Equations with Fractions

Can someone please show me how to work this question out. Im really stuck. Thanks.

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.

The 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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The present age of the mother is 26.4 years.the age of the mother and the age of the daughter and then combined them to solve for the age of the mother. The answer is that the present age of the mother is 26.4 years.

Let x = present age of the mother ,Let y = present age of the daughter.According to the question, x + y = 90 and(x+5)=5(y+5).Substituting the value of x + y from the first equation in the second equation,(x+5)=5(y+5.Simplifying the equation, 2y + 5 = 5xRearranging the equation, 2y = 5x - 5,Dividing both sides by 2, y = (5x - 5) / 2 ,Substituting the value of y in the first equation, x + ((5x - 5) / 2) = 90 Simplifying, 2x + 5x - 5 = 180 .7x = 185 .Dividing both sides by 7, x = 185 / 7 ,x = 26.4 Therefore, the present age of the mother is 26.4 years.

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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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The mass of the bicycle rider is approximately 68.75 kg.

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.

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:

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:

What 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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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

It should be noted that the provided assertion indicates that (A) is 41° (b) is -17.16 (a) is 5.41

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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There are 15 + 12 = <<15+12=27>>27 sixth and seventh-grade members.

The total number of members is 15 + 12 + 13 = <<15+12+13=40>>40.

The fraction of members that are either sixth- or seventh-grade members is 27/40.

To convert this to a percentage, we multiply by 100: 27/40 × 100% = 67.5%

Therefore, the answer is (C) 67.5%.

The area of the floor of the hall is 96 square meters.

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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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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The required average speed of the given train is 42 km/hour.

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?

I think they are vertical angles.

Hope this helps

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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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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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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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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y = 26.4

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 ✓

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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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 ;)

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.

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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The graph of the solution to the system of inequalities is added as an attachment

Given that

x + y ≥ 6

8x + 16y ≤ 160

To graph the solution to a system of inequalities, follow these steps:

See attachment for the system of inequalities

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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

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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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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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.

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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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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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.

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.

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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Answer:

Step-by-step explanation: