In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.
Answers
1/2*x - length of the base
so:
[tex]P=2\cdot x+\dfrac{1}{2}x\\\\\\50=2x+\dfrac{1}{2}x\\\\\\50=2\dfrac{1}{2}x\\\\\\50=\dfrac{5}{2}x\quad|\cdot\dfrac{2}{5}\\\\\\x=50\cdot\dfrac{2}{5}\\\\\\x=\dfrac{100}{5}\\\\\\\boxed{x=20\text{ cm}}\qquad\qquad\text{(leg)}[/tex]
and
[tex]\dfrac{1}{2}\cdot x=\dfrac{1}{2}\cdot20=\boxed{10\text{ cm}}\qquad\qquad\text{(base)}[/tex]
To solve this question, we have to:
Understand the concept of an isosceles triangle.Use this concept, along with the perimeter concept, to build the equation to find the length of the sides.Doing this, we get that the length of the base is 10 cm and the length of the legs is 20 cm.
Isosceles triangle:
In an isosceles triangle, two sides have the same measure. An example is given by the picture at the end of this answer.
Perimeter:
The perimeter of a polygon, in this case a triangle, is the sum of all it's sides.
In this question:
Perimeter of 50 cm;Two legs of l;Base is half the leg, so l/2.Then, the equation is:
[tex]l + l + \frac{l}{2} = 50[/tex]
[tex]2l + \frac{l}{2} = 50[/tex]
[tex]\frac{4l + l}{2} = 50[/tex]
[tex]5l = 100[/tex]
[tex]l = \frac{100}{5}[/tex]
[tex]l = 20[/tex]
Thus:
The length of the legs is of 20 cm.The length of the base is of 20/2 = 10 cm.A similar question is found at https://brainly.com/question/20321307
Related Questions
Jonah and his friends went to the movie theater. He bought a movie ticket, and he split the cost of a giant popcorn with his friends. Jonah's costs are represented by the expression 11+15/x . What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Cost of movie ticket Total cost of popcorn Jonah's portion of popcorn cost
Answers
Answer:
Cost of movie ticket = 11
Total cost of popcorn = 15
Jonah's portion of popcorn cost = 15/x
Step-by-step explanation:
1. I
2. Took
3. The
4. Test
The range for a set of data is estimated to be 36.
a. what is the planning value for the population standard deviation?
Answers
Given that the range of a data set is 36, the planning value for the population standard deviation is given by [tex]\sigma= \frac{1}{6} (36)=6[/tex].
The planning value for the population standard deviation can be found by dividing the range by 4.
Explanation:To estimate the population standard deviation, we can use the planning value formula. The planning value for the population standard deviation is equal to the range divided by 4. Thus, in this case, if the range is estimated to be 36, the planning value for the population standard deviation would be 9.
The map scale is 1in: 40 miles . the distance on the map is 3.5 inches . what is the actual distance
Answers
3.5 inches is 40 miles*3.5 inches or 140 miles
You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
Answers
To earn $500 in interest at a 4% annual rate, you need to leave $2000 in the account for approximately 6.25 years.
The formula for simple interest is given by:
[tex]\[ I = P \times r \times t \][/tex]
Where:
- I is the interest earned,
- P is the principal amount (initial deposit),
- r is the annual interest rate (expressed as a decimal), and
- t is the time the money is invested or borrowed in years.
In this case, you want to find t, so rearrange the formula to solve for t:
[tex]\[ t = \frac{I}{P \times r} \][/tex]
Given that P = $2000, r = 0.04 (4% as a decimal), and I = $500, plug these values into the formula:
[tex]\[ t = \frac{500}{2000 \times 0.04} \][/tex]
Calculate the result to find out how long you must leave the money in the account to earn $500 in interest.
[tex]\[ t = \frac{500}{2000 \times 0.04} \]\[ t = \frac{500}{80} \]\[ t = 6.25 \][/tex]
Therefore, you must leave the money in the account for approximately 6.25 years to earn $500 in interest at a simple annual rate of 4%.
truck was caught in a haistorm that left his truck body damaged and his paint ob ruined Ned is fully insured through hi insurance company Which of the following components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm? a, bodily injury b. property damage c. collision d. comprehensive damage
Answers
It was damage not caused by another vehicle, but by weather.
Since Ned's truck suffered body damage due to a hailstorm, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.
What is comprehensive car insurance coverage?A comprehensive coverage is an insurance policy which covers the cost of damages to a vehicle which has been involved in an accident that is not caused by a collision.
Comprehensive insurance covers losses such as:
theft,vandalism,hail, etc.Therefore, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.
