Inverse of the given matrix is
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
the matrix in question is
−1 0 1
2 2 0
1 0 1
now, we are given that inverse of the matrix exists.
A⁻¹ = adjoint of A/|A|
The determinant of the matrix A is:
det(A) = (-1) [(2)(1) - (0)(0)] - 0 [(2)(1)-(0)(1)] + 1 [(2)(0) - (2)(1)] = -4
The adjoint of the matrix A is:
2 2 −2
0 −2 −2
−2 −2 −2
Therefore, the inverse of the matrix A is:
A⁻¹ = 1/(-4) [2 2 −2]
[0 −2 −2]
[−2 −2 −2]
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
So, the inverse of the matrix A is:
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
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i need help please!!
a) The probability of selecting two different colors is obtained as 9/10.
b) The probability of not selecting a yellow marble is obtained as 3/20.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a) To find the probability of selecting two different colors, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
So the probability of selecting two different colors can be found by calculating the probability of selecting two marbles of the same color and subtracting that from 1.
The probability of selecting two marbles of the same color from the first bag is (2/5) x (1/4) = 1/10, since there are 2 red marbles out of 5 total marbles in the bag, and the probability of selecting a second red marble is 1/4.
The probability of selecting two marbles of the same color from the second bag is 0, since there is only one marble of each color.
So the probability of selecting two different colors is -
1 - (1/10 + 0) = 9/10
Therefore, the probability value is 9/10.
b) To find the probability of not selecting a yellow marble, we can again use the complement rule.
The probability of not selecting a yellow marble is equal to 1 minus the probability of selecting a yellow marble from either bag.
The probability of selecting a yellow marble from the first bag is 1/5, since there is one yellow marble out of 5 total marbles in the bag.
The probability of selecting a yellow marble from the second bag is also 1/4, since there is one yellow marble out of 4 total marbles in the bag.
So the probability of not selecting a yellow marble is -
1 - (1/5 + 1/4) = 3/20
Therefore, the probability value is 3/20.
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At a restaurant, 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant?
Answer: The correct answer would be Graph H.
Step-by-step explanation:
Answer:
top right
Step-by-step explanation:
600 per 10 hours is a rate of 60/hour.
You need a graph that has a slope of 60 and includes the point (1, 60).
Answer: top right
Use the ruler provided to measure the dimensions of the parallelogram shown to the nearest 0.5 centimeter.
Which measurement is closest to the area of the parallelogram in square centimeters?
F.14 cm2
G.16.5 cm2
H. 4114
cm2
J.8.5 cm2
The closest answer choice to 26.25 cm² is G. 16.5 cm².
What is area ?
Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).
Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.
From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:
Area = base x height
Area = 7.5 cm x 3.5 cm
Area = 26.25 cm² (rounded to the nearest 0.5 cm)
Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.
Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².
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HELP PLS BRAINLIEST AND FIVE STAR IF ALL OF THESE ARE CORRECT
a)√(x^2-14x+49)=x-7
b)√(4x^2-20x+25)=5-2x
C)√(y^4+2y^2+1)=y^2+1
d)√(x^2+2x+1)=x+1
e)√(y^2-20y+100)=y-10
f)√(y^6-2y^3+1)=y^3-1
pls answer all pls pls pls
(also the answer is most likely NOT all real numbers or no solutions)
The solution to the all given equations is that they have infinite many real solutions
How to determine the solution to the equationsEquation (a)
From the question, we have the following parameters that can be used in our computation:
√(x^2-14x+49)=x-7
When both sides of the equations are squared, we have:
x^2 - 14x + 49 = x^2 - 14x + 49
Evaluate the like terms
0 = 0
This represents infinite many solutions
Equation (b)
Here, we have:
√(4x^2-20x+25)=5-2x
When both sides of the equations are squared, we have:
4x^2-20x+25 = 25 - 20x + 4x^2
Evaluate the like terms
0 = 0
This represents infinite many solutions
For the remaining expressions, we have the following (using the above steps)
Equation (c)
√(y^4+2y^2+1) = y^2 + 1
y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1
0 = 0
Equation (d)
√(x^2+2x+1)=x+1
x^2 + 2x + 1 = x^2 + 2x + 1
0 = 0
Equation (e)
√(y^2-20y+100)=y-10
y^2 - 20y + 100 = y^2 - 20y + 100
0 = 0
Equation (f)
√(y^6-2y^3+1)=y^3-1
y^6-2y^3+1 = y^6-2y^3+1
0 = 0
Hence, the equations have infinite solutions
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Help me with this please
Answer:
we have to check the chemical property of the daisy perfume
Create Frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds. Josue's Dogs
The frequency of a repeated event is its number of instances for every unit of time. In below given way frequency table can be constructed.
