Answer:
a. The product of each pair of numbers is:
1 x 49 = 49
2 x 48 = 96
10 x 40 = 400
b. The pair of numbers that will produce the largest possible product is when the two numbers are equal to half of the sum, which is 25. So the pair of numbers is 25 and 25, and the product is 25 x 25 = 625.
c. We can determine the pair of numbers that have the largest product by using the following reasoning: For any two numbers whose sum is fixed, their product is maximized when the two numbers are as close together as possible. This is because the product of two numbers that are far apart is always smaller than the product of two numbers that are closer together and have the same sum. In this case, the sum is 50, so the two numbers that are closest together and add up to 50 are 25 and 25, which give the largest possible product.
Write the equation of a circle with a center of (1, -5) and a radius of √5
Simplifying this equation gives: [tex](x - 1)^2+(y+5/8)^2=5[/tex].
What is the circle?A circle is a geometrical shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is calculated as 2 times pi (π) times the radius. Circles are found in many areas of mathematics and the physical world, and they have important applications in geometry, trigonometry, calculus, physics, and engineering, among other fields.
The equation of a circle with center (a, b) and radius r is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (1, -5/8) and the radius is √5. So, the equation of the circle is:
[tex](x - 1)^2 + (y + 5/8)^2 = (\sqrt5)^2[/tex]
Simplifying this equation gives:
[tex](x - 1)^2+(y+5/8)^2=5[/tex]
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Convert 330 litres per hour into millimeters per minute
330 litres per hour = 5489.64 millimeter³ per minute.
Given that330 litres per hour needs to be converted into millimeters per minute.
Conversion factor: 1 litre =1000 cubic centimeter 1 cubic centimeter =1 millimeter³
∴ 1 litre=1000 millimeter³
∴ 1 litre per hour=1000 millimeter³ per hour
Also, 1 hour = 60 minutes
∴ 1 hour = 60 × 60 seconds = 3600 seconds
∴ 1 second = 1/3600 hours=0.0002778 hours
Thus, 1 litre per hour =1000/3600 millimeter³ per second =0.2778 millimeter³ per second
Therefore, 330 litres per hour = 330 × 0.2778 millimeter³ per second=91.494 millimeter³ per second
Also, 1 minute =60 seconds
∴ 1 minute = 60 × 60 seconds=3600 seconds
∴ 1 second = 1/60 minutes=0.01667 minutes
Thus, 91.494 millimeter³ per second = 91.494/0.01667 millimeter³ per minute = 5489.64 millimeter³ per minute
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what value makes a expressions equivalent 5 11 15 30
The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.
What is value?Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.
This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.
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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.
What is value?Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.
This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.
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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x
A. 5
B.11
C.15
D.30
f a barometer were built using water instead of Hg, how high would the column of water be if the pressure were 1 atm, knowing that the density of water is 13.6 times lower than that of mercury?
The height of the water column would be 1033.6 cm if the pressure were 1 atm.
SOLUTION:
If a barometer were built using water instead of mercury, and the pressure were 1 atm, the height of the water column would be:
1. First, find the height of the mercury column at 1 atm. The standard height is 760 mm (or 76 cm) for mercury.
2. Since the density of water is 13.6 times lower than that of mercury, the water column needs to be 13.6 times higher than the mercury column to exert the same pressure.
3. Multiply the height of the mercury column (76 cm) by 13.6:
76 cm x 13.6 = 1033.6 cm.
So, the height of the water column would be 1033.6 cm if the pressure were 1 atm.
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a store owner wants to develop a new snack mix by mixing chocolate and trail mix. how many pounds of chocolate costing $21.10 per pound should be mixed with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.
To solve this problem, we can use the method of mixtures. Let x be the number of pounds of chocolate to be mixed with the trail mix. We can set up the following equation based on the given information:
(21.10x + 3.10(14)) / (x + 14) = 12.41
Simplifying and solving for x, we get:
21.10x + 43.40 = 12.41x + 173.54
8.69x = 130.14
x = 15
Therefore, the store owner should mix 15 pounds of chocolate costing $21.10 per pound with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.
To check this answer, we can verify that the total cost of the mixture equals the total cost of the chocolate and trail mix:
15(21.10) + 14(3.10) = 315 + 43.40 = 358.40
And the total weight of the mixture is:
15 + 14 = 29
So the cost per pound of the mixture is:
358.40 / 29 = 12.41
which matches the desired cost per pound.
