A wire is first bent into the shape of a rectangle with width 5in and length 13in. Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].
What is perimeter?" Perimeter is defined as the total length around the boundary of any two dimensional geomertic shape."
Formula used
Perimeter of a rectangle [tex]= 2 ( L + W)[/tex]
[tex]L =[/tex] length of the rectangle
[tex]W =[/tex] Width of the rectangle
Perimeter of a triangle with equal length [tex]= 3s[/tex]
[tex]s =[/tex] side length of a triangle
According to the question,
Given,
Length of a rectangle [tex]'L'= 13 in[/tex]
Width of a rectangle [tex]'W' = 5 in[/tex]
Substitute the value in the formula we get,
Perimeter of a rectangle [tex]= 2( 13 + 5)[/tex]
[tex]= 36 in[/tex]
Substitute the value in the perimeter of a triangle with equal side length,
[tex]3s = 36 in\\\\\implies s = \frac{36}{3} \\\\\implies s = 12in[/tex]
Hence, Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].
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The cube will be enlarged by a scale factor of 8.
What will be the volume of the new cube?
8 cubic units
64 cubic units
192 cubic units
4,096 cubic units
solve this equation 3\5(x-10)=18-4x-1
Simplify using distributive property. Which number can be distributed across two terms inside parentheses?
Answer choices:
-10
3\5
x
3/5 is the number which can be distributed across two terms inside parentheses
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 3/5 (x-10) = 18-4x-1
According to the distributive property, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
To solve the above equation we have to distribute 3/5 on LHS
3/5x-30/5 = 18-4x-1
3/5x-6 = 17-4x
Hence, 3/5 is the number which can be distributed across two terms inside parentheses
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What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees
The value for ss can never be less than zero.
a. True
b. False
if x is a prime number, then x+1 is not a prime number. A counterexample is x=
Answer: The required example is x = 5.
Step-by-step explanation: Given that if x is a prime nu mber, then x+1 is not a prime number.
We are to give a counterexample for this.
Let us consider that
[tex]x=5.[/tex]
Then, we know that x is a prime number.
But, we get
[tex]x+1=5+1=6,[/tex] which is not a prime number.
Thus, the required example is x = 5.
A circle with a radius of inches has a central angle of 0.25 radians that intercepts an arc of inches.
Answer:
Step-by-step explanation:
Given that there is a circle of .... inches with central angle 0.25 inches
by formula we have arc = radius *central angle in radians
The radii are given three options as 10,20,4 and corresponding arcs as
25,5, 16 inches.
By matching we find that 10(0.25) not equals 25
But 20(0.25) = 5 inches
Also 4(0.25) not equals 16 inches
Hence correct answer is radius = 20 and central arc = 5 inches
X and y are supplementary angles y measures 97
at 3:00a.m,the temperature is -5°F. Between 3:00a.m. and 6:00 a.m.,the temperature drops by 12°F. Between 6:00a.m. and 9:00a.m., the temperature rises by 4°F. What is the temperature at 9:00a.m.?
By what transformation can the set representing the inverse of a function be found? 1) reflection in the origin 2) reflection in the line y = x 3) rotation of 90o about the origin
Answer:
2) reflection in the line y = x
Step-by-step explanation:
A function is transformed to its inverse by swapping the independent and dependent variables. Reflection in the line y = x does that.
For what value of the constant c is the function f continuous on (-infinity, infinity) for the equation f(x) = cx^2 + 2x if x < 2 and x^3 - cx if x> or = 2
To find the constant c that makes the given piecewise function continuous for all real numbers, the two parts of the piecewise function need to be equal at x = 2. By setting these two equal and solving for c, you will find the value that makes the function continuous.
Explanation:The question presents a piecewise function and asks for which value of the variable c does it become continuous for all real numbers. To make a function continuous at a certain point, both parts of the function must be equal at that point. In this case, the two parts meet at x = 2. We need to set the two parts equal to each other at x = 2 and then solve for c.
For the first part of the piecewise function,
[tex]f(x) = cx^2 + 2x[/tex], when we substitute x = 2, it becomes f(2) = 4c + 4.
For the second part of the piecewise function,
[tex]f(x) = x^3 - cx[/tex], substituting x = 2 again gives us f(2) = 8 - 2c.
In order for the function to be continuous, these two results must be equal. We set 4c + 4 = 8 - 2c and solve it for c. Solving this equation will provide the value of c for which the function is continuous for all x .
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How do you tell the difference between a obtuse angle, a right angle and a acute angle?
In the Founder's Day Parade in Happy, USA, many organizations participate by building floats. The Float Committee has issued a decree that each float can only have 300,000 flowers on it this year. The Happy Campers have already attached 15,625 flowers to their float. If the flowers come in containers which hold 125 flowers, which equation represents how many more containers they can use on their float?
