What graph would represent the solution of p-5>7
Answer:
suiiiii
Step-by-step explanation:
The solution of p-5>7 can be represented on a number line.We start by adding 5 to both sides of the inequality:p - 5 + 5 > 7 + 5p > 12This means that any value of p that is greater than 12 would satisfy the inequality.On a number line, we would represent this by shading the region to the right of 12, since any number to the right of 12 is greater than 12.
On the axes below, graph f(x)=|3x|. If g(x) = f(x)-2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) = f(x-4), how is the graph of f(x) translated to form the graph of h(x)?
The graph of the given piecewise functions will open towards for all.
What exactly is a piecewise function?
A piecewise function is a mathematical function that is defined by different expressions or formulas over different intervals or "pieces" of the domain. In other words, a piecewise function is defined by multiple "pieces" or "cases," each of which is defined over a different interval of the domain. The domain of the function is partitioned into intervals, and each interval has its own expression or formula that describes the function's behavior over that interval. The different pieces of the function are typically joined together at the boundaries of the intervals to create a continuous function overall.
Now,
Graph of f(x)=|3x| (y=|3x|):
The graph of g(x) = f(x) - 2 (y=|3x|-2) is obtained by shifting the graph of f(x) downward by 2 units. Therefore, the graph of g(x) is:
The graph of h(x) = f(x-4 )(y=|3x|-4) is obtained by shifting the graph of f(x) to the right by 4 units. Therefore, the graph of h(x) is:
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- Ansel is a maid at the hotel. He receives tips from the guests at the
ends of their stay. One week he earned $452.67 in tips and $5.23
per hour for 40 hours. What did he earn?
To calculate Ansel's earnings, we need to add up his tips and his hourly wages for the week.
First, let's calculate his earnings from his hourly wage:
$5.23 per hour x 40 hours = $209.20
Now, let's add that to his earnings from tips:
$209.20 + $452.67 = $661.87
Therefore, Ansel earned $661.87 for that week.
HELP PLS!!!! if you could do it asap, that would be greatly appreciated
The angle between the intersecting tangents is 128° and the value of a is calculated to be 26° which makes the option A. 26° correct.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
The 2 right angles formed are congruent which implies that the sum of half the angle between the intersecting tangents and (a + 90) will be 180°.
angle between the intersecting tangents = 180 - 52
angle between the intersecting tangents = 128
half angle between the intersecting tangents = 128/2
half angle between the intersecting tangents = 64
a + 90 + 64 = 180° {sum of interior angles of a triangle}
a = 180 - 154
a = 26.
Therefore, the angle between the intersecting tangents is 128 which makes the value of a equal to 26.
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Solve the equation for the variable.
2b^4 - 13 = 73
=
Enter your answers in increasing order, rounded to three decimal places.
b =
b =
After answering the provided question, we can conclude that Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Starting with the given equation:
[tex]2b^4 - 13 = 73\\2b^4 = 86\\b^4 = 43\\b = (43)^(1/4)\\b =1.973\\b = -1.973, 1.973\\[/tex]
Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.
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Solve each right triangle. Round answers to the nearest tenth
It should be noted that the provided assertion indicates that (A) is 41° (b) is -17.16 (a) is 5.41
What does a triangle actually mean?Having three sides, three angles, and three points, a triangular is a closed, two-dimensional object.
We know that a right angle is , and we are given another angle that is , so that means that angle is:
A + 49 +90 = 180
A + 139 = 180
A = 180 - 139
A = 41°
To find side length b, we can use the sin function:
sin(49) = b/18
18 ×-0.53 = b
b = -17.16
To find side length a, we can use the cos function:
cos(49) = a/18
18 × 0.300 = a
a = 5.41
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The length of a hall is three times and width is two times of its height. If the room contains 384 cubic metres of air, find the area of its floor.
The area of the floor of the hall is 96 square meters.
What is the area of the floor of the hall?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length.
Given that, the length of a hall is three times and width is two times of its height.
