Which expression is equivalent to the expression 5(3x+4-x)

Answer:

[tex]5[/tex]

First Method:

This isn't the only method, but it seems the least likely to result in an incorrect answer.

If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)(-2)+7(1)^2-3(1)^2(-2)+3(-2)^2(1)-2(1)^2-2(1)(-2)+4(1)^2(-2)-2(-2)^2(1)[/tex]

[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]

[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]

[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)[/tex]

[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2+4+4(-2)-2(4)\\-6+7+6+12-2+4-8-2(4)\\-6+7+6+12-2+4-8-8\\[/tex]

[tex]-6+7+6+12-2+4-8-8\\7+4+6+12-6-2-8-8\\11+18-8-16\\29-24\\5[/tex]

Our final answer is [tex]5[/tex].

Here's another method:

If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\[/tex]

[tex]3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\3y+7-3y+3y^2-2-2y+4y-2y^2\\3y^2-2y^2+3y-3y-2y+4y+5\\y^2+2y+5[/tex]

[tex]y^2+2y+5\\(-2)^2+2(-2)+5\\4-4+5\\5[/tex]

To find the number of 2 kg and 4 kg sugar bags in the shipment, we use a system of equations. By setting x as the number of 2 kg bags and y as the number of 4 kg bags, we determine that there are 750 bags of 2 kg sugar and 350 bags of 4 kg sugar.

To solve the problem of determining how many 2 kg bags and 4 kg bags of sugar are in the shipment of 1100 bags with a total mass of 2900 kg, we need to set up a system of equations and solve for the variables representing the quantities of each type of bag. Let's denote x as the number of 2 kg bags and y as the number of 4 kg bags.

The first equation represents the total number of bags:
x + y = 1100.

The second equation represents the total weight of the bags:
2x + 4y = 2900.

We can solve these equations using substitution or elimination methods. For simplicity, let's multiply the first equation by 2 and subtract it from the second equation:

Now that we know y, we can substitute it back into the first equation to find x:

Therefore, there are 750 bags of 2 kg sugar and 350 bags of 4 kg sugar in the shipment.

Answer:

y=1/2x -2. Hope this helps!

Answer:

x=8

Step-by-step explanation:

First you want to distribute -6 to (2x+6) which you will then get -12x-36=-132. Now you want to get x by itself by getting rid of -36, so add 36 on both sides of the equation to get -12x=-96. Isolate x by dividing by -12 on both sides of the equation which will leave you with the equation x=8

Answer:

[tex]5 \sqrt{5} [/tex]

Step-by-step explanation:

We want to find the distance between (-8,-4) and (2,-9).

We use the distance formula:

[tex]d = \sqrt{ {(x_2-x_1)^2} +(y_2-y_1)^2 } [/tex]

We substitute the coordinates to get:

[tex]d = \sqrt{ {(2- - 8)^2} +( - 9 - - 4)^2 } [/tex]

We simplify to obtain:

[tex]d = \sqrt{ {(2 + 8)^2}+( - 9 + 4)^2 } [/tex]

Add the numbers within the parenthesis to get:

[tex]d = \sqrt{ {(10)^2}+( -5)^2 } [/tex]

Find the squares of the numbers under the radical

[tex]d = \sqrt{ {100}+25} [/tex]

[tex]d = \sqrt{125} = 5 \sqrt{5} [/tex]

Answer:

x = 3

Step-by-step explanation:

Given

3x = x + 6 ( subtract x from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

Step-by-step explanation:

3x = x + 6.....subtract x from both sides

3x - x = x - x + 6

2x = 6 ...divide both sides by 2

(2/2)x = 6/2

1x = 6/2

x = 3 <=====

Dot bikes 7m+10 miles this week.

Step-by-step explanation:

Distance of one loop = m miles

Distance of 2 loops = 2m

Distance of 3 loops = 3m

Distance covered on Sunday = 10 miles

Total distance = Monday + Wednesday + Friday + Sunday

Total distance = 2 loops + 2 loops + 3 loops + 10 miles

Total distance = 2m + 2m + 3m + 10

Total distance = (7m+10) miles

Dot bikes 7m+10 miles this week.

Keywords: addition, distance

Learn more about distance at:

#LearnwithBrainly

Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)

Step-by-step explanation:

In order to find the functions whose graph includes the point we will put the point in the functions one by one

So,

A. y=2x

Putting x = 16 and y = 4

[tex]4 = 2(16)\\4\neq 32[/tex]

B. y=x^2

Putting x= 16 and y=4

[tex]4 = (16)^2\\4 \neq 256[/tex]

C. y=x+12

Putting x= 16 and y=4

[tex]4 = 16+12\\4 \neq 28[/tex]

D. y=x−12

Putting x= 16 and y=4

[tex]4 = 16-12\\4 = 4[/tex]

E. y=1/4x

Putting x= 16 and y=4

[tex]4 = \frac{1}{4} * 16\\4 = 4[/tex]

Hence,

Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)

Keywords: Functions, graphing

Learn more about functions at:

#learnewithBrainly

Answer:

Step-by-step explanation:

The answers are D and E

Amount spent by the wife is $70

Step-by-step explanation:

Given:

the total amount  = $200

Amount spent on Lunch = $15.00

They buy three items at $20.00 each

The wife spends twice what her husband spends

They return home with $20.00 cash.

