simplify the polynomials:5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3

Answer:Temperature of 10 degrees

Step-by-step explanation:

The others involve a decrease of 10 units, justifying use of a megative number.

The situation would not be represented by the integer -10 is Temperature of 10 degrees.

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Integers come in three types:

Given:

The representation of integer -10.

first, You owe $10

Owning is taken which can be represented as -10.

Temperature of 10 degrees have no clear idea of above or below 0 degree.

and, hole 10 feet deep can be represented as -10.

if we take ground at 0 then the above will positive integer and depth will be negative integer.

Lastly, 10 yard penalty can be represented as -10.

Penalty means deduction which can be shown as negative integer.

Learn more about Integers here:

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C). The function is linear because it decreases at a constant rate.

y changes by -1 every time x changes by +2. When the rate of change is constant, the function is linear.

Answer:

D. 13

Step-by-step explanation:

Multiply the given equation by 39x/27:

... x = 9·39/27 = 39/3

... x = 13

______

The usual approach

You may have learned to "cross multiply" to eliminate fractions. That means you multiply by the product of the denominators, 39x:

... 9·39 = 27x

Now, you divide by the coefficient of x, which is 27.

... 9/27 · 39 = x = 39/3 = 13 . . . . . . in the end, the same as above

To find the unknown value in the given proportion, we can cross-multiply and solve for the variable.

To find the unknown value in the proportion 9/x = 27/39, we can cross-multiply. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and multiplying the denominator of the first fraction with the numerator of the second fraction. So, we have 9 * 39 = 27 * x.

Now, we can solve for x by dividing both sides of the equation by 27. So, x = (9 * 39) / 27. Simplifying further, we have x = 351 / 27 = 13.

Therefore, the unknown value in the proportion is 13. Hence, the correct option is D.

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$67.45

There are a couple of ways you can go at these.

1. Compute the tip, then add that to the bill.

... 15% × $58.65 = $8.7975 ≈ $8.80

... $58.65 + 8.80 = $67.45

2. Compute the effect of adding the tip, then use that result to multiply by the bill amount.

... bill + (15% × bill) = bill × (1 +0.15) = 1.15 × bill

... 1.15 × $58.65 = $67.4475 ≈ $67.45

_____

Comment on percentages

The symbol % is a fancy (shorthand) way to write /100. The terminology "per cent" means "per hundred" or "divided by 100".

So, 15% = 15/100.

From your knowledge of place value and the meaning of decimal numbers, you know 15/100 (fifteen hundredths) = 0.15 (fifteen hundredths).

_____

Comment on 15% tip

10% = 10/100 = 1/10 of something can be computed by moving the decimal point one place left (dividing by 10).

5% of something is half of 10% of it.

15% is the sum of 10% and 5%.

Your bill is 58.65, so 10% of the bill is 5.865 ≈ 5.87. Half that is 2.9325 ≈ 2.93. The sum of 10% and 5% will be 5.87 +2.93 = 8.80, the amount that is 15% of the bill. Often, the numbers are such that this arithmetic can be done in your head.

Answer:

Step-by-step explanation:

Given:

Length (l) = 12 cm

Width (w) = 4 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(12 + 4)

P = 2 (16)

P = 32

Answer:

58

Step-by-step explanation:

The midsegment has a length that is the average of the lengths of the parallel sides it is halfway between.

... LM = (38 +78)/2 = 116/2 = 58

Hi there! :)

Answer:

Subtract 43 from 20 raised to the 7th power; then multiply by 3. The answer is: 3,839,999,871

Step-by-step explanation:

"Subtract" means to take away a number from another.

" 20 raised to the 7th power" is the same thing as 20 exponent 7: [tex]20^{7}[/tex]

SO, you want to take away 43 from [tex]20^{7}[/tex] and then multiply the answer by 3:

([tex]20^{7}[/tex] - 43) × 3

[tex]20^{7} =[/tex] 1,280,000,000

(1,280,000,000 - 43) × 3

1,280,000,000 - 43 = 1,279,999,957

1,279,999,957 × 3

1,279,999,957 × 3 = 3,839,999,871

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

I got 3839999831

Step-by-step explanation:

So 20^7(calculator), then subtract and mult

Answer:

72.25 in^2

Step-by-step explanation:

Formula

Area = s^2 where s is the length of a side.

