What is the range of the function f = [0,00) + R, defined by the rule f(t) = -247 (a) (0,1) (c) R (b) (0,11 (d) (0,00)

A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.

Hence, option (b) is correct choice.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.

For that particular value of the number, the limitation renders the value of the rational statement undefinable.

To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.

For more questions on rational expression

https://brainly.com/question/25292194

#SPJ4

The missing option may be:

(a) 1

(b) 0

(c) always positive

(d) Indefinite

Answer:

10a²+5ab+2b²

Step-by-step explanation:

Start by combining like terms aka the ones that match:

Step 1: (4a²-5ab-6b²) + (10ab+6a²+8b²)

Step 2: (10a²-5ab-6b²) + (10ab+8b²)

Step 3: (10a²+5ab-6b²+8b²)

Final answer: 10a²+5ab+2b²

In step 1, I added the 4 and 6. In step 2, I added -5 and 10. In step 3, I added -6 and 8. For each I attached the proper ending (a², ab, and b²).

I hope this clears some confusion!

The perimeter of the triangle is 188.1 m

The perimeter of a triangle can be determined by adding the three lengths of the triangle.

From the image, the coordinates of vertices of the triangle are:

(-3, 3), (-3, -2) and (3, 3)

distance between (-3, 3) and (-3, -2) is:

3-(-2) = 5  (we use y coordinates only because x are the same)

       = 50 m  (Each unit on the map represents 10 meters)

distance between (-3, 3) and (3, 3) is:

3-(-3) = 6    (we use x coordinates only because y are the same)

       = 60 m

distance between (3, 3) and (-3, -2) is:

= √(50² + 60²)     (Pythagoras)

= 78. 1 m

Perimeter = 50 + 60 + 78.1 = 188.1 m

Learn more about perimeter on:

https://brainly.com/question/17297081

#SPJ1

Complete Question

Check attached image

Answer:

Step-by-step explanation:

1 Factor out the common term 33.

3(y-x)=4.

3(y−x)=4.

2 Divide both sides by 33.

y-x=\frac{4.}{3}

y−x=

3

4.

​

3 Subtract yy from both sides.

-x=\frac{4.}{3}-y

−x=

3

4.

​

−y

4 Multiply both sides by -1−1.

x=-\frac{4.}{3}+y

x=−

3

4.

​

+y

5 Regroup terms.

x=y-\frac{4.}{3}

x=y−

3

4.

​

Answer:

89 more boys than girls

Step-by-step explanation:

801 * 4/9 = 356

So 356 boys

rest are girls so 801-356 = 445 girls

445-356 = 89

89 more boys than girls (there are more boys but question says there are more girls?)

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.

An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

   2x⁴ − 3x³ − 2x² − 4x − 1

 +---------------------------------------

x  |   2x⁵    -3x⁴    -2x³    -4x²   -x

 |

3  |   6x⁴    -9x³    -6x²    -12x    -3

 +---------------------------------------

c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.

    x + 8      x - 5

 +--------------------

x  |  x² + 8x   x² - 5x

 |

-5 | -5x + -40   -5x + 25

 +--------------------

The final total area can be found by adding up the areas of the smaller rectangles:

Total area = x² + 8x + x² - 5x - 5x - 40 + 25

= 2x² - 10x - 15

= 2x² - 10x - 15.

Read more about area model on https://brainly.com/question/30729476

#SPJ1

Answer:

I believe the answer is 24.

Step-by-step explanation:

hope it helps.

For f(x) = sin(Tr), there exists at least one point 0 < c < 2 such that f (2) - f(0) = f'(c) (2 - 0)^2. However, for f(x) = |x|, there is no such c that satisfies f(1) - f(-1) = f'(c) (2). The Mean Value Theorem does not apply over the interval [-1, 1] for f(x) = |x|.

For f(x) = sin(Tr), we can apply the Mean Value Theorem which states that for a function f(x) that is continuous on the interval [a, b] and differentiable on (a, b), there exists at least one point c in (a, b) such that:

f(b) - f(a) = f'(c) (b - a)

Here, a = 0, b = 2, and f(x) = sin(Tr). Thus,

f(2) - f(0) = f'(c) (2 - 0)

sin(2T) - sin(0) = cos(cT) (2)

2 = cos(cT) (2)

cos(cT) = 1

cT = 2nπ, where n is an integer

0 < c < 2, so 0 < cT < 2π

Thus, cT = π/2, and c = π/4

Therefore, f'(π/4) satisfies the Mean Value Theorem condition.

For f(x) = |x|, we can find f'(x) for x ≠ 0:

f'(x) = d/dx|x| = x/|x| = ±1

However, at x = 0, the function f(x) is not differentiable because the left and right derivatives do not match:

f'(x=0-) = lim(h->0-) (f(0) - f(0-h))/h = -1

f'(x=0+) = lim(h->0+) (f(0+h) - f(0))/h = 1

Thus, the Mean Value Theorem does not apply over the interval [-1, 1] for f(x) = |x|.

