We can determine that TC owns one cow using exponential calculations.
Exponential equations: what are they?Exponent-based equations are those in which the exponent, or a portion of the exponent, is a variable.
For illustration, [tex]3^{x}[/tex] = 81.
In the question given,
TC is drinking no. of cups = 17
Let no. of cows TC has = x
Now according to the question, we can for the equation as:
[tex](\sqrt[5]{x} )^{2}[/tex] = 17 -1
⇒ x = [tex]\sqrt[5]{4}[/tex]
⇒ x = 1.319
⇒ x ≈ 1
Hence, TC owns 1 cow.
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help please !!! need help
Answer: The second and last one
Step-by-step explanation:
Complete the array to find 208 ÷ 8. Show your work.
Answer:
One possible way to complete the array is:
8 | 2 0 8
|
------
|
2 | 2 6
5 | 5 2
1 | 1 7
6 | 2 0
The answer is 26, so 208 ÷ 8 = 26.
To complete the array, we start by dividing the hundreds digit (2) by 8, which gives 0 with a remainder of 2. We write the remainder (2) in the ones place of the first row. Then we bring down the tens digit (0) and add it to the remainder to get 20. We divide 20 by 8, which gives 2 with a remainder of 4. We write the remainder (4) in the tens place of the second row, and bring down the ones digit (8) to the ones place of the second row. Finally, we add the digits in the second row to get 26, which is the quotient of the division
Step-by-step explanation:
A tank contains 12 litres of water in which is dissolved 24 grams of chemical A solution containing 4 grams per litre of the chemical flows into the tank at a rate of 4 litres per minute, and the well-stirred mixture flows out at a rate of 2 litres per minute. Determine the amount of chemical in the tank after 15 minutes.
The amount of chemical in the tank after 15 minutes is 154.14 grams.
To determine the amount of chemical in the tank after 15 minutes, we need to use the formula for the concentration of a solution:
C = m/V
Where C is the concentration of the solution, m is the mass of the chemical, and V is the volume of the solution.
Initially, the tank contains 12 litres of water and 24 grams of chemical A, so the initial concentration of the solution is:
C0 = 24/12 = 2 grams per litre
The solution flows into the tank at a rate of 4 grams per litre and 4 litres per minute, so the amount of chemical flowing into the tank per minute is:
4 grams per litre × 4 litres per minute = 16 grams per minute
The well-stirred mixture flows out of the tank at a rate of 2 litres per minute, so the amount of chemical flowing out of the tank per minute is:
C × 2 litres per minute = 2C grams per minute
The net change in the amount of chemical in the tank per minute is:
16 grams per minute - 2C grams per minute = 16 - 2C grams per minute
After 15 minutes, the net change in the amount of chemical in the tank is:
(16 - 2C) grams per minute × 15 minutes = 240 - 30C grams
The final amount of chemical in the tank is:
m = 24 + 240 - 30C = 264 - 30C grams
The final volume of the solution in the tank is:
V = 12 + 4 litres per minute × 15 minutes - 2 litres per minute × 15 minutes = 42 litres
The final concentration of the solution in the tank is:
C = m/V = (264 - 30C)/42
Solving for C, we get:
42C = 264 - 30C
72C = 264
C = 264/72 = 3.67 grams per litre
The final amount of chemical in the tank is:
m = C × V = 3.67 grams per litre × 42 litres = 154.14 grams
Therefore, the amount of chemical in the tank after 15 minutes is 154.14 grams.
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what is the 20th term of the sequence 1,3,9,27
Answer:
1162261467
Step-by-step explanation:
Note that this is a geometric sequence.
1,3,9,27
The pattern is to multiply the number by 3 to get to the next term.
a = 1
r = 3
n=20
arⁿ⁻¹ = nth term
You then substitute the values of a,r and n into the nth term:
arⁿ⁻¹=3¹⁹
3¹⁹=1162261467 which is the 20th term of the sequence
Hoped this helped
Answer:
To find the 20th term of the sequence 1, 3, 9, 27, we need to first identify the pattern of the sequence. It appears that each term of the sequence is obtained by multiplying the previous term by 3. This means that the sequence is a geometric sequence with first term (a) = 1 and common ratio (r) = 3.
