. 4m is actually the radius so just plug that into the equation 2pi(4)=25.13m
what is the area of the trapozoid?
Answer:
8units²
Step-by-step explanation:
area of trapezoid=½(a+b)*h
a=2
b=6
h=2
area of trapezoid=½(2+6)*2
area of trapezoid=½(8)*2
area of trapezoid=4*2
=8units²
Write a recursive formula and an explicit formula for the following arithmetic sequence.
5, 3, 1, -1, ...
A recursive formula is a1 = , an = |
(Simplify your answers. Use integers or decimals for any numbers in the expressions.)
An explicit formula is an =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answer:
Step-by-step explanation:
Write the equation of the line that passes through (7,-4) and (-1,-2) in slope-intercept form.
Answer:
y = -1/4x - 5/2
Step-by-step explanation:
-2- -4 /-1-7 = 2/-8 = -1/4
y+2 = -1/4(x+2)
y+2 = -1/4x - 1/2
y = -1/4x -5/2
1) Solve 2 + 7x + 12 = 0 using factoring and the zero product property.
a) Factor2+7x+12
b) Use the zero product property to solve for x
b) Use the zero product property to solve for x
Answer:
7x+14=0, 7x=-14, x= -2
Step-by-step explanation:
add like terms, then get x on one side, number on the other, then divide both sides by 7
What is the value of this expression when a= -3 and b=5? a + b^2*
Answer:
22
Step-by-step explanation:
a+b^2
= -3+(5^2)
= -3+25
=22
Tristian has 35 rock songs, 50 dance songs and 15 rap songs on his play list. If his music player randomly selects a song, what is the probability that it is a dance song?
Answer:
1/2
Step-by-step explanation:
35+50+15 = 100
probability of the dance song = 50/100 = 1/2
Answer:50%
Step-by-step explanation:
35+15+50=100
50 divided by 100 is 0.5 or you can do it as a fraction and get 50/100
Identity the coterminal angle between 360° and 360° for the angle - 120°
No
help pls ! need it asap
Answer:
m∠X = 110°
m∠V = 60°
Step-by-step explanation:
1.) Angle Y and W are equal from the markers, which means the angles are equal
35*2 = 70
180 - 70 = 110 ( You know it has to be greater than 90 because it's larger than a corner angle)
2.) This is another isosceles (equal angle and sides)
Some times all sides aren't equal on isosceles but you can see these are
180/3 = 60°
Which of these graphs represents a function ?
Answer:
Graph C
Step-by-step explanation:
need help please.........
Answer:
Step-by-step explanation:
C
Answer:
A.
Step-by-step explanation:
k=am+3mx=m(a+3x)
⇒ [tex]m=\frac{k}{a+3x}[/tex]
2^3=4^p find the value of p
Answer:
Exact form: p= 3/2
Decimal form: p= 1.5
Mixed Number: p=1 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Find the measure of <4.
{
44
158°
{
44 = [?]
Answer:
<4 = 22
Step-by-step explanation:
<4 = x
x + 158 = 180
x = 22
Same side interior angles are supplementary
<4+158=180<4=180-158<4=22°Tell whether b=6 is a solution of 8b=48
Answer:
b= 6 for sure
Step-by-step explanation:
Anyone else been saved by brainly?
Answer:
Yes, many times actually. I've aced tests because of brainly
Step-by-step explanation:
help me plssssssssssss☺☺☺☺
Answer:
1. supplementary angles
2. vertically opposite angles
3. corresponding angles
4. alternate interior angles
5. alternate exterior angles
6. corresponding angles
7. corresponding angles
8. alternate exterior angles
hope this helps
good day mate
what makes 1/3 x > 12 true
Answer:
I dont know I am sorry I really had to ask a question and i don't have enough points so sorry you can report me if you want but I really need some
HELP!! TY IF YOU ANSWER
Find the volume of the sphere. Round to the nearest tenth.
The volume is about _____ cubic meters.
What's the exact value of tan 15°?
O A) 2 + √3
B) 1
OC2
C) 2 - V3
OD) 1 + v3
Please Help!!!!
Answer:
C
Step-by-step explanation:
Split
15
into two angles where the values of the six trigonometric functions are known.
The result can be shown in multiple forms.
Exact Form:
2−√3
The exact value of tan 15° is,
⇒ tan 15° = - (2 - √3)
What is mean by Function?
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
To find the exact value of tan 15°.
Now, We can formulate;
tan 15° = tan (45 - 30)°
= tan 45° - tan30° / (1 + tan45° tan30°)
= (1 - √3) / (1 + √3)
= (1 - √3) (1 - √3) / (1 + √3) (1 - √3)
= (1 + 3 - 2√3) / (1² - √3²)
= (4 - 2√3) / (1 - 3)
= 2 (2 - √3) / - 2
= - (2 - √3)
Thus, The exact value of tan 15° is,
⇒ tan 15° = - (2 - √3)
Learn more about the function visit:
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Will you explain it
Answer:
there is literally nothing in the picture
Answer:
it's a black screen sized 200x200
A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink
marbles.
What is P(not yellow)?
A 1/5 B 2/5 C 4/5
Answer: c 4/5
Step-by-step explanation: out of 5 only four are chosen leaving us with an answer of 4/5 :D hope it helped
Pls help with this problem. This is due today!
Answer:
2.8 > 2.8< i think
Step-by-step explanation:
Help on this one please
Answer:
74.2
Step-by-step explanation:
First think of a whole circle. The area of a circle is pi*r^2., which is 81 pi. Then the fraction of the circle is 105/360. Times this by 81 pi and you get about 74.2 and that is the answer.
By the way, can you follow me? Thanks!
please help!! Area of Trapezoids and Triangles
Answer: Area of the shape is 168 ft.
Step-by-step explanation: Split the shape into 2 shapes: A rectangle and a triangle.
Area of the rectangle shape is 144 and the area of the triangle is 24. Add them and you get 168.
