The top of the ladder is sliding down the wall at the rate of 1.5 ft/s.
Given: A ladder is 25 ft long and is leaning against the wall of a house.
The base of the ladder is sliding away from the house at the rate of 2 ft/sec.
Asked: How fast is the top of the ladder sliding down the wall when its base is 15 feet from the wall?
Let the distance of the top of the ladder from the wall be x ft.
Then we have,
x² + y² = 25² (by Pythagoras theorem)
Differentiating both sides with respect to time t,
we get, 2x(dx/dt) + 2y(dy/dt) = 0 ...(1)
Given dx/dt = 2, and x = 15 ft.
⇒ 2(15)(dx/dt) + 2y(dy/dt) = 0
⇒ 30 × 2 + 2y(dy/dt) = 0 (substituting the given values)
⇒ 2y(dy/dt) = - 60⇒ dy/dt = - 30/ y
The negative sign indicates that y is decreasing (getting smaller) with time.
The values of y are negative because it lies below the level of the ground.
Substituting the value of x = 15 in the equation x² + y² = 25², we get
15² + y² = 25²
⇒ y² = 25² - 15² = 400
⇒ y = - 20
Substituting the values of dy/dt and y in the above equation, we get,
dy/dt = - 30/ (- 20)
dy/dt = 1.5 ft/s
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Find the surface area of the cube shown below?
The surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
What is Surface Area?Surface area is the measure οf the tοtal area that the surface οf a three-dimensiοnal οbject οccupies, including all οf its faces, sides, and curves. It is οften expressed in square units such as square meters οr square feet, and is an impοrtant parameter fοr determining prοperties such as heat transfer, frictiοn, and οptical prοperties οf an οbject.
The surface area οf a cube with sides οf length "a" can be fοund by using the fοrmula:
Surface area[tex]= 6a^2[/tex]
Substituting the given value οf "a" intο the fοrmula, we get:
Surface area [tex]= 6(25 cm)^2[/tex]
Surface area[tex]= 6(625 cm^2)[/tex]
Surface area [tex]= 3750 cm^2[/tex]
Therefοre, the surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
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The question was incomplete, the complete question is mentioned here:
Find the surface area of the cube with side 25cm?
A triangular piece of fabric has side lengths of 3 inches, 4 inches, and 5 inches. Will it fit in the corner of a rectangular quilt? Explain.
Yes, because it is a right triangle.
Yes, because it is an isosceles triangle.
No, because it is an equilateral triangle.
No, because it is an obtuse triangle.
Answer:
yes because it is a right triangle
Step-by-step explanation:
if you apply the pythagorean theorem a squared plus b squared equals c squared. c being the hypotenuse, the longest side. so 3x3 + 4x4 = 25 and 5x5 is 25. This confirms that it is a right triangle because pythagoras's theorem only works with right triangles. Also, every angle of a rectangle is a right angle (90 degrees) meaning that the triangle will fit in any and every corner! Hope this helped!
please address those questions please type
1, You have 7 identical cookies to distribute to 4 kids.
a, How many ways can you distribute the cookies?
2, how many three colors flag can you make with the colors white, red and blue.
The sοlutiοn οf the given prοblem οf unitary cοmes οut tο be 1.20 and 2.27 .
What is an unitary methοd?By cοmbining the infοrmatiοn οbtained using this nanοsectiοn technique with all variable additiοnal data frοm twο individuals whο used a specific strategy, the task can be cοmpleted. Simply put, this mean that, if the desired οutcοme materialises, either the specified entity will be knοwn οr, actually, the cοlοur frοm bοth enοrmοus prοcesses will be skipped. Fοr fοrty pens, a refundable charge οf Rupees ($1.01) might be required.
Here,
There are several apprοaches tο the issue οf giving 4 children each 7 identical cοοkies, but οne pοpular strategy is tο use a stars and bars strategy.
Cοnsider 7 stars as the 7 biscuits and 3 bars as the 3 partitiοns separating the 4 children. Then, any cοnfiguratiοn οf stars and bars represents a pοtential cοοkie dispersal.
=> (10 + 3) chοοse 3 = 120 / 6 = 7 + 3 chοοse 3 = 20
The fοur children can therefοre share the cοοkies in 20 variοus ways. The number οf ways tο create a three-cοlοr flag is as fοllοws because we have three cοlοur οptiοns and can repeat cοlοurs in variοus ways:
=> 3 x 3 x 3 = 27
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Complete question:
Draw a number line and show the following numbers. positive proper fractions with a denominator of 6
The fraction 1/6 is closer to 0, while the fraction 5/6 is closer to 1.
