Answer:
The length of the sides of the square is 9.0015
Step-by-step explanation:
Given
The diagonal of a square = 12.73
Required
The length of its side
Let the length and the diagonal of the square be represented by L and D, respectively.
So that
D = 12.73
The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:
[tex]D^{2} = L^{2} + L^{2}[/tex]
Solving further, we have
[tex]D^{2} = 2L^{2}[/tex]
Divide both sides by 2
[tex]\frac{D^{2}}{2} = \frac{2L^{2}}{2}[/tex]
[tex]\frac{D^{2}}{2} = L^2[/tex]
Take Square root of both sides
[tex]\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}[/tex]
[tex]\sqrt{\frac{D^{2}}{2}} = L[/tex]
Reorder
[tex]L = \sqrt{\frac{D^{2}}{2}}[/tex]
Now, the value of L can be calculated by substituting 12.73 for D
[tex]L = \sqrt{\frac{12.73^{2}}{2}}[/tex]
[tex]L = \sqrt{\frac{162.0529}{2}}[/tex]
[tex]L = \sqrt{{81.02645}[/tex]
[tex]L = 9.001469325[/tex]
[tex]L = 9.0015[/tex] (Approximated)
Hence, the length of the sides of the square is approximately 9.0015
How would one be able to apply algebra to solve a random number problem?
Algebra can be used to solve a random number problem by considering order of operations.
Step-by-step explanation:
Algebra is one of the broad parts of mathematics, together with number theory, geometry, and mathematical analysis. It is used to represent the letters and symbols than numbers and quantities.
Algebra is of two types
i.) Elementary algebra , ii.) Abstract algebra
Elementary algebra is used for any study and their applications.
Abstract algebra is used for advanced mathematics by professionals.
The order of operations in algebra means solving first for exponents or roots, then multiplication, division, addition, and last for subtraction. The steps for the order of operations also require attention to mathematical grouping symbols, such as parentheses and brackets.
To solve a random number problem using algebra, understand the problem's context, convert the numbers into usable formats, apply algebraic techniques, and verify the results. For instance, Lisa uses random numbers generated by a calculator to select class members uniquely. These steps help solve such problems efficiently.
Applying Algebra to Solve a Random Number Problem:
To apply algebra to solve a random number problem, follow these steps:
First, understand the context and problem requirements. For example, suppose Lisa needs to select class members using random numbers generated by a calculator.Convert the random numbers into usable groups or categories. In Lisa's case, she reads .94360 as 94, 43, 36, and 60, with each number representing a potential class member.Apply algebraic techniques to manage and convert these numbers appropriately. For example, if you need to sum, multiply, or find an average of these numbers, use algebraic operations like addition or division.Verify your final answer by ensuring it meets all the problem’s criteria and constraints. Since each random number may only contribute one class member, Lisa checks that she selects unique members.By following these steps, you can solve random number problems efficiently using algebra.
Random numbers can be generated using various tools like tables or calculators, and their manipulation often requires algebraic techniques. Using a combination of these methods allows one to solve real-world problems, such as selecting class members or calculating probabilities.
Add polynomials (intro)
Add.
Your answer should be an expanded polynomial in standard form.
(7a3 - 2a - 2)+(-5a + 3) =
Stuck? Watch a video or use a hint.
V2
What type of triangle has three equal angles?
Answer:
Equilateral Triangle Has Three ⚟ equal angles because it sides are equal then opposite angle are also equal.
Thank You ☺️ ☺️.
☆ ★ Make It Brainlist Answer....Equilateral triangle has three equal angles.
there are three types of triangle.They are scalene triangle,isosceles raingle and equilateral triangle.Equilateral triangles are also the types of triangle which have three equal sides.
Question Progress
Homework Progress
a) Complete the table of values for y = x2 - 4x
1
xuo1 2 3 4 5
b) Which of the three curves drawn
matches the graph of y = x2 - 4x ?
Step-by-step explanation:
X Y
-5 45
-4. 32
-3. 21
-2. 12
-1. 5
0 0
1. -3
2. -4
3. -3
4 0
5 5
To complete the table of values for y = x^2 - 4x, substitute the given values of x into the equation. To determine the matching graph, compare the shape, direction, and intercepts of the given curves to y = x^2 - 4x.
Explanation:
For part a), you need to substitute the given values of x into the equation y = x^2 - 4x to find the corresponding values of y.
So for x = 1, y = (1)^2 - 4(1) = 1 - 4 = -3.
For x = 2, y = (2)^2 - 4(2) = 4 - 8 = -4.
Similarly, you can find the values of y for the other given values of x.
