Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has.

[tex]\dfrac 56 x + \dfrac25 y - \dfrac14 x + \dfrac3{10} y[/tex]

First, combine like terms:

[tex]\left(\dfrac 56 - \dfrac14\right) x + \left(\dfrac25 + \dfrac3{10}\right)y[/tex]

Now just simplify the coefficients of x and y. We do this by converting each pair of fractions to ones with a common denominator. Then we can combine them easily.

[tex]\dfrac56 - \dfrac14 = \dfrac56\cdot\dfrac22 - \dfrac14\cdot\dfrac33 = \dfrac{5\cdot2}{6\cdot2} - \dfrac{1\cdot3}{4\cdot3} = \dfrac{10}{12} - \dfrac3{12} = \dfrac{10-3}{12} = \dfrac7{12}[/tex]

[tex]\dfrac25 + \dfrac3{10} = \dfrac25\cdot\dfrac22 + \dfrac3{10} = \dfrac{2\cdot2}{5\cdot2} + \dfrac3{10} = \dfrac4{10} + \dfrac3{10} = \dfrac{4+3}{10} = \dfrac7{10}[/tex]

So the simplified expression would be

[tex]\dfrac7{12} x + \dfrac7{10} y[/tex]

Answer:

x +2y = 2 ...... 1

7x + 10y = 2 ..... 2

x = 2 - 2y ..... 3

substitute 3 in 2

7(2 - 2y) + 10y = 2

14 - 14y + 10y = 2

14 - 4y = 2

- 4y = 2 - 14

- 4y = - 12

divide by - 4 on both sides

y = 3

substitute the value of y in 3

× = 2 - 2(3)

x = - 4

(x ; y )

(- 4 ; 3)

Answer:

Step-by-step explanation:

Let "n" be the first number

n + (n + 2) + (n + 4) + (n + 6) = 36

                                4n + 12 = 36

                                       4n = 24

                                         n = 6

as "n" itself is even, it qualifies

6 + 8 + 10 + 12 = 36

Answer:

11, 12, 13

Step-by-step explanation:

let's put the first number of the three as a:

a; a+1; a+2

The sum of the first and the twice second is 35 means:

a + 2(a+1) = 35

a + 2a + 2 = 35

3a = 33

a=11

now that we know a, we just need to add 1 and 2 as they are consecutive:

11, 12, 13

Answer:

D

Step-by-step explanation:

Pluck in the values, we have:

4.5/2.4 - 6 = 20/2 = 10

Answer:

The bottom right is a linear equation.

Step-by-step explanation:

Answer:

right side down one

Step-by-step explanation:

as you know linear means supplementary having 180 °

Answer:

answer is below

Step-by-step explanation:

ok so i kinda want u to learn so im just gonna tell you how to do them!

for the first set, what you do is put (y2-y1)/(x2-x1). for example, (16-6)/(3-18) is the slope.

for the second set, every problem is in y=mx+b form, where m is the slope. so for example in 37 the slope is 1/2

for the third set, use midpoint formula. x is (x1+x2)/2, and y is (y1+y2)/2

hope this helps!

Answer:

  m∠C = 72°

Step-by-step explanation:

The sum of the angles in the triangle is 180°.

  A +B +C = 180°

  (2x +11)° +(3x -8)° +(4x -12)° = 180°

  9x = 189 . . . . . . . . divide by °, add 9

  x = 21 . . . . . . . . . divide by 9

Angle C is ...

  (4x -12)° = (4(21) -12)° = 72° . . . . angle C

_____

Additional comment

Angle A is 53°; angle B is 55°.

Answer:

x=8

Step-by-step explanation:

5x+10+130=180

5x+140=180

5x=40

x=8

Step-by-step explanation:

6y +4x=-12

6y=-4x-12

y= -4/6x -12/6

y= -2/3x -2

Answer:

Step-by-step explanation:

I believe it’s yes

Answer:

Yes

Step-by-step explanation:

A function has only one output value for each input value.

Answer:

∠ B ≅ ∠ E

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent

ABC ≅ DEF

The corresponding angles are B and E

Answer:

The answer is [tex]\angle B\cong \angle E[/tex]

Step-by-step explanation:

Given that

[tex]\Delta ABC \cong \Delta DE[/tex][tex]F[/tex]

Hence corresponding angles are congruent

[tex]\angle B\cong \angle E[/tex]

Answer:

A: 2400

B: 600

C: 1800

Step-by-step explanation:

A= x+3x=4x

C = x+2x= 3x

4x+x+3x = 4800

8x= 4800

x= 600

share of A= 2400$

share of B= 600$

share of C= 1800$

Answer:

The answer is false

Step-by-step explanation:

Unlike any symmetric distribution, the chi-square distribution is non-symmetric. Accordingly, this statement cannot be trusted—b.