Given

s = 8.5 in

Solution

Area = s^2

Area = 8.5^2 = 8.5 * 8.5

Area = 72.25 in^2

Answer:

The greatest value is q-n

The smallest value is n-q

q is closest to 0

Step-by-step explanation:

The further to the left we go, the more negative it gets

n < q

from looking at the graph

n<q

Subtract q from each side

n-q < q-q

n-q < 0

This is less than 0

Now subtract n from each side

n<q

n-n < q-n

0 < q-n

This is greater than 0

Lets compare n-q  and q

n = -4

q = -1

n-q  = -4 --1 = -4 +1 = -3

-3 < -1

n-q < q

Lets look at q-n

-1 --4

-1 +4 = 3

q is closer to 0 than q-n

The greatest value is q-n

The smallest value is n-q

q is closest to 0

Answer:

2b³ +2a -2c . . . . degree 3 polynomial

Step-by-step explanation:

The monomials are ...

... 4a . . . . degree 1 in a

... -5b·b² = -5b³ . . . . degree 3 in b

... -3c . . . . degree 1 in c

... 7b³ . . . . degee 3 in b (like term with -5b³)

... +c . . . . degree 1 in c (like term with -3c)

... -2a . . . . degree 1 in a (like term with 4a)

So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.

The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)

... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms

... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms

... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms

In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.

... = 2b³ +2a -2c . . . . a 3rd degree polynomial

D. There are no solutions

First inequality:

... -16 ≥ 8x . . . . . . . add 8x-60 to the inequality

... -2 ≥ x . . . . . . . . divide by 8

Second inequality:

... -8 < 4x . . . . . . . . add 4x-58 to the inequality

... -2 < x . . . . . . . . . divide by 4

The problem statement requires a solution satisfy both conditions on x. The two solution sets are disjoint (have no points in common), so ...

... there are no solutions.

1.50

Let h and f represent the cost of 1 hamburger and 1 order of fries, respectively. Then you can write two equations for the cost of the orders.

... 5h +3f = 9.90

... 3h +5f = 8.50

Using Cramer's rule, the cost of a hamburger can be found to be ...

... h = (3·8.50 -5·9.90)/(3·3 -5·5) = (25.50 -49.50)/(9 -25)

... = -24/-16

... h = 1.50

The cost of one hamburger is 1.50.

_____

Formulation of Cramer's Rule

For equations ...

... ax +by = c

... dx +ey = f

The rule tells you ...

... x = (bf -ec)/(bd -ea)

... y = (cd -fa)/(bd -ea)

_____

Note that we have chosen this method of solution because we only needed the value of one of the variables. It is effectively the same as substitution (or elimination), but does all the steps in one formula.

Using the matrix solution methods on a calculator is another fast way to solve a pair of equations like this.

38 m/s

The formula tells you Rachael's distance to the exit decreases by 38 m for each passing second. Her speed is 38 m/s.

Answer:

38 m/ s

Step-by-step explanation:

We are given that Rachel is a stunt driver , and she escaping from a building .

D(t) models Rachel's remaining  distance ( in meters) a s  function of times t ( in seconds)

D(t)=-38 t+220

We have to find the speed of Rachel's

We know that speed is a absolute value of velocity

We are finding velocity

[tex]v=\frac{ds}{dt}[/tex]

[tex]v=\frac{d(-38t+220)}{dt}[/tex]

[tex]v=-38 m/s[/tex]

Speed=38 m/s

Hence, speed of Rachel's=38 m/s

Answer:

31.25 %

Step-by-step explanation:

The fraction bar also means divide:

5 / 16

=

5 Divided By 16

=

0.3125

0.3125 * 100

= 31.25

- I.A -

The fraction 5/16 is converted to a percent by dividing 5 by 16 and then multiplying the result by 100, which equals 31.25%.

To convert the fraction 5/16 into a percent, we want to know how many parts out of 100 this fraction represents.

A percent is a way of expressing a fractional amount as a part of 100.

To do this, we can set up a proportion or multiply the fraction by 100.

So, we take 5 divided by 16 and then multiply the result by 100.

Doing the math:

= (5 / 16) x 100

= 0.3125 x 100

= 31.25%.

Therefore, the fraction 5/16 expressed as a percent is 31.25%.

QUESTION 1a

The given polygon has vertices [tex]A(-2,3),B(3,1),C(-2,-1),D(-3,1)[/tex].

We plot the points and connect them to obtain the figure as shown in the attachment.

The polygon has four sides and two pairs of adjacent sides equal.

Therefore Polygon ABCD can be classified as a quadrilateral, specifically a kite.

QUESTION 1b

We can find the perimeter by adding the length of all the sides of the kite

[tex]Perimeter=|AB|+|BC|+|CD|+|AD|[/tex]

Or

[tex]Perimeter=2|AB|+2|AD|[/tex]

Recall the distance formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We use the distance formula to find the length of each side.