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For the given figure, can you conclude mlln? Explain.
The image shows a circular pizza cutter that has a diameter of 8 centimeters
The pizza would be covered by approximately 100.48 centimeters of the pizza cutter if it is rotated exactly 4 times.
Calculating the cover of the pizzaThe circumference of a circle can be calculated using the formula:
circumference = π x diameter
where π is approximately equal to 3.14.
Given that the diameter of the pizza cutter is 8 centimeters, we can calculate its circumference as:
circumference = π x diameter
circumference = 3.14 x 8
circumference = 25.12 centimeters
If the pizza cutter is rotated exactly 4 times, it will cover a distance equal to 4 times its circumference:
distance covered = 4 x circumference
distance covered = 4 x 25.12
distance covered = 100.48 centimeters
Therefore, approximately 100.48 centimeters of the pizza would be covered by the pizza cutter if it is rotated exactly 4 times.
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Complete question
The image shows a circular pizza cutter that has a diameter of 8 centimeters. Approximately how many centimeters would the pizza cutter cover if it is rotated exactly 4 times
El precio de unos zapatos se ha disminuido en un 20% vendiéndose actualmente en 40,39e cual era el precio primitivo ?
Answer:15%
Step-by-step explanation:
make your first point the origin. what does your second point have to be to get an output of 5 from the function?
To get an output of 5 from a function, the second point must be at a distance of 5 units above the x-axis.
The function represents the relationship between the inputs and the outputs. The function's domain is the set of all possible input values, while the range is the set of all possible output values. The function's graph is the set of all ordered pairs (x, y), where x is the input and y is the output.To get an output of 5 from the function, the second point must be at a distance of 5 units above the x-axis. This implies that the y-value of the second point is 5. The x-value of the second point is arbitrary, and it can be any value. The point (0,5) is an example of a point that is 5 units above the x-axis.
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1) Is 2nd drawing a reduction or enlargement?
2) What is the scale factor?
Answer:
1. reduction
2. scale factor of 1/2
Step-by-step explanation:
1. the second image is smaller than the original
2. 18*1/2= 9 and 6*1/2=3
the elephant population in northwestern namibia and etosha national park can be predicted by the expression 2 , 649 ( 1.045 ) b , where b is the number of years since 1995. what does the value 2,649 represent?
The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.
The formula for population growth can be represented as:
P = P0ert
Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.
Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,
P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0
Taking the natural logarithm on both sides,
ln e1.045(b-1995) = ln (2649/P0)
Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)
vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95
Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4
Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.
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Helppppppppppppppppppppppppppp
Answer:
No.
Step-by-step explanation:
Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.
[tex](XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \neq L.H.S[/tex]
Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.
Answer:
not a tangent
Step-by-step explanation:
if XY is a tangent to the circle then ∠ WXY = 90°
using converse of Pythagoras' identity.
if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.
longest side is WY
WY² = 87² = 7569
WX² + XY² = 66² + 54² = 4356 + 2916 = 7272
since WY² ≠ WX² + XY² , then Δ WXY is not right
then XY is not a tangent to the circle
Let x represent the height of first graders in a class. This would be considered what type of variable:NonsensicalLaggingContinuousDiscrete
The height of first graders in a class, represented by x, would be considered a Continuous variable. Continuous variables can take on any value within a specified range and are often used to measure physical attributes, such as height.
Let x represent the height of first graders in a class. Discrete variables are those that can be measured using whole numbers, such as the number of people in a room, the number of items on a grocery list, or the number of pages in a book. Continuous variables, on the other hand, are those that can take on any value, such as height, weight, and time.Continuous variables are those that can take on any value between two points on a measurement scale. For example, the height of first graders in a class can be measured in inches or centimeters and can take on any value between the smallest and largest heights in the class.
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Answer for x=
Please
Answer:
53°
Step-by-step explanation:
it’s vertical, verticals are always identical, I think
Mayte es una estudiante extranjera y recibe de
sus padres $977 por semana. Ella ahorra $200 y
el resto lo distribuye entre los 7 días de la semana,
¿cuánto dinero puede gastar diariamente?
The amount of money Mayte can spend on a daily basis is given by $ 111 .
Sellers and purchasers of products and services both accept money as a form of payment. When we purchase goods like food, clothing, a house, groceries, etc., we provide money in exchange. We exchange money for everything we buy. This is a straightforward swap.
