Solve the system of linear equations in two variables by elimination or substitution.
2x + 4y = 4
2x - y=1

Answer:

The price of the cake is $24 and the price of the Pie is $15

Step-by-step explanation:

Given

Represent price of Cake with C and Price of Pie with P

[tex]C = 9 + P[/tex]

Cakes sold = 8

Pies sold = 14

[tex]Total = \$402[/tex]

Required

Determine C and P

To represent the cakes and pies sold, we have the following expression

[tex]8C + 14P = 402[/tex]

Substitute 9 + P for C

[tex]8(9+P) + 14P = 402[/tex]

Open the bracket

[tex]72 + 8P + 14P = 402[/tex]

Collect Like Terms

[tex]8P + 14P = 402 - 72[/tex]

[tex]22P= 330[/tex]

Divide both sides by 22

[tex]P = \frac{330}{22}[/tex]

[tex]P = 15[/tex]

Recall that

[tex]C = 9 + P[/tex]

[tex]C = 9 + 15[/tex]

[tex]C = 24[/tex]

Hence, the price of the cake is $24 and the price of the Pie is $15

Answer: 24x^6e^4/7ry^3

Step-by-step explanation:

Answer:

1357 sq.m

Step-by-step explanation:

50*32= 1600

27*9= 243

Area left = 1600 - 243 = 1357

Answer:

1

Step-by-step explanation:

la respuesta sería un por que si multiplicas el 2 y luego más tres te da un resultado como uno

Answer:

Step-by-step explanation:

Answer:

  plot two points and draw a line through them

Step-by-step explanation:

The graph is created for this the same way it is for any function: find some points on the graph, plot them, and draw an appropriate curve through them.

Since this is a linear equation, the graph is a straight line. Only two points are needed to allow you to plot the entire line.

For b=0, the point is (b, C) = (0, 4.95)

For b=5, the point is (b, C) = (5, 24.90)

The graph might look like the attached.

_____

For b=5, the equation gives ...

  C = 4.95 +3.99(5) = 4.95 +19.95 = 24.90

Answer:

Hence the positive numbers are 246, and 41

(246, 41)

Step-by-step explanation:

From the question,

Let the first positve number be [tex]x[/tex]

and the other number be [tex]y[/tex]

Hence,

[tex]x = 6y[/tex] ....... (1)

Also,

That is,

[tex]x - y =205[/tex] ........(2).

To solve for the two unknowns, substitute the value of [tex]x[/tex] in equation (1) into equation (2).

Since,

[tex]x = 6y[/tex]

Then

[tex]x - y =205[/tex] becomes

[tex](6y) - y =205\\[/tex]

Then,

[tex]6y - y = 205\\5y = 205\\[/tex]

Divide both sides by 5

[tex]\frac{5y}{5} = \frac{205}{5} \\ y = 41\\[/tex]

∴ the value of [tex]y[/tex] is 41

Now, substitute the value of y into equation (1) to find [tex]x[/tex]

Then,

[tex]x = 6y[/tex] becomes

[tex]x = 6(41)\\x = 246\\[/tex]

∴ the value of [tex]x[/tex] is 246

Hence the positive numbers are 246, and 41

(246, 41)

Answer:

50

Step-by-step explanation:

2(3^2+4^2)=

3^2/(3x3) = 9

4^2/(4x4) = 16

9+16=25        

so.... rewritten it is

2(25)= or 2 x 25= 50

Answer:

A

Step-by-step explanation:

oh steps are here!

Answer:

a) 5

Step-by-step explanation:

2x² - 6x + 2y² + 2y = 45

Complete the square and get it in the form (x-a)² + (y -b)² = r²

2x² - 6x +  2y² + 2y  = 45

Divide the equation by 2

x² - 3x + y² + y = 45/2

x² -  3x + ? + y² + y + ?? = 45/2

? -----> (x coefficient by 2)² = (3/2)² = 9/4

?? ----> (y coefficient by 2)² = (1/2)² = 1/4

Add (9/4) & (1/4) to both sides,

x² -3x +(9/4) + y² + y + (1/4) = (45/2)+ (9/4) + (1/4)

(x - 3/2)² + (y + 1/2)² = (90/4) + (9/4) + (1/4)

[tex](x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{90+9+1}{4}\\\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{100}{4}\\\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=25\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=5^{2}[/tex]

Radius  = 5

Answer:

W = -3

Step-by-step explanation:

Answer:

w = - 3

Step-by-step explanation:

Given

[tex]\frac{2}{5}[/tex] (w + 5) = [tex]\frac{4}{5}[/tex]

Multiply both sides by 5 to clear the fractions

2(w + 5) = 4 ( divide both sides by 2 )

w + 5 = 2 ( subtract 5 from both sides )

w = - 3

Answer:

5

Step-by-step explanation:

Whenever you multiply square roots that have the same number inside the radicand, you get the number under the radicand. For example, the square root of 4 squared will equal four. Similarly, you are simply squaring the square root of 5, so you should get 5 as your answer.