Let the height of the hall be h.
Then the length = 3h and width = 2h
Volume of the hall = Length × Width × Height
384 = (3h) × (2h) × (h)
384 = 6h³
6h³ = 384
Divide both sides by 6
h³ = 64
Take the cube roots
h = ∛64
h = 4
Hence;
Length = 3h = 12
Width = 2h = 8
Area of the floor = Length x Width
Area of the floor = 12 × 8
Area of the floor = 96 square meters.
Therefore, the area is 96 square meters.
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helppp
solve the inequality
11x + 2 > 57
x > ?
Answer:
x>5
Step-by-step explanation:
11x+2> 57
11x>55
x>5
Answer:
x>5
Step-by-step explanation:
11x + 2 > 57
-2 -2
11x > 55
divide both sides by 11, the 11's cancel and
x > 5
what is the best point estimate for the population's standard deviation if the sample standard deviation is 46.8 ?
The best point estimate for the population's standard deviation, given a sample standard deviation of 46.8, is 46.8 itself.
In mathematical terms, let's denote the population standard deviation as σ, and the sample standard deviation as s. The formula for calculating s is:
s = √(∑(x - [tex]\bar{x}[/tex])² / (n - 1))
where x is the value of each data point, [tex]\bar{x}[/tex] is the sample mean, n is the sample size, and ∑ means "sum of".
Now, if we assume that the sample is a representative sample of the population, we can use the sample standard deviation as an estimate for the population standard deviation. In other words:
σ ≈ s
This means that we can use 46.8 as an estimate for the population standard deviation.
However, it's important to keep in mind that this is just an estimate, and there is some level of uncertainty associated with it. The true population standard deviation may be slightly higher or lower than this estimate.
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solve (2.58) (1.2×10^-5)/1.9×10^-5
Answer:
[tex] 1\frac{299}{475} [/tex]
Step-by-step explanation:
[tex] \frac{2.58 \times 1.2 \times {10}^{ - 5} }{1.9 \times {10}^{ - 5} } = \frac{2.58 \times 1.2}{1.9} = \frac{3.096}{1.9} = \frac{774}{475} = 1\frac{299}{475} [/tex]
Answer:
Step-by-step explanation:
(2.58) (1.2×10^-5)/1.9×10^-5;
=(2.58) (1.2×[tex]\frac{1}{10^{5} }[/tex])/1.9×[tex]\frac{1}{10^{5} }[/tex];
=(2.58)([tex]\frac{1.2}{100000}[/tex])/1.9×[tex]\frac{1}{100000}[/tex];
=0.000031/1.9×[tex]\frac{1}{100000}[/tex];
=0.0000163×[tex]\frac{1}{100000}[/tex];
=0.000000000163;
=1.63×10^-10
What justifies the use of the normal distribution for the sampling distribution of proportion? The ability of the normal distribution to approximate the binomial distribution under appropriate conditions The Central Limit Theorem The large population size The Law of Large Numbers Question 3 0.25 pts The sampling distribution of the proportion follows the normal distribution when the values np and nq are greater than or equal to 0.05 50
The Central Limit Theorem justifies the use of the normal distribution for the sampling distribution of proportion.
The Central Limit Theorem states that under certain conditions, the sampling distribution of the mean of a random sample drawn from any population will be approximately normal, regardless of the shape of the population distribution. One of these conditions is that the sample size should be large enough, typically n >= 30. For the sampling distribution of proportion, the Central Limit Theorem applies because the proportion is essentially a mean of a sample of binary data of a normal distribution (e.g. success or failure). If the sample size is large enough, the sampling distribution of the proportion will be approximately normal, regardless of the shape of the population distribution. The condition np >= 5 and nq >= 5 is used to ensure that the sample size is large enough for the normal approximation to be valid. In essence, this condition ensures that there are enough successes and failures in the sample to satisfy the conditions of the Central Limit Theorem. If this condition is not met, then the normal approximation may not be valid and alternative methods, such as the binomial distribution, should be used instead.
