A rectangle has length x and width x - 3. The area of

the rectangle is 10 square meters.

Complete the work to find the dimensions of the

rectangle

Х

x(x - 3) = 10

x? - 3x = 10

x2 - 3x - 10 = 10 - 10

10 m2

X-3

(x + 2)(x - 5) = 0

What are the width and length of the rectangle?

O The width is 1 meter and the length is 10 meters.

O The width is 10 meters and the length is 1 meter.

The width is 2 meters and the length is 5 meters.

The width is 5 meters and the length is 2 meters.

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and one.

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and 1.

The image is contracted if the scale factor is less than 1 (0< k <1).

The image is enlarged if the scale factor is more than 1 (k > 1).

The image remains the same if the scale factor is 1 (k = 1).

Hence, the scale factor k should be between 0 and 1.

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expression h-9 is represented as statement 'h decreased by 9'.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".

Given expression

h-9

Here h is a variable, 9 is constant and - is the symbol of subtraction.

the phrase "decreased by" tells us to use subtraction.

Statement for the above expression

h decreased by 9.

Hence, the statement 'h decreased by 9' represents expression h - 9.

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The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.

a₁ = 3

a₂ = 4.5

a₃ = 4.5 + (4.5 × 50%) = 6.75

.............

Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5

n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.

Area of mold after n days = 3 × (1.5)ⁿ⁻¹

Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.

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As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

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The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

To determine the angle the ladder needs to make with the house, we can use the tangent function.

First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.

Opposite side = 18 feet

Adjacent side = 25 feet

We can then use the tangent function to find the angle:

tan(angle) = opposite / adjacent

Solving for the angle, we get:

angle = arctan(18/25) = approximately 54.7 degrees

Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

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Answer:

-3 (x - 4) (x - 1)

Step-by-step explanation:

The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.

Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.

Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.

In this case, probability lies between zero and one.

Odds of a coin coming up either heads or tails every time = 1:7

The sum of ratios = 8 (1 + 7)

Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)

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The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

5⁻³

This can be written as 1/5³ which is equal to 1/125

-5⁻³

This can be written as -1/5³ which is equal to -1/125

(-5⁻³)⁻¹

We have an exponential property

[tex](x^{a} )^{b} =x^{ab}[/tex]

So (-5⁻³)⁻¹=(-5)³=-125

(-5⁻³)⁻¹  equivalent expression is -125

(-5⁻³)⁰

=(-5)⁰=1

Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

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Answer:

Step-by-step explanation:

x² = 17² - 8²

x² = 289 - 64

x² = 225

x = √225

x = 15in

8 + 15 + 8 + 15 =

46in

The bake sale sign has a 6 ft2 space.

An object's area is how much space it takes up in two dimensions.

It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space.

A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

But a shape's area is a two-dimensional measurement. In order to measure something in a square, it is done so using measurements like square inches (in2), square feet (ft 2), square yards (yd2), etc.

The majority of forms and things have corners and edges. 

According to our question-

The opposite sides of a rectangle's quadrilateral (it has four sides and four angles) are equal and parallel.

Area of a rectangle equals length times width.

The area of the bake sale sign = length * breadth

Hence, The bake sale sign has a 6 ft2 space.

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The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95.

Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.

Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.

The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.

In this case:

μ = 505 mL (population mean)

σ = 10 mL (population standard deviation)

n = 16 (sample size)

The standard error (SE) of the sample mean is:

SE = σ/√n = 10/√16 = 10/4 = 2.5 mL

Now, we need to find the z-scores for 500 mL and 510 mL:

z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2

z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2

Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(z < -2) ≈ 0.0228

P(z < 2) ≈ 0.9772

Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:

P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544

So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95

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3x-y=-9

Step-by-step explanation:

Answer: 3x - y = - 9

Step-by-step explanation:

Re-write the equation in the following form:

3x + 9 = y

Take the y to LHS:

3x + 9 - y = 0

Now, take the 9 to the RHS:

3x - y = -9. This is your answer.

Answer:

(1/3) (44.5)π cm3.

Step-by-step explanation:

The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:

Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π

Volume of scoop = (1/6) π d3 = (1/6) (3)π

Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.

The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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We need to assume the sample was randomly selected because we are making inferences about means. Means refers to the average of a sample of data points, which can be used to estimate the value of an unknown population parameter.

If the sample was not randomly selected, then our estimates of the population parameter could be biased or inaccurate. This is because the sample may not be representative of the population as a whole, which could lead to incorrect estimates of the population parameter.

In order to make valid inferences about a population, it is essential to use random sampling. This is because random sampling ensures that the sample is representative of the population as a whole, meaning that the estimates of the population parameter that you obtain from the sample will be unbiased and accurate. If the sample is not randomly selected, then there is a risk that the sample is not representative of the population, which could lead to incorrect estimates of the population parameter.