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What classification best represents a triangle?
Answers
a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244
c^2 < a^2 + b^2
Triangle is acute triangle
answer is A.
acute because 10^2 + 12^2 > 15^2
Find the slope of a line parallel to the line through the given points. P(-2, 4), Q(6, -2) 4/3 3/4 -3/4
Answers
Answer:
Option 3 - [tex]m=-\frac{3}{4}[/tex]
Step-by-step explanation:
Given : P(-2, 4), Q(6, -2)
To find : The slope of a line parallel to the line through the given points?
Solution :
First we find the slope of the line passes through given points P(-2, 4), Q(6, -2)
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-4}{6-(-2)}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=-\frac{3}{4}[/tex]
When two lines are parallel then there slope are equal.
Therefore, The slope of a line parallel to the line through the given points is
[tex]m=-\frac{3}{4}[/tex]
So, Option 3 is correct.
A rectangle has a length of 8 cm and breadth 6cm . What is the perimeter in cm of the rectangle
Answers
8+8+6+6=28cm
So we have to do 2*(8+6)=2*14=28
So the perimeter is 28
brainiest to best answer!
The deepest part of the Mariana trench (the deepest trench in the world’s oceans) is at an elevation of -11.033 kilometers. The elevation of the deepest part of the Atacama trench is -8.065 kilometers. What is the net change in elevation from the Atacama trench to the Mariana trench?
19.098 kilometers
2.968 kilometers
-2.968 kilometers
-19.098 kilometers
Answers
The net change in elevation from the Atacama trench to the Mariana trench is 2.968km.
What is the net change in elevation from the Atacama trench to the Mariana trench?
We know that the deepest part of Mariana trench is at -11.033 km, while the deepest part of the Atacama trench is -8.065km.
To find the net change, we need to find the difference between the largest value and the smallest value.
So we get:
D = -8.065km - (-11.033 km) = 2.968km
Then the correct option is the second one.
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WILL GIVE BRAINIEST TO FIRST ANSWER
Which of the following inequalities is graphed on the coordinate plane?
A. y > 1/2x - 1/2
B. y is less than or equal to 1/2x - 1/2
C. y is greater than or equal to 1/2x - 1/2
D. y < 1/2x - 1/2
Answers
Answer:
Option C
Step-by-step explanation:
Equation of any line is of the form y=mx+b where m is the slope and b the y intercept.
The given line has y intercept [tex]\frac{-1}{2}[/tex] and slope as [tex]\frac{1}{2}[/tex]
Hence equation of given line is :
[tex]y= \frac{1}{2}x-\frac{1}{2}[/tex]
Taking point (0,0) to check the inequality we have:
0≥[tex]\frac{-1}{2}[/tex]
The statement is true so option C [tex]y\geq \frac{1}{2} x-\frac{1}{2}[/tex] is right .
In a rhombus, which of the following are always equal? Select all that apply.
opposite angles
diagonals
opposite sides
consecutive angles
Answers
opposite angles
hope it helps
An athlete eats
60
grams of protein per day while training. How much is this in milligrams?
Be sure to include the correct unit in your answer.
Answers
Suppose you have 74 feet of fencing to enclose a rectangular dog pen. The function a=37x-x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary
Answers
Standard form: ax² + bx + c
Given equation: -x² + 37x + 0
Since the "a" coefficient is negative, the parabola is flipped upside down making the maximum point the vertex.
Vertex = (-b/2a, y)
-b/2a = -37/(-1*2) = 37/2 = 18.5
This is the x-value, width which gives the maximum area
put in x = 18.5 and solve for maximum area, A.
A = -(18.5)² + 37(18.5)
A = -342.25 + 684.5
A = 342.25
round to nearest tenth
A = 342.3
Answer: width = 18.5 ft; area = 342.3 ft2
Step-by-step explanation:
you plug in the width with the function , where ever there is an x replace it with the width for the maximum area
Given the functions f(x) = 2x −1 and g(x) = 2x + 4, which operation results in the largest coefficient on the x term? addition subtraction multiplication two operations result in the same coefficient
Answers
f(x) + g(x)
2x-1 + 2x + 4
4x -1 + 4
4x + 3
Largest coefficient on x = 4
Second lets do the subtraction. f(x) - g(x)
f(x) - g(x)
(2x-1) - (2x+4)
2x - 2x - 1 - 4
-5
Largest coefficient on x = 0
Third lets do the multiplication. f(x) *g(x)
(2x-1) * (2x+4)
[tex]4x^2 + 8x - 2x - 4[/tex]
[tex]4x^2 + 6x - 4[/tex]
Largest coefficient on x = 6
Answer: Multiplication will result in the largest coefficient on the x term.
