MATHEMATICS HIGH SCHOOL

Y = x + 1
    3x + y = 21

Answers

Answer 1
Answer: y=x+1
3x+y=21
-----------
-x+y=1
3x+y=21

First do this. Change one (or both) of the equations so that the x and y are on one side, and the number is on the other. Make sure either the x or the y is the same in both equations (in this case, y) and then take one away from the other. The y will cancel out so you can work out x.

3x+y=21 -
-x+y=1
-----------
4x = 20
x = 5

Then add the x into one of the two equations to find out y.

3x + y = 21
(3*5) + y = 21
15 + y = 21
y = 6

To check, put both x any y into the other equation.

-5 + 6 = 1

If the answer is correct, you have correctly solved the equations.

x = 5
y = 6

:D
Answer 2
Answer: \left \{ {{y=x+1} \atop {3x+y=21}} \right.\ \ \ Using\ substitution\ method\n\n 3x+x+1=21\n 4x=20\ \ |:4\n x=5\n y=6

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How do I find the calculated sum of 1/7 and 1/2

Answers

(1)/(7)+(1)/(2)=(1 * 2)/(7 * 2)+(1 * 7)/(2 * 7)=(2)/(14)+(7)/(14)=(2+7)/(14)=\boxed{(9)/(14)}
first make the denomenators (bottom numbers) the same

find the smallest number that 7 and 2 can both go into
the number is 14

multiply both by 1 or x/x where x is the same

1/7 times 1 or
 1/7 times 2/2=2/14

1/2 times 1 or
1/2 times 7/7=7/14

sum of numbers
2/14+7/14
add numberators (top numbers)
2+7=9
answer=9/14

determine the most precise name of the quadrilateral ABCD from the information given. for #13 & #14

Answers

Answer:14\n\nbecause\ in\ 13\ \overline{AE}=\overline{CA}\ and\ \overline{BE}=\overline{DE}\ is\ a\ rhombus.
Hello,
----------------------
Answer ⇒ 14
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Dixie packaging co has contracted to manufacture a box with no top that is to be made by removing squares of width x from the corners of a 15-in by 60-in piece of cardboard.a) Write a function for the VOLUME of the box as a function of x.

b) Determine x so that the volume of the box is at least 450 cubic inches.

c) Determine x so that the volume of the box is maximum.

Answers

The volume of the box as a function of x V(x) = x ( 60 -2x )( 15-2x )

The volume of the box as a function of x inches 0.55 inches ≤ x ≤ 6.79

The volume of the box is maximum x ≥ 6.79 inches

Given ,

The box with no top that is to be made by removing squares of width x

The corners of a 15-in by 60-in piece of cardboard.

  • Volume can be represented by this function below

         V(x) = x ( 60 -2x )( 15-2x )

Where : x = height ,  ( 60 - 2x ) = length , ( 15 -2x ) = width

The volume of the box as a function of x is  V(x) = x ( 60 -2x )( 15-2x )

  • To determine x so that,

The volume of the box ≥ 450 inches

V(x) = x ( 60 -2x )( 15-2x )

The volume of the box is at least 450 cubic inches.0.55 inches ≤ x ≤ 6.79 inches

  • The value of x for which volume of the box is maximum  will be x ≥ 6.79 inches.

For more information about Volume of the square click the link given below

//httpsbrainly.com/question/23245822

Answer:

a) V(x) = x ( 60 -2x )( 15-2x )

b) 0.55 inches ≤ x ≤ 6.79 inches

c) x ≥ 6.79 inches

Step-by-step explanation:

Given data:

No top, cardboard dimensions ; 15-in by 60-in

a) A function for the volume of the box as a function of x the Volume can be represented by this function below

= V(x) = x ( 60 -2x )( 15-2x )

where : x = height ,  ( 60 - 2x ) = length , ( 15 -2x ) = width

b) determine x so that the volume of the box ≥ 450 inches

450 = x( 60 - 2x ) ( 15 -2x ) ( solving the equation )

0.55 inches ≤ x ≤ 6.79 inches

c ) The value of x for which volume of the box is maximum

will be x ≥ 6.79 inches

AB¯¯¯¯¯ and BC¯¯¯¯¯ are tangent to ⊙ O. Identify BC.

Answers

Answer:

52

Step-by-step explanation:

2(3x-7)=4x+8\nx=11\n4(11)+8=52

Simplify: -m(7m + 3) – 4m2
A. 12m+4
B. -11m2-3m
C. -11m2+6m
D.5 m + 4 ​

Answers

Answer:

- m(7m + 3) - 4 {m}^(2) \n - 7m^(2) - 3m - 4 {m}^(2) \n - 11 {m}^(2) - 3m

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?a) (x-3)^2 = 20(y-1)
b) (y-1)^2 = 20(x-3)
c) (y-1)^2 = -20(x-3)
d) (x-3)^2 = 20(y-1)

Answers

Answer with Step-by-step explanation:

We have to find:

the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2

General form of Parabola that opens left or right:

(y−k)²=4p(x−h)

Vertex =(h,k)  

Directrix: x=h−p

Here, h=3,k=1 and h-p=-2  i.e. p=h+2=5

Hence, equation of parabola in this case equals

  (y-1)²=4×5(x-3)

i.e. (y-1)²=20(x-3)

Hence, correct option is:

b)  (y-1)²=20(x-3)
Hello,

Remenber:
if S=(0,0) y²=2px then F=(p/2,0 and d:x=-p/2


Let's pose
x'=x-3
y'=y-1 axes passing by the point (3,0) in base (x,y) and (0,0) in base (x',y')

y'²=2p'x'
d': x'=-5=-p'/2 ==> p'=10 and y²=20x'
Returning in base (x,y) : (y-1)²=20(x-3)

Answer B
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