For more questions like Integer click the link below:

https://brainly.com/question/490943

#SPJ11

The width and length of the rectangle is 4.5ft and 12ft.

Width of a rectangle = b = x ft.

Length of a rectangle = l = (2x+3) ft.

Area of the rectangle = l×b = 54 sq.ft.

                                    = x (2x + 3) = 54

                                    = 2x² + 3x = 54

                                      (2x-9)(x+6) = 0

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.

 It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

To learn about Area :

https://brainly.com/question/8294080

#SPJ4

If there is no difference between the distributions of scores in two groups, the effect size will be equal to zero.Effect size is a measure used to quantify magnitude of a difference or relationship between variables.

It provides information about the practical significance or importance of an observed effect. In the context of comparing distributions of scores between two groups, a non-zero effect size indicates that there is a difference between the groups.

However, when there is no difference between the distributions of scores in the two groups, it implies that the effect size is zero. This means that the observed effect or relationship is negligible, indicating that the groups are essentially similar and there is no meaningful distinction between them.

To learn more about effect size click here : brainly.com/question/31454248

#SPJ11

Answer:

-2/7

Step-by-step explanation:

2/5 x (-5/7)

multiply and reduce

-2 x 1/7

calculate

-2/7

Have a great day!!!

Answer: -2/7

Step-by-step explanation: For fraction multiplication, multiply the numerators and then multiply the denominators. This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 10 and 35 using GCF(10,35) = 5.  Apply the fractions formula for multiplication and solve. Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(10,35) = 5. Therefore: 2/5×−5/7=−2/7

Strawberry Hope: "Hey there, Strawberry Cow here! Hope this helps! Have a fantastic Afternoon!"

~Strawberry Cow~

Answer:

linear

Step-by-step explanation:

you can tell its linear bc its in a straight line

hope this helps <3

Therefore, the result is 133/20

To find the result, we'll first calculate the difference between 1 1/4 and 1/5.

1 1/4 is equivalent to 5/4, and 1/5 can be written as

1/5 * 4/4 = 4/20.

Subtracting these fractions, we get

(5/4) - (4/20) = 25/20 - 4/20 = 21/20.

Next, we add this difference to 5 6/10. 5 6/10 is equivalent to 56/10. Adding the fractions, we get

(21/20) + (56/10) =

(21/20) + (112/20) = 133/20.

For such more question on fractions

https://brainly.com/question/78672

#SPJ8

Answer:

27

Step-by-step explanation:

129-(-1) = 130

130/5 = 26

26+1 = 27

Answer:

n = 27

Step-by-step explanation:

This is Arithmetic sequence

a = -1

Common difference = 4 - (-1) = 4 +1 = 5

an = a + (n-1)d

129 = -1 + (n-1)*5

129 + 1 = (n-1)*5

130 = (n-1)*5

130/5 = n - 1

26 = n - 1

n = 26 + 1

n =27

There are C(n,3) terms in this formula that are intersections of 3 sets.

What is combination?

The combination is outlined as “An arrangement of objects wherever the order within which the objects square measure chosen doesn't matter.” the mix means that “Selection of things”, wherever the order of things has no importance.

Main body:

According to inclusion-exclusion principle :

Cardinatlity of a₁∪ a₂∪. ∪aₙ is the sum of the individual cardinalities minus the sum of the cardinalities of intersections of any two sets plus the sum of the cardinalities of intersections of any three sets minus the sum of the cardinalities of intersections of any four sets and so on , which means

n(a₁∪a₂∪a₃) = n(a₁) +n(a₂) + n(a₃) - n(a₁∩a₂) - n(a₂∩ a₃) - n(a₁∩ a₃) +                                                              n(a₁∩a₂∩a₃)

so in this example ,

intersections of 3 sets is 1 where n = 3

So correct option is C(n,3).

Hence correct option is A.

To know more about combination , visit:

https://brainly.com/question/11732255

#SPJ4

The probability that all 6 flips result in heads is 1/64

The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0

For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64

P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64

Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.

Learn more about  probability and coin flipping:https://brainly.com/question/30544804

#SPJ11

The area of the third square is 24 units square.

The squares forms a right angle triangle.

The side length of a square are equal.

Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.

area of a square = l²

where

area of the first square = l²

√8 = l

l = 2√2 units

area of the second square = l²

√16 = l

l = 4 units

The length of the squares are the legs and hypotenuse of the right triangle formed.

using Pythagoras theorem,

Therefore,

(2√2)² + 4² = c²

16 + 8 = c²

c = √24

c = 2√6 units

area of the third square = (2√6)² = 24 unit²

learn more on area here: https://brainly.com/question/24170638

#SPJ1

Answer:

0....4.... 8....12....16

The given function is f(x) = (4-x)/29. We need to find the x-values where f is not continuous and determine whether the discontinuities are removable or nonremovable.

