Answer: 16 men should be assigned to finish the work in 20 days.
Step-by-step explanation:
Let's assume that the number of men needed to complete the work in 20 days is y. Then, the rate of work done by each man is given by 20/16=5/4 units of work per day.
So, the rate of work done by y men is given by 5/4 * y units of work per day.
Since the total work is constant, we have 20 men * 20/16 units of work per day = y men * 5/4 units of work per day.
Dividing both sides by 5/4, we get:
y = 20 * 20/16 / (5/4) = 20 * 4/5 = 16 men.
Therefore, 16 men should be assigned to finish the work in 20 days.
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are ________ angles, they are congruent according to the ________ Angles Theorem. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality.
Which term accurately completes the proof?
The transitive term accurately completes the proof
What is the vertical angle theorem?
According to the vertical angle theorem, the vertical angles that are created when two lines intersect are congruent. The opposing angles of two intersecting lines must be congruent, or identical in value.
Here, we have
Given: segment UV is parallel to segment WZ. According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem.
we are given a line of thought trying to prove different entities proven to be congruent by different arguments or proof.
Eventually, the two are associated using a property called transitivity. This property is used to associate A and C when A is equal to B and B is equal to C.
Hence, the transitive term accurately completes the proof.
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Match each polynomial in the first column with a factoring technique in the second column. If none of the techniques can be used to factor the polynomial, select none.
The factorization case for each polynomial is listed below:
Sum and product Grouping Perfect square trinomial Difference of two squares None GCFHow to identify the factorization case of a given polynomial
In this problem we find six cases of polynomials, whose factorization case must be found. Now we proceed to show and indicate what kind of factorization case is used for each polynomial:
Case 1: z² + z - 90 (Sum and product)
z² + z - 90
z² - (- 10 + 9) · z + (- 10) · 9
(z + 10) · (z - 9)
Case 2: x² - 4 · x + 6 · x - 24 (Grouping)
x² - 4 · x + 6 · x - 24
x · (x - 4) + 6 · (x - 4)
(x + 6) · (x - 4)
Case 3: 16 · x² + 24 · x · y + 9 · y² (Perfect square trinomial)
16 · x² + 24 · x · y + 9 · y²
(4 · x + 3 · y)²
Case 4: 49 · x² - 100 · y² (Difference of two squares)
49 · x² - 100 · y²
(7 · x - 10 · y) · (7 · x + 10 · y)
Case 5: 121 · m² + 64 (None)
Case 6: 8 · x³ · y² + 4 · z³ (GCF)
8 · x³ · y² + 4 · z³
4 · (2 · x³ · y² + z³)
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simplify. 5+√3 / √2-√3
please give step by step! ty!
The simplified expression is (- 5√2 - 5√3 - √6 - 3).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
(5 + √3) / (√2 - √3)
The given expression is -
(5 + √3) / (√2 - √3)
We can write -
{(5 + √3) x (√2 + √3)} / {(√2 - √3) x (√2 + √3)}
{5(√2 + √3) + √3(√2 + √3)} / (√2² - √3²)
(5√2 + 5√3 + √6 + 3) / (- 1)
- (5√2 + 5√3 + √6 + 3)
- 5√2 - 5√3 - √6 - 3
Therefore, the simplified expression is (- 5√2 - 5√3 - √6 - 3).
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A box is in the shape of a right rectangular prism. The area of one of the bases is shown. What is the height h of the box? Use the formula V = B x h, where V is the volume of the right rectangular prism, B is the area of the base, and h is the height.
The height of the rectangular prism is 5 feet.
How to find the height of a rectangular prism?A box is in the shape of a right rectangular prism. The area of one of the bases is shown.
Let's find the height of the box.
Using the volume of a rectangular prism,
volume of a rectangular prism = Bh
where
B = base areah = height of the boxV = B × h
where V is the volume of the right rectangular prism, B is the area of the base, and h is the height.
Hence,
h = V / B
h = 60 / 12
Therefore,
h = 5 ft
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Use the sum of cubes identity to find the factors of the expression 8x^6 + 27y^3. Write your answer in the form of the expression on the right of the sum of cubes identity.
The sum of cubes identity states that a^3 + b^3 = (a+b)(a^2 - ab + b^2). To find the factors of 8x^6 + 27y^3, we can apply this identity to the expression by identifying a and b:
What is the identity of the sum of cubes?
What Does the Algebraic Sum of Cubes Formula Mean? One of the key algebraic identities is the sum of cubes formula. Its symbol is written as a3 + b3 and is interpreted as a cube plus a cube. A3 + b3 = (a + b) (a2 - ab + b2) is how the sum of cubes formula (a3 + b3) is written.
8x^6 + 27y^3 = (2x^2)^3 + (3y)^3
We can then apply the identity to get:
(2x^2)^3 + (3y)^3 = (2x^2 + 3y)((2x^2)^2 - 2x^2*3y + (3y)^2)
This gives us the factors of 8x^6 + 27y^3 as (2x^2 + 3y)(4x^4 - 6x^2y^2 + 9y^2).
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Thi i a pond in the hape of a prim. It i completely full of water. Colin ue a pump to empty the pond. The level goe down by 20cm in the firt 30min. How many minute until completely empty
This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.
We have a pond which is completely filled with the water.
Area of the side face ( trapezium shaped)
= 1/2 x (1.4 + 0.6) x 2
= 2 m²
Volume = area x height (here width)
V = 2x1 = 2 m³
The level goes down by 20cm in the first 30 mins
Volume of water that will be taken down =
=0.2 x 1 x 2
=0.4 m³ ( upper water will form cuboid face)
Now,
⇒0.4 m³ water is taken out in 30 minutes
⇒1 m³ water is taken out in 30/0.4 minutes
⇒2 m³ water is taken out in 30/0.4 x 2 minutes
⇒30x2/0.4
⇒150 minutes.
So the pond will be completely empty in 150 min that is 2hrs30mins.
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What is the range of this function?
(1, -2)
(-6, 6)
(9, -1)
(2, 0)
Answer:
-2, -1, 0, 6
Step-by-step explanation:
The range is the outputs or the y values. I just put them in order from least to greatest
(1, -2)
(9, -1)
(2, 0)
(-6, 6)
PLEASE HURRY
no links please!
Answer the questions to show how Adam could find the area of the scale drawing, and then use this strategy to find the area of the electronics board.
1. What is the area of the board shown on the scale drawing? Explain how you found the area. ( 3 points)
2. How can Adam use the scale factor to find the area of the actual electronics board? remember, he used a different method than jason. ( 3 points)
3. What is the area of the actual electronics board. (4 points)
1. The area of the scale drawing is 1800 cm².
2. We can multiply the dimensions of the drawing by the scale factor of 5.
3. The area of the actual board is 45000 cm².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a rectangle is (length×width).
1. Therefore, The area of the scale drawing is (50×36) cm².
= 1800 cm².
2. Given, The scale factor is in the ratio of 5 : 1.
Therefore, The actual length is 50×5 cm = 250 cm and the width is 180 cm.
3. The area of the actual board is 250×180 = 45000 cm².
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Please Help I will Mark Brainlist its Math Question!!
When two or more roads or lines cross each other, they come together. You may also remark that two roads or lines cross.
What is the intersect command?They are referred to be intersecting lines when two or more lines in a plane cross each other.The common point shared by all intersecting lines is known as the point of intersection, and it can be found on all of them. Point O in this case represents the intersection of lines P and Q.
A line is something that is made up of indivisible points that stretch in many directions, to put it simply. Let's use the two points A and B as an example. Now, a line connecting points A and B can be drawn.
Line AB is the name of this line, which stretches in both directions. Arrows are used to represent lines to show that they have no ends and go on forever.
solve log(x)=-x+6
log(x)=-x+6 it can be written as
⇒log(x)+x+6=0
⇒log(1/x+6)=0
It will be in the form of lod(1/a+b)
so we can write log(x)+log(1+6/x)
Therefore, if modulus of 6/x <0 then it can be written as
∞ =log(x)-∑xn/n
n-1
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suppose we wish to estimate the percentage of students who smoke cigarettes at each of several colleges and universities. two of the colleges are wabash college (enrollment 900) and purdue university (enrollment 36,000). what should the relative size of our samples be from each school if we want the two sampling distributions to have approximately the same standard deviation?