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "," or occasionally "/," is used in computer code.
Mayte get a total money of $977 from her parents so,
total = 977
She saves $200 for herself so now the remaining sum is
977 - 200 = 777
The rest she has to distribute in 7 days so, by using the simple dividation rule we get,
777/7 = 111
Therefore, much money can you spend daily is $111.
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Complete question:
Mayte is a foreign student and receives his parents $977 per week. She saves $200 and the rest is distributed among the 7 days of the week, How much money can you spend daily?
Find the measure of x.
29°
X
3.7
x = [?]
X
Round to the nearest hundredth.
Answer:
x ≈ 3.24
Step-by-step explanation:
using the cosine ratio in the right triangle
cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )
3.7 × cos29° = x , then
x ≈ 3.24 ( to the nearest hundredth )
4. Which of the following is the square of a binomial?
A. r² - 2rs +s²
B. c² + d²
C. 16x² - 25y²
D. d² - de + e²
The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.
What exactly are binomials?
In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:
ax + b
where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.
Now,
The correct answer is (A) r² - 2rs +s².
This is a perfect square trinomial, which can be written as (r - s)².
Option (B) c² + d² is not a binomial, it is the sum of two squares.
Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).
Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.
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please help find the slope of the line between the points
Answer:
m(slope) = -1.8 or -1 and 4/5s
Step-by-step explanation:
To find the slope between any two points, a good equation to always remember would be the slope equation.
y2-y1
--------
x2-x1
Or in simple words, the difference of y divided by the difference of x.
-10-8= -18, so the difference in y= -18.
3- (-7)= 3+7= 10, so the difference in the x values= 10.
Finally, divide -18/10= -1.8 or -1 and 4/5s
PROOFS help needed badly will give many points as possible! 1.
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II Given: AD AB, AC bisects ZDAB
Prove: AADC = AABC
4.
Statements
1.
Statements
2.
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12 Given: JM NM, L is the midpoint of JN
Prove: AJLM ANLM
4.
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Triangle DAC and triangle CAB are congruent triangles using the SAS criteria.
What are congruent triangles?Both triangles are said to be congruent if the three sides and three angles of one triangle match those of the other triangle's corresponding angles and sides. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They have a similar size and form. In triangles, there are several congruence criteria. The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its form by its three angles.
Given that, AD = AB and AC bisects angle DAB.
As AC bisects DAB, it divides the angle in two half angles that is:
angle DAC = angle CAB
In triangle DAC and triangle CAB.
AD = AB (Given)
angle DAC = angle CAB (AC bisects DAB)
AC = AC
Thus, triangle DAC and triangle CAB are congruent triangles using the SAS criteria.
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Convert the mixed number below to an improper fraction 4 1/2
Answer:9/2
Step-by-step explanation:
Answer:
To convert mixed number 4 1/2 to improper fraction, you follow these steps: Multiply the whole number by the denominator 4 × 2 = 8 Add the product from Step 1 to the numerator
Step-by-step explanation:
First, note that 4 1/2 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:
4 = whole number
1 = numerator
2 = denominator
To convert mixed number 4 1/2 to improper fraction, you follow these steps:
Multiply the whole number by the denominator
4 × 2 = 8
Add the product from Step 1 to the numerator
8 + 1 = 9
Write answer from Step 2 over the denominator
9/2
The mixed number 4 1/2 converted to improper fraction is therefore :
9/2
Out of 80 customers at an ice cream van, 48 had syrup, 28 had sprinkles and 16 had both
toppings on their ice cream. Use a Venn diagram to find the probability that a randomly
selected customer doesn't have either topping, given that they don't have sprinkles.
I know the answer is 20/52, I just can’t work out how to get to that answer…
Answer:
20/52 or simplified to 5/13
Step-by-step explanation:
The Venn Diagram is provided
Let
n(A) = number of customers who had syrup
n(B) = number of customers who had sprinkles
n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region
n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60
Therefore number of customers who had neither topping = 80 - 60 = 20
This number is indicated outside both circles but within the rectangle
The number of customers who had only syrup is given by set difference
= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32
This is the figure inside the left circle
Let's consider the statement: Customers who didn't have sprinkles
This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52
Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13
A rectangle has an area of 717. 8m2. One of the sides is 7. 4m in length. Work out the perimeter of the rectangle
The perimeter of the rectangle is approximately 208.9 meters.