For this function, there are no nonremovable discontinuities. The only type of discontinuity that could occur is a removable discontinuity. This occurs when a point is undefined, but the limit exists and is finite. In other words, the function can be made continuous by redefining it at that point.

To find any possible removable discontinuities, we need to find the values of x for which the denominator becomes zero, because division by zero is undefined. The denominator is always 29, which is never zero, so there are no values of x for which the denominator is zero. Therefore, there are no removable discontinuities.

In conclusion, the function f(x) = (4-x)/29 is continuous for all values of x, and there are no removable or nonremovable discontinuities.

To learn more about denominator, click here:

brainly.com/question/15007690

#SPJ11

Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

For more such questions on function

https://brainly.com/question/29631554

#SPJ8

Answer:

4/9

Step-by-step explanation:

if you make 1/3 x 3 to put it at /9, it will give you 3/9, now, 3/9+1/9=4/9 sorry for bad english

Answer:

Step-by-step explanation:

Car drive 31.4 miles/gallon

for 358 miles, Leah needs 358/31.4 =~ 11.40 gallons

since it cost $2.18 / gallon, it will cost Leah 2.18 * 11.4 = $24.85

Answer:

He spent 11.25 minutes running

Step-by-step explanation:

Mr. Boyd completed a 3.19 mile walk/ run.

For every 5 minutes of walking, he ran for 1.5 minutes.

He completed his workout in 48.52 minutes.

Hence, we have the equation:

1.5x + 5x = 48.52 minutes

6.5x = 48.52 minutes

x = 48.52/6.5

x = 7.4646153846

Approximately = 7.5 minutes

Therefore the time spent running = 1.5 × 7.5 minutes

= 11.25 mimutes

The slope of the line = rise of the line / run of the line = 2/2 = 1.

The slope (m) of a line can be determined by finding the ratio of the rise of the line to the run of the line, which is, the change in y over the change in x.

Referring to the image attached below, the blue line in the given graph shows the rise of the line while the red line shows the run of the line.

Therefore:

Rise of the line = 2 units

Run of the line = 2 units

Slope of the line (m) = rise/run = 2 units/2 units

Slope of the line (m) = 1

Learn more about slope on:

https://brainly.com/question/13861479

#SPJ1

Given that the household is located in the northeast, there is a 0.230 probability that the randomly chosen US household makes more than $75,000.

Given info;

19.1% of US households, according to the US Census Bureau, are in the Northeast. Additionally, 4.4% of households in the US earn $75,000 or more annually and are situated in the northeast.

let, A represents the U.S. households in the Northeast.

     B represents the U.S. households earning $75,000 or more.

To determine the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast.

P(A) = 19.1% = 0.191

P(A ∩ B) = 4.4% = 0.044

P(B I A) = P(A ∩ B) / P(A)

            = 0.044 / 0.191

            = 0.230

Hence, the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast is 0.230.

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

3 burritos would cost $23.31.

Let's assume that the cost of one taco is "t" and

the cost of one burrito is "b".

Then we can set up a system of two equations based on the given information:

4t + 6b = 62.58

7t + 5b = 66.78

Solving simultaneously using a calculator results to

t = 3.99

b = 7.77

Therefore, one burrito costs $7.77.

To find the cost of 3 burritos, we can multiply the cost of one burrito by 3:

3 * $7.77 = $23.31

Learn more about linear function at:

https://brainly.com/question/4025726

#SPJ1

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

The best description for this type of test is a one-tailed hypothesis test.

What is One-tailed test?

A one-tailed test, also known as a one-sided test, is a statistical hypothesis test in which the alternative hypothesis is formulated to detect a difference or relationship in a specific direction. It is used when the researcher has a prior expectation or theory about the direction of the effect.

In hypothesis testing, a one-tailed test is used when the researcher has a specific direction in mind for the alternative hypothesis. The alternative hypothesis states that there is a difference or relationship in a specific direction, such as "greater than" or "less than" a certain value.

In this scenario, Susan's alternative hypothesis states that the population mean (μ) of the students from the private school is greater than 572. This indicates that she is specifically interested in determining if the students' scores are higher than the stated value.

The null hypothesis, on the other hand, assumes no difference or relationship and is typically denoted as the opposite of the alternative hypothesis. In this case, the null hypothesis would be μ = 572, suggesting that there is no difference between the students' scores and the given value.

Since Susan's alternative hypothesis focuses on a specific direction (greater than), it aligns with a one-tailed test. The test will involve calculating the test statistic and comparing it to the critical value or p-value associated with the chosen significance level to make a decision regarding the hypothesis.

To know more about One-tailed test. visit

https://brainly.com/question/14053535

#SPJ4