If two angles are complementary, then they total 90o. converse: inverse: contrapositive:
Answers
Converse:If two angles equal 90, then they are complementary
contrapositive: If two angles do not equal 90, then they are not complementary
15 - (-3) - 4
-16
22
-8
14
Answers
15 - [-3]- 4
Note that when two minuses come together the product is a plus sign.
15 +3 - 4
You have to add before you subract
18 - 4 =14
Therefore, 15- [-3] - 4 = 14.
The area of a rectangle is 24 square cm. the length of the rectangle is 8 cm. find the perimeter
Answers
Would x + x + x +x be 4 or 4x?
Answers
Answer:
x+x+x+x = 4x.
Step-by-step explanation:
x + x + x + x can represent 4x since there are 4 x’s. Those 4 x’s represent x being multiplied by 4, since there are 4 x’s.
Therefore, your answer is 4x.
Graph the equation 5x+2y=10
Answers
5x+2y=10: Displayed in the image below
Tom usually earns $40.85 per hour. he has a 6% pay raise. which keys must he press on his calculator?
Answers
total pay raise= (6/100)x40.85
Total pay raise= $2.450
This can be a final answer. Your question is incomplete I think.
"+" & "=" button key Tom will press in the calculator.
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
To calculate Tom's pay raise, he can perform the following calculation on his calculator:
= 40.85 x 0.06
= 2.4510
So Tom's pay raise is $2.45 per hour.
To calculate Tom's new hourly rate, he can perform the following calculation:
= 40.85 + 2.45
= 43.30
So Tom's new hourly rate is $43.30.
Here is how the calculation can be done on most calculators:
Enter 40.85 and then press the "+" button.
Enter 2.45 and then press the "=" button.
The result should be 43.30, which is Tom's new hourly rate with a 6% pay raise.
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least common denominator of 3/s and -3/6s
Answers
2s
What is the remainder of 4^31 when divided by 10
Answers
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
[tex](4^1)^2 \equiv 4^2 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 16 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^2)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^4)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^8)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
So far we have found that,
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]
Multiply out all of the left sides of those equations above. Multiply out the right sides as well to balance things out
[tex](4^1)*(4^2)*(4^4)*(4^8)*(4^{16}) \equiv 4*6*6*6*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{1+2+4+8+16} \equiv 24*36*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4*6*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 24*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 24 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4 \ (\text{mod} \ 10)[/tex]
-------------------------------------------------------------------------
-------------------------------------------------------------------------
The final answer is 4
Final answer:
The remainder of 4^31 when divided by 10 is 4, determined by examining the repeating last-digit pattern of powers of 4.
Explanation:
To find the remainder of 4^31 when divided by 10, we can use the concept of powers and properties of numbers related to modulo arithmetic. Specifically, we look at the last digit pattern that emerges when calculating powers of 4, since the remainder when dividing by 10 depends solely on the final digit of the number.
The powers of 4 have a cycle: 4^1 ends with 4, 4^2 ends with 6, 4^3 ends with 4 again, and so on. This cycle repeats every two powers, so we only need to consider the power of 4 modulo 2 to determine the last digit of 4^31. Since 31 is an odd number, we know that 4^31 will end with a 4. Hence, the remainder of 4^31 divided by 10 is 4.
Melanie made 72 peanut butter cookies and oatmeal cookies. She wants to make identical groups of cookies for her friends. Each group will be as large as possible, and she will use all of the cookies. How many cookies will each friend receive? Explain. Please help me
Answers
If a set of data is in the direction of a downward line, which of the following would be the best model for this data?
Quadratic regression model
Exponential regression model
Linear regression model
None of the above
Answers
The length of the base of a triangle is twice its height. if the area of the triangle is 100 square kilometers, find the height.
Answers
a=1/2b·h
If h=x
b=2x
a=1/2(2x)·x
a=x²
100=x²
x=10
h=x=10
If 5x + 5 =25 + 3x then x = ? (im in pre algebra)
Answers
[tex]5x+5 = 25+3x[/tex]
Isolate the variables
[tex]5x -3x = 25 -5[/tex]
[tex]7x = 21[/tex]
[tex]x=21/7[/tex]
[tex]x=3[/tex]
Hope I helped (:
Have a great day!
To solve the equation 5x + 5 = 25 + 3x, subtract 3x from both sides, subtract 5 from both sides, and divide by 2 to find x = 10.