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A juice factory labels bottles with customary and metric units. Do you think a bottle labeled 32fl oz and 960 mL is correctly labeled? Explain.
Quantity US Customary FL oz. UK (Imperial) US Nutrition labeling
960 ml 32,46 FL oz. 33,79 FL oz. 32,00 FL oz.
Which means 960 milli liter is equal to 32,46 FL oz.
This one is relatively simple. Once you know how much liquid a liter contains, you just need to divide it by a conversion factor equal to 1000. The result is 1 ml. That's what "mili" means - 1/1000th. If you have 1000 ml, it's actually 1 liter.
For this page, we are talking about fluid ounces (FL oz.). We're not talking about ounces, which are used to measure solids like metals. The fluid phone (fl Oz) is only for measuring the volume of liquids.
The problem is that you first need to know what fluid you are using. If you're a US citizen, you probably use US customary fluid ounces (US fl oz.).
As you can see, the numbers you need to divide 960 can be very impractical and unwieldy. Typing those long strings of numbers can be tedious. But you can also round them off to get a result that isn't too far off from a more accurate calculation.
For US v oz, divide volume in ml by 29.58 to get v oz.
So, 960ml equals 32.46oz when rounded up.
For amounts in milliliters on US food labels, divide the amount in milliliters by 30 to get the US fluid ounce equivalent. Similarly, you divide 960 by 30 to get 32.00 fluid ounces (fl oz).
For UK (Imperial) fluid ounces, divide 960 ml by 28.41 to get 33.79 UK fluid ounces.
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Shirley is asked to sketch a graph of y = 5* for x > or equal to 0. She produces the following.
The graph has two errors. How should they be corrected?
Answer:
Step-by-step explanation:
HELP ASAP!
Jason decides to see a movie. When he arrives at the snack counter to buy his popcorn, he has two choices in the shape of the popcorn container.
Using what you know about unit rate, determine which container is a better buy per $1.
One popcorn container is a cone and costs $6.75 the other is a cylinder and costs $6.25 .
Find the volume of BOTH popcorn containers. Determine which popcorn container will hold THE MOST popcorn.
Answer:
The cylinder is better to buy because it can hold more.
Step-by-step explanation:
If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone. Cylinder has a greater volume.
Example:
let's say you have a container. one shaped as a cylinder and one as a cone. both of them have a height of 1. Which one do you think will hold more?
the cylinder will hold more because of its shape and volume.
I hope this helps
hang in there ;)
Find the area of each figure.
Parallelogram ABDE is made up of square ACDF, triangle ABC, and
triangle FDE. Triangle ABC and triangle FDE are identical. The area of
square ACDF is 36 square meters. Find the area of triangle ABC.
Then find the area of parallelogram ABDE.
4 m
B
4 m
F
D
E
The area of Triangle ABC is 12² m while the area of parallelogram ABDE is 60² m.
What is parallelograms?
A parallelοgram is a simple quadrilateral with twο sets οf parallel sides in Euclidean geοmetry. A parallelοgram is a quadrilateral with twο sets οf οppοsite sides that are parallel and equal. There are fοur types οf parallelοgrams, three οf which are unique. Parallelοgrams, squares, rectangles, and rhοmbuses are the fοur different shapes.
When a quadrilateral has twο sets οf parallel sides, it is a parallelοgram. A parallelοgram's οppοsing sides and angles are bοth the same length. Internal angles οn the same side οf a Angles can alsο be hοrizοntal lines. There are 360 internal angles in tοtal.
Area of ACDF = 36² m (side × side)
Each side = √36
Each side = 6
AB = 6
Area of Triangle = 1/2(b)(h)
Area of Triangle ABC = 1/2(4)(6)
Area of Triangle ABC = (2)(6)
Area of Triangle ABC = 12² m
Area of parallelogram = (b)(h)
Area of parallelogram ABDE = (4 + 6)(6)
Area of parallelogram ABDE = (10)(6)
Area of parallelogram ABDE = 60² m
Thus, The area of Triangle ABC is 12² m while the area of parallelogram ABDE is 60² m.
