9.) Jenny refinished a wooden table. She used 1/3 can of varnish for a first coat, 1/4 can for a second coat, and 1/6 can for a third coat. What fraction of the can did she use in all?​

Multiplying each side of a false equation by the same number will result to a false equation

A false equation refers to equation where the left hand side of the equation is not equal to the right hand side of the equation.  

False equations are not useful and hence in math, converted effort are made towards getting a true equation.

A true equation refers to an equation where each side of the equation are same hence the equality sign is truly represented.

Example of true equation say 2x = 10 for x = 5

2 * 5 = 10 correct

multiplying the two sides by 3 results to

6x = 30

plugging in x = 5

6 * 5 = 30

for false equation, say 2x = 10 for x = 6

2 * 6 = 10 incorrect

multiplying the two sides by 3 results to

6x = 30

plugging in x = 6

6 * 6 = 30 incorrect hence false equation remains false

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Using this equation  9 + 4x = 21 - 2x, the value of x is 2.

A word problem is a mathematics exercise used in science classes where the subject's significant background information is conveyed in sentences rather than mathematical notation.

A real word problem that can be solved using this equation 9 + 4x = 21 - 2x is

you have to subtract 9 from both sides. 21-9= 12

you have to add 2x to both sides. 4x+2x= 6x

6x divided by both sides =

x=2

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The length of the new cylinder is 8. 78m

The formula for determining the volume of a cylinder is expressed as;

V = πr²h

Where;

Now, substitute the values into the formula, we have;

Volume = 3. 14 × ( 0.28)² × 7

Multiply the values, we get;

Volume = 1. 72m³

For the new length, we have to substitute the value of the volume and the new radius

1. 72 = 3. 14 × (0. 25)² × l

Find the square

1. 72 = 0. 196l

Divide both sides by the coefficient of l

l = 8. 78 m

Hence, the value is 8. 78m

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Answer:

73 x 8 =678

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

We need to find the radio between earth weight and venus weight, which is:

120 ÷ 106 = 1.1320754717

This number means 1 pound of venus weight is equal to 1.1320754717 of earth weight.

if there's a 180 pound earth weight and we need to find the venus weight, the calculation might loooks like this:

180 ÷ 1.1320754717 = 159 pounds

Answer: g(x + 4) = (x + 4)² + 9(x + 4)

= x² + 8x + 16 + 9x + 36

= x² + 17x + 52

So, an expression for g(x + 4) in the form a2 + ax + b, where a and b are numbers, is 1x^2 + 17x + 52

Step-by-step explanation:

Answer:

28x + 12

Step-by-step explanation:

4(7x + 3) = 4 times 7x +4 times 3 = 28x +12

Answer: when you expand the expression you get 21x+12
simplified- 21x+12, there's no other way to simplify it

Step-by-step explanation:

Answer:

9 because 1, 2,6,are factors of 18 and since 8 is not a factor of 10 9 is a factor because9×2 =18

The plane flew 95.08 miles.

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given,

A plane veered off its course at an angle of 14°.

Plane ends up 23 miles due west of its planned destination.

By the figure,

Sin 14° = AB/AC

           = 23/AC

AC = 23/Sin 14°

AC = 23/0.2419

AC = 95.08 miles

Hence, 95.08 miles, the aero plane flew.

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Answer:

not sure

Step-by-step explanation:

lolshjshebshuzhsbbsjxhgdpsizhgxe

The result of the polynomial division in which case the numerator is quadratic while the denominators equal is linear is; ( x - 3 ) remainder 13.

As evident in the task content; the result of the polynomial division which is as given in the task content is required to be determined.

Since the given polynomial division is; ( x² + 1 ) / ( x + 4 ).

The division can be carried out by long division method as in the attached image.

Hence, the result of the polynomial division is; ( x - 3 ) remainder 13.

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The standard form of the expression is -5-81i.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

A complex number is a number system element that extends the real numbers with a specific element denoted by 'i' known as the imaginary unit.

The given expression is -5 - √81. The number in a standard form will be written as,

Number = -5 - √81

Number = -5 - 81i      i = √-1

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The end behavior is

Generally, End behavior refers to the long-term behavior or trend of a function as the input values (x-values) approach positive or negative infinity. It is often determined by the leading term of the function, which is the term with the highest degree of x. For example, the end behavior of a function like f(x) = x^2 is that it increases without bound as x approaches positive infinity, and similarly it decreases without bound as x approaches negative infinity.

[tex]\sqrt[3]{6x}[/tex] has an end behavior of as x approaches positive infinity, it approaches positive infinity and as x approaches negative infinity it approaches negative infinity.

[tex]$\sqrt[3]{x-5}-6$[/tex] has an end behavior of as x approaches positive infinity, it approaches negative infinity and as x approaches negative infinity it approaches negative infinity.