The relative size of the samples from each school should be proportional to the square root of the enrollment at each school.
The relative size of the samples from each school should be proportional to the square root of the enrollment at each school. So, for Wabash College, we would want to sample approximately √(900) = 30 students, and for Purdue University, we would want to sample approximately √(36,000) = 180 students.
This would ensure that the standard deviation of the sample proportions from each school would be approximately the same.
So, the relative size of the samples from each school should be proportional to the square root of the enrollment at each school.
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normal approximation for binomial distribution
when n is large we can use this to determine probabilities for binomial settings
In mathematical terms, if X is the sum of successes in n different Bernoulli trials, and p is the likelihood of success in each trial, then X may be represented as a normal distribution with mean increasing as n rises.
μ = np
variance σ^2 = np(1-p)
What is binomial distribution?The binomial distribution is a discrete probability distribution that produces just two outcomes in an experiment: success or failure. In a binomial distribution, the chance of success must remain constant during the trials under consideration. For example, because there are only two possible outcomes when tossing a coin, the chance of flipping a coin is 1/2 or 0.5 for each experiment we do.
Here,
When the sample size (n) is high, the distribution of the total of successes (k) in n separate Bernoulli trials approaches a normal distribution, according to the normal approximation for the binomial distribution.
In mathematical terms, if X is the total of successes in n separate Bernoulli trials, with p being the chance of success in each trial, then X may be represented by a normal distribution with mean as n increases.
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when calculating the percent of pitches thrown at least 92 mph, why did we have to subtract from 100%?
When calculating the percent of pitches thrown at least 92 mph, we subtract from 100% to find the percentage of pitches that fall within a certain threshold (in this case, 92 mph).
When calculating the percentage of pitches thrown at a certain speed, say 92 mph, we use 100% as a reference point. 100% means all of the pitches. By subtracting the percentage of pitches thrown below 92 mph from 100%, we find the percentage of pitches that were thrown at 92 mph or above. This helps us understand what proportion of pitches were thrown at this speed or higher, compared to the total number of pitches thrown. By doing this, we can see how many pitches fall within a certain threshold, in this case 92 mph or above.
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on what interval is the function f (x) = e3x−exincreasing?
The function f(x) = e^(3x) - e^x is increasing on the interval (-∞, +∞).
On the range (-∞, +∞), the function f(x) = e^(3x) - e^x increases. This is because the exponential function e^x is increasing for all x, so the difference of two increasing functions is also increasing.
A mathematical function called an exponential function is applied in numerous instances in the real world. It is mostly used to calculate investments, model populations, and do other tasks like determining exponential growth or decay. In an exponential growth model, the quantity increases initially extremely slowly and subsequently quickly. As time goes on, the rate of change quickens.
Correct Question :
On what interval is the function f (x) = e^(3x)−e^x increasing?
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-10
#1.
A system of equations is graphed on the grid. Which
system of equations is best represented by the graph?
10
A.
y = x + 2
y = -x - 3
y = - 3x + 1
y = 2x + 2
B.
D.
y = -x + 2
y = 2x - 3
y =
y =
x + 2
-x + 4
The equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are: y = - 4/3x + 2 y = 2x -3. Hence, option B is the correct answer.
What is y-intercept?The point where a graph intersects the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, is known as y intercept. Therefore, a x-coordinate of y intercept is 0.
The equation of the line is given by the following formula:
y = mx + c
where, c is the y-intercept of the line.
From the graph we can observe that the y-intercept of the red line is +2 and the y-intercept of the blue line is -3.
Hence, the equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are:
y = - 4/3x + 2
y = 2x -3
Hence, option B is the correct answer.
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I NEED HELP ASAP!!!! PLS HELP ME!!!!
What is the missing number in the factor tree?
A) 9
B) 8
C) 5
D) 2
The missing factor is 9.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The factors of 360 are 10 and 36.
