Solve each inequality.


a. 9t-5(t - 5) ≤ 4(t - 3)

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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In the given triangle the value of the ratios are Sin (P) = 5/13. tan (T) = 12 /5. cos (T) = 5/13.

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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The length of the x is 9 units.

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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If x and y have a proportional relationship, we may write: y = kx where k is the proportionality constant. To calculate k, we may utilise the supplied data point (x=29, y=275.5) and plug .

The following values into the equation: 275.5 = k(29) (29) When we solve for k, we get: k = 275.5/29 ≈ 9.5 As a result, the proportionality constant is 9.5. We can utilise this constant to obtain x for y=408.5 by plugging y=408.5 and k=9.5 into the equation and solving for x: 408.5 = 9.5x x = 408.5/9.5 ≈ 43 As a result, when y equals 408.5, x is around 43. By charting the data and seeing if the points fall on a straight line flowing through the origin, we may determine if a connection is proportional (0,0). If the points are lost.

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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 area of the composite figure is 186.5 m².

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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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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Answer:

2 Is the Ans

Step-by-step explanation:

As per the Picture....

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:

The length οf the missing side is 10 cm.

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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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°

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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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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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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The probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.

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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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!

Step-by-step explanation:

I'm sorry, but I cannot provide a specific answer to this question without additional context. The value of v100 could refer to many different things depending on the context.

If you could provide more information about what v100 represents or what it pertains to, I would be happy to try and help you with your question.

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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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).

The half-life of the radioactive substance,1/2 = 18.905 years.

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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Answer:6

Step-by-step explanation:

Absolute value is just how many units, it is away from 0.

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.

Answer: what's the queston?

Step-by-step explanation:

Answer:

um question ?

Step-by-step explanation:

u have to pay me to do it for you thanks

[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]

Using the angle of intersecting chords theorem, the measure of x = 175°.

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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a)  2 - 3i.

Given that z1 = 2-3i and z2=3+i. We are to find a) z1. Let's learn the concept of complex numbers and solve the problem. The complex number is a combination of a real number and an imaginary number expressed as a + bi, where a and b are real numbers, and i is an imaginary number. The given complex numbers are,z1 = 2-3iz2 = 3+i(a) z1. To find z1, it is already given as 2-3i. Therefore, the answer is 2 - 3i. Hence, a) z1 is 2 - 3i.

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The fraction 1/6 is closer to 0, while the fraction 5/6 is closer to 1.

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 sοlutiοn οf the given prοblem οf unitary cοmes οut tο be 1.20 and 2.27 .

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:

The surface area οf the cube with sides οf 25 cm is 3750 square centimeters.

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?

Answer:

24

Step-by-step explanation: