Mathematics High School

Solve the simultaneous equations:

3a-2b=14
4a+3b=13

Answers

Answer 1

Answer:

Step-by-step explanation:

3a-2b=14 multiply by 3

9a - 6b = 42 (1)

4a+3b=13 multiply by 2

8a +6b = 26 (2)

sum up (1) and (2)

17a = 68

a =4

b=-1

Answer 2

Answer:

a = 4 b = -1

Step-by-step explanation:

13 = 4a - 3b  (1)

14 = 3a + 2b  (2)

(1) x 2

(2) x 3

26 = 8a - 6b   (3)

42 = 9a + 6b   (4)

(3) + (4)

68 = 17a

68/17 = 17a/17

a = 4

Substitute back in to original equation

14 = 3(4) - 2b

14 = 12 - 2b

14 - 12 = 12 -12 - 2b

2 = -2b

Divide by -2 both sides

b = -1

Check

3(4) - 2(-1)

12 + 2 = 14

Related Questions

An ice chest contains 7 cans of apple​ juice, 6 cans of grape​ juice, 6 cans of orange​ juice, and 4 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of mango juice.

Answers

Answer:

4/1771

Step-by-step explanation:

Step one:

given

sample space

7 cans of apple​ juice,

6 cans of grape​ juice,

6 cans of orange​ juice, and

4 cans of mango juice

Sample size= (7+6+6+4)

                       = 23

Step two:

Required

The probability of randomly selecting three cans of mango juice in succession

Note: we are selecting without replacement

let the probability of selecting three cans of mango juice be

the first selection is= 4/23

The second = 3/22

the third= 2/21

[tex]P(x)= 4/23*3/22*2/21[/tex]

[tex]P(x)= \frac{4*3*2}{23*22*21} \\\\P(x)= \frac{4}{23*11*7}\\\\P(x)= \frac{4}{1771}[/tex]

A garden with dimensions 50 feet by 70 feet is surrounded by a walkway of
uniform width. The total area of the walkway is greater than 350 square feet but is less than 500 square feet. Find the possible widths of the walkway.

Answers

bulok man ko og math guys. wakoy ika tabang nimo

Please help me
Which one do I choose for each one

Answers

For the first one i would choose the second answer, Not both.

what is the answer for 7(x+2) = 6(x+1)

Answers

Answer:

x= -8

Step-by-step explanation:

Simple math

Answer: x = -8

7(x + 2) = 6(x + 1)

⇔ 7x + 14 = 6x + 6

⇔ 7x - 6x = 6 - 14

⇔ x = -8

Step-by-step explanation:

A manufacturer is considering building a new and better mousetrap. She estimates the probability that the new mousetrap will be successful is . If it is successful, it would be able to make $120,000. Of course, she would make nothing if it were unsuccessful. The development costs for the mousetrap are $98,000. What is the expected value?

Answers

Answer:

$22,000 if successful

Step-by-step explanation:

So if She is able to make $120,000 on the trap, but it cost$98,000, just subtract $98,000 from $120,000 and you get $22,000 if she is successful she can expect that much

Answer:

22,000

Step-by-step explanation:

Please help meeee

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

Answers

Answer:

<1=33, <2=90, <3=57

Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

When parallel lines are cut by a transversal and you have one acute angle and one obtuse angle, those two angles will always add up to

Answers

Answer:

180 maybe ...........

180 degrees
A straight line is 180 so that’s why

What is the answer to −9x−2 when x=−4.

Answers

Answer:

-72

Step-by-step explanation:

Answer:

I believe the answer is 34

Step-by-step explanation:

(-9 times -4 = 36)

36-2=34

Which is the equation of the parabola that
opens to the right, has a focus at (3.0), and
has a directrix at x=-3?

Answers

Answer:

The equation of the parabola will be:

[tex]\:y^2=12x[/tex]

Step-by-step explanation:

The vertex  (h, k)  is halfway between the directrix and focus.

Find the  x  coordinate of the vertex using the formula

x = (x-coordinate of focus + directrix)/2

 = (3-3)/2

 = 0/2

 =0

The  y -coordinate will be the same as the y-coordinate of the focus.

so the vertex will be: (0, 0)

Finding the distance from the focus to the vertex

The distance from the focus to the vertex and from the vertex to the directrix is |p|.

Subtract the  x  coordinate of the vertex from the x -coordinate of the focus to find  p .

[tex]p=3-0[/tex]

[tex]p=3[/tex]

Substitute in the known values for the variables into the equation

[tex]\left(y-k\right)^2=4p\left(x-h\right)[/tex]

[tex]\left(y-0\right)^2=4\left(3\right)\left(x-0\right)[/tex]

[tex]\:y^2=12x[/tex]

Therefore, the equation of the parabola will be:

[tex]\:y^2=12x[/tex]

Question 5(Multiple Choice Worth 4 points) (04.07A) A line passes through (2, 8) and (4, 12). Which equation best represents the line?
y = 1 over 2x + 6
y = 2x + 7
y = 2x + 4
y = 1 over 2x + 10

Answers

Answer:

y- 2x + 4

Step-by-step explanation:

Answer:

y- 2x + 4

Step-by-step explanation:

What is the slope for line m

Answers

Answer:

1

Step-by-step explanation:

Find the perimeter of LMNO. (Hint: Solve for x and y first.)

Answers

6x-7=2x+9

4x=16

x=4

12=y^2+3

9=y^2

3=y -3=y

Okay?

Step-by-step explanation:

6x -7 = 2x +9

4 x = 16

X= 4

y2 +3 =12

y2 = 9

y2 =3

two side is 17 ,12

Perimeter =( 17+12 )x 2 = 58

Jasmin's dog weighs 55 pounds. Her vet told her that a healthy weight for her dog would be less than or equal to 41 pounds.
Jasmin's dog can lose an average of 0.5 pounds every week. Write the solution to an inequality that describes all possible number of
weeks 2 for which her dog can be at a healthy weight.

