Point P is located at (2, 2) and point T is located at (7, 17).
What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of
partitioning point.

soo this may seem a little awkwark but it still should provide the same resault however its faster :)

so we have

(48x^5-16x^3+40x)/8x

What we are going to be doing is factoring out any and all possibilities for

(48x^5-16x^3+40x)

first factor

(8x(6x^4-2x^2+5))/8x

when we get to this step simplify 8x

we are left with 6x^4-2x^2+5

in order to get an answer that would often be used by long devision just get rid of the +5

This is just a remainder using long devision your instructer may ask for

6x^4-2x^2

Hope it helps

Answer:

6x⁴ - 2x² + 5

Step-by-step explanation:

[48x⁵ - 16x³ + 40x] ÷ 8x

[8x(6x⁴ - 2x² + 5)] ÷ 8x

6x⁴ - 2x² + 5

Check:

(6x⁴ - 2x² + 5)(8x)

= 48x⁵ - 16x³ + 40x (verified)

Answer: each person ate 3 slices of watermelon.

Step-by-step explanation:

The total number of people at the party was 7.

Total number of watermelon slices that Lindsay brought to the party is 12. Total number of watermelon slices that Caroline brought to the party is 9. Total number of slices that that both of them brought to the party would be

12 + 9 = 21 slices

The 7 people at the party each ate the same number of watermelon slices. It means that the number of slices that each person ate would be

21/7 = 3

Answer:

3. I checked.

Step-by-step explanation:

Answer:

The length of the rope between the boat and the dock is of 30 feet.

Step-by-step explanation:

Given:

tan(40) ≈ 0.839

Angle of depression = 40 (deg)

Distance between boat and the floor of the ocean = 25.17 feet

If we look into the diagram we can see that,they form 2 right angled triangle.

Where we can say that :

Distance between boat and dock  = Rope's distance = Base of the triangle.

Let the length of the rope be 'x' feet.

Considering the dotted triangle:

[tex]tan\ (40) =\frac{opposite}{adjacent}[/tex]

⇒ [tex]tan\ (40) =\frac{25.17}{x}[/tex]

⇒ [tex]tan\ (40)\times x =\frac{25.17}{x}\times x[/tex]

⇒ [tex]tan\ (40)\times x =25.17[/tex]

⇒ [tex]\frac{tan\ (40)\times x}{tan\ (40)} =\frac{25.17}{tan\ (40)}[/tex]

⇒ [tex]x =\frac{25.17}{0.839}[/tex]

⇒ [tex]x= 30[/tex]

Length of the rope between the boat and the dock is 'x' = 30 feet.

Explanation:

It isn't clear what the elements of your flowchart are supposed to look like. In general, the proof would go like this:

1. List the "givens": PQ=6=TS; ∠P=120°=∠T; ∠PRQ and ∠TRS are vertical angles.

2. Note that the vertical angles are congruent

3. Claim ΔPRQ ≅ ΔTRS by the AAS congruence postulate since two corresponding adjacent angles and the corresponding sides not between them have been shown to be congruent.

Answer:

Chandra have 97 baseball cards.

Step-by-step explanation:

Given:

Chandra and Simone have 152 baseball cards together. Chandra's collection has 42 more baseball cards in it than Simone's collection.

Now, to find baseball cards Chandra have.

Let the baseball cards Simone's have be [tex]x.[/tex]

As, given  Chandra's collection has 42 more baseball cards in it than Simone's collection.

So.  Chandra's collection of cards is [tex]x+42.[/tex]

Together Chandra and Simone have baseball cards = 152.

According to question:

[tex]x+(x+42)=152[/tex]

[tex]x+x+42=152[/tex]

[tex]2x+42=152[/tex]

Subtracting both sides by 42 we get:

[tex]2x=110[/tex]

Dividing both sides by 2 we get:

[tex]x=55.[/tex]

Thus, Simone's collection of cards = 55.

Now, to get the baseball cards Chandra have we substitute the value of [tex]x[/tex]:

[tex]x+42\\=55+42\\=97.[/tex]

Therefore, Chandra have 97 baseball cards.

Yo sup??

total number of cards that Chandra and Simone have =152

let number of cards that Simone have be x

then chandra will have 42+x

from the statement given to us we can say that

x+x+42=152

2x=110

x=55

therefore Simone has 55 cards and chandra has 97 cards

Hope this helps

We set up the equation (70+64+83+x)/4=75

Multiply by 4 on both sides: 70+64+83+x=300

Combine like terms on left side: 217+x=300

Subtract 217 from both sides: x=83

So Sara must get at least an 83% in order to maintain a final average of 75%

Hope this helped!

