**Answer:**

4

**Step-by-step explanation:**

Because the height would be half of the base.

Hope this helps ^-^

Is reflection same as rotation 180 degrees?

Similar to the plane **reflection**, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.

A reflection is referred to as a flip in geometry.

A reflection is the shape's mirror image.

A line, called the line of reflection, will allow an image to reflect through it.

Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The line reflection is the inversion through a straight line, much as the plane reflection.

Actually, it undergoes the same change as a 180-degree **rotation**.

For this reflection, the rule would be written as RX-axis (x,y)→(x,y).

Rule of Notation: This notation rule tells you that image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1.

It has the form by-axis A→B = axis (x,y)→(x,y).

Therefore, similar to the plane reflection, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.

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What is the factor of 3xÂ² 6x?

The **factors form** of the given equation 3x²−6x is 3x(x−2)

Given that:

3x²−6x

To find : The factor form of 3x²−6x

The splitting or decomposition of an entity (such as a number, a matrix, or a** polynomial)** into the product of another entity, or factors, whose multiplication results in the original number, **matrix**, etc., is known as **factorization** or factoring in mathematics. You will mostly learn this idea in your lower secondary studies, which run from grades 6 to 8.

=3×x×x−2×3×x, **factor** each monomial

=3x(x−2), factor out common factor 3x

The factors form of 3x²−6x is 3x(x−2)

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Solve the system

(4x + 7y= 41

(x-7y=-16

**Answer:**

{ X = 5} {Y = 3} pls mark brainliest

**Step-by-step explanation:**

Add the two equations: 4x + 7y + (x-7y) = 41 + (-16)

Remove parentheses: 4x + 7y + x-7y = 41 + -16

Cancel one variable:4x + x + = 41 + -16

Combine like terms: 5x = 41 - 16

Calculate the sum or difference: 5x = 25

Divide both sides of the equation by the coefficient of variable: x = 25/5

Cross out the common factor: X = 5

Substitute into one of the equations: 5 - 7y = -16

Rearrange unknown terms to the left side of the equation: 5 - 7y = -16 - 5

Calculate the sum or difference: -7y = -21

Divide both sides of the equation by the coefficient of variable: -21/-7

Determine the sign for multiplication or division: y = 21/7

Cross out the common factor: y = 3

The solution of the system is: { X = 5} {Y = 3}

Use the summation notation to rewrite the following expression. 1 2 3 n + + + + 2! 3! 4! (n + 1)! Σ k = 1

The** rewritten **expression using the **summation notation** is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a **summation symbol (**∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the **starting value **of the index, and a **colon** (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.

To rewrite the given expression using the summation notation, we can use the following steps:

Identify the series of terms: 1 + 2 + 3 + ... + n.

Write the series of terms below the summation symbol: ∑ k = 1

Replace the **variable** in each term with the index: 1! + 2! + 3! + ... + (n+1)!

The rewritten **expression** using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

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At which root does the graph of f x x 5 3 x 2 2 touch the x axis?

The **root **of the graph of **function **f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

Given that,

The function is f(x)= (x-5)³(x+2)²

We have to find at which root does the **graph **function touch the x-**axis**.

We know that,

What is a function?Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to **arithmetic**, a function is represented as a rule that produces a different result for each input x.

Take the function

f(x) = (x-5)³(x+2)²

f(x) = 0 if a **curve **touches the x-axis.

⇒ (x - 5)³(x + 2)² = 0.

But if ab = 0

So, a=0 and b=0

⇒ (x - 5)³ = 0 and (x + 2)² = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x=5 and x=-2.

Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

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plssss answer thiss!!!!

**Answer:**

A = 3

B = 6

C = 4

D = 5

left rectangle = 4 x 6 = 24

mid = 5 x 6 = 30

right = 6 x 3 = 18

both triangles = 4 x 3 = 12

24 + 30 + 18 + 12

= 84 cm²

**Answer: 84**

**Step-by-step explanation:**

15. If l//m, find the measure of each angle.

If q ║ r, **value** of x is 17.

When a transversal connects two or more parallel lines at different locations, **alternate** **exterior** **angles** are created. The word exterior refers to something that is located outside. Whenever the transversal intersects two lines, alternate external angles are always outside of those two lines and are situated on the opposing sides of the transversal. As a result, the pair of alternate external angles—two outside angles—that arise at the opposing ends of transversals in the exterior section are always equal. When a transversal splits two parallel lines, we obtain two of these pairs of alternate exterior angles.

Given

q ║ r

**Alternate** **exterior** **angle**,

7x - 10 = 9x - 44

9x - 7x = 44 - 10

2x = 34

x = 17

If q ║ r, **value** of x is 17.

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find the weight ? needed to hold the wall shown in fig. p2.76 upright. the wall is 10 m wide.

As per the given **height **of the wall, the approximate weight is **149kN**

The term Hydrostatic refers to the force exerted by **static **water on the plate or object and its **magnitude **depends upon the positioning of the object inside the water.

Here we have given the following values,

Height = 2.76 upright

Width = 10 m

Here we have to consider the hydrostatic **force **acting on the wall about the pinned point say P then the **expression **is looks like,

=> F = ωAx

=> F = 9810(10 × 4) × 2

=> F = 784800 N = 785KN

Now, the weight is calculated as per the **Hydrostatic **method as,

=> W = (1.33/7) x 785

=> W = 149 kN

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name the image point when the object point (4,4) is mapped by the following translations. (x,y)-->(x+1,y-1)

The **image **of the point after the **translation** is (5,3)

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

Point =(4, 4)

This **point **can be represented as

(x, y) = (4, 4)

The **translation **equation is given as

(x,y)-->(x+1,y-1)

Substitute the known values in the above equation, so, we have the following representation

(x,y)-->(4+1,4-1)

Evaluate

(x,y)--> (5,3)

Hence, the **image **is (5,3)

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I need help i will choose you as the brainlyest answer is you get it right.

**Answer:**

6/4

1 2/4

1 1/2

**Step-by-step explanation:**

3 x 2/4 = 3/2 or 1 1/2

6/4 reduces to 3/2 as factors of 2

1 2/4 simplifies to 1 1/2

1 1/2 is equal to 3/2

Answer your looking for is A, C and D

What does it mean more than 2?

**More than** 2 in **mathematical expression** is written as >2.

The relationship between** two quantities **can be described using **comparison terms**. There are primarily three comparison terms: more than (>), less than (<), and equal to (=).

**More than** (>): When one quantity is greater than the other quantity, we use “more than”. For example, 5 > 3.

**Less than **(<): When one quantity is less than the other quantity, we use “less than”. For example, 8 < 10.

**Equal to** (=): When two quantities are the same, we use “equal to”. For example, 15 = 15.

More than 2 means, **greater than** but **not including** 2, which is written as >2

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FIND THE FIRST DERIVATIVE OF g(x)=√x² + 2x

We are asked to find the first derivative of,

[tex]\longrightarrow g(x) = \sqrt{x^2+2x}[/tex]

Here we can write the term [tex]x^2+2x[/tex] by adding and subtracting 1 as,

[tex]x^2+2x = x^2+2x+1-1[/tex]

[tex]x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2][/tex]

Thus,

[tex]\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)[/tex]

Now take,

[tex]x+1=\sec\theta\quad\dots(2)[/tex]

[tex]x=\sec\theta-1[/tex]

[tex]dx=\sec\theta\tan\theta\, d\theta[/tex]

[tex]\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)[/tex]

Then (1) becomes,

[tex]\longrightarrow g(x) = \sqrt{sec^2\theta-1}[/tex]

We have,

[tex]\sec^2\theta-1=\tan^2\theta[/tex]

So we get,

[tex]\longrightarrow g(x) = \tan\theta[/tex]

Now,

[tex]\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta][/tex]

By chain rule,

[tex]\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}[/tex]

[tex]\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}[/tex]

[tex]\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)[/tex]

But we have,

[tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]

[tex]\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}[/tex]

Hence (4) becomes,

[tex]\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}[/tex]

This is the first derivative of the given function.

answer the question pls

**Answer:**

**a) 47**

**b) 61**

**Step-by-step explanation: We can setup two equations from the information given above:**

**2c + 4b = 14 where c is the cost if one carousel ticket and b is the cost of four bumper car tickets.**

**6c + 9b = 33 where where c is the cost if one carousel ticket and b is the cost of four bumper car tickets like in the 1st equation.**

**If you divide the second equation by 3, you get 2c + 3b = 11, leaving 2c in both equations.**

**If you subtract both equations by the elimination method:**

** 2c + 4b = 14**

**-**

** 2c + 3b = 11**

**---------------------------**

**b = 3, which solves for the cost of one bumper car ticket**

**If you plug this value back into the first (or second) equation,**

**ex. 2c + 4(3) = 14 -> 2c = 2 -> c=1**

**You get c = 1, which solves for the cost of one carousel ticket.**

**Then you plug these values (c=1 and b=3) in a) and b):**

**a) 8*1 + 13*3 = 47**

**b) 10*1 + 17*3 = 61**

Find (x^3 + x^2 − 20x + 24) divided by (x − 3).

