algebra 1 Solve number 10 !!!

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

10.2 + 5.8 > 4.5

16 > 4.5

Now we add 5.8 and 4.5

5.8 + 4.5 > 10.2

10.3 > 10.2

Now we add 10.2 and 4.5

10.2 + 4.5 > 5.8

14.7 > 5.8

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.

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Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Assumed: expressions

Finding the expression with a value that is closest to e

Solution:

e is worth 2.718, which equals (1 + 1/19).

(1 + 1/19)^19

=> (20/19)^19 = 2.65

=> (1+ 1/22)^22

= >(23/22)^22 = 2.659

=> (1 + 1/20)^20

= >(21/20)^20 = 2.653

=>(1 + 1/21)^21

= > (22/21)^21 = 2.656

As a result, the value of e is closest to the value of 2.659.

Option B is hence the appropriate choice.

Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

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The inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is denoted by f-1 or F-1 if the function is represented by  [tex]f^{-1}(x)[/tex].

The given function is:

f(x) = 7x -2

Write the function in the form of a function:

y = 7x - 2

Interchange the variables in the equations:

x = 7y - 2

Isolate the value of y:

y = x/7 + 2/7

Replace y with [tex]f^{-1}(x)[/tex]:

[tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex]

Hence, the inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].

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Answer: (5x^2-7)(x-4)

Step-by-step explanation:

5x^2(x-4)-7(x-4)

= (5x^2-7)(x-4)

Answer:

20 feet

Step-by-step explanation:

Using the Pythagorean theorem, the distance is [tex]\sqrt{12^2+16^2}=20[/tex] feet.

Answer:1096.6332

Step-by-step explanation:

Answer: Use

1096.6332

Step-by-step explanation:

Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The value for Simple Interest is given as = $180

The value for rate is given as = 4.5%

The value for time is given as = 3 years

To find the value for Principal amount, follow the formula for Simple Interest -

SI = P R T/100

Where P is the principal amount, R is the rate and T is the time.

Substitute the values in the equation -

180 = (P × 4.5 × 3)/100

180 = 13.5P / 100

P = (180 × 100) / 13.5

P = 18000 / 13.5

P = 1333.33

Therefore, the value for principal amount is $1333.33.

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Therefore , the solution to the given problem of expression comes out to be 80.

Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as subtraction, multiplication , addition, or division etc.) You can contrast phrases and expressions.

Here,

The formula for the number of points Han's team scores in a single round if each player has a perfect score is 20 4.

Each player is limited to a maximum of 20 points.

Han's team has four members.

Thus, assuming each participant receives a perfect score, the expression that will indicate the total points that Han's team receives in one round is:

= 20 × 4

= 80

Therefore , the solution to the given problem of expression comes out to be 80.

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Answer:

225 minutes

Step-by-step explanation:

[tex]\displaystyle \frac{40\text{ gallons}}{\text{min}}=\frac{9000\text{ gallons}}{\text{x min}}\\\\x=\frac{9000\text{ gallons}}{40 \text{gallons}}=225\text{ min}[/tex]

By square root 5 this we get the value √5 = 2.2360…Or √5 ≈ 2.24 with correct two decimal number fraction .

1. First, the number 5 can be expressed as 5.00000000, or 5 = 5.00 00 00 00.

2.Take the number whose square is less than five. The perfect square of the number 2 is 4, which comes after the number 5.

3..Enter 2 in both the divisor and quotient places so that it may be multiplied by 2 to get the answer 4. Add 4 to 5 to obtain the answer, which is 1.

4.Write two zeros after one and add them to the quotient. Add the decimal point after the first zero.

5.Now multiply by 2 to make 4 in the divisor. Pick a number that will go next to 4, ensuring that the result of multiplying the combination with that number will be less than or equal to 100. In order to make 42 times 2 equal 84, which is less than 100, we shall use 2 in this instance. To get the remainder, take 100 out of it immediately. The remainder is therefore 16.

6.Repetition of Step 5 up to 4 places of decimals with the addition of two more zeros.

7.Ultimately, you arrive at the quotient value, which is 2.2360, or around 1.236.

In light of this, the value of root 5 is, √5 = 2.2360… Or √5 ≈ 2.24

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choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.

Measurement of the likelihood that an event will occur or a claim is true is done via probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating how likely it is that the event will occur. A probability is a numerical representation of how likely it is that a certain occurrence will take place. Probabilities can also be expressed as ranges of 0% to 100% or 0 to 1. the proportion of occurrences in a whole set of equally likely options that lead to a particular event relative to the entire number of outcomes.

given

All of the blackbirds were numbered and tagged from 00 to 99. With a random number generator,

choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.

