Factor the polynomial, 3x^2+x-10

The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.

Given that,

James is keeping an eye on the fish population in the pond he created. He constructed a pond and added 900 fish to it. Every year, the fish population doubles.

We have to find the equation by using x represent the number of years and y represent the number of fish.

We know that,

We get

Number of fish at starting =900

Number of fish after 1 year =900×2=1800

Number of fish after 2 year =1800×2=3600=900×(2)²

Number of fish after 3 year =3600×2=7200=900×(2)³

So,

Here we can see that the number of fish are in Geometric progression (G.P) with a=900 and r=2

So,

Tₙ=arⁿ⁻¹

We get

y=900×(2)ˣ

Therefore, The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.

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Answer:

Step-by-step explanation:

-1<x<0

x<0

so x is negative.

Hence -x is positive.

and -1<x

or

x>-1

or

x+1>0

x+5=x+1+4>0+4

hence x+5 is positive.

x is negative .

∴x-2 is negative.

f(x)=(+)×(+)×(+)×(-)=-

B

Based on the Pythagorean theorem, the set of side of lengths that will form a right triangle are:

2, √5, 3

2, 2, √8

Based on the Pythagorean theorem, any set of side lengths that will form a right triangle would have the following relationship:

b² = a² + c², where b is the longest side or the hypotenuse of the right triangle and "b and c" are the lengths of the legs of the triangle.

For side lengths, 4, 8, and 12, we have:

12² = 4² + 8²

144 = 16 + 64

144 = 80 [not true, cannot form a right triangle]

For side lengths, 2, √5, 3, we have:

3² = (√5)² + 2²

9 = 5 + 4 [true, this set will form a right triangle]

For side lengths, 2, 2, √8, we have:

(√8)² = 2² + 2²

8 = 4 + 4

8 = 8 [true, this set will form a right triangle]

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The inequality which represents the range of temperature at which water boils is 100 ≤ b thus, option (C) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Water boils at a minimum temperature of 100 degrees Celsius.

Suppose b is the temperature at which water boils.

100 ≤ b

Hence "The inequality which represents the range of temperature at which water boils is 100 ≤ b".

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The measure of an interior angle (in degrees) of an [tex]n[/tex]-sided regular polygon is [tex]\frac{180(n-2)}{n}[/tex].

[tex]n=45 \implies \frac{180(n-2)}{n}=\boxed{172^{\circ}}[/tex]

The degree measure of one angle of a 45-sided regular polygon is 172°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, the polygon has 45 sides.

To find the measure of an interior angle of a regular polygon,

we make use of the formula for each angle = (n - 2) × 180 / n.

The formula calculated is only valid in cases of regular-sided polygons.

n =  45 substituting the value of n to the formula.

(n - 2) × 180 / n

= 180 ( 45-2) / 45

= 180 x 43 / 45

= 7740 / 45

= 172°

Therefore, the measure of one angle is 172°.

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The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively

Step-by-step explanation:

Answer:

29 hrs

Step-by-step explanation:

439 = 14t + 29

439-29 = 14t

410 = 14t

t = 410/14

t= 29.28

t = 29

Answer: 132 degrees

Step-by-step explanation:

Because the lines are parallel, and the line intersecting them is straight, the angle on top should be the same as the angle on the bottom.

So that makes x=132

Evan made a mistake to add. As the sign of 4 positive and the sign of [tex]2\frac{1}{2}[/tex]. The subtraction operation must be performed for this.

What is a number line?

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.

The given expression is

[tex]-2\frac{1}{2}[/tex] +4

It can be written as 4  [tex]-2\frac{1}{2}[/tex] .

Now perform the subtraction operation:

= 4 - 5/2

= (8-5)/2

=3/2

= [tex]1\frac{1}{2}[/tex]

The number line that represents the given operation is attached below.

Evan added 4 and  [tex]2\frac{1}{2}[/tex] which is incorrect way.

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Step-by-step explanation:

in a fraction as exponent the numerator defines the pure exponent of the base, and the denominator gives the degree of root of the base.

so, this is

[tex] \sqrt[5]{y^{3} } [/tex]

Answer:

[tex] \sqrt[5]{ {y}^{3} } [/tex]

Step-by-step explanation:

When converting an expression with a fractional exponent to its radical form, the base number goes inside the radical(which means it becomes the radicand) along with the numerator(which remains an exponent). Whereas the denominator of the exponent becomes the index, or what dictates whether the radical is a square root, cube root, etc.

EX:

[tex] {y}^{ \frac{a}{m} } = \sqrt[m]{ {y}^{a} } [/tex]

Answer:

3 3/4 cups of sugar per cup of salt

Step-by-step explanation:

To find the unit rate of salt to sugar in the recipe, we need to divide the number of cups of sugar by the number of cups of salt. In this case, the unit rate of salt to sugar is 1 1/4 cups of sugar divided by 1/3 of a cup of salt, which can be simplified to 3 3/4 cups of sugar per cup of salt.

Answer:

The unit rate of cups per teaspoon is 1 1/3

Step-by-step explanation:

-A recipe calls for 2 by 3 cup of sugar for every 1 by 2 teaspoon of vanilla.

Based on the above information, the calculation is as follows:

=(2/3)/(1/2)

=(2/3)/(1/2)

=(2/3)x(2/1)

=(2x2)/(3x1)

=(4/3)

= 1 1/3

The aggregate sum of perusing time for seven days as a blended number and an ill-advised part will be 1 ¹/₂ hour.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

An educator gives understudies free understanding 1/2 time for 1 hour, three times each week.

The aggregate sum of perusing time for seven days as a blended number and an ill-advised division is given as,

⇒ 1/2 x 3

Simplify the expression, then we have

⇒ 1/2 x 3

⇒ 3/2

⇒ 1 ¹/₂ hours

The aggregate sum of perusing time for seven days as a blended number and an ill-advised part will be 1 ¹/₂ hour.

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Answer:

Step-by-step explanation: To find the x let y=0

We substitute into the equation 3x+2y=15

3x+2 *0=15

3x=15

x=15/3=5

To find the y let x=0

we substitute into the equation x =0

3*0+2y=15

2y=15

y=15/2

The percentage equation states that the part equals the percent multiplied by the whole.

What is percent?

A percentage is a number that indicates how much is 100 and can also be expressed as a decimal or fraction.

What is Percentage Equation?

Percentage equations allow you to find parts or ratios of amounts (or wholes). Percentages are specified with a % sign after the number of hundredths.

The formula for percentage equation is given below

Percent=(Part/Whole)x100

Example: 45 is 60% of what number?

Modifying the above percentage equation, we get

Whole= (Part/Percent) x 100

⇒Whole= (45/60) x 100

⇒Whole= (3/4) x 100

⇒Whole= 3 x 25

⇒Whole= 75

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The equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is  y = 3x - 5.

The equation of a line can be represented in slope intercept form, point slope form, standard form and general form.

Linear equation in slope intercept form is as follows:

y = mx + b

where

Therefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x −2.

parallel lines have the same slope.

Therefore, the slope of the line is 3.

The y-intercept can be found as follows:

using (3, 4)

y = 3x + b

4 = 3(3) + b

b = 4 - 9

b = -5

Therefore, the equation in slope intercept form is y = 3x - 5.

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To solve this expression, we need to use the rules of order of operations, which dictate the order in which mathematical operations should be performed. The order of operations is typically abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Using the order of operations, we can solve the expression as follows:

64 - (-2)⁵ ÷ 2³ + (-1)³ · (0.5)²

= 64 - (-2)⁵ ÷ 8 + (-1)³ · 0.25

= 64 - (-32) ÷ 8 + (-1)³ · 0.25

= 64 + 32 + (-1)³ · 0.25

= 96 + (-1)³ · 0.25

= 96 + (-1) · 0.25

= 96 - 0.25

= 95.75

Therefore, the final result of the expression is 95.75

The required polynomial is x⁵ - 2x⁴ - 35x³ + 36x² + 180x.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, We have to construct a polynomial of degree 5, a positive lead

co-efficient and zeros or roots are -5, -2, 0, 3, 6.

If roots are -5, -2, 0, 3, 6 factors are (x + 5), (x + 2), (x + 0), (x - 3), (x - 6).

∴The required polynomial is  (x + 5)(x + 2)(x + 0)(x - 3)(x - 6).

= x(x + 5)(x + 2)(x - 3)(x - 6).

= (x² + 5x)(x² - 3x + 2x - 6)(x - 6).

=  (x² + 5x)(x² - x - 6)(x - 6).

=  (x² + 5x)(x³ - 6x² - x² + 6x -6x + 36).

=  (x² + 5x)(x³ - 7x²+ 36).

= x⁵ - 7x⁴ + 36x² + 5x⁴ - 35x³ + 180x.

= x⁵ - 2x⁴ - 35x³ + 36x² + 180x.

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Answer:

D

Step-by-step explanation:

5*1 = 5

5*2 = 10

5*3 = 15

5*4 = 20

5*5 = 25

Answer:

Answer:

Step-by-step explanation:

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Given numbers :

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Let's convert percent and fraction into like decimals.

[tex]\frac{4}{9}\ = 0.444[/tex]

We know that to convert percentage into decimals, we need to divide it by 100, we get

[tex]40.5 = \frac{40.5}{100} = 0.405[/tex]

[tex]\frac{11}{25} = 0.400[/tex]

Now , placing the above decimal numbers in order  from least to greatest

[tex]0.400, 0.405, 0.440, 0.444[/tex]

[tex]=0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Therefore the given function is a polynomial function consisting of the constant 0 and the leading term 1.

A polynomial function is a function in an equation that only employs non-negative integer powers or only positive integer exponents of a variable, such as in a quadratic equation, cubic equation, etc. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

Exponents are positive integers for the polynomial function given.

The positive integer 2x has an exponent of 1.

[tex]x^{5}[/tex], where is a positive integer with exponent 5, and.

Real numbers like 5 and 1 are among the coefficients in the function.

Consequently, a polynomial describes the function.

Having a degree of 5, it is a polynomial.

A polynomial is written in standard form by beginning with the term with the highest exponent and writing the remaining terms in descending order of terms with lower exponents.

Standard form for the polynomial is f(x)=2x+ [tex]x^{5}[/tex].

consisting of the constant 0 and the leading term 1.

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Answer:

ong

Step-by-step explanation:

The maximum number of individuals who can visit the amusement park is 4.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question

The number of persons who can visit the theme park will be determined by the inequality that can be used to compute x and the information provided in the question:

8 + 23(x) ≤ 100

8 + 23x ≤ 100

23x ≤ 100 - 8

23x ≤ 92

x ≤ 92/23

x ≤ 4

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Answer: x= 2

Step-by-step explanation:

X+3/2(-1/2x+5/3)+2=3x-1

= x - 3/4x + 15/6 +2 = 3x -1

= 1/4x + 15/6 + 2 = 3x -1

= 1/4x + 27/6 = 3x -1

= 1/4x + 33/6 = 3x

= 33/6 = 11/4 x

= x = 2

The computation of the depreciation expense using the following methods are as follows:

                                                      2022          2023

A) Straight-line Method              $2,472        $2,472

B) Units Of Activity Method       $3,048        $2,448

C) Declining Balance method   $5,200        $4,160

The depreciation expense is the periodic recognition of the cost for a long-term asset over its useful life.

The costs of long-term assets are spread over their estimated life through depreciation, depletion, or amortization.

The various depreciation methods include:

The cost of the delivery truck on January 1, 2022 = $26,000

Expected salvage value = $1,280

Depreciable amount = $24,720

Estimated useful life = 103,000 miles or 10 years

Depreciation Expenses:

Straight-line method = $2,472 annually ($24,720/10)

Units of activity method per mile = $0.24 ($24,720/103,000)

2022 = $3,048 (12,700 x $0.24)

2023 = $2,448 (10,200 x $0.24)

Declining-balance method rate = 20% (100/10 x 2)

2022 = $5,200 ($26,000 x 20%)

2-23 = $4,160 ($20,800 x 20%)

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The statement that is not consistent with the display of the graphs of the z-distribution and of the z-distribution is given as follows:

The critical value for the t-distribution with this degrees of freedom will be less than 0.68.

The graph shows two curves, given as follows:

The z-distribution curve is more centered around the mean, meaning that most it's sample means will be closer to the mean than for the t-distribution.

Along the tails, the t-distribution curve is higher, meaning that it has a higher percentage of sample means around the tails and a higher critical value.

The critical value of 0.68 is for values one standard deviation for the mean for the z-distribution, while for the t-distribution it is higher, hence it is the false statement.

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The length of the segment AE on the triangle is 45/7

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

DE parallel to BC,

Also, we have

AD/DB=3/4

The above parameters mean that

AD/AB = AE/AC

Also, we know that

AB = AD + DB

From the ratio values, we have

AB = 3 + 4

Evaluate the sum

AB = 7

Updating the initial ratio, we have

AE/15 = 3/7

Multiply both sides by 15

So, we have the following representation

AE = 15 * 3/7

Evaluate the products

AE = 45/7

Hence, the length of AE is 45/7

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Twenty-five people in a survey were asked to give their current checking account balances and the frequency = 4.

What is frequency and example?

Given that;

Class intervals              Class frequency

(Account Balance)          (No of people)

 $0 - $99                                ?

Entries in this ($0 - $99) range are $29 , $60 , $28 , $83 = 4

Therefore, class frequency (no of people) = 4

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The equivalent fraction for 12/16 will be A. 3/4, 24/32

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

It should be noted that equivalent fraction for 12/16 will be found by reduction to lowest term. This will be:

12/16 = 3/4

Also multiply the numerator and denominator by 8 will give 24/32. In conclusion, the correct option is A.

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If her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.

The full name of APR is the annual percentage rate. It is defined as the percentage rate applied on borrowing money in the form of interest but APR is applied annually.

It is given that, Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.

1 year = 12 month

30 year = 360 month

We have to find the total amount she will pay for the house,

Total amount = Monthly payment × 360 + intreast over 30 years

Total amount =1,350 × 360 + 186,175

Total amount =$ 672175

Thus, if her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.

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Answer:

x = 2 or –6

Step-by-step explanation:

x² + 4x –12 = 0

x² +6x –2x –12 = 0

x(x + 6) –2( x + 6) = 0

(x–2)(x+6)= 0

x–2= 0

x= 2.

x+6= 0

x= –6

x = 2 or –6