Mathematics High School

system of equations solve y=2x+1 and 2x-y=3

Answers

Answer 1

For this case we have the following system of equations:

[tex]y = 2x + 1\\2x-y = 3[/tex]

We cleared "y" of the second equation:

[tex]y = 2x-3[/tex]

Now we equate the equations:

[tex]2x+1=2x-3\\1 = -3[/tex]

Since 1 is not equal to -3 then the system has no solution.

This can also be observed, knowing that the lines are parallel since they have the same slope, [tex]m = 2.[/tex]

Answer:

The system has no solution.

Related Questions

A rhombus exists. This rhombus has 2 diagonals. The diagonals touch the side forming angles. These angles are in the ratio 4:5. Solve for all the angles in this rhombus based on the theorems for rhombuses and parallelograms.

Answers

as you know, the diagonals in a rhombus meet in the center at right-angles, check the picture below.

and the pair of angles at each opposite vertex, are twins.

now, since the diagonals center meeting point, makes 4 right-triangles, let's use the one on the upper-left, recall that a triangle has a sum of all interior angles to be 180°, so the missing angles in that triangle are "complementary angles", namely, they add up to 90°.

so, let's check 90 in a 4:5 ratio then, we simply divide 90 by (4+5) and distribute the pieces accordingly, let's do so,

[tex]\bf 90\qquad 4:5\qquad \cfrac{4}{5}\qquad \cfrac{4\cdot \frac{90}{4+5}}{5\cdot \frac{90}{4+5}}\implies \cfrac{40}{50}\implies 40:50[/tex]

so the ratio of 4 angle, is really 40°, and the ratio of 5 angle is really 50°.

since the diagonal is bisecting the vertex, the angle made at the vertex is twice as much as that in the triangle we used, thus, 2(40) are the angles at the top and bottom, and 2(50) are the angles at the left and right.

80°, 80° and 100° and 100°.

what is the answer to g(r)=−5r+13

Answers

Final answer:

The function g(r) is a linear equation with a slope of -5 and a y-intercept of 13. You can find the value of g(r) by plugging in different values for r.

Explanation:

The student's question is regarding the function g(r)=−5r+13. However, the rest of the information provided appears to be disjointed and not directly related to the function in question.

To answer their question, g(r)=−5r+13 is a linear function where -5 is the slope and 13 is the y-intercept. In this equation, r is the independent variable, and g(r) is the dependent variable. You would insert a value for r to find the corresponding output of g(r). For example, if r = 2, then g(2) = -5(2) + 13 = -10 + 13 = 3.

what is the answer im so confused

Answers

The correct answer is $70

Answer:

Step-by-step explanation:

their income for the month of may is $3500

2% of this income was spent on movies

2% of $3500 = 2/100 × 3500

=0.02 ×3500

= $70

What is log5(4*7)+log5^2 as a single log?

Answers

log5(4*7)+log5^2=log5*28*25=log3500
It would be better if you sent a photo task
I'm not sure what I understood correctly

Answer with explanation:

The four options are

(A) log5 21 (B) log5 26 (C) log5 30 (D) log5 56

[tex]\rightarrow\log_{5}(4\times 7) +\log_{5}(2)\\\\ \rightarrow \log_{5}28+\log_{5}2\\\\\rightarrow \log_{5}(28 \times 2)\\\\=\log_{5}(56)\\\\ \text{Used this property of log}\\\\ \log_{m} a+\log_{m} b=\log_{m} ab[/tex]

Option D

Which of the following values could represent the probabilities of complementary events and 28% and 82% and 10% and 80%
1/7and2/7
2/5and3/5

Answers

The answer is 2/5 and 3/5 as they both add up to 1.00 or 100%

Answer:

2/5 and 3/5

Step-by-step explanation:

Complementary events have probabilities that sum to 100%, or 1.

28+82 = 110; this is not 100.

10+80 = 90; this is not 100.

1/7+2/7 = 3/7; this is not 1.

2/5+3/5 = 1; this is correct.

What is the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced?
A) one over fifty one
B) one over fifty two
C) twelve over fifty one
D) thirteen over fifty two

Answers

Answer: C) twelve over fifty one

Step-by-step explanation:

Formula for probability =[tex]\dfrac{\text{Favorable outcomes}}{\text{Total ouctomes}}[/tex]

We know that , a standard deck has 52 cards.

Number of hearts = 13  

If a heart was drawn on the first draw and not replaced, then the number of hearts left = 13-1=12          (favorable outcomes)

The total number of cards left = 52-1=51     (total outcomes)

Therefore, the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced would be :-

[tex]\dfrac{\text{Number of hearts left}}{\text{Total cards left}}\\\\=\dfrac{12}{51}[/tex]

Hence, the correct answer is option C) twelve over fifty one

Help me I don’t get this!!!

Answers

101 yeo don't venture know

The area of a rectangle is 77ft^2 , and the length of the rectangle is 3ft more than twice the width. What are the dimensions of the rectangle ?

Answers

Area = 77 ft^2
W = W
L = 2W + 3

Area = L * W
Area = (2W + 3)*W
Area = 2W^2 + 3W
The area is also 77
So 
Area = 2w^2 + 3W = 77
Area = 2w^2 + 3W - 77 = 0
Now factor the question
77 can only factor into 1,77 which is highly unlikely and 7 and 11
As a guess I'm going to try 7. It that's true, we get
(x + 7)(2x - 11) = 0 This might work.
x^2 + 14x - 11x - 77 = 0
x^2 + 3x - 77 = 0 So the factoring is correct.

x + 7 = 0
x = - 7
2x - 11 = 0
2x = 11
x = 11/2
x = 5.5 
W = 5.5 <<<< Answer

The minus seven is meaningless.
Width = 5.5
Length = 2*5.5 + 3
Length = 11 + 3
Length = 14 <<<< answer

Now we have to check the area.
Area = L * W
Area = 14 * 5.5
Area = 77. You have a complete answer.

Charlotte bought packs of hot dogs for $4 each. Eack pack has 8 hot dogs. If she spent $16 how many hot dogs did she get

Answers

Charlotte bought 32 hot dogs for $16 a pack
32 hotdogs
16/4=4
8*4=32

PLEASE HELP!!!!!
TIME SENSITIVE! Will mark brainliest!

Part 1.] Match the following items.
1. 2, 4, 8, 16, . . ., 64
2. 3, 6, 9, 12, . . .
3. 3 + 9 + 27 + 81 + . . .
4. 3 + 5 + 7 + 9 + . . .
5. 3, -3, 3, -3, 3,-3, . . .
A. arithmetic series
B. finite sequence
C. infinite sequence
D. geometric series
E. alternating sequence

Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
A. [tex] (-1)^{n} 3^{n} [/tex]
B. [tex] (-1)^{n} 3n[/tex]
C. [tex] (-1)^{n+1}3[/tex]

Part 3.] The first attached picture
A. 35
B. 14
C. 11

Part 4.] The second attached picture
A. 6
B. 9
C. 18

Part 5.] The third attached picture
A. 10
B. 14
C. 28

Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
A. Arithmetic Sequence
B. Geometric Series
C. Geometric Sequence
D. Arithmetic Series

Answers

we have that

   Part 1.] Match the following items.   
1. 2, 4, 8, 16, . . ., 64---------- > B. finite sequence
2. 3, 6, 9, 12, . . . ------------- > C. infinite sequence
3. 3 + 9 + 27 + 81 + . . .------> D. geometric series
4. 3 + 5 + 7 + 9 + . . .----------> A. arithmetic series
5. 3, -3, 3, -3, 3,-3, . . .-------- >E. alternating sequence

  Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
A. (-1^n)*(3^n)
for n=1-----------> (-1^1)*(3^1)=-3
for n=2-----------> (-1^2)*(3^2)=9 -------------- a2=6 no represents

B. (-1^n)*(3n)
for n=1-----------> (-1^1)*(3*1)=-3
for n=2-----------> (-1^2)*(3*2)=6
for n=3-----------> (-1^3)*(3*3)=-9
for n=4-----------> (-1^4)*(3*4)=12
for n=5-----------> (-1^5)*(3*5)=-15

C. (-1^(n+1))*(3)
for n=1-----------> (-1^(1+1))*(3)=3---------- > a1=-3 no represents

the answer part B is option B. (-1^n)*(3n)

