9514 1404 393
Answer:
(b) x = 7, AB = 9, AC = 12
Step-by-step explanation:
ΔAEB ~ ΔCDB so corresponding sides are proportional.
AB/CB = AE/CD
(x+2)/(x -4) = 12/4
x +2 = 3(x -4) . . . . . . multiply by x-4
x +2 = 3x -12 . . . . . . eliminate parentheses
14 = 2x . . . . . . . . . . . add 12-x
7 = x . . . . . . . . . . . . . divide by 2
AB = x +2 = 7 +2 = 9
BC = x -4 = 7 -4 = 3
AC = AB +BC = 9 +3 = 12
__
In summary, ...
x = 7, AB = 9, AC = 12 . . . . . matches the 2nd choice
_____
Additional comment
Please note the other choices make no sense.
(a) AB = x +2 = -5 +2 = -3 ≠ -9
(c) AC = 2x-2 = 2(7) -2 = 12 ≠ 9
(d) segment lengths are never negative in a geometrical figure
help will give brainliest
Answer:
B
Step-by-step explanation:
2/5 is equal to 40 percent
Find the volume of the composite figure. First, find the volume of the triangular prism. 4 cm Triangular prism Volume = [?] cm 5 cm 5 cm 6 cm Rectangular prism Volume = [ ] cm? 10 cm Total Volume of Composite Figure = [ ]cm 8 cm Enter
Answer: See attached image.
The total volume of the composite figure is 530 cm³.
To find the volume of the composite figure, we need to calculate the volumes of the individual prisms and then add them together.
Triangular Prism:
The volume of a triangular prism is given by the formula:
Volume = base area × height
The base of the triangular prism is a triangle with a base of 5 cm and a height of 5 cm.
Therefore, the base area is:
Base area = (1/2) × base × height = (1/2) × 5 cm × 5 cm = 12.5 cm².
Now, we can calculate the volume of the triangular prism:
Triangular prism volume = base area × height = 12.5 cm² × 4 cm = 50 cm³.
So, the volume of the triangular prism is 50 cm³.
Rectangular Prism:
The volume of a rectangular prism is given by the formula:
Volume = length × width × height.
Given the dimensions of the rectangular prism as length = 6 cm, width = 10 cm, and height = 8 cm, we can calculate its volume:
Rectangular prism volume = length × width × height = 6 cm × 10 cm × 8 cm = 480 cm³.
So, the volume of the rectangular prism is 480 cm³.
Total Volume of Composite Figure:
To find the total volume of the composite figure, we add the volumes of the individual prisms:
Total Volume = Triangular prism volume + Rectangular prism volume = 50 cm³ + 480 cm³ = 530 cm³.
Therefore, the total volume of the composite figure is 530 cm³.
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Mark multiplied a number by itself. He found a
product of 30. What is the number, rounded to the
nearest tenth?
A. 4.5
B. 5.4
C.5.5
D. 15.0
Answer:
5.5×5.5=30.5
we rounded 30.25 in nearest tenth it becomes 30
Answer:
C.] 5.5
Step-by-step explanation:
It is mentioned that the number was multiplied by the number itself.
Let's take 'x' as the number. It was multiplied by itself and the product is 30. So the equation will be:
x × x = 30
[tex]x^{2}[/tex] = 30
x = [tex]\sqrt{30}[/tex]
x = 5.47 = 5.5 (to the nearest tenth)
Figure o of a tile pattern has 3 tiles. This pattern grows
by 5 tiles each figure.
Answer:
Figure 0 = 5 tiles
Figure 1 = 5 + 7 = 12 tiles
So, the equation is:
y = 7x + 5
because, it adds 7 tiles in every new figure.
The equation is y = 7x +5.
Answer is y = 7x +5
18m+42n in distributive property
Adnswer:
18m+42n in distributive property=6(3m+7n)
Step-by-step explanation:
Answer and Step-by-step explanation:
The answer to this expression would be 6(3m + 7n).
18m + 42n is the distributive version of the same expression.
To un-distribute, you would find the greatest common factor of both numbers, and pull it out of the expression.
18 and 42 have a greatest common factor of 6.
18 divided by 6 is 3.
42 divided by 6 is 7.
That leaves us with 6(3m + 7n).
#teamtrees #PAW (Plant And Water)
ellus
Corresponding Angles are congruent.
Which angle corresponds with <3?
42141
4443
«[?]
45 46
47 48
Answer:
<8 corresponds with <3
This one please help out
Answer:
15. there are 11 cubes
16. there are 18 cubes
17. there are 6 cubes
18. the pencil case
19. the stapler
20. The Pencil Case is heavier than the wallet
21. The stapler is lighter than the wallet
Step-by-step explanation:
Okay so looking at the unit cubes you must count how much there are and see how much unit cubes the weight is equivalent to
15. there are 11 cubes
16. there are 18 cubes
17. there are 6 cubes
18. the pencil case
19. the stapler
20. The Pencil Case is heavier than the wallet
21. The stapler is lighter than the wallet
your work is correct!! Good job!!
Hope this helps!!
-Ketifa
Pls Answer correctly and I’ll give you the brainliest
Answer:
y = -x - 1
y = 1.5x + 6
(-3, 2)
Step-by-step explanation:
y = mx + b
y-intercepts are plotted on the graph
slope = rise over run
Solution is plotted on the graph
Answer:
the answer is (-3, 2)
value of x = -3
value of y = 2
can someone help me with this? all of the info is in the pic
Answer:
there is no pic -_-
Step-by-step explanation:
the scientific notation, 170.04 is written as
Answer: 1.7004 × 10^2
Step-by-step explanation:
A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is pumped out at a rate of 6 gals/min. Find the number A(t) of pounds of salt in the tank at time t. A(t) = 1500(1−e−0.02t) lb How long (in minutes) will it take for the tank to be empty after this process has started? min
Answer:
(a) [tex]A = 1500(1 - e^{-0.01t})[/tex]
(b) [tex]t = 0[/tex]
Step-by-step explanation:
Given
[tex]V= 300gal[/tex] --- Volume of tank
[tex]B = 5lb/gal[/tex] --- Brine solution
[tex]R_1 = 3gal/min[/tex] --- Rate in, in gallon/min
[tex]R_2 = 6gal/min[/tex] --- Rate out, in gallon/min
Required
Determine A(t)
First, calculate the rate in (R in) and (R out) in lb/min
[tex]R_{in} = B * R_1[/tex]
[tex]R_{in} = 5lb/gal * 3gal/min[/tex]
[tex]R_{in} = 15lb/min[/tex]
R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2
So, we have:
[tex]R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min[/tex]
[tex]R_{out} = \frac{3*A(t)}{300} lb/min[/tex]
[tex]R_{out} = \frac{A(t)}{100} lb/min[/tex]
The change in the amount of brin e in the tank at time t is given as:
[tex]A'(t) = R_{in} - R_{out}[/tex]
[tex]A'(t) = 15 - \frac{A(t)}{100}[/tex]
Rewrite:
[tex]\frac{dA}{dt} = 15 - \frac{A}{100}[/tex]
Multiply through by dt
[tex]dA = [15 - \frac{A}{100}]* dt[/tex]
Make dt stand alone
[tex]\frac{dA}{15 - \frac{A}{100}} = dt[/tex]
[tex]ln|15 - \frac{A}{100}| = -0.01t + ln\ c[/tex]
Express as exponents
[tex]15 - \frac{A}{100} = ce^{-\frac{t}{100}}[/tex]
Multiply through by 100
[tex]1500 - A = 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-0.01t}[/tex]
Apply initial conditions
[tex]A(0) = 0[/tex]
Substitute 0 for t in: [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]0 = 1500 - 100ce^{-0.01*0}[/tex]
[tex]0 = 1500 - 100ce^{0}[/tex]
[tex]0 = 1500 - 100c[/tex]
[tex]100c = 1500[/tex]
[tex]c = 15[/tex]
Substitute 15 for c in [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]A = 1500 - 100*15e^{-0.01t}[/tex]
[tex]A = 1500 - 1500e^{-0.01t}[/tex]
Factorize:
[tex]A = 1500(1 - e^{-0.01t})[/tex]
How long to empty the tank
Set A to 0
[tex]1500(1 - e^{-0.01t}) = 0[/tex]
Divide through by 1500
[tex]1 - e^{-0.01t} = 0[/tex]
Collect Like Terms
[tex]e^{-0.01t} = 1[/tex]
Take ln of both sides
[tex]ln\ (e^{-0.01t}) = ln\ 1[/tex]
[tex]-0.0t = 0[/tex]
[tex]t = 0[/tex]
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 76 people in the 18-21 age bracket and finds that 65 of them respond and 11 refuse to respond. When 281 people in the 22-29 age bracket are contacted, 263 respond and 18 refuse to respond. Assume that 1 of the 357 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
Answer:
0.9692 = 96.92% probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
357 people.
