Answers
Answer:
option B
Step-by-step explanation:
Given :
[tex]y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\[/tex]
Step 1 : simplify the equation :
[tex]3y = 2x + 9\\\\2y = 5x + 7\\[/tex]
Step 2: Arrange the terms :
[tex]2x - 3y = - 9\\\\5x -2 y = -7[/tex]
Step 3 : Solve for x and y :
2x - 3y = - 9 ------ ( 1 )
5x - 2y = - 7 --------- ( 2 )
_____________________
( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )
( 2) x 2 => 10x - 4y = - 14 ----------- (4 )
_______________________
( 3 ) - ( 4 ) => 0x - 11y = - 31
- 11 y = - 31
[tex]y = \frac{31}{11}[/tex]
Substitute y in ( 1 ) :
2x - 3y = - 9
[tex]2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}[/tex]
Therefore the solution to the sytem is [tex]( - \frac{3}{11} , \frac{31}{11})[/tex]
The solution of the system of equation is a point which lies
on the both the lines.
Option A : False , It says the solution lies above one of the given line.
But the solution of the system of equation always lies on
both the line.
Option B : True , says the solution is a point on the coordinate plane.
Option C : False, because if the solution is on the x-axis , then
the y coordinate in the solution would be zero.
But it is not zero.
Option D : False , the solution is the point where both the lines intersect.
Related Questions
the integers -10 and 10 are
Answers
Sandy went to her local zoo where 50% of it's exhibits featured reptiles. If the zoo features 44 exhibits in total, then how many of the zoo's exhibits feature reptiles?
Answers
Answer:
22 exhibits
Step-by-step explanation:
We are told from the above question that:
Sandy went to her local zoo where 50% of it's exhibits featured reptiles.
If the zoo features 44 exhibits in total, then the number of the zoo's exhibits that feature reptiles is calculated as:
50% of 44
50/100 × 44
= 50 × 44/100
= 22
Therefore, the number of the zoo's exhibits that feature reptiles is 22 exhibits.
Triangles ABC and XYZ are similar figures, because angles A, B, and C are congruent to angles X, Y, and Z, respectively.
If side AC equals 3 cm, BC equals 9 cm, and XZ equals 15 cm, what is the length of side YZ?
Answers
Answer:
45cm
Step-by-step explanation:
Since they are simliar, they are proportional.
SO, you can do AC/XZ = BC/YZ
You can also see that XZ is 5 times larger than AC
SO multiply BC by 5.
Find the volume of this cone.
Use 3 for pi
Answers
Answer:
81 cm^3
Step-by-step explanation:
We know that we have to use 3 for pi.
Formula given for formula of cone is:
πr^2h ÷3
Use formula with the given pi and dimensions:
3(3^2)(9) ÷ 3
= 3(9)(9) ÷ 3
= 243 ÷ 3
= 81
Volume is measured in cubic centimeters.
FINAL ANSWER:
81 cm^3
Hope this helps!
See image for question.
Answers
Answer:
#7(a)
Sample space:
1*1, 1*2, 1*3, 1*4,2*1, 2*2, 2*3, 2*4,3*1, 3*2, 3*3, 3*4,4*1, 4*2, 4*3, 4*4Total 16 outcomes
(b)
(i) P(even) = 12/16 = 3/4(ii) P(3x) = 7/16(iii) P(perfect square) = 4/16 = 1/4#8(a) Sample space:
1T, 1H, 2T, 2H, 3T, 3H, 4T, 4HTotal 8 outcomes
(b)
(i) 1T, 3T
P(T and odd) = 2/8 = 1/4(ii) 1H, 4H
P(H and square) = 2/8 = 1/4(iii) 1H, 2H, 3H, 4H
P(H) = 4/8 = 1/2___ is the branch of mathematics that uses alphabetic symbols to represent unknown numbers or specific sets of numbers in order to make generalizations about arithmetic operations and mathematical relationships.
Answers
Answer:
I believe it's Algebra because it contains variables and equations where you have to do what you just described in your question.
Hope I helped, have a nice day :)
joseph cao bao nhiêu, nếu anh ấy cao 72 inch? Nếu anh ta là bao nhiêu feet, thì anh ta là bao nhiêu thước? nếu anh ta là bao nhiêu thước, anh ta là bao nhiêu cm?
Answers
Answer:
im not sure
Step-by-step explanation:
Answer:
joseph là 6 feet hoặc 2 thước Anh hoặc 182 cm.
Given the table below, determine the initial value/y intercept. PIC IS ABOVE! ANSWER!
Answers
Answer:
The initial value is the y value when x is zero. Look at the table to help you determine the y value when x is zero and that is your answer.
Step-by-step explanation:
Answer this for me please! thanks very much <3
Answers
the answer is b lil boy ggggggg
Which graph is likely to have a leading coefficient value of -1/8?
Answers
Answer:
The second graph: only this one opens downward.
A coach divided 13 liters of water into water bottles so that each bottle contained 0.65 liter of water how many water bottles are there
Answers
Answer:
there would be 20 bottles.
Step-by-step explanation:
13 divided by .65 = 20
A city held a bike parade. 52 bikers rode in the parade, and 8 of them rode a fixed-gear bicycle.
What is the probability that a randomly chosen bike in the parade was a fixed-gear bicycle?
Write your answer as a fraction or whole number.
P(fixed-gear bicycle) =
Answers
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
Find the probability by dividing the number of fixed gear bikers by the total number of bikers in the parade.
Since there are 8 fixed gear bikers and 52 bikers in total, this will be found by dividing 8 by 52.
So, the probability as a fraction is [tex]\frac{8}{52}[/tex]
This can be simplified by dividing both the numerator and denominator by 4:
= [tex]\frac{2}{13}[/tex]
So, the probability is [tex]\frac{2}{13}[/tex]
The sum of four consecutive numbers equals b+6. What are the numbers?
Answers
Answer:
0,1,2 and 3
Step-by-step explanation:
let the first number be b
therefore the second,third and fourth numbers are b+1,b+2 and b+3
b+b+1+b+2+b+3=b+6
4b+6=b+6
4b-b=6-6
3b=0
b=0
Which best describes the vertex of this parabola?
Answers
Answer:
The correct option is (2,1);maximum. The explanation is given below. The vertex of the parabola is the point where the parabola crosses its axis of symmetry. the vertex will be the lowest point on the graph, the point at the bottom of the " U "-shape.
Step-by-step explanation:
thank me later
Using the table from part I and your knowledge of exponents, write an equation that describes the doubling of the rabbit population every 6 months.
Answers
Answer:
Let P be thd population of rabbit
P = 2 to the power of n
where n is the period of month
prove the following [tex]\bold{algebraically}[/tex]:
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 30 }{ {29}^{4} - 1} = \frac{1}{28} [/tex]
Answers
Answer:
see below
Step-by-step explanation:
we are given
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 30 }{ {29}^{4} - 1} = \frac{1}{28}[/tex]
we want to prove it algebraically
to do so rewrite 30:
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 29 + 1}{ {29}^{4} - 1} \stackrel{ ? }{= }\frac{1}{28}[/tex]
let 29 be a thus substitute:
[tex] \displaystyle \frac{ {a}^{3} + {a}^{2} + a + 1}{ {a}^{4} - 1} \stackrel{ ? }{= }\frac{1}{28}[/tex]
factor the denominator:
[tex] \rm\displaystyle \frac{ {a}^{3} + {a}^{2} + a + 1}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
Factor out a²:
[tex] \rm\displaystyle \frac{ {a}^{2} ({a}^{} + 1)+ a + 1}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
factor out 1:
[tex] \rm\displaystyle \frac{ {a}^{2} ({a}^{} + 1)+1( a + 1)}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
group:
[tex] \rm\displaystyle \frac{ ({a}^{2} +1)( a + 1)}{ ({a}^{2} + 1) (a + 1)(a - 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
reduce fraction:
[tex] \rm\displaystyle \frac{ \cancel{({a}^{2} +1)( a + 1)}}{ \cancel{({a}^{2} + 1) (a + 1)}(a - 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
[tex] \displaystyle \frac{1}{a - 1} \stackrel {?}{ = } \frac{1}{28} [/tex]
substitute back:
[tex] \displaystyle \frac{1}{29 - 1} \stackrel {?}{ = } \frac{1}{28} [/tex]
simplify substraction:
[tex] \displaystyle \frac{1}{28} \stackrel { \checkmark}{ = } \frac{1}{28} [/tex]
hence Proven
Answer:
Step-by-step explanation:
Identity to use:
1+N+N^2+N^3 = (N^4-1)/(N-1)
Let N=29
1+29+29^2+29^3 = (29^4-1) / (29-1)
30+29^2+29^3 = (29^4-1) / 28
Transpose and re-arrange
(29^3+29^2+30) / (29^4-1) = 1 / 28 QED
write a proportion and find the missing side lengths. show work!! 30 points.
Answers
Answer:
Step-by-step explanation:
34 . since the given two figure are similar their corresponding sides are proportonal.
let the missing side be x
take these ratios
15/18 = x/30
do cross multiplication
18*x = 30*15
18x = 450
x = 450/18
x = 25
therefore missing side is 25
35.since they are also similar their corresponding sides are proportional.
let the missing side be x
for this take these ratios
8/12 = 10/x
do cross multiplication
12*10 = 8*x
120/8 =x
15 =x
therefore missing side is 15.