Using the formula for the nth term of a geometric sequence:
an = a * r^(n-1)
where an is the nth term of the sequence, a is the first term, r is the common ratio, and n is the term number.
Substituting the values we have:
a = 1, r = 3, and n = 20
an = 1 * 3^(20-1) = 1 * 3^19 = 1162261467
Therefore, the 20th term of the sequence 1, 3, 9, 27 is 1162261467.
Step-by-step explanation:
brainliest pls
2. (4 marks) Find a basis for \( \mathbb{R}^{4} \) containing \( v=(1,-1,1,-1), \quad w=(0,1,0,1) \).
A basis for \( \mathbb{R}^{4} \) containing \( v \) and \( w \) is \( \{v, w, e_{1}, e_{2}\} = \{(1,-1,1,-1), (0,1,0,1), (1,0,0,0), (0,1,0,0)\} \).
A basis for \( \mathbb{R}^{4} \) is a set of four linearly independent vectors that span \( \mathbb{R}^{4} \). We are given two vectors \( v=(1,-1,1,-1) \) and \( w=(0,1,0,1) \) that are part of the basis. To find the other two vectors, we can use the standard basis vectors \( e_{1}=(1,0,0,0) \) and \( e_{2}=(0,1,0,0) \) and check if they are linearly independent with \( v \) and \( w \).
First, we check if \( e_{1} \) is linearly independent with \( v \) and \( w \). We can do this by setting up the equation \( a_{1}v + a_{2}w + a_{3}e_{1} = 0 \) and solving for the coefficients \( a_{1}, a_{2}, \) and \( a_{3} \).
\( a_{1}(1,-1,1,-1) + a_{2}(0,1,0,1) + a_{3}(1,0,0,0) = (0,0,0,0) \)
This gives us the system of equations:
\( a_{1} + a_{3} = 0 \)
\( -a_{1} + a_{2} = 0 \)
\( a_{1} = 0 \)
\( -a_{1} + a_{2} = 0 \)
We can see that the only solution is \( a_{1}=a_{2}=a_{3}=0 \), which means that \( e_{1} \) is linearly independent with \( v \) and \( w \).
Next, we check if \( e_{2} \) is linearly independent with \( v \), \( w \), and \( e_{1} \) by setting up the equation \( a_{1}v + a_{2}w + a_{3}e_{1} + a_{4}e_{2} = 0 \) and solving for the coefficients \( a_{1}, a_{2}, a_{3}, \) and \( a_{4} \).
\( a_{1}(1,-1,1,-1) + a_{2}(0,1,0,1) + a_{3}(1,0,0,0) + a_{4}(0,1,0,0) = (0,0,0,0) \)
This gives us the system of equations:
\( a_{1} + a_{3} = 0 \)
\( -a_{1} + a_{2} + a_{4} = 0 \)
\( a_{1} = 0 \)
\( -a_{1} + a_{2} = 0 \)
Again, we can see that the only solution is \( a_{1}=a_{2}=a_{3}=a_{4}=0 \), which means that \( e_{2} \) is linearly independent with \( v \), \( w \), and \( e_{1} \).
Therefore, a basis for \( \mathbb{R}^{4} \) containing \( v \) and \( w \) is \( \{v, w, e_{1}, e_{2}\} = \{(1,-1,1,-1), (0,1,0,1), (1,0,0,0), (0,1,0,0)\} \).
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may someone please give me the answer to this question?
Answer:
[tex]\huge\boxed{\sf 116\ in.\²}[/tex]
Step-by-step explanation:
The composite figure is made up of two shapes.
RectangleSemicircleArea of rectangle:= Length × Width
Where L = 13 in., W = 7 in.
= 13 × 7
= 91 in.²
Area of semi-circle:[tex]\displaystyle =\frac{\pi r^2}{2} \\\\\underline{Where \ r:}\\\\= \frac{13-5}{2} \\\\= \frac{8}{2} \\\\= 4 \ in.\\\\So,\ the \ above\ equation \ becomes\\\\= \frac{(3.14)(4)^2}{2} \\\\= \frac{(3.14)(16)}{2} \\\\= (3.14)(8)\\\\= 25.13 \ in.^2[/tex]
Area of composite figure:= Area of rectangle + Area of semi-circle
= 91 + 25.13
= 116.13 in.²
≈ 116 in.²[tex]\rule[225]{225}{2}[/tex]
John has a jar filled with juice. After he poured 350 ml of juice in each 8 glasses he was still left with 200 ml juice in the jar. What was the capacity of jar in liters?