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What angle??? I’ll mark Brainliest;)
I think they are vertical angles.
Hope this helps
Select all that apply. Which of the following are linear factors of p(x) = x3 - 2x2 - 5x + 6 ?
Numbers 2, 3, and 4 are the following are linear factors of p(x).
What does a linear equation mean in mathematics?
A linear equation is one that only has a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Occasionally, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The term "linear equation" refers to equations with power 1 variables. Where ax+b = 0 is one example with only one variable, where a and b are real numbers and x is the variable.
We can know the answer to this by letting p(x) be equal to zero and by substituting the values of x to the function.
p(x) = x3 - 2x2 - 5x + 6
To know what to substitute, we equate all factors to zero since even if only one of these factors is zero, the product of all factors would immediately be zero.
1 . x + 1 = 0 ; x = -1
2. x + 2 = 0 ; x = -2
3. x - 1 = 0 ; x = 1
4. x - 3 = 0 ; x = 3
We then try to substitute each value of x to the original polynomial and see if it will equal to zero.
1. (-1)³ - 2(-1)² - 5(-1) + 6 = 8 ≠ 0
2. (-2)³ - 2(-2)² - 5(-2) + 6 = 0
3. (1)³ - 2(1)² - 5(1) + 6 = 0
4. (3)³ - 2(3)² - 5(3) + 6 = 0
As we can see, all but number 1 equated to zero therefore numbers 2, 3, and 4 are all linear factors of p(x).
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A bicycle rider is going 4 m/s on her bike. If her kinetic energy is 550 J, what is her mass?
The mass of the bicycle rider is approximately 68.75 kg.
What is kinetic energy?Kinetic energy is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity²
where mass is the mass of the object and velocity is the speed at which it is moving. Kinetic energy is a scalar quantity and is measured in joules (J) in the SI system.
We can use the formula for kinetic energy to solve for the mass of the bicycle rider:
Kinetic Energy = 1/2 * mass * velocity²
Substituting the given values, we have:
550 J = 1/2 * mass * (4 m/s)²
Simplifying and solving for mass, we get:
mass = 550 J / (1/2 * (4 m/s)²
mass = 550 J / (8 kg m²/s²
mass = 68.75 kg
Therefore, the mass of the bicycle rider is approximately 68.75 kg.
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Hello and greetings lilliepruiett.
The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.
Step-by-step explanation:It is an exercise of kinetic energy, which is the energy that an object possesses due to its movement. It is defined as the energy required to accelerate an object of a given mass from rest to its current speed. Kinetic energy can be calculated using the following formula:
Ek = (m × v²)/2
where:
Ek is the kinetic energy in joules (J).m is the mass of the object in kilograms (kg).v is the speed of the object in meters per second (m/s).This formula indicates that the kinetic energy increases as the mass of the object increases and/or its speed increases. Kinetic energy is a direct measure of an object's ability to do work due to its motion.
We have that the cyclist is going at a speed of 4 m/s, when his kinetic energy is 550 Joules, we calculate the mass.
As we are asked to calculate the mass, we solve the formula:
Ek = (m × v²)/2m = (2 × Ek)/v²What we do now is; substitute the data into the cleared formula and solve for the mass of the cyclist.
m = (2 * Ek)/v²
m = (2 × 550 J)(4 m/s)²
m = (1100 J)/(16 m²/s²)
m = 68.75 kg
The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.
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3y + 7y -84 = 180 supplementary find the value for y
y = 26.4
Step-by-step explanation:Given: 3y + 7y - 84 = 180
First, we should combine any value that is similar.
3y + 7y - 84 = 180
10y - 84 = 180
Next, we will substitute.
10y - 84 + 84 = 180 = 84
10y = 264
Now we will divide by the value before the variable.
[tex]\frac{10y = 264}{ 10}[/tex] = y = 26. 4
Lastly, we will plug in the values.