Answer:

x=7

Step-by-step explanation:

Start with the left side

-5x+7x+8

combine like terms

2x+8=1+3x

subtract 2x from both sides to get 8=1+x

subtract 1 from both sides to get 7

put the variable on the left

x=7

Hope this helps :-)

Answer:

The final answer is "$2387.85 and $2594.85".

Step-by-step explanation:

Given values:

The bank statement balance= $2,253.18

The checkbook balance = $2,324.34

outstanding check amounts= $105.50 and $158.10

transit amount= $605.27

account earnin(credits)= $68.51

service charge= $5.00

Adjusted Checkbook Balance =?

Adjusted  Statement Balance=?

Adjusted the Checkbook Balance:

checkbook balance = $2,324.34

[tex]\text{total checkbook balance = checkbook balance+ credits}\\[/tex]

                                      [tex]= \$ 2,324.34+ \$ 68.51\\\\= \$ 2392.85[/tex]

[tex]\text{ Adjust check book balance= total checkbook balance - servicec charge}[/tex]

                                         [tex]= \$2392.85 - \$5.00\\\\= \$ 2387.85[/tex]

Adjusted the Statement Balance:

bank statement balance= $2,253.18

[tex]\text{total Statement balance = bank Statement balance+ transit amount}\\[/tex]

                                      [tex]= \$ 2,253.18+ \$ 605.27\\\\= $ 2,858.45[/tex]

[tex]\text{outstanding check amounts = $105.50+ $158.10}[/tex]

                                           [tex]= \$263.60[/tex]

[tex]\text{ Adjust statement balance= total statement balance - outstanding check amount }[/tex]                                        [tex]= \$ 2,858.45 - \$263.60\\\\= $ 2,594.85[/tex]

Answer:

Another number is 28

Step-by-step explanation:

Given:

Number = 12

Another number = x

The tripled product = 120

Find:

Number

Computation:

3(x + 12) = 120

x + 12 = 40

x = 40 - 12

x = 28

Another number is 28

Answer:

11 units

Step-by-step explanation:

Length of side PS can be calculated using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] P(-2, 5) = (x_1, y_1) [/tex] (the coordinate of P is gotten from the graph)

[tex] S(9, 5) = (x_2, y_2) [/tex] (given)

[tex] PS = \sqrt{(9 - (-2))^2 + (5 - 5)^2} [/tex]

[tex] PS = \sqrt{(11)^2 + (0)^2} [/tex]

[tex] PS = \sqrt{121} = 11 units [/tex]

Answer:

The difference between the greatest and the smallest angle of the triangle PBQ is 98°.

Step-by-step explanation:

The question is:

In a triangle ABC, angle B measures 64 ° and angle C measures 72°. The inner bisector CD intersects the height BH and the bisector BM at P and Q respectively. Find the difference between the greatest and the smallest angle of the triangle PBQ.

Solution:

Consider the triangle ABC.

The measure of angle A is:

angle A + angle B + angle C = 180°

angle A = 180° - angle B - angle C

             = 180° - 72° - 64°

             = 44°  

It is provided that CD and BM are bisectors.

That:

angle BCP = angle PCH = 36°

angle CBQ = angle QBD = 32°

angle BHC = 90°

Compute the measure of angle HBC as follows:

angle HBC = 180° - angle BHC + angle BCH

                  = 180° - 90° - 72°

                  = 18°

Compute the measure of angle BPC as follows:

angle BPC = 180° - angle PCB + angle CBP

                  = 180° - 18° - 36°

                  = 126°

Then the measure of angle BPQ will be:

angle BPQ = 180° - angle BPC

                  = 180° - 126°

angle BPQ = 54°

Compute the measure of angle PBQ as follows:

angle PBQ = angle B - angle QBD - angle HBC

                  = 64° - 32° - 18°

angle PBQ = 14°

Compute the measure of angle BQP as follows:

angle BQP = 180° - angle PBQ - angle BPQ

                  = 180° - 14° - 54°  

angle BQP = 112°

So, the greatest and the smallest angle of the triangle PBQ are:

angle BQP = 112°

angle PBQ = 14°

Compute the difference:

d = angle BQP - angle PBQ

  = 112° - 14°

  = 98°

Thus, the difference between the greatest and the smallest angle of the triangle PBQ is 98°.

The simplified expression of 1.5g - 10 + 6.5g - 3 is 8g - 13.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

As per the given,

1.5g - 10 + 6.5g - 3

Bring near of likely terms,

1.5g + 6.5g - 10 - 3 = 8g - 13

Hence "The simplified expression of 1.5g - 10 + 6.5g - 3 is 8g - 13".

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ2

Answer:

  D.  miles/hour

Step-by-step explanation:

The units analysis tells you the units are ...

  [tex]\dfrac{\text{m}}{\text{s}}\times\dfrac{\text{s}}{\text{h}}\times\dfrac{\text{mi}}{\text{m}}=\boxed{\dfrac{mi}{h}}[/tex]

Units of meters and seconds cancel, leaving miles/hour.

Answer:

19

Step-by-step explanation

Let the sum of n terms of A.P. = Sn

Answer:

36°

Step-by-step explanation:

I’m assuming <AOC is a right angle.