For part b), look at the three curves drawn and find the one that matches the graph of y = x^2 - 4x. Compare the shape, direction, and intercepts of the graph to determine the correct curve.
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-8-(-2)=−8−(−2)=
also im not sure if this is pre calc. , regular calc. or algebra
If 45% of the class are boys what percent is girls
Answer:
55%
Step-by-step explanation:
100% - 45% = 55%
Step-by-step explanation:
We know that
Total percentage = 100%
Percentage of boys = 45%
Percentage of girls = ( 100 - 45)%
=55%
Reflect shape A in the y axis
Answer: The shape would be on the same numbers but all positive and would just be looking the to the right.
Step-by-step explanation: So put it on the right side of the line going up and make it look the oppisite way it is now. on the same numbers but positive.
Reflection of an L-shaped object with respect to the y-axis is a horizontal flip resulting in a mirror image with opposite signs
When an L-shaped object is reflected with respect to the y-axis,
It means that every point on the object is reflected across the line that divides the object into two halves, with each half on either side of the y-axis.
This reflection results in the object being flipped horizontally.
The new orientation of the object is a mirror image of the original but with opposite signs.
The reflection of an L-shaped object with respect to the y-axis is an important concept in geometry and is often used in practical applications such as graphic design and architecture.
So the reflection of Figure A in the y-axis is A' which is attached below.
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In which of the following was E.W. Marland least successful?
Answer:
In cooperating with government
Step-by-step explanation:
Heavy borrowing by Marland led to financiers obtaining control of stock and ownership of Marland Oil, which then became Continental Oil Company, or Conoco. Marland continued to work for his former company but was made destitute by the Great Depression. He lost his oil empire, attributing his economic woes to lack of government regulation over banking.
i just had this question on an assignment, hope this helps.
7s + 5 for s =3 evaluate the expression
Answer: 26
Step-by-step explanation: Here, we have the expression 7s + 5 and we want to evaluate the expression when s is equal to 3.
To evaluate an expression, we simply plug the value
of the variable into the expression and solve.
So here, since s is equal to 3,
we have 7(3) + 5.
Notice that I used parentheses around the 3. It's always a good idea to use parentheses when substituting/plugging in numbers for variables.
Solving from here, 7(3) is equal to 21.
So we have 21 + 5 which is equal to 26.
So the value of our expression
when s is equal to 3 is 26.
Which expression correctly shows x6+2x3+1 factored completely over the integers?
a) (x3+1)2
b) (x+1)2(x2−x+1)2
c) (x+1)(x2−x+1)
d) (x2+1)(x4−x2+1)
Answer:
Option a.
Step-by-step explanation:
The given expression is
[tex]x^6+2x^3+1[/tex]
Splitting the middle term, it can be rewritten as
[tex]x^6+x^3+x^3+1[/tex]
[tex](x^6+x^3)+(x^3+1)[/tex]
Taking out GCF fro each parenthesis.
[tex]x^3(x^3+1)+1(x^3+1)[/tex]
[tex](x^3+1)(x^3+1)[/tex]
[tex](x^3+1)^2[/tex]
Therefore, the correct option is a.
The ratio of males to females in a Math 092 class is 2:3.
How many males are there in a class with 24 females?
Answer:
16
Step-by-step explanation:
2:3=x:24
2/3=x/24
(24)(2/3)=x
x=16
If 3x = -36 then x = ?
[tex]3x=-36|:3\\x=-12[/tex]
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
P.S. Hello from Russia :^)
\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
Answer:
-12
Step-by-step explanation: To put it simple you want to get the x by itself which means you'll have to multiply both sides by 3
3x/3 = x
-36/3 = -12
x = -12
Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplified expression to represent the number of members this year.
Answer: a simplified expression to represent the number of members this year is: x = 1.15 * (m)
Step-by-step explanation:
For this case what you can do is the following rule of three:
m ---> 100%
x ----> 115%
Clearing the value of x we have:
x = (115/100) * (m)
x = 1.15 * (m)
The mean of 5 numbers is 12. If four of the numbers are 1, 2, 3, 20, what is the last number?
So the last number is 34.
Hope this will help u...
The cereal box shown below is a rectangular prism. the height is 25, the length is 15, the width is 4. find the surface area of the cereal box.
Answer:
1070 (no unit of measurement is given)
Step-by-step explanation:
What we know:
height = 25
length = 15
width = 4
surface area formula: 2(wl+hl+hw)
w = width l = length h = height
2·(4·15+25·15+25·4)=1070
The surface area of the cereal box is 980 square units.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and add them together.
The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Substituting the given values, we have:
Surface area = 2(15 x 4) + 2(15 x 25) + 2(4 x 25)
Surface area = 30 + 750 + 200
Surface area = 980 square units
Therefore,
The surface area of the cereal box is 980 square units.
