FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.
Let a = first side
Let b = second side
Let c = third side
NOW, we can turn the words into equations:
"a triangle has a perimeter of 165 cm."
a + b + c = 165
"the first side is 65cm less than twice the second side."
a = 2b - 65
"the third side is 10cm less than the second side."
c = b - 10
Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]
If we could get this to have only one variable, we could solve it. Substitution to the rescue!
a + b + c = 165 (rewrote equation from above)
(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)
See how that works? Let's solve it.
2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)
4b - 75 = 165 (combined like terms)
4b = 240 (added 75 to both sides)
b = 60 (divided both sides by 4)
We found the second side! We can find the first and third sides using those equations from above:
a = 2b - 65
a = 2*60 - 65
a = 120 - 65
a = 55
c = b - 10
c = 60 - 10
c = 50
All done.
PLEASE MARK ME AS BRAINLIEST
Step One - Define the Unknown Variable
First we need to define our unknown variable. For this case, I am going to use the letter 's' for the second side of the triangle (no actually because the question told you to). The reason I am using the second side as the unknown is because the second side is independent. The first and third sides' lengths depend on the length of the second side.
Step Two - Write an Equation
We need to use what we know to write the equation. First, we know that the perimeter of a polygon is the sum of the lengths of all the sides. The first side is 65 less than two times 's'. This would be 2s-65. The second side is just s. The third side is 10 less than 's'. So it would be s-10. The perimeter is all of the sides added up, so the expression for all the sides added up is (2s-65)+(s)+(s-10). The first, second, and third side added up is 165. So the equation for 1. is (2s-65)+(s)+(s-10) = 165.
Step Three - Solve the Equation
To solve the equation, you need to isolate the variable, which is 's'.
First, let's simplify the equation.
(2s-65)+(s)+(s-10) = 165.
4s-75 = 165.
Now we need to remove the 75. To get rid of the 75, you must add 75. But since you are adding 75 to one side of the equation, you must add 75 to the other side of the equation to make it equal.
4s-75+75 = 165+75
4s = 240
Now we need to remove the 4. To get rid of the 4, you have to divide each side by 4.
4s÷4 = 240÷4
s = 60
The length of the second side is 60 cm.
Step Four - Find the Lengths of all Sides
Now we know the length of the second side, we can find the length of the other sides.
The first side is 65 less than two times of 60.
Two times of 60 is 60×2 or 120.
65 less than 120 is 120-65 or 55.
The first side is 55 cm.
The third side is 10 less than 60.
10 less than 60 is 60-10 or 50.
The third side is 50.
So the lengths of the three sides are 55, 60, and 50.
Step Five - Check Your Answer
Now let's see if the three sides added up equals to 165.
Well, 55+60+50 does equal 165, so we know this is right.
The equation that represents the perimeter of the triangle is (2s + 65) + (s) + (s + 10) = 165. The length of each side of the triangle is 55, 60, and 50.
?can someone help meh
Answer:
Step-by-step explanation:
C
what is the directrix of a parabola with focus (4,-1) and a vertex at (4,-5)?
Answer:
y = -9Step-by-step explanation:
The directrix is at the same distance from the vertex as the focus but on the opposite side of the vertex.
x coordinate the same for a focus and a vertex (4) means the parabola opens up or down and the directrix is parallel to the x-axis.
y coordinate of the focus greater than y coordinate of the vertex means the parabola opens up and the directrix lays below the vertex.
-1-(-5) = - 1 + 5 = 4
so: - 5 - 4 = -9 is the y coordinate of points of the directrix
Jane is selling handmade hair bows for $5.25 each. A woman came by to buy some for the girls in her daughter's girl scout troop. She spent $84. How many hairbows did she buy?
Answer:
16
Step-by-step explanation:
Jane is selling handmade bows at $5.25 each
A woman came and spent $84 buying bows
Therefore the number of bows bought by the woman can be calculated as follows
= 84/5.25
= 16
Hence the woman bought 16 bows
Help meee PLEAAASEEEEEEEEEEEE
A rectangular carpet measures 12 m by 5 m.
Part of the carpet is covered by a square rug of length 2 m.
What fraction of the carpet is covered by the rug? Give your answer in its simplest form.
I'm pretty sure the answer is 1/15 or 4/60 because the whole carpet measures 60m and the covered part's area is 4m and that would be 4/60 but simplified 1/15. Sorry if this is wrong!
To find the fraction of the carpet covered by the rug, we need to determine the area of the rug and divide it by the total area of the carpet.
The area of the square rug can be calculated by squaring its side length: 2m x 2m = 4m². The total area of the rectangular carpet can be found by multiplying its length and width: [tex]12m x 5m = 60m²[/tex]. To find the fraction, divide the area of the rug by the area of the carpet: 4m² / 60m².
To simplify the fraction, we can find the greatest common divisor (GCD) of 4 and 60, which is 4. Dividing both the numerator and denominator by the GCD, we get: [tex]4m² ÷ 4 / 60m² ÷ 4 = 1m² / 15m²[/tex] . Therefore, the fraction of the carpet covered by the rug is 1/15, which means that 1/15th of the carpet is covered by the rug.
To know more about denominator visit:
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i need help with this slope problem
Answer:
It is the first one and the second one. If it is the same, then the slope will be constant.
Step-by-step explanation:
Answer:
I think it's the second one ( Any two points on the line will produce the same slope)
Step-by-step explanation:
Any two points on a line will ALWAYS have the same slope. There's no way that it won't be that way. That's why you are able to choose any two points on a graph to find a slope.
For the first one, i think it's wrong because although the slope is 1/2, Jennifer used the slope 2/4 while Marshall used 1/2. Even though it's the same, Jennifer didn't technically use 1/2...
And the third option is wrong. The slope isn't 2.
Hopefully this wasn't confusing... :)
Find the unit rate.
$4.80 for 6 cans
The unit rate is $
per can.
Answer:
0.8
Step-by-step explanation:
Answer:
0.8
Step-by-step explanation:
Is a repeating decimal a rational number
A. Yes because it can be written as a/b and a and b are integers and b =0
B. Yes because it can be written in the form a•b where a and b are integers
Answer:
Option A
Step-by-step explanation:
The answer to this question is option A or "Yes because it can be written as a/b and a and b are integers and b =0." Any number that can be written as a fraction is a rational number. In this case repeating decimals can be written as a fraction using different types of algebraic methods making it a rational number.
Hope this helps.
Solve for x and y
Need a answer plz
Answer:
Angle x = 12
Angle y = 49
Property = Isosceles triangles
The scale of the map measures 1 inch : 1250 miles. if the distances between two cities measure 3 inches on the map, find the actual distance between the two city on the ground
Answer:
3,750 miles
Step-by-step explanation:
Because one inch is 1250 miles so time that by three you get 3,750
Complete the steps to solve for x - 0.64x + 0.44x = 4.8
Answer:
x=40/3 or x=13.3
Step-by-step explanation:
−10)−3 = A) 0.01 B) 1000 C) −0.001 D) −1000
Answer:
A
Step-by-step explanation:
I am kinda positive this is it but it might not be
-10^-3 = -0.001
the answer is C
what is 9 time 64 what does it equal to
Answer:
It's 576 if you mean 64 times 9!
Step-by-step explanation:
Solve for x plsss helpppp
Answer:
x=30
Step-by-step explanation: First we would have to find the two angles of the corner of the triangle. 55° in the bottom left because of verticle angles. And 180-120= 60. And 60+55=115. 180-115=65. 65-5= 60. 60/2= 30. So x=30. (Sorry ik its sloppy) :)
The lunchroom tables were clean except for some plates and napkins.
In this sentence, which word should be replaced with precise language?
a.) Tables
b.) Plates
c.) Clean
d.) Some
Consider the following graph which represents the solutions to a system of inequalities. Which of the following systems of inequalities does the graph represent?
Answer:
The system of inequalities is -2x + y > 0 -x + y ≥ 0
Step-by-step explanation:
The form of the equation of a line is y = m x + b, where
m is the slopeb is the y-interceptThe line passes through the origin, then
The value of b = 0The form of the equation is y = m xLet us look at the graph to find the correct answer
∵ One of the lines are solid and the other is dashed
∵ The shaded area is over the two lines
∴ The signs of the two inequalities are ≥ and >
∵ The two lines pass through the origin
→ That means the y-intercepts are 0
∴ The form of the inequalities are y ≥ m[tex]_{1}[/tex] x and y > m[tex]_{2}[/tex]
There are only two answers that have these forms, so we must find the slope of each line
∵ m = [tex]\frac{y2-y1}{x2-x1}[/tex] , (x1, y1) and (x2, y2) are two points on the line
∵ The solid line passes through points (0, 0) and (2, 2)
∴ m[tex]_{1}[/tex] = [tex]\frac{2-0}{2-0}[/tex] = [tex]\frac{2}{2}[/tex] = 1
→ Substitute it in the form of the equation
∴ y ≥ 1(x)
∴ y ≥ x
→ Subtract x from both sides
∴ -x + y ≥ 0
∵ The dashed line passes through points (0, 0) and (1, 2)
∴ m[tex]_{2}[/tex] = [tex]\frac{2-0}{1-0}[/tex] = [tex]\frac{2}{1}[/tex] = 2
→ Substitute it in the form of the equation
∴ y > 2(x)
∴ y > 2x
→ Subtract 2x from both sides
∴ -2x + y > 0
The system of inequalities is -2x + y > 0 -x + y ≥ 0
Answer:
The system of inequalities is -2x + y > 0 -x + y ≥ 0
Step-by-step explanation:
i did it
I need help on this. Only right answers only please..
At the carnival, Sally purchased 20 tickets and a drink that was $4.50. Her total for everything was $44.50.
What was the cost of each ticket at the carnival
60 8th grade students chose to watch a movie on the last day of school. this is 20% of the class. how many students are there in 8th grade?
Answer:
the answer is 300 8th grade students
Step-by-step explanation:
Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following functions, h(t) represents the height of the ball above the ground, in feet, with respect to time, t, in seconds, after the ball was thrown. Which of the following functions models the amount of time the ball is in the air?
h(t)= -4(t-1)^2 +3
h(t)= -16(t-1)^2 -4
h(t)= -16(t-1)^2 +12
h(t)= -16(t-1)^2 +28
Answer:
Your answer will be the third function
Step-by-step explanation:
The base function you need to know is h(t)= 1/2at^2
Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12
Pls help its confuzing
Answer:
Step-by-step explanation:
x-int (2/7, 0)
y-int (0, -2)
x-int
7x - 0 = 2
7x = 2
x = 2/7
(2/7, 0)
7(0) - y = 2
-y = 2
y = -2
(0, -2)
Can someone solve 6÷2(1+2)
Answer: 9
Step-by-step explanation:
To solve this problem, we need to use our order of operations, or PEMDAS.
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
6÷2(1+2) [parenthesis]
6÷2(3) [multiply/divide from left to right]
3(3) [multiply]
9
Now, we know that the answer is 9.
Find "both answers.
The answer to the different" question is
The answer to the same three questions is
The slope of the line is 3
The difference between the consecutive term of the sequence is (1, 3)
To get the slope of the graph, we will use the coordinate points (2, 10) and (3, 13)
Slope = 13-10/3-2
Slope = 3/1
Slope = 3
Hence the slope of the line is 3
The difference in the term for the x-coordinate is given as:
x = 3 - 2 = 4 - 3 = 5 -4 = 1The difference in the term for the y-coordinate is given as:
x = 13 - 10 = 16 - 13 = 19 -16 = 3Hence the difference between the consecutive term of the sequence is (1, 3)
Learn more about slope at: https://brainly.com/question/19417700
what this dont get it
Answer:
[tex]4p+3[/tex]
Step-by-step explanation:
All this question is asking you to do is simplify the given expression by combining like terms.
The point of combining like terms is that you can only combine, well, like terms. Like terms are terms that have the same variables and are raised to the same power. This means that in this case, we can't combine [tex]4[/tex] and [tex]6[/tex] because [tex]4[/tex] is attached to a variable. However, we can combine 6 and -3 because they are like terms; neither is attached to a variable. So, you end up with [tex]4p+3[/tex].
I hope this helps!
Find the percent change from 120 to 192
Answer:
The percent change is 60
[tex]60% [/tex]
Answer: 60% increase
Step-by-step explanation:
please help i will mark brainliest
Answer:
Reflections and rotations
Step-by-step explanation:
Reflections and rotations preserves the distance and angle measurements.
30 POINTS GUYS!!!
What is the value of x?
Enter your answer, as a decimal, in the box.
x=
Answer:
[tex]x=3.5[/tex]
Step-by-step explanation:
Notice that CD bisects Angle C.
Then by the Angle Bisector Theorem, we can write the following proportion:
[tex]\frac{6}{4.2}=\frac{5}{x}[/tex]
Now, we can solve for x. Cross multiply:
[tex]5(4.2)=6(x)[/tex]
Multiply:
[tex]21=6x[/tex]
Divide both sides by 6:
[tex]x=21/6=7/2=3.5[/tex]
Hence, the vale of x is 3.5.
Answer:
4.2
Step-by-step explanation:
Whats the answer I will give brainliest, thanks, and five star
Answer:
B
Step-by-step explanation:
the one you have selected is correct
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute.
How does the rate for Printer B compare to the rate for Printer A? Use the drop-down menus to explain your answer.
Printer Rates
y
40
30
Printer A
Number of Pages
20
10
0
0
х
2 4 6
Time (min)
The rate for Printer Bis Choose..
the rate for Printer A because the rate of 25 pages per minute is choose...
the
rate of Choose
pages per minute for Printer A.
Answer:
printer A = 10 pages a min
Step-by-step explanation:
i need help please.
Which of the following expressions are equivalent to 7x + 14 − 3x + 12?
1. 21x + 8x
2. 7x − 3x + 14 + 12
3. 4x + 14 + 12
4. 4x − 2
5. 7x + 26 − 3x
Answer:
I just did this quetio with the tutor the answers are 2, 3, and 5.