Part 3.] The first attached picture

Σ (2n+1)  for n=1 to 5
n1---------> (2*1+1)=3
n2---------> (2*2+1)=5
n3---------> (2*3+1)=7
n4---------> (2*4+1)=9
n5---------> (2*5+1)=11
Σ (2n+1)  for n=1 to 5=[3+5+7+9+11]=35

the answer part C is 35

Part 4.] The second attached picture

Σ (3n)  for n=1 to 3
n1---------> (3*1)=3
n2---------> (3*2)=6
n3---------> (3*3)=9
Σ (3n)  for n=1 to 3=[3+6+9]=18

the answer part 4 is 18

Part 5.] The third attached picture
Σ (2n+2)  for n=1 to 4
n1---------> (2*1+2)=4
n2---------> (2*2+2)=6
n3---------> (2*3+2)=8
n4---------> (2*4+2)=10
Σ (2n+2)  for n=1 to 4=[4+6+8+10]=28

the answer part 5 is 28

Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
8-6=2
10-8=2
12-10=2
the next number is obtained by adding 2 to the previous number
this is an  Arithmetic Series

the answer is the option D. Arithmetic Series

One owl has a wingspan of 1⁄2 foot. A second owl's wingspan is 3⁄4 foot. How much longer is the wingspan of the second owl?

Answers

To find the second owl's wingspan, we need to subtract 1/2 from 3/4.

First, we'll need to find the common denominator:

1/2 = 2/4

Then, we can subtract.

3/4 - 2/4 = 1/4

With this, we now know that 1/4 is the answer.

The wingspan of the second owl is 3 inches longer than that of the first owl.

The question asks to find out how much longer the wingspan of the second owl is compared to the first owl. The first owl has a wingspan of 1/2 foot, while the second owl has a wingspan of 3/4 foot. To find the difference in wingspan, we subtract the first owl's wingspan from the second owl's wingspan:

3/4 foot - 1/2 foot = 2/4 foot - 1/2 foot = 2/4 foot - 2/4 foot = 1/4 foot.

Since there are 12 inches in a foot, we can convert this difference to inches:

1/4 foot times 12 inches/foot = 3 inches.

What is the slope of a line parallel to line B?


-1/3

2/5

5/2

5/3

Answers

 2/5is the answer. Hope is helps

Write an expression to show the sum of fourteen and triple eight.

Answers

14x8³

have a good day!! :)
hope this helps!!! :D
plz give brainliest!! XD

How many sets of 7 questions can be chosen from a file of 25 questions?

Answers

If all 25 questions are different,

When order of selection counts:
P(25,7)
=25!/(25-7)!
=15511210043330985984000000/6402373705728000
=2422728000

When order of selection does not count count:
C(25,7)
=25!/(7!*(25-7)!)
=15511210043330985984000000/(6402373705728000*5040)
=480700

What do you say when you meet a two headed dragon

Answers

hello hello is the answer please give me brainliest
Final answer:

In literature, when a character meets a two-headed dragon, their response may vary based on the story's context. Dragons often symbolize challenges; thus, a character may respond with caution and respect. This concept, however, is symbolic and represents various elements in different literatures.

Explanation:

In literature, the response to meeting a two-headed dragon can vary greatly depending on the context of the story and the characteristics assigned to the creature. Dragons, particularly two-headed ones, often symbolize challenges or adversities. So, one way to respond practically when you meet a two-headed dragon would be with caution and respect.

For example, in fantasy literature, a protagonist might say 'Well met, noble dragon. What do you require of me?' This politeness and respect can often turn a potentially dangerous encounter into an opportunity for dialogue. Remember, in literature, fantastic creatures like headed dragons are often symbolic, representing something else entirely in the context of the story.