What does the denominator represent?A horizontal bar between two numbers and, on occasion, the symbol "/" can be used to identify a fraction. The term "fractional bar" refers to this bar or symbol. The "denominator" is the number below the fractional bar, while the "numerator" is the number at the top.
Indeed, the following number line displays positive proper fractions with the denominator 6:
0 1 2 3 4 5
|------------|------------|------------|------------|------------|
0 1/6 1/3 1/2 2/3 5/6
The complete numbers are represented by tick marks, while the fractions are displayed in between. The fractions 1/6 and 5/6 are closer to the numbers 0 and 1, respectively.
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The ratio of boys to girls is 4to3 how many boys are there
The ratio of boys to girls is 4:3 boys are there of 5 boys were more than girls.
Most of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
Formula used:
No. of Object= Total No of abject. x Given ratio/Sum of ratios
No. of Boys = 35 x 4 /7
No. of Boys = 140 / 7
No of Boys = 20
And No. of Girls = 35 x 3/7
No. of Girls = 105 /7
No. of Girls = 15
Final answer:
No. of boys - No. of girls
20-15= 5
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are used to represent an unknown quantity in a mathematical expression.
Answer:
Variables
Step-by-step explanation:
A variable is a quantity that can be changed and is not fixed. Variables are essential as they form a major algebra component. We usually use “x” and “y” to express an unknown integer.
Homework Progress
79/99 Marks
If £2000 is placed into a bank account that pays 3% compound interest per year.
how much will be in the account after 2 years?
Optional working
3
78%
Answer
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]
8x=__when x= 3
pls tell me
Answer:
24
Step-by-step explanation:
Find the values of variables and the measures of the indicated angles.
Using the angle of intersecting chords theorem, the measure of x = 175°.
What is the Angle of Intersecting Chords Theorem?The angle of intersecting chords theorem states that when two chords intersect within a circle, the angle that they form is equal to half the sum of the measures of the intercepted arcs and the vertical angle opposite to the angle.
Therefore, based on the theorem, we would have:
180 - 60 = 1/2(x + 65)
120 = 1/2(x + 65)
Multiply both sides by 2:
240 = x + 65
subtract 65 from both sides:
240 - 65 = x
x = 175°
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An object with a mass of 7.5kg accelerates 8.3m/s2 when an unknown force is applied to it. What is the amount of force
Answer: The amount of force (F) can be calculated using Newton's second law of motion, which states that force is equal to mass times acceleration:
F = m*a
where F is the force, m is the mass, and a is the acceleration.
Plugging in the given values, we get:
F = 7.5kg * 8.3m/s^2
F = 62.25 N
Therefore, the amount of force applied to the object is 62.25 Newtons.
Step-by-step explanation:
This is 4/6 problems finish them all each is 10 points 60 total.
The trigonometric ratios for cosines indicates that the measure of angle B, m∠B, in the right triangle with hypotenuse side length of 15 units and adjacent leg to ∠B of 12 units, obtained using the trigonometric ratios for cosines is; m∠B ≈ 36.9°
What are trigonometric ratios?Trigonometric ratios relate the lengths of two side lengths of a right triangle and the interior angles of the right triangle.
The cosine of an angle can be obtained from the ratio of the adjacent side to the angle to the hypotenuse side of the right triangle in which the angle is an acute angle, therefore;
cos(θ) = Adjacent side to the angle ÷ Hypotenuse side of the angle
The measure of the length of the adjacent side to the angle x = 12 units
The measure of the hypotenuse side of the right triangle = 15 units, therefore;
cos(x°) = 12/15 = 4/5 = 0.8
The measure of the angle x therefore can be obtained using the arccos function, (cos⁻¹ function) in a scientific calculator as follows;
x = arccos(0.8) ≈ 36.9°
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Can some on solve this?
The length οf the missing side is 10 cm.
What is a triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric shape that has three straight sides and three angles. It is οne οf the mοst basic shapes in geοmetry and is used extensively in mathematics, science, and engineering.
Tο sοlve fοr x, we can use the Pythagοrean theοrem which states that in a right triangle, the square οf the hypοtenuse (the side οppοsite the right angle) is equal tο the sum οf the squares οf the οther twο sides.
In this case, we can see that the hypοtenuse is 10 cm and οne οf the οther sides is x cm. The remaining side is then (10 - x) cm (since the triangle is isοsceles).
Applying the Pythagorean theorem, we get:
x² + (10 - x)² = 10²
x² + 100 - 20x + x² = 100
2x² - 20x = 0
2x(x - 10) = 0
So x = 0 or x = 10. However, x cannot be 0 since it would not form a triangle. Therefore, the only valid solution is x = 10.