281 in the 22-29 age bracket + 65 in the 18-21 that agree to respond. So
[tex]p = \frac{281+65}{357} = 0.9692[/tex]
0.9692 = 96.92% probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
Find the value for x.
A. 76°
B. 285°
C. 256°
D. 105°
can someone please help me find the value of p and q?
Answer:
[tex]q=31.7\\p=28.4[/tex]
Doing all calculations with 3 significant figures.
Step-by-step explanation:
First, we'll obtain the value of 'q', this by realizing how the two angles together form a right triangle with inner angles of 30, 60, 90.
Furthermore, the opposite side of the angle of 30 is 'q' and its adjacent is given as 55. Hence, we can solve for 'q' using tangent as follows:
[tex]tan(30)=\frac{q}{55} =.577[/tex]
We solve for 'q':
[tex]q=.577*55=31.7[/tex]
Now to solve for 'p', we first will calculate what '55-p' is equal to.
First, we realize '55-p' corresponds to the adjacent side to the angle of 50 inside the small right triangle (the one with inner angles of 50, 40, 90) and q (which we now know is 31.7) correspond to the opposite side. Hence, we again use tangent as follows:
[tex]tan(50)=\frac{q}{55-p} =\frac{31.7}{55-p} =1.19[/tex]
We solve for 'p':
[tex]1.19(55-p)=31.7\\65.5-1.19p=31.7\\1.19p=33.8\\p=\frac{33.8}{1.19}=28.4[/tex]
What is 5/9=14c-5/12
Answer:
c=5/72
Step-by-step explanation:
5/9=14c-5/12
Switch sides
14c-5/12=5/9
Add 5/12 tp both sides
14c-5/12+5/12=5/9+5/12
Simplify;
14c-5/12+5/12
=14c
Simplify;
5/9+5/12
LCM of 9, 12;
36
The least common multiplier of a, b is the smallest positive number that is divisible by both a and b.
Prime factorization of 9;
3*3
Prime factorization of 12;
2*6
=2*2*3
=3*3*2*2
=36
5/9=5*4/9*4=20/36
5/12=5*3/12*3=15/36
=20/36+15/36
20+15/36
=35/36
14c=35/36
14c/14=35/36/14
14c/14=c
35/36*14
=35/504
=5/72
Answer c=5/72
Answer to the following question is as follows;
Value of C = 5 / 72
Step-by-step explanation:
Given:
[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]
Find:
Value of C
Computation:
[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]
By taking 5/12 to LHS Side
[tex]\frac{5}{9} + \frac{5}{12} = 14c\\\\[/tex]
By taking LCM;
[tex]\frac{(4)(5) + (3)(5)}{36} = 14c\\\\[/tex]
[tex]\frac{20 + 15}{36} = 14c\\\\[/tex]
[tex]\frac{35}{36} = 14c\\\\[/tex]
By transfer 14 to LHS side
[tex]\frac{35}{36 \times 14 } = c\\\\[/tex]
[tex]\frac{5}{36 \times 2 } = c\\\\[/tex]
[tex]\frac{5}{72} = c\\\\[/tex]
Value of C = 5 / 72
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What kind of triangle is shown
Answer:
scalene triangle
..... .
What is the probability that you know will not wear a white shirt on the first day of her trip
Answer:
what is the question yaaar
combined the like terms to create an equivalent expression 5t+10-4-t
Acellus
Alternate exterior angles are congruent.
Which angle forms a pair of alternate
exterior angles with angle 2?
4241
4443
46145
4847
42 =<[?]