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helppppppppppppppppppppppppppppppppp

Answers

Answer:
Third choice is the correct one

Explanation:
We are asked to use the u substitution. Therefore, we will assume that:
u = x^2

Substitute with u in the given expression as follows:
9x^4 - 2x^2 - 7 = 0
9u^2 - 2u - 7 = 0
(u-1)(9u+7) = 0
either u = 1
or u = -7/9

Now, u = x^2, this means that:
at u = 1:
x^2 = 1
x = ± √1 = ±1

at u = -7/9
x = ±i√7/9 (the i indicates the imaginary value)

Hope this helps :)

maxine hosted a dinner party at her favorite restaurant. she had to pay $12 per guest. the restaurant took $72 off the bill due to a mistake in the order. if the finale bill is $300, which equation will help the restaurant determine the number of guests at the dinner party

Answers

" $300 = $12g - $72 " .

a. In order for ΔABC to be similar to ΔDEF, what must be true about the angles? Be specific. b. If you know that ΔABC is similar to ΔDEF, and you know that m∠A = 52° and m∠E = 65°, what is m∠C? Explain how you arrived at your answer. c. What is the difference between two figures being similar and two figures being congruent?

Answers

i) if the triangles are similar then the corresponding angles are congruent. this means that the angles are of the same size.

ii)  If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
thus, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, thus to get m∠C; 
180- (52+65)
=  63 , therefore; m∠C= 63

iii) if two figures are similar they have the same shape and not necessarily the same size while if two figures are congruent then they have the same shape and size

Answer:

 If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,

though, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, though to get m∠C;  

180- (52+65)

=  63 , so then, m∠C= 63

Step-by-step explanation:

Write an equation for the translation of y = 4 x that has the given asymptotes. 15. x = 0, y = 3

Answers

y = 4/x +3

____
We are a bit mystified regarding the role of "15." in this question. We suspect it is an irrelevant question number.

factor the following polynomial completely 30y^6+25y^5-10y^4

Answers

5y^4 * (6y^2 + 5y-2)

PLZ HELP!!!!!!! Can a kite be formed by drawing a triangle and then reflecting one or more times? Explain.

Select one:
a. Yes. Draw any triangle ABC. Reflect this triangle across the perpendicular bisector of line AB, creating triangle A'B'C' for which A'=B and B'=A. By the definition of a reflection, sides A'C and B'C' are congruent. In addition, sides B'C and A'C' are congruent. The quadrilateral CC'B'A' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
b. Yes. Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
c. No. Since the reflection of a triangle is always another triangle, there is no way to create a quadrilateral using a triangle or its reflection.
d. No. It is not possible to reflect a triangle in such a way that the result is quadrilateral with any consecutive sides that are congruent.

Answers

The answer is (B).

Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.

Hi guys can you help me factor these two equations?

5x^2-13x-6

4x^4 – 28x^3 + 48x^2

please show your work on both of them, and thank you so much!

Answers

A) 5x^2-13x-6

 1. First, you must find the roots of the quadratic equation, by applying the quadratic formula, which is:

 x=-b√(b²-4ac)/2a

 2. The roots are:

 x1=3
 x2=-2/5

 3. Then, you have:

 5(x-3)(x+2/5)

 4. When you simplify, you obtain:

 (x-3)(5x+2)

 B) 4x^4-28x^3+48x^2 

 1. First, you must factor the common term, which is 4x^2. Then:

 4x^2(x^2-7x+12)

 2. Now, you must apply the quadratic formula to obtain the roots of the quadratic equation: x^2-7x+12. Then, you have:

 x1=4
 x2=3

 3. Finally, you obtain:

 4x^2(x-4)(x-3)

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.

△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.

Answers

Answer:

2/3 i got it right

Step-by-step explanation:

Final answer:

To find the scale factor between △ABC and △DEF, compare their corresponding side lengths and calculate the scale factor as 2.5 or 5/2.

Explanation:

To verify that two triangles △ABC and △DEF are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

Calculate the scale factor using the corresponding sides of the triangles: AB/DE = BC/EF = CA/FD.

Substitute the values: 10/25 = 16/40 = 20/50. Simplify to find the scale factor.

Therefore, the scale factor of △ABC to △DEF is 2.5 or 5/2.

help me plsss i really need did that but still dont get it

Answers

see attached picture for the answers:

A clock is constructed using a regular polygon with 60 sides. The polygon rotates everybody minute. How much has the polygon rotated after 7 minutes
•14 degrees
•21 degrees
•35 degrees
•42 degrees

Answers

360/60 = 6

6 minutes = 1 degree

6 X 7 = 42

42 degrees is your Answer

A rental company charges $75 a day and 20 cents a mile for renting a truck. michael rents a truck for 2 days, and his bill came to $238. how many miles did he drive?

