Answers
Answer:
7. C. 6
8. H. √34
9. A. (1, 3.5)
10. J. 10
Step-by-step explanation:
7. AB = 2y, BC = 6y, AC = 48
AB + BC = AC (segment addition theorem)
Substitute the above values into the equation
2y + 6y = 48
Solve for y
8y = 48
Divide both sides by 8
8y/8 = 48/8
y = 6
8. Distance between P(2, 8) and Q(5, 3):
[tex] PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] P(2, 8) = (x_1, y_1) [/tex]
[tex] Q(5, 3) = (x_2, y_2) [/tex]
[tex] PQ = \sqrt{(5 - 2)^2 + (3 - 8)^2} [/tex]
[tex] PQ = \sqrt{(3)^2 + (-5)^2} [/tex]
[tex] PQ = \sqrt{9 + 25} [/tex]
[tex] PQ = \sqrt{34} [/tex]
9. Midpoint (M) of segment LB, for L(8, 5) and B(-6, 2) is given as:
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Let [tex] L(8, 5) = (x_1, y_1) [/tex]
[tex] B(-6, 2) = (x_2, y_2) [/tex]
Thus:
[tex] M(\frac{8 + (-6)}{2}, \frac{5 + 2}{2}) [/tex]
[tex] M(\frac{2}{2}, \frac{7}{2}) [/tex]
[tex] M(1, 3.5) [/tex]
10. M = -10, N = -20
Distance between M and N, MN = |-20 - (-10)|
= |-20 + 10| = |-10|
MN = 10
Related Questions
In the sequence 1. 2. 3. 4. 1.2.3.4... the numbers 1.2.3.4
repeat indefinitely. What is the sum of the first 150 terms?
A. 300
B. 77
C 37
D.3
Answers
=============================================
Explanation:
The sequence {1,2,3,4,1,2,3,4...} has "1,2,3,4" repeat forever. We can say that the cycle is 4 terms before it restarts the pattern again. Because of this 4-cycle pattern, we know that 150/4 = 37.5 = 37 full cycles happen. The leftover part is of length 150-37*4 = 2.
In short we have 37 full cycles of {1,2,3,4} happening. The last leftover bit has {1,2} only
In the subsquence {1,2,3,4} its sum is 1+2+3+4 = 10. Having 37 copies of {1,2,3,4} leads to a sum of 37*10 = 370 so far.
Then we add on the last bit 1+2 = 3 to get 370+3 = 373.
Therefore, the sum of the first 150 terms is 373. I think your teacher made a typo when listing out the answer choices. Please double check to make sure.
What is the axis of symmetry, vertex and y intercept for 2x^2-8x-5
Answers
Answer:
Axis of symmetry: x = 2
Vertex at: (2, -13)
y-intercept is (0, -5)
Step-by-step explanation:
The equation for the x-value of the vertex in a quadratic of the form:
[tex]y=ax^2+bx+c[/tex]
is given by:
[tex]x_{vert}=-\frac{b}{2\,a}[/tex]
which in our case gives:
[tex]x_{vert}=\frac{8}{2*2} =2[/tex]
Then the equation for the axis of symmetry is given by: x = 2
and the y of the vertex can be calculated as:
[tex]y_{vert}=2 (2)^2-8\,(2)-5=-13[/tex]
Then the vertex is at the point: (2, -13)
And the y-intercept is found when x=0, that is:
y-intercept is (0, -5)
(6h + 8) - (3h + 2) = 15
PLEASE HELP I ALSO NEED TO SHOW WORK
Answers
Answer:
[tex]h=3[/tex]
Step-by-step explanation:
So we have the equation:
[tex](6h+8)-(3h+2)=15[/tex]
First, let's distribute the negative:
[tex](6h+8)+(-3h-2)=15[/tex]
Combine like terms:
[tex](6h-3h)+(8-2)=15[/tex]
Subtract or add:
[tex]3h+6=15[/tex]
Subtract 6 from both sides:
[tex]3h=9[/tex]
Divide both sides by 3:
[tex]h=3[/tex]
And we're done!
Answer:
h=3
Step-by-step explanation:
1 Remove parentheses.
6h+8-3h-2=156h+8−3h−2=15
2 Simplify 6h+8-3h-26h+8−3h−2 to 3h+63h+6.
3h+6=153h+6=15
3 Subtract 66 from both sides.
3h=15-63h=15−6
4 Simplify 15-615−6 to 99.
3h=93h=9
5 Divide both sides by 33.
h=\frac{9}{3}h=
3
9
To solve the equation y – 4 = 9 for y, what operation must be applied to both sides in order to isolate the variable y?
Answers
Answer:
[tex]y-4=9[/tex]
The opposite of subtraction is addition, so you would have to add 4 to both sides:
[tex]y-4+4=9+4[/tex]
[tex]y=13[/tex]
The value of the y for the equation,y – 4 = 9 will be y=13 and e have to apply the subtraction operation must be applied to both sides in order to isolate the variable y.
What are arithmetic operations?The subject of arithmetic operations includes the study of numbers and their operations, which are important to all other branches of mathematics. These systems' fundamental operations are addition, subtraction, multiplication, and division.
It is given that the equation is,y – 4 = 9.
We have to solve the equation y – 4 = 9 and find the operation that must be applied to both sides in order to isolate the variable y.
The following steps are to be taken to isolate the variable y.
y – 4 = 9
y-4+4=9+4
y=13
Thus, the value of the y in the equation, y - 4 = 9, will be 13, and in order to isolate the variable y, the subtraction operation must be done on both sides.
Learn more about the arithmetic operations here,
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PLEASE HELP 100 POINTS PLEASE HELP 100 POINTS The ratio between the number of students (s) on a field trip and the number of teachers (t) on the field trip is 21/4. There are 84 students going on a field trip. How many teachers must go?
Answers
Answer:
16 teachers.
Step-by-step explanation:
84 / 21 = 4
4 * 4 = 16
Hope this helped. Please give brainly if its the best!
Answer:
[tex] \huge \colorbox{blue}{16 students}[/tex]
Step-by-step explanation:
we are given the ratio of students and teachers:
[tex] \displaystyle \: \frac{21}{4} [/tex]
which means if the number of students is 21 then the number of teachers should be 4
to find how many teachers should go if students 84 we have to divide 84 by [tex]21/4[/tex] :
[tex] \displaystyle \: 84 \div \frac{21}{4} [/tex]
simplify division:
[tex] = \displaystyle \: 84 \times \frac{4}{21} [/tex]
simplify multiplication:
[tex] = \displaystyle \: \cancel{ 84} \: ^{4} \times \frac{4}{ \cancel{21}} \\ = 4 \times 4 \\ = 16 [/tex]
The initial mass of a certain species of fish is million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of /yr. However, commercial fishing removes fish mass at a constant rate of million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be?
Answers
The question is incomplete. Here is the complete question.
The initial mass of a certain species of fish is 7 millions tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 2/yr. However, comercial fishing removes fish mass at a rate of 15 million tons per year.
(a) When will all fish be gone?
(b) If the fishing rate is changed so that the mass of fish remains constant, what should the rate be?
Answer: (a) t = 1.35 years.
(b) Rate = 14,000,000
Step-by-step explanation:
(a) Initial mass is [tex]m_{0}[/tex] = 7,000,000
Rate of increase and comercial fishing gives an equation of growth:
[tex]\frac{dm}{dt}=2m-15,000,000[/tex]
m' - 2m = - 15,000,000
This is an ordinary linear equation (ODE) of first order, of type:
y' + a(x)y = f(x)
where a(x) and f(x) are continuous.
To solve this type of linear equation, first calculate integrating factor, using:
[tex]u(x) = e^{\int\limits {a(x)} \, dx }[/tex]
In our case,
[tex]u(t) = e^{\int\limits {-2} \, dt }[/tex]
Solving:
[tex]u(t) = e^{-2t }[/tex]
The general solution of a ODE can be written as
[tex]y=\frac{1}{e^{u(x)}}[\int\ {u(x).f(x)} \, dx + c][/tex]
In our case:
[tex]m=\frac{1}{e^{-2t}}[\int\ {-2t.(-15)} \, dt + c][/tex]
Solving:
[tex]m=\frac{1}{e^{-2t}}[\frac{15}{2}e^{-2t}+c ][/tex]
To find constant c, use initial condition, i.e., m(0)=7,000,000:
[tex]7,000,000=\frac{1}{e^{-2.0}}[\frac{15}{2}e^{-2.0}+c ][/tex]
[tex]c=-500,000[/tex]
Then for the fish growth, general equation is:
[tex]m=7500,000-500,000e^{2t}[/tex]
When the fish is gone, means m = 0, then:
[tex]7500,000-500,000e^{2t}=0[/tex]
[tex]500,000e^{2t}=7500,000[/tex]
[tex]e^{2t}=15[/tex]
[tex]ln(e^{2t})=ln(15)[/tex]
[tex]t=\frac{ln(15)}{2}[/tex]
t = 1.35
It will take 1.35 years for the fish to be gone.
(b) For the mass to be constant, rate of growth must be zero:
[tex]\frac{dm}{dt}=0[/tex]
Suppose the changed fishing rate is k:
[tex]2m_{0}-k=0[/tex]
[tex]-k=-2.7,000,000[/tex]
k = 14,000,000
To remain constant, rate must be 14,000,000.
Answer:I think it’s 40 sorry if it’s wrong :/
Step-by-step explanation:
f(x)=-4xto the power of 2 what is the range
Answers
Answer:
(-infinity, 0]
Step-by-step explanation:
I'm assuming you meant f(x) = -4x^2. If so, the graph is that of a parabola that opens down and has vertex at (0, 0). In other words, f(x) is always zero or below zero.
Thus the range is (-infinity, 0]
A box contains colored poker chips. There are 100 red, 100 white, and 100 blue chips. Without looking, what is the minimum number of poker chips that must be drawn to be assured of getting 30 chips of one color?
Answers
Answer:
draw all 100 of two colors to be assured
Step-by-step explanation:
if wrong plz tell me i can help on other things if wrong
What is the quotient? 457.6 divided by negative 286 –16 –1.6 1.6 16
Answers
Answer:
-1.6
Step-by-step explanation:
The quotient when 457.6 is divided by - 286 is - 1.6.
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
We know A number N divided by D with quotient Q and the remainder R can be written as,
N = DQ + R.
Given, The quotient when 457.6 is divided by - 286 is - 1.6.
learn more about quotient here :
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I need help I don’t understand it at all
Answers
Answer:
Correct Answer Is 3160 Maybe
Step-by-step explanation:
Answer:
3160
Step-by-step explanation:
3.16*10^3
=31.6*10^2
=316*10
=3160
F(x)=-2|x| describe the transformation from the parent function f(x)=|x|
Answers
Answer:
reflect it about the x axis and stretch it by 2 in the y direction
Step-by-step explanation:
f(x) = |x| to f (x)=-2|x|
y = −f(x) Reflects it about x-axis
y = Cf(x) C > 1 stretches it in the y-direction
so we reflect it about the x axis and stretch it by 2 in the y direction
Answer: reflect it about the x axis and stretch it by 2 in the y direction
Step-by-step explanation:
12-21-3x5
What is the answer to this Order of operation question
Answers
Answer:
-24
Step-by-step explanation:
first multiply -3 and 5 to get -15
so it will be 12-21-15 then subtract 12-21 and you get -9
then do -9-15=24
hope this helps :)
So for this multiplication goes first (3x5) = 15
Then we are left with (12-21-15)*left to right*
So (12-21) =-9
Finally we are left with (-9-15) = -24
The answer is -24
is 16 less than 10 write that as a inequality
Answers
Answer:
16 < 10
Step-by-step explanation:
Less than = <
[tex]16 < 10[/tex]
By the way, this inequality is FASLE
Let L be the line with parametric equations x=2+t, y=1-t, z=1+3t.Let v=(1,2,0).Find vectors w1 and w2 such that v= w1 + w2, and such that w1 is parallel to L and w2 is perpendicular to L.
Answers
Answer:
w1 = (-1/11, 1/11, -3/11)
w2 = (12/11, 21/11, 3/11)
Step-by-step explanation:
Direction ratio of w1 = Direction ratio of L (because parallel) = K+(1, -1, 3)
Let <a,b,c> be direction ratio of w2.
Then, <a,b,c>. <1,-1,3> = 0
a-b+3c = 0
v = w1 + w2
(1, 2, 0) = k(1, -1, 3) + (a, b, c)
a + k = 1
b - K = 2
c - 3k = 0
Solving 4 equations, a = 12/11, b= 21/11, c = 3/11, k=-1/11
So, w1 = -1/11(1, -1 ,3) = (-1/11, 1/11, -3/11)
w2 = (12/11, 21/11, 3/11)
For every $2 Pam saves, her brother saves $7. If Pam has $20 in her account how much does her brother have?