[tex]|AB|=\sqrt{(3--2)^2+(1-3)^2}[/tex]

[tex]|AB|=\sqrt{(3+2)^2+(1-3)^2}[/tex]

[tex]|AB|=\sqrt{(5)^2+(-2)^2}[/tex]

[tex]|AB|=\sqrt{25+4}[/tex]

[tex]|AB|=\sqrt{29}=5.385[/tex]

Length of side AD

[tex]|AD|=\sqrt{(-3--2)^2+(1-3)^2}[/tex]

[tex]|AD|=\sqrt{(-3+2)^2+(1-3)^2}[/tex]

[tex]|AD|=\sqrt{(-1)^2+(-2)^2}[/tex]

[tex]|AD|=\sqrt{1+4}[/tex]

[tex]|AD|=\sqrt{5}=2.24[/tex]

[tex]Perimeter=2(5.1)+2(2.236)[/tex]

[tex]Perimeter=10.77+4.472[/tex]

[tex]Perimeter=15.242[/tex]

The perimeter of the kite to the nearest tenth is 15.2 units

QUESTION 1c

The area of kite ABCD is twice the area of ΔABD

[tex]Area\:of\:ABD=\frac{1}{2}\times |BD| \times |AE|[/tex]

[tex]Area\:of\:ABD=\frac{1}{2}\times 6 \times 2[/tex]

[tex]Area\:of\:ABD=6\:square\units[/tex]

Therefore the are of the kite is

[tex]=2\times 6=12[/tex]

The area of the kite is 12 square units.

QUESTION 2a

The vertices of the given polygon are

[tex]P(-3,-4),Q(3,-3),R(3,-2),S(-3,2)[/tex].

We plot all the four points as shown in the diagram in the attachment.

The polygon has one pair of opposite sides parallel and has four sides.

The polygon is a quadrilateral, specifically a trap-ezoid.

QUESTION 2b

The area of the trap-ezoid can be found using the formula

[tex]Area=\frac{1}{2}(|RQ|+|PS|)\times |RU|[/tex].

We use the absolute value method to find the length of RQ,PS and RU because they are vertical and horizontal lines.

[tex]|RQ|=|-3--2|[/tex]

[tex]|RQ|=|-3+2|[/tex]

[tex]|RQ|=|-1|[/tex]

[tex]|RQ|=1[/tex]

The length of PS is

[tex]|PS|=|-4-2|[/tex]

[tex]|PS|=|-6|[/tex]

[tex]|PS|=6[/tex]

The length of RU

[tex]|RU|=|-3-3|[/tex]

[tex]|RU|=|-6|[/tex]

[tex]|RU|=6[/tex]

The area of the trap-ezoid is

[tex]Area=\frac{1}{2}(1+6)\times 6[/tex].

[tex]Area=(7)\times 3[/tex].

[tex]Area=21[/tex].

Therefore the area of the trap-ezoid is 21 square units.

QUESTION 2c

The perimeter of the trap-ezoid

[tex]=|PQ|+|RS|+|QR|+|PS|[/tex]

We use the distance formula to determine the length of RS and PQ.

[tex]|RS|=\sqrt{(3--3)^2+(-2-2)^2}[/tex]

[tex]|RS|=\sqrt{(3+3)^2+(-2-2)^2}[/tex]

[tex]|RS|=\sqrt{(6)^2+(-4)^2}[/tex]

[tex]|RS|=\sqrt{36+16}[/tex]

[tex]|RS|=\sqrt{52}[/tex]

[tex]|RS|=7.211[/tex]

We now calculate the length of PQ

[tex]|PQ|=\sqrt{(3--3)^2+(-3--4)^2}[/tex]

[tex]|PQ|=\sqrt{(3+3)^2+(-3+4)^2}[/tex]

[tex]|PQ|=\sqrt{(6)^2+(1)^2}[/tex]

[tex]|PQ|=\sqrt{36+1}[/tex]

[tex]|PQ|=\sqrt{37}[/tex]

[tex]|PQ|=6.083[/tex]

We already found that,

[tex]|PS|=6[/tex]

and

[tex]|RQ|=1[/tex]

We substitute all these values to get,

[tex]Perimeter=6+1+7.211+6.083[/tex]

[tex]Perimeter=20.294[/tex]

To the nearest tenth, the perimeter quadrilateral PQRS is 20.3 units.

QUESTION 3a

The given polygon has vertices

[tex]E(-4,1),F(-2,3),G(-2,-4)[/tex]

We plot all the three points to the polygon shown in the diagram. See attachment.