Solve for w -8.5 = 3.46
Answers
Done done done, W=3.46+8.5
W=11.96!
Hit the heart if it was helpful!
Answer:
11.96
Step-by-step explanation:
Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2.
Answers
Answer:
geometric
arithmetic
Step-by-step explanation:
there are no statements to check. you did not copy them in.
but I can solve the first part of the question.
sequence 1 :
-10, 20, -40, 80, -160, 320, -640, ...
I extended the sequence by a few more terms.
but it is clear that each new term is the previous term multiplied by -2.
since the sequence is built by multiplication, it is geometric.
sequence 2:
15, -5, -25, -45, -65, -85, ...
so, it is clear that each new term is the previous term subtracted by -20.
since the sequence is built by adding or subtracting, it is arithmetic.
Simplify. pls pls help
-2 √35
-24 √35
24 √35
Answers
Write the equation of the circle:
center: (-9, 0), diameter: 10
Answers
Answer:
[tex](x+9)^2+y^{2}=25[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center of the circle and [tex]r[/tex] is the radius of the circle.
Given the circle's diameter is [tex]d=10[/tex], then its radius is [tex]r=\frac{10}{2}=5[/tex].
Therefore, the equation of the circle is [tex](x+9)^2+y^{2}=25[/tex]
HELP‼️‼️‼️‼️‼️‼️‼️‼️
Answers
Answer:
a. x^(5/6) + 2x^(7/3)
Step-by-step explanation:
____
f(x) = 3x – 5. Find the average rate of change of the function between x = 3 and x = 7.
Answers
Given:
The function is:
[tex]f(x)=3x-5[/tex]
To find:
The average rate of change of the function between x = 3 and x = 7.
Solution:
We have,
[tex]f(x)=3x-5[/tex]
For [tex]x=3[/tex],
[tex]f(3)=3(3)-5[/tex]
[tex]f(3)=9-5[/tex]
[tex]f(3)=4[/tex]
For [tex]x=7[/tex],
[tex]f(7)=3(7)-5[/tex]
[tex]f(7)=21-5[/tex]
[tex]f(7)=16[/tex]
The average rate of change of the function f(x) between x = a and x = b is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The average rate of change of the function between x = 3 and x = 7 is:
[tex]m=\dfrac{f(7)-f(3)}{7-3}[/tex]
[tex]m=\dfrac{16-4}{4}[/tex]
[tex]m=\dfrac{12}{4}[/tex]
[tex]m=3[/tex]
Therefore, the average rate of change of the function between x = 3 and x = 7 is 3.
Which graph best represents a
quadratic function that has
only one zero?
A
с
B
Answers
Answer:
c
Step-by-step explanation:
right
3. If 2x +9 32, then x could be
11.5?
Answers
2x= 32-9
2x= 23
x= 23:2
x= 11.5
Answer:
Yes
Step-by-step explanation:
We can see step by step how to solve for x, and get 11.5:
2x+9=32
Subtrract the 9 from both sides. You should always try to get the number on one side, and the variable on the other:
2x+9-9=32-9
=
2x=23
In the end, once the number values are on one side, and the variable value on the other, you want you varaible to be 1.
When I mean 1, I mean you want 1x, or just x.
Here we see 2x=23, meaning we need to divide both sides by 2, to get 1x:
2x/2=23/2
=
x=11.5
So x equals 11.5, and you were correct.
Hope this helps!
An ice cream store sells 2 drinks, in 4 sizes, and 6 flavors. In how many ways can a customer order a drink?
Answers
A test is worth 30 points. Multiple-choice questions are worth 7 point and
short-answer questions are worth 2 points. If the test has 20 questions, how
many multiple-choice questions are there?
Answers
Answer:cvg
Step-by-step explanation:
- 3/10h = 15 what does h =
Answers
Answer:
h = -50
Step-by-step explanation:
- 3/10h = 15
Multiply each side by -10/3 to isolate h
-10/3 * - 3/10h = 15 * -10/3
h = -150/3
h = -50
Answer:
h = -50
Step-by-step explanation:
In the diagram of △EHG below, JF ∥HG, EJ=12, JH=24, and EF=6. What is the length of EG?
Answers
FG = JHxEF/EJ = 12 + 6 = 18
Hi, please help me with this math problem.
Answers
9514 1404 393
Answer:
-x +2
Step-by-step explanation:
The expression can be simplified as follows.
[tex]\sqrt{x^2-4x+4}=\sqrt{(x-2)^2}=|x-2|[/tex]
For negative values of its argument, the absolute value changes the sign.
For x < 1, x-2 is negative, so the simplified form is ...
-(x -2) . . . . . for x < 1
-x +2 . . . . . for x < 1