360 = 10 x 36
The factors of 10 are 2 and 5.
10 = 2 x 5
The factors of 36 are 4 and 9.
36 = 4 x 9
The factors of 4 are 2 and 2.
The factors of 9 are 3 and 3.
Thus,
9 is the missing factor.
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an inverted cone has a height of 15 mm and an initial radius of 16 mm. the volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant. what is the rate of change of the radius, in mm per second, when the radius is 6 mm?
The rate of change of radius is 2.832 mm per second, when the radius is 6 mm.
A height of cone = 15 mm
An initial radius of cone = 16 mm
The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant.
The formula of Volume of cone;
V = 1/3 πr^2h
where, r = radius of the cone and h = height of the cone
To determine the rate of change of the radius we differentiate the volume with respect to t.
dV/dt = 2/3 πrdr/dt h
Now putting the values
534 = 2/3 × 22/7 × 6 × dr/dt × 15
534 = 3,960/21 × dr/dt
Multiply by 21 on both side, we get
3960 dr/dt = 11,214
Divide by 3960 on both side, we get
dr/dt = 2.832
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Abag of cat treats has 170 individual treats inside. My cat can eat 5 treats per day. What is the rate of change? How many treats are left in the bag after 20 days?
The rate of change is -5.
The number of treat left in the bag after 20 dyas is 70.
How to find rate of change?A bag of cat treats has 170 individual treats inside. Your cat can eat 5 treats per day. Therefore, the rate of change can be calculated as follows:
The rate of change is the rate at which one quantity is changing with respect to another quantity.
Therefore, using equation
y = mx + b
where
m = slope = rate of changeb = y-interceptTherefore,
y = 170 - 5x
where
y = treat left in the bagx = number of daysHence,
rate of change = -5
Let's find the treat left in the bag after 20 days
y = 170 - 5x
y = 170 - 5(20)
y = 170 - 100
y = 70
Therefore, 70 treat is left in the bag.
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which function is graphed?
(image is attached)
A new refrigerator comes in a box shaped like a rectangular prism. The base of the box measures 4 feet by 5 feet. The total surface area of the box is 148 square feet.
What is the height of the box in feet?
The height of the box in feet is 6 feet.
What is surface area of rectangular prism?The surface area of a rectangular prism is the overall region or area that is covered by all of its faces. A three-dimensional shape is a rectangular prism. It has six faces, each of which is rectangular in shape. Consequently, a rectangular prism's two bases must likewise be rectangles.
The surface area of the rectangular prism is given by the formula:
A = 2(wl + hl + hw)
Substitute the value of A = 148, l = 4 and w = 5:
148 = 2((5)(4) + (4)h + (5)h)
148 = 40 + 8h + 10h
148 = 40 + 18h
108 = 18h
h = 6
Hence, the height of the box in feet is 6 feet.
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(1 point) if (1)=−2, (5)=−7, and ∫51()=−8, evaluate the integral ∫51′().
Combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. , the integral of ∫51′() is equal to -5.
In order to evaluate the integral ∫51′(), we need to use the Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus states that the integral of a function's derivative is equal to the function value evaluated from one point to another. For example, if f'(x) is the derivative of a function f(x), then the integral of f'(x) from x = a to x = b is equal to f(b) - f(a).
Using the given information, we can solve the integral ∫51′() as follows. We know that the derivative of our function is 1, so the integral of 1 from x = 1 to x = 5 is equal to f(5) - f(1). Therefore, combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. Therefore, the integral of ∫51′() is equal to -5.
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a five card hand of cards is dealt from a deck of 52 cards. how many ways can the hand have 3 hearts and 2 diamonds?
The number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.
The number of ways to choose 3 hearts from the 13 available hearts is given by the binomial coefficient C(13,3). The number of ways to choose 2 diamonds from the 13 available diamonds is given by C(13,2). The total number of ways to choose 3 hearts and 2 diamonds from the deck of 52 cards is the product of these two binomial coefficients: C(13,3) * C(13,2).
i.e.
There are 13 hearts and 13 diamonds in a deck of 52 cards.