To Find:

Amount spent by the wife  = ?

Solution:

Initially after spending $15.00 on lunch they balance cash with them will be

200 - 15.00 = $185

Then they are buy 3 items each of which costs $20.00

So the balance after buying the 3 items will be

= 200 - 3(20)

= 185- 60.00

= $125

Now the wife is spending twice what her husband spends

so let the amount spent be the husband be x then the amount spent by the wife will be 2x.

Now  after spending 2x+x amount they are  left with $20.00

that is

125 -2x+x  = 20

125 -3x = 20

125 -20 = 3x

105 = 3x

[tex]x = \frac{105}{3}[/tex]

x = 35

So the wife will be spending 2(35) = $70

Answer: 10 Acme and 15 Zenith.

She can buy 10 Acme and 15 Zenith calculators.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A math teacher wants to buy 25 new scientific calculators for the classroom.

Acme and Zenith makes two different type of calculators.

Acme calculators cost $15 each.

Zenith calculators cost $12 each.

The math teacher has $330 to spend.

Let x represents the number Acme calculators and y represents Zenith.

Now, we have the system of equations,

x + y = 25

So, y = 25 - x

And 15x + 12y = 330

Substituting the value of y,

15x + 300 - 12x = 330

3x = 330 - 300

3x = 30

x = 10

So, y = 15

Therefore, 10 Acme and 15 Zenith calculators.

To learn more about the system of equation;

brainly.com/question/13729904

#SPJ2

Answer:

Nonrigid

Segment lents are not

Step-by-step explanation:

Answer:

answer in picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

it seems to me that if he wants the same rate of acceleration as the first trip, then he would need the same amount of soil as the first trip.

Therefore, he should reduce the amount of soil by one half and apply the same force. <====

Because the first time it was half full.....and since the second trip was all the way full, if he reduced it by one half, it would contain the same amount as the first trip....so he can then get the same rate of acceleration.

Answer:

A.

Step-by-step explanation:

According to Newton's second law of motion, an object with a larger mass requires more force to accelerate it at a certain rate than an object with less mass. This means that an object with a larger mass requires more force to accelerate.

To move the wheelbarrow at the same rate of acceleration for the second trip, the amount of soil must be the same as in the first trip. Since the gardener first filled only one-half of the wheelbarrow with soil, the gardener must reduce the amount of soil by one-half and apply the same amount of force.

Answer:

The co - ordinates of another end point is

(x,y) = (3, 12)

Step-by-step explanation:

step :-

mid point formula:-

Let [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] be any two end points

Mid point of two given points are

[tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]

let (x,y ) be the another end point

given one end point is (5,-6)

now by using mid-point formula , we get

[tex](\frac{x+5}{2} , \frac{y-6}{2} )[/tex]  this is equating to given mid-point is M(4,3)

now [tex](\frac{x+5}{2} , \frac{y-6}{2} )=(4,3)[/tex]

simplify , we get

[tex]\frac{x+5}{2} =4 and \frac{y-6}{2} =3[/tex]

cross multiplication and simplify

[tex]x+5 = 8 and y-6=6[/tex]

x = 3 and y = 12

The another point is (x,y) = (3,12)

Answer:

4y+14m+1

Step-by-step explanation:

Remove the brackets

-3y-5+5m+7y+6+9m

Rearrange the terms

7y-3y+5m+9m+6-5

Adding like terms

4y+14m+1

Answer:

Step-by-step explanation:

a - 7 = 3(b + 2)

a - 7 = 3b + 6

a - 7 - 6 = 3b

a - 13 = 3b

(a - 13) / 3 = b <====

Answer:

-13-1/4 b

Step-by-step explanation:

b is on the outside of the fraction not with the four.

-13-\frac{1}{4b}

Answer:

7x + 14y

Step-by-step explanation:

7(x + 2y)

Multiply 7 by the values inside the parenthesis (x + 2y)

7x + 14y

Hope this helps :)

Answer:

Balanced chemical equations only show formulae, not names. A balancing number, written in normal script, multiplies all the atoms in the substance next to it.

Good evening ,

Answer:

Step-by-step explanation:

From the table :

f(x) = g(x) only when x = -1 then -1 is the only solution

f(-1) = 9 = g(-1)

note : the equation could have some other solutions not shown in the table

:)

Answer:

The  length of the rectangle is[tex](4+7y^3)[/tex] and its  width is[tex]3y^2[/tex]

Step-by-step explanation:

Given:

The Area of the rectangle =[tex]12y^2+21y^5[/tex].

