how are solutions, roots, and x-intercepts of a quadratic related?

Answer:

A) 3

Step-by-step explanation:

The notation f(x)=[x] represents the greatest integer function, with the integer being less than or equal to x.

Since we have to find the nearest integer smaller than the given number, we can say that greatest integer function always rounds down its input to the nearest integer.

We have to find the value of [3.6]. So we have to round down 3.6 to its nearest integer, which will be 3.

Therefore, the option A gives the correct answer.

Answer: Hello mate!

the function f(x) = [x] is equal to the closest smaller or equal integer to the number x.

for example:

[1] = 1

[1.3] = 1

[1.9998] = 1

then, the closest smaller or equal integer to the number 3.6 is the number 3.

this means that f(3.6) = [3.6] = 3, then the right option is the first one.

Answer:

7092.82

Step-by-step explanation:

i took the quiz

Answer:

Step-by-step explanation:

Definition of Square: a parallelogram whose area is equal to the product of its sides. The circle is a plane figure whose area is calculated by the formula r².

The length of the side of the square is .

Given:

The radius of the circle is = r cm.

Length of the side of square = a cm

Now,

Area of Square is = a²

Area of Circle  = r²

Since, given that radius of a circle is equivalent to the length of the square, such that:

a² =  r²

a² =   r²

a =

a =

Thus, the value of the length of the square is r√π.

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The total cost of purchase of Jack is $ 45.88

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The cost of two sweaters is = $ 17.99

The cost of pair of slacks is = $ 25.50

So ,

The cost of two sweaters and pair of slacks = $ 17.99 + $ 25.50

                                                                         = $ 43.49

Now the equation will be ,

The tax percentage on the cost of purchase = 5 1/2 %

                                                                          = 5.5 %

The cost of purchase including the tax percentage =
The cost of two sweaters and pair of slacks x tax percentage

The cost of purchase including the tax percentage = 43.49 x ( 5.5/100 )

                                                                                     = $ 2.39195

So the equation will be ,

The total cost of purchase =
The cost of two sweaters and pair of slacks + cost of purchase including the tax percentage

The total cost of purchase = $ 43.49 + $ 2.39195

                                            = $ 45.88195

                                            ≈ $ 45.88

Hence , the total cost of Jack's purchase is $ 45.88

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Answer: d) the point of concurrency of the perpendicular bisectors

Step-by-step explanation:

The product of -9(5-2x) is found by multiplying -9 by each term inside the parentheses resulting in -45 + 18x.

The product of -9(5-2x) is found by distributing the -9 to both terms inside the parentheses. Following the rules of multiplication, when a negative number multiplies a positive number, the result is negative, and when a negative number multiplies a negative number, the result is positive. Hence:

-9 x 5 = -45

and

-9 x -2x = 18x.

Combining these results, we get the final expression:

-45 + 18x

Keep in mind that when simplifying expressions or performing multiplication, we need to adhere to the rules for multiplication of numbers with different signs, as described earlier.

Final answer:

The product of -9(5-2x) is calculated by using the distributive property to multiply -9 by each term inside the parentheses, yielding 18x - 45.

Explanation:

The product of -9(5-2x) can be found by applying the distributive property of multiplication over subtraction. This property states that you multiply the term outside the parentheses by each term inside the parentheses. Here are the steps:

Multiply -9 by the first term inside the parentheses (5), which is -45.

Multiply -9 by the second term inside the parentheses (-2x), which gives us +18x (note that a negative multiplied by a negative gives a positive).

Combine these two products to get the final result, -45 + 18x, or 18x - 45.

This demonstrates the rules of multiplication where multiplying two numbers with opposite signs results in a negative product, and multiplying two numbers with the same sign results in a positive product.

Answer:

-4 -5i

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

None of the answers listed are correct.

3x + 11 = k

SUBTRACT 11 from both sides:

3x + 11 = k

      -11    -11

You are then left with:

3x = k-11

DIVIDE 3 by both sides:

3x/3 = k-11/3

You are then left with:

x= k-11/3

The value of x for the equation 3x + 11 = k is [tex]\frac{k-11}{3}[/tex].