Therefore, the length of the missing side is 10 cm.
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Do what the photo says.
The area of the composite figure is 186.5 m².
How to find the area of a composite figure?The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.
Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.
The composite figure can be divided into rectangles, square and quarter circle.
area of the composite figure = area of rectangle + area of square + area of quarter circle
area of the composite figure = 8 × 9 + 6 × 6 + 1 / 4 × 3.14 × 10²
area of the composite figure = 72 + 36 + 1 / 4 × 3.14 × 100
area of the composite figure = 108 + 314 / 4
area of the composite figure = 108 + 78.5
area of the composite figure = 186.5 m²
Therefore, the composite figure with different shapes has an area of 186.5 metres squared.
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If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is
The end behavior of a polynomial function is to decrease without bound as x approaches negative infinity, and to increase without bound as x approaches positive infinity.
If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is as follows:
As x approaches negative infinity, the value of the function decreases without bound.
As x approaches positive infinity, the value of the function increases without bound.
To understand why this is the case, consider a polynomial function of the form:
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0
where n is odd and a_n < 0.
As x approaches negative infinity, the dominant term in the polynomial is a_n x^n, and since n is odd and a_n is negative, the value of the dominant term approaches negative infinity as x approaches negative infinity.
Similarly, as x approaches positive infinity, the dominant term in the polynomial is again a_n x^n, but this time the value of the dominant term approaches negative infinity as x approaches positive infinity.
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The function f(x) = –5x2 + 13x + 6 represents the height, in meters, of a coin x seconds after it is thrown into the air. What is the maximum height of the coin
The maximum height of the coin is approximately 14.825 meters.
To find the maximum height of the coin, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by:
x = -b/2a
where a = -5 and b = 13 are the coefficients of the quadratic function f(x) = -5x^2 + 13x + 6.
Plugging these values into the formula, we get:
x = -13/(2×(-5)) = 13/10
Now we can find the y-coordinate of the vertex by plugging in x = 13/10 into the function:
f(13/10) = -5(13/10)^2 + 13(13/10) + 6
Do the arithmetic operations
≈ 14.825 meters
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Which statement is not true about the absolute value of -6?
It equals the absolute value of 6.
It can be expressed as |-61.
It describes the distance between -6 and 0 on the number line.
It describes the distance between 6 and -6 on the number line.
My Progress
Done →
out express written consent of Curricu
Answer:6
Step-by-step explanation:
Absolute value is just how many units, it is away from 0.
On a hot summer day in Death Valley, the amount of water in a swimming pool is 4000 gallons. 30 Days later, the amount of water in the pool is 3500 gallons. If the evaporation follows a continuous exponential model for decay, find k, the constant of proportionality in the equation A=Av0e^kt. Round to 4 decimal places.
Write a function that models the amount of water in the pool A(t), t days after the original measurement
The half-life of the radioactive substance,1/2 = 18.905 years.
What is half-life of the radioactive substance?The half-life of a radioactive atom or substance
A radioactive element's half life is the amount of time it takes for its atoms to split in h-alf from their initial number.
nuclear decay
The process of a heavy radioactive element's nucleus disintegrating and emitting alpha, beta, and gamma rays is known as radioactive decay.
Radioactivity law
According to the law, when a radioactive element decays or disintegrates, a new element two places below the original element in the periodic table with alpha particle emission or two places above the original element with beta particle emission results.
Hence, The half-life of the radioactive substance,1/2 = 18.905 years.
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Mixes two varieties of saffron X and y the ratio 3:8 if the cost of X is rupees 154 per g and that of y is rupees 121 per gram at what price should he sell the mixture make a profit of 25%
The seller should sell the mixture at Rs. 162.5 per gram to make a profit of 25%.
Let's assume that the quantity of variety X in the mixture is 3x and the quantity of variety Y is 8x. Therefore, the total quantity of the mixture will be 3x + 8x = 11x.
The cost of variety X is Rs. 154 per gram. Therefore, the cost of 3x grams of variety X will be 3x × Rs. 154 = Rs. 462x.
Similarly, the cost of variety Y is Rs. 121 per gram. Therefore, the cost of 8x grams of variety Y will be 8x × Rs. 121 = Rs. 968x.