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A) -5,2
B) 2,-5
C) no solution
D)all real number
Answer:
(-5,2)
Step-by-step explanation:
The solution to the system is where the two lines cross
x = -5
y = 2
Answer:
Option A, (-5, 2)
Step-by-step explanation:
Step 1: Determine the solution
The solution is where both of the lines intersect. In this graph, they intersect at the x-value -5 and at a y-value of 2.
Answer: Option A, (-5, 2)
The ratio of nickels to dimes that Wade had saved in his bank was 10/13. If total number of nickels and dimes saved was 391, how many of them were dimes?
Answer:
The answer is 221.
Step-by-step explanation:
It is 221 because you find what number you can multiply both sides of the ratio by to get 391.
If you add both sides, 10 and 13, you get 23.
Divide 391 by 23 and you get 17.
Finally, multiply 13 by 17 and you get 221.
a shape is randomly selected from the following quadrilaterals: parallelogram, rhomus, trapaziod, rectangle, square. what is probability that it has 4 congruent sides
Answer:
Step-by-step explanation:
So, it's hard to know if the sides on the parallelogram are equal or not, but both a rhombus and square have four congruent sides, but only a square has four right angles.
So 1/2 shapes fit both parameters. Therefore there is a 50% probability it has four right angles, given that it has four congruent sides.
Complete the table for the given rule y=5x
Answer:
1
.8
.6
Step-by-step explanation:
what’s the length of the mid segment of a trapezoid with bases of length 16 and 24
Answer:
20
Step-by-step explanation:
The midsegment of a trapezoid is calculated as
[tex]\frac{sumofbases}{2}[/tex] = [tex]\frac{16+24}{2}[/tex] = [tex]\frac{40}{2}[/tex] = 20
Final answer:
The length of the mid-segment of a trapezoid with bases of length 16 and 24 is 20 units.
Explanation:
The length of the mid-segment of a trapezoid is the average of the lengths of the two bases. To calculate it, you add the lengths of the bases and then divide by 2. Since the bases of the trapezoid in question have lengths of 16 and 24, you would perform the following calculation:
(16 + 24) / 2 = 40 / 2 = 20
Therefore, the length of the mid-segment is 20 units.
Find the sum
(2x^3-x-9)+(7x^2-5x-2)
A) 9x^2-6x-11
B)2x^3+7x^2-4x-11
C) 2x^3+7x^2-6x-7
D)2x^3+7x^2-6x-11
Answer:
D)2x^3+7x^2-6x-11
Step-by-step explanation:
(2x^3-x-9)+(7x^2-5x-2) and simplify
into 2x^3+7x^2-6x-11 (steps shown in attachment)
Emily says she can prove the Pythagorean Theorem using the following diagram. She explains that she can divide the squares on the two shorter sides into grids with equal-sized grid squares. She says she can then rearrange the grid squares to cover the area of the square on the hypotenuse, which proves that the sum of the squares on the two shorter sides equals the square on the hypotenuse.
Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles?
Answer:
The last bit is correct, a2 + b2 = c2 for all right triangles? You do not divide the measurements you can only add up the squares to find the square of the hypotenuse as the sum, and then square root the totaled squares back to a new number. It does not cover the area like the statement said so only the question is true as Pythagoras theorem can be used to find a missing side or to find the missing hypotenuse.
Step-by-step explanation:
Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles?
Answer yes but only for c2 if we area adding.
This is because if we were looking and missing for a smaller side to the triangle measure and was already given the hypotenuse as one measure, then we can subtract either given alternative side would be; c2 - b2 = a2 to find an alternative side we subtract.
and c2- b2 = a2 works the same as c2 -a2 = b2.
None of the above formula finds the area, for the area we would need to multiply to find the height.
A = 1/2 x a x b
We have a different understanding to area
The area of a triangle is 1/2 given by the equation:
AΔ=(1/2)∗(base)∗(height) which is the smae as A= 1/2 x a x b
Eg)
Given: Measurements of A + B In attachment picture.
A = 3 cm
B = 4 cm
What is the area of the right triangle ABC?
Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:
AΔ=(1/2)∗3∗4=6cm2
So to find area we multiply A by 1/2 and multiply that product by the length of B (base).
Solve (t - 3)2 = 6. The arrow is at a height of 48 ft after approximately _ s
and after _s
Answer:
The arrow is at a height of 48 ft after approximately 0.55 s and after 5.45 s
Step-by-step explanation:
The following information is missing:
The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?