Answer: she must score 83% on her 4th test if she wants to get a final average of 75%

Step-by-step explanation:

The formula for determining average is expressed as.

Average = sum of the score/ number of tests.

Sara got a 70%, 64%, and 83% on her first three tests. Her former average would be

(70 + 64 + 83) 217/3 = 72.3℅

Let x represent the score that she needs to get on her 4th test if she wants to get a final average of 75%.

Therefore,

(x + 217)/4 = 75

Cross multiplying by 4, it becomes

x + 217 = 300

x = 300 - 217

x = 83%

Answer:

Step-by-step explanation:

Let "o" and "s" represent the number of pounds of orange slices and strawberry leaves in the mix, respectively. We want ...

  o + s = 13 . . . . . . . . . . . . . . . total weight

  1.29o +1.79s = 19.27 . . . . . .total cost

Solving the first equation for o, we can substitute that result into the second equation to get ...

  o = 13 -s

  1.29(13 -s) +1.79s = 19.27

  0.50s +16.77 = 19.27 . . . . eliminate parentheses

  0.50s = 2.50 . . . . . . . . . . . subtract 16.77

  s = 5 . . . . . . . . . . . . . . . . . . multiply by 2

  o = 13 -5 = 8

5 pounds of strawberry leaves should be mixed with 8 pounds of orange slices to get the desired mixture.

To find out how many pounds of both orange slices and strawberry leaves are needed for the mixture, we need to solve a system of equations involving weight and total cost.

The question involves solving a system of linear equations to determine how many pounds of orange slices and strawberry leaves should be mixed to achieve a 13-pound mixture that totals $19.27. Let's define two variables:

We have two equations based on the weight and cost of the mixture:

Solving this system will provide us with the values for x and y that satisfy both equations.

Answer:

[tex]C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]

Step-by-step explanation:

We are given the following in the question:

The length of the pen will be 5 feet more than twice as long as the width of the pen.

Let y be the length and x be the width. Thus, we can write:

[tex]y = 2x +5[/tex]

Fencing = Perimeter of rectangular pen

[tex]\text{Perimeter of rectangle} = 2(\text{length} + \text{width})\\ P = 2(y+x)\\P=2(2x+5+x)\\P= 2(3x+5)\\P = (6x + 10)\text{ feet}[/tex]

The cost of the pen will be $7.50 per foot of fencing.

Total Cost of fencing =

[tex]\text{Cost of fencing}\times \text{Perimeter}\\C(x) = 7.50\times (6x+10)\\C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]

is the required cost function.

Final answer:

The cost function for fencing a rectangular pen, given the width x and a cost of $7.50 per foot, is c(x) = 45x + 75, representing the total cost as a function of the width x.

Explanation:

The student is asking for a function that represents the cost of fencing a rectangular pen when the width is given. Let x be the width of the pen. The length of the pen, according to the problem, is 5 feet more than twice the width, so it can be expressed as 2x + 5 feet.

The cost of the fencing is $7.50 per foot. To find the total cost of the pen, we have to calculate the perimeter of the rectangular pen, which is 2 times the width plus 2 times the length. Hence, the perimeter P(x) can be represented as P(x) = 2x + 2(2x+5).

Multiplying through and simplifying gives us the cost function c(x) = 7.50 * P(x). Therefore, c(x) = 7.50 * (2x + 2(2x + 5)) = 7.50 * (6x + 10) = 45x + 75. This function represents the cost of fencing the pen as a function of its width x.

Answer:

Mean speed is 55.7 mph.

Step-by-step explanation:

The provided frequency distribution is:

Speed Cars

30-39 4

40-49 19

50-59 50

60-69 15

70-79 12

The formula to compute the mean for the grouped data is:

[tex]\bar{X} =\frac{\sum(mf)}{\sum(f)}[/tex]

Here, m is mid point and f is frequency.

The mean speed can be computed as:

Thus, the mean speed is 55.7 mph.

To find the mean of data from a frequency table, multiply each speed by its frequency, sum those products, and then divide by the total number of items. This produces a weighted average that reflects the frequency of each speed value in the dataset.

To calculate the mean from a frequency table, we should multiply each speed by its frequency to get the 'combined speed' for each group. Add those combined speeds together, then divide by the total number of cars (or the sum of the frequencies).

