On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.
What is equation?A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.
a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.
b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.
c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.
d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.
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The height, h, of the triangle is 11 cm greater than its corresponding base.
What is the area of the triangle?
A=
cm²
33 cm
10 cm
Answer:
If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.
Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:
A = (1/2) (b)(b + 11)
A = (1/2) b^2 + (1/2) 11b
If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:
A = (1/2) (10^2) + (1/2) 11 * 10
A = 50 + 55
A = 105 cm^2
So, the area of the triangle is 105 cm^2.
Step-by-step explanation:
17. A class has 20 students. In how many different ways can five students form a group? (Assume
that the order of the students is not important)
Answer: The number of ways to form a group of 5 students from a class of 20 students is calculated using the combination formula:
C(20,5) = 20! / (5! * (20-5)!) = 15504
So, there are 15,504 different ways in which 5 students can form a group.
Step-by-step explanation:
Can anyone help me with this? I’ll give brainliest and 20 points
Based on the Venn diagram, the number of people in each set are follows:
A∩B = 11 peopleThe number of people in A alone = 13The number of people in B alone = 19What is the number of people in each set in the Venn diagram?The number of people in each set in the Venn diagram is calculated as follows:
The universal set has a total of 50 people
Let the intersection of A and B be x
A∩B = x
The number of people in A alone = 24 - x
The number of people in B alone = 30 - x
x + (24 - x) + (30 - x) + 7 = 50
61 - x = 50
x = 61 - 50
x = 11
A∩B = 11
Hence;
The number of people in A alone = 24 - 11
The number of people in A alone = 13
The number of people in B alone = 30 - 11
The number of people in B alone = 19
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whay are mixed fractions
Answer:
hope this helps!! <3
Step-by-step explanation:
A fraction is represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Problem: Solve the equation AB = BC for A, assuming that A, B, and C are square and B is invertible.
I do know how to solve for A to show that it's invertible which is by finding a matrix C such that AC = CA = i, then C = A^-1
Theorem: If A and B are invertible then AB is invertible
(AB)^-1 = B^-1A^-1
Please help in finding B
Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is invertible. We can conclude that B is invertible.
To do this, we will use the fact that if A is invertible, then we can multiply both sides of the equation by its inverse to isolate B:
AB = BC
[tex]A^-1 AB = A^-1 BC[/tex]
B = A^-1 BC
Here, A^-1 is the inverse of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.
Now, let's consider the invertibility of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.
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read the story. clara snacked on a mix of almonds and pecans. she ate 3 almonds for every 1 pecan. pick the diagram that models the ratio in the story. if clara ate 10 more almonds than pecans, how many nuts did she eat altogether?
In all together, Clara ate 20 nuts.
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.
Let the number of pecans be x and the number of almonds is y.
We can write the system of equations as:
y = 3x
y = x + 10
Equating the value of {y}, we get -
3x = x + 10
2x = 10
x = 5 ...(1)
y = x + 10 = 15
y = 15 ...(2)
x + y = 15 + 5 = 20
Therefore, in together, Clara ate 20 nuts.
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What additional piece of information do you need to prove that ALKN-AKNM by the SAS similarity theorem?
A. MN=1/2
B.MN=1
C. MN/LK||MN
D. LN=2/5
The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is option C, MN/LK||MN.
What is SAS (Side-Angle-Side) similarity theorem?The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.
In this case, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.
However, we need to establish that MN/LK||MN, which means that MN is parallel to LK and forms a transversal with LN.
This information is necessary to establish that the included angles between the corresponding sides are congruent, which is required for the triangles to be similar.
Therefore, option C is the correct additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.
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PQRS is a trapezium, and AB ∥ PS ∥QR. If PA = 3 cm, AQ = 1.4 cm, BR = 2.1 cm,
then SB =
Answer:
In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:
SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm
Time spent listening to music a sample of 200 college freshman was asked how many hours per week they spent listening to music the following distribution presents the results
Answer:
Step-by-step explanation:
200 rimwjh hdwqheywgygwuivug
solve the right triangle by completing the table below :) help asap
The missing sides of the two right triangles are B ≈ 75.5, b ≈ 10.7 and a ≈ 6.9.
How to find the missing sides of a system formed by two similar right triangles
In this problem we find two similar right triangles. Two triangles are similar when they have congruent angles and sides that are not congruent but proportional. Sides in right triangles are related each other by means of Pythagorean theorem:
r² = x² + y²
Where:
r - Hypotenusex, y - LegsAccording to the statement, we need to use the following relationships:
B = √(C² - A²)
a / A = b / B = c / C
If we know that A = 49, C = 90 and c = 12.7, then the lengths of missing sides are:
B = √(90² - 49²)
B = √5699 (approx. 75.5)
b = B × (c / C)
b = √5699 × (12.7 / 90)
b = 127√5699 / 900 (approx. 10.7)
a = A × (c / C)
a = 49 × (12.7 / 90)
a = 6233 / 900 (approx. 6.9)
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To solve the system of equations by
graphing, graph each line on a
coordinate grid and find the point of
intersection. Graph both equations on
the coordinate plane even if they
represent the same line.
y = -x-1
y = -x + 2
The equation shows the parallel line.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Given:
y = -x-1......................(1)
y = -x + 2...................(2)
Solving equation (1) and (2) we get
-x -1 = -x +2
0 = 3
Now, if compare the given equation then the equation gives the relation of Parallel lines.
