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.
Simplify the expression:
6(5 + x) - 2x
Answer: 30+4x
Step-by-step explanation: Expanding the expression you would get 30+6x-2x and then you subtract the 6x and 2x to get 4x
Answer:
30+4x.
Step-by-step explanation:
yehdbebdbejeiiwiwuebdbsjjjwiwjeurnfnd
The length of segment GI is 8. True or false?
Answer: false
Step-by-step explanation: that’s what my teacher told me sorry if it’s wrong
Answer:
It is false
Definetely false
It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10 and out of calibration if μ ≠ 10. A test is made of the hypotheses H0 : μ = 10 versus H1 : μ ≠ 10. Which of the three conclusions is best if H0 is rejected?
Complete question :
It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let µ be the population mean reading on the scale, so that the scale is in calibration if µ = 10. A test is made of the hypotheses H0:µ = 10 versus H1:µ ≠ 10. Consider three possible conclusions: (i) The scale is in calibration, (ii) The scale is out of calibration, (iii) The scale might be in calibration.
Which of the three conclusions is best ifH0 is rejected?
Answer:
The scale is out of calibration
Step-by-step explanation:
The null hypothesis ; H0
H0 : μ = 10 ; if this hold true, then the scale is in calibration
Alternative hypothesis ; H1
H1 : μ ≠ 10 ; if this holds true, then the scale is out of calibration
If the Null hypothesis, H0 is rejected, it means that, there is significant evidence to support the alternative hypothesis ; that the scale is out of calibration.
Hence, the best conclusion is that, the scale is out of calibration.
Verify a - (- b) = a + b for the following values of a and b.
() a = 23, b = 14
(ii) a = 128, b = 105
23 - (-14) = 23 + 14 = 37
128 - (-105) = 128 + 105 = 233
A contractor is building a fence around a square garden that has a side length of 3 inches in a scale drawing. The scale factor of the drawing is 1 1/2 inches : 4 feet. If one link of fence measures 2 2/3 feet, shade the correct number of links needed to build a fence around the entire garden
The number of fences needed to build around the entire garden is 12.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Side of the square garden = 3 inches
Scale factor.
1(1/2) inches = 4 feet
3/2 inches = 4 feet
3 inches = 8 feet
Now,
Length of one fence.
= 2(2/3) feet
= 8/3 feet
Now,
The perimeter of the square.
= 4 side
= 4 x 3 inches
= 12 inches
= 4 x 8 feet
= 32 feet
Now,
The number of fences needed to build the fence around the garden.
= 32 ÷ 8/3
= 32 x 3/8
= 12 fences
Thus,
12 fences are needed to cover the entire garden.
Learn more about squares here:
https://brainly.com/question/22964077
#SPJ1
(1 point) Solve the following inequality, giving your answer in interval notation.
1 - x > 2
Answer:
-1
Step-by-step explanation:
1-x>2
-x>2-1
-x>1
-x/-1>1/-1
x<-1
Answer:
[tex]x < - 1[/tex]
Step-by-step explanation:
first step
try to leave x's in your left and number in your right
-x > 2-1
-x>1
step 2
by moving the sign minus to right it will become plus
and the inequality sign will change also
so x<-1
the region will ( - infinity to -1 )
[tex]( - \infty - 1)[/tex]
Hellpppppppppppppppppppppppppppppppppppppppp
Answer:
._. -_- -.- .-. --__--
Step-by-step explanation:
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,200 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,200 and $14,500.
a. Suppose you bid $12,000. What is the probability that your bid will be accepted?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
c. What amount should you bid to maximize the probability that you get the property?
d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?
Answer:
0.4185;
0.8835;
$14500;
No
Step-by-step explanation:
Given that :
a = 10200
b = 14500
f(y) = 1 /(b - a) = 1/(14500 - 10200) = 1/4300 = 0.0002325
A.)
P(x <12000) = ∫fydy at(12000 ; 10200) = ∫0.0002325dy at(12000 ; 10200)
P(x < 12000) = 0.0002325(12000) - 0.0002325(10200) = 0.4185
B.)
P(x <14000) = ∫fydy at(14000 ; 10200) = ∫0.0002325dy at(14000 ; 10200)
P(x < 14000) = 0.0002325(14000) - 0.0002325(10200) = 0.8835
(c.) 14500 ; because competitor's bid is at most 14500
D.) No ; Because by bidding $14500 ; getting the property is certain ; once the property is gotten, then it could be resold for $16000, to make a profit of $1500 ; by bidding less, winning the bid becomes uncertain which may means the profit might be lost in the long run.
.......,,,,,,;,,.,.........
Answer:
lol dababy ur my idol
Step-by-step explanation:
84b /32b
3b
Answer:
3b^2
Step-by-step explanation:
12b^7 / 4b^5
=12b^7/ 4b^5
=12b^2/4
=3b^2
ery Test
1
Select the correct answer.
Who is a consumer?
OA.
a person who buys items in a store
OB.
a person who owns a store
O C.
a person who works at a store
Which of the following statements about opposites is true? Choose all correct answers.
A. The opposite of 5 is −5.
B. −(−8)=−8
C. The opposite of 0 is 0.
D. −(−2)=2
Answer:
A
Step-by-step explanation:
if d is 55 degrees then what is F and E degrees. Explain how you know
Answer:
F=55
E=70
Step-by-step explanation:
The total degree of a triangle is 180.
So we have 180-55*2
E=180-110
E=70
what is importance of banks to ecomics
Answer:
They do transactions from such a large distance
Step-by-step explanation:
Banks make it far easier for a complex economy to carry out the extraordinary range of transactions that occur in goods, labor, and financial capital markets. Banks are a critical intermediary in what is called the payment system, which helps an economy exchange goods and services for money or other financial assets.