What is frequency?The frequency of a repeated event is its number of instances for every unit of time. It differs from angular frequency and is sometimes made reference to as temporal resolution for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.
The time elapsed between events is measured by the period, which is the opposite of the frequency. For instance, the period, T—the time between beats—is equal to half a second if a heart beats 120 times per minute. Frequency tables to represent the morning and afternoon dogs as two sets of data are:
range frequency
0- 9 2
10- 19 3
20-29 1
30-39 2
40-49 1
50-59 1
Therefore, in above given way frequency table can be constructed.
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Can someone answer this for me
Continue the sequence by increasing each number in powers of 1000:
11345,____,____,____,____,____.
Answer:
12345,13345,14345,15345,16345
Step-by-step explanation:
Determine whether each expression is equivalent or not equivalent to 16^t-0.25?
A) 4^2t/4^0.5
B) 16^t/2^4
C) 16^t/2
The sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be examples abοve are equal tο 16t - 0.25.
What is the expressiοn?Mathematical prοcesses like multiplying, dividing, adding, and nοw even deleting are required. If they were merged, the fοllοwing claim wοuld be made: An equatiοn, sοme statistics, and a mathematical fοrmula Values, cοmpοnents, and mathematical prοcesses like additiοns, subtractiοns, reversals, algebraic fοrmulas, and divisiοns make up a statement οf truth. Wοrds and phrases can be rated and analyzed.
Here,
We pοssess 16t – 0.25.
A) The fοrmula 42t/40.5 equals (22t)² / (20.5) = 24t / (20.5) = 16t / (20.5)4 = 16t / 4 = 4(16t).
Expressiοn A is nοt equal because 4(16t) is nοt the same as 16t - 0.25.
B) [tex](16)^t/2^4 = (2^4)^t / 2^4[/tex]
=> [tex]2^{4t} / 2^4 = 2^{(4t-4)} = 16^{(t-1)} (t-1).[/tex]
Expressiοn B is not equivalent because 16(t-1) is nοt equal to 16(t - 0.25).
C) [tex]16^t/2 = (2^4)^t / 2[/tex]
[tex]= > 2^{4t} / 2 = 2^{(4t-1)} = 16^t \times 0.5.[/tex]
Expression C is nοt equivalent because 16t * 0.5 does not equal 16t - 0.25.
Hence, As a result, nοne of the examples above are equal to 16t - 0.25.
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Answer:
Step-by-step explanation:
Find the fourth term of an arithmetic sequence with a_(1)=3 and a recursive formula of a_(n)=a_(n-1)-9.
The fourth term of the arithmetic sequence is -24.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term after the first is formed by adding a constant, called the common difference, to the preceding term.
The fourth term of an arithmetic sequence with a1=3 and a recursive formula of an=an-1-9 can be found by using the recursive formula repeatedly until the fourth term is reached.
