Answer: By the Vertical Angles Theorem, we know that vertical angles are congruent. Therefore:
x + 8 = 5x - 148
Solving for x:
8 + 148 = 5x - x
156 = 4x
x = 39
So, we have:
x + 8 = 39 + 8 = 47 degrees
5x - 148 = 5(39) - 148 = 47 degrees (by the Vertical Angles Theorem)
Step-by-step explanation:
Mengxi has $10 000 to invest. She invests part in a term deposit paying 5% /year, and the remainder in Canada Savings Bonds paying 3. 5% /year. At the end of the year, she has earned simple interest of $413. How much did she invest at each rate? (Algebra)
Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.
Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.
At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).
Thus, we can write the following equation to represent the total interest earned:
0.05x + 0.035(10000 - x) = 413
Simplifying the equation, we get:
0.015x + 350 = 413
0.015x = 63
x = 4200
Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.
To check the answer, we can calculate the interest earned from each investment and add them up:
0.05(4200) + 0.035(5800) = 210 + 203 = 413
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Help me with this please
Answer:
we have to check the chemical property of the daisy perfume
The angles in a triangle are in a 1:2:3 ratio
show that the triangle is right angled
The triangle with measure of the angle is 30°, 60°, and 90° proves that it is right angled triangle.
Let us consider 'x' be the measure of the angles in a triangle.
Ratio of the angles in a triangle is 1 : 2 : 3
Measure of angle 1 = 1x
Measure of angle 2 = 2x
Measure of angle 3 = 3x
Sum of all the interior angles in a triangle = 180°
Substitute the value of the measure of the angles we get,
⇒ 1x + 2x + 3x = 180°
⇒ 6x = 180°
⇒ x = 180° / 6
⇒ x = 30°
Measure of angle 1 = 30°
Measure of angle 2 = 2× 30°
= 60°
Measure of angle 3 = 3× 30°
= 90°
Therefore, as measure of one of the interior angle is 90 degree this implies it is a right angled triangle.
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Abstract Algebra (6408 Math) Homework (3) Let \( R \) be a ring. Question 1 Show that \( 0_{R} x=0_{R} \) for all \( x \in R \). Question 2 If \( a, b \in R \), show that \( -(a b)=(-a) b \). Best wis
Abstract Algebra
By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.
Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.
Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.
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At the movie theatre, child admission is $5.30 and adult admission is $8.70. On Saturday, 163 tickets were sold for a total sales of $1169.90. How many child tickets were sold that day?
The number of child tickets were sold that day are 73.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of child admission= $5.30
Cost of adult admission= $8.70
Now,
Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:
c + a = 163 (equation 1: the total number of tickets sold)
5.30c + 8.70a = 1169.90 (equation 2: the total sales)
We can use equation 1 to solve for "a" in terms of "c":
a = 163 - c
Substituting this expression for "a" into equation 2, we get:
5.30c + 8.70(163 - c) = 1169.90
Simplifying and solving for "c", we get:
5.30c + 1418.10 - 8.70c = 1169.90
-3.4c = -248.20
c = 73
Therefore, by algebra the answer will be 73.
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help................................................
Answer:
I think question #1 is C
Question #2 is C
and Question #3 is A
Find the zeros of the function and state the multiplicities. c(x)=6x^(3)+3x^(2)-3x
The zeros of the function c(x) = 6x^3 + 3x^2 - 3x are x = 0, 1/2, and -1, all with a multiplicity of 1.
To find the zeros of the function c(x) = 6x^3 + 3x^2 - 3x, we need to factor the equation and set it equal to zero.
First, we can factor out a common factor of 3x from all of the terms:
c(x) = 3x(2x^2 + x - 1)
Next, we can use the quadratic formula to find the zeros of the remaining quadratic equation:
2x^2 + x - 1 = 0
x = (-1 ± √(1^2 - 4(2)(-1)))/(2(2))
x = (-1 ± √(1 + 8))/4
x = (-1 ± √9)/4
x = (-1 ± 3)/4
So, the two zeros of the quadratic equation are:
x = (-1 + 3)/4 = 1/2
x = (-1 - 3)/4 = -1
Finally, we can combine the zero from the factored term with the zeros from the quadratic equation to find all of the zeros of the function:
x = 0, 1/2, -1
The multiplicities of these zeros are:
x = 0 has a multiplicity of 1
x = 1/2 has a multiplicity of 1
x = -1 has a multiplicity of 1
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Every day Ms.Twinkle walks around a park near her house. The park is the shape of a rectangle 2 mi long and 1 3/10 mi wide. How far does she walk.