As chi-square does not depend on all degrees of freedom, it is a non-symmetric distribution that excludes symmetric data.

[tex]Hiya![/tex]

Sokka is here to help!!

Here's a explanation!

[tex]26.52[/tex] × [tex]90.7 = 2405.364[/tex]

[tex]OR:[/tex]

Here's a paper I wrote of your answer.

Sorry, if my picture is blurry.

Hopefully, this helps you!!

[tex]Sokka[/tex]

Answer:

23

Step-by-step explanation:

let the number be n then twice the number is 2n and 4 times the number is 4n

Then

2n = 4n - 46 ( subtract 4n from both sides )

- 2n = - 46 ( divide both sides by - 2 )

n = 23

The number is 23

Answer:

34.5

Step-by-step explanation:

23 x 2 = 46 less than 4 times = 11.5

46 - 11.5 = 34.5

Answer:

i think 4x+3y = -24 is answer

Answer:

1/1

Step-by-step explanation:

Answer:

Option B is the correct answer

Step-by-step explanation:

Given that

[tex]\sin \theta =\frac{-1}{\sqrt{2}}[/tex]

Value of sine function is negative in third and fourth quadrant

Hence this is true for

[tex]\theta =225^{0},315^{0}[/tex]

Option B is the correct answer

14

This should be right!

Answer:

  45°, 45°, 90°

Step-by-step explanation:

You have described an isosceles right triangle. The angle measures are ...

  45°, 45°, 90°

_____

If x is the smaller angle measure, then the total of angles is ...

  x + x + 2x = 180°

  x = 180°/4 = 45°

Answer:easy it’s 8

Step-by-step explanation:I just did that same ixl/quiz!

Answer:

-12.5

Step-by-step explanation:

-7x+8+11x=-42

-7x+11x=-42-8

4x=-50

x=-12.5

Hope this helped! :)

Hey There!

Question:-

[tex] \sf \: - 7x+8+11x= - 42[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto - 7x + 8 + 11x = - 42[/tex]

Combine Like terms:-

[tex]\sf \longmapsto \: ( - 7x+11x)+(8)= - 42[/tex]

On Simplification :-

[tex]\sf \longmapsto \: 4x +8 = - 42[/tex]

Subtract 8 from both sides:-

[tex]\sf \longmapsto \: 4x+8 - 8= - 42 - 8[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 4x + 0 = - 42 - 8[/tex]

Note that (-) and (-) equals to (+).

[tex]\sf \longmapsto \: 4x = - 50[/tex]

Divide both sides by 4:-

[tex]\sf \longmapsto \: \dfrac{4x}{4} = \dfrac{ - 50}{4} [/tex]

On Simplification:-

[tex]\sf \longmapsto \: \dfrac{ \cancel2x}{ \cancel2} = \dfrac{ \cancel{- 50}}{ \cancel4} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{ - 25}{2} [/tex]

Or in Decimal :-

[tex]\sf \longmapsto \: x = -12.5[/tex]

______________________________________

Henceforth, the value of x is :-

[tex]\boxed{\huge \red{x = - \dfrac{25}{2}}} [/tex]

In Decimal:-

[tex] \boxed{\huge\red{ x = -12.5}}[/tex]

________________________________

Please let me know if you have any questions.

~MisterBrian

Answer:

You can download app to help you I hope you find your answer

Answer:

75 m, 96 m

Step-by-step explanation:

a. Area = length x width

7050 = 94 x width

7050/94 = w

75 m is width

b. perimeter = 2L + 2W

356 = 2L + 2(82)

356 = 2L + 164

192 = 2L

96 m = L

Answer:

B. [tex]\frac{\pi }{4} Rad>30^{0}[/tex]

Step-by-step explanation:

[tex]\frac{\pi }{4} Rad=(180/4)^{0} =45^{0}[/tex]

Hope this helps

Answer:

y=1.09x

Step-by-step explanation:

The rates of change of points earned by both players tell us that;

Player A gains more point than Player B does for each correct answer in this round.

We are told that x is the number of

number ofquestions answered correctly and y is the score.

Now, for player B;

For 1 correct answer, he got a score of 4

For 2 correct answers, he got a score of 5

For 3 correct answers, he got a score of 6

For 4 correct answers, he got a score of 7

This means that rate of change of Player B is;

3 points for every extra question answered correctly. .

Now, the formula for player A's points is;

y = 4x + 3

Rate of change of points here is gotten by finding the derivative. Thus;

dy/dx = 4

This means player A earns 4 points for every extra question answered correctly.

In conclusion, it mean that Player A gains more point than Player B does for each correct answer in this round.

Read more on slope intercept form of equation at; https://brainly.com/question/19249035