For example, suppose we had 5 cars with a speed of 60 mph and 10 cars with a speed of 70 mph. We multiply each speed by its frequency (5*60 + 10*70), then sum these values to get the total combined speed. Divide this total combined speed by the total number of cars (5 + 10) to get the mean speed.

This method averages out the impact of each speed, weighted by how frequently each occurs in the dataset.

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Answer: the combined time he spent studying is 281/36 hours

Step-by-step explanation:

The first step is to convert all mixed numbers to improper fraction.

On Monday Billy spent 4 1/4 hour study. Converting 4 1/4 hours to improper fraction, it becomes 17/4 hours.

On Tuesday he spent another 3 5/9 hour study. Converting 3 5/9 hours to improper fraction, it becomes 32/9 hours.

The combined time he spent studying answer as a mixed number would be

17/4 + 32/9 = (153 + 128)/36

= 281/36 hours

Answer:

Step-by-step explanation:

Let x represent the number of hours that he works. babysitting his neighbors children.

Let y represent the number of hours that he works at the other job.

He earns $10 per hour babysitting his neighbors children. This means that the amount that he earns, babysitting his neighbors children for x hours would be

10x

He earns $12 per hour working at the other job. This means that the amount that he earns, working at the other job for y hours would be

12y

Therefore, the inequality that represent the number of hours that he needs to work at both jobs to earn a minimum of $120 is

10x + 12y ≥ 120

Answer:

A

Step-by-step explanation:

y = mx + c

y = -½x + 1

Answer:

595 Trout

Step-by-step explanation:

90 - 45 = 45

450 + 45 = 495

The estimated number of trout in the lake is 495 trouts.

The total number of trouts in the lakes that were initially tagged is added with the number of untagged trout that are caught afterward to find the total number of trout in the lake.

It is given that 450 trout were initially caught and tagged by a conservationist and were later released into the lake.

Therefore the total number of tagged trout = 450

Later, when the trout are caught again, we notice that 90 are caught and of those 90 trout, 45 have been tagged. This means that there are 45 untagged trout.

Therefore, total number of untagged trout = 90 - 45

= 45

Therefore, the total number of trout in the lake = 450 + 45

= 495

Thus, we have found that the estimated number of trout in the lake is 495 trouts.

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Answer:

96 ft/s

Step-by-step explanation:

We can start by deriving the equation of the velocity, which is the derivative of the position equation:

[tex]v(t) = \frac{ds}{dt} = (-16t^2)' + 800' = -32t[/tex]

After 3 seconds, the wrench would achieve a speed of

v(3) = -32t = -32*3 = -96 ft/s

So it's falling at the rate of 96 ft per second after 3 s

Final answer:

To calculate the velocity of the falling wrench after 3 seconds, the first derivative of the position function s(t) is taken to get v(t) = -32t. By substituting t with 3, the velocity at three seconds is -96 feet per second.

Explanation:

To find how fast the wrench will be falling after 3 seconds, we need to calculate the first derivative of the position function s(t) to get the velocity function v(t). The position function given is s(t) = −16t² + 800. Differentiating this with respect to t gives v(t) = d/dt (-16t² + 800) = -32t.

To find the velocity after 3 seconds, we substitute t = 3 into the velocity equation, which gives v(3) = -32(3) = -96 feet per second.

Therefore, the wrench will be falling at a velocity of -96 feet per second after 3 seconds.

Answer:

Step-by-step explanation:

The correct written form of the scientific name that uses the rules of binomial nomenclature is "Felis domesticus." Each binomial nomenclature identifies each species by a scientific name of two Latin words. The first name is capitalized, the second is not.

The correct written form of the scientific name using binomial nomenclature is 'Felis domesticus'. Developed by Carolus Linnaeus, the system assigns every organism a unique two-part name, made up of genus and species.

The correct written form of the scientific name, using the rules of binomial nomenclature, is Felis domesticus. Binomial nomenclature is a system developed by Swedish botanist Carolus Linnaeus that gives every organism a unique, two-part scientific name. This two-part name consists of the genus name first (capitalized) and the species name second (lowercase). Both parts of the name are italicized in print to differentiate them.

For instance, the scientific name for humans is Homo sapiens with 'Homo' representing the genus and 'sapiens' the species. Similarly, in the case of Felis domesticus, 'Felis' is the genus and 'domesticus' is the species describing a domestic cat.