Ms. Twinkle walks a total of 6.6 miles around the park.
What is perimeter ?
Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
To find how far Ms. Twinkle walks, we need to find the perimeter of the rectangle-shaped park, which is the sum of the lengths of all its sides.
The length of the park is 2 miles and the width is 1 3/10 miles. We can write the width as a mixed number of 1 + 3/10 = 13/10 miles.
Therefore, the perimeter of the park is:
Perimeter = 2(length + width)
Perimeter = 2(2 + 13/10)
Perimeter = 2(20/10 + 13/10)
Perimeter = 2(33/10)
Perimeter = 66/10
Perimeter = 6.6 miles
Therefore, Ms. Twinkle walks a total of 6.6 miles around the park.
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PLEASE HELP! 10 POINTS! ITS URGENT! NO EXPLANATION NEEDED!
Answer:its 80 i did the same problem
Step-by-step explanation:
please helppp!!!!!!!
Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
What is the definition of the Right Angle postulate?
The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.
Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
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Answer:
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Chase starts an IRA (Individual Retirement Account) at the age of 26 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65 his retirement savings is $838,879.58, Determine the amount of money Chase deposited over the length of the investment and how much he made in interest upon retirement Formulas
The total number of months he made deposits and multiply that by the monthly deposit amount.
Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.
Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468
Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200
To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.
Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58
Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.
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simplify all the exponets
The simplified form of the given expression by the laws of indices is; x^(-3/10).
What is the simplified form of the expression?As evident in the task content; the given expression is;
1 / ⁵√√x³
Therefore, we have that;
By the laws of indices we have that;
= 1 / ⁵√x^(3/2)
= 1 / x^(3/10)
On this note, the simplified form of the expression as required is; x^(-3/10).
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find the measure of rhf
Answer:
<RHF = 68°
Step-by-step explanation:
<RHG and <FHY are vertical opposite angle which mean they equal to each other.
<RHG = <FHY
(6m+88) = (7m+84)
88 - 84 = 7m - 6m
4 = m
Plug m=4 into the <RHG to solve for the measurement.
<RHG = 6m+88
<RHG = 6*4+88
<RHG = 24+88
<RHG = 112°
<RHG and <RHF are supplementary angle which mean they both linear adding up to 180°
<RHF + <RHG = 180°
<RHF + 112° = 180°
<RHF = 68°
Letf(x)=x−21andg(x)=x3+2. Find the following functions. Simplify your answers.f(g(x))=g(f(x))=
The simplified functions of f(g(x)) and g(f(x)) are: f(g(x))=x3 and g(f(x))=x3−6x2+12x−6
To find the function f(g(x)), we need to substitute g(x) into f(x). This means we will replace the x in f(x) with the expression for g(x):
f(g(x))=f(x3+2)=(x3+2)−2
Simplifying this expression gives us:
f(g(x))=x3
Similarly, to find the function g(f(x)), we need to substitute f(x) into g(x):
g(f(x))=g(x−2)=(x−2)3+2
Simplifying this expression gives us:
g(f(x))=x3−6x2+12x−6
Therefore, the functions f(g(x)) and g(f(x)) are:
f(g(x))=x3
g(f(x))=x3−6x2+12x−6
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the circle has a central angle of 56° as shown in the diagram. what is the length of minor arc ab
In the diagram, the length of minor arc AB is approximately 3.9 inches
Calculating the length of an arcFrom the question, we are to calculate the length of the minor arc AB
To calculate the length of an arc, we can use the formula:
Arc Length = (Central Angle / 360) x (2πr)
Where:
Central Angle is the angle formed by the two radii at the center of the circle
r is the radius of the circle
From the given information,
Central angle = 56°
r = 4 in
Substituting the given values, we get:
Arc Length = (56° / 360) x (2π x 4 in)
Arc Length = 3.9095 in
Arc Length ≈ 3.9 in
Hence, the length of minor arc AB is approximately 3.9 inches
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Logan invested $3,800 in an account paying an interest rate of 5% compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
Answer:
Step-by-step explanation:
The formula to calculate the doubling time for continuously compounded interest is:
t = ln(2) / (r * ln(1 + (r/n)))
where t is the time in years, r is the annual interest rate as a decimal, and n is the number of times the interest is compounded per year (which is infinity for continuous compounding).