Answers
Answer:
70
Step-by-step explanation:
Which equation is true if s = -3
Answers
Answer:
3s + 22 = 13
Step-by-step explanation:
-Removable discontinuity at 3, jump discontinuity at 5
Answers
3(5x - 2) - 6x = 3(3x + 2)
Answers
9x-9x=6+6
x=12
Answer:
x=12
Step-by-step explanation:
Determine the quail’s and pheasant’s speeds in miles per hour. Quail: 20yards in 2 1/2 minuts and pheasant’s : 200yards in 5/6 minuts.
Answers
write (7x - 4)(3x - 1) in standard form
Answers
Answer:
21x² - 19x + 4
Step-by-step explanation:
Step 1: Write factors
(7x - 4)(3x - 1)
Step 2: FOIL (First Outside Inside Last)
21x² - 7x - 12x + 4
Step 3: Combine like terms
21x² - 19x + 4
An unknown fraction is between 0 and 1. Which is true about the equivalent percent and decimal?
A. The percent and decimal are between 0 and 1
B. The percent and decimal are greater than 1 and less than 100
C. The percent is between 0 and 1, and the decimal is greater than 0 and less than 100,
D. The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.
Answers
Answer:
The answer is C.
Step-by-step explanation: The number between 0 and 1. Think of decimals as cents, 100 cents makes a whole. So the number will be greater than 0 but less than 100.
Answer:
Right answer is D.
Step-by-step explanation:
I just tried a couple of fractions like 3/4 =.75=75% 1/2=.5=0.5%
Then I got it right on test :)
15. What percent of the people
surveyed prefer strawberry ice cream?
Favorite Flavors
Number of
Responses:
82- vanilla
chocolate- 76
strawberry- 42
Answers
Answer:
The answer is, 21%
Step-by-step explanation:
by adding all the responses, you get a total of 200. Then, you do 42/200 and then simplify, and 21/100 is 21%
2 squared+ 1 squared=?
Answers
2 squared = 4
1 squared = 1
4+1=5
Therefore 5 is your answer
Answer:
the answer is five(5).
portia has 72 postcards this is. 8 time as many as jonathan has how many postcards does jonathan have
Answers
The age of employees at a company is an example of _____.a. quantitative datab. label datac. time series datad. categorical data
Answers
Answer:
Quantitative data
Step-by-step explanation:
When we measure something, then we can quantify them. By also making a count, we are trying to quantify a particular entity.
Now in this case, we know that age is something we can quantify or measure. By nothing the difference between the year of birth and the present year, we can simply give the number of years or simply how
old a person is.
This clearly show that we have measured the count of that entity. This makes age an example of quantitative data
categorical data Step-by-step explanation:
10.) A meat shop sold 4 1/6 pounds of sausage and 4 times as much burger as sausages. How
many pounds of burgers were sold?
Answers
you just need to multiply 4 1/6 by 4
What is the area of the bottom of a circular tank that is 100 ft. in diameter? Give
your answer in square feet.
Answers
7850 ft²
Step-by-step explanation:Hi there !
d = 2r => r = d/2 = 100ft/2 = 50 feet
A = πr²
= 3.14×(50ft)²
= 3.14×2500ft²
= 7850 ft²
Good luck !
Subtract 23.4 – 8.78 =_____
Answers
Answer:
14.62
Step-by-step explanation:
Answer:
14.62
Step-by-step explanation:
23.40
- 8.78
________
1 4 .6 2
For you to answer you need to place the commas correctly. The commas must be below each other to help you place the other numebrs correctly vertically. And after that you subtract and remember borrowing :)
HOPE IT HELPED
steps of 17/3 - 3/4x = 1/2x + 5
Answers
Answer:
Step-by-step explanation:
12(17/3 - 3/4x = 1/2x + 5)
68 - 9x = 6x + 60
-15x = -8
x = 8/15
1. Solve the equation: p + 15 = 51
a. p = 65
b. p = 46
C. p = 66
d. p = 36
Answers
Answer:
D. 36
Step-by-step explanation:
51-15= 36