If the arrow is at a height of 48 ft and its initial velocity is 96 ft/s, then:
48 = 96*t - 16*t²
16*t² - 96*t + 48 = 0
16*(t² - 6*t + 3) = 0
t² - 6*t + 3 = 0
t² - 6*t + 3 + 6 = 0 + 6
t² - 6*t + 9 = 6
(t - 3)² = 6
t - 3 = √6
t - 3 = 2.45; t = 2.45 + 3; t = 5.45
or
t - 3 = -2.45; t = -2.45 + 3; t = 0.55
Answer: 0.55 & 5.45
Step-by-step explanation:
Can someone please help me with this question please ?
Answer:
x=43
Step-by-step explanation:
Since the lines are parrallel, the angle underneath the one you are finding is equal to 65. To find the total value of (x+72) you subtract 65 from 180, giving you 115.
x+72 = 115
then you subtract 72 from both sides
x=43
Five cubes are lined up in norder of size to form a solid. the side of each smaller cube is completely touching the side of the adjacent larger cube. The side lengths of the cubes are 1ft , 2ft, 3ft , 4ft, and 5ft. What is the surface area of the solid?.
Answer:
246 Square Feet
Step-by-step explanation:
The cubes are of side length 1ft , 2ft, 3ft , 4ft, and 5ft in that order.
If the side of each smaller cube is completely touching the side of the adjacent larger cube.
In the first and last cubes, 5 sides out of 6 are visible, so we use the formula [tex]5l^2[/tex] for their surface area.In the 2nd, 3rd and 4th cubes, only 4 sides out of 6 are visible, so we use the formula [tex]4l^2[/tex] for their surface area.Surface Area of the Solid [tex]= 5(l_1)^2+4(l_2)^2+4(l_3)^2+4(l_4)^2+5(l_5)^2, where \: l_1,l_2,l_3,l_4,l_5[/tex]
are the length of the cubes in that order
Surface Area of the Solid
[tex]= 5(1)^2+4(2)^2+4(3)^2+4(4)^2+5(5^2)\\=5+16+36+64+125\\=246 \:Square\: feet[/tex]
Triangle ABC and its transformation DEF are shown. What transformation of triangle ABC produced triangle DEF?
A.vertical translation
B.horizontal translation
C.rotation about point A
D.reflection across a vertical line
Answer: a
Step-by-step explanation:
Construct a linear equation in standard form.
Answer:
1
2
Step-by-step explanation:
Suppose that $17,183 is invested at an interest rate of 5.4% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?
Answer:
Total = Principal * e ^ (rate * years)
Total = 17,183 * 2.718281828459 ^ (.054 * years)
After 1 year = 18,136.39
After 2 years = 19,142.68
After 5 years = 22,509.12
After 10 years = 29,486.15
We'll use this formula to find the doubling time:
Years = ln (total / principal) / rate
we'll use 200 for total and 100 for principal
Years = ln (200 / 100) / rate
Years = ln (2) / .054
Years = 0.69314718056 / .054
Years = 12.8360588993 Years Doubling Time
Step-by-step explanation:
The question is about continuous compound interest. An initial amount of $17,183 is invested with a 5.4% annual interest rate. An exponential function depicts the amount over time, you find the balance by substituting the values of time into the function, and the doubling time is calculated to be approximately 12.8 years.
Explanation:The subject matter of this question deals with the concept of continuous compound interest in Mathematics. No additional deposits are made, only the principal amount is growing over time at a continuous compound interest. The formula for the balance in a continuously compounding account is given by P(t) = P0*e^(rt), where P0=initial balance, r=annual interest rate (as a decimal), t=time in years, and e=approximately 2.71828. In this case, P0 = $17,183 and r = 5.4% = 0.054.
a) The exponential function that describes the amount in the account after time t is: P(t) = $17,183*e^(0.054t)
b) Using this function, you can substitute the values of t to find the balance after each year, for example, for 1 year, it's P(1) = $17,183*e^(0.054*1) and similarly for 2, 5, and 10 years.
c) Doubling time can be obtained by equating P(t) = 2 * P0, which can be solved to obtain t = ln(2) / r (natural logarithm of 2 divided by the annual interest rate). Hence, it would approximately be 12.8 years.
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X-6
Use the expression X+4
How many excluded value(s) are there?
Answer:
There is 1 excluded value
The excluded value is -4
Step-by-step explanation:
This is correct on edge
Answer:
last one is -3 and -2
Step-by-step explanation:
on edge
In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation
can be used to determine if the triangle is a right triangle?
a2=c2
2a2=c2
a4=c2
2a=c
Answer:
b
Step-by-step explanation:
bc both legs have same measurement.
Answer:B
Step-by-step explanation:
Did the test