Answer:
The Proof is below.
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
Step-by-step explanation:
Let the Christmas Paper have Dimensions as
Length = 8 feet
Width = 8 feet
To Show:
Perimeter of Christmas Paper = 32
Solution:
Christmas Paper is in Rectangle Shape,
Therefore Perimeter of a Rectangle is given as
[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]
Substituting the values we get
[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.
Explanation:This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.
Since each side is 8 feet, the perimeter P is given by:
P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft
So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.
12+b=
26
Solve by using substitution
Answer:
14
Step-by-step explanation:
12+b=26
b=26-12
b=14
Answer:14
Step-by-step explanation:You first want to do 12+12 because that =24 and then keep on adding until u get 26
For which pairs of functions is (fg)(x)= x?
Answer:
A function and its inverse
Step-by-step explanation:
The property (fg)(x)= x holds for a function and its inverse.
For instance:
Let
[tex]f(x) = 2x[/tex]
and
[tex]g(x) = \frac{x}{2} [/tex]
These two functions are inverse of each other.
[tex]f(g(x)) = 2( \frac{x}{2} ) = x[/tex]
The correct pair is B: [tex]\(f(x)=\frac{2}{x}\) and \(g(x)=\frac{2}{c}\)[/tex], satisfying [tex]\((f \circ g)(x)=x\).[/tex]
To find which pairs of functions satisfy the condition [tex]\((f \circ g)(x) = x\),[/tex] let's compute [tex]\(f(g(x))\)[/tex] for each pair of functions and see if it equals [tex]\(x\).[/tex]
A. [tex]\(f(x) = x^2\) and \(g(x) = \frac{1}{x}\):[/tex]
[tex]\[f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}\][/tex]
[tex]\(f(g(x)) \neq x\),[/tex] so option A is not correct.
B. [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\):[/tex]
[tex]\[f(g(x)) = f\left(\frac{2}{c}\right) = \frac{2}{\frac{2}{c}} = c\][/tex]
[tex]\(f(g(x)) = x\)[/tex] if [tex]\(c = x\).[/tex] So, option B is correct.
C. [tex]\(f(x) = \frac{x - 2}{3}\) and \(g(x) = 2 - 3x\):[/tex]
[tex]\[f(g(x)) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x\][/tex]
[tex]\(f(g(x)) \neq x\)[/tex], so option C is not correct.
D. [tex]\(f(x) = \frac{1}{2x - 2}\) and \(g(x) = \frac{1}{2x + 2}\):[/tex]
[tex]\[f(g(x)) = f\left(\frac{1}{2x + 2}\right) = \frac{1}{2\left(\frac{1}{2x + 2}\right) - 2}\][/tex]
[tex]\[= \frac{1}{\frac{1}{x + 1} - 2}\][/tex]
[tex]\[= \frac{1}{\frac{1 - 2(x + 1)}{x + 1}}\][/tex]
[tex]\[= \frac{1}{\frac{-2x - 1}{x + 1}}\][/tex]
[tex]\[= \frac{x + 1}{-2x - 1}\][/tex]
[tex]\(f(g(x))\)[/tex] does not simplify to [tex]\(x\)[/tex], so option D is not correct.
Thus, the correct answer is option B: [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\).[/tex]
Complete Question:
For which pairs of functions is (fg)(x)=x?
A. f(x)=x^2 and g(x)=1/x
B.f(x)=2/x and g(x)=2/c
C. f(x)=x-2/3 and g(x)=2-3x
D. f(x)=1/2x-2 and g(x)=1/2x+2
without doing any calculations or modeling, explain how you know that the 24 inch by 32 inch mirror and the 20 inch by 32 inch mirror are not similar. Explain
one satellite radio station service charges $10 per month plus an activation fee of $20. A second service charges $11 per month plus an activation fee of $15. In what month will the cost of both plans be the same?
