Answer:
The factored form of 4x+16 is (4x + 8)(2). This can be found by using the distributive property, or by using the prime factorization method.
the shortest leg of a triangle is 2 centimeters shorter than the other leg. the hypotenuse of this triangle is 10 centimeters. what are the lengths of the two legs of this triangle?
Lengths of the legs of triangle are 6 cm and 8 cm by Pythagoras theorem of right triangle.
Let One short leg = x
then other = x+2
And hypotenuse is = 10 cm
so x²+(x+2)²=10²
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
From Pythagoras theorem : a^2 + b^2 = c^2
Where c is the hypotenuse and a,b are the other sides of a right angle triangle.
x²+ x²+4x+4=100
[(a + b)^2 = a^2 +2.a.b +b^2]
2 x²+4x-96=0
x²+2x-48=0
(x+8)(x-6)=0
x= -8 or 6
Neglecting - value x=6 as the length can not be negative.
So legs of triangle are 6 cm and 8 cm.
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58 2/3 as a fraction in simplest form
Answer:
176/3
Step-by-step explanation:
58 2/3 = 58 + 2/3 = 58/1 + 2/3 = 174/3 + 2/3 = 176/3
Help would be so appreciated!
Find the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0.
A.
y = 2
B.
y = 2x
C.
y = 2x + 2
D.
y = –2x + 2
Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:
Find the derivative of the function f(x) = 3x3 − x2 + 2
f'(x) = 9x^2 - 2x
Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point
f'(0) = 9(0)^2 - 2(0) = 0
Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.
y - f(a) = m(x - a)
y - (3*0^3 - 0^2 + 2) = 0(x - 0)
y - 2 = 0
So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:
y = 2
Therefore, the correct answer is A. y = 2
Step-by-step explanation:
consider the 12 face diagonals of a rectangular block. how many pairs of them are skew lines? (two lines in space are skew if they do not intersect and they are not parallel.)
Considering the 12-face diagonals of a rectangular block, 30 pairs of these diagonals are skew lines.
In a rectangular block, there are a total of 12 face diagonals. These diagonals are formed by connecting the opposite vertices of each face of the block. To determine the number of pairs of skew lines among these diagonals, we can consider the following:
There are 6 faces in a rectangular block, each with 2 diagonals.
Every diagonal on one face is unique and does not intersect with any other diagonal on the same face.
However, diagonals on opposite faces are parallel to each other and therefore, do not form skew lines.
So, we will be selecting one diagonal from one face, so we have 6 options, then we select another diagonal from another face, which would be 5 options, and we repeat this process until we exhaust all the diagonals. This will give us 6*5 = 30 pairs of skew lines.
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Valentino is a patient in a nursing home for 61 days of 2020. While in the nursing home, he incurs total costs of $27,816. Medicare pays $16,690 of the costs. Valentino receives $30,598 from his long-term care insurance policy, which pays while he is in the facility. Assume that the Federal daily excludible amount for Valentino is $380.
Of the $30,598, what amount may Valentino exclude from his gross income?
A person who purchases his/her own policy can exclude the benefits from gross income. It's also good to note that statutory limitations exist for the following amounts:
Benefits that have been collected under the employer's plan
Premiums that have been paid by the employer
benefits that have been collected from the individuals' policy. Therefore the amount Valentino may exclude will be calculated as follows;
Daily statutory amount in 2020 (380 * 61)
= $23180.
Actual cost of care $27816 $23180
Less: Amount received from Medicare ($16690)
Equal amount of exclusion ($6490)
Thus:
Valentino must include (30598 - 6490)=$6800 of the long-term care benefits received in his gross income.
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1. Express 40 1/4% as a fraction (simplest form)
2. Express 65 5/8% as a fraction (simplest form)
Answer: To express 40 1/4% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 40 1/4% = 40.25/100.
To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 25.
So, (40.25/100) = (4025/10000) = (161/400)
To express 65 5/8% as a fraction, we can convert the percentage to a fraction with a denominator of 100: 65 5/8% = 65.625/100.
To simplify this fraction we can divide both the numerator and denominator by the greatest common factor (GCF) which is 625.
So, (65.625/100) = (65625/10000) = (261/400)
Therefore, the simplest form of 40 1/4% as a fraction is 161/400, and 65 5/8% as a fraction is 261/400
Step-by-step explanation:
Find the missing side length of the following right triangle. x
Answer24
Step-by-step explanation:
The area of this rectangle is given by the quadratic function
A = 50W - W2
.
What is the reasonable domain for this function?