For Logan's investment, we have:
r = 0.05
n = infinity
t1 = ln(2) / (0.05 * ln(1 + (0.05/infinity)))
t1 ≈ 13.86 years
For Qasim's investment, we have:
r = 0.06
n = 1
t2 = ln(2) / (0.06 * ln(1 + (0.06/1)))
t2 ≈ 11.55 years
To find the difference in the time it takes for their investments to double, we can subtract t2 from t1:
t1 - t2 ≈ 13.86 - 11.55 ≈ 2.31
So it would take Logan's money approximately 2.31 years longer to double than Qasim's money, to the nearest hundredth of a year.
Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through twelve!
Even Unlikely Impossible
The answer response are:
A duck with wings: Likely Duck number 7: Unlikely A duck with a number greater than 3: Certain Duck number 15: Impossible A duck with a number greater than 10: Unlikely A duck with a number: Certain Duck number 4: Likely A duck with sunglasses: Impossible A duck with a hat: Unlikely An even-numbered duck: LikelyHow do you explain the probability?A duck with wings: Likely
There is a high likelihood that all the ducks have wings since it is a natural characteristic of ducks.Duck number 7: Unlikely
There are 12 ducks in total, and only one of them is duck number 7, so the probability of choosing duck number 7 is 1/12, which is unlikely.A duck with a number greater than 3: Certain
There are 9 ducks with numbers greater than 3 (4, 5, 6, 7, 8, 9, 10, 11, 12), so it is certain that you will choose a duck with a number greater than 3.Duck number 15: Impossible
There are only 12 ducks, and none of them are numbered 15, so it is impossible to choose duck number 15.A duck with a number greater than 10: Unlikely
Only two ducks have numbers greater than 10 (11, 12), so the probability of choosing a duck with a number greater than 10 is 2/12 or 1/6, which is unlikely.A duck with a number: Certain
All ducks have numbers from 1 to 12, so it is certain that you will choose a duck with a number.Duck number 4: Unlikely
There is only one duck numbered 4, so the probability of choosing duck number 4 is 1/12, which is unlikely.A duck with sunglasses: Impossible
There is no information given that any of the ducks have sunglasses, so it is impossible to choose a duck with sunglasses.A duck with a hat: Unlikely
There is no information given that any of the ducks have hats, so the probability of choosing a duck with a hat is unlikely.Lastly, An even-numbered duck: Likely
There are six even-numbered ducks (2, 4, 6, 8, 10, 12), so the probability of choosing an even-numbered duck is 6/12 or 1/2, which is likely.Learn more about probability here:
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See transcribed text below
Date:
Period:
What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).
33
1. A duck with wings
2. duck number 7
3. a duck with a number greater than 3
4. duck number 15
5. a duck with a number greater than 10
6. a duck with a number
7. duck number 4
8. a duck with sunglasses
9. a duck with a hat
10. an even-numbered duck
The ducks are numbered From one through twelve!
Kibb
Certain
Likely
Even
Unlikely Impossible
ว
What are three equivalent ratios for 15/35
1) 3/7
2) 9/21
3) 150/350
Sadie is making punch. How many more more quarts of lemon-lime juice will she use than orange juice
Volume is the quantum of space an object occupies. Saddie uses 8 pints of lemon- lime juice rather of orange juice.
This is simply because there are 4 cups of juice in 1 liter. volume is a measure of space possessed by matter.
It is frequently quantified using SI deduced units or colorful US Customary or Imperial units. The description of length refers to volume.
A liter is a measure of commodity liquid, like milk or makeup. A gallon is four liters.
Question:
Sadie is making punch. how numerous further quarts of bomb lime juice will she use than orange juice?
constituents for punch-
8qts Lemon Lime Juice. 4 scoops of vanilla ice cream and 8 mugs of orange juice
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The sum of two numbers is 72. The difference of the two numbers is 50. Let x be the larger number and ybe the smaller number. Set up and evaluate a system of equations to determine the values of x and y.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
First equation:
Write an equation that expresses the information in the sentence "The difference of the two numbers is 50."
Second equation:
Solve the system you have written above to find x and y.
x= . y= .
the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50
The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:
First equation: x + y = 72
Second equation: x - y = 50
To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:
x + y = 72
x - y = 50
--------------
2x = 122
Next, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 122/2
x = 61
Now that we know the value of x, we can plug it back into one of the equations to find the value of y:
61 + y = 72
y = 72 - 61
y = 11
So the solution to the system of equations is x = 61 and y = 11.
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Just need answers thanks alot !! Problems in picture
The quadratic equation f(x) = 3 · x² + 36 · x + 33 shows the quickest choice to determine the y-intercept. The y-intercept is equal to (0, 33).