**Answer: olynomial Long Division**

**Dividing : x3 + x2 - 20x + 24 **

** ("Dividend")**

**By : x - 3 ("Divisor")**

**dividend x3 + x2 - 20x + 24 **

**- divisor * x2 x3 - 3x2 **

**remainder 4x2 - 20x + 24 **

**- divisor * 4x1 4x2 - 12x **

**remainder - 8x + 24 **

**- divisor * -8x0 - 8x + 24 **

**remainder 0**

**Quotient : x2+4x-8 Remainder: 0 **

**Factoring x2+4x-8 **

**The first term is, x2 its coefficient is 1 .**

**The middle term is, +4x its coefficient is 4 .**

**The last term, "the constant", is -8 **

**Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8 **

**Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is 4 .**

** -8 + 1 = -7 **

** -4 + 2 = -2 **

** -2 + 4 = 2 **

** -1 + 8 = 7 **

**Observation : No two such factors can be found !!**

**Conclusion : Trinomial can not be factored**

** Find roots (zeroes) of : F(x) = x3 + x2 - 23x + 24**

** See theory in step 1.3**

**In this case, the Leading Coefficient is 1 and the Trailing Constant is 24.**

** The factor(s) are:**

**of the Leading Coefficient : 1**

** of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,8 ,12 ,24**

** Let us test ....**

** P Q P/Q F(P/Q) Divisor**

** -1 1 -1.00 47.00 **

** -2 1 -2.00 66.00 **

** -3 1 -3.00 75.00 **

** -4 1 -4.00 68.00 **

** -6 1 -6.00 -18.00 **

** -8 1 -8.00 -240.00 **

** -12 1 -12.00 -1284.00 **

** -24 1 -24.00 -12672.00 **

** 1 1 1.00 3.00 **

** 2 1 2.00 -10.00 **

** 3 1 3.00 -9.00 **

** 4 1 4.00 12.00 **

** 6 1 6.00 138.00 **

** 8 1 8.00 416.00 **

** 12 1 12.00 1620.00 **

** 24 1 24.00 13872.00 **

**Polynomial Roots Calculator found no rational roots**

**Answer: x3 + x2 - 23x + 24**

** ——————————————————**

** x **

**Step-by-step explanation:**

just give me the straight answers for 1-6

**Answer:**

1. y=x 2. x=4 3. y=3x-10 4. y=-2/5x-1/5 5. y=-8x-13 6. y=-x+3

**Step-by-step explanation:**

A corporate bond has a face value of p dollars. The interest each year is 6% of the face value. After received each year. The payout is the sum of the face value and the total interest. years the total interest is the product of the number of years, 1, and the interest (a) Express the total interest /, in dollars, as a function of the age f, in years, of the bond. Note that "I is already provided. Do not include this in your submitted response to this question. I .06t+p Edit (b) Express the payout P, in dollars, as a function of f. Note that "P is already provided. Do not include this in your submitted response to this question. P= Edit

A **corporate bond **has a face value of p dollars. The **interest **each year is 6% of the face value. the total interest /, in dollars, as a function of the age f, in years, of the **bond **is

a)I(f) = 0.06 * f * p

b) P(f) = I(f) + p

What is the function?Generally, (a) Th**e total interest**, in dollars, as a function of the age f, in years, of the **bond **can be expressed as:

I(f) = 0.06 * f * p

This represents the** total interest paid over** f years, which is calculated by multiplying the annual interest rate (0.06), the number of years (f), and the face value of the bond (p).

(b) The payout P, in dollars, as a function of f can be expressed as:

P(f) = I(f) + p

This represents the** total payout **over f years, which is calculated by adding the total interest paid (I(f)) and the face value of the bond (p).

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10. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot

35 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 51°. What is the height of the tower, to the nearest meter? (show work pls)

The **height **of the **tower **where surveyor positions a **transit **that is 2 m tall = 45.19 m

**Sine**, **Cosine**, **Tangent**, **Secant**, **Cosecant**, and **Cotangent** are the six **trigonometric functions**. The **trigonometric functions **in mathematics are real **functions **that link the angle of a right-angled triangle to the ratios of the lengths of the two sides.

given:

transit **height **= 2 m

distance from the base of the **tower **= 35 m

angle of elevation = 51°

Utilize **trigonometric functions **to solve this problem. The tangent **trigonometric function** connects the opposite side and the neighboring side.