To choose 3 hearts, we have C(13,3) = 13!/(3!(13-3)!) = 286 ways.
To choose 2 diamonds, we have C(13,2) = 13!/(2!(13-2)!) = 78 ways.
Therefore, the number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.
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How many times more material was used to build the Hoover dam than the American falls down record your answer to the nearest whole number
57 times more material was used to build the Hoover dam than the American falls .
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Volume of Hover dam = 4 x [tex]10^6[/tex]
Volume of American Falls dam = 7 x [tex]10^4[/tex]
So, the number of times more material used
= Volume of Hover dam / Volume of American Falls dam
= 4 x [tex]10^6[/tex] / 7 x [tex]10^4[/tex]
= 400 x [tex]10^4[/tex] / 7 x [tex]10^4[/tex]
= 57.14
Hence, 57.14 times more material used.
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Jenny drives from London to Swindon at an average speed of 54 miles per hour.
She drives for 1 1/2 hours
Work out the distance from London to Swindon.
The distance from London to Swindon is 81 miles.
What is Speed- distance Formula?Speed = Distance/TimeDistance = Speed X Time, and Time = Distance / Speed.We have,
Jenny drives from London to Swindon at an average speed of 54 miles per hour.
Time = 1 1/2 hour = 3/2 hour
Using Speed = distance / Time
Distance = speed x time
Distance = 54 x 3/2
Distance = 27 x 3
Distance = 81 miles
Thus, the distance is 81 miles.
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Determine whether the value given below is from a discrete or continuous data set
When a car is randomly selected and weighed it is found to weigh 1628.3 kg.
a. A discrete data set because there are infinitely many possible values
b. A discrete data set because the possible values can be counted
c. A continous data set because the possible values can be counted
d. A continous data set because there are infinitely many possible values
The value given is from a continuous data set because there are infinitely many possible values.
In statistics, a discrete data set is a set of data that can only take certain values, typically whole numbers, that can be counted. A continuous data set is a set of data that can take any value within a certain range, and the values can't be counted as they are infinite in number.
In the given scenario, the weight of a car can take any value within a certain range, and there are infinitely many possible values between any two values. For example, between 1628.3 kg and 1628.4 kg, the car's weight could be an infinite number of values. Hence, the weight of the car is a continuous variable, and the given value of 1628.3 kg is part of a continuous data set.
Hence, the correct answer is d.
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Consider the experiment of rolling a die, S={1,2,3,4,5,6). Let the random variable X denote the outcome. What is the variance of X? A. 6 B. 7/2 C. 35/42D. None of the above
The variance of X is (C) 35/12.
The formula for variance of a discrete random variable X is:
Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2
where E[X] represents the expected value of X.
To calculate the variance, we first need to find the expected value of X, which is:
E[X] = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5
Next, we find the expected value of X^2:
E[X^2] = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 = 91/6
Now we can substitute the values into the variance formula:
Var(X) = E[X^2] - (E[X])^2 = 91/6 - (3.5)^2 = 91/6 - 12.25 = 35/12.
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Find the vertical, horizontal, and slant asymptotes, if any,
The vertical asymptote is x = 1 or 7
There is no horizontal asymptote
What is asymptote?An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
To find vertical asymptote we set the denominator to 0 and we find the value of x
:. x² - 8x +7 = 0
x² -7x-x+7 = 0
(x²-7)(-x+7) = 0
x( x-7) -1(x-7) = 0
(x-1)(x-7) = 0
x-1 = 0 or x-7 = 0
therefore x = 1 or 7
to find the horizontal asymptote:
Since the degree of the numerator is higher than the denominator, there is no horizontal asymptote
to find the slant asymptote, we divide the numerator by the denominator.
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Examine the paragraph proof. Which theorem does it offer proof for?
Segments JK and HI are parallel, segment LO intersects segment JK at point N, segment LO intersects segment HI at point M, and points N and M are between points L and O on segment LO.