3(26.4) + 7(26.4)- 84 = 180
76.2 + 184.8 - 84 = 180
264 - 84 = 180
180 = 180 ✓
classic golf inc. manages five courses in the jacksonville, florida, area. the director of golf wishes to study the number of rounds of golf played per weekday at the five courses. he gathered the following sample information. day rounds monday 145 tuesday 125 wednesday 135 thursday 100 friday 120 at the 0.05 significance level, is there a difference in the number of rounds played by day of the week?
Using a significance level of 0.05, we found a statistically significant difference in the number of rounds played by day of the week.
To determine if the test statistic is significant, we need to compare it to a critical value from an F-distribution table.
The critical value is based on the degrees of freedom, which is calculated as follows: df between = k - 1 (where k is the number of groups being compared, in this case 5) and df within = N - k (where N is the total sample size, in this case 5).
Using these values, we can find the critical value from the F-distribution table to be 2.866.
Comparing this critical value to our calculated test statistic of 3.60, we can see that the test statistic exceeds the critical value.
This means that we can reject the null hypothesis and conclude that there is a statistically significant difference in the number of rounds played by day of the week at the 0.05 significance level.
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As of 2019, the Burj Khalifa, located in Dubai, was the tallest building in the world. Suppose a scale model of the Burj Khalifa (without antennae) is 30 inches tall.
1. To what scale is this model? You will need to use the internet or another resource to find the actual height of the building.
2. How tall would a model of the Eiffel tower be at this scale?
This scale is commonly referred to as 1/90.56.
A model of the Eiffel Tower at the same scale as the model of the Burj Khalifa would be 11.7 inches tall.
What is a model?A model is a simplified version of reality that can help explain the workings of a complex system.
The actual height of the Burj Khalifa is 2,717 feet (828 metres).
To determine the scale of the model, we must divide the actual height by the model height:
Scale = (Actual Height)/(Model Height)
= (2,717 feet)/(30 inches)
= 90.56 feet/inch
This scale is commonly referred to as 1/90.56.
To calculate the height of a model of the Eiffel Tower, we must multiply the actual height of the tower (1,063 feet) by the scale:
Model Height = (Actual Height) x (Scale)
= (1,063 feet) x (1/90.56)
= 11.7 inches
Therefore, a model of the Eiffel Tower at the same scale as the model of the Burj Khalifa would be 11.7 inches tall.
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Molly is filling bags of marbles. She makes each bag so that 3 out of every 8 marbles are blue. Which equation correctly compares the number of marbles she uses, x, to the number of blue marbles, y?
The equation y = 3/8x can be used to compare the number of marbles Molly uses, x, to the number of blue marbles, y, in each bag.
To calculate the number of blue marbles Molly uses, we can use the equation y = 3/8x.
To start, we need to identify the variables in the equation. In this case, x represents the number of marbles Molly uses and y represents the number of blue marbles.
Next, we can substitute in the given information. In this case, we know that 3 out of every 8 marbles are blue, so we can set y equal to 3 and x equal to 8.
This gives us the equation 3 = 3/8x. We can then solve for x by dividing both sides by 3/8 to get x = 8.
This tells us that for every 8 marbles Molly uses, 3 of them are blue.
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Argyle has 10 T-shirts and 7 pairs of shorts that he wears with either sandals or sneakers. If all the colors and patterns coordinate, how many
different outfits can he make?
Using multiplication principle of counting, Argyle can make 140 different outfits.
How many different outfits can he make?Argyle has 10 T-shirts and 7 pairs of shorts, which he can wear with either sandals or sneakers. To find out how many different outfits he can make, we can use the multiplication principle of counting, which states that the total number of outcomes for a sequence of events is the product of the number of outcomes for each event.
First, we need to determine the number of ways Argyle can choose a T-shirt and a pair of shorts. He can choose one of 10 T-shirts and one of 7 pairs of shorts, giving us:
10 x 7 = 70
Next, we need to determine the number of ways Argyle can choose shoes. For each outfit, he can choose either sandals or sneakers, giving us:
shoes = 2
Finally, we can find the total number of different outfits by multiplying the number of ways to choose a T-shirt and shorts by the number of ways to choose shoes:
70 x 2 = 140
Therefore, Argyle can make 140 different outfits if all the colors and patterns coordinate.
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A rack of bowling balls behind John and Judy’s lane holds at least 6 bowling balls. Each of the bowling balls weights either 8 pounds or 16 pounds, and the total weight of the bowling balls on the rack is no more than 160 pounds. Assuming x represents the number of 8-lb balls and y represents the number of 16lb bowling balls, the system of equations below can be used to represent the situation(x+y>6) (8x+16y<160) graph the solution to the system
The graph of the solution to the system of inequalities is added as an attachment
How to graph the solution to the system of inequalitiesGiven that
x + y ≥ 6
8x + 16y ≤ 160
To graph the solution to a system of inequalities, follow these steps:
Graph each inequality on the same coordinate plane.Shade the region of the plane that satisfies each inequality.The solution to the system of inequalities is the overlapping region of the shaded regions.See attachment for the system of inequalities
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based on the performance of those who took the gre exam between july 1, 2004 and june 30, 2007, the average verbal reasoning score was calculated to be 462. in 2011 the average verbal score was slightly higher. do these data provide convincing evidence that the average gre verbal reasoning score has changed since 2004?
Without more information and statistical analysis, it is difficult to determine whether the data provide convincing evidence that the average GRE verbal reasoning score has changed since 2004.
To determine whether the average GRE verbal reasoning score has changed since 2004, we would need to conduct a hypothesis test. We could set up a null hypothesis that the population mean for the verbal reasoning score has not changed since 2004, and an alternative hypothesis that the population mean has increased.
Assuming a normal distribution of scores, we could use a two-sample t-test to compare the means of the two populations (scores from 2004-2007 and scores from 2011). We would need to collect a random sample of scores from both time periods and calculate the sample means and standard deviations.
Without knowing the sample size or standard deviation of the 2011 scores, it is difficult to determine whether the difference in average scores is statistically significant. However, if the sample sizes are large enough and the difference in means is significant, then we could conclude that there is convincing evidence that the average GRE verbal reasoning score has changed since 2004.
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Please answer and explain well
Answer:
a) 11:09
b) 31 minutes it should take to arrive at newtown
Step-by-step explanation:
a) you have to read the table
b) you need to know how many minutes are in an hour and for 11:38 to 12 is 22 minutes and you need an extra 9 so add them both together which will give the answer of 31 minutes.
Determine the intercepts with the axes X³-12x²+36x
The intercepts of x- axis is (0, 0) (6,0) and y - axes is (0,0)
The x-intercept is the point on the x-axis that is the shortest distance from the origin to the point where the line cuts the x-axis, and the y-intercept is the point on the y-axis that is the shortest distance from the origin to the point where the line cuts the y-axis. Both of these are referred to as the origin.
The polynomial function is :
f(x) = [tex]x^3-12x^2+36x[/tex]
[tex]x^3-12x^{2} +36x=0[/tex] [x intercepts]
[tex]x(x^{2} -12x+36)=0[/tex]
[tex]x(x - 6)^2=0[/tex] [=> x = 0 x = 6]
x = 0 [y intercepts]
x = 0 [=> y = 0]
=> (0, 0) (6,0) [Interception point with x -axis]
=> (0, 0) [Interception point with y- axis]
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The area of a square can be determined by the function A=s^2 , where A represents the area of the square and s represent the length of one side. Jada is buying square picture frames to hang her high school graduation pictures in her college dorm room
a.if the length of one side of the picture is s inches, what expression represents the area of the frame?
b.If Jada decides that she actually needs four picture frames, what expression represents the total area?
c.If Jada decided to buy one picture frame with a side 4 times longer than the first, what expression represents its area?