[tex]$-3 \sqrt[3]{x+3}+7$[/tex] has an end behavior of as x approaches positive infinity, it approaches positive infinity and as x approaches negative infinity it approaches positive infinity.

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Answer: b

Step-by-step explanation:

When two angles add up to 180 degrees, they are supplementary (a Straight Angle). As long as the sum is 180, they don't have to be close to each other.

Given, a graph in which two lines g and f intersect each other at a point "Q" on a plane "V".

Two rays that have a common endpoint and are referred to as the angle's sides and vertices, respectively, form an angle. Two rays can form angles in the plane where they are positioned.

Angles with a sum of 180 degrees are referred to be complementary angles. Complementary angles are those formed by straight lines.

The 90-degree angles between the two lines are known as supplementary angles.

Therefore, WQ and QW are two other names for line g. R, Q, and S intersect at R. Point Q on Plane V is where two lines meet. WQ, RQ, and SQ are the three segments that have endpoint q. Every angle that has the vertex M is JMK and KML. KML and KLM are the two nearby angles. JMK and KML are the pair of supplementary angles.

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Answer:

Step-by-step explanation:

The distance of the trenches is 13 feet.

Joseph wants to dig a trench in his back yard to bury a cable.  He mapped out his back yard so that it is a coordinate plane so that each unit represents 1 foot, He needs to dig from (-4,1) to (8,6).  He digs a straight line.

The length of the trenches can be calculated using distance formula as follows:

Therefore,

d = √(y₂ - y₁)² + (x₂ - x₁)²

using (-4, 1) and (8, 6)

x₁ = - 4

x₂ = 8

y₁ = 1

y₂ = 6

Hence,

distance of the trenches = √(6 - 1)² + (8 + 4)²

distance of the trenches = √5² + 12²

distance of the trenches = 25 + 144

distance of the trenches = √169

Therefore,

distance of the trenches = 13 feet

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Both numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4

Two or more expressions with an Equal sign is called as Equation.

The given equation is  1/12 + 2/3

The LCM of 12 and 3 is 12

1+8/12

9/12

Cross-cancellation can be used to make math easier when fractions are divided.

The numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4

Hence,  numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4

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The percent of games lost by the baseball team is 20%

From the question, we have the following parameters that can be used in our computation:

Games won = 24

Games lost = 6

The percent of games lost by the baseball team is then calculated as

Percentage lost = Games lost/(Games lost + Games won) * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage lost = 6/(6 + 24) * 100%

Evaluate

Percentage lost = 20%

Hence, the percentage lost is 20%

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2x³ + 3x² - 8x - 12 polynomial in  product of two factors is (2x+3)(x²-2²)

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is  2x³ + 3x² - 8x - 12.

Factor out the greatest common factor from each group.

x²(2x+3)-4(2x+3)

Factor the polynomial by factoring out the greatest common factor,  2x+3

(2x+3)(x²-4)

Rewrite 4 as 2²

(2x+3)(x²-2²)

(2x+3)(x+2)(x-2)

Hence,  2x³ + 3x² - 8x - 12 polynomial in  product of two factors is (2x+3)(x²-2²)

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The area of the yellow region to the nearest tenth is 48.4 cm².

The diagram is a square. Part of the square is cut to form quarter of a circle. Therefore, let's find the area of the yellow region.

Area of the yellow region = area of the square - area of the quarter circle

area of the square = l²

where

area of the square = 15²

area of the square = 225 cm²

area of the quarter circle = 1 / 4 πr²

area of the quarter circle = 1 / 4 × 3.14 × 15²

area of the quarter circle = 1 / 4 × 3.14 × 225

area of the quarter circle = 706.5 / 4

area of the quarter circle = 176.625

Therefore,

Area of the yellow region = 225 - 176.625

Area of the yellow region = 48.4 cm²

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After solving, the measure of angle BCD is 25 degree.

In the given question, we have to find the measure of angle BCD.

As we know that the angle of line is 180 degree.

From the graph we can see that angle yAD = 25 degree

So, the value of angle DAB = 180 - 25

The value of angle DAB = 155

As we know that in the quadrilateral the sum of opposite angle is equal to 180 degree.

So ∠DAB + ∠BCD = 180

155 + ∠BCD = 180

Subtract 155 on both side, we get

∠BCD = 25 degree

Hence, the measure of angle BCD is 25 degree.

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The measure of angle BCD is 45 degrees.

To solve for the measure of angle BCD, we need to use the Triangle Angle Sum Theorem which states that the measure of the angles of a triangle add up to 180 degrees.

Let us use the following figure to illustrate the calculation:

We have angle BCD with unknown measure, angle ABC with measure 45 degrees, and angle ACD with measure 90 degrees.

We can now use the Triangle Angle Sum Theorem to find the measure of angle BCD.

180 degrees = 45 degrees + 90 degrees + x

x = 180 degrees - 135 degrees

x = 45 degrees

Therefore, the measure of angle BCD is 45 degrees.

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The kWh a house uses in a year is 11050 kWh

From the question, we have the following parameters that can be used in our computation:

Average in 4 weeks = 850 kWh

There are 52 weeks in a year

So, the kWh used in a year is calculated as

kWh used = Average in 4 weeks * Number of weeks in a year/4

Substitute the known values in the above equation, so, we have the following representation

kWh used = 850 kWh * 52/4

Evaluate

kWh used = 11050 kWh

Hence. the kWh used is 11050 kWh

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a) 250

b)200

c)500

d)5%

e)3 times

The amount Anne has is $31.

The amount James has is $66.

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,

James amount = x

Anne amount = y

x + y = 97

x = y/2 - 2

Now,

y/2 - 2 + y = 97

y/2 + y = 97 + 2

y + 2y = 99 x 2

3y = 198

y = 66

Now,

x = y/2 - 2

x = 66/2 - 2

x = 33 - 2

x =31

Thus,

Anne has $31.

James has $66.

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We have 3 pairs of congruent sides to show that two triangles are congruent by SSS.

In geometry, two triangles are said to be congruent if they have the same size and shape. There are several ways to show that two triangles are congruent, and one of these is the Side-Side-Side (SSS) Congruence Theorem. This theorem states that if three pairs of sides in two triangles are congruent in length, then the triangles are congruent. In other words, if you have two triangles and you can find three pairs of sides such that the sides in each pair are equal in length, then the two triangles must be congruent. This is because the three pairs of congruent sides uniquely determine the shape and size of the triangles. Therefore, to show that two triangles are congruent using the SSS Congruence Theorem, you need to have three pairs of congruent sides.

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We have 3 pairs of congruent sides to show that two triangles are congruent by SSS.

(1) SSS (side-side-side) : If three sides of a triangle are congruent to three sides of another triangle then the triangles are congruent.

(2) SAS (side-angle-side) : If two sides and included angle of a triangle are congruent to another triangle then the triangles are congruent.

(3) ASA (angle-side-angle) : If two angles and included side of a triangle are congruent to another triangle then the triangles are congruent.

(4) RHS (right angle-hypotenuse-side) : If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

As we are given two triangles.

Side AM = Side OB

Side MN = Side BY

Side AN = Side OY

In geometry, two triangles are said to be congruent if they have the same size and shape. There are several ways to show that two triangles are congruent, and one of these is the Side-Side-Side (SSS) Congruence Theorem. This theorem states that if three pairs of sides in two triangles are congruent in length, then the triangles are congruent. In other words, if you have two triangles and you can find three pairs of sides such that the sides in each pair are equal in length, then the two triangles must be congruent. This is because the three pairs of congruent sides uniquely determine the shape and size of the triangles. Therefore, to show that two triangles are congruent using the SSS Congruence Theorem, you need to have three pairs of congruent sides.

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The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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Why do phospholipids make a phospholipid bilayer with the heads facing out towards water and the tails facing each other

Phospholipids are composed of a polar, hydrophilic head and a non-polar, hydrophobic tail. The polar head of a phospholipid is attracted to water, while the non-polar tail is repelled by water.

Repair the phospholipid membrane

When phospholipids are placed in an aqueous environment, they will naturally arrange themselves in a way that maximizes their stability. This is achieved by forming a phospholipid bilayer with the heads facing out towards the water and the tails facing each other.

This arrangement therefore allows the polar heads to interact with the water while keeping the non-polar tails sequestered away from the water, thus protecting the cell's interior and maintaining the stability of the cell membrane.

How many phospholipids did it take?

The number of phospholipids that it takes to repair a phospholipid membrane would depend on the size and nature of the damage to the membrane. In general, the repair process involves the addition of new phospholipids to the membrane, either by the insertion of pre-formed lipids or by the synthesis of new lipids by the cell. The exact number of lipids required would depend on the extent of the damage and the rate of lipid turnover in the membrane.

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The area of the region consisting of all points Charlyn can see during her walk is 49sq/km.

Algebra aids in the solution of mathematical problems and enables the derivation of unknown numbers, such as interest rates, ratios, and percentages. In order to recast the equations, we can express the associated unknown values using variables from algebra.

Given that, path visible = 1km

Each Side of the boundary = 5km long

This would be the same as having a 1 km border all the way around a 5km square, thus (5+2) * (5+2) = 49 sq/km

Hence, the area of the region consisting of all points Charlyn can see during her walk is 49 sq/km.

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The area of the region consisting of all points Charlyn can see during her walk is 49sq/km.

this is a question of algebra and solution is as follows: -

Given that, path visible = 1km

Each Side of the boundary = 5km long

This would be the same as having a 1 km border all the way around a 5km square, thus (5+2) * (5+2) = 49 sq/km

Hence, the area of the region consisting of all points Charlyn can see during her walk is 49 sq/km.

Algebra

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

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