Explanation:To solve the equation 5x + 5 = 25 + 3x, you need to isolate the variable x. First, subtract 3x from both sides of the equation to combine like terms: 5x - 3x + 5 = 25. Simplify: 2x + 5 = 25. Next, subtract 5 from both sides of the equation to isolate the variable: 2x = 20. Finally, divide both sides of the equation by 2 to solve for x: x = 10.
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What is the result of dividing 2x3+6x2+6x+22x3+6x2+6x+2 by x+1x+1 ? A")2x2+4x+102x2+4x+10
B) 2x2+4x+22x2+4x+2
C:)2x2+6x+22x2+6x+2
D)2x2+6x+12
Answers
Answer:
[tex]2x^2+4x+2[/tex]
Step-by-step explanation:
[tex]2x^3+6x^2+6x+2[/tex] divide by x+1
Divide the first term of numerator by the first term of denominator and put it at the top. then multiply the answer by x+1 . write the expression at the bottom and subtract it. Repeat the process till we get remainder.
[tex]2x^2+4x+2[/tex]
-------------------------------------------------------
[tex]x+1[/tex] [tex]2x^3+6x^2+6x+2[/tex]
[tex]2x^3+2x^2[/tex]
-----------------------------------------(subtract)
[tex]4x^2+6x[/tex]
[tex]4x^2+4x[/tex]
-------------------------------------------Subtract
[tex]2x+2[/tex]
[tex]2x+2[/tex]
------------------------------------------Subtract
0
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers
Answers
The root of the function is such point [tex]x_0,[/tex] for which [tex]f(x_0)=0.[/tex]
The attached graph of the function [tex]f(x) = 2x^3 - 19x^2 + 57x - 54[/tex] shows, that the graph of the function intersects the x-axis in three points (2,0), (3,0) and (4.5,0).
This means that for
x=2, f(2)=0;x=3, f(3)=0;x=4.5, f(4.5).Thus, x=2, x=3 and x=4.5 are rational roots of the polynomial function f(x).
Answer: three rational roots.
The polynomial function f(x) = 2x^3 - 19x^2 + 57x - 54 has three rational roots at x=2, x=3, and x=4.5, as confirmed by the graph intersecting the x-axis at these points.
The graph of the function f(x) = 2x^3 - 19x^2 + 57x - 54 intersects the x-axis at three points: (2,0), (3,0), and (4.5,0). This implies that x=2, x=3, and x=4.5 are the roots of the polynomial function.
Since these values are rational, the function has three rational roots. Rational roots occur when the function evaluates to zero for specific rational input values.
In this case, f(2) = 0, f(3) = 0, and f(4.5) = 0. The graph crossing the x-axis at these points confirms their status as roots. The polynomial f(x) has three rational roots, which are x = 2, x = 3, and x = 4.5.
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How do you solve cot^2x + cscx= 1
(0,2pi)
Answers
[tex]\bf csc(x)-2=0\implies csc(x)=2\implies \cfrac{1}{sin(x)}=2\implies \cfrac{1}{2}=sin(x) \\\\\\ sin^{-1}\left( \frac{1}{2} \right)=\measuredangle x\implies \frac{\pi }{6}~~,~~\frac{5\pi }{6}=\measuredangle x\\\\ -------------------------------\\\\ csc(x)+1=0\implies csc(x)=-1\implies \cfrac{1}{sin(x)}=-1 \\\\\\ \cfrac{1}{-1}=sin(x) \implies -1=sin(x)\implies sin^{-1}(-1)=\measuredangle x\implies \frac{3\pi }{2}=\measuredangle x[/tex]
Daniel mows lawns on the weekend. He graphed his earnings below. What is the rate he charges to mow? A. $15.00 per lawn B. $7.50 per lawn C. $60.00 per lawn D. $1.50 per lawn
Answers
To determine Daniel's rate per lawn mowing, we would need to divide his total earnings by the total number of lawns mowed. The answer can also be found by evaluating the slope of a graph with earnings on the y-axis and lawns mowed on the x-axis as the slope would represent his earnings per mow.
Explanation:Without the graph provided, we can't determine the exact answer to this problem. However, conceptually, Daniel's rate per lawn would be calculated by dividing the total amount he earned by the total number of lawns he mowed. For example, if he earned $60 from mowing 4 lawns, his rate would be $15 per lawn.
To find the answer using a graph, you would need to evaluate the slope of the line if the y-axis represents earnings and the x-axis represents lawns mowed. The slope of the line provides the rate, which is Daniel's earnings per mow.
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