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Question

the perimeter of a rectangle is 160 m. The length is 30 m more than the width. Find the width of a rectangle.

Two angles are complementary. The difference of their measures is 24 degrees. Find the measure of the larger angle.

The difference between two numbers is 26. The larger is 30 less than twice the smaller. Find the smaller number.

Two angles are supplementary. The difference of their measures is 172 degrees. Find the measure of the larger angle.

Two angles are complementary. One of them is 4 times the other. Find the measure of the smaller angle.

Two angles are complementary. The larger is 15 degrees less than twice the smaller. Find the larger angle.

Answer 1

1.L=W+30
2[(w+30)+w]=160
4w=100
w=25m
L=55m

2.2x+24=90
2x=66
x=33
the angles are 33 and 57*

3.x-y=26
x=2y-30
x-2y=-30
y=56
x=82

4.2x+172=180*
x=48
the angles are 176* and4*

5.x+4x=90
x=18
the angles are 18* and 72*

6.x+y=90
x=2y-15
x-2y=-15
3y=105*
y=35*
cx=55*

Answer 2

1. rectangle perimeter is 2* length + 2* width
let w = width
length = w + 30
perimeter = 160
160 = 2(w+30) + 2*w
160 = 2w +60 +2w
160 = 4w +60
100=4w
25= w
width is 25, length is 55
check is lenght 30 more than width ...25 + 30 = 55
does perimeter = 160 ? 25+25+55+55 = 160

2. complementary means they sum to 90
<1 =x
<2 = x +24
x + x + 24 = 90
2x +24 = 90
2x =66
x = 33
x + 24 = 57
check in words is the difference in the angles 24? 57-33=24
do they sum to 90?
57 + 33 = 90
larger angle is 57

3. let x = smaller number
larger # is x + 26
Change the larger (x+26) is (=) thirty less than (means subtract 30) twice the smaller (2x) to an equation
x + 26 = 2x - 30
-x -X
26 = x - 30
+30 +30
x = 56
56 + 26 = 82 the larger #
check in words

supplementary mean sum to 180
x is 1st angle
x + 172 is 2nd angle
x + x +172 = 180
2x + 172= 180
2x = 8
x = 4
large angle is 4 + 172 = 176

complementary means sums to 90...
ist angle is x
4x is 2nd angle
x + 4x = 180
5x = 180
x = 36
4x = 4*36=144 the large angle


complementary means sums to 90...
x is larger
2x - 15 is smaller
x + 2x -15 = 90
3x - 15 = 90
3x = 75
x = 25

I'm leaving the checks to you...CHECK IN THE WORDS OF THE PROBLEM not in the equations

Answer 3

Here's the general method of solving all of these problems.

The first sentence tells you the relationship between two things. For example: "The perimeter of a rectangle is 160m". That means that 2L + 2W = 160.

The second sentence tells you something else connecting the two quantities (numbers, lengths, angles). Like in the first question, the length is 30m more than the width, which means that L = 30 + W.

Dealing with the equations is easier than dealing with the words - that's why math is helpful!

Here are your two equations:
2L + 2W = 160
L = 30 + W

Now substitute. We use 30+W as another name for L, because they are equal!

2(30+W) + 2W = 160. From here you can solve for W (yes, you can. Do it!)

Now you know W, so you can find L = 30 + W.

Each of these problems can be solved in the same way.

1. Write your first equation, and say what the variables are. (for example, "x and y are the measures of the two angles")

2. Write your second equation.

3. Your second equation can replace a variable in the first equation, giving you one, slightly longer equation, with one variable, instead of two smaller ones, with two variables.

4. Solve that new equation for the one variable.

5. Plug into the old #2 equation, to find the other variable.

6. Check both in the old #1 equation, to make sure you're right!

Answer 4

For increasing cubic binomials the final formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 5

alright
the
>formula is 2l+2w=p...ur l is 30, so 2(30)+2w=160
so 60+2w=160....2w=100 & therefore w=50
>equation is x+x+24=90......so 2x+24=90......2x=66......x=33
and bigger angle is 57
>do it the same way as last 1 but make it equal to 180
>5x=90.......x=18
>3x-15=90.......3x=105......so x=35
that should work