How to find the y-intercept of a quadratic equation
In this problem we must look up for the quickest way to determine the y-intercept of a quadratic equation, this can be done by evaluating at x = 0 when the expression is of the form, that is, standard form:
f(x) = a · x² + b · x + c
Where a, b, c are real coefficients.
The standard form f(x) = 3 · x² + 36 · x + 33 may help us to determine the y-intercept quickly. The y-intercept is equal to (0, 33).
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Find the domain and range for the following functions:
(3 Marks)
a) y=1/√ x2-4
y=(2x^2)-2x+5
y=
1/(1-1/(x-1))
The domain and range for the given functions are: a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞) b) Domain: (-∞, ∞), Range: [9/2, ∞) c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
The domain of a function is the set of all possible values of x that can be input into the function. The range of a function is the set of all possible values of y that can be output from the function.
a) y = 1/√(x^2 - 4)
The domain of this function is all values of x that make the denominator nonzero and the square root positive. Therefore, x^2 - 4 > 0, which means (x - 2)(x + 2) > 0. The solution to this inequality is x < -2 or x > 2. So the domain is (-∞, -2) ∪ (2, ∞).
The range of this function is all positive values of y, since the square root in the denominator is always positive. So the range is (0, ∞).
b) y = (2x^2) - 2x + 5
The domain of this function is all real numbers, since there are no restrictions on the values of x. So the domain is (-∞, ∞).
The range of this function is all values of y greater than or equal to the vertex of the parabola. The vertex of this parabola is (-b/2a, f(-b/2a)), which is (1/2, 9/2). So the range is [9/2, ∞).
c) y = 1/(1 - 1/(x - 1))
The domain of this function is all values of x that make the denominator nonzero. Therefore, 1 - 1/(x - 1) ≠ 0, which means x ≠ 2. So the domain is (-∞, 2) ∪ (2, ∞).
The range of this function is all values of y except 0, since the denominator can never be zero. So the range is (-∞, 0) ∪ (0, ∞).
In conclusion, the domain and range for the given functions are:
a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞)
b) Domain: (-∞, ∞), Range: [9/2, ∞)
c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
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a library has fiction and nonfiction books. The ration of the number of fiction books to the total number of books is 5:8. What is the ratio of the fiction to the nonfiction books in the library?
The ratio of fiction books to nonfiction books in the library is 5:3.
What are Ratios?
A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.
Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).
Then, the number of nonfiction books in the library is 8x - 5x = 3x.
Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:
5x/3x = 5/3
So, the ratio of fiction books to nonfiction books in the library is 5:3.
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Mr. Silverstone invested some money in 3 different investment products. The investment was as follows: a. The interest rate of the annuity was 2%. b. The interest rate of the annuity was 4%. c. The interest rate of the bond was 5%. d. The interest earned from all three investments together was $950. Which linear equation shows interest earned from each investment if the total was $950? a.) a + b + c = 950 b.) 0.04a + 0.06b + 0.05c = 9.50 c.) 0.04a + 0.06b + 0.05c = 950 d.) 4a + 6b + 5c = 950
The linear equation that shows the interest earned from each investment is (d): "4a + 6b + 5c = 950"
What is investment?Investment refers to the act of allocating money or other resources to an asset or venture with the expectation of generating a profit or some other form of return over a period of time. The primary goal of investing is to use the available resources to generate a return that is greater than the initial investment, thus growing wealth over time.
What is linear equation?A linear equation is an algebraic equation in which the highest power of the variable is one. In other words, a linear equation is a polynomial of degree one. It represents a straight line when plotted on a graph. The general form of a linear equation with one variable, x, is:
ax + b = 0
In the given question,
Let's assume that Mr. Silverstone invested a dollars in the first annuity with an interest rate of 2%, b dollars in the second annuity with an interest rate of 4%, and c dollars in the bond with an interest rate of 5%. The interest earned from each investment can be calculated as follows:
Interest earned from the first annuity = 0.02a
Interest earned from the second annuity = 0.04b
Interest earned from the bond = 0.05c
The total interest earned from all three investments together is given as $950. Therefore, we can write the equation:
0.02a + 0.04b + 0.05c = 950
This is the same as option (c) given in the question: "0.04a + 0.06b + 0.05c = 950". However, option (c) has some errors in the coefficients, as the interest rates for the annuities were given as 2% and 4%, not 4% and 6%.