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question.

We have a linear equation in one variable

[tex]3x + 11 = k[/tex]

For the above equation the value of x is given by

[tex]3x + 11 = k[/tex]

⇒[tex]3x = k -11[/tex]    ( subtracting 11 from both the sides)

⇒[tex]x = \frac{k-11}{3}[/tex]         ( dividing both the sides by 3)

Hence, the value of x for the equation 3x + 11 = k is [tex]\frac{k-11}{3}[/tex].

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Answer:

17.89

Step-by-step explanation:

The original floor could be rectangle in shape.

If we consider the length of floor to be 'L' and width of floor to be 'W',

then area of original floor = length x width = LW.

And if its dimensions are dilated by scale factor of 4 to make new floor, then new length and width would become four times of older values. So new length would be '4L' and new width would be '4W'

Now area of new floor = length x width = 4L x 4W = 16LW.

It is clear that the area of new floor is 16 times of the area of original floor.

So, option C i.e. 16 is the final answer.

To find the range you would have to but the data(numbers) in order from least to greatest, then subtract the smallest number from the largest. The disadvantage of using range is that it does not measure the spread of the majority of values in a data set it only measures the spread between highest and lowest values. As a result, other measures are required in order to give a better picture of the data spread.

Answer:

y>x+1;y<=10;x>=0

Step-by-step explanation:

5 is correct I did this quiz

5 is  the best estimation of mean for the given data set.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

In the given data, the number of sites ae given in y axis and number of shield daters on x axis.

From the given dart let us construct a table

Number of sites     Number of shield darters

   2                                        3

   3                                         1

   4                                        4

   6                                        2

   7                                         3

  8                                         1

  9                                          1

By using the mean formula we get the mean as 5

Hence, 5 is  the best estimation of mean for the given data set.

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The triangle ABC and triangle DEF are similar so the value of the length of BC is 20 cm and this can be determined by using the properties of a similar triangle.

Given :

The following steps can be used to determine the length of BC:

Step 1 - According to the given data, triangle ABC is similar to triangle DEF.

Step 2 - So, according to step 1:

[tex]\rm \dfrac{AC}{DF} = \dfrac{BC}{EF}[/tex]

Step 3 - Substitute the values of length AC, DF, and EF in the above equation.

[tex]\rm \dfrac{12}{9} = \dfrac{BC}{15}[/tex]

Step 4 - Multiply 15 on both sides in the above expression.

[tex]\rm \dfrac{12}{9}\times 15 = BC[/tex]

Step 5 - Simplify the above expression in order to get the value of the length BC.

BC = 20 cm

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Answer: 39.8 and 50.2

Step-by-step explanation:

Here, the triangles has the legs 2.5 ft and 3 ft.

Since, by the Pythagoras theorem,

Hypotenuses of the triangle,

[tex]=\sqrt{2.5^2+3^2}=\sqrt{6.25+9}=\sqrt{15.25}\text{ feet}[/tex]

Now, let [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the angles opposite to the sides 2.5 and 3 respectively,

Hence, by the law of sine,

[tex]\frac{sin\theta_1}{2.5}=\frac{sin\theta_2}{3}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex]

When,

[tex]\frac{sin\theta_1}{2.5}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex]

[tex]\implies sin\theta_1=\frac{2.5}{\sqrt{15.25}}=0.64018439966 [/tex]

[tex]\implies \theta_1=39.8055710923 \approx 39.8^{\circ}[/tex]

Similarly,

[tex]\frac{sin\theta_2}{3}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex]

[tex]\implies sin\theta_2=\frac{3}{\sqrt{15.25}}=0.76822127959  [/tex]

[tex]\implies \theta_2=50.1944289077 \approx 50.2^{\circ}[/tex]

Hence, First option is correct.

Answer:

B

Step-by-step explanation:

There are 5 prime numbers less than 100 that have a units digit of 1.

To determine how many prime numbers less than 100 have a units digit of 1, we need to follow these steps:

The prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

The primes with a units digit of 1 are: 11, 31, 41, 61, 71.