For table # 1:
x= 1 * 3.5 = 3.5
x = 2*3.5 = 7
x = 3*3.5 = 10.5
x = 4* 3.5 = 14
For table #2
x=1 * 3 = 3
x =2 * 3 = 6
x = 3*3 = 9
x = 4* 3 = 12
Hence, the data sets show multiplicative relationships:
For data set 1 is 3.5 times x, and in data set 2 y is 3 times x.
Why is c speed of light in albert einseins eqation e=mc squared
Answer:
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The speed of light (c) is considered a fundamental constant of nature. In the famous relativity equation, E = mc², the speed of light (c) serves as a constant of proportionality, linking the formerly disparate concepts of mass (m) and energy (E).
Graph the equation. Identify the intercepts.
1.) y + 2 = -4(x - 2)
x-int:
y-int:
For the following equation, the x-intercept is (3/2, 0) and the y-intercept is (0, 6).
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
y+2=-4(x-2)
for x-intercept=(x,0)
2=-4(x-2)
2=-4x+8
4x=6
x=6/4=3/2
for y-intercept=(0,y)
y+2=-4(*-2)
y=6
The x-intercept is (3/2,0) and y-intercept is (0,6) for given equation.
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The sum of two integers is 9. Their difference is 5.
What are the two integers?
A 7 and 12
B-7 and 16
C -12 and -7
D 2 and 7
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The correct answer is (( D )) .
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Look :
\(7 + 2 = 9\)
\(7 - 2 = 5\)
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6. Determine the system of equations based on the following relationships and then solve
for the two integers.
a. Fourteen more than twice the first integer gives the second integer
b. The second integer increased by one is the square of the first integer
Answer: (-3,8) and (5,24)
The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).
To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.
According to the given information:
a. Fourteen more than twice the first integer gives the second integer:
This can be expressed as: 2x + 14 = y
b. The second integer increased by one is the square of the first integer:
This can be expressed as: y + 1 = x^2
Now, we have a system of equations:
1) 2x + 14 = y
2) y + 1 = x^2
To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):
2x + 14 + 1 = x^2
2x + 15 = x^2
Rearranging the equation, we have:
\(x^2 - 2x - 15 = 0\)
Factoring the quadratic equation, we get:
(x - 5)(x + 3) = 0
Setting each factor equal to zero:
x - 5 = 0 --> x = 5
x + 3 = 0 --> x = -3
Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':
For x = 5:
2(5) + 14 = y
10 + 14 = y
y = 24
For x = -3:
2(-3) + 14 = y
-6 + 14 = y
y = 8
Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).
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What is the meaning of "\(F=\left \{ (x,y):\varphi (x,y,p) \right \}\)"?
The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.
The expression "F = {(x, y) : φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function φ, which takes the variables x, y, and p as inputs.
To fully understand the meaning of F, we need to delve into the function φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.
For instance, let's consider a specific example where vraphi(x, y, p) is defined φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.
It is important to note that the specific meaning and implications of F heavily rely on the nature of the function φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.
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how would you solve the following quadratic equation using the square root property (x-2)^2=4.
We have
\(\begin{gathered} (x-2)^2=4\rightarrow \\ (x-2)^2-4=0 \\ (x-2+2)(x-2-2)=0 \\ (x)(x-4)=0\rightarrow \\ x=0\lor x=4 \end{gathered}\)Using the square root property is:
\(\begin{gathered} x-2=2\lor x-2=-2 \\ x=2+2\lor x=-2+2 \\ x=4\lor x=0 \end{gathered}\)A -1/2
B 2
C -2
D 1/2
Answer:
A
Step-by-step explanation:
Find m/CAD.
A. 55°
B. 125°
C. 110°
D. 35°
A
B
55°
D
C
For which values of x is the expression undefined
which mortal kombat character is yalls favorite? Mine is kabal.
Answer:
omg! mine is Kabal tooo
Step-by-step explanation: i love mortal combat lol
Answer:
Scorpion
I am a normie yes I know
Leave me alone
Step-by-step explanation:
I feel like the answers obvious but apparently from other peoples answers its not 11 lol.
Answer:
11
Step-by-step explanation:
Translate 2 3 y − 9 < y + 1 into a sentence. Nine than two-thirds of number is less than the number .
The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:
"2/3y" represents two-thirds of a number.
"9" represents the number nine.
"y + 1" represents the number increased by one.
Now let's construct the sentence:
"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.
"is less than" - This is the comparison symbol in the inequality.
"the number" - This refers to the expression "y + 1," representing the number increased by one.
Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."
Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
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❗❗100 POINTS FOR CORRECT ANSWER AND EXPLANATION❗❗~math question~
thanks)
Answer:
k = 110
Step-by-step explanation:
You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.
Area of a circleThe area of a circle is given by the formula ...
A = πr²
Then the area of the outer circle is ...
A = π(14 cm)² = 196π cm²
The area of the inner circle is ...
A = π(8 cm)² = 64π cm²
Donut areaThe area of the whole donut is the difference of these areas:
whole donut area = (196 -64)π cm² = 132π cm²
Shaded areaThe shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...
shaded area = (300°/360°)×whole donut area
shaded area = 5/6 × 132π cm² = 110π cm²
Comparing this to the expression kπ cm², we see that ...
k = 110
The table shows the age of a painting (x) in years, and its estimated dollar value (y).
A 4-column table with 6 rows. Column 1 is labeled x with entries 50, 54, 62, 65, 68, sigma-summation x = 299. Column 2 is labeled y with entries 1,200, 1,500, 2,400, 3,200, 4,100, sigma-summation y = 12,400. Column 3 is labeled x squared with entries 2,500, 2,916, 3,844, 4,225, 4,624, sigma-summation x squared = 18,109. Column 4 is labeled x y with entries 60,000, 81,000, 148,800, 208,000, 278,800, sigma-summation x y = 776,600.
Which regression equation correctly models the data?
y = 41.47x + 0.09
y = 41.47x + 1,279.93
y = 153.32x – 6,688.54
y = 153.32x – 6,325.76
Regression equation correctly models the data is: y = -43.98x + 1,279.93
To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.
Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.
The slope (m) can be calculated using the formula:
\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)
Plugging in the values from the table:
m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)
m = (776,600 - 3,708,800 / 6(18,109) - 89,401)
m = (-2,932,200 / 66,654)
m ≈ -43.98
The y-intercept (b) can be calculated using the formula:
b = (Σy - m(Σx)) / n
Plugging in the values from the table:
b = (12,400 - (-43.98)(299)) / 6
b ≈ 1,279.93
The correct regression equation that models the data is:
y = -43.98x + 1,279.93
Out of the given options, the correct regression equation is:
y = -43.98x + 1,279.93
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A population of rare birds in town is currently listed at 2,000. It is declining at a rate of 2% per year. How many birds will be left after 20 years? Round your answer to the nearest whole number.
A. 1,335 birds
B. 1,980 birds
C. 2,972 birds
D. 23 birds
Option(A) is the correct answer is A. 1,335 birds.
To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.
We can use the formula for exponential decay:
N = N₀ * (1 - r/100)^t
Where:
N is the final number of birds after t years
N₀ is the initial number of birds (2,000 in this case)
r is the annual decline rate (2% or 0.02)
t is the number of years (20 in this case)
Plugging in the values, we get:
N = 2,000 * (1 - 0.02)^20
N = 2,000 * (0.98)^20
N ≈ 2,000 * 0.672749
N ≈ 1,345.498
Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.
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PLEASE HELP AND SHOW THE WORK U DID PLEASs
Answer:
A. 33° B. 52° | A. 55° B. 97° C. 83°
Step-by-step explanation:
triangle angles equal 180°
180 - (116 + 31) = 33° A
180 - (38 + 90) = 52° B
Problem 2.
28 + 53 = 81
180 - ( 81 + 44 ) = 55 A
180 - ( 55 + 28) = 97 B
180 - (53 + 44) = 83 C
( super sorry if it's wrong but I think this is right)
5/6 having denominator 35
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
What is the range of the function? f(x)=3^x−1−2
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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(6x-3)(4x-1) standard form
Answer:
6x+3
Step-by-step explanation:
24x-6x-12x+3
6x+3
It costs James $4 to make an order of a dozen cookies. If he sells them for $20, what percentage is each order of cookies marked up?
HELP ASAP THANK YOU SO MUCH
A) 20%
B) 80%
C) 400%
D) 500%
Answer:
Step-by-step explanation:] Answer would be 400%
New value - Original Cost
Original value
= 20 - 4/4
= 16/4
= 4 x 100
= 400%
A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270 degrees
Use 3.14 for pi and round the decimal to the nearest tenth.
42.8 ft
37.7 ft
12 ft
9.4 ft
The area of the sector is 37.7 ft.
What is sector:
A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.
The formula for the area of a sector is given by
A = (θ/360)πr²Where θ is the central angle in degrees, and r is the radius of the circle
Here we have
A circle has a radius of 4 ft.
The central angle of sector formed = 270°
Using the formula, Area of sector = (θ/360°) × π r²
Area of the given sector = [ 270/360] × 3.14 × (4)²
= [0.75 ] × [50.24]
= 37.68 ft
= 37.7 ft
Therefore,
The area of the sector is 37.7 ft.
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Find the equivalent expression using distributive property.
Answer:
it's A
Step-by-step explanation:
7(x+6)
7x + 7 × 6
7x + 42
Increase 2,400 by 5%
Increasing 2400 by 5% gives us 2520
we can increase the value by using the formula:
\(initial value+ percentage increase *initial value\) = increased percentage
in the aforementioned question we have
initial value = 2400
percentage increase = 5%
thus we can find out the increased percentage by:
2400 + 2400 X (5/100)
=2400 + 120
=2520
the value by which 2400 is increased is 120
to arrive at the increased value which is 2520
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(a) Un ángulo mide 47°. ¿Cuál es la medida de su complemento?
(b) Un ángulo mide 149°. ¿Cuál es la medida de su suplemento?
El supplemento y el complemento de cada ángulo son, respectivamente:
Caso A: m ∠ A' = 43°
Caso B: m ∠ A' = 31°
¿Cómo determinar el complemento y el suplemento de un ángulo?De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:
Ángulo y su complemento
m ∠ A + m ∠ A' = 90°
Ángulo y su suplemento
m ∠ A + m ∠ A' = 90°
Donde:
m ∠ A - Ángulom ∠ A' - Complemento / Suplemento.Ahora procedemos a determinar cada ángulo faltante:
Caso A: Complemento
47° + m ∠ A' = 90°
m ∠ A' = 43°
Caso B: Suplemento
149° + m ∠ A' = 180°
m ∠ A' = 31°
ObservaciónEl enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.
The statement is written in Spanish and its answer is written in the same language.
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There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. Which of the following is closest to the rate at which the area of the forest is increasing, in square kilometers per decade? (Use 1 kilometer=0.62mile.)
A.0.0006
B.0.0010
C.0.0025
D.0.0041
The rate at which the area of the forest is increasing, in square kilometers per decade, is 0.0041.
What does the rate of change mean?
How quickly one variable changes in relation to another is known as the rate of change. Speed is an example of a "rate of change." Speed is defined as the rate at which the distance to an object varies in relation to the time spent.
It is given that there are 640 acres in 1 square mile which can also be written as 640 acres= 1\(mi^2\).
The area of forest is increasing at a rate of 1 acre/decade.
It is given that 1 km= 0.62mi
By squaring on both sides we will get 1 \(km^2\) = 0.3844 \(mi^2\).
The rate at which the area of forests is increasing in square kilometers per decade is
\(\frac{1acre}{decade} *\frac{1mi^2}{640acre} *\frac{1km^2}{0.3844mi^2} =0.00406478\frac{km^2}{decade}\) .
Therefore the closest value is \(0.0041\).
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The volume of a cube is 64 cubic centimeters. What is the length of each edge of the cube?
4 centimeters
2 centimeters
8 centimeters
6 centimeters
Answer:
4 centimetres is the length of each edges of the cube
Answer:
4 centimeters
Step-by-step explanation:
Divide the fractions.
9/2 divided by 4/10
Answer:
11 1/4
Step-by-step explanation:
9/2/4/10
9/2/2/5
9/2*5/2
45/4
11 1/4
Final Answer:
45/4
Step-by-step explanation:
9/2 ÷ 4/10
9/2 ÷ 10/49/2 × 10/4 = 90/890/8 ⇒ 45/4
A cone has a volume of 8tt cubic inches, the height is 6 inches. What is the radius of the cone?
Answer:
48
Step-by-step explanation:
multiply 8x6 which is 48 .....8,16,24,32,40,48
Shirley can sew a skirt in 0.8 hours. To the nearest tenth, how many skirts could she make in 10.08 hours
Answer:
12.6
Step-by-step explanation:
10.08/.8 = 12.6, dividing the amount of time by the amount of time to make a skirt to get the number of skirts she can make
answer from the 4 options.
ASAP
Answer :
From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.
Opposite sides of Parallelogram are equal.XY = WZ
3a - 4 = a + 2
3a - a = 2 + 4
2a = 6
a = 6/2
a = 3
Now put the value of a in XY
XY = 3a - 4
XY = 3(3) - 4
XY = 9 - 4
XY = 5Similarly,
XW = YZ
2b = b + 1
2b - b = 1
1b = 1
b = 1
Now put the value of b in YZ
YZ = 2b
YZ = 2 × 1
YZ = 2XY = 5 and YZ = 2Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1→ 2b = b + 1
→ 2b - b = 1
→ b = 1
Since, YZ = 2b
→ YZ = 2 × 1
→ YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4WZ = a + 2→ 3a - 4 = a + 2
→ 3a - a = 2 + 4
→ 2a = 6
→ a = 6/2
→ a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
→ 9 - 4
→ 5
XY = 5.
Therefore, Option D is the required answer.