Therefore, the linear equation that shows the interest earned from each investment if the total was $950 is:
0.02a + 0.04b + 0.05c = 950
This can also be simplified as:
2a + 4b + 5c = 95000 (by multiplying both sides by 100 to remove the decimals)
So, the correct option is (d): "4a + 6b + 5c = 950".
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(px + 4) (9x + 3) = 18x^2 + rx + 12 for all values of x, and p + q = 9. What are the two possible values of r? A) 3 and 6 B) 9 and 24 C) 12 and 18 D) 30 and 33
Expanding the left-hand side, we have:
(px + 4) (9x + 3) = 9px^2 + 3(4p + 9)x + 12
Comparing this to the right-hand side, we see that we must have:
9p = 18 (to get the x^2 term on the right)
4p + 9 = r (to get the x term on the right)
The first equation gives us p = 2, and substituting into the second equation gives us:
4(2) + 9 = r
r = 17
So one possible value of r is 17. To find the other, we use the fact that p + q = 9. Substituting p = 2, we have:
2 + q = 9
q = 7
Now we can use the same equation as before to find the other value of r:
4(2) + 9 = r
r = 17
So the two possible values of r are 17 and 17.
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The width of a rectangle is 4 units less than the length. The area of the rectangle is 21 square units. What is the length, in units, of the rectangle?
Answer:
Let's call the length of the rectangle "L" and the width "W".
From the problem, we know that:
W = L - 4
And
Area = Length x Width
Substituting the first equation into the second equation, we get:
Area = L x (L - 4)
We also know that the area is 21 square units, so we can set up the following equation:
21 = L x (L - 4)
Expanding the right side of the equation:
21 = L^2 - 4L
Rearranging the terms:
L^2 - 4L - 21 = 0
Now we can solve for L using the quadratic formula:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -4, and c = -21
L = (-(-4) ± sqrt((-4)^2 - 4(1)(-21))) / 2(1)
L = (4 ± sqrt(100)) / 2
L = (4 ± 10) / 2
L = 7 or L = -3
Since the length cannot be negative, we choose L = 7.
Therefore, the length of the rectangle is 7 units.
For each of the following, find the formula for an exponential
function that passes through the two points given.
a. (-2, 3/4) and (2,12)
f(x)=?
b. (-3,6) and (3,2)
g(x)=?
The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).
To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.
For part a:
3/4 = ab⁻²
12 = ab²
Dividing the second equation by the first equation gives us:
16 = b⁴
Taking the fourth root of both sides gives us:
b = 2
Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3
So the formula for the exponential function is:
f(x) = 3(2ˣ)
For part b:
6 = ab⁻³
2 = ab³
Dividing the second equation by the first equation gives us:
1/3 = b⁶
Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)
Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)
So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))
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PLEASE HURRY ITS DUE IN 24 MINUTES
A chicken breeder has chickens that are white, black or speckled. Speckled chickens have both black and white feathers. This is a co-dominant trait. The allele for white feathers is A and the allele FB for black feathers is F Determine the genotypes for the rooster and hen that the breeder should cross to produce the greatest percentage of speckled chickens. A. Place the alleles for the rooster and the hen that the breeder should cross in the blank boxes outside the Punnett square. B. Place the number that shows the percentage of speckled offspring that will result from this cross in the blank box. . You may use the allele labels more than once. • There may be more than one correct answer. • Place only one label in each blank box F F 25 50 75 100 2/5- Hen Rooster =% speckled
Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.
The Punnett square for this cross would be:
| F F
A | A F A F
A | A F A F
This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.
Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:
| F F
A | A F A F
A | A F A F
Hen Rooster
y = -15 x -5
11 x + y = -17
I need help with this.
Answer:
system of equation:
(x,y)
(3,-50)
Step-by-step explanation:
equation solving
Which situation could be described by the expression f + 1/2
Use the / as a fraction bar
A. Lela walked f miles yesterday, and mile today.
B. Lela walked f miles yesterday, and miles fewer today.
C. Lela walked mile yesterday, and f miles fewer today.
D. Lela walked mile yesterday, and f times as far today.
B. Lela walked f miles yesterday, and miles fewer today.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
The situation that could be described by the expression f + 1/2 is:
B. Lela walked f miles yesterday, and miles fewer today.
The expression f + 1/2 represents the total distance that Lela walked over two days, where "f" represents the distance she walked yesterday, and "1/2" represents the distance she walked today.
Option B describes the situation where Lela walked "f" miles yesterday and "1/2" times fewer miles today (or, equivalently, "1/2" times the distance she walked yesterday).
Therefore, the expression f + 1/2 is a valid way to describe this situation.
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