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Answer:

5.4

Step-by-step explanation:

"The 'Angle Bisector' Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle."

thus,

DB/AB = DC/AC

2.8/AB = 3/5.8

multiply both sides by AB to make it a numerator

2.8 = 3*AB/5.8

multiply both sides by 5.8/3 to isolate AB

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

In a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

According to the "Angle Bisector Theorem," a triangle's opposing side will be divided into two segments that are proportional to the other two sides.

thus,

DC/AC = DB/AB.

2.8/AB = 3/5.8

By multiplying both sides by AB, the numerator is created.

2.8 = 3*AB/5.8

To distinguish AB, multiply both sides by 5.8/3.

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

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When we subtract 3xy from 5 we will get 3xy - 5.Both are different 3xy is a polynomial in xy and 5 is a constant we can not simplify further.

First, let's try to learn subtraction in the case of polynomials.

3xy is a polynomial.

5 is a constant.

Polynomials can be subtracted using a method that involves changing the signs to the opposite sign. The process resembles adding polynomials. Depending on the specific equation, we transform the sign while subtracting polynomials to either positive or negative. Learn more about subtracting polynomials, their techniques, procedures, and examples by reading on.

For instance, subtract 5x + 8y - 20z from 4x - 10y + 15z.

The polynomials should first be arranged in standard form. In this illustration, it has already been set up.

Place them horizontally in step two.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: By using parenthesis, modify the second polynomial's sign.

4x-10y-15z, and 5x+8y 20z

Step 4: Group terms that are similar together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Resolve the problem

-x - 18y + 35z

As a result, we get -x - 18y + 35z when we subtract 4x - 10y + 15z from 5x + 8y - 20z.

In the same way, if we subtract 3xy from 5 we will get 3xy - 5.

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Therefore, the fraction 5/4 in this equation represents the growth factor of the height of the item over time.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The total number of equally sized components chosen is shown in the numerator. The denominator, however, shows the total number of equal pieces.

The fraction 5/4 in this equation represents the growth factor of the height of the item over time. The value of 3 in front of the fraction is the initial height and the exponent x represents the number of days that have passed, so the height of the item increases by a factor of 5/4 for every additional day. The height equation represents exponential growth.

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Consequently, the answer to the above fraction problem comes out to be 1/2 .

An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.

Here,

Given here is: (4√(2) - √(2)) × √(2) /  (2) (2) × √(18) (18)

The radical is then simplified in order to determine its value.

=> 3√(2) × √(2) / 2√(2) × 3√(2)

=> 3(2) / 6(2)

=> 3/6

=> 1/2 or 0.5

so,

after simplification, the answer is 1/2.

Consequently, the answer to the above fractional problem comes out to be 1/2 .

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Answer:

Holy has $85 dollars remaining.

Step-by-step explanation:

(There is no model given in the question, so I'll tell you what the model should be equal to)

If she has $125 to spend, and she spends $35 of that money on gas, she will have $85 left.

$125 - $35 = $85

Answer:

Can you please show the picture

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 6.5 when x = 1.3

6.5 = 1.3k ( divide both sides by 1.3 )

5 = k

y = 5x ← equation of variation

Answer:

$302

Step-by-step explanation:

p(x) 3x^4 = x^4-3x^2+5

We put 3 in for x and solve

3(3)^4 = 3^4 -3(3)^2 + 5

3(81) = 81 -3(9) + 5

243 = 81 - 27 + 5

243 = 59

Then we add 243 with 59 and get

$243 + $59 = $302

So, they spend together $302

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In 5 years the population will be fewer than 13000.

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified percentage.

20000( 1 - 9% )^5

≈ 12481

12481 < 13000

ie 5 years

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Answer:

6

Step-by-step explanation:

The growth factor is the number that is raised to an exponent.

Answer: 6

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

The two triangles in the shown figure are similar, therefore conclusion can be made that :

Ratio of its it's corresponding sides is equal.

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 36 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 34[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 17[/tex]

Therefore, The value of x is " 17 "

Now, the measure of side BC is :

[tex]\qquad \sf  \dashrightarrow \: 2x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 (17) - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 34 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 30 \: \: units[/tex]

So, its perimeter will be :

[tex]\qquad \sf  \dashrightarrow \: p = AB + AB + BC [/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 24 + 26 + 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 80 \: \: units[/tex]

Answer:

------------------------------------

According to Triangle Proportionality Theorem we have the following equal proportions:

The missing side is:

The perimeter is:

Answer:

9 ft

Step-by-step explanation:

assuming the 3 was a mistake T'T volume is l x w x h so if the base is l x w then 12 x 14 (168) is the base then divide the volume from the base (1512 / 168) the answer is 9 ft

We have P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.

P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)

East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.

P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)

Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.

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The volume of Hannah's suitcase in cubic inches is: C: 7938.

The volume can be determine using this formula

Volume = Length × Width × Depth

Where:

Length = 27 inches

Width = 21 inches

Depth = 14 inches

Let plug in the formula

Volume = 27 inches × 21 inches × 14 inches

Volume = 7,938

Therefore we can conclude that the volume is 7,938.

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