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Answer:

[tex]7\frac{29}{36}\ hours[/tex]

Step-by-step explanation:

Given:

Time spent on Monday (M) = [tex]4\frac{1}{4}\ hours[/tex]

Time spent on Tuesday (T) = [tex]3\frac{5}{9}\ hours[/tex]

Now, the total combined time spent on study is equal to the sum of the times spent on Monday and Tuesday.

So, we need to add both the times to get the combined time spent on studying.

The combined study time is given as:

Total time spent = Time spent on Monday + Time spent on Tuesday

[tex]Total\ time=4\frac{1}{4}+3\frac{5}{9}\\\\Total\ time = \frac{4\times 4+1}{4}+\frac{3\times 9+5}{9}\\\\Total\ time = \frac{17}{4}+\frac{32}{9}\\\\\textrm{Taking LCD of 9 and 4 as 36, we get:}\\\\Total\ time = \frac{17\times 9}{4\times 9}+\frac{32\times 4}{9\times 4}\\\\Total\ time = \frac{153}{36}+\frac{128}{36}\\\\\textrm{Since the denominators are same, we add the numerators.}\\\\Total\ time = \frac{153+128}{36}\\\\Total\ time = \frac{281}{36}\ hours[/tex]

Divide 281 by 36. The quotient is the whole number part, the remainder is the numerator part and the denominator remains the same.

So, on dividing, we get 7 as quotient and 29 as remainder. So, converting to mixed fractions, we get:

[tex]Total\ time = 7\frac{29}{36}\ hours[/tex]

Therefore, the  the combined time he spent studying is [tex]7\frac{29}{36}\ hours[/tex]

Answer:

Sampling Frame

Step-by-step explanation:

If you are finding the representation of this style than it isHilton Honors membership list represents the Sampling frame

Answer:

Step-by-step explanation:

The slope intercept form equation of a straight line is expressed as

y = mx + c

Where

m represents slope

c represents y intercept.

Comparing the given equations with the slope intercept form equation,

2) y = 4x + 14 is in the slope intercept form. Its slope is 4 and the intercept is 14.

3) y = -4x + 14 is in the slope intercept form. Its slope is - 4 and the intercept is 14.

4) y = 2x + 7 is in the slope intercept form. Its slope is 2 and the intercept is 7.

5) y = -2x + 7 is in the slope intercept form. Its slope is - 2 and the intercept is 7.

Answer:

the answer would be: y = 2x + 7 .

Step-by-step explanation:

Answer:

The answer is c. 8 hours

Step-by-step explanation:

Since her battery dropped 25% in 2 hours then for it to drop 100% would take 8 hours.

25%+25%+25%+25%= 100%

so with this logic

25%= 2 hours

2+2+2+2=8

Hoped this helped !

Cheers, Z

Zoey can expect 8 hours of use from her iPad on a full battery charge (c).

To find the total hours Zoey can expect from her iPad on a full battery charge, we need to determine how many hours the battery percentage dropped for each hour of use.

If the battery dropped by 25% in 2 hours, that means it dropped by 12.5% (25% divided by 2) per hour.

To find the total hours, we divide 100% (full battery charge) by the percentage dropped per hour. In this case, 100% divided by 12.5% equals 8 hours.

Therefore, Zoey can expect 8 hours(c) of use from her iPad on a full battery charge.

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The space left inside the tree is 300 cubic feet.

David and Karen have to paint 275 square feet on the outside.

Explanation:

It is given that the length of the tree house is 7.5 feet

The width of the tree house is 8 feet

The height of the tree house is 5 feet

The tree house is in the shape of a rectangular prism.

The volume of the rectangular prism is given by

[tex]\text {Volume}=\text {length } \times \text {width} \times \text {height}[/tex]

Substituting the values, we have,

[tex]Volume$=7.5 \times 8 \times 5$\\Volume $=300$[/tex]

Thus, the volume of the rectangular prism is 300 cubic feet

Hence, the space left inside the tree is 300 cubic feet.

The area they have to paint on the outside can be determined using the formula for surface area of the prism .

[tex]Area=2(w l+h l+h w)[/tex]

Substituting the values, we get,

[tex]Area=2[(8*7.5)+(5*7.5)+(5*8)][/tex]

Multiplying the terms within the bracket, we get,

[tex]Area=2(60+37.5+40)[/tex]

Adding the terms, we have,

[tex]Area=2 \times 137.5[/tex]

Multiplying, we get,

[tex]Area =275[/tex]

Thus, David and Karen have to paint 275 square feet on the outside.