To find the perimeter of the rectangle, we need to know the length of the other side.
Let's use the formula for the area of a rectangle:
area = length x width
We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:
length = area / width
length = 717.8 / 7.4
length ≈ 97.05 m
Now we have both the length and width of the rectangle, so we can find the perimeter:
perimeter = 2 x (length + width)
perimeter = 2 x (97.05 + 7.4)
perimeter = 2 x 104.45
perimeter = 208.9 m
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Math help. HEEEEEEEEEEELP.
The expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6.
What is a function f(x)?A function f(x) is a mathematical relationship that assigns a unique output value (or range value) for every input value (or domain value) from a specified set. In other words, a function takes one or more input values and produces a single output value based on a specific rule or set of rules.
According to question:To find g(f(x)), we need to substitute the expression for f(x) into g(x) wherever x appears, since g(x) is being evaluated at the value of f(x). That is, we need to substitute -2x+5 for x in the expression for g(x). This gives:
g(f(x)) = g(-2x+5)
= 3(-2x+5) - 9
= -6x + 15 - 9
= -6x + 6
So, g(f(x)) = -6x + 6.
Therefore, the expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6. Thus, we can express the response as follows:
g(f(x)) = -6x + 6
= [-6]x + [6]
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Corey spies a bald eagle in a tall tree. He was able to measure the angle of elevation to the bird from where he stands at 62°. The leaves on the tree make it difficult for Corey to watch the bird, so he moves 10 feet further away from the tree to get a better view. Now his angle of elevation is 56°.
What is the height of the tree? Round your answer to the nearest foot.
pls help
The height of the tree is approximately 76 feet.
What is the angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
We can use tangent to set up the following two equations based on the given angles of elevation:
tan(62°) = h/x
tan(56°) = h/(x+10)
We can rearrange the first equation to solve for "h":
h = x * tan(62°)
tan(56°) = (x * tan(62°)) / (x+10)
We can solve for "x" by multiplying both sides by (x+10) and rearranging:
x = 10 * (tan(62°) - tan(56°)))
Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:
h = x * tan(62°) ≈ 76 feet
Therefore, the height of the tree is approximately 76 feet.
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Boris paid for dinner and added $8 tip (which is 20% of the total). What was the total before the tip.
HELPP PLSSSSS NOW!!!!!!
Calculate 3198 × 750 without using a calculator
3198 x 750 equals 2,398,500. We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.
We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.
markdown
3198 \s x 750
23970 (8 x 0), 319800 (9 x 0 + 9 x 5) and 2398500 (9 x 0 + 9 x 7 + 8 x 5) are the numbers.
Because of this, 3198 x 750 equals 2,398,500.
When a problem or question asks to be solved "without using a calculator," it signifies that the answer must be determined by hand without the aid of a calculator or any other electronic instrument. This is frequently used to assess a person's math prowess and to motivate them to hone their problem-solving and mental math ability.
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13. The area of the kite is 30 m². What is the value
of x? Explain.
4m
xm
6 m
xm
14.
Answer:
answer is 3
Step-by-step explanation:
if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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what are the properties of the relation in which a college student is related to another iff the they have attended class together? you answered transitive you answered anti-symmetric you answered anti-reflexive correct! reflexive correct! symmetric
The relation in which a college student is related to another if and only if they have attended class together is an example of an equivalence relation.
An equivalence relation must satisfy three properties :Reflexivity: Every element of the set is related to itself. In this case, every student has attended class with themselves, so the relation is reflexive.
Symmetry: If one element is related to another, then the second element is also related to the first. In this case, if student A has attended class with student B, then student B has also attended class with student A, so the relation is symmetric.
Transitivity: If one element is related to a second, and the second is related to a third, then the first is related to the third. In this case, if student A has attended class with student B, and student B has attended class with student C, then student A has also attended class with student C, so the relation is transitive.
Therefore, the relation in which a college student is related to another if and only if they have attended class together satisfies all three properties of an equivalence relation, and is an example of such a relation.
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Solve for x 5x
-2(x+1)=10
Step-by-step explanation:
5x-2(x+1)=10
5x-2x+2=10
3x+2=10
3x=10-2
3x=8
8/3
2.7 if you do round it
2.666666667 before you do
x=2.7
(I think it's right Because I've already been taught this if not just tell me.)