Step By Step Explanation
Filled jar = ?
How much poured or (x) = 350ml × 8 glasses
=2800 ml
How much left or (y) = 200ml
Capacity = How much poured + How much left
Capacity = x + y
Capacity = 2800 ml + 200 ml
Capacity = 3000ml
Give answer in litres
1 litre = 1000 millilitre
So 3000ml = 3000 ÷ 1000
So 3000 ml = 3 litres
Capacity = 3 litres
Let \( \vec{a}=\langle 1,-3\rangle \) and \( \vec{b}=\langle 3, k\rangle \). Find \( k \) so that \( \vec{a} \) and \( \vec{b} \) will be orthogonal (form a 90 degree angle). \( k= \) Question Help: Mesege instructor
The value of \( k \) that makes \( \vec{a} \) and \( \vec{b} \) orthogonal is \( k=1 \).
Two vectors are orthogonal if their dot product is zero. The dot product of two vectors \( \vec{a}=\langle a_1,a_2\rangle \) and \( \vec{b}=\langle b_1,b_2\rangle \) is given by \( \vec{a}\cdot\vec{b}=a_1b_1+a_2b_2 \).
In this case, we have \( \vec{a}=\langle 1,-3\rangle \) and \( \vec{b}=\langle 3, k\rangle \). So the dot product is:
\( \vec{a}\cdot\vec{b}=(1)(3)+(-3)(k)=3-3k \)
We want this dot product to be zero, so we can set it equal to zero and solve for \( k \):
\( 3-3k=0 \)
\( 3k=3 \)
\( k=1 \)
Therefore, the value of \( k \) that makes \( \vec{a} \) and \( \vec{b} \) orthogonal is \( k=1 \).
Answer: \( \boxed{k=1} \).
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Use substitution to solve
The solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We can solve this system of equations using substitution. Solving the second equation for y, we get:
y = 3x - 3
Substituting this expression for y into the first equation, we get:
9x - 3(3x - 3) = 9
9x - 9x + 9 = 9
Therefore, the equation is true for any value of x.
Hence, the solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.
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Evaluate the following expression.
2
7/8 ÷ 1/8 + 2
Answer:
9
Step-by-step explanation:
7/8 divided by 1/8 is 7
7+2 = 9
Brainliest?
Someone help pls, I need this answer fast
Answer:
Step-by-step explanation:
North Dakota is 34 times larger
Puerto Rico
North Dakota = 1.83x[tex]10^{5}[/tex] [tex]Km^{2}[/tex]
Puerto Rico = 5.33 x [tex]10^{3}[/tex] [tex]Km^{2}[/tex]
1.83 x [tex]10^{5}[/tex]
5.33 x [tex]10^3[/tex] = 0.34 x [tex]10^2[/tex]
Think about the following relation: {(5,0),(8,4),(5,2),(-2,4)} What is the domain of the relation? {} {} What is the range of the relation? {} {}
The domain of a relation is the set of all the first elements of the ordered pairs in the relation, and the range of a relation is the set of all the second elements of the ordered pairs in the relation.
So, for the given relation {(5,0),(8,4),(5,2),(-2,4)}, the domain would be {5, 8, -2} and the range would be {0, 4, 2}.
To find the domain, we simply take the first element of each ordered pair and put them in a set. Similarly, to find the range, we take the second element of each ordered pair and put them in a set.
Therefore, the domain of the relation is {5, 8, -2} and the range of the relation is {0, 4,2}.
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solve for x (interior and exterior angles)
Answer:
-11
Step-by-step explanation:
*The sum of all three angles of a triangle is 180*
So,
80+60
140 + (x + 51) = 180
-140 -140
x + 51 = 40
- 51 - 51
x = - 11
HOPE this helped
The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the output for the initial value?