The reasonable domain for this function is 0 < x < 50
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Given;
A = 50W - W2
The area of a rectangle cannot be negative;
The practical domain of A is determined when;
50W-W^2>0
Taking common factor W
W(50-W)>0
Since W must be positive W>0
50-W>0
Or equivalently
50>w
W<50
The total interval is
0<W<50
Therefore, the domain of the function will be 0 < x < 50
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5 2/5 divided by 7 =?? Whats the answer?
Answer:189/2
Step-by-step explanation:
Vanessa and Jo share £128 in the
ratio 5: 3. Work out how much money
Vanessa receives.
Answer:
vanessa gest 80
Step-by-step explanation:
128/8 =16
5 * 16 =80
3*16. =48
Answer: £80
Step-by-step explanation:
Step 1:
Make a proportion:
5 - 8
x - 128
Step 2:
Cross multiply:
5*128=8x
640=8x
Step 3:
Divide by 8:
80=x or x=80
Identify the Constant of Proportionality From a Graph
The graph of constant of proportionality is determined and attached with a green check on the mark box
How to find the graph of constant of proportionalityThe ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
The equation shows that y = kx and the y intercept is zero, because of this the graph will start from the origin
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Helppppp!!!! Question: Jimmy’s friend Tom also wants to save money to buy concert tickets. He draws up the following savings plan. Each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. Use summation notation to write the sum and find the total amount Tom will save in three weeks.
The summation notation of the sum is:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
The total amount is $84.
How to use summation notation to write the sum?Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.
Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.
Let n represent the number of weeks
Thus, this can be written using summation notation as:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
Thus, the total amount = 4¹ + 4² + 4³ = $84
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i need answers asap or pls
Answer:
see attached
Step-by-step explanation:
HELP ME PLEAE ASAP!!!!!!!!!!!!
Pt.2 Can someone review my answers please? Thank you!
Answer:
Step-by-step explanation: Whats you answer? cant see it.
PLEASE HELP E ASAP!!!!!!!!!!
Answer:
78.4 meters
Step-by-step explanation:
Need help solving this question
Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.
Step-by-step explanation:
Speed = Distance/Time
The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.
x / 4.5 = 171 / 3
x = 256.5 miles
I hope this helps!
true or false correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items
Correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items is true.
To evaluate a hypothesis about a population, hypothesis testing uses sample data. A hypothesis test evaluates the result's unusualness, determining if there is a reasonable amount of random variation or whether the result is too extreme to be accounted for by chance.
Reliability can be measured by internal consistency. When a measurement is said to be reliable, it means that it will always produce the same result, given all other factors being equal.
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The solution set to 6 + 2n> 12 is n> 3. Which are correct representations of this solution? Select two options.
{n\n<3}
{n\n≥3)
-5-4-3-2-1 0 1 2 3 4 5
-5-4-3-
(3,0⁰0)
0
2 3 4
5
-5-4-3- is the solution for {n\n<3} and 2-1-0 is the correct set for this solution {n\n≥3).
What is the set?A set is a well-defined collection of distinct objects, known as elements or members of the set. The objects can be anything, such as numbers, letters, words, animals, or even other sets. The defining feature of a set is that its elements are unique and distinct, meaning that no element can appear more than once in the set.
The solution set to 6 + 2n > 12 is n > 3. The correct representations of this solution are:
{n | n ≥ 3}
(3, ∞)
Option 1 {n | n < 3} is incorrect, as it represents the solution set of n being less than 3, which is the opposite of the solution set provided.
Option 2 -5-4-3- is Correct, as it is not in the correct format to represent a solution set.
Option 3 (3,0⁰0) is correct because it represents a point, not a set.
Option 4 and 5 -5-4-3-2-1 0 1 2 3 4 5 and 0 2 3 4 5 are also incorrect as they are not in the correct format to represent a solution set, and does not include the value 3.
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Divide 3x^2 + 6 by 3x – 3.
Which expression represents the quotient and remainder?
because i couldn't find it anywhere
the answer is c
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
Division of Polynomials :To divide polynomials by a polynomial, we use the long division method.
When there is no common factor in both the numerator and the denominator, we can use the long division.
It may be used to find reminders and quotients while dividing.
Here we have
Divide 3x² + 6 by 3x – 3
On dividing 3x² + 6 by 3x – 3 in long division method
we get the remainder as 9 and the quotient as (x - 1)
For more understanding understand the long division in the given picture.
Therefore,
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
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Find the area of the shaded region.
13.