Answers

75(2)+.20x=238
You then solve for x by multiplying 75 by 2 to get 150. Then subtract 150 from both sides of the equation, so this is what you get .20x=88. Finally divide by .20 on both sides to get x= 440

Answer:

440 miles.

Step-by-step explanation:

A rental company charges for rent a truck = $75 per day

and the charges per mile = 20 cents

100 cents = 1 dollar

20 cents =  [tex]\frac{20}{100}[/tex]

               = $0.20

Michael rents a truck for 2 days.

Let Michael drove the truck in 2 days = x miles

and his bill came to $238.

the equation will be : (75 × 2) + 0.20x = 238

150 + 0.20x = 238

0.20x = 238 - 150

0.20x = 88

x =  [tex]\frac{88}{0.20}[/tex]

x = 440

Michael drove the truck 440 miles in 2 days.

Which algebraic expression is equivalent to the expression below? (3x + 12) + 8x

A.
(3x + 8x) + 12
B.
(3x - 8x) + 12
C.
23x
D.
(3x + 12x) + 8

Answers

7(4x+4)+5x, 28x+28+5x, 33x+28. Answer: A.

30 POINTS!!!!! WILL MARK BRAINLIEST!

Karel and her family have just moved into a new neighborhood. Karel wants to earn money by baby-sitting for families with young children. She asked other students her age how much they charged for babysitting. The results are listed in the chart below.

LOOK AT CHART!

1. Suppose Karel wants to be the least expensive babysitter in the neighborhood. How much should she charge? This response will be graded for the correct numerical information.

2. Suppose Karel wants to charge the same hourly rate as most of the other baby-sitters. How much should she charge? This response will be graded for the correct numerical information.

3. Suppose Karel wants her hourly rate to be higher than the rate of half of other baby-sitters, but lower than the hourly rate of the rest of the babysitters. How much should she charge? This response will be graded for the correct numerical information.

4. In addition to the babysitting rates charged by others, what might Karel consider when she sets her rates? Respond in complete sentences, not only with calculations. Write as if you are verbally explaining what you are thinking.

Answers

1. She should charge less than $2.00.
Since the cheapest babysitter charges $2.00, Karel should charge less to be cheapest.

2. $3.25
Most of the other babysitters charge $3.25.

3. $2.50
The median of this set is $2.50, so she should be at the median of $2.50 for this question.

4. Karel should also consider the range of the hourly costs of the babysitters. For this, she would charge $1.00.
Final answer:

Karel should charge $7 per hour to be the least expensive babysitter, $10 per hour to charge the same rate as most other babysitters, and $12 per hour to have a higher rate than half of the other babysitters.

Explanation:

1. To be the least expensive babysitter, Karel should charge $7 per hour as it is the minimum rate.

2. To charge the same hourly rate as most other babysitters, Karel should charge $10 per hour as it is the mode or the most frequently occurring rate.

3. To have a higher rate than half of the other babysitters but lower than the rest, Karel should charge $12 per hour as it lies in the middle of the range from $7 to $15.

4. When setting her rates, Karel should consider factors like her experience, qualifications, the number of children she can handle, the neighborhood's average income, and any additional tasks she may be asked to perform.

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What makes a parallelogram, a square, a rhombus, a rectangle, a kite and a trapezoid unique?

Answers

Parallelogram: It is a quadrilateral where both pairs of opposite sides are parallel.

Square: All sides are congruent.

Rhombus: Is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal.

Rectangle: It is a quadrilateral which has two pairs of parallel and equal sides. It is also a parallelogram with its all four internal angles equal to right angles.

Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

Trapezoid: Has a pair of parallel sides. is an Isosceles trapezoid when both angles coming from a parallel side are equal, and the sides that aren't parallel are equal in length

ms.black paid $32 intrest at the rate of 8% on a loan of $200. For how long was the loan?

Answers

[tex]\bf~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$32\\ P=\textit{original amount deposited}\to& \$200\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ t=years \end{cases} \\\\\\ 32=200(0.08)t\implies \cfrac{32}{200(0.08)}=t[/tex]
Other Questions
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