Answers
BD = 2x-4
But it's also BE - CE + CD
BE is 3x-1
CE is 2x-3
CD is 2
so
BD = 3x-1 -(2x-3) +2
simplified
BD = 1x +4
since BD = BD (obviously), we can also say that the righthand sides of the two equation must be equal
2x -4 = 1x +4
let's solve for x and that put it into either of the 2 equations.
2x -4 = 1x +4
subtract 1x on both sides
x -4 = 4
add 4 on both sides
x = 8
substitute x for its value in 2x -4 = 1x +4
(this way we double check BD in two expressions at once. the equation should come out true, meaning same value for BD in each expression. both sides should be equal).
2*8 -4 = 1*8 +4
12 = 12
seems true
BD is safely 12
Related Questions
The table of values represents an exponential function f(x). What is the average rate of change over the interval −2≤x≤2? Enter your answer, as a decimal rounded to the nearest hundredth, in the box.
−3 64
−2 16
−1 4
0 1
1 1/4
2 1/16
3 1/64
(Worth 60pts)
Answers
Answer:
-1456
-864
4
-11
-5,25
-1,93
Step-by-step explanation:
Answer:
-3.98Step-by-step explanation:
Rate of change is:
[f(2) - f(-2)]/[2 - (-2)] = (1/16 - 16)/4 = -255/16*1/4 = -255/64 = -3.98The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice.
Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant
owner bought the rice.
Complete the table. Type the answers in the boxes below.
WEEKS
KILOGRAMS OF RICE LEFT
6
12
Answers
Answer:
6 weeks = 48 kg
12 weeks = 21 kg
Step-by-step explanation:
6 weeks:
4.5 x 6 = 27 kg
75 - 27 = 48 kg
12 weeks:
4.5 x 12 = 54 kg
75 - 54 = 21 kg
Hope this helps!
Find the shaded sector and the length of the arc. Round to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
I'll show you how to do the first one; the other are exactly the same, so pay attention.
The formula for arc length is
[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:
[tex]AL=\frac{40}{360}*2(3.1415)(3)[/tex]. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):
[tex]AL=\frac{1}{9}*2(3.1415)(3)[/tex] which makes
AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:
[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:
[tex]A_s=\frac{1}{9}*(3.1415)(3)^2[/tex] which simplifies a bit to
[tex]A_s=\frac{1}{9}*(3.1415)(9)[/tex]. As you can see, the 9's cancel each other out, leaving you with
[tex]A_s=3.14[/tex] units²
Answer:
Step-by-step explanation:
[tex]Arc \ Length = 2 \pi r \frac{ \theta}{360}[/tex]
[tex]Sector \ Area = \pi r^2 \frac{ \theta }{360}[/tex]
[tex]1) Arc \ Length = 2 \pi \times 3 \times \frac{40}{360} = 2\pi \times 3 \times \frac{1}{9} = \frac{2}{3} \pi = 2.09[/tex]
[tex]Sector \ Area = \pi \times 9 \times \frac{40}{360} = 9\pi \times \frac{1}{9} = \pi = 3.14[/tex]
[tex]2) Arc \ Length = 2 \pi \times 5 \times \frac{88}{360}= 7.68[/tex]
[tex]Sector \ Area = \pi \times 25 \times \frac{88}{360} = 19.2[/tex]
[tex]3) Arc \ Length = 2 \pi \times 6 \times \frac{260}{360} = 27.22[/tex]
[tex]Sector \ Area = \pi \times 36 \times \frac{260}{360} = 81.68[/tex]
1. Two identical cubes each of total surface area of 6 cm2 are joined end to end. Which of the following is the total surface area of the cuboid so formed?
Answers
Answer:
10 cm³
Step-by-step explanation:
The total surface area of a cube = 6 cm²
The formula for the surface area of the cube is :
A = 6a², a is the side of the cube
6 = 6a²
a = 1 cm
Now, the length of the formed cuboid = 2 cm
Breadth = 1 cm
Height = 1 cm
Required volume of the formed cubiod is :
V = 2(lb+bh+hl)
Put all the values,
V = 2(2(1)+1(1)+2(1))
V = 10 cm³
So, the required volume of the formed cuboid is equal to 10 cm³
what is the answer? becuase i am just confused
Answers
Answer:
Step-by-step explanation:
radius of circle is 12
also there is 2 right angles in the triangle if you wanted to solve this problem yourself
but here's the answer:
arc angle of the triangle inside the sircle is double the angle closest to x.
(the pointy area of the triangle is half the angle length of the arc)
i can add more though:
a ball is shot out of a homemade air cannon. It flies through the air such that its height, as a function of time, is given by: h= -16t^2 + 64t + 10. where h is the height of the ball in feet and t is the time since it was fired in seconds. Max estimates that it takes 4 seconds for the ball to hit the ground and Cole estimates it takes 5 second. Algebraically determine who is closer and support your answer.
Answers
Answer:
Max
Step-by-step explanation:
the function given that h = -16t³+64t+10
the general function Equation:
h = at²+bt+c
=> t at the highest point is defined by t = -b/2a
= -64/2(-16) = -64/-32 = 2 second
the total times that the ball hits the ground
= 2× 2 seconds = 4 seconds.
so, Max is right
Answer:
Solution given:
Let h=0=when the ball hit the ground,the height=0.
h= -16t^2 + 64t + 10.
0=16t²-64t-10
8t²-32t-5=0
∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]
taking positive
t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]
t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]
So
t=4.15seconds closer to 4seconds.So
Max is closer.
If both spinners are spun simultaneously, what is the probability that either spinner will land on orange?
5/64
5/8
3/8
4/64
Answers
Answer:
I am not completly sure, cause the answer might be a bit more complex but, for the spinner on the left 4/8 and the right 1/8 chances
Step-by-step explanation:
Answer: 5/8 is the correct answer.
Step-by-step explanation: The other dude is completely wrong.
solve the following the unknown -3(×+1)-2=4×-5(×-3)
Answers
Answer:
x = - 10
Step-by-step explanation:
Expand the equation first then simplify it
- - - - - - - - - - - - - - - - - - - - - - - - -
Answers
Answer:
x = ±3 sqrt(2)
Step-by-step explanation:
x^2 = 18
Take the square root of each side
sqrt(x^2) = sqrt(18)
x = ± sqrt(18)
x =±sqrt(9*2)
x = ±sqrt(9) sqrt(2)
x = ±3 sqrt(2)
In the diagram, the measure of angle 3 is 105°.
A transversal intersects 2 lines to form 8 angles. Clockwise from the top, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
Which angle must also measure 105°?
Angle1
Angle4
Angle6
Angle8
Answers
Answer:
angle 8
Step-by-step explanation:
not sure but if correct 1 heart pls and comment
Answer: A is Correct
Step-by-step explanation:
angle 1 is opposite of angle 3 which means its also 105°
Olivia went to a dance party. She paid $12 as an entry fee. Once inside the dance party, she paid $2 per snack. She started the night with $30 and spent all her money.
write an equation that represents this situation?
Pls help
Answers
Answer:
30-12=18
18-18=0
Step-by-step explanation:
2x + 12 = 30
X represents the snacks, 2 represents the $2 per snack, 12 represents the $12 entry fee, and 30 represents the $30 Olivia had.
Adam is refinishing his basement. 30 ft by 50 ft are the dimensions of Adam's rectangular basement. How much tile would he need to cover the floor? If the height of the basement is 6 ft, how much wall area is there to paint?
Answers
Answer:
Area of four walls is 3960 square feet.
Step-by-step explanation:
length, L = 30 ft
Width, W = 50 ft
height, H = 6 ft
The area of walls is
= 2 (L W + W H + H L)
= 2 (30 x 50 + 50 x 6 + 6 x 30)
= 2 (1500 + 300 + 180)
= 3960 square feet
Answer/Step-by-step explanation:
How much tile would he need to cover the floor?
Answer: 1500 Ft^2
If the height of the basement is 6 ft, how much wall area is there to paint?