Width is the greatest common factor of  [tex]12y^2[/tex] and[tex]21y^5[/tex]

To Find:

The length and width of the rectangle = ?

Solution:

Step 1: Finding the greatest common factor of [tex]12y^2[/tex]and[tex]21y^5[/tex]

[tex]12 y^2[/tex]= 2 x 3 x 3 x y x y

[tex]21y^5[/tex] = 3 x 7 x y x y x y x y x y

Thus the greatest common factor is [tex]3y^2[/tex] which is the width

Step 2: Finding the length and width

The area of the rectangle  = length x breath

width x length=  [tex]12y^2+21y^5.[/tex]

Taking[tex]3y^2[/tex] commonly from each term, we get

width x length= [tex](3y^2)(4 + 7y^3)[/tex]

Answer:

Option D.

8.05 inches

Step-by-step explanation:

Let

x ----> Length of Foot in inches

y ----> Length of Forearm in inches

we have

[tex]y=1.11x-0.83[/tex]

For x=8 in

substitute the value of x in the linear equation and solve for y

[tex]y=1.11(8)-0.83=8.05\ in[/tex]

Answer:

[tex]A'(-3,0),B'(8,3),C'(2,-9)[/tex]

Step-by-step explanation:

we know that

the triangle is translated 4 units right and 6 units down

so

The rule for the translation is

[tex](x,y) -----> (x+4,y-6)[/tex]

Applying the rule for the translation find the image of each vertex

1) [tex]A(-7,6) -----> A'(-7+4,6-6)[/tex]

[tex]A(-7,6) -----> A'(-3,0)[/tex]

2) [tex]B(4,9) -----> B'(4+4,9-6)[/tex]

[tex]B(4,9) -----> B'(8,3)[/tex]

3) [tex]C(-2,-3) -----> C'(-2+4,-3-6)[/tex]

[tex]C(-2,-3) -----> C'(2,-9)[/tex]

Answer:

i would say wait abought 50 mins

Step-by-step explanation:

i dont know whow to explain i might be wrong but its some whaere around 50 mins irl

Using Newton's Law of Cooling with a cooling constant of 0.035, it will take approximately 42.53 minutes for the brownies to cool from 400 degrees F to 160 degrees F.

To estimate the time it would take for brownies to cool from 400 degrees F to 160 degrees F using Newton's Law of Cooling, we can use the equation [tex]T(t) = T_s + (T_0 - T_s)e^{(-kt)[/tex], where T(t) is the temperature of the object at time t, T_s is the surrounding temperature, T_0 is the initial temperature of the object, and k is the cooling constant (0.035 in this case).

First, set T(t) = 160 degrees F (the desired temperature), T_s = 70 degrees F (room temperature), and T_0 = 400 degrees F (initial temperature of brownies). Plug in the values into the equation: 160 = 70 + (400 - 70)e^(-0.035t).

Simplify and solve for t. Subtract 70 from both sides: 90 = 330e^(-0.035t). Divide both sides by 330: 90/330 = e^(-0.035t), which simplifies to 0.2727 ≈ e^(-0.035t).

Take the natural logarithm of both sides to solve for t: ln(0.2727) = -0.035t. Solving for t gives t ≈ -ln(0.2727)/0.035, which calculates to approximately t ≈ 42.53 minutes.

Hence, the brownies should cool to 160 degrees F in about 42.53 minutes.

Answer:

1. X= 25.9 meters

2.X= 21.3 meters

Step-by-step explanation:

1. Tan 50°= X/21

2. Tan 12°= X/100

Answer:

Step-by-step explanation:

Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...

  f + t = 60

  f - t = 10

Adding these two equations, we get ...

  (f +t) +(f -t) = (60) +(10)

  2f = 70 . . . . . eliminate parentheses

  f = 35 . . . . . . divide by 2

She has 35 5-lb weights, and 25 3-lb weights.

The required fraction is [tex]\bold{\frac{1}{3}}[/tex]

Solution:

Given:

Cost of 32 ounces tub = $6

Cost of 8 ounces tub = $2

To find:

what fraction of the cost of the large tube is the small tub.

From the given, here we can understand that the large tub is the 32 ounces tub and the smaller one is the 8 ounces tub.

Let k be the required fraction.

Therefore, [tex]\bold{k\times6=2}[/tex]

On solving we get,

[tex]\bold{\Rightarrow k=\frac{2}{6}\rightarrow k=\frac{1}{3}}[/tex]

Answer:

-6/5

Step-by-step explanation:

-2 2/5=-12/5

1/2*-12/5=-12/10=-6/5

Answer:

1.75, 0.4375

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

r = 28 ÷ 112 = 7 ÷ 28 = 0.25

Thus the sequence is geometric.

To obtain a term in the sequence multiply the previous term by 0.25

7 × 0.25 = 1.75

1.75 × 0.25 = 0.4375

The next 2 terms in the sequence are 1.75, 0.4375

Answer:

3

Step-by-step explanation:

30 x 3