d.if the length of one side of the original frame was 8 inches, what was the area of
i. The original picture frame?
ii. Four of the original picture frames"
iii. One picture frame with a side 4 times as long?
please please help mee
The equation A=[tex]s^2[/tex] can be used to calculate the area of a square, where A stands for the square's surface area and s for one of its sides.
a. The area of the frame is equal to 4x * s + [tex]4x^2[/tex] if one side of the image is s inches long.
b. The overall area is 16x * s + [tex]16x^2[/tex] if Jada determines she actually wants four photo frames.
a. If the length of one side of the picture frame is s inches, then the length of one side of the frame is (s + x) inches, where x is the width of the frame (assuming the frame is a uniform width on all sides). The following expression is used to represent the frame's area:
Area of the frame = (s + 2x) * (s + 2x) - s * s
Area of the frame = 4x * s + [tex]4x^2[/tex]
b. In the event that Jada determines she actually requires four photo frames, the statement that denotes the entire space is:
Total area = 4 * (4x * s + [tex]4x^2[/tex])
Total area = 16x * s + [tex]16x^2[/tex]
c. If Jada decided to buy one picture frame with a side 4 times longer than the first, then the length of one side of the larger frame is 4s inches. The expression that represents the area of the larger frame is:
Area of the larger frame = (4s + 2x) * (4s + 2x) - (4s) * (4s)
Area of the larger frame = 16x * s + [tex]4x^2 + 16s^2[/tex]
d. If the length of one side of the original frame was 8 inches, then:
i. The original picture frame has an area of A = [tex]s^2[/tex]
The original picture frame has an area of A = [tex]8^2[/tex]
The original picture frame has an area of A = 64 square inches.
ii. Four of the original picture frames have a total area of:
Total area = 4 * A
Total area = 4 * 64
Total area = 256 square inches.
iii. One picture frame with a side 4 times as long has an area of:
Area of the larger frame = [tex](4s)^2[/tex]
Area of the larger frame = [tex]16s^2[/tex]
Area of the larger frame = [tex]16 * 8^2[/tex]
The area of the larger frame is 1024 square inches.
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Using the circle below, find each arc length. Round to the nearest hundredth.
ST = ____
RPT = ____
For given circle, the length of arc ST and RPT are 13.44 ft and 50.8 ft respectively.
What exactly is a circle?
A circle is a geometric object made up of all the points on a plane that are equidistant from the centre. A circle, in other terms, is a collection of points that are all the same distance from a centre point. This distance is known as the circle's radius.
The circumference of a circle is the distance around the outside of the circle, and it can be calculated using the formula C = 2πr, where π (pi) is a mathematical constant and r = radius of the circle.
Now,
For given circle
radius=14 ft
then
circumference=2*π*r=2*22/7*14
=88 ft
angle for the arc ST=180-125
=55°
then length of arc ST=55/360*88
=13.44 ft
and angle of arc RPT=180-97+125
=208°
then length of arc RPT=208/360*88
=50.8 ft
Hence,
the length of arc ST and RPT are 13.44 ft and 50.8 ft respectively.
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A train travels at a certain average speed for a distance of 90 km and then travels a distance of 99 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, then what is its original average speed?
The required average speed of the given train is 42 km/hour.
What is speed?Speed is what it means. the speed at which an object's location changes in any direction.
The distance traveled in relation to the time it took to travel that distance is how speed is defined.
As speed simply has a direction and no magnitude, it is a scalar quantity.
So, we have:
63/x + 72/6+x = 3
63(x+6)+72x/x(x+6) = 3
63x + 378 + 72x/x²+6x = 3
378 + 135x = 3x² = 18x
3x² - 117x - 378 = 0
x² - 39x - 126 = 0
x² - 42x + 3x - 126 = 0
x(x-42)+3(x-42) = 0
(x+3)(x-42) = 0
x = 42, -3
As speed cannot be zero, the first average speed is 42 km per hour.
Therefore, the required average speed of the given train is 42 km/hour.
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Correct question:
A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?