The polygon has three unequal sides, therefore it is a triangle, specifically scalene triangle.

QUESTION 3b

We can calculate the area of this triangle using the formula,

[tex]Area=\frac{1}{2} \times |FG| \times |EH|[/tex] see attachment

We can use the absolute value method to find the length of FG and EH because they are vertical or horizontal lines.

[tex]|FG|=|-4-3|[/tex]

[tex]|FG|=|-7|[/tex]

[tex]|FG|=7[/tex]

Now the length of EH is

[tex]|EH|=|-4--2|[/tex]

[tex]|EH|=|-4+2|[/tex]

[tex]|EH|=|-2|[/tex]

[tex]|EH|=2[/tex]

The area is

[tex]Area=\frac{1}{2} \times 7 \times 2[/tex]

[tex]Area=7[/tex]

Therefore the area of the triangle is 7 square units.

QUESTION 3c

The perimeter of the triangle can be found by adding the length of the three sides of the triangle.

[tex]Perimeter=|EF|+|FG|+|GE|[/tex]

The length of EF can be found using the distance formula,

[tex]|EF|=\sqrt{(-2--4)^2+(3-1)^2}[/tex]

[tex]|EF|=\sqrt{(-2+4)^2+(3-1)^2}[/tex]

[tex]|EF|=\sqrt{(2)^2+(2)^2}[/tex]

[tex]|EF|=\sqrt{4+4}[/tex]

[tex]|EF|=\sqrt{8}[/tex]

[tex]|EF|=2.828[/tex]

The length of EG can also be found using the distance formula

[tex]|EG|=\sqrt{(-4--2)^2+(1--4)^2}[/tex]

[tex]|EG|=\sqrt{(-4+2)^2+(1+4)^2}[/tex]

[tex]|EG|=\sqrt{(-2)^2+(5)^2}[/tex]

[tex]|EG|=\sqrt{4+25}[/tex]

[tex]|EG|=\sqrt{29}[/tex]

[tex]|EG|=5.385}[/tex]

We found [tex]|FG|=7[/tex]

The perimeter of the triangle is

[tex]Perimeter=5.385+7+2.828[/tex]

[tex]Perimeter=15.213[/tex]

Therefore the perimeter of the triangle is 15.2 units to the nearest tenth

See the attachment for graphs.

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

Answer:

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.

Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) The mean of a normal distribution is also the median. Half the population will have values above the mean. Half of 200 is 100, so ...

... 100 students will have grades above 70%.

b) 84% is 14% above the mean. Each 7% is 1 standard deviation, so 14% is 2 standard deviations above the mean. The empirical rule tells you 95% of the population is within 2 standard deviations of the mean, so about 5% of students (10 students) got grades higher than 84% or lower than 56%. The normal distribution is symmetrical, so we expect about 5 students in each range.

... about 5 students will have grades above 84%.

1. The number of students who received a grade greater than 70% is about 100.

2. The number of students who got a grade higher than 84% is about 195.

To find the number of students who received a grade greater than 70%,

you need to calculate the area under the normal distribution curve to the right of 70%.

Similarly, to find the number of students who got a grade higher than 84%,

you need to calculate the area under the normal distribution curve to the right of 84%.

You can use the z-score formula to convert the given grades to z-scores, then look up the corresponding areas in the standard normal distribution table.

For a grade of 70%:

[tex]\[ Z = \frac{X - \mu}{\sigma}[/tex]

[tex]= \frac{70 - 70}{7}[/tex]

= 0

For a grade of 84%:

[tex]\[ Z = \frac{X - \mu}{\sigma}[/tex]

[tex]= \frac{84 - 70}{7}[/tex]

[tex]\approx 2[/tex]

Then, you look up the corresponding areas in the standard normal distribution table:

Now, to find the number of students:

Students with grades greater than 70%:

Number of students = Total students × Area to the right of 70%

= 200 × (1 - 0.5000)

= 200 × 0.5000

= 100

Students with grades higher than 84%:

Number of students = Total students × Area to the right of 84%

= 200 × (1 - 0.0228)

≈ 200 × 0.9772

≈ 195

So, the number of students who received a grade greater than 70% is about 100, and the number of students who got a grade higher than 84% is about 195.

about 0.04023

My probability calculator says that probability is about 0.04023.

B. MN/LN = RS/QR

ΔQRS ~ ΔLMN so corresponding segments are ...

Corresponding segments have the same ratio. So, ...