Gas in Marco’s Car
Seconds Spent Pumping Gas
0
12
24
36
48
Gallons of Gas in Car
3
5
7
9
11
3 gallons are the starting value determined by the slope-intercept relation.
What is slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.
To determine how much gas is entering his car each second, we must determine the rate of change:
Rise / Run is the rate of change.
Rate of change: (11 - 3 - 11) / (48 - 0)
Change rate: 8/48 = 1/6 gallons
Making use of the slope-intercept relationship:
Y = b(x) + c(slope); c(initial gas amount)
Choose any (x, y) point pair on the table:
(0, 3)
3 = 1/6x + c 3 = 1/6(0) + c\s3 = 0 + c\sc = 3
As a result, the starting point is 3 gallons.
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Let X (3, 0.02). Given Tx = 300 calculated by the Esscher Premium Principle with parameter 1, calculate h
The value of h is 99.969.
The Esscher Premium Principle is a method of calculating insurance premiums that considers the risk of an event occurring and the potential severity of the loss. The formula for the Esscher Premium Principle is:
Ex = ln(∑eαx Px)/α
Where Ex is the Esscher premium, α is the parameter, x is the loss amount, and Px is the probability of the loss occurring.
In this case, we are given X (3, 0.02), meaning that the loss amount is 3 and the probability of the loss occurring is 0.02. We are also given that the Esscher premium is 300 and the parameter is 1. Plugging these values into the formula, we get:
300 = ln(∑e1(3) 0.02)/1
Simplifying the equation, we get:
300 = ln(0.02e3)
Taking the natural logarithm of both sides, we get:
e300 = 0.02e3
Dividing both sides by 0.02, we get:
e300/0.02 = e3
Taking the natural logarithm of both sides again, we get:
300 - ln(0.02) = 3
Solving for h, we get:
h = (300 - ln(0.02))/3
h = 99.969
Therefore, the value of h is 99.969.
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Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) g(x) = 8- x / 8+ 7 ; g(2), g(-8), g(1/2), g(a), g(a – 8), g(x^2 - 8) g(2) = 6/10 g(-8) = UNDEFINED g(1/2) = (8-(1/2) / 8+(1/2))
g(a) = (8-a) – (8+a)
g(a-8) = _________
g(x^2 – 8) = ________
The function values.
To evaluate the function g(x) = 8 - x / 8 + 7 at the indicated values, we need to substitute the values into the function and simplify.
g(2) = 8 - 2 / 8 + 7 = 6 / 15 = 2 / 5
g(-8) = 8 - (-8) / 8 + 7 = 16 / 15 = 16 / 15
g(1/2) = 8 - (1/2) / 8 + 7 = (15.5) / 15 = 31 / 30
g(a) = 8 - a / 8 + 7 = (15 - a) / 15
g(a - 8) = 8 - (a - 8) / 8 + 7 = (16 - a) / 15
g(x^2 - 8) = 8 - (x^2 - 8) / 8 + 7 = (16 - x^2) / 15
So, the function values are:
g(2) = 2 / 5
g(-8) = 16 / 15
g(1/2) = 31 / 30
g(a) = (15 - a) / 15
g(a - 8) = (16 - a) / 15
g(x^2 - 8) = (16 - x^2) / 15
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The 6% state income tax on a $42,00 salary
The income tax amount of 6% will be equal to $252 on a salary of $4200.
What is Percentage?A number or ratio that can be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies.
A percentage is a figure or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A percentage is a figure without dimensions and without a standard measurement.
We must divide the value by the overall value to find the percentage, and then multiply the resulting number by 100.
What is Income Tax?A tax placed on people or organisations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable revenue are typically used to calculate income taxes. Tax rates can change depending on the taxpayer's characteristics and sort of income.
The word "income tax" refers to a category of tax that governments levy on income generated by businesses and people under their jurisdiction.