6x-12+3x+30=90

9x+18=90

9x=90-18

9x=72

x=8

<AOB=6x-12=6*8-12=48-12=36°

Answer:

1. 37

2. 5

4. -22

5. -3

6. -10

7. 5

8. -7

Step-by-step explanation:

Given the functions:

[tex]f(n) = 8n - 3 \\g(n) = 3n - 10[/tex]

To find:

[tex]1. f(5) = ?\\2. g(5) =?\\4. g(-4) =?\\5. f(0) =?\\6. g(0)=?\\7. f(1) =?\\8. g(1) =?\\[/tex]

Solution:

Let us put the given values one by one in the functions [tex]f(n), g(n)[/tex] to find the various values required.

1. [tex]f(5)[/tex] means to replace the value of [tex]n[/tex] with 5 in [tex]f(n)[/tex]:

[tex]f(5) = 8\times 5 - 3 = \bold{37}[/tex]

2. [tex]g(5)[/tex] means to replace the value of [tex]n[/tex] with 5 in [tex]g(n)[/tex]:

[tex]g(5) = 3\times 5 - 10 = \bold{5}[/tex]

4. [tex]g(-4)[/tex] means to replace the value of [tex]n[/tex] with -4 in [tex]g(n)[/tex]:

[tex]g(-4) = 3\times -4 - 10 = \bold{-22}[/tex]

5. [tex]f(0)[/tex] means to replace the value of [tex]n[/tex] with 0 in [tex]f(n)[/tex]:

[tex]f(0) = 8\times 0 - 3 = \bold{-3}[/tex]

6. [tex]g(0)[/tex] means to replace the value of [tex]n[/tex] with 0 in [tex]g(n)[/tex]:

[tex]g(0) = 3\times 0 - 10 = \bold{-10}[/tex]

7. [tex]f(1)[/tex] means to replace the value of [tex]n[/tex] with 1 in [tex]f(n)[/tex]:

[tex]f(1) = 8\times 1 - 3 = \bold{5}[/tex]

8. [tex]g(1)[/tex] means to replace the value of [tex]n[/tex] with 1 in [tex]g(n)[/tex]:

[tex]g(1) = 3\times 1 - 10 = \bold{-7}[/tex]

Answer: When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. Example: a and e are corresponding angles. When the two lines are parallel Corresponding Angles are equal.

Answer:

V=378 inch³

Step-by-step explanation:

The package is in the shape of a cuboid. The volume of a cuboid is given by :

V = lbh

l=length, b=breadth and h=height

Area of base = 54 inch²

Height of box, h = 7 in

It means that, volume of the package is :

V = 54 × 7

V=378 inch³

So, the volume of the package is 378 inch³.

Answer:

X=1/5

Step-by-step explanation:

Please see the attachment.

Answer:

Maybe? kinda confused

Step-by-step explanation:

3/4x+1/4=2x

-3/4       -3/4

  x+1/4=1 1/4

      -1/4  -1/4

           x=1

Answer:

[tex] - 4x - 8[/tex]

Step-by-step explanation:

[tex] - 4(x + 2) = - 4x - 8[/tex]

Hope this helps ;) ❤❤❤

Answer: It's -4x- 8

Step-by-step explanation: Hope it hepls.

Answer:

x = -2

Step-by-step explanation:

-2x + 4x = -4 + 0

2x = -4

2x/2 = -4/2

x = -2

Hope this helps.

Answer:

The answer is -2

Step-by-step explanation:

You add the 4x to the -2x to get 2x, then you add -4 to zero to get -4. You are then left with 2x=-4 meaning that x would be -2

Answer:

What was it?

Step-by-step explanation:

Answer: 75+30 = 15 x 7

Step-by-step explanation:

The given expression is 75+30 (=105) which defines the sum of 75 and 30.

Prime factorization of 75 and 30 are as below:

75 = 5 x 5 x 3

30 = 5 x 3 x 2

GCD (75,30) = 5x 3 = 15  [Note: GCD = Greatest common divisor]

Consider 75+30 = (15 x 5) + (15 x 2)   [75 = 15 x 5 and 30= 15 x 2]

=  15 (5+2)   [taking 15 as common ]

= 15 x (7)

(=105)

So,  75+30 which is sum of the numbers and it is expressed as 15 x 7 which  a product of their GCF.

Ur solution is in the attachment.

Answer:

d)  ? = 5

e)   ? = -2x

f)    ? = x

Step-by-step explanation:

d) 20 = (4)(?)

    20/4 = ?

     5 = ?

    Check:

    20 = 4*5

e)   -14x = (7)(?)

     -14x/7 = ?

      -2x = ?

      Check:

      -14x = 7*-2x

f)    x³ =x² (?)

      x³/x² = ?

      x³⁻² = ?

      x¹ = ?

       x = ?

      Check:

     x³ = (x²)(x)      

Answer:

20%

Step-by-step explanation:

2.5 min =(60×2.5)sec=150 sec

30sec to 150sec=30×100/150=20%

Answer:

20 %

Step-by-step explanation:

2.5 mins = 150 sec

30 sec of 150 sec in % = 30/150 × 100

= 20 %