Thus, the equation do not represent the same line.
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Divide £88 in the ratio 1:7
The value of the number 88 in the ratio of 1:7 will be 11:77.
What is a ratio?The ratio is defined as the division of the numbers into two parts according to the requirements. The ratio generally compares one value is how many times the other value.
Given that the £88 is distributed in the ratio of 1:7. The distributed form of the number will be calculated as:-
x + 7x = 88
8x = 88
x = 11
The two values will be,
x = £11
7x = 7 x 11
7x =£77
Therefore, the value of the number 88 in the 1:7 ratio is 11:77.
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In what time will the simple interest on Rs7560 be Rs1102. 50 at 25/4% per annum
The simple interest on Rs 7560 will be Rs 1102.50 at a rate of 25/4% per annum after approximately 1 month (0.09 years).
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, and not on any accumulated interest. It is usually calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.
We can use the formula for simple interest to solve this problem:
Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)
We know that the principal is Rs 7560, the rate is 25/4% per annum, and the interest is Rs 1102.50. Substituting these values into the formula, we get:
1102.50 = 7560 x (25/4) x T
Simplifying:
1102.50 = 47250T/4
Multiplying both sides by 4 to eliminate the fraction:
1102.50 x 4 = 47250T
4410 = 47250T
Dividing both sides by 47250:
T = 4410/47250
T = 0.093 or approximately 0.09 years.
To convert this to months or days, we can multiply by 12 or 365, respectively.
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Polaris, the North Star, is very important in navigation because it does not appear to move in the sky.
True
False
7. Show that the equation 2x² + 5cx = 3c has real and
distinct roots for all positive values of c.
The solution is, Right answer: C) -7 is a solution.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
We have the equation 2x² +5x -63 = 0
First, let's find the coefficients a, b and c as ax² +bx +c = 0:
• a = 2
• b = 5,
• c = -63
Now, we will use the formula below to solve this equation:
x = -b ±√b²-4ac/2a
Let's replace the coefficients with the values that we already found:
putting the values we get,
x = -5±23/4
Now, let's divide it into two solutions, look:
x1 = 9/2
x2 = -7
Right answer: C) -7 is a solution.
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30 minutes twice a day for 184 days how many gallons of water will be used in each hole
30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.
Assuming that each hole uses one gallon of water per 30 minutes.
1 hole = 1 gallon of water
The total amount of water used in each hole over 184 days would be 184 gallons.
So, in 184 days = 184 gallons of water
This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.
= 184 × 2
= 368 gallons
The total amount of water used would be 368 gallons.
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The complete question is:
How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?
Uhmmm I don’t know this pla
Answer:
y = 2x - 3
Step-by-step explanation:
Pick two random points for slope
slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]
y intercept form:
y = 2x - 3
a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a diamond or a seven? express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
Total cards = 52
Total diamond cards = 13
So, probability of getting a card of diamond,
P(diamond) = 13/52 = 1/4
Now,
Total cards with number seven = 4
So, probability of getting a seven,
P(seven) = 4/52 = 1/13
Hope it helps~
(-2,6)(-4,3)(3,-2)(8,6) is the relation a function
The given relation (-2,6)(-4,3)(3,-2)(8,6) is a function as every input has a single output.
A relation is set to be a function when every input has a single output.
In the given relation, -2,-4,3,8 has single output. Therefore, it is a function.
So, -2,-4,3 and 8 are the elements of the domain of the given
relation.
Here domain ={-2,-4,3,8} and range ={6,3,-3}
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An item is regularly priced at $33. Ashley bought it at a discount of 15% off the regular price.
The amount that was paid by Ashley is $ 28.05.
Calculating discount:To find the discount on a given price, multiply the discount that is given by the original price and divide the result by 100.
To find the amount that can be paid by the consumer, subtract the resultant discount from the original price.
Final price of item = Original price - Discount
Here we have
An item is regularly priced at $33.
The discount that Ashley bought it = 15% off the regular price.
The amount that Ashely paid for it = $ 33 - 15% of $ 33
=> $ 33 - $ (15/100 × 33)
=> $ 33 - $ (0.15 × 33)
=> $ 33 - $ 4.95
=> $ 28.05
Therefore,
The amount that was paid by Ashley is $ 28.05.
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A small town has a cylindrical water tower with a radius of 10 feet and a capacity of 12,560 gallons. Explain how you could use the formula for the volume of a cylinder to determine the height of the water tower.
Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, height of the water tower is 40.16 feet tall.
To calculate the height of the water tower, we can use the formula for the volume of a cylinder. This formula is V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 10 feet and the volume of the cylinder is 12,560 gallons. We can rearrange the formula to solve for h, giving us h = V/πr^2. Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, the water tower is 40.16 feet tall.