Dan has save 3200 cents from selling lemonade how many dollars does DAn have
Answer:
$32
Step-by-step explanation:
a dollar is 100 cents. so simply sake away the two zeros at the end.
Answer:
$32
Step-by-step explanation:
the answer is thirty two dollars because a dollar is 100 cents and 3200 ÷ 100 =32
Solve the system by Graphing
Step-by-step explanation:
What is the area of the polygon below?
A. 120 square units
9
10
B. 174 square units
16
C. 66 square units
12
D. 84 square units
Answer:
D
Step-by-step explanation:
12-9 = 3 square unit
10 x 3 = 30 square unit
9×6 = 54 square unit
54+30 = 84 square units
and thats the answer
The area of the polygon is 84 square units, option D is correct.
What is Area of Rectangle?The area of Rectangle is length times of width.
The given polygon has two rectangles.
Area of rectangle with length 9 and width is 6 units
Area of rectangle 1 =9×6
=54 square inches
Now Area of rectangle with length 10 and width is 3 units
Area of rectangle 2 =10×3
=30 square inches
Total area = 54+30
=84 square units
Hence, the area of the polygon is 84 square units, option D is correct.
To learn more on Area click:
https://brainly.com/question/20693059
#SPJ5
Please help! Find the perimeter of Trapezoid ABCD. (round your answer to the nearest tenth.)
Answer + explanation please!
Answer:
19.8 units
Step-by-step explanation:
BC = 5
AD = 8
CD = 1²+3²=c²
1+9=c²
√10=c
c=3.1627766
AB = 2²+3²=c²
4+9=c²
√13=c
c=3.6
5+8+3.6+3.16=19.76
1.4
2
Lawrence wants to drive from Durban to Johannesburg 550 km. if he travels at
an average speed of 100 km/hr, how long does he tale to get there?
If he leaves at 08:42 what time will he arrive at his destination
1.5
2
Answer:
5 hr 30 minutes
2:12 pm
Step-by-step explanation:
s= 550km
v = 100km/hr
t = ?
SPEED = DISTANCE/ TIME TAKEN
or, v = s/t
or, 100km/hr = 550km/ t
or, t = 550/100
t = 5.5
t = 5 hrs 30 minutes
8:42
+5:30
13 :72
which is 14 :12 = 2 :12
Can you guys help me real quick please
Answer: I believe the answer is 23k.
Step-by-step explanation:
Use the figure below to complete the sentence.
B
A
E
39°
o
BGC and ZFGE are (select)
angles, so mZFGE =
Answer:
<BGC and <FGE are vertical angles
<BGC=90°-42°=48°
So m<FGE=48°
Hope it helps...
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Step-by-step explanation:
You have to click the number of Xs for each kilometer travelled. For example, there are 2 "3 km" answers, so under the 3 column, you click 2 Xs.
Kacie has a bag of
pretzels. She eats 1/3 of
the bag and gives 1/2 of
the bag to her brother.
How much of the bag
does she have left?
Answer: .
Step-by-step explanation:
Please please please help I will mark you brainiest
Answer: b then!
Step-by-step explanation:
James invests $5400 in two different accounts. The first account paid 14 %, the second account paid 6 % in interest. At the end of the first year he had earned $580 in interest. How much was in each account?
Given:
Total invested amount = $5400
Rate of interest for first account = 14%
Rate of interest for second account = 6%
Total interest after one year = $580
To find:
The amount invested in each account.
Solution:
Let the amount invested in the first account be $x, then the amount invested in the second account is $(5400-x).
Total interest = 14% of $x + 6% of $(5400-x).
[tex]580=\dfrac{14}{100}x+\dfrac{6}{100}(5400-x)[/tex]
Multiply both sides by 100.
[tex]58000=14x+6(5400-x)[/tex]
[tex]58000=14x+32400-6x[/tex]
[tex]58000-32400=8x[/tex]
[tex]25600=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{25600}{8}=x[/tex]
[tex]3200=x[/tex]
Now,
[tex]5400-x=5400-3200[/tex]
[tex]5400-x=2200[/tex]
Therefore, the amount invested in first account is $3200 and the amount invested in the second account is $2200.
Add 1/4+9/14+6/7. Simplify the answer and write it as a mixed number.
Answer:
In words - thirty-nine ninths minus twenty-five ninths = fourteen ninths.
1. Determine the three-dimensional figure that will be created using the following nets.
Answer:
The figure is a triangular prism
Step-by-step explanation:
it's bc the bases are triangles
A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. The given net will form a triangular prism.
What is a triangular prism?A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. A right triangular prism has rectangular sides and is oblique otherwise.
A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. The given net will form a triangular prism.
Learn more about Triangular Prism:
https://brainly.com/question/24046619
#SPJ2
Aidans hourly salary is $11. If Aidan normally works a 40 hour week , then how much is normally earned in a week?
Answer:
$440
Step-by-step explanation:
40x11=440
hope it helped
plz mark me as brainliest.
HELP PLEASE!!! I need to name each angle
Answer:
XWZ and ZWX are the only ways to label this angle
Step-by-step explanation:
A small box measures 7 in. by 10 in. by
3/4 in. high. Find the volume of the box.
Answer:
Volume = 52.5
Step-by-step explanation:
volume of a rectangular 3d shape can be calculated by length*width*height. In this case:
7*10*0.75 = 52.5
Brainliest for correct answer
Answer:
4
Step-by-step explanation:
The pre-image is the starting coordinates and it then gets larger. when you multiply four by 3 you get 12 and when you multiply four by -4 you get 16. So the pre-image dilated by 4.