Opposite side / Adjacent side = tan Ф

solving opposite side = Opposite side = Adjacent side x tan Ф

Opposite side = 35 x tan 51°

Opposite side = 35 x 1.234

Opposite side = 43.19 m

calculating the **tower height **= 43.19 + 2 m

= 45.19 m

therefore the **height **of the **tower **= 45.19 m

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What will be the nature of roots of quadratic equation 2xÂ² 4x?

The** roots **of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the nature of the roots is **real and equal**.

The nature of the roots of a **quadratic equation** ax2 + bx + c = 0 with real coefficients a, b, and c can be determined by using the quadratic formula. The quadratic formula states that the **two roots** of the equation are given by:

x = (-b ± √(b2 - 4ac)) / 2a

For the equation 2x2 + 4x = 0, a = 2, b = 4, and c = 0. **Substituting** these values into the quadratic formula, we get the two roots of the equation as:

x = (-4 ± √(42 - 4(2)(0))) / 2(2)

x = (-4 ± 0) / 4

x = -1, 0

Therefore, the roots of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the **nature** of the roots is real and equal.

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A woman on a billboard is 8 3/8 feet tall. If the scale of the billboard is 1 foot = 8 inches, what is her actual height?

So, we can start off by listing what information the question has given us:

Billboard height - 8 3/8 ft

Scale - 1 ft = 8 in

With this info, we can undergo a conversion. We know 1 foot is eight inches but we have been given 8 feet. Since every one foot is eight inches, we will multiply the 8 feet by 8 inches.

8ft x 8in = 64 in

We have converted the 8 feet but still have the 3/8th of a foot. Since every number is a fraction over 1, we can multiply 3/8ft by 8/1 inches to convert it.

3 8 24

— x — = —

8 1 8

24 over 8 can be simplified into 3 over 1, aka 3 (8 divided by 8 is 1, and 24 divided by 8 is 3).

3 + 64 = 67

The woman’s actual height is 67 inches or 5.58 ft (since every 12 in make a ft).

Billboard height - 8 3/8 ft

Scale - 1 ft = 8 in

With this info, we can undergo a conversion. We know 1 foot is eight inches but we have been given 8 feet. Since every one foot is eight inches, we will multiply the 8 feet by 8 inches.

8ft x 8in = 64 in

We have converted the 8 feet but still have the 3/8th of a foot. Since every number is a fraction over 1, we can multiply 3/8ft by 8/1 inches to convert it.

3 8 24

— x — = —

8 1 8

24 over 8 can be simplified into 3 over 1, aka 3 (8 divided by 8 is 1, and 24 divided by 8 is 3).

3 + 64 = 67

The woman’s actual height is 67 inches or 5.58 ft (since every 12 in make a ft).

Please help 90pts! :D

Find the product of 6b(2 over 3b).

20 over 3b

4b

23 over 3 b2

4b2

**Answer:**

Answer is 4, but in the answer choices provided it is** 4b. **

**Step-by-step explanation:**

*Use PEMDAS! (Order of PEMDAS: Parenthesis, exponent, Multiplication, division, addition, subraction)*

1. Multiply 6b x 2= 12b.

2. Divide 12b by 3b = 4. or 4b

**Answer:**

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

Given[tex]6b\ (\cfrac{2}{3}\ b)[/tex]Find the product[tex]6b\ (\cfrac{2}{3}\ b) = b^2\ (\cfrac{12}{3})\)=4b^2[/tex]Correct **choice **is **D.**

What is the link between the transformation and congruence and similarity?

If we can move one thing without affecting its size or shape such that it perfectly overlays the other picture, then two objects are congruent. These motions are what are known as congruence **transformations**.

While the image's size and shape are unaffected by rigid body **motion**, its location and orientation are. The three **fundamental movements** of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

In order for two items to be congruent, one of them must be able to be moved over the other without affecting its size or form. Congruence changes are what we refer to as these motions. The transformation of an object into a congruent object is known as a congruence transformation.

∠A = ∠B

And, also

AB = BC

AD = BD

Therefore,

ΔABC ≅ ΔDEF

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Thanks for all of the helpers

here is another slope question

**Answer:**

**m = 5**

**Step-by-step explanation:**

The equation is y = mx + b

The m here is the slope; in this case, the slope is 5

What is the mean of 20 and 10?

15 is the **mean **of 20 and 10 .

**What are the mean, median, and example?**

A** data collection** is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as** the mode.**

Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

x = 20 + 10/2

x = 30/2

x = 15

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What kind of polynomial is 3xÂ²?

The polynomial 3xA² is a linear **monomial **having one term and a degree one.