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the correct question is :- In search of a mosquito repellent that is safer than the ones that are currently on the market, scientists have developed a new compound that is rated as less toxic than the current compound, thus making a repellent that contains this new compound safer for human use. Scientists also believe that a repellent containing the new compound will be more effective than the ones that contain the current compound. To test the effectiveness of the new compound versus that of the current compound, scientists have randomly selected 100 people

As the sides of the triangle 10 cm, 24 cm and 26 cm are triplets, the triangle will be a right angle triangle with side having length 26 cm as hypotenuse.

What is meant by triangle?

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Statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday

A number system is defined as a system of writing to express numbers.

In the given number line each unit is 10⁰ F

On Monday at 11:00 p.m. the temperature is 40⁰ F

Tuesday at 11:00 p.m. the temperature is -10⁰ F

The difference between two temperatures is 40⁰ F-( -10⁰)

40⁰ F+10⁰F

50⁰ F

The temperature on Monday is 50⁰ F lesser than Tuesday

Hence, statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday

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The gear ratio for the bike based on the information is 3:1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

From the information, the gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket,

The gear ratio for the bike will be:

= 36 / 12

= 3 / 1

= 3:1

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The lower bound of c-d is 42.70 and the upper bound of c-d is 42.69.

In the given question, a number, c, rounded to 1 d.P. is 47.3.

A number, d, rounded to 1 d.P. is 4.6.

We have to find the lower and upper bound of c-d.

The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits.

Error intervals are a useful tool for expressing the upper and lower bounds.

This is the lower bound for c; the smallest integer that will round to 47.3 is 47.25.

47.33999... is the highest number of c that may be rounded down to 47.3. Therefore, we define 47.34 as the upper bound.

This is the lower bound for d; the smallest integer that will round to 4.6 is 4.55.

4.64999... is the highest number of c that may be rounded down to 4.6. Therefore, we define 4.65 as the upper bound.

So, the lower bound of c-d = 47.25-4.55 = 42.70

So, the upper bound of c-d = 47.34-4.65 = 42.69

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A factor of a polynomial function is a polynomial that divides the function evenly when using polynomial division.

To check if x - 8 is a factor of the function f(x) =[tex]2x^3 - 17x^2 + 64[/tex]  , we can use polynomial division.

When dividing f(x) by x - 8, the remainder should be zero.

x - 8 is a factor of the function when the remainder is zero.

In this case, the quotient is [tex]2x^2 + x + 8[/tex] , and the remainder is zero, so x - 8 is a factor of the function f(x) = [tex]2x^3 - 17x^2 + 64.[/tex].

So we can say [tex]f(x) = (x-8)(2x^2 + x + 8)[/tex]

Alternatively, we can also use synthetic division to check if x - 8 is a factor of the function.

Synthetic division is a shorthand method of dividing a polynomial by a linear factor such as x - 8.

If the remainder is zero, then x - 8 is a factor of the function.

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Polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.

What is a complex number?

A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Polynomial identities are equations that are always true for any values of the variables, regardless of whether the variables represent real numbers or complex numbers. Complex numbers can be represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit.

For example, the identity[tex](x + y)^2 = x^2 + 2xy + y^2[/tex] is true for any real numbers x and y, and it also applies to complex numbers a + bi and c + di. The identity becomes [tex](a + bi + c + di)^2 = (a + c)^2 + 2(a + c)(bi + di) + (bi + di)^2[/tex]

Another example is the identity [tex](a+bi)^2 = a^2 + 2abi - b^2[/tex] which is always true for any complex number a+bi. This identity applies to any complex number and can be used to simplify polynomials involving complex numbers.

Hence, polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.

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The correct options for the line are-

Coordinate are: (−2, 0) and (2, −4)

Slope m = y2 - y1 / x2 - x1

m = (-4 + 0)/(2 + 2)

m = -4/4 = -1

Slope is -1 , option A incorrect.

For the y-intercept

Use point (-2, 0) and slope m = -1

0 = -1(-2) + b

b = -2

As, y-intercept is -2.  

Option B correct.

Find equation of the line.

y = mx+ b

y = -x + (-2)

y = -x - 2

Thus, equation of the line is y = −x − 2.

Option C is also correct.

Find the x-intercept.

if y = 0

0 = -x - 2

x = -2

Thus, line intersects the x-axis at (−2, 0).

The option D is also correct.

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The complete question is-

Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

A. The slope of the line is 1.

B. The line intersects the y-axis at (0, −2).

C. The equation of the line is y = −x − 2.

D. The line intersects the x-axis at (−2, 0).

6 with an exponent of 2 is 36. 6 with an exponent of 2 means 6 multiplied by 6.

When a number is raised to a certain power, it means that the number is multiplied by itself that many times.

Exponents are a way of shorthand for repeated multiplication. When a number has an exponent of 2, it means that the number is multiplied by itself once. When a number has an exponent of 3, it means the number is multiplied by itself twice.

In this case 6 with exponent of 2, means 6 multiplied by itself twice, which is equal to 36.

It's important to note that the exponent is also known as the power, so 6^2 is also read as 6 to the power of 2.

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The boxes of oranges that Tim need to sell in order to sell 60 boxes will be 13 oranges.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this situation, Tiana sells 47 boxes of orders for a fundraiser. Therefore, the boxes of oranges that Tim need to sell in order to sell 60 boxes will be:

= 60 - 47

= 13

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The probability of having a flip flop is 4/9.

In the question, we can see from the data that we have that Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6.

Recall that probability deals with the possibility that an event may occur or not occur under a given circumstance. We know that;

Total number of the shoes = 4 + 6 + 8 = 18

Probability of a flip flop = 8/18 = 4/9

This is the possibility that what would be picked is a flip flop.

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As the triangle cannot be equilateral since the sides are not equal. So the obtuse triangle has side lengths 5, 7 and 11.

Assume that a triangle has sides that measure 5, 7, and 11.

Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle.

A triangle must be sharp in order to:

Let a = 5, b = 7 and c = 11

a^2 + b^2 =  (5)^2 + (7)^2 = 25 + 49 = 74

c^2 = (11)^2 = 121

(1) If the triangle is

a^2 + b^2 > c^2

Therefore, the triangle is not acute.

(2) Eqviangular means that each internal angle must be 60 degrees in length.

As a result, the triangle is not eqviangular.

(3) The triangle cannot be equilateral since the sides are not equal.

(4) We note that a^2 + b^2 = c^2.

The triangle is hence obtuse.

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Answer:

The correct answer is D. 225pi cm^3.

To find the volume of a cylinder, you use the formula:

V = πr^2h

Where V is the volume, π is pi, r is the radius of the base, and h is the height of the cylinder.

In this case, the height is 9cm, and the width is 10cm. To find the radius, we divide the width by 2:

r = 10cm / 2 = 5cm

Now we can plug in the values into the formula:

V = πr^2h

V = π(5cm)^2(9cm)

V = π(25cm^2)(9cm)

V = 225π cm^3

So the volume of the cylinder is 225π cm^3

Step-by-step explanation:

Answer: D)  225pi cm^3.

Step-by-step explanation:

A quadratic regression equation for the stream of water is,

⇒ y = -0.139x² + 1.667x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, The vertex = (6, 5)

Axis of symmetry is line, x = 6

And, A third point in the parabola is, (12, 0)

Hence, The quadratic regression equation for the stream of water is,

⇒ y = - a(x - 6)² + 5

      = -a(x² - 12x + 36) + 5

      = -ax² + 12ax - 36a + 5

Since the parabola passes through point (0, 0),

i.e. -36a + 5 = 0

⇒ a = 5/36

⇒ a = 0.139

Therefore, The equation is,

⇒ y = -0.139x² + 12(0.139)x

⇒ y = -0.139x² + 1.667x

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Answer:

Its A

Step-by-step explanation:

∠6 and ∠7 are the angles which are supplementary to ∠1.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

In the given figure lines l and m are parallel lines.

A transversal passed through parallel lines.

∠1+∠2=180 degrees

∠1+∠3=180 degrees.

∠2 is corresponding angle of ∠6.

∠1+∠6=180 degrees.

∠3 is corresponding angle of ∠7.

∠1+∠7=180 degrees.

Hence, ∠6 and ∠7 are the angles which are supplementary to ∠1.

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Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.

What do you mean by relation of a function?

A relation that states that there should be only one output for each input is known as a function. Alternatively, we could say that a special sort of relation (a set of ordered pairs) that adheres to the rule that every X-value should be associated with only one y-value is known as a function.

To ascertain whether a graph accurately depicts a function, use the vertical line test. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

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The equation that can be used to find the car's distance, d, at any time is  d = 30 × t.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that;

First, we determine the speed of the car.

Speed = Distance ÷ time

Speed = 180 / 6

Speed = 30 m/s

Now, to get the distance traveled at any time, plug the value of the speed of the car into the speed formula and solve for distance d.

Speed = Distance ÷ time

Speed = d / t

d = Speed × t

d = 30 × t

Therefore, the equation is d = 30 × t.

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Two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

The sine graph or sinusoidal graph is an up-down graph and repeats every 360 degrees i.e. at 2π.

The general form of a cosine function is:

y = a cosb (θ±c) ± d

Here, amplitude, a  is = 1

For b, period is = π

2π/b = π

b = 2

c = 0

vertical shift = D = -3

Putting the value into formula

y = 1 cos2 (θ + 0) - 3

y = 1 ×−0.416(θ + 0) - 3

y = −0.416θ−3  

y = −0.416x −3  (cosine function)

y = 1 sin2 (θ + 0) - 3

y = 1 ×0.909(θ + 0) - 3

y = 0.909θ−3

y = 0.909x−3 (sine function)

Thus, two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

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