The perimeter of the figure is 20.56 centimetres
Explain perimeter
Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.
According to the given information
The perimeter of the figure is 4+4 + circumference of the circle with diameter 4= 8+12.56= 20.56
To know more about perimeter visit
brainly.com/question/6465134
#SPJ1
A right rectangular prism has a base with an area of 25 1/2 square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism? Please help!!
Answer:
[tex]25.5h = 153[/tex]
[tex]h = 6[/tex]
The height is 6 feet, so A is correct.
A cylinder has a height of 9 millimeters and a radius of 14 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
As a result, the cylinder's volume is roughly **5541.48 mm³**.
DEFINE THE CYLINDER'S VOLUME?The capacity of a cylinder is defined as its volume, and this definition aids in determining how much material the cylinder can hold .The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density.. The formula r²πh, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.
V = r²πh, where V is the volume, r is the radius of the cylinder's base, and h is the cylinder's height, is the formula for calculating a cylinder's volume.
When we enter the specified values into the formula, we obtain:
V = π(14)²(9)
V = 1764π
Rounding to the closest hundredth using 3.14, we obtain:
V ≈ 5541.48 mm³
To know more about volume of cylinder visit:
brainly.com/question/16788902
#SPJ1
In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.
What is percentage?The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.
Here,
According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.
This suggests that between 30% and 60% of people have brown eyes.
Let's figure out what proportion of the entire population is equal to 30% of 60%:
=> 30% of 60% = (30/100) * (60/100)
=> 0.3 * 0.6
=> 0.18 or 18%
Therefore, brown eyes are present in Math Town's overall population of 18%.
Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.
Therefore, D) 28% is the right response.
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
Find the area
(Please do not guess )
Answer:
A = 50.24 m²
Step-by-step explanation:
A = π r²
d = 8 m
r = d/2
r = 8/2
r = 4 m
A = 3.14 × (4)² m
A = 3.14 × 16 m
A = 50.24 m²
Answer:
50.24 m²
Step-by-step explanation:
Diameter = 8 m
Formula
Radius ( r ) = Diameter/2
r = 8/2
r = 4 m
Formula
Area of circle = π r²
Note
The value of π is 3.14 ( approximately )
Area of circle
= 3.14 × 4²
= 3.14 × 4 × 4
= 3.14 × 16
= 50.24 m²
Hence,
The area of circle is 50.24 m².
Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.
i will mark brainliest for whoever answers this pls just help me
Answer:
The area of the shape is 56 to the nearest tenth
Step-by-step explanation:
r=d/2
d=2r
d=2×3=6
Area of shape=Area of rectangle+Area of semi circle
A=L×B+1/2pir²
A=7×6+1/2×22/7×3²
A=42+11/7×9
A=42+99/7
A=42+14.14
A=56.14
A=56 to the nearest tenth
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y² -5y = 750750 -y(y -5) = 0(y +25)(y -30) = 0Step-by-step explanation:
You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.
AreaThe area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...
A = LW
750 = y(y -5)
This equation can be rearranged into several different forms:
y² -5y = 750 . . . . . . . multiply it out
750 -y(y -5) = 0 . . . . . subtract the right side expression
(y +25)(y -30) = 0 . . . . factor it
what is the weight of a 38kg child
Calculate employer's total FUTA and SUTA tax. As TCLH Industries operates in North Carolina, assume a SUTA tax rate of 1.2% and a taxable earnings threshold of $26,000. Current period taxable earnings for FUTA and SUTA taxes are the same as those for FICA taxes. Year-to-date taxable earnings for FUTA and SUTA taxes, prior to the current pay period, are as follows: Zachary Fox: $0 Calvin Bell: $20,478.57 David Alexander: $198,450 Michael Sierra: $117,600
the employer's total FUTA and SUTA tax is: $2,928
What is tax rate?
The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate.
$7,000 (for Zachary Fox) + $7,000 (for Calvin Bell) + $7,000 (for David Alexander) + $7,000 (for Michael Sierra) = $28,000
The FUTA tax for this amount is:
$28,000 × 6.0% = $1,680
Therefore, the total taxable earnings subject to SUTA tax is:
$26,000 (for each employee) × 4 (number of employees) = $104,000
The SUTA tax for this amount is:
$104,000 × 1.2% = $1,248
The year-to-date FUTA and SUTA taxes are not given explicitly, so we cannot calculate the current period FUTA and SUTA taxes.
