Determine the solution by using substitution. Write your answer as a point below (x,y).

Answer:

To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]

Step-by-step explanation:

A function, let say [tex]f(x)[/tex], is defined at [tex]x = c[/tex] is continuous at [tex]x = c[/tex]

If the limit of [tex]f(x)[/tex] as [tex]x[/tex] approaches [tex]c[/tex] is equal to the value of [tex]f(x)[/tex] at  [tex]x = c[/tex].

Mathematically it is written as:

if

[tex]\lim _{x\to c}\:f\left(x\right)=f\left(c\right)[/tex]

then

[tex]f(x)[/tex] is continuous at  [tex]x = c[/tex].

So from the above definition, we conclude that:

To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]

i.e.

if

[tex]\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)[/tex]

then

[tex]f(x)[/tex] is continuous at  [tex]x = 2[/tex].

To make f continuous at x=2, define f(2) to be equal to 4. This makes the left-hand limit, right-hand limit, and function value at x=2 all equal to 4, which satisfies the definition of continuity.

To make a function continuous at a point, the left-hand limit and right-hand limit at that point must be equal to the function's value at that point. In other words, if a function is continuous at x=a, then

[tex]\lim_{x \to a^+} f(x)=f(a)[/tex]

Therefore, to make f continuous at x=2, we must define f(2) to be equal to the limit of f(x) as x approaches 2 from both the left and the right.

We can see that the limit of f(x) as x approaches 2 from the left is 4. This is because f(x) approaches 4 as x approaches 2 from the left, even though f(2) is undefined.

We can also see that the limit of f(x) as x approaches 2 from the right is 4. This is because f(x) approaches 4 as x approaches 2 from the right, even though f(2) is undefined.

Therefore, to make f continuous at x=2, we must define f(2) to be equal to 4.

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When a point is reflected across the y-axis, the x-coordinate remains the same, but the sign changes. The distance of the new point from the y-axis is the same as the distance of the original point from the y-axis.

When a point is Reflecting points across the y-axis, the x-coordinate remains the same, but the sign changes.

So, if the original point is (3, 5), the new point will be (-3, 5). The distance of the new point from the y-axis is still 3 units.

This is because the distance between any point and the y-axis is the distance between the x-coordinate of that point and 0 on the number line.

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Answer:

B. y = -3/8x - 4

Step-by-step explanation:

Given equation: 3x - 8y = 12

Find a parallel line that matches one of the equations shown.

First, find the slope by solving for y:

3x - 8y = 12

8y = -3x + 12

y = -3/8x + 12/8

y = -3/8x + 3/2

Slope m = -3/8

Since the slope of a line parallel is the same slope, the only equation that fits the conditions is B because in the form y = mx + b, m = -3/8

Answer:

-15/2  (or  -7 1/2)

Step-by-step explanation:

-7.5 is equal to -75/10.

When you simplify it, you get:

-15/2  which simplifies to -7 1/2

Answer:

The expression that represents his total time is given by "t = 7.5/s" where s is his speed against the wind.

Step-by-step explanation:

In order to solve this problem we will assign a variable to Curtis speed on the first leg of the trip, this will be called "s". Since the speed on the first part is "s" and the speed on the second part is 20% higher, then the speed on the second part is "1.2s". Each leg of the course is 9 miles long, therefore the time it took to go each way is given by:

time = distance/speed

First part:

t1 = 9/s

Second part:

t2 = 9/1.2s = 7.5/s

The expression for the whole course is the sum of each, so we have:

t = t1 + t2

t = 9/s + 7.5/s

t = (9 + 7.5)/s = (16.5)/s

Complete Question:

The rectangle below has an area of x^2-6x-7 square meters and a width of x-7 meters. What expression represents the length of the rectangle?

Answer:

Solution:

Given that,

[tex]\text{Area of rectangle} = x^2 - 6x - 7 \\\\Width = x - 7[/tex]

TO FIND: LENGTH = ?

We know that,

[tex]Area\ of\ rectangle = length \times width \\\\Therefore\\\\x^2 - 6x - 7 = length \times x - 7\\\\length = \frac{x^2 - 6x - 7 }{x - 7 }\\\\length = \frac{(x-7)(x + 1)}{x - 7}\\\\\text{cancel out x-7 from numerator and denominator} \\\\length = x + 1[/tex]

Thus expression represents the length of the rectangle is (x + 1) meter

Answer:

5m

Step-by-step explanation:

The GCF is 5m assuming that the question was actually:

5m⁴, 50nm, 15m³n²

Final answer:

The greatest common factor of the given monomials 5m⁴, 50nm, and 15³n² is 5m.

Explanation:

To find the greatest common factor of the given monomials 5m⁴, 50nm, and 15³n², we need to factorize each monomial and find the common factors.

Now, we can find the common factors by looking at the factors that are present in each monomial.

The common factors are 5 and m.

So, the greatest common factor is 5m.

Answer:

Milk $3.60

Water $1.80

Chips $0.90.

Step-by-step explanation:

If w = cost of 1 bottle of water, m = cost of 1 gal of milk and c cost of 1 bag of chips we have.

4m + 6w + 5c  = 29.7

Also we have w = 2c and m = 1.8 + w.

From the first equation we have c = w/2.

So substituting for c and m in the initial equation we have:

4(1.8 + w) + 6w + 5(w/2) = 29.7

7.2 + 4w + 6w + 2.5w = 29.7

12.5w = 22.5

w = 1. 80.

So c = w/2 = 1.8/2 = 0.90.

and  m = 1.8 + 1.8 = 3.60.

The cost of bag of chips is $5.58 , bottle of water is $ 11.16 and gallon of milk is $12.96.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

It is given that

4 gallons of milk, 6 bottles of water and 5 snack size bags of chips costs $29.7

Let the price of bag of chips is $x

Then

bottle of water , y costs twice as much as a bag of chips

y = 2x

a gallon of milk , z costs $1.80 more than a bottle of water

z = y +1.8

z = 2x +1.8

The equation that will be formed is

x + 2x + 2x +1.8 = 29.7

5x +1.8 = 29.7

5x = 27.9

x = $5.58

y = $11.16

z = $12.96

Therefore the cost of bag of chips is $5.58 , bottle of water is $ 11.16 and gallon of milk is $12.96.

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Answer:

You can prove it by the SAS postulate.

Step-by-step explanation:

Answer:

x^2-7x+2x-14 or x squared minus seven x plus two x minus fourteen

Step-by-step explanation:

(x+2)*(x-7)=  x^2-7x+2x-14

First: x^2

Outer: -7x

Inner: 2x

Last: -14

Answer:

x²-5x-14

Step-by-step explanation:

Write the equation (x+2)(x-7)

Multiply (F in FOIL)

x*x =x²

Multiply (O in FOIL)

x*-7 = -7x

Multiply (I in FOIL)

2*x = 2x

Multiply (L In FOIL)

2*-7 = -14

Combine like terms

-7x + 2x = -5x

Write the equation

x²-5x-14

Answer:

The next term should be 19

Step-by-step explanation:

Each time you add 3, from 10 to 13, and 13 to 16

The next number would be 19 because 16 + 3 = 19

Answer:

solution is 7. graphing is: open circle on 7 with the arrow pointing right. -->

Step-by-step explanation:

the answer has to be more than 4, so five or more. Then you add 2 to 5 and get 7. 7-2=5 which is greater than 4.

Answer:

Additive inverse property

Step-by-step explanation:

-1/3 + 1/3 =0

We are adding opposites to get to zero

a+ -a =0

the volume of the​ sculpture is [tex]Volume = 64.11ft^3[/tex] .

Step-by-step explanation:

Here we have , An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumference of 21.980 feet, We need to find the volume of the​ sculpture . Let's find out:

We know that

⇒ [tex]Circumference = 2\pi r[/tex]

According to question ,

⇒ [tex]21.980 = 2\pi r[/tex]

⇒ [tex]\frac{21.980}{2\pi} = r[/tex]

⇒ [tex]r=3.5[/tex]

Now , We know that Volume of cone :

⇒[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

⇒[tex]Volume = \frac{1}{3}(3.14) (3.5)^25[/tex]

⇒[tex]Volume = 64.11ft^3[/tex]

Therefore , the volume of the​ sculpture is [tex]Volume = 64.11ft^3[/tex] .

Answer:

81

Step-by-step explanation:

Answer:

n = 18

Step-by-step explanation:

2n - 5 = 31

Add 5 to each side

2n - 5+5 = 31+5

2n = 36

Divide each side by 2

2n/2 = 36/2

n = 18

Answer:

c.

Step-by-step explanation:

All of the things are correct with this one.

Answer:

53

Step-by-step explanation:

tanx=opp/adj

x=tan^-1(72/54)

x=53.130

Answer:

D

Step-by-step explanation:

Answer is D.

Answer:

d.

the indirect connection between weight and leaf content

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Answer:

8 and -8

Step-by-step explanation:

The definition of a square root is 'a number which produces a specified quantity when multiplied by itself.' Though a negative number cannot have a square root or be a perfect square, it can be a square root.

8 is the only positive square root, but every number that has a square root, also has a second one, the negative version.

-8 is also the square root because it can be multiplied by itself to get 64 :D

The real square roots of the integer 64 will have 8 and -8.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Let's say the square root of 64 is x.

x = √64

Square both sides

x² = (√64)² = 64

x² = 64

Now, find two equal number that gives 64 by multiplying.

Consider, 8 and 8 → 8² = 64

Thus, x = 8

Another could be -8 and -8 → (-8)² = 64

Hence "The real square roots of the integer 64 will have 8 and -8".

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Answer:

∠ RQU = 25°

Step-by-step explanation:

The opposite angles of an inscribed circle are supplementary, thus

∠ URS + ∠ UTS = 180°, that is

∠ URS + 124° = 180° ( subtract 124° from both sides )

∠ URS = 56°

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ URS is an external angle to Δ QUR, that is

∠ RQU + 31° = 56° ( subtract 31° from both sides )

∠ RQU = 25°

Answer:

Distributive property does not apply here because there is nothing to distribute nor is there any parenthesis.

Answer:

mean=10.625=10.6

median=12

Step-by-step explanation:

Mean

The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the "mean" changes. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used

Median

The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same

plz mark brainliest

First , second and last option are relevant to hyperbola . So , they are correct.

Review each statement to determine if it is true for a hyperbola

It is confirm that the first statement is true because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis

It is It is confirm that the second statement is true because the center of a hyperbola is the midpoint of the vertices

It is confirm that the third statement is false because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis

It is confirm that the fourth statement is false because the transverse axis of a hyperbola is the line segment that contains the vertices and the foci

It is confirm that the fifth statement is true because the directrices of a hyperbola are two lines parallel to the conjugate axis and located a distance from the center equal to the distance from the center to the foci.

Therefore, the first, second, and last options are correct.

Question :

Equation of the axes: The equation of the axes of a hyperbola is x = h, where h is the x-coordinate of the center of the hyperbola.

Equation of the asymptotes: The equation of the asymptotes of a hyperbola is y = ±(b/a)x, where a and b are the distances from the center to the vertices along the transverse and conjugate axes.

Equation of the conjugate hyperbola: The equation of the conjugate hyperbola can be found by interchanging a and b in the equation of the original hyperbola.

Review each statement to determine if it is true for a hyperbola

1. "A point on a hyperbola that sits on the transverse axis is called a vertex." - True. That's because the vertices of a hyperbola are indeed points on the hyperbola that line up with the transverse axis.

2. "The center of a hyperbola is right in the middle of its vertices." - True. Think of it like finding the midpoint between two ends. That's where the center of the hyperbola sits.

3. "A hyperbola's vertex is exactly where it meets the transverse axis." - false.

4. "The transverse axis of a hyperbola is the line connecting its vertices and foci." - False. The transverse axis actually links the vertices directly, not the vertices and the foci.

5. "The directrices of a hyperbola are two lines that run parallel to its conjugate axis, and they're positioned at a distance from the center to match the distance from the center to the foci." - True. It's like setting up boundaries at a certain distance from the center to guide the shape of the hyperbola.

So, yes, you're right about the first, second, and last statements being true.

incomplete question

Each time x goes up by 2, y decreases by 4

This indicates we have a linear function. The slope in this case would be

m = rise/run = (change in y)/(change in x) = -4/2 = -2

The y intercept can be found by following these steps

y = mx+b

0 = -2(5)+b

0 = -10+b

10 = b

b = 10

Therefore, the equation of this line is y = -2x+10. Plug in something like x = 1 and it should lead to y = 8. The same applies for any other column of x,y values.

Answer:

15

Step-by-step explanation:

subtract 11 from 26 which the opposite operation to get your answer.