In this question,
Salary amount= $4200
Income tax= 6%
The amount to be paid in income tax= 6% of $4200
= (6/100)*4200
= $252
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Suppose you applied for positions at four different companies and let X be the number of offers you received.
a- Find the mean
b- standard deviation
of the number of offers you received. Round your answer to two decimal places
The answer of the number of offers you received are as follow,
1. Mean is equal to 1.96.
2. Standard deviation is equal to 1.17 (rounded to two decimal places) .
1.Mean (or expected value) is represented by E(X)
Formula of the expected value is,
E(X) = ∑xP(x)
Substitute the value from the table we get,
⇒E(X) = (0)(0.19) + (1)(0.12) + (2)(0.38) + (3)(0.16) + (4)(0.15)
⇒E(X) = 0 + 0.12 + 0.76 + 0.48 + 0.6
⇒E(X) = 1.96
2. Standard deviation of the number of offers received ,
⇒ Standard deviation 'σ' = √[ Σ(x - E(X))² P(x) ]
Substitute the values from the table we get,
⇒ Standard deviation 'σ'
= √[ (0 - 1.96)² (0.19) + (1 - 1.96)² (0.12) + (2 - 1.96)² (0.38) + (3 - 1.96)²(0.16) + (4 - 1.96)²(0.15) ]
= √[ 1.3728 ]
≈ 1.171665
≈1.17(rounded to two decimal places)
Therefore, the mean and the standard deviation of the number of offers received is approximately 1.96 and 1.17 (rounded to two decimal places) respectively.
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The above question is incomplete, the complete question is:
Suppose you applied for positions at four different companies and let X be the number of offers you received
X : 0 1 2 3 4
P(x) : 0.19 0.12 0.38 0.16 0.15
1. Find the mean
2. standard deviation
of the number of offers you received. Round your answer to two decimal places
5
Use Scratchpad to fill in the missing dimensions on the figure.
9 ft.
ft.
ft.
2 ft.
3 ft.
10 ft.
5 ft.
Calculate the area of the figure.
The area of the figure is
4 ft.
ft²
The method for calculating the area of a figure depends on the type of figure.
How to calculate the areaHere are some common formulas for finding the area of different shapes:
Square: To find the area of a square, you multiply the length of one side by itself: Area = side x side or A = s²
Rectangle: To find the area of a rectangle, you multiply the length by the width: Area = length x width or A = lw
Triangle: To find the area of a triangle, you multiply the base by the height and divide by 2: Area = 1/2 x base x height or A = 1/2 bh
Circle: To find the area of a circle, you multiply pi (3.14) by the radius squared: Area = pi x radius^2 or A = πr^2
Trapezoid: To find the area of a trapezoid, you multiply the average of the bases by the height: Area = 1/2 x (base1 + base2) x height or A = 1/2 (b1 + b2)h
These are just some of the formulas for calculating the area of different shapes. Depending on the figure you're working with, you may need to use a different formula or combination of formulas to find the area.
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I need help with question 10. I need to find the value of x
The solution is, the value of x is, x = 12.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
from the given figure, we get,
the triangles are similar,
so, we know that, the sides are proportional to each other.
i.e. 8:4 = x: 6
or, x = 8 * 6 / 4
or, x = 2 * 6
or, x = 12
Hence, The solution is, the value of x is, x = 12.
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Richard’s Supplies sold 100 calculators in the month of August. Joseph’s Deals sold 30 calculators in the first week of October. A business consultant concluded that Richard's Supplies sells more calculators than Joseph's Deals. Explain why the statistic is misleading
The statistic that "Richard's Supplies sells more calculators than Joseph's Deals" based solely on the information given is misleading because it compares the total sales of one business for an entire month with the sales of another business for only one week.
What should be the most acceptable way to make the sales comparison in statistic?It's possible that Joseph's Deals could sell more calculators than Richard's Supplies in a given week or even in the entire month of October, despite the fact that they only sold 30 calculators in the first week but we don't have enough information to compare the sales of these two businesses accurately.
In addition, we don't know if Richard's Supplies and Joseph's Deals are similar businesses with similar customer bases, pricing strategies, and marketing efforts. These factors could also affect their respective sales numbers.
In conclusion, to draw a meaningful comparison between the sales of these two businesses, we would need to gather more data about their sales over a longer period of time and under similar conditions.
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Carrie can bicycle 24 miles in the same time as it takes her to walk 6 miles. She can ride 9 mph faster than she can walk. How fast can she walk?
Carrie can walk at a speed of 3 mph.