Therefore, the employer's total FUTA and SUTA tax is:
$1,680 (FUTA tax) + $1,248 (SUTA tax) = $2,928
To know more about tax rate visit,
https://brainly.com/question/29800484
#SPJ1
Find three consecutive integers such that 4 times the first added to the third is 92
Solve quickly Thanks
The three consecutive integers are 18, 19, and 20.
What is consecutive integers?Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.
According to question:Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:
4x + (x+2) = 92
Simplifying this equation, we get:
5x + 2 = 92
Subtracting 2 from both sides, we get:
5x = 90
Dividing both sides by 5, we get:
x = 18
Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:
4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.
To know more about consecutive integers visit:
https://brainly.com/question/1767889
#SPJ1
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the given diagram of the triangle are m∠2 + m∠3 = m∠6, m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°. Therefore, options (4) and (5) are not always true.
What is an exterior angle?An exterior angle of a polygon is an angle that forms a linear pair with an interior angle of the polygon. In other words, it is an angle formed by extending one of the sides of the polygon. For any given vertex of the polygon, the exterior angle is the angle between a line containing the side of the polygon next to the vertex and a line that is an extension of the adjacent side. The measure of an exterior angle is equal to the sum of the measures of its corresponding remote interior angles (interior angles that are not adjacent to the exterior angle). The sum of the exterior angles of any polygon, including a triangle, is always equal to 360 degrees. Exterior angles are used in a variety of geometric proofs and constructions.
We know that the sum of all the interior angles of any triangle is 180 degrees. Therefore, we can use this fact to determine which statements are always true regarding the given diagram.
Now, we can use the following relationships between the interior and exterior angles of a triangle:
Exterior angle = Sum of interior angles adjacent to it
Interior angle = 180 - Exterior angle
Using these relationships, we can determine which statements are always true:
m∠5 + m∠3 = m∠4: This is true because the exterior angle at angle 3 is equal to the sum of angles 3 and 4, and the exterior angle at angle 5 is equal to the sum of angles 5 and 6. Therefore, m∠5 + m∠3 + m∠6 = m∠4 + m∠3, which simplifies to m∠5 + m∠3 = m∠4.
Given m∠3 + m∠4 + m∠5 = 180°: This is true because the sum of all the interior angles of a triangle is 180 degrees.
m∠5 + m∠6 = 180°: This is not always true because sum of all the angles should be 180. It is true in this specific case because angle 1 is a straight angle, which means that m∠5 + m∠6 = 180°. However, in general, this statement is not always true.
m∠2 + m∠3 = m∠6: This is true because the exterior angle at angle 2 is equal to the sum of angles 2 and 6. Therefore, m∠2 + m∠3 = m∠6.
Given m∠2 + m∠3 + m∠5 = 180°: This is may not always true. It is true in this specific case because angle 1 is a straight angle, which means that m∠2 + m∠3 + m∠5 = 180°. However, in general, this statement is not always true.
Therefore, the three statements that are always true from the diagram are:
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 = m∠6
To know more about exterior angles visit:
brainly.com/question/28835566
#SPJ1
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent.
63% of people Surveyed shop at a local grocery store.
What is percentage ?A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.
For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.
In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.
What are proportions ?The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;
it is frequently stated as a fraction.
For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.
An assertion of equality between two ratios is a proportion.
For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,
hence the sentence "3/5 = 6/10" is a proportion.
Analysis: -
people surveyed at store = 45
total no. of people = 72
the
Percent of peopla = 45/72 x100
= 0.625 × 100
= 62.5 %
= 63 %
63% of people Surveyed shop at a local grocery store.
To learn more about percentage visit:
https://brainly.com/question/29306119
#SPJ1
A particular sound wave can be graphed using the function y= -1sin 5x. Find the period of the function
Answer:
The period of a sine function of the form y = a sin bx is given by:
period = (2π) / |b|
In this case, the function is y = -1 sin 5x, which can be rewritten as y = -sin(5x). So, we can see that b = 5.
Substituting b = 5 into the formula, we get:
period = (2π) / |5|
period = π / 5
Therefore, the period of the function is π/5.
A pair of dice are tossed twice.
Find the probability that the first roll is a total of at least 3 and the second roll is a total of at least 12
The probability is 35/1296, or approximately 0.027 or 2.7%.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
The total number of outcomes when rolling a pair of dice is 36 (since each die has 6 faces and can result in 6 possible outcomes).
To find the probability of the first roll resulting in a total of at least 3, we need to determine the favorable outcomes. The only combination that does not result in a total of at least 3 is when both dice show a 1, which is only one possible outcome. So, there are 35 favorable outcomes (36 total outcomes - 1 unfavorable outcome) for the first roll.
To find the probability of the second roll resulting in a total of at least 12, we need to determine the favorable outcomes. The only combination that results in a total of 12 is when both dice show a 6, which is only one possible outcome. So, there is only 1 favorable outcome for the second roll.
Therefore, the probability of the first roll resulting in a total of at least 3 and the second roll resulting in a total of at least 12 is:
(35/36) * (1/36) = 35/1296
Hence, the probability is 35/1296, or approximately 0.027 or 2.7%.
To learn more about probability, Visit
https://brainly.com/question/13604758
#SPJ1
5. Apply Math Models A science teacher uses a fair spinner
simulate choosing 1 of 5 different field trips for her classes.
spinner has 5 equal sections, each representing a different
trip. The teacher spins the spinner 50 times and records the
results in the table below.
Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.
What is frequency?
Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).
The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.
The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.
The experimental and theoretical probabilities do not match exactly. For example, the experimental of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.
The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.
Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).
To know more about frequency visit:
https://brainly.com/question/254161
#SPJ1
Commplete Question:
A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:
Field Trip Number of times selected
A 8
B 16
C 9
D 12
E 5
Apply math models to analyze the data and answer the following questions:
What is the experimental probability of selecting each field trip?
What is the theoretical probability of selecting each field trip?
Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?
What is the relative frequency of selecting each field trip?
Based on the data, which field trip appears to be the most popular?
Que alguien me resuelva este ejercicio
Your Equifax score is 650, Transunion at 600, and Experian at 635, what is your mean score? Round to the nearest whole point.
The mean score is 628.
What is mean?
In statistics, the mean is a measure of central tendency, which represents the average value of a data set. It is also known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of observations in the data set. The formula for calculating the mean is:
mean = (sum of all values) / (number of observations)
Now,
To find the mean score, you need to add up the three scores and then divide by 3:
(650 + 600 + 635) / 3 = 628.33
Rounding to the nearest whole point, the mean score is 628.
To know more about Mean visit the link
brainly.com/question/30112112
#SPJ1
Two cars leave the same parking lot, one heading north and the other east. After several minutes, the eastbound car traveled 5 kilometers. If the two cars are now a straight-line distance of 13 kilometers apart, how far has the northbound car traveled?
Based on the information given, we can use the Pythagorean theorem to determine the distance traveled by the northbound car.
Let's denote the distance traveled by the northbound car as 'x' kilometers.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the straight-line distance between the two cars) is equal to the sum of the squares of the other two sides (the distances traveled by each car).
In this case, the northbound car's distance is 'x' kilometers and the eastbound car's distance is 5 kilometers.
So we have the equation:
x^2 + 5^2 = 13^2
Simplifying, we get:
x^2 + 25 = 169
Subtracting 25 from both sides, we get:
x^2 = 144
Taking the square root of both sides, we get:
x = 12
So the northbound car has traveled 12 kilometers.
Answer: 12 km
Step-by-step explanation:
As seen in the figure the distance that the northbound car traveled equals to the distance from point N to the parking lot.
pythagorean: [tex]\sqrt{13^{2}-5^{2} }=12km[/tex]
Help me this is a Screensho
t
Answer:
21.8 - 0.1 = 21.7
21.7 is 0.1 less than 21.8
Answer:
The answer is 21.7
Step explanation
21.8 - 0.1 = 21.7
I hope it helped you.
Please Mark me brainliest
Please help me. Giving brainliest to whoever gets it right!!