Seven years ago Maya opened a savings
account with her bank. She started with a
balance of $218. If her interest rate is 6%
per year, how much interest has accrued
using simple interest? What is Maya's
new total balance?
Answer:
accrued interest: $91.56total balance: $309.56Step-by-step explanation:
The amount of simple interest is ...
I = Prt = $218·0.06·7 = $91.56
The total account balance is this amount added to the original deposit:
$218.00 + 91.56 = $309.56
Find the difference
83456 - 728.88
Final answer:
To find the difference between 83456 and 728.88, subtract the second number from the first, resulting in the answer 82727.12.
Explanation:
To find the difference between the two numbers 83456 and 728.88, we simply subtract the second number from the first:
Write the numbers in a vertical column, aligning the digits by place value.
Perform the subtraction, starting from the rightmost digits (the ones place) and moving to the left, borrowing as needed.
Subtract each digit in the smaller number from the corresponding digit in the larger number.
83456
- 728.88
_______
82727.12
The difference is 82727.12.
Help trigonometry (angles of evaluation and depression)
Answer:
x ≈ 745.5 ft
Step-by-step explanation:
The angle at the lower right of the triangle is 28° ( alternate angle )
Using the sine ratio in the right triangle
sin28° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{350}{x}[/tex]
Multiply both sides by x
x × sin28° = 350 ( divide both sides by sin28° )
x = [tex]\frac{350}{sin28}[/tex] ≈ 745.5 ft ( to the nearest tenth )
The scale on a map is 1 : 320 000
What is the actual distance represented by 1 centimetre
Give your answer in kilometres.
Step-by-step explanation:
Given that , the scale on map is 1 : 320000.
Its means that if the scale shows 1 unit then actual length is 320000 units
So If the shows 1 cm then the actual distance = 320000 cm
=[tex]\frac{320000}{100000}[/tex] km = 3. 2 km
Therefore the actual distance represented by 1 centimeter is = 3.2 kmwhich expression is equivalent to 2+y+y+y+y+y+3 ?
Answer:5y+5
Step-by-step explanation:
2+y+y+y+y+y+3
Collect like terms
y+y+y+y+y+3+2
5y+5
The diagram represents the process of creating a scale
drawing from an original using a scale factor of 0.4. The
base of the original drawing must be:
A. 17.6
B. 18 cm
C. 33.5 cm
D. 45 cm
Answer: 18cm
Step-by-step explanation:
Let original drawing's base be b.
We are using scale factor of 0.4, so
0.4 of b = 7.2cm
0.4 × b = 7.2cm
b = (7.2/0.4)cm
b = 18cm
The base of the original drawing must be 18 cm.
Option B is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
Scale factor = 0.4.
From the figure,
Original height = 25.6 cm
Original base = b cm
Scale height.
= 25.6 x 0.4
= 10.24 cm
Scale base = 7.2 cm
Now,
Original base.
b x 0.4 = 7.2
b = 7.2 / 0.4
b = 18 cm
Thus,
The base of the original drawing must be 18 cm.
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ating a Line with a Positive Slope
A line passes through the point (0, –1) and has a positive slope. Which of these points could that line pass through? Check all that apply.
(12, 3)
(–2, –5)
(–3, 1)
(1, 15)
(5, –2)
Answer:
The points (12,3), (-2,-5) and (1,15) through which the line can pass.
Step-by-step explanation:
A line passes through the point (0, –1) and has a positive slope.
(i) The slope of the line passing through the points (0,-1) and (12,3) will be
[tex]\frac{- 1 - 3}{0 - 12} = \frac{1}{3} > 0[/tex]
(ii) The slope of the line passing through the points (0,-1) and (-2,-5) will be
[tex]\frac{- 1 + 5}{0 + 2} = 2 > 0[/tex]
(iii) The slope of the line passing through the points (0,-1) and (- 3,1) will be
[tex]\frac{- 1 - 1}{0 + 3} = - \frac{2}{3} < 0[/tex]
(iv) The slope of the line passing through the points (0,-1) and (1,15) will be
[tex]\frac{- 1 - 15}{0 - 1} = 16 > 0[/tex]
(v) The slope of the line passing through the points (0,-1) and (5,-2) will be
[tex]\frac{- 1 + 2}{0 - 5} = - \frac{1}{5} < 0[/tex]
Therefore, the points (12,3), (-2,-5) and (1,15) through which the line can pass. (Answer)
Answer:
A, B, D
Step-by-step explanation:
just took it on edg
If an item is 40% off, and then you take another 30% off, what is the total price you will pay?
what plus 3/4 equals 1 1/2
Determine the non-permissible value(s) of the variable(s).
Answer:
i) the value of a = 0 is non-permissible
ii) the value of b = 0 is non-permissible
Step-by-step explanation:
i) the given expression is [tex]\frac{5a^{2} + 80a }{50ab^{2} }[/tex]
ii) if a = 0 then the expression will become infinity hence the value of a = 0 cannot be used
iii) if b = 0 then the expression will become infinity, hence the value of b = 0 also cannot be used.
iv) In the numerator of the expression if it is factorized we get 5a[tex]\times[/tex] ( a + 16)
if a = -16 then the value of the expression becomes zero.
A baker has 10 cups of sugar to make cookies. Each batch calls for 113 cups of sugar.
How many batches of cookies can he make?
Enter your answer, as a mixed number in simplest form, in the box.
The number of batches of cookies made is [tex]7\frac{1}{2}[/tex]
Solution:
Given that, baker has 10 cups of sugar to make cookies
Each batch calls for [tex]1\frac{1}{3}[/tex] cups of sugar
To find: Number of batches of cookies can be made
From given information,
Total number of cups of sugar = 10
Cups of sugar for 1 batch = [tex]1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}[/tex]
Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch
Thus we get,
[tex]\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}[/tex]
Substituting the values, we get
[tex]\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}[/tex]
Thus number of batches of cookies made is [tex]7\frac{1}{2}[/tex]
Factor the expression completely. 1/4x + 19/4
The expression 1/4x + 19/4 can be factored by taking out the common factor of 1/4, resulting in the completely factored form (1/4)(x + 19).
Explanation:The student has asked to factor the expression 1/4x + 19/4 completely. To begin with, we note that both terms in the expression share a common factor of 1/4. Thus, we can factor out this common factor. The expression becomes:
(1/4)(x + 19)
The 1/4 is factored out, and we are left with the binomial x + 19 inside the parentheses. This is the completely factored form of the expression. Remember that factoring is essentially reversing the distribution process. In this case, we took out the common factor of 1/4 that was distributed across the x and 19.
-x+5y=5 in function notation
Answer:
[tex]y = f(x) = \frac{1}{5}x + 1[/tex]
Step-by-step explanation:
The function notation of a linear function is given by y = f(x) = ax + b.
Now, the given equation is - x + 5y = 5
So, we have to arrange it for the function notation.
Now, - x + 5y = 5
⇒ 5y = x + 5
⇒ [tex]y = \frac{1}{5}(x + 5)[/tex]
⇒ [tex]y = \frac{1}{5}x + 1[/tex]
Therefore, the function notation of the given equation will be
[tex]y = f(x) = \frac{1}{5}x + 1[/tex] (Answer)
Fin find the slope of the line passing through the points (-2, -7) and (9, -7)
Answer:
The slope of the line passing through the given points (-2,-7) and (9,-7) is m=0
Step-by-step explanation:
Given that the line passing through the points (-2,-7) and (9,-7)
To find the slope of the line passing through the points :
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-2,-7) and (9,-7) respectively
Substitute the points in the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7-(-7)}{9-(-2)}[/tex]
[tex]=\frac{-7+7}{9+2}[/tex]
[tex]=\frac{0}{11}[/tex]
Therefore m=0
Therefore Slope m is 0
Therefore the slope of the line passing through the given points (-2,-7) and (9,-7) is m=0
Awodden doll of height 8cm is made of with a pyramid of slant height 5cm on its upper part and a prism of base 6×6 on its lower part. if all the faces of the doll is painted at the rate of Rain 200 per cm^2, what will be the total cost? Find it.
Answer:
Total cost of painting the pyramid including the base = 19,200
Total cost of painting the pyramid excluding the base = 12,000
Step-by-step explanation:
Data provided in the question:
Height of the doll = 8 cm
Slant height of the pyramid, s = 5 cm
Base dimensions = 6 × 6
Cost of painting = 200 per cm²
Now,
Area of the base = 6 × 6 = 36 cm²
Area of the Pyramid = Area of the base + [tex]\frac{1}{2} \times P\times s[/tex]
here,
P is the perimeter of the base = 4 × side
= 4 × 6
= 24 cm
Thus,
Area of the Pyramid = 36 + [tex]\frac{1}{2} \times24\times 5[/tex]
or
Area of the Pyramid = 36 + 60 = 96 cm²
Total cost of painting the pyramid including the base = 96 cm² × 200
= 19,200
Total cost of painting the pyramid excluding the base = 60 cm² × 200
= 12,000
1 times 10 to the 21st power
Answer:
I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.
PLEASE HELP!!!! Which of the following would be a possible solution to the system of inequalities given below?
Answer:
B is the answer to the equation
Which of the following best describe(s) the slope of a linear function?
Select all that apply.
o rise over run
o run over rise
O average rate of change
o intersection with the y-axis
NEXT QUESTION
ASK FOR HELP
Answer:
Last one is your answer
Step-by-step explanation:
A regression line was calculated as ŷ = -3.2x + 9.7. Determine the slope of this line. Type a numerical answer in the provided space. Do not type spaces in your answer.
Answer:
Therefore the slope of
[tex]y= -3.2x + 9.7[/tex]
is
[tex]Slope =-3.2[/tex]
Step-by-step explanation:
Given:
A regression line was calculated as
[tex]y= -3.2x + 9.7[/tex]
To Find:
Slope = ?
Solution:
General Slope-Point Form is given as
[tex]y=mx+c[/tex]
Where,
[tex]m=Slope\\c=y-intercept[/tex]
On Comparing with given Regression line we get
[tex]Slope = m = -3.2[/tex]
Therefore the slope of
[tex]y= -3.2x + 9.7[/tex]
is
[tex]Slope =-3.2[/tex]
If it snows tomorrow, the probability is 0.9 that John will practice his trombone. If it does not snow tomorrow, there is on a 0.5 chance that John will practice. Suppose the chance of snow tomorrow is 50%. What is the probability that John will practice his trombone?
The probability that John will practice his trombone is 34%.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
If it rains tomorrow, the probability is 0.9. If it does not rain tomorrow, there is only a 0.5 chance. And, the chance of rain tomorrow is 70%.
Calculation of probability:
= 0.9 (0.1) + 0.5 (0.5)
= 0.34
= 34%
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The probability that John will practice his trombone is 0.7 or 70%, calculated using the law of total probability considering the two scenarios of snow and no snow.
To calculate the probability that John will practice his trombone, we need to consider two scenarios: one where it snows and one where it does not. We can solve this by using the law of total probability.
Let's denote the probabilities as follows:
P(Snow) is the probability it will snow, which is given as 0.5.
P(Practice|Snow) is the probability John will practice given that it snows, which is 0.9.
P(Practice|No Snow) is the probability John will practice given that it does not snow, which is 0.5.
The total probability that John will practice is:
P(Practice) = P(Snow) * P(Practice|Snow) + P(No Snow) * P(Practice|No Snow)
= 0.5 * 0.9 + 0.5 * 0.5
= 0.45 + 0.25
= 0.7
Therefore, the probability that John will practice his trombone is 0.7 or 70%.
I need help please help
Answer:
B
Step-by-step explanation:
Substitute the value of (2,1) into the equations, and you find that only B works.
Demand is in elastic if elasticity is?
Less than 1?
Equal to 1?
Greater than1?
Equal to 0?
It is equal to 0..... it is
Step-by-step explanation:
yes
Final answer:
Demand is considered inelastic when the elasticity of demand is less than one, signifying that consumers are less responsive to price changes.
Explanation:
When discussing the elasticity of demand, it is important to understand how demand responds to changes in price. If the elasticity of demand is less than one, this is known as inelastic demand. In this scenario, a 1 percent increase in the price that consumers pay will lead to a less than 1 percent change in the quantity purchased, showing a low responsiveness to price changes.
Conversely, demand is considered elastic when elasticity is greater than one, showing high responsiveness to price changes. If elasticity is exactly one, it is referred to as unitary elasticity, indicating that the percentage change in quantity demanded is equal to the percentage change in price.
Consider the following system of equations and their graph as picture
Answer:
(-2,5) and (7,23)
Step-by-step explanation:
we have
[tex]y=x^{2} -3x-5[/tex] ---> equation A
[tex]y=2x+9[/tex] ---> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
Using a graphing tool
The intersection points are (-2,5) and (7,23)
see the attached figure
therefore
The solutions are (-2,5) and (7,23)
The solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].
It is given equations are,
[tex]y=x^2-3x-5[/tex][tex]y=2x+9[/tex]Explanation:
From the given graph it is clear that the curve and line intersect each other at two points. These points are the solutions for the given system of equations.
The graph of line and curve intersect each other at [tex](-2,5)[/tex] and [tex](7,23)[/tex].
Thus, the solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].
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What is the value of the following expression 1.8 + 0.5(y + 6) - 2 t the power of 3 when y = 14?
Answer:
The value of given expression is 3.8.
Step-by-step explanation:
Given:
[tex]1.8+0.5(y+6)-2^3[/tex]
We need to find the simplified value of given expression using y =14
Solution:
Now we will substitute y =14 we get;
[tex]1.8+0.5(y+6)-2^3\\\\1.8+0.5(14+6)-2^3[/tex]
Now using PEDMAS we will first solve the parenthesis we get;
[tex]1.8+0.5\times20-2^3[/tex]
Now we will solve the exponent function we get;
we know that;
[tex]2^3=8[/tex]
So we can say that;
[tex]1.8+0.5\times20-8[/tex]
Now we will solve the multiplication operation.
[tex]1.8+10-8[/tex]
Now we will perform addition operation.
[tex]11.8-8[/tex]
And finally we will perform subtraction operation.
3.8
Hence The value of given expression is 3.8.
Drag the amounts to order them from greatest to least.
1 in. = 2.54 cm
1 ft = 12 in.
A 20 in.
B 1.8 in.
C 56 cm.
Answer:
answer is c i did the test
Step-by-step explanation:
The first Ferris wheel was built in 1893 in Chicago. It's diameter was 250 feet. How many feel did the Ferris wheel rotate with one complete turn?
The wheel covered 785 feet in one complete turn
Solution:
Given that, The first Ferris wheel was built in 1893 in Chicago
Diameter of wheel = 250 feet
Let us find the radius of wheel
[tex]Radius = \frac{diameter}{2}\\\\Radius = \frac{250}{2}\\\\Radius = 125[/tex]
Thus radius of wheel is 125 feet
We have to find the distance covered in one complete turn
The number of feet the wheel rotated in one turn is equal to its circumference
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14
Substituting the values we get,
[tex]C = 2 \times 3.14 \times 125\\\\C = 785[/tex]
Thus the wheel covered 785 feet in one complete turn