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Help me quick pls help fast
Answer: 46ft
Step-by-step explanation:
Alright so for this you must reference the pythagorean theorem which is:
a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.
You can therefore set this up like this:
a^2+20^2=50^2 (where a is the side you are looking for- listed as x)
Solve:
a^2=50^2-20^2
a^2=2500-400
a^2=2100
sqrt(a^2)=sqrt(2100)
a= 45.8257569496
Round: a (or x)=46
Which pair of ratios can form a true proportion? I would usually give 45 points but i have 35 soo ye..
A. 9/12, 5/8
B. 25/20, 16/21
C. 6/27, 2/9
D. 7/12, 10/15
Pair of ratios can form a true proportion I would usually give 45 points but i have 35 soo ye 25/20, 16/21.
What is ratios?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) A ratio in mathematics displays the multiplicative relationship between two numbers. For instance, if there are eight oranges and six lemons in a dish of fruit, the ratio of oranges to lemons is eight to six. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.To learn more about ratios refer to:
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GUYS I NEED HELP ASAP
An individual who files a local income tax return has a probability of the return being audited. If 12,000 tax returns are received by the city, which of the following is the best prediction of the number of income tax returns that were audited?
A.3,000
B.2,000
C.3,500
D.2,500
7. consider four values for the predictor. in which instance(s) would you have a trustworthy prediction when using the simple linear regression equation?
The trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
To determine the trustworthiness of a prediction using a simple linear regression equation, we need to assess the degree of linearity and the strength of the relationship between the predictor and the response variable.
If the relationship between the predictor and response is linear, the simple linear regression model is appropriate, and if the relationship is strong, the predictions will be more trustworthy.
So, if we have four values for the predictor, we would need to evaluate the scatterplot of the predictor and response variable to determine the linearity and strength of the relationship.
If the scatterplot shows a clear and strong linear relationship between the predictor and the response variable, with a relatively small amount of scatter around the line of best fit, then we can be more confident that our predictions using the simple linear regression equation will be trustworthy.
On the other hand, if the scatterplot shows a weak or non-linear relationship, or a high amount of scatter around the line of best fit, then the predictions using the simple linear regression equation may not be as trustworthy.
Therefore, the trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
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In circle M, m/NMO = 144º and the area of the shaded sector = 107. Find the
length of MN.
In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.
What is the sector of the circle?
That the portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.
The area of the shaded sector of circle M can be represented as follows:
Area of sector = (m/NMO / 360) * π * r²
We know that m/NMO = 144° and the area of the sector is 107, so we can substitute these values into the equation and solve for the radius:
107 = (144 / 360) * π * r²
Multiplying both sides of the equation by 360 / 144 gives:
360 * 107 / 144 = π * r²
Dividing both sides of the equation by pi gives:
r² = 360 * 107 / (144 * π)
Taking the square root of both sides of the equation gives:
r = √(360 * 107 / (144 * π))
Now that we know the radius, we can use it to find the length of MN.
The length of the minor arc MN is equal to the length of the central angle NMO in radians times the radius:
MN = m/NMO * π * r / 180
Substituting in the values for m/NMO and r gives:
MN = 144 * π * √(360 * 107 / (144 * π)) / 180
Hence, In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.
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The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
The average rate of change of the function is 1.6
How to to determine the average rate of change of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
−4≤x≤1.
From the graph, we have
f(-4) = -4
f(1) = 4
The average rate of change at this interval is calculated as
Rate = Change in function values/Change in x values
So, we have
Rate = (-4 - 4)/(-4 - 1)
Evaluate
Rate = 1.6
Hence, the rate is 1.6
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Mya uses a potato chip can to store small items. each cylindrical can has a radius of 2.5 inches and a height of 9 inches. what is the approximate surface area of the can? (use 3.14 for π.)
The approximate surface area of the can is 180.55 sq.inches
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth. A group of circular discs placed on top of one another might be thought of as a cylinder. The cylinder has both surface area and volume since it is a solid with a three-dimensional geometry.
The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
The Surface Area of Cylinder = Curved Surface + Area of Circular bases
S.A. (in terms of π) = 2πr (h + r) sq.unit
Where, π (Pi) = 3.142 or = 22/7
r = Radius of the cylinder
h = Height of the cylinder
cylindrical can has a radius of 2.5 inches and a height of 9 inches
surface area =2πr (h + r) sq.unit
= 2π*2.5(9+2.5)
=180.55 sq.inches
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There are approximately 1. 06 quarts per liter. There are 4 quarts per gallon. If gasoline cost $0. 50 per liter, how much does gasoline cost per gallon?
A. $1. 42/gal
B. $1. 75/gal
C. $1. 89/gal
D. $2. 12/gal
E. $4. 24/gal
Answer:
$1.89/gal
Step-by-step explanation:
A hospital has a nursing staff of 250 nurses, working four shifts: A (7:00 AM to 1:00 PM); B (1:00 PM to 7:00 PM); C (7:00 PM to 1:00 AM); D (1:00 AM to 7:00 AM)
The number of nurses apportioned to each shift is based on the average number of patients, per shift, given the following table:
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.
What is number?Number mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.
Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.
The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.
In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.
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