A. 125x + 15,625 = 300,000
B. 125x = 300,000 + 15,625
C. 0x = 300,000 + 125
D. 0x + 125 = 300,000
What is the simplified form of the following expression?
4/7^3
A: 343/64
B: 21,952
C:407
D: 64/343
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex](\frac{4}{7})^3[/tex]
According to the property of exponent.
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]
Using this property the given expression can be written as
[tex](\frac{4}{7})^3=\frac{4^3}{7^3}[/tex]
[tex](\frac{4}{7})^3=\frac{64}{343}[/tex]
The simplified form of the given expression is [tex]\frac{64}{343}[/tex].
Therefore the correct option is D.
How to factor: 15x^2y^3 + 10xy^2z
Please help ;u;
which expression shows how 5 . 37 can be rewritten using the distributive property?
1) 5 . 30 + 5 . 37
2) 15 . 30 + 5 . 37
3) 5 . 30 + 5 . 7
4) 5 . 30 + 7
Answer:
5x30 + 5x7
Step-by-step explanation:
hope this helps :)
which points lies on the line described by the equation? y+4=(x-3)
what is the name of the line that the function approaches?
a. y-axis
b. there is no such line
c. the unknown line
d. asymptote
2/11 x 5/7 = ? PLEASE ALSO EXPLAIN THAAAANKS
Write a compound inequality that represents the situation. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour.
A. 20 ≥ x ≥ 50
B. 20 > x > 50
C. 20 < x < 50
D. 20 ≤ x ≤ 50
What is the reason for each step in the solution of the equation? 2x−1=4(x+1)2x−1=4(x+1)
Drag and drop the reasons into the boxes to correctly complete the table.
2x−1=4(x+1)2x−1=4(x+1)-
2x−1=4x+42x−1=4x+4-
2x=4x+52x=4x+5-
−2x=5−2x=5-
x=−52-
Given
Distributive property
Commutative property
Addition or suptraction property of equality
The altitude of an equilateral triangle is 9 inches. Find the perimeter of the triangle in inches.
The perimeter of the triangle will be 31.18 inches.
what is perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
If we draw a perpendicular line from one of the vertices of the triangle we get 2 right angled triangles each with altitude 9 ins and vertex angle = 30 degrees. So:-
[tex]Cos 30 =\dfrac{ 9} {h}[/tex]
where h = one of the sides of the equilateral triangle
[tex]h = \dfrac{9 }{ cos 30} = 10.392 \ inches[/tex]
Therefore the perimeter of the triangle =
[tex]3 \times 10.392 = 31.1769 \ inches[/tex]
Answer is 31.18 inches to the nearest hundredth.
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What is the rate of change of the volume of a ball with respect to the radius when the radius is?
One fourth of a number q is 3 more than three times a number w. Solve for q.
To solve for q, multiply both sides of the equation 1/4q = 3 + 3w by 4. This eliminates the fraction and gives us q = 12 + 12w.
Explanation:To solve for q, we need to translate the given information into an equation. The problem states that one fourth of q is 3 more than three times a number w. Written as an equation, this is represented as:
1/4 q = 3 + 3w
To solve for q, we can multiply both sides of the equation by 4 to eliminate the fraction:
q = 12 + 12w
This gives us the solution for q in terms of w.
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What is 30 1/4% as a fraction in simplest form
The simplest form is 3/40
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given:
30 * 1/4%
= 30* 1/400
= 30/400
=3/40
=0.075
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How to get "4" of 4s to equal 4 using any order of operation
Shilo is trying to compute the value of 27 + 55 + 13. She adds 27 + 13 to get 40, and then adds on 55. Which of the following properties is Shilo using? commutative distributive associative identity
the answer is commutative. hope this helps!
Shilo is using commutative and associative
What is commutative property?"For any numbers 'a' and 'b', a + b = b + a"
What is distributive property?"For any real numbers 'a', 'b' and 'c',
a × (b + c) = a × b + a × c"
What is associative property?For any numbers 'a', 'b' and 'c',
(a + b) + c = a + (b + c)
What is identity?For any real number a,
the additive identity is a + 0 = 0 + a = a
For given question,
Shilo is trying to compute the value of 27 + 55 + 13.
She adds 27 + 13 to get 40, and then adds on 55.
⇒ 27 + 55 + 13
= 27 + 13 + 55 ...........(commutative property, 55 + 13 = 13 + 55)
= (27 + 13) + 55 ...........(associative property)
= 40 + 55
= 95
Therefore, Shilo is using commutative and associative property.
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The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?
Answer: the answer is D
Step-by-step explanation:
Factor completely p^2 - 8p + 7
4v=64 how do I solve this and what’s the answer