Prove: ∠JNM ≅ ∠NMI
According to the given information in the image, segment JK is parallel to segment HI while ∠JNM and ∠LNK are vertical angles. ∠JNM and ∠LNK are congruent by the Vertical Angles Theorem. Because ∠LNK and ∠NMI are corresponding angles, they are congruent according to the Corresponding Angles Theorem. Finally, ∠JNM is congruent to ∠NMI by the Transitive Property of Equality.
Alternate Interior Angles Theorem
Corresponding Angles Theorem
Vertical Angles Theorem
Same-Side Interior Angles Theorem
Based on the given information, the theorem the paragraph proof offers proof for is: A. Alternate Interior Angles Theorem
What is the Alternate Interior Angles Theorem?The Alternate Interior Angles Theorem states that when two parallel lines are intersected by a transversal (a line that intersects two or more other lines), the pairs of alternate interior angles formed are congruent.
In other words, if you have two parallel lines and a transversal intersecting them, and you draw a line segment connecting two nonadjacent interior angles on opposite sides of the transversal, then those two angles will be congruent. This is because they are alternate (they are on opposite sides of the transversal and between the parallel lines) and interior (they are inside the parallel lines).
Therefore, the theorem the paragraph proof offers is: Alternate Interior Angles Theorem.
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Answer: (A) Alternate Interior Angles Theorem
Step-by-step explanation: cyberia
A table of data is given.
x f(x)
−2 71
−1 13
0 3
1 0.6
2 0.1
Which exponential model best represents the data?
The equation of the exponential model is f(x) = 3 * 0.2^x
What is a logarithmic or exponential function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
Given a data set:
x f(x)
−2 71
−1 13
0 3
1 0.6
2 0.1
An exponential model is represented as:
f(x) = ab^x
When x= 0 and f(x) = 3;
We have:
ab^0 = 3
This gives
a = 3
When x= 1 and f(x) = 0.6
We have:
ab^1 = 0.6
This gives
ab = 0.6
Substitute 3 for a
3b = 0.6
Divide both sides by 3
b = 0.2
Substitute b = 0.2 and a =3 in f(x) = ab^x
f(x) = 3 * 0.2^x
Hence, the equation of the exponential model is f(x) = 3 * 0.2^x
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12. The volume, in cubic meters of a rectangular box can be expressed as the product of its three
dimensions and with the function V(x) = x³ - 9x² + 23x - 15. The length of the box is represented
by the expression (x - 1). Find linear expressions with integer coefficients for the width and height.
Hint: The width is greater than the height. Show your work.
The linear formulas with integer coefficients for width and height are (x - 1)(x+3)(x+4).
what is coefficient ?A algebraic, a set, or the multiplying coefficient of a specific term in an equation have all been examples of variables in mathematics. Usually numeric, but any phrase is acceptable. If the coefficients are variables, they can also be referred to as "parameters" by themselves. A coefficient is a number multiplied by a variable. Examples of coefficients include: In the expression 14c 14c 14c, the coefficient is 14. Word g has a coefficient of 1, which doubles the element by this figure. example The coefficient is 6 because "z" is a constant and the term is defined as is 6z. The square of x's coefficient is one.
given
by long division method
x³ - 9x² + 23x - 15 / (x - 1)
= x2 + 4x + 3
( x2 + 4x + 3 ) (x - 1)
= (x - 1)(x+3) (x+4)
The linear formulas with integer coefficients for width and height are (x - 1)(x+3)(x+4).
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A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday they wrapped 12 small gifts and 45 large gifts earning a total of $339. Today they wrapped 35 small gifts and 42 large gifts, and earned $364. How much did they charge to wrap the gifts
The price for wrapping small gifts is $2 and the price for wrapping large gifts is $7
How to find the amount charged to wrap the giftsThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Yesterday they wrapped 12 small gifts and 45 large gifts earning a total of $339
say small gifts = g and large gifts is = G
12g + 45G = $339
Today they wrapped 35 small gifts and 42 large gifts, and earned $364
35g + 42G = $364
The simultaneous equation
12g + 45G = $339
35g + 42G = $364
solving the simultaneous equation gives
g = $2 and G = $7
Hence the price for wrapping small gifts is $2 and that of big gifts is $7
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