First, find the second term by plugging in n=2 into the recursive formula:
a2=a2-1-9=a1-9=3-9=-6
Next, find the third term by plugging in n=3:
a3=a3-1-9=a2-9=-6-9=-15
Finally, find the fourth term by plugging in n=4:
a4=a4-1-9=a3-9=-15-9=-24
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Plot the points A(-6,-4), B(3, -8), C(7, 1) on the coordinate axes below. State the coordinates of point � D such that � A, � B, � C, and � D would form a rectangle.
The coordinates of point D are (-2,5) and the points given have been plotted. The solution has been obtained by using the distance formula.
What is distance formula?
The distance between two points can be calculated using the xy-plane distance formula.
We are given that ABCD should form a rectangle.
We know that opposite sides of a rectangle are equal.
So, AB = CD
Using the distance formula which is
d = √(x₂ - x₁)² + (y₂ - y₁)²
We get
⇒AB = √(3 - (-6))² + (-8 - (-4))²
⇒AB = √(3 + 6)² + (-8 + 4)²
⇒AB = √(9)² + (-4)²
⇒AB = √81 + 16
⇒AB = √97 ...(1)
Let the coordinates of Point D be (x, y)
So, similarly
⇒CD = √(x - 7)² + (y - 1)² ...(2)
On equating (1`) and (2), we get
⇒√97 = √(x - 7)² + (y - 1)²
On squaring both sides, we get
⇒97 = (x - 7)² + (y - 1)²
⇒97 = x² + 49 - 14x + y² + 1 - 2y
⇒97 = x² + 50 - 14x + y² - 2y
⇒47 = x² - 14x + y² - 2y ...(3)
Also, AC = BD as these are the opposite sides of the rectangle.
Using the distance formula, we get
⇒AC = √(7 - (-6))² + (1 - (-4))²
⇒AC = √(7 + 6)² + (1 + 4)²
⇒AC = √(13)² + (5)²
⇒AC = √169 + 25
⇒AC = √194 ...(4)
Similarly,
⇒BD = √(x - 3)² + (y - (-8))²
⇒BD = √(x - 3)² + (y + 8)² ...(5)
On equating (4`) and (5), we get
⇒√194 = √(x - 3)² + (y + 8)²
On squaring both sides, we get
⇒194 = (x - 3)² + (y + 8)²
⇒194 = x² + 9 - 6x + y² + 64 + 16y
⇒194 = x² + 73 - 6x + y² + 16y
⇒121 = x² - 6x + y² + 16y ...(6)
On subtracting (3) and (6), we get
8x + 18y = 74
On dividing by 2, we get
4x + 9y = 37
From this, we get
x = (37 - 9y) / 4
Substituting this in (3), we get
⇒47 = [(37 - 9y) / 4]² - [14 * [(37 - 9y) / 4]] + y² - 2y
On solving this, we get
y = 5
On substituting this in x, we get
x = (37 - 9(5)) / 4
x = (37 - 45) / 4
x = -8 / 4
x = -2
Hence, the coordinates of point D are (-2,5) and the points given have been plotted.
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BMV Entertainment has more than 72 demos in the vault. In December, each of the 6 executives will receive an equal number of demos to review.
Which number sentence below represents the number of demos, D, that each executive will receive?
A. 72 + D > 6
B. 72 ÷ 6 < D
C. 72 - 6 < D
D. 72 × 6 > D
The number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D. Option B
How to find the sentence that represents the number of demosSince there are more than 72 demos
Each executive will receive at least 72/6 = 12 demos.
The number of demos that each executive will receive is 12 demos
Therefore, the number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D.
Hence, the correct inequality is 72 ÷ 6 < D.
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Elisa has homework assignments in seven subjects she only has time to do five of them
Answer: What else? Is that the whole sentence to this story i dont get it?