A polynomial is an algebraic expression.

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

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

There are many types of polynomials according to the number of terms they have.

If a polynomial has one term it is called a monomial, Has two terms called a binomial, and having three makes it a trinomial.

Given, A polynomial 3xA².

Now, The **variable **is 'x' and raised to the power of 1 so it is linear and consists of only one term so it is a monomial as 3 and A are constants.

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A cubic polynomial with rational coefficients has the roots 7+√5 and 1/4. Find on additional root.

A. 7-√5

B. 7+√5

C. 5+√7

D. 5-√7

**Answer:**

Additional root of 7+√5 and 1/4 is:

D.5-√7

Rohit earns rupees 1500 and spends rupees 1250 per month. Find the ratio between his:

a) savings and expenditure b) expenditure and income c) income and savings

**Step-by-step explanation:**

To find the ratio between Rohit's savings and expenditure, we need to divide his savings by his expenditure:

Savings / Expenditure = (1500 - 1250) / 1250 = 250 / 1250 = 1/5

The ratio between Rohit's savings and expenditure is 1/5.

To find the ratio between Rohit's expenditure and income, we need to divide his expenditure by his income:

Expenditure / Income = 1250 / 1500 = 5/6

The ratio between Rohit's expenditure and income is 5/6.

To find the ratio between Rohit's income and savings, we need to divide his income by his savings:

Income / Savings = 1500 / (1500 - 1250) = 1500 / 250 = 6/1

The ratio between Rohit's income and savings is 6/1.

How do you prove triangles are congruent using ASA?

You must find the corresponding parts of the two triangles first. Then, you must find the angle measure of one pair of corresponding angles. You would then find the length of a pair of corresponding legs or sides in between the two angles. Lastly, you would need to find the angle measure of another pair of corresponding angles.

If you have a corresponding pair of congruent angles, a pair of congruent, corresponding sides, and another pair of congruent, corresponding angles, then both triangles are congruent.

Here’s an example:

Notice that the triangle’s side is in between the two angles; this is required when using ASA.

If you have a corresponding pair of congruent angles, a pair of congruent, corresponding sides, and another pair of congruent, corresponding angles, then both triangles are congruent.

Here’s an example:

Notice that the triangle’s side is in between the two angles; this is required when using ASA.

How do you check continuity of a function?

Continuity of a **function **can be checked by examining the limits of the function as x approaches a certain value and ensuring the function's output is equal to the **value **of the function at that point.

**Continuity **of a function is an important concept in calculus and other branches of mathematics. In order to check the continuity of a function, the limits of the function must be examined as x approaches a certain **value**. This means that the left-hand limit and the right-hand limit must be equal. If the limits are equal, then the **function **is continuous at that point. If the limits are not equal, then the function is not continuous at that point. Additionally, the value of the function at that point must also be equal to the limits in order for the function to be continuous. If the function is discontinuous at any point, then it is not considered continuous. Continuity is necessary for certain properties of functions, such as **derivatives **and integrals, to be defined.

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i am a number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44. what number am i?

The number less than 3,000.when you **divide** me by 32, my remainder is 30. when you divide me by 58, my remainder is 44 is one of this {798, 1726, 2654}.

There exists a, b∈N such as

N= 30+32a=44+58b

Therefore,

16a-29b= 22-15=7

Let us notice that 5×29-9×16=1

Therefore, 35×29-63×16=7

Hence, a= -63 is a **non-fundamental** solution to our equation.

We can show that the other solution are of the form a=-63+29k, with k∈Z

Therefore, the first **positive** solutions are

a= -63+3×29= 24

N= 798

a= -63+4×29= 53

N= 1726

a= -63+5×29=82

N= -63+6×29= 111

N= 3582

Therefore, the number is one of {798, 1726, 2654}.

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What is the formula for finding the altitude?

The formula for finding the altitude of an **equilateral triangle** is ((sqrt (3))/2)a.

As we know, the sides of an equilateral triangle are equal. Let the side of the triangle be 'a'.

Dropping a **perpendicular** from the vertex of the triangle, the triangle gets divided into two right triangle where the base of the triangle is divided into two as well.

Therefore, by using the **Pythagoras' theorem**,

we can get the altitude (say 'h') of the triangle by:

h^2 = a ^ 2 - (a/2) ^ 2 = 3a ^ 2/4

h = sqrt (3a^2/4) = ((sqrt (3))/2)a.

The question is incomplete, the complete question is:

What is the formula for finding the altitude of an equilateral triangle?

To know more about the **altitude **of triangles:

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