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4 years ago

How do i do substitution if x is on the same side as y

1 answer:

5 0

Cancel out one kind of variable from that side and put it on the other side.

Examples:

5x + 5y = 15
---- - 5y ------- - 5y

5x = 15 - 5y

6c - 2b = 48
---- +2b -------- + 2b

6c = 48 + 2b

Hope this helps!

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The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a buil

photoshop1234 [79]

Answer:

Option A -The height of the building is 105 ft

Step-by-step explanation:

to get the height of the building, we calculate using SOH CAH TOA

TOA = OPPOSITE / ADJACENT

Tan 59° = h / 63

Height = tan 59° X (63)

Height = 1.6643 X 63

Height = 104.85

Height = 105 ft

4 0

3 years ago

A rectangle has an area of 24 sq. inches and a perimeter of 50 in. what are the dimensions of the rectangle

gulaghasi [49]

Answer:

Length of rectangle = 24 inches

Width of rectangle = 1 inches

Step-by-step explanation:

Area of rectangle = 24 square inches

Perimeter of rectangle = 50 inches

Formulas:

Area of rectangle = $l\times w$

Perimeter of rectangle = $2(l+w)$

where $l$ represents length of rectangle and $w$ represents width of rectangle.

So, we can get two equations for $l$ and $w$

A) $l\times w=24$ [Area]

B) $2(l+w)=50$ [ Perimeter ]

Simplifying equation B.

Dividing both sides by 2.

$\frac{2(l+w)}{2}=\frac{50}{2}$

$l+w=25$

Solving for $l$ in terms of width.

Subtracting $w$ both sides.

$l+w-w=25-w$

∴ $l=25-w$

Substituting value of $l$ in terms of $w$ in equation A.

$(25-w)w=24$

Using distribution.

$25w-w^2=24$

Adding $w^2$ both sides.

$25w-w^2+w^2=24+w^2$

$25w=24+w^2$

subtracting $25 w$ both sides

$25w-25w=24+w^2-25w$

$0=w^2-25w+24$

We have a quadratic equation. $w^2-25w+24=0$

We solve for $w$ by factor method.

Splitting middle term into two terms such that the sum of the two = $-25w$ and product of two = $24w^2$

$w^2-24w-w+24=0$

Factoring in pairs.

$w(w-24)-1(w-24)=0$

Factoring as a whole

$(w-24)(w-1)=0$

So, we have

$w-24=0$ and $w-1=0$

By adding 24 to one equation and adding 1 to other we get

$w-24+24=0+24$ and $w-1+1=0+1$

$w=24$ and $w=1$

So length can be found out by plugging value of $w$ in the length equation.

$l=25-24=1$ and $l=25-1=24$

Since length is always the longer side of rectangle so, the dimensions of rectangle can be given by.

length = 24 inches (answer)

width = 1 inches (answer)

6 0

3 years ago

Please help!! Which of the following is a solution to one of the inequalities graphed below but not a solution to the entire sys

murzikaleks [220]

Answer:

B. (-1,-5)

Step-by-step explanation:

In this graph, the darkest portion represents where the two inequalities intersect with each other. The areas with lighter shading is a solution of one of the inequalities.

From the question we can see that we are looking for which point ends up in the light grey area.

A. (4,-3) White

B. (-1,-5) Light Grey

C. (4,-2) White (This point lies on the inequalities's line. As this line is dotted, the points on it are not included, so this one is white.)

D. (3,1) Dark Grey.

As B is the only one that lies in the light grey area, this is the only correct answer.

7 0

4 years ago

2x + y =5 solve the system of equations by inspection

olga2289 [7]

Answer:

Slope=− 2.000/4.000 =−2.000

x−intercept= 2/5=2.50000

y−intercept= 1/5=5.00000

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x+y-(5)=0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x+y-5 = 0 and calculate its properties

Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000

y-intercept = 5/1 = 5.00000

When y = 0 the value of x is 5/2 Our line therefore "cuts" the x axis at x= 2.50000

x-intercept = 5/2 = 2.50000

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 1.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.000 - 5.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.000/2.000 = -2.000

8 0

3 years ago

Sandra rode her bike 5 times as many miles as Barbara. If b, the distance Barbara rode, equals 3.4 miles, what is the correct ex

uranmaximum [27]

Well, Sandra would've had to ride her bike 17 miles, so the answer is b because when a number is next to a letter, you have to times it. So, 5 times by b equals 17, so that is the answer. Hope it helps!

6 0

4 years ago

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