the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.

Length of rectangle in cm:

Width of rectangle in cm:

Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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The table of original value and rounded values are

x        y

0.2    0

0.5     1

0.9     1

1.08    1

1.49     1

1.72     2

2.3      2

2.94    3

The graph is attached

The graph is made in a cartesian coordinate by tracing the point of intersection of the two points

The table is represented as ordered pair as (original value, rounded value) for the given x and y values:

(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)

The graph is a scattered plot and its attached

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The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

The mixture has a total of 20 pounds, hence:

x + y = 20.

y = 20 - x.

The total cost of the mixture is of $108, as 108/20 = 5.4, hence:

7x + 3y = 108

Replacing the second equation into the first, the value of x is given as follows:

7x + 3(20 - x) = 108

4x = 48

x = 12.

Then the value of y is given as follows:

y = 20 - 12

y = 8.

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Answer:

Step-by-step explanation:

a. Sara's estimate is reasonable because:

Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.

If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.

b. If x stands for the miles Dan still needs to bike, then:

(29*3) + (32*4) + x = 300

c. 87 + 128 + x = 300

x = 85

Answer: 0.24z

Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .

The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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Answer:

D) 115.2π cm².

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

Answer: 19 tickets

Step-by-step explanation:  $45 - $7 = 38      38 divided by $2 = 19 tickets

The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.

So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:

(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons

Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be  approximately 6.58 gallons.

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The complete question is :

What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?

The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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Answer: The answer should be 20 hours

Step-by-step explanation:

That is when the 2 lines meet up so that is when they are the same difference from Kansas City.

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.

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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.

The numbers on teddy bears are sorted as 656, 666, 676, 686.

Now, observe the pattern.

656 + 10 = 666

666 + 10 = 676

676 + 10 = 686

This indicates that the pattern rule is "adding 10", which means the next number in series is:

686 + 10 = 696

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The complete question is as follows:

The value of x in the rectangle is 36.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.

Therefore, let's find the value of x in the angles.

Hence,

∠2 = x + 30

∠5 = 2x - 48

Therefore,

∠2 + ∠5 = 90°

x + 30 + 2x - 48 = 90

3x - 18 = 90

3x = 90 + 18

3x = 108

divide both sides by 3

x = 108 / 3

x = 36

Therefore,

x = 36

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The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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Answer:

To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:

(a+bx)(c+d) = (c+dx)(a+b)

Expanding the terms on both sides:

ac + adx + bc + bdx^2 = ac + abx + cdx + bd

Simplifying and rearranging the terms:

adx + bdx^2 - abx - cdx = bd - ac

dx(ad - ab - c) = bd - ac

Now, since we know that cb=ad, we can substitute ad=cb into the equation:

dx(cb - ab - c) = bd - ac

dx(cb - ab - c) = b(cd - ac)

x = b(cd - ac)/(d(cb - ab - c))

Therefore, the solution for x is:

x = b(cd - ac)/(d(cb - ab - c))

An angle is  a geometric figure formed by two rays or line segments that share  a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by  symbol ∠ followed by the name of the vertex, like ∠ABC.

The size of angle is determined by  amount of rotation needed to bring one of  rays or line segments into coincidence with others.

Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).

Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.

This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.

However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.

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Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.

b) The standard deviation of the distribution is 2.46.

The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.

The formula for the mean is given as E(x) = ∑x P(x).

On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.

No. of shots    Probability    Expected        Squared      Squared Deviation

                       of scoring    No. of shots     Deviation     x Probability

0                         0.02               0                   9.6721            0.193442

1                          0.13                0.13               8.8804           1.154452

2                         0.34               0.68              5.9049          2.007666

3                         0.32               0.96              4.6225          1.4792

4                         0.16                0.64              6.1009          0.976144

5                         0.02               0.1                9.0601            0.181202

6                         0.01               0.6                6.3001            0.063001

The expected (mean)

 number of shots =                3.11                                     6.055107

Standard Deviation = Square root of 6.055107 = 2.46

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Answer:

To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.

Plotting the lines corresponding to the inequalities, we get:

Graph of the feasible region:

The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).

Next, we evaluate the objective function at each of these vertices to find the maximum value of z.

At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23

At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31

At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35

At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58

Therefore, the maximum value of z is 58, which occurs at the point (8, 2).

Hence, the answer is: the maximum value of z is 58.

Answer:

To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.

1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)

1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)

Now, we can multiply these two fractions together:

4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18

To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:

32/18 = (2 x 16) / (2 x 9) = 16/9

Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.

Answer:

60:61.8 OR 10:10.3

Step-by-step explanation:

Cant be simplified - unless your in advanced classes. If so

10:10.3

Answer:

Step-by-step explanation:

1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1

The successor of -34 is -33 using the formula "n+1".

A phrase that follows or is right after a specific number, term, or value is known as a successor.

The successor of n is "n+1" if n is a number (and n belongs to any whole number).

The terms just after, immediately after, and next number/next value are also used to describe a successor.

As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.

The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.

So, the successor of -34:

= -34 + n

= -34 + 1

= - 33

Therefore, the successor of -34 is -33 using the formula "n+1".

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Answer:

Step-by-step explanation:

To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:

Present Value (PV) = Future Value (FV) / (1 + r)^n

where:

- FV is the future value, which is R85 000

- r is the annual interest rate, which is 6%

- n is the number of years until the liability needs to be paid, which is 4

To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:

FV = PMT x [(1 + r)^n - 1] / r

where:

- PMT is the annuity payment, which is R16 000

- r is the annual interest rate, which is 6%

- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)

Plugging in the numbers:

FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06

FV = R61 719.56

Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:

FV = R85 000 + R61 719.56

FV = R146 719.56

Plugging in the numbers to the present value formula:

PV = R146 719.56 / (1 + 0.06)^4

PV = R116 442.12

Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.

Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]

[tex].142 \times 59.5 = 8.449[/tex]

So 8.449 square centimeters of this figure is green.

As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.

Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.

First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.

Maximum weight limit = 2020 kg = 2020000 g

Weight of empty suitcase = 33 kg = 33000 g

Weight of clothes = 55 kg = 55000 g

Weight of electrical accessories = 44 kg = 44000 g

Weight of 55 hardback books = 55 x 720720 g = 39639600 g

Weight of toiletries = 46004600 g

Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g

Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g

Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.

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The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.

The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:

Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.

The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).

In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.

These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.

In the given triangle using the sum of interior angle of triangle we have:

180 - 90 - 29 = 61

The measure of the third angle is 61 degrees.

Now, tan(61) = XZ/XY

XZ = XY * tan(61)

XZ = 18 * 1.927 = 34.686

Now, using the Pythagoras theorem we have:

ZY² = XZ² + XY²

ZY² = 34.686² + 18²

ZY² = 1712.3996

ZY = 41.38

Now, the value of:

sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435

cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838

tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518

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