Enter
Answer:
angle 7
Step-by-step explanation:
Answer:
angle 7 angle forms a pair of alternate
exterior angles with angle 2.
How many students were over 145
Can some one help me 2⅛-1⅜
Answer:
6 / 8 or 3 / 4
Step-by-step explanation:
Subtraction lol
Solve for u.
5u - 15 = 10
Solve for u
|5u-15|=10
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
U =
=
No
solution
D
Answer:
5u-15=10 |+15
5u=25 |:5
u=5
The solution is 25
I hope it helps
have anice day
i need help with b and jk
Answer:
b = 1
JK = 3
Step-by-step explanation:
5b - 2 = 9b - 6
4b = 4
b = 1
JK = 3
Write the quadratic function in the form f (x)= a (x - h)' + k.
f (x) = 3x² - 6x+6
Answer:
[tex]f(x) = 3(x - 1)^2-3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3x^2 - 6x + 6[/tex]
Required
Write as:
[tex]f(x) = a(x - h)^2 + k[/tex]
In [tex]f(x) = 3x^2 - 6x + 6[/tex], the coefficient of x is -6
Divide by 2: -3
Square: 9
Add 9 - 9 to the above equation
[tex]f(x) = 3x^2 - 6x +9-9+ 6[/tex]
Split to 2
[tex]f(x) = [3x^2 - 6x +9]-[9- 6][/tex]
[tex]f(x) = [3x^2 - 6x +9]-[3][/tex]
Factorize:
[tex]f(x) = [3x^2 - 3x -3x+9]-[3][/tex]
[tex]f(x) = [3x(x - 1) -3(x-1)]-[3][/tex]
[tex]f(x) = [(3x - 3)(x-1)]-[3][/tex]
Factorize 3x - 3
[tex]f(x) = [3(x - 1)(x-1)]-[3][/tex]
[tex]f(x) = 3(x - 1)^2-[3][/tex]
[tex]f(x) = 3(x - 1)^2-3[/tex]
For a math assignment, Jane has to roll a set of six standard dice and record the results of each
trial. She wonders how many different outcomes are possible after rolling all six dice.
What is the total number of possible outcomes for each trial?
46,656
0 36
0216
0 7,776
SAVE AND CONTINUE
Answer:36
Step-by-step explanation: 6 sided dice = 6 possible outcomes
6×6=36
The required number of outcomes is 36 after rolling all six dice. Option B is correct.
Jane has to roll a set of six standard dice and record the results of each
trial. She wonders how many different outcomes are possible after rolling all six dice. the total number of possible outcomes for each trial to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events for a system of the certain events.
For 1 dice, sample space = { 1 2 3 4 5 6}
total possible outcome = 6
Now 6 dice roll at once and the total outcome = 6 * 6
= 36
Meanwhile, Jane has a total of 36 outcomes.
Thus, the required number of outcomes is 36 after rolling all six dice. Option B is correct.
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Please show work will give alot of points
Amella bought roast beef for $6.85 per pound. Find the total cost Amelia bought 4
pounds of roast beef.
She bought $27.40 worth of roast beef.
Express the radical using the imaginary unit,
ii
i
i
.
Express your answer in simplified form.
±−55=±\pm\sqrt{-55}=\pm
±
−55
=±
Answer:
Step-by-step explanation:
Answer:
[tex]+\sqrt{55i}[/tex]
Step-by-step explanation:
Khan <3
the first two terms of an arithmetic sequences are 7 and 3.
1.1.1 determine the eighteen term.
1.1.2 which term of the sequences Will be equal to -157?
Answer:
1.1.1) -61
1.1.2) Term 42
Step-by-step explanation:
Tn= dn (difference) + t0 (term 0)
Tn= -4n+ 11
You can now take this general rule to find out the other terms.
Tn= -4(18)+11
Tn= -61
And the term -157
Tn= -4n+11
-157= -4n + 11
-157 - 11= - 4n
-168= -4n
-168/-4= n
42= n
Is 12/8 less than, equal to, or greater than 11/6?
Answer:
it's less than
Step-by-step explanation:
12/8 simplified is 3/2
11/6 cannot be further simplified
3/2<11/6