Answers

Answer:

55-0.5x ≤ 41 (x will represent the weeks)

Step-by-step explanation:

i made x represent the weeks and we know that jasmin's dog can lose about 0.5 pound a week. and the base is 55 lbs since that is what jasmin's dog weighs. 55 minus all the weight that jasmin's dog will lose in a certain amount of weeks is the first part. then we know jasmin's dog has to be less than or equal to 41 lbs. so put that there with the less than or equal to sign.

which ordered pair is a solution to the equation y=3x-10 is it (11,7) (5,15) or (-2,-16)​

Answers

Answer:

(-2,-16)

Step-by-step explanation:

Cause

y=3(-2)-10

y=-16

there for it the solution to the equation

A nurse has an annual income of $52, 175. The income tax that she must pay is 9%. How much does she have to pay in taxes in dollars and cents?

Answers

ответ на картинке !!!!

What are all the zeroes of the function (4x^2+9)(4x^2-9)=0

Answers

Answer:

x=1.5,-1.5

Step-by-step explanation:

16x^4=81

x^4=5.0625

x=[tex]\sqrt[4\\]{5.0625}[/tex] => x = 1.5,-1.5

Answer:

3/2 and 3/2i

Step-by-step explanation:

Got it correct on edge

What is your favorite place to get wings and what type of wings do you like?​

Answers

american deli and honey hot

The value of x In the proportion
1/2:2/3 = 3/4x Is

A.1
B. 1/4
C.17/9
D.4/9​

Answers

Answer:

A

Step-by-step explanation:

[tex]\frac{1}{2} : \frac{2}{3} =\frac{3}{4} x\\\\\frac{1}{2} * \frac{3}{2} =\frac{3}{4} x\\\\\frac{3}{4}= \frac{3}{4} x\\\\\frac{3}{4}*\frac{4}{3}=x\\\\\frac{12}{12}=x\\\\x=1[/tex]

Bart budgeted $285.75 each month for utilities. His utility bills this month were $130.50 for electric, and $240 for gas. How much over budget is he? *
!!

Answers

Answer:

$84.75 over budget

Step-by-step explanation:

Barts' budget is 285.75

Bills: 240 + 130.50 = $370.50

(subract by his budget)

370.5 - 285.75 = $84.74

:)

5. Lee uses 6 boxes to pack 24 items. Yesterday, he packed 288 items. How many boxes did Lee use yesterday? (HINT-- Comparing two different units-- SET UP Proportion; Cross Multiply and then Divide) *

Answers

Answer:

72

Step-by-step explanation:

24/6=4

288/4=72

Nel salone di un rivenditore di automobili, il 20% delle macchine sono SUV, il 35% sono monovolume e 27 sono berline. Calcola il numero di SUV.

Answers

Answer: 12

Step-by-step explanation: 27 sedanes son 45% (de 100 - (35 + 25)) es necesario hacer 27/45 para averiguar la tasa unitaria, multiplicar la tasa unitaria por porcentaje para averiguar la respuesta

A banner company sells 5-foot banners to retailers for x dollars. The St. James Sign Shop marks them up 90%. Express the retail price at the St. James store algebraically.

Answers

Answer:

$1.9x

Step-by-step explanation:

Given that :

Cost of banner = x dollars

Markup percentage at st. James store = 90%

Retail price at st. James store :

Initial cost + markup

Cost of banner + 90% of cost

x + 0.9x

= 1.9x

Hence, retail.price at st. James store is $1.9x

The perimeter is 36.what dose x have to be

Answers

The answer would be 4

A rectangular cartoon is 80 cm x60 cm x40 cm .then, how many packets of shops can each of 10 cm x 5cm x 4 cm be kept inside the cartoon
​

Answers

Answer:

8

Step-by-step explanation:

10 x 5 x 4

Multiply everything by 8

80 x 40 x 32

You can't go over that because 80 is at it's limit.

8

Explicación paso a paso:

10 x 5 x 4

Multiplica todo por 8

80 x 40 x 32

No se puede pasar de eso porque 80 está en su límite.

espero te sirva

I need help on number 5 plz

Answers

Answer:

x5-8x+3y i don't sure for my answer hihihi understand my answer heheh sorry if I don't help you

Using the protractor, find the angle measure.

Answers

Which angle i need to see

Write the equation of the line that passes through the point (-4, -9) and has a slope of 1/2​

Answers

Y = 1/2x + b
Plug in the point :)
-9 = 1/2(-4) + b
-9 = -2 + b
b = -7
Y = 1/2 -7

Answer:

The answer is y=1/2x-7

Step-by-step explanation:

y-y=m(x-x¹)

y-(-9)=1/2(x-(-4)

y+9=1/2x+2

-9 -9

y=1/2x-7

A pair of shoes cost $12 for Nike to make. If Nike marks up the price 430%, what is the price of the mark-up?

Answers

Answer:

The price of the mark-up is $51.60

Step-by-step explanation:

What is the answer to this problem?

Answers

Answer:

x = 4.

Step-by-step explanation:

These are exterior  alternate angles which are congruent.

So 21x + 6 = 90

21x = 84

x = 4.

simplify -13.5a+34.12b+65.5-32.5b-35.8a

Answers

Answer:-49.3a-1.62b+65.5

Step-by-step explanation:

Combine Like terms:

-13.5a-35.8a=-49.3a

-34.12b+32.5b=-1.62b

Answer: -49.3a-1.62b+65.5

Answer:

16.2a + 1.62b

Step-by-step explanation:

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