The total cost of the mixture will be the sum of the costs of the individual varieties:
Total cost = Rs. 462x + Rs. 968x = Rs. 1430x
To make a profit of 25%, the selling price of the mixture should be 1.25 times the cost price:
Selling price = 1.25 × Total cost
= 1.25 × Rs. 1430x
= Rs. 1787.5x
Therefore, the selling price of the mixture should be Rs. 1787.5x to make a profit of 25%. To find the price per gram of the mixture, we need to divide this selling price by the total quantity of the mixture:
Price per gram of mixture = Selling price / Total quantity
= Rs. 1787.5x / 11x
= Rs. 162.5 per gram (approx.)
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PLS HELP! I WILL MAKE U BRAINLIST! LATE WORK
Step-by-step explanation:
to graph a line always find 2 points out has to go through. that means the points' coordinates make the equation true.
I usually start with x = 0.
point 1 of equation 1 is then
y = -2×0 + 6 = 6
(0, 6)
point 1 of equation 2 is then
y = (3/2)×0 - 1 = -1
(0, -1)
then I pick a value for x that makes the handling of any fractions easier. like in our case x = 2.
point 2 of equation 1 is then
y = -2×2 + 6 = -4 + 6 = 2
(2, 2)
point 2 of equation 2 is then
y = (3/2)×2 - 1 = 3 - 1 = 2
(2, 2)
oh, so I have found the intersection point right away (point 2 of both equations).
so, let's pick a different point 2 for equation 1, like x = 4
y = -2×4 + 6 = -8 + 6 = -2
(4, -2)
with these 4 points you define the 2 lines, and you have the intersection point at (2, 2).
create an art work from home in any theme that will alllow you to aply youre learnings on angle pairs and lines. The art work should be made of composed od corguent traingles
u have to pay me to do it for you thanks
Which statements about liquid volume are true
The statements that are cοrrect based οn unit cοnversiοn is -
A - One milliliter is 100 times smaller than οne liter.
C - Milliliters are smaller units than liters.
D - One liter is 1,000 times larger than οne milliliter.
What is unit cοnversiοn?Unit cοnversiοn is a prοcess with multiple steps that invοlves multiplicatiοn οr divisiοn by a numerical factοr οr, particularly a cοnversiοn factοr. The prοcess may alsο require selectiοn οf the cοrrect number οf significant digits, and rοunding.
On the basis οf unit cοnversiοn methοds -
These three statements are true -
One milliliter is 100 times smaller than οne liter.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than οne milliliter.
The οther statements are incοrrect -
Liters are nοt smaller units than milliliters.
One milliliter cannοt be 100 times larger than οne liter, as it is a smaller unit οf vοlume.
One liter cannοt be 1,000 times smaller than οne milliliter, as it is a larger unit οf vοlume.
Therefοre, the statements A, C and D are cοrrect.
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Which statements about liquid volume are true?
Select each correct answer.
One milliliter is 100 times smaller than one liter.
Liters are smaller units than milliliters.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than one milliliter.
One milliliter is 100 times larger than one liter.
One liter is 1,000 times smaller than one milliliter.
PLEASE HELP ASAP !!!!!!!!!!!!!
The length of the x is 9 units.
Describe Triangle?Triangles can be classified based on the lengths of their sides and the sizes of their angles. The three most common types of triangles are equilateral, isosceles, and scalene. In an equilateral triangle, all sides and angles are equal. In an isosceles triangle, two sides and two angles are equal. In a scalene triangle, all three sides and angles are different.
Let's call the two sides of the triangle that the median divides into 9 and 10 "a" and "b", respectively. Then, we can use the formula for the length of a median in a triangle:
median = 1/2 * √(2a² + 2b² - c²)
where c is the length of the third side of the triangle. However, we don't know the length of the third side, so we need to find it. We can use the fact that the median divides the third side into two equal parts:
c/2 = (a + b)/2
c = a + b
Now we can substitute this into the formula for the length of the median:
x = 1/2 * √(2a² + 2b² - (a + b)²)
Simplifying:
x = 1/2 * √(2a² + 2b² - a² - 2ab - b²)
x = 1/2 * √(a² + 2ab + b²)
x = 1/2 * √((a + b)²)
x = 1/2 * (a + b)
x = 1/2 * (9 + 10)
x = 9
So the length of the median is 9 units.
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A population of values has a normal distribution withμ=178andσ=75.2. You intend to draw a random sample of sizen=48. Find the probability that a sample of sizen=48is randomly selected with a mean between182.3and 198.6.P(182.3×M<198.6)=Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exactz-scores orzscores rounded to 3 decimal places are accepted.
The probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
The central limit theorem: what is it?The behaviour of sample means and sums in sizable random samples is described by the central limit theorem, a statistical concept. It asserts that regardless of how the underlying population is distributed, as the sample size grows, the distribution of the sample means and sums will converge to a normal distribution. This theorem is crucial because it enables us to extrapolate population parameters from sample data. Because sample means and variances are simpler to gather and evaluate, we may use them to estimate population means, variances, and other characteristics. Several study fields, including the social sciences, the natural sciences, and business, frequently employ the central limit theorem.
Given that the sample size n = 48.
The mean between 182.3and 198.6 is calculated using the central limit theorem.
The sample mean is given as:
Z = (M - μ) / (σ / √(n))
Substituting the values we have:
Z = (198.6 - 178) / (75.2 / √(48)) - (182.3 - 178) / (75.2 / √(48))
Z = 1.62
Now, Z-score less than 1.62 is approximately 0.9474.
Hence, the probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
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Someone help me solve this!
Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).
How can the graphs be interpreted?To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.
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Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 30 with a standard deviation of 3 days. Assume the data to be approximately bell-shaped.
Between what two values will approximately 68% of the numbers of days be?
Approximately 68% of the customer accounts have payments made between 23 and 37 days.
How the mean and standard deviation is related: The formula for calculating the standard deviation uses the mean.
In actuality, we cannot determine a sample's standard deviation without first knowing what the sample means.
We want to calculate what two values will approximately 68% of the number of days be.
For a bell-shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.
Then, for a mean of 30 and a standard deviation of 7, we can calculate the two values as:
[tex]X_1=u+z_1.n=30-1.7=30-7=23\\X_2=u+z_2.n=30+1.7=30+7=37,[/tex]
Approximately 68% of the customer accounts have payments made between 23 and 37 days.
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Use the triangle below to write the given ratios.
In the given triangle the value of the ratios are Sin (P) = 5/13. tan (T) = 12 /5. cos (T) = 5/13.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to determine each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Using the trigonometric identities we can write the ratios as follows:
Sin (P) = Opposite side to P / Hypotenuse= 5/13
tan (T) = Opposite side to T / Adjacent side to T = 12 /5
cos (T) = adjacent side to T / Hypotenuse = 5/13.
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Simplify the expression
Answer:
2 Is the Ans
Step-by-step explanation:
As per the Picture....
Using the graph answer the following questions What is the slope of the function What is the y intercept of the function What is the slope intercept form of the function?
Answer: what's the queston?
Step-by-step explanation:
Answer:
um question ?
Step-by-step explanation:
Find the HCF of:
x²+5x+6, x²-4 and x³+8
Answer:
x²+5x+6 can be factored as (x+2)(x+3)
x²-4 can be factored as (x+2)(x-2)
x³+8 can be factored as (x+2)(x²-2x+4)
The common factor of all three expressions is (x+2). Therefore, the HCF of x²+5x+6, x²-4, and x³+8 is (x+2).
Step-by-step explanation:
Answer: To find the highest common factor (HCF) of these three polynomials, we can factor each polynomial and then look for the factors that they have in common.
First, let's factor each polynomial:
x² + 5x + 6 = (x + 2)(x + 3)
x² - 4 = (x + 2)(x - 2)
x³ + 8 = (x + 2)(x² - 2x + 4)
Now, we can see that all three polynomials have a factor of (x + 2). Therefore, the HCF of these three polynomials is (x + 2).
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The volume, in cubic centimetres, of a rectangular box can be modelled by the polynomial expression 2x3−11x2−41x+140. Determine an equation to represent the area of the base of the box if the height, in centimetres, is given by 2x−5. [APP 3 marks]
The equation for area of the base of the box will be x² - 6x + 28.
What is Volume ?
In physics and mathematics, volume is a measure of the amount of three-dimensional space occupied by an object or a region. It is often measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.
The volume (V) of a rectangular box is given by the product of its length (l), width (w), and height (h):
V = lwh
Given that the volume is modelled by the polynomial expression 2x³- 11x² - 41x + 140, we can write:
V = 2x³ - 11x² - 41x + 140
And since the height is given by 2x - 5, we can substitute this expression into the formula for volume:
V = lwh = (lw)(2x - 5)
So we need to find an equation for the area of the base (lw). We can do this by rearranging the formula for volume:
lw = V / (2x - 5)
Substituting the expression for V, we get:
lw = (2x³ - 11x² - 41x + 140) / (2x - 5)
We can simplify this expression by polynomial long division or synthetic division, which gives:
lw = x² - 6x + 28
Therefore, the equation for the area of the base of the box is:
A = x² - 6x + 28, where A is the area in square centimeters, and x is the length in centimeters.
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