12
Geometry IF8763
12
2014
11
86
15, 1111717-74
27
12.5
27
10 mm
24
27
27
MCMXCIV Instructional Fair,
Answer: need photo
Step-by-step explanation:
AOB is a line . Ray OP is perpendicular to AB OC is another ray between rays OA and OP . If ray OD is perpendicular to OC , prove ∠COP = ∠BOD.
The proof of ∠COP = ∠POD is below.
What is a ray?When viewed as a vector, a ray is a vector from a point to a point . In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and. taken to be at infinity.
Given is that AOB is a line. Ray OP is perpendicular to AB. OC is another ray between rays OA and OP. If ray OD is perpendicular to OC.
Refer to the figure attached.
In ΔOCP and ΔODP -
∠OPC = ∠OPD = 90° {right angles}
OP = OP {Common}
OC = OD
By SAS criteria, ΔOCP ≅ ΔODP.
So, we can write -
∠COP = ∠POD
Therefore, the proof of ∠COP = ∠POD is given above.
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janine speds 1/10 hour making the bed, 1/5 hour getting dressed, 1/2 hour eating breakfast. what is the total fraction of an hour
The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast is 4 / 5 hour.
The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast can be calculated by adding the fractions of time she spends on each activity:
1/10 hour + 1/5 hour + 1/2 hour
= (2 + 1 + 5) / 10 hour
= 8 / 10 hour
= 4 / 5 hour
The addition of two or more fractions with the same denominator is straightforward.
Simply add the numerators and keep the same denominator. For example:
(1/5) + (2/5) = (1 + 2) / 5 = 3/5
If the fractions have different denominators, you will need to find a common denominator before adding the numerators. The common denominator is the least common multiple of the denominators. Once you have found the common denominator, convert each fraction to an equivalent fraction with the common denominator and then add the numerators.
For example:
(1/5) + (2/3) = (3/15) + (10/15) = (3 + 10) / 15 = 13/15
So the addition of two or more fractions is performed by finding a common denominator, converting the fractions to equivalent fractions with the common denominator, and then adding the numerators.
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When Landon moved into a new house he planted two trees in his backyard. At the time of planting tree a what 24 inches tall and tree B was 40 inches tall. Each year there after three A grew by 9 inches per year and tree B grew by 5 inches per year. Let A represent the height of tree A t years after being planted and let B represent the heights of tree B t years after being planted. Write an equation for each situation in terms of t, and determine the height of both trees at the time when they have an equal height.
Answer:
A=24+9t
B=40+5t
Step-by-step explanation:
see attached
what metric unit would be best to measure the amount of spices put into a batch of cookies? responses
Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).
A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:
The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.
You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.
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what is the domain of the function shown in the graph below?
The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By using set builder notation, the domain of this function shown in the graph above can be written as follows;
Domain = {-4, ∞}
Domain = {x|x ≥ -4}
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Juwan makes 12 baskets in 40 minutes. If he continues making baskets at this rate, how many baskets will he make in 90 minutes?
The required number of baskets made in 90 minutes are 27 baskets.
It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.
Number of baskets made in 90 minutes = ?
So, let us calculate the number of baskets made in 1 minute.
40 min - 12 baskets
1 min - 12/40 baskets
Now, we need to find out the number of baskets made in 90 minutes.
90 min - ?
1 × 90 min - 90 × 12/40 = 27 baskets
Thus, the required number of baskets made in 90 minutes are 27 baskets.
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here is an equation: 4x - 4 = 4x + _. What could you write in the blank so the equation would be true for:
a. No values of x
b. All values of x
c. One value of x
The value to write in the blank so the equation would be true is -4. Option A. no values of x
How to determine the valueIt is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.
These algebraic expression also consist of mathematical operations, such as;
MultiplicationDivisionFloor divisionSubtractionAdditionParenthesesBracketFrom the information given, we have the equation;
4x - 4 = 4x + _
To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;
4x - 4 = 4x + (-4)
expand the bracket
4x - 4 = 4x - 4
0 = 0
Hence, the value is -4
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Use your formula to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
Here is the formula: 1/2(a+b)h
Answer:
Step-by-step explanation:
Find the distance between the given points. Round your answer to the nearest tenth. ( 1 , 2 ) and (5, 9)
The distance between the given points is 8.1 units
How to find the distance between the given points?Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)
From the given info, we have:
( 1 , 2 ) and (5, 9),
where x1 = 1, y1 = 2 and x2 = 5 and y2 = 9
d=√((x2 – x1)² + (y2 – y1)²)
d=√((5 – 1)² + (2 – 9)²)
d=√((4)² + (-7)²)
d = √65
d = 8.1 units
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