The equation of the line is: y = 0.5x + 4 and the inequality is H > 74.25
The equation of the graphTo find the equation of a line that passes through two points, we need to use the slope-intercept form of a linear equation:
y = mx + b
The slope is calculated as
m = (y2 - y1) / (x2 - x1)
m = (11 - 4) / (14 - 0)
m = 7/14
m = 1/2
m = 0.5
Next, we have
y = mx + b
4 = 0.5(0) + b
b = 4
So the equation of the line is: y = 0.5x + 4
Jacy's music downloadPart A: The equation that could be used to find the value of s is:
12s + 5.04 = 15.48
To find the value of s, we need to isolate the variable on one side of the equation.
We can do this by subtracting 5.04 from both sides and then dividing both sides by 12:
12s + 5.04 - 5.04 = 15.48 - 5.04
12s = 10.44
s = 10.44/12
s = 0.87
Therefore, Jacy paid $0.87 to download each song.
Tara's inequalityTo represent the number of hours, h, that Tara plans to work this month as an inequality, we can use the fact that she plans to work more hours than last month.
Let H be the total number of hours that Tara works this month.
Then we can write:
H > 16.5 + 19 + 23 + 15.75
Simplifying the right-hand side, we get:
H > 74.25
Therefore, the inequality that represents the number of hours, h, Tara plans to work this month is: H > 74.25
Read more about linear relation and inequality at
https://brainly.com/question/30318449
https://brainly.com/question/30390162
#SPJ1
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Answer: 0.6954
Step-by-step explanation:
To find the area between two z scores, in this case P(-0.82<z<1.29), we can either use a z score calculator or a standard normal distribution table, which I will use for this.
The probability of P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82).
To find P(z<2.01), we use a positive z score standard normal distribution table and find that P(z<1.29)=0.9015
Using a negative z score standard normal distribution table, we can find that (z<-0.82)=0.2061.
So, P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82)=0.6954.
Find the surface Area
Math step by step Answer
(a) The total surface area of the triangular prism is 560 in².
(b) The surface area of the cuboid is 944 ft².
(c) The surface area of the cylinder is 678.58 in².
What is the surface area of the cuboid, cylinder and prism?Cuboid;
The surface area of the cuboid is calculated as;
S.A = 2(12 x 16 + 12 x 10 + 16 x 10)
S.A = 944 ft²
Cylinder:
The surface area of the cylinder is calculated as follows;
S.A = 2π x 6 (6 + 12)
S.A = 678.58 in²
The surface area of a triangular prism can be calculated by summing the areas of its individual faces.
A triangular prism has three rectangular faces and two triangular faces.
The formula for the surface area of a triangular prism is:
Surface Area = Area of triangular faces + Area of rectangular faces
To calculate the area of a triangular face, we can use the formula for the area of a triangle:
Area of a triangle = (base × height) / 2
Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.
The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:
Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²
The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:
Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²
The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:
Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²
Now, let's calculate the area of the rectangular faces.
Area of rectangular face 1 = 18 in × 12 in = 216 in²
Area of rectangular face 2 = 18 in × 12 in = 216 in²
Finally, we can sum up all the areas to get the total surface area of the triangular prism:
Surface Area = Area of triangular faces + Area of rectangular faces
Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²
Learn more about surface area here: https://brainly.com/question/76387
#SPJ1
A walk alongside a railway track is represented on a map by an 86 mm straight line.
The walk is 17.2 km.
What is the scale of the map?
First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
find the value of x
Therefore, the height of the right triangle is 9.6 units.
What is triangle?A triangle is a geometric figure that consists of three line segments that intersect at three endpoints, called vertices. The line segments are called sides, and the vertices where they intersect are called angles. A triangle can be classified based on the length of its sides and the measure of its angles. Triangles are fundamental to many areas of mathematics and physics, and they have a wide range of applications in real-life situations, such as in architecture, engineering, and surveying.
Here,
To find the height of a right triangle, we can use the formula:
h = (a * b) / c
where "a" and "b" are the lengths of the legs of the right triangle, and "c" is the length of the hypotenuse.
In this case, we have a right triangle with legs of lengths 12 units and 16 units, and a hypotenuse of length 20 units. Therefore, we can substitute these values into the formula and solve for the height:
h = (12 * 16) / 20
h = 192 / 20
h = 9.6
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
A certain disease has an incidence rate of 0.8%. If the false negative rate is 4% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.
The probability that a person who tests positive actually has the disease is ≈0.0158.
what is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. 1 is the probability of every event in a sample space.
