If f is differentiable at x = c, then f is continuous at x = c.

True
False

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.

The area of the frame if the frame is 1 inch thick will be 30 inch².The area of the frame is found as the product of the length and breadth of the frame.

The space filled by a flat form or the surface of an item is known as the area.

If the  frame is 1 inch thick then the total area is found as;

The area of the rectangular picture is;

[tex]\rm A = 5 \times 8 \\\\\rm A =40 \ inch^2 \\\\[/tex]

The total area of the frame is found as;

Area of frame = Total area -  area of the picture

Area of frame =70 -40

Area of frame = 30 inch²

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Answer:

-4 -5i

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The answer would be a im sure

Step-by-step explanation:

Answer:

The answer is 2. hope it helps!

Step-by-step explanation:

Answer:  The area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]

Correct option is 2.

Step-by-step explanation:  We are given to find the area of the shaded portion in the figure.

Since, the centre point of each arc is the corresponding central point of the line and the arcs intersect at the centre point of the circle,

so let us divide the figure into four equal parts, one of them is square ABCD as shown in the attached figure.

The area of the square ABCD will be

[tex]A_{ABCD}=\left(\dfrac{1}{2}\times 2\right)^2\\\\\\\Rightarrow A_{ABCD}=1~\textup{sq. units}.[/tex]

Now, area of the shaded portion inside the square ABCD will be

[tex]A_s=2\times \textup{area of the quarter circle with radius 1 unit}}-\textup{area of square ABCD}\\\\\Rightarrow A_s=2\times \left(\pi\times \left(\dfrac{1}{2}\right)^2\right)-A_{ABCD}\\\\\\\Rightarrow A_s=2\times\left(\dfrac{\pi}{4}\right)-1\\\\\\\Rightarrow A_s=\left(\dfrac{\pi}{2}-1\right)~\textup{sq. units}.[/tex]

Since all the four squares are identical in the attached figure, so the required area of the total shaded portion in the figure is

[tex]A=2\times\left(\dfrac{\pi}{2}\right)\\\\\\\Rightarrow A=(\pi-2)~\textup{sq. units}.[/tex]

Thus, the area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]

The correct option is 2.

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

Step-by-step explanation:

Answer:

7092.82

Step-by-step explanation:

i took the quiz

Answer:

30 + 0.15m

Step-by-step explanation:

base rate = 40(1 − 0.25) = 40(0.75) = 30

per mile = 0.15m

thus,

30 + 0.15m

The correct expression represents the situation is,

⇒ 30 + 0.15m

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

Given that;

Eric plans to rent a car for a day from Easy Car Rental.

Here,  He has a coupon for 25% off the daily base rate of $40.

And,  He will also have to pay an additional $0.15 for each mile he drives.

Let m represents the number of miles.

Hence, We can formulate;

⇒ 40 (1 - 0.25) + 0.15m

⇒ 40 × 0.75 + 0.15m

⇒ 30 + 0.15m

Thus, The correct expression represents the situation is,

⇒ 30 + 0.15m

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The given statement "An equiangular triangle can never be scalene." is true.

An equiangular triangle is a triangle that has three equal angles.

A scalene triangle is a triangle that has three unequal sides.

Therefore, a scalene triangle has three different angles.

Therefore, an equiangular triangle and scalene triangle are two completely different triangles.

Hence, an equiangular triangle can never be a scalene triangle.

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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.

The two consecutive even integers that satisfy the given condition are 6 and 8. When the smaller one (6) is added to three times the larger one (8), the sum is 30.

The student has asked for help in finding two consecutive even integers such that the smaller added to three times the larger gives a sum of 30. To solve this, let's designate the smaller even integer as x. Since the numbers are consecutive even integers, the next integer will be x + 2.

The equation based on the problem statement will look like this:

x + 3(x + 2) = 30

Expanding the equation gives:

x + 3x + 6 = 30

Combining like terms:

4x + 6 = 30

Subtracting 6 from both sides:

4x = 24

And dividing by 4:

x = 6

Now, the two consecutive even integers can be determined:

The smaller integer is 6, and the larger integer is 6 + 2, which equals 8. Therefore, the two integers are 6 and 8, and if we check:

6 + 3(8) = 6 + 24 = 30, which matches the required sum.

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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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:

13/35

Step-by-step explanation:

gradpoint

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.

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.

The true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex]. The correct option is b. [tex]x=2[/tex].

[tex]3 \log 2+\log8 =2\log(4x)[/tex].

We have to calculate the value of [tex]x.[/tex]

We know that,  

[tex]n \log m= \log(m)^n[/tex]

and

[tex]\log m + \log n = \log(mn)[/tex]

Solving the equation:

[tex]3 \log 2+\log8 =2\log(4x)[/tex][tex]\log(2)^3+\log8 =\log(4x)^2[/tex]

{using [tex]n \log m= \log (m)^n[/tex]}

[tex]\log8+\log 8= \log 16x^2[/tex]

[tex]\log (8 \times8)=\log16x^2[/tex] {using [tex]log m + log n = log(mn)[/tex]}

Since log is on both sides so it is eliminated from both sides,

[tex]8 \times8=16x^2\\64=16x^2\\[/tex]

[tex]x^{2} =\frac{64}{16}\\x^{2}=4\\x=2[/tex]

Hence the true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex].

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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:the answer is d

Step-by-step explanation:

5x - y ≥ 2