To find out how fast Carrie can walk, we can use the formula distance = speed × time. Let's call the speed at which Carrie walks x, and the time it takes her to walk 6 miles t.
Since she can ride 9 mph faster than she can walk, her biking speed will be x + 9. We can set up the following equations:
6 = x × t (for walking)
24 = (x + 9) × t (for biking)
Since the time it takes her to walk 6 miles and bike 24 miles is the same, we can set the two equations equal to each other:
x × t = (x + 9) × t
Simplifying the equation gives us:
x = x + 9
Subtracting x from both sides gives us:
0 = 9
This is not a valid solution, so we need to go back to our original equations and solve for t:
t = 6/x (for walking)
t = 24/(x + 9) (for biking)
Setting these two equations equal to each other gives us:
6/x = 24/(x + 9)
Cross-multiplying gives us:
6(x + 9) = 24x
Distributing the 6 gives us:
6x + 54 = 24x
Subtracting 6x from both sides gives us:
54 = 18x
Dividing by 18 gives us:
x = 3
So Carrie can walk 3 mph.
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which equation represents the rule
The equation that represents a linear function rule for the following set of ordered pairs is A. y = -3x + 2
How can the equation that represents a linear function rulebe determined?We can express the Equation of a linear function, as y = mx + b.
m= slope
b= y-intercept
We can determine the slope (m):
= (change in y)/(change in x )
then we can substitute the values as :
= (-7 -(-4)) / (3 - 2)
= -3/1
= -3
Then thevalue of b can be found through the substituting of m = -3 into the equation knowing that (1, -1) = (x, y)
Then we have;
-1 = [-3(1) + b]
-1 = [-3 + b]
[-1 + 3] = b
b = 2
In this case , we can put m = -3 , b = 2
y = mx + b
y = [-3(x) + 2]
Therefore, we have
y = -3x + 2
Hence option A is correct.
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complete question:
Which equation represents a linear function rule for the following set of ordered pairs?
x y
1 -1
2 -4
3 -7
A. y = -3x + 2
B. y = -3x - 2
C. y = -2x + 3
D. y = -2x - 3
Describe the long run behavior of f(x)=5(2)x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.
The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.
As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1
As x approaches negative infinity, the value of the function approaches 1.
As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞
As x approaches positive infinity, the value of the function approaches infinity.
As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.
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7. A realtor took $32,500 made on the sale of a home and placed it in a new account that earns
6% compounded annually. Find the total amount in the account after 5 years.
Please help!
Answer: The amount is $43492.35 and the interest is $10992.35.
Step-by-step explanation:
To find amount we use formula:
A = P(1+r/n)^nt
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
In this example we have
P=32,000 , R=6% , N = 1 T= 5 YEARS
After plugging the given information we have
A=32000(1+0.06/1)^1.5
A=32500*1.06^5
A=32500*1.338226
A=$43492.35
To find interest we use formula A=P+I , since A= 43492.35 P =32500 we have:
A=P+I
$43492.35 = 32500+I
I=$43492.35-32500
I=$10992.35
If a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers. Then [[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]]
The value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.
According to the given equation, a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers, we can rearrange the equation to find the value of one of the variables in terms of the others. For example, we can rearrange the equation to find the value of x in terms of the other variables:
x = b+y-a = c+z+1-a
Similarly, we can rearrange the equation to find the value of y and z in terms of the other variables:
y = a+x-b = c+z+1-b
z = a+x-c-1 = b+y-c-1
Now, we can substitute these values into the given matrix to find the value of each element:
[[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]] = [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z+1-c-1]]
Simplifying the matrix, we get:
[[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]]
Therefore, the value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.
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 can someone help me with these two questions I don’t need any explanation just answer and I would really appreciate you.
(a) m∠BAC = 73°
(b) The value of y is 2.
What is an isosceles triangle?A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.
(a) Given:
m∠BEA = 62°.
Assuming ABCD is a square.
The diagonal of the square divides the square into two isosceles right-angled triangles.
So, m∠BAD = 90° and m∠ABD = m∠ADB = m∠ABE = 45°.
So, the angle measure of ∠BAC,
m∠BAC = 180° - (45 + 62)
m∠BAC = 180° - 107°
m∠BAC = 73°
(b) Given:
BE = 6y + 2 and CE = 4y + 6.