For instance, when we flip a coin, there are just two possible results: Head OR Tail. (H, T). However, if two coins are tossed, there are four possible results: (H, H), (H, T), (T, H), and (T, T).
we solve the given question using BAYE's theorem:
Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.
P(disease/positive)= [tex]\frac{P(disease)P(positive/disease)}{P(disease)P(positive/disease)+P(no disease)P(positive/disease)}[/tex]
P(disease/positive)= [tex]\frac{(0.008)(0.04)}{(0.008)(0.04)+(0.992)(0.02)}[/tex] ≈ 0.0158
To know more about Bayes' Theorem visit:
brainly.com/question/29598596
#SPJ1
Help fast please, it should be asap please
The function has a vertical asymptote at x = 1, x-intercepts are x = 1 and x = 5, hole at x = 5 and horizontal asymptote is y = 0.
Define rational functionA rational function is a function that can be expressed as the ratio of two polynomial functions. In other words, it is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero for any value of x.
To plot the rational function f(x) = (x² - 6x + 5)/(-x + 1)
Vertical asymptote: The denominator of the function (-x + 1) is equal to zero when x = 1.
Therefore, there is a vertical asymptote at x = 1.
x-intercept: To find the x-intercept, we set the numerator equal to zero and solve for x:
x² - 6x + 5 = 0
This quadratic equation can be factored as:
(x - 5)(x - 1) = 0
Therefore, the x-intercepts are x = 1 and x = 5.
y-intercept: To find the y-intercept, we set x equal to zero:
f(0) = (0² - 6(0) + 5)/(-0 + 1) = 5
Therefore, the y-intercept is (0, 5).
Hole: The function has a hole at x = 5 because both the numerator and the denominator become zero at x = 5.
Horizontal asymptote: To find the horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of the numerator is 2 and the degree of the denominator is 1, so the horizontal asymptote is y = 0.
Now, we can plot the function by choosing some values of x and calculating the corresponding values of y:
x y = f(x)
-1 4
0 5
0.5 3.25
1 undefined
2 -1
Image is attached below.
To know more about asymptote, visit:
https://brainly.com/question/4084552
#SPJ1
Here is another question DUE SOON PLEASE ASAP
Question 5(Multiple Choice Worth 1 points)
(08.07 MC)
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of p(x) in vertex form is;
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
What is vertex?In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.
To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.
To find the vertex, we can use the formula:
x = -b/2a, where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.
Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.
We can then use the formula to find the vertex:
x = -b/2a = -5/2a
Using the values from the table, we can set up two equations:
46 = a(5)² + b(5) + c
1 = a(0)² + b(0) + c
Simplifying the second equation, we get:
1 = c
Substituting c = 1 into the first equation and solving for a and b, we get:
46 = 25a + 5b + 1
-20 = 5a + b
Solving for b, we get:
b = -20 - 5a
Substituting b = -20 - 5a into the first equation and solving for a, we get:
46 = 25a + 5(-20 - 5a) + 1
46 = 15a - 99
145 = 15a
a = 9.67
Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:
b = -20 - 5(9.67) = -71.35
Therefore, the equation of p(x) in vertex form is:
p(x) = 9.67(x - 5)² + 1
Simplifying, we get:
p(x) = 9.67(x² - 10x + 25) + 1
p(x) = 9.67x² - 96.7x + 250.85 + 1
p(x) = 9.67x² - 96.7x + 251.85
Rounding to the nearest hundredth, we get:
p(x) = 9.67(x - 5² + 1 = 9.67(x + 1.04)² - 10.25
Therefore, the answer is:
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
To know more about vertex visit:
https://brainly.com/question/29476657
#SPJ1
Solve: 24b=6
A b=1/6
B b=1/2
C b=1/3
D b=1/4
Answer:
D. b=1/4
Step-by-step explanation:
I need help I haven’t been here a week and I don’t understand my homework
Solve either
Answer: you need to add
Step-by-step explanation: I would ask your teacher to help you understand the lesson.
1 1/4 - 1 1/5
Pls answer it today!
Answer:
fraction form: 1/20
decimal form:0.05
Which one is the correct choice?
Therefore, the correct response From these integral is option D is.
``` 10 + ∫₅¹ R(t) dt
What is an integral?An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.
Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.
The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.
``` 10 + ∫₅¹ R(t) dt
To know more about integral visit:
brainly.com/question/30900582
#SPJ1