Answer: 960 Ft^2
How many three digit numbers greater than 540 can be formed using the digits
0,2,4,5,6,8 ?
Answers
Answer:
At least 12
Step-by-step explanation:
I created 12 different number patterns greater than 540. I hope I was able to help you out :)
simplify
x2 + 6 − (3x2 − 2x − 5)
Answers
Solve the equation. 5 = g/8 what does g equal
Answers
Answer:
Step-by-step explanation:
multiply both sides by 8
do over and write g=8x5
solve 8x5=40
g=40
Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone (Prasad et al., 2000). Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 4.5 days, and the standard deviation of overall duration of symptoms was 1.6 days. For the placebo group, the mean overall duration of symptoms was 8.1 days, and the standard deviation was 1.8 days.
a. Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges.
b. Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges.
c. On the basis of the intervals computed in parts (a) and (b) and/or the picture you constructed in part (c), is it reasonable to conclude generally that taking zinc loz-enges reduces the overall duration of cold symptoms more than if taking a placebo? Explain why you think this is or is not an appropriate conclusion.
d. In their paper, the researchers say that they checked whether it was reasonable to assume that the data were sampled from a normal curve population and decided that it was. How is this relevant to the calculations done in parts (a) and (b)?
Answers
Answer:
a. (3.83952, 5.16049)
b. (7.32, 8.88)
c. The difference in the range of the confidence intervals suggest that taking the zinc loz-enges reduces the overall duration of cold symptoms
d. The assumptions required for the validity validity of a t-test include that the data is sampled from a source that have data that are normally distributed
Step-by-step explanation:
The given parameters are;
The number of participants that took zinc lozenges, n₁ = 25
The number of participants that took a placebo, n₂ = 23
The mean duration of the symptoms for the zinc lozenge group, [tex]\overline x_1[/tex] = 4.5 days
The standard deviation of overall duration, s₁ = 1.6 days
The mean duration of the symptoms for the placebo group, [tex]\overline x_2[/tex] = 8.1 days
The standard deviation, s₂ = 1.8 days
a. The 95% confidence interval if everyone in the population were to take zinc lozenges is given as follows;
[tex]CI=\bar{x}_1\pm t_{\alpha/2} \times \dfrac{s_1}{\sqrt{n_1}}[/tex]
n₁ = 25, the degrees of freedom (df) = n₁ - 1 = 24
The t-value for 95% confidence interval, with df = 24, with t = 2.064
Therefore, we have;
[tex]CI_{zl}=4.5 \pm 2.064 \times \dfrac{1.6}{\sqrt{25}}[/tex]
[tex]CI_{zl}[/tex] = 4.5 ± 0.66048
[tex]CI_{zl}[/tex] = (3.83952, 5.16049)
b. The 95% confidence interval if everyone in the population were to take the placebo is given as follows;
[tex]CI_p=\bar{x_2}\pm t_{\alpha/2} \times \dfrac{s_2}{\sqrt{n_2}}[/tex]
n₂ = 23, the degrees of freedom (df) = n₂ - 1 = 22
The t-value for 95% confidence interval, with df = 22, with t = 2.074
Therefore, we have;
[tex]CI_p =8.1 \pm 2.074 \times \dfrac{1.8}{\sqrt{23}}[/tex]
[tex]CI_p[/tex] = 8.1 ± 0.7784
[tex]CI_p[/tex] = (7.32, 8.88)
c. Based on the difference in the range of the 95% confidence interval for the mean duration of cold symptoms of the group that take zinc lozenges, (3.83952, 5.16049), and the mean of the group that are on a placebo, (7.32, 8.88), there is sufficient statistical evidence to suggest that there is a difference between the mean and taking zinc lozenges reduces the overall duration of cold symptoms more than if taking placebo
d. The assumptions required for validity when carrying out a t-test include;
i) The measurement scale is ordinal or continuous
ii) The sample is a simple random sample
iii) The data gives a normal distribution curve
iv) The sample size is reasonably large
v) The variance are homogeneous
Among these assumptions, the data must be randomly sampled from the population of interest and that the data variables follow a normal distribution
The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation
Find surface area plzzzzz
Answers
Answer:
184 m²
Step-by-step explanation:
Surface Area = 2(10*2) + 2(10*6) + 2(2*6)
Surface Area = 2(20 + 60 + 12)
Surface Area = 2(92)
Surface Area = 184 m²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Can you please help me with this
Answers
can someone help my find the fraction and explain how you got it please please
Answers
Help a bab out with something, please?