Step-by-step explanation:
Find the logistic function f with the given properties.
f(0) = 1, f has limiting value 11, and for small values of x, f is approximately exponential and grows by 75% with every increase of 1 in x.
f(x) = ____
The logistic function is then given by f(x) = 11 / (1 + e^(-0.75x))
The logistic function with the given properties is given by: f(x) = 11 / (1 + e^(-0.75x))
To understand this, we can start by noticing that for small values of x, f is approximately exponential and grows by 75% with every increase of 1 in x. This implies that the function can be written as f(x) = e^(0.75x). Since the limiting value of f is 11, the function can be written as f(x) = 11e^(0.75x). The logistic function is then given by f(x) = 11 / (1 + e^(-0.75x)), which satisfies the given conditions.
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Perform the addition or subtraction and simplify.
x
x − 4
−
3
x + 8
The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.
Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.
3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3
The simplified expression is -1/3.
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Pls help1 1/2-3/4 I need. Help please
Answer:
3/4
Step-by-step explanation:
a. 7cm 12cm and 13cm
b. 5cm 12cm and 13 cm
c. 4cm 8cm and 12cm
d. 5cm 10cm and 13cm
Answer: B : 5cm, 12cm and 13cm
Step-by-step explanation:
it says the amount of centimeters on each side on the ruler. its the small numbers
x=1/2 and y= -5
4(1/2) (4) -3 (-5)
The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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Complete question -
Find the value of 4x - 3y when x=1/2 and y=-5.
The wait time for a new roller coaster is at least 90 minutes. State the null and alternative hypothesis for the scenario using math symbols and words.
The Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.
What are the Null Hypothesis and Alternative Hypothesis?The null hypothesis states that a population parameter is equal to a value. The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.
Null Hypothesis (H0): The wait time for a new roller coaster is equal to or less than 90 minutes (H0: μ ≤ 90).
Alternative Hypothesis (Ha): The wait time for a new roller coaster is greater than 90 minutes (Ha: μ > 90).
In words, the null hypothesis states that the average wait time for the new roller coaster is equal to or less than 90 minutes.
The alternative hypothesis states that the average wait time is greater than 90 minutes.
We use the symbol μ to represent the population means of wait times for the new roller coaster.
Therefore, the Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.
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Evaluate the following expressions. Your answer mill be an angle in radians and in the interval [- π/2, π/2]
(a) sin^-1 (1) = ___
(b) sin^-1 (√2 / 2)= ____
(c) sin^-1 (- √2 / 2)= ____
a) The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.
b) The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.
c) The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.
Evaluate the following expressions. Your answer will be an angle in radians and in the interval [-π/2, π/2]
(a) sin^-1 (1) = π/2
(b) sin^-1 (√2 / 2)= π/4
(c) sin^-1 (- √2 / 2)= -π/4
(a) sin^-1 (1) = π/2
The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.
(b) sin^-1 (√2 / 2)= π/4
The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.
(c) sin^-1 (- √2 / 2)= -π/4
The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.
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Given thatf(x)=x2−3andg(x)=−5x+2, find(gt)(52), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A.(gf)(52)=B. The value for(gf)(52)does not exis
From function f(x)=x2−3andg(x)=−5x+2,The correct answer is A. (gf)(52)= -6.75
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between a variable quantity and another variable quantity.
To find (gf)(52), we first need to find f(52) and then substitute that value into g(x).
First we need to Find f(52)
f(x)=x2−3
f(52)=(52)2−3
f(52)=52−3
f(52)=1.75
Then we can Substitute f(52) into g(x)
g(x)=−5x+2
g(f(52))=−5(1.75)+2
g(f(52))=−8.75+2
g(f(52))=−6.75
Therefore, (gf)(52)=−6.75
The final answer is A. (gf)(52)=−6.75
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Math 1050 Written Homework - Section 5.3
1. Find an equation fro the parabola with vertex (3,5) and focus
(7,5).
The equation of the parabola is (y-5)^2=16(x-3)
To find the equation for the parabola with vertex (3,5) and focus (7,5), we can use the formula for a parabola with a horizontal axis of symmetry:
(y-k)^2=4p(x-h)
Where (h,k) is the vertex and p is the distance from the vertex to the focus.