V= L x W x H

Leight x with x height = V

5 x 8 x 7.5= V

=300feet2

Step-by-step explanation:

Hope it helps

Final answer:

George will weigh 172 pounds after four years of college, gaining 0.25 pounds per month. If he continues this trend for 10 more years, he will weigh 202 pounds at his 10-year college reunion.

Explanation:

To calculate the weight gain of George after college and for the next 10 years, we can use simple arithmetic. George starts at 160 pounds and gains 0.25 pounds each month.

Weight After College

Four years of college is equivalent to 4 years × 12 months/year = 48 months. If he gains 0.25 pounds each month, then over 48 months he will have gained:

0.25 pounds/month × 48 months = 12 pounds.

So, after college, his weight will be:

160 pounds + 12 pounds = 172 pounds.

Weight After Next 10 Years

To calculate his weight after the next 10 years, which is 10 years × 12 months/year = 120 additional months, we do the following calculation:

0.25 pounds/month × 120 months = 30 pounds gain.

Adding this to his weight after college:

172 pounds + 30 pounds = 202 pounds.

Therefore, for his 10-year college reunion, George will weigh 202 pounds.

The 6th value in a sequence is -26.

Step-by-step explanation:

an = -2n-14

⇒ a6 = -2(6)-14

⇒ a6 = -12-14

⇒ a6 = -26

∴ The 6th value in a sequence is -26.

Answer: You loss is 65bucks.

Step-by-step explanation:

First, you win 25 bucks.

Next, the past 10 weeks 50 bucks.

For 10 weeks, you lost 2 bucks everyday:

10 × 7= 70days × 2= 140bucks.

In total you won) 25 + 50= 75 bucks.

You dropped 140bucks in total.

140- 75= 65 bucks.

Therefore, You lost 65bucks.

This question deals with Mathematics, specifically the concept of profit and loss. Despite winning a total of $75 over 10 weeks at the slots, you lose $2 everyday, totaling to $140 in losses over the ten weeks. Hence, you end up with a net loss of $65.

The subject of this question is related to Mathematics and more specifically on the concept of profit and loss. Here you have won a total of $75 over 10 weeks, but each day you play slot machines you lose $2. Given that a week has 7 days, you’ve lost $2 * 7 days/week * 10 weeks = $140 over the course of 10 weeks. So, despite seeming to 'win' at the slot machine, when we subtract the total loss from total gain, $75 - $140, we find that you've actually ended up with a net loss of $65.

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Answer:

Option B.

Step-by-step explanation:

The given vertices of the polygon are (-6,-2),(-5,1),(-1,4),(1,1),(5,3),(1,-2).

We need to find the area of the polygon.

Plot the given vertices and on a coordinate plane and draw the polygon. Divide the polygon in 4 parts as shown below.

Area of rectangle is

[tex]A=length\times width[/tex]

Area of triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

Area of each figure is

[tex]A_1=\dfrac{1}{2}\times 1\times 3=1.5[/tex]

[tex]A_2=\dfrac{1}{2}\times 6\times 3=9[/tex]

[tex]A_3=\dfrac{1}{2}\times 4\times 3=6[/tex]

[tex]A_4=6\times 3=18[/tex]

Area of polygon is

[tex]A=A_1+A_2+A_3+A_4[/tex]

[tex]A=1.5+9+6+18=34.5[/tex]

The area of polygon is 34.5 units².

Therefore, the correct option is B.

Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.

It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.

2) Let S=Z and define R = {(x,y) |x and y have the same parity}

i.e., x and y are either both even or both odd.

The parity relation is an equivalence relation.

a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.

b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.

c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.

Step-by-step explanation:

1) By definition,

a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.

That is, x works at the same place of x.

b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx

That is if x works at the same place y, then y works at the same place for x.

c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz

That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.

2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.

QED!

Answer:

[tex]\angle ACD=124\°\\\\\angle CED=64\°[/tex]

Step-by-step explanation:

To solve this exercise you need to remember:

1. The sum of the Interior angles of a triangle is 180 degrees.

2. Straight angles are those angles that measure 180 degrees.

3. Supplementary angles are those angles whose sum is 180 degrees.

4. Vertical angles are angles that share the same vertex and they are opposiste to each other. They are congruent.

Knowing the above, you can set up the following equation:

[tex]31\°+93\°+\angle ACB=180\°[/tex]

Solving the equation, you get:

[tex]\angle ACB=180\°-124\°=56\°[/tex]

Since [tex]\angle ACB[/tex] and [tex]\angle DCE[/tex] are Vertical angles:

[tex]\angle ACB=\angle DCE=56\°[/tex]