Assuming ABCD is a square.
The diagonals of squares divide the diagonals into two equal parts.
So, BE = CE
6y + 2 = 4y + 6.
2y = 4
y = 2
Therefore, the value of y is 2.
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Rewrite without parentheses. (3x^(4)z^(2)-8x^(5))(-6xz^(6)) Simplify your answer as much as possible.
The equation (3x⁴z² - 8x⁵)(-6xz⁶) is rewritten without parenthesis as 48x⁶z⁶ - 18x⁵z⁸
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Given the equation:
(3x^(4)z^(2)-8x^(5))(-6xz^(6))
Simplifying gives:
= (3x⁴z² - 8x⁵)(-6xz⁶)
Opening the parenthesis gives:
= -18x⁵z⁸ + 48x⁶z⁶
= 48x⁶z⁶ - 18x⁵z⁸
The equation is equivalent to 48x⁶z⁶ - 18x⁵z⁸
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How many solutions does the system have?{ 2 x + 3 y =-6 3 x − 4 y = − 12
Therefore , the solution of the given problem of equation comes out to be which is (x, y) = (-60/17, 58/17).
How do mathematics equation work?The same letter is frequently used in mathematical formulas to attempt to enforce unity between two claims. Mathematical expression equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using y + 6 = 12 like an example, the normalise separates 12 but rather b + 6 in to the two pieces. The relationship between each sign variable and the amount of lines can be identified. A symbol's meaning typically runs counter to itself.
Here,
Elimination is one approach that could be used to solve the problem. So that the component of y in each equation is -12, we can do this by multiplying the first equation by 4 and the second equation by 3:
=> 4(2x + 3y = -6) -> 8x + 12y = -24
=> 3(3x - 4y = -12) -> 9x - 12y = -36
The two formulae combined give us:
=> 8x + 12y + 9x - 12y = -24 - 36
=> 17x = -60
=>x = -60/17
We can find y by substituting x into either equation:
=> 2(-60/17) + 3y = -6
=> 3(-60/17) - 4y = -12
When we simplify each solution, we obtain:
=> -120/17 + 3y = -6
=>-180/17 - 4y = -12
By y in each solution and solving, we obtain:
=> 3y = 174/17
=> y = 58/17
As a result, there is only one solution to the system, which is (x, y) = (-60/17, 58/17).
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Complete a dilation with scale factor of 1/2 around the origin and then reflect over the y-axis. What are the new ordered pair of A’?
The new ordered pair of A’ are (-1, -2.25). Hence the correct option is b.
What are cο-οrdinates?A cοοrdinate system in geοmetry is a technique that uses οne οr mοre integers οr cοοrdinates tο establish the accurate pοsitiοning οf geοmetrical οbjects οn a manifοld, such as Euclidean space. When lοcating a pοint οr οbject οn a twο-dimensiοnal plane, cοοrdinates—pairs οf numbers—are utilized.
The x and y cοοrdinates serve as a representatiοn οf a pοint's lοcatiοn οn a 2D plane. a grοup οf numbers used tο denοte certain lοcatiοns. The figure usually cοnsists οf twο integers. The frοnt-tο-back and tοp-tο-bοttοm distances are represented by the first and secοnd numbers, respectively. When there are 12 units belοw and 5 abοve, as in (12.5), the ratiο is 1.
Tο cοnduct a dilatiοn with a scale factοr οf 1/2 arοund the οrigin, multiply each pοint's cοοrdinates by 1/2. If the initial cοοrdinates οf pοint A are (x, y), then the dilated pοint A' cοοrdinates are:
A' = (1/2 * x, 1/2 * y)
We negate the x-cοοrdinate while keeping the y-cοοrdinate cοnstant tο represent the dilated pοint A' οver the y-axis. As a result, the final cοοrdinates οf A" are:
A'' = (-1/2 * x, 1/2 * y)
As a result, Anew "'s οrdered pair is (1/2 * x, 1/2 * y)
= ((1/2 × -2), (1/2 × -5))
= (-1, -2.25)
Thus, the new ordered pair of A’ are (-1, -2.25). Hence the correct option is b.
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