In this case, the vertex is (3,5) and the focus is (7,5), so we have:
(y-5)^2=4p(x-3)
The distance from the vertex to the focus is 4, so p=4. Plugging this value into the equation gives us:
(y-5)^2=16(x-3)
This is the equation for the parabola with vertex (3,5) and focus (7,5).
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What is the value of 6 = 3 × 2³? 2/03/0 16 64
The value of 6 = 3 × 2³ is 24 by using PEMDAS operations, the correct option is (d).
To understand why, we can simplify the equation using the order of operations, which is PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction). To evaluate the expression 3 x 2³, we first need to simplify the exponent, which means multiplying 2 by itself three times:
2³ = 2 x 2 x 2
2³ = 8
Now we can substitute the value of 2³ into the original expression:
3 x 2³ = 3 x 8
3 x 2³ = 24
However, the value of 6 = 3 x 2³, is equal to 24 the correct option is (d).
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The complete question is:
What is the value of 6 = 3 × 2³?
a. 16
b. 64
c. 42
d. 24
Alex goes to a movie on Saturday for $10. While there, he pays $3 for each item he buys at the concession stand.
Which equation best represents this information?
y = 10x + 3
y = 3x - 10
y = 3x + 10
y = 10x - 3
Answer:
y = 3x + 10
Step-by-step explanation:
y represents total he pays
x represents items he buys
total he pays = $3 for each item + $10 movie
y = 3x + 10
What is the difference in area between a circle with a
radius of 10cm and regular pentagon inscribed in it, to the nearest
whole?
The difference in area between a circle with a radius of 10cm and regular pentagon inscribed in it is 142cm².
The difference in area between a circle with a radius of 10cm and a regular pentagon inscribed in it can be found by first finding the area of the circle and then the area of the pentagon, and then subtracting the two values.
To find the area of the circle, we use the formula
A = πr²,
where r is the radius of the circle. In this case, r = 10cm, so the area of the circle is:
A = π(10cm)²
A = 100π cm²
To find the area of the regular pentagon, we can use the formula
A = (1/4)n*a² * cot(π/n),
where n is the number of sides of the polygon and a is the length of one side. Since the pentagon is inscribed in the circle, we can use the radius of the circle to find the length of one side of the pentagon.
The length of one side of the pentagon is:
a = 2r * sin(π/n)
a = 2(10cm) * sin(π/5)
a = 11.756cm
Now we can plug this value into the formula for the area of the pentagon:
A = (1/4)(5)(11.756cm)² * cot(π/5)
A = 172.047cm²
Finally, we can subtract the area of the pentagon from the area of the circle to find the difference in area:
Difference in area = 100π cm² - 172.047cm²
Difference in area = 314.159cm² - 172.047cm²
Difference in area = 142.112cm²
To the nearest whole, the difference in area between the circle and the pentagon is 142cm².
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need some help with this problem. I don't understand it but I would like if someone could help give me a good explanation. Thanks
Answer: Triangle 1: -6x + 105 Triangle 2: 20x - 30 Triangle 1 would have a greater perimeter if x = 5
Step-by-step explanation:
The perimeter of a shape is the sum of all the sides. (Add them together)
Triangle 1:
17 + 6x + 4(-3x + 22)
Simplify:
17 + 6x -12x + 88
Perimeter = -6x + 105
Triangle 2:
24 + 5x + 3(5x - 18)
Simplify:
24 + 5x + 15x - 54
Perimeter = 20x - 30
If x = 5: (Plug in 5 for x)
Triangle 1:
If x = 5: (Plug in 5 for x)
-6(5) + 105
-30 + 105 = 75
Triangle 2:
20(5) - 30
100 - 30 = 70
75 > 70
Triangle 1 would have a greater perimeter if x = 5
Hope this helps!
Write the function in standard form and determine the end behavior. Be sure to use limit notation. 7. f(x)=-4 x^{3}-10 x^{12}+13 x) 8. ( f(x)=8 x^{21}-5 x^{2}+13 x ) 9. ( f(x)=x^{32}-10 x^{14}
The function in standard form of f(x)=-4 x³-10 x¹²+13 is f(x)=-10 x¹²-4 x³+13 x. The function in standard form of f(x)=8 x²¹-5 x²+13 x ) is f(x)=8 x²¹-5 x²+13 x. The function in standard form of ( f(x)=x^³²-10 x¹⁴ is f(x)=8 x²¹-5 x²+13 x
7. To determine the end behavior, we look at the highest degree term, which is -10 x^{12}. As x approaches positive infinity, -10 x^{12} will approach negative infinity. As x approaches negative infinity, -10 x^{12} will approach positive infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = -∞
lim_{x→-∞} f(x) = ∞
8. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is 8 x^{21}. As x approaches positive infinity, 8 x^{21} will approach positive infinity. As x approaches negative infinity, 8 x^{21} will approach negative infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = ∞
lim_{x→-∞} f(x) = -∞
9. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is x^{32}. As x approaches positive infinity, x^{32} will approach positive infinity. As x approaches negative infinity, x^{32} will approach positive infinity. Therefore, the end behavior is:
limx→∞ f(x) = ∞
limx→∞f(x) = +∞
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Determine if the sequence is geometric. If it is, find the common ratio, the term named in the problem, the explicit-formula, and the three terms in the sequence after the last one given.
Show work
Find f(10)
7) -4, -12, -36, -108, ...
The common ratio is equal to 3.
The tenth term of this geometric sequence is -78,732.
The explicit-formula of this geometric sequence is aₙ = -4(3)ⁿ⁻¹.
The three terms in the sequence after the last one given are -324, -972, and -2916.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -12/-4
Common ratio, r = 3.
For the explicit formula, we have:
aₙ = a₁rⁿ⁻¹ = -4(3)ⁿ⁻¹
Now, we can determine three terms in the sequence after the last one given;
a₅ = a₁r⁵⁻¹ = -4(3)⁴ = -324.
a₆ = a₁r⁶⁻¹ = -4(3)⁵ = -972.
a₇ = a₁r⁷⁻¹ = -4(3)⁶ = -2916.
f(10) = a₁₀ = a₁r¹⁰⁻¹ = -4(3)⁹ = -78,732.
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Workspace: Given pardlelogram WxY 2, where Wxx =2x+15,xY= x+27 and yz=4x-21, delemine the length of 2W in inches.
The length of 2W in inches can be calculated by using the measurements of the parallelogram. Wxx is 2x+15, and xY is x+27. Since the length of W xx and xY is referring to the same line, x+27=2x+15. Solving for x, x=12. Knowing the value of x, Wxx=2(12)+15=39 inches and xY=12+27=39 inches. Therefore, 2W=2(39)=78 inches.
The length of a line in a parallelogram can be calculated by adding the two measurements of the two lines containing the same point. Since the line containing point W is the same line containing point x, the two measurements can be solved for the same variable, x. Once the variable is determined, the value of the two lines containing the same point can be determined. The value of the two lines can then be multiplied by 2 to determine the length of the line in the parallelogram.
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Compare the numbers 144 and 12. 9329....
Select from the drop-down menu to correctly complete the statement.
√144 is
is Choose... v 12.9329...
Two comparations can be done:
√144 is rational and 12.9329... is irrational.12.9329...> √144 How to compare the two numbers?I understand that we want to compare the numbers:
√144 and 12.9329...
Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.
For the first one, we know that:
12*12 = 144
So 144 is a perfect square, then when we apply the square root we will get:
√144 = 12
Then the two comparations are:
√144 is rational and 12.9329... is irrational.
And:
12.9329...> √144
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