Knowing the measure of [tex]\angle DCE[/tex]  , you can write the following equation to find [tex]\angle CED[/tex]:

[tex]56\°+60\°+\angle CED=180\°[/tex]

Solve the equation:

[tex]\angle CED=180\°-116\°=64\°[/tex]

As you can observe in the figure, the angles [tex]\angle DCE[/tex] and [tex]\angle ACD[/tex] are Supplementary. Then:

[tex]\angle ACD+\angle DCE=180\°\\\\\angle ACD+56\°=180\°[/tex]

Solving for [tex]\angle ACD[/tex], you get:

[tex]\angle ACD=180\°-56\°=124\°[/tex]

Explanation:

A yard is a larger unit of measure than an inch, so it takes fewer yards to equal the distance of a larger number of inches.

__

As it happens, 1 yard is exactly the same as 36 inches (by definition). So the measurement that is 36 inches will be a measurement that is 1 yard.

Final answer:

Josh's desk appeared to have different measurements because of the change in units from inches to yards; 1 yard is equal to 36 inches, so the desk's height didn't actually decrease.

Explanation:

The question seems to contain a typo. Assuming the question should read as 'Josh's desk is 36 inches tall, when he measured the desk using a yard stick, it was 1 yard tall,' the discrepancy in numbers is because of the different units used to measure the desk. There was no actual decrease in size; it is merely a difference in the units of measurement. Inches and yards are both units used to measure length or height, with 1 yard being equivalent to 36 inches. When Josh used a yard stick, he measured the desk in yards, which is a larger unit compared to inches. This is why the number appears to be smaller (1 instead of 36), even though the height of the desk remained the same.

Answer:

8

Step-by-step explanation:

Hi,

When we divide 5655 by N, we get remainder of 11, which means that 5655-11 is a multiple of N.

5655 - 11 = 5644 is a multiple of N.

Similarly, 5879-14 should be a multiple of N.

5879 - 14 = 5865 is a multiple of N.

Because 5644 and 5865 are both multiples of N, their difference must be a multiple of N.

5865 − 5644 = 221 then 221 is a multiple of N.

We have three number of which N can be a multiple of, however we choose to factorize the smallest possible number amongst these three, which is 221. (This is only for simplification of the solution, smaller the number, less the factors)

221 : 1, 13, 17, 221.

There are only two two - digit factors: 13 and 17.

We divide 5865 and 5644 by both numbers.

[tex]\frac{5865}{13} = 451.15 \\\frac{5865}{17} = 345 \\\frac{5644}{13} = 434.15 \\\frac{5644}{17} = 332\\[/tex]

Looking at these results, we know only 17 divides all three numbers.

Hence N=17.

The sum of both digits will be: 1 + 7 = 8

Subtract the two given numbers excluding their identical remainders to find a multiple of the divisor N. By then finding a two-digit factor of this multiple that can divide both numbers, we get N = 28. The sum of its digits is 10.

When a number is divided by a divisor and leaves the same remainder, the difference between these numbers is a multiple of that divisor. Therefore, as given, when 5655 is divided by a positive two-digit integer N, the remainder is 11, and also when 5879 is divided by N, the remainder is 11. To find N, we subtract the two numbers before considering the remainder, which will give us a number that is a multiple of N: 5879 - 5655 = 224.

So, N divides 224 perfectly. The factors of 224 that are two-digit numbers are 14, 16, and 28. However, since the remainder when dividing both 5655 and 5879 by N is identical and equal to 11, we need to make sure that both 5655-11 and 5879-11 are divisible by N equally, thus 5644 and 5868 should be divisible by N. The correct N which fulfills this condition is 28.

The sum of the digits of N or 28 is: 2 + 8 = 10.

Answer:

Step-by-step explanation:

Triangle BCZ is a right angle triangle. Triangle BCU is also a right angle triangle. Side BU is common to both triangles.

To determine m∠ZBC, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan B = 8/6 = 1.33

m∠ZBC = Tan^-1(1.33) = 53.06

m∠UBC = m∠ZBC/2 = 26.53

To determine CU, we would apply

the tangent trigonometric ratio.

Therefore,

Tan 26.53 = CU/6

CU = 6Tan26.53

CU = 6 × 0.4992

CU = 2.9952

Answer:

20 percent

Step-by-step explanation:

Percentage score = [tex]\frac{actual score}{total score}[/tex] × 100

                              = [tex]\frac{6}{30}[/tex] × 100

                               = 20 percent