Answers
Answer:
18
Step-by-step explanation:
please i need help, right now!!! i give the person the brainliest answer!! im giving 15 points… please help
Answers
Answer:
Ummmm its just a black screen
Step-by-step explanation:
5 oranges cost $2. Find the cost of 20 oranges.
Answers
===================================================
Work Shown:
(5 oranges)/(2 dollars) = (20 oranges)/(x dollars)
5/2 = 20/x
5x = 2*20 .... cross multiply
5x = 40
x = 40/5 .... dividing both sides by 5
x = 8
20 oranges cost $8
--------------
Another way to approach the problem is to note that the jump from "5 oranges" to "20 oranges" is "times 4".
5*4 = 20
So we'll apply the "times 4" operation to the old cost of $2 to get the new cost being 2*4 = 8 dollars
Answer:
$8
Step-by-step explanation:
if 5 oranges cost $2 then 1 orange costs 2/5 of a dollar, or 40 cents
20 oranges multiplied by 40 cents is $8
or you can set up a proportion:
2/5 = x/20
cross-multiply to get:
5x = 40
x = 8
Câu 4: Cho chiết suất tuyệt đối của nước là n= 4/3 . Một người nhìn một hòn sỏi nhỏ S nằm ở đáy một bể nước sâu 1,2 m theo phương gần vuông góc với mặt nước, thấy ảnh S' nằm cách mặt nước một khoảng bằng
Answers
goodStep-by-step explanation:
WILL GIVE BRAINLIEST
Determine whether each scenario below is an example of a BIASED or UNBIASED sample
Answers
Answer:
First : Unbiased
Second : Biased
The number of spectators at the 2010 World Cup match between Argentina and Mexico was 82000 correct to the nearest thousand. If each spectator paid 2600 Rand to attend the game what is the lower bound for the total amount paid? Write your answer in standard form
Answers
Answer:
$213,200,000 or 2.132*10[tex]^{5\\}[/tex]
Step-by-step explanation:
82000*2600
Pls help i'm struggling with this
Answers
Answer:
Click the second one, I truly hope that worked! :)
help me solve this pleaseeee
Answers
Answer:
f(n) = 6n + 12
Step-by-step explanation:
There is a common difference in consecutive number of seats, that is
42 - 36 = 36 - 30 = 30 - 24 = 24 - 18 = 6
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 18 and d = 6 , then
f(n) = 18 + 6(n - 1) = 18 + 6n - 6 = 6n + 12
[tex]64y + 6x = [/tex]
Answers
[tex]\longrightarrow{\blue{ 2 \: ( \: 32 \: y + 3 \: x \: )}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]64 \: y + 6 \: x[/tex]
[tex] = 2 \: ( \: 32 \: y + 3 \: x \: )[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Answer:
2 ( 32y + 3 x)
Step-by-step explanation:
64 y + 6x
factor out 2 from the equation
2 ( 32y + 3 x)
14+ (42 + 7) + 32
Pls help me
Answers
Answer:
95
Step-by-step explanation:
14 + (42 + 7) + 32
14 + 49 + 32
63 + 32
95
Answer:
95
Step-by-step explanation:
Let's use BEDMAS to solve this (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)
1. Calculate the brackets.
42 + 7 = 49
2. Add 14 + 49 + 32
14 + 49 + 32 = 95
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Have a great summer :)
Question: A sample contains 68 grams of radioactive Bruinium. Sixteen days later, the sample had decayed to 47 grams.
A) what is the decay rate, k?
B) what is half-life of bruinium to the nearest 0.1 day?
C) how much bruinium would be left in another 10 days? (After the first 16)
D) how much time is required for the sample to decay to 25 grams (from t=0)?