... LM/LN = QR/QS . . . . does not match A

... MN/LM = RS/QR . . . . matches B

... LM/MN = QR/RS . . . . does not match C

... MN/LM = RS/QR . . . . does not match D

Answer:

The height of the Mantis is 145 feet

Step-by-step explanation:

There is a table with the roller coasters' heights at Cedar Point amusement park in the assignment that is missing from the post.

Looking up the info online, the Millennium Force is 310 feet tall.

The Mantis is 165 feet shorter than the Millennium Force.

So the height of the Mantis is 310 - 165 = 145 feet

To find the height of the Mantis roller coaster, subtract 165 feet from the height of the Millennium Force roller coaster.

The problem states that the Mantis is 165 feet shorter than the Millennium Force. To find the height of the Mantis, we need to subtract 165 feet from the height of the Millennium Force.

If we let x represent the height of the Millennium Force, then the height of the Mantis would be x - 165 feet.

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A)

B) It is a matter of definition: speed = distance/time. Speed is proportional to distance and inversely proportional to time.

Speed is defined as the ratio of distance to the time required to cover that distance:

... speed = distance/time

Solving this relation for time, we have ...

... time = distance/speed

a) For each of the modes of transportation, we can find the time by using this relation.

... motorcyle: (150 km)/(75 km/h) = 2 h

... bus: (150 km)/(60 km/h) = 2.5 h

... truck: (150 km)/(50 km/h) = 3 h

... bicycle: (150 km)/(20 km/h) = 7.5 h

b) For a given distance, speed and time are inversely related as a matter of definition.

The average rate of change of the function  (x) = (−2)x + 3 from x = 0 to x = 9 is calculated as  (9) -  (0) divided by 9 - 0, resulting in −2.

The average rate of change of a function over a given interval is calculated as the change in the function's value (((9)) -  (0)) divided by the change in the interval's value (9 - 0). For the function  (x) = (−2)x + 3, to find the average rate of change from x = 0 to x = 9, we must first evaluate the function at these points:

Now, subtract the value of the function at x = 0 from the value at x = 9 and divide by the change in x (9 - 0):

Average Rate of Change =  rac{(9) -  (0)}{9 - 0} =  rac{−15 - 3}{9} =  rac{−18}{9} = −2

Therefore, the average rate of change of the function over the interval from x = 0 to x = 9 is −2.

$392.16 in interest saved

The payoff in 1 year costs a total of 12 × $366.72 = $4400.64.

The payoff in 2 years costs a total of 24 × $199.70 = $4792.80.

Paying off the balance in 1 year saves interest charges of ...

... 4792.80 -4400.64 = $392.16

Answer:

y=1/2x+15

y=x/2+15

Step-by-step explanation:

Every y-value is the sum of one-half of x and 15.

y = 1/2 x+15

We can rewrite this as

x/2 +15

Answer:

B. -2

Step-by-step explanation:

We have been given an expression [tex]\frac{P}{3Q}[/tex] and we are asked to evaluate our expression, when P=-24 and Q=4.

Let us substitute P=-24 and Q=4 in our given expression.

[tex]\frac{-24}{3*4}[/tex]

Let us multiply 3 by 4.

[tex]\frac{-24}{12}[/tex]

[tex]-\frac{24}{12}[/tex]

Upon dividing 24 by 12 we will get,

[tex]-\frac{24}{12}=-2[/tex]

Therefore our expression simplifies to -2 and option B is the correct choice.

Answer:

86%

Wouldn't you just be finding the ratio of pennies to Canadian.

Step-by-step explanation:

The amount of pennies to Canadian pennies are 13/15

And the amount of Canadian pennies to pennies are 2/15

If you pick a random penny out of your pocket it would be a larger possibility to get the regular pennies.

So the ratio would be I think:

There would be an 86% more chance of grabbing a regular penny than the 13% chance of getting a Canadian penny.

The probability of not picking a Canadian penny from a total of 15 pennies, with 2 being Canadian, is 13/15 or approximately 86.7%.

To find the probability of not picking a Canadian penny (P(not Canadian)), we first consider the total number of non-Canadian pennies. Since there are 15 pennies in total and 2 of them are Canadian, there must be 15 - 2 = 13 non-Canadian pennies.

The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of picking a non-Canadian penny is:

P(not Canadian) = Number of non-Canadian pennies / Total number of pennies

P(not Canadian) = 13 / 15

This simplifies to approximately 0.867, or 86.7% when expressed as a percentage.

Answer:

A, D, and E

Step-by-step explanation:

So the function 350-45t for t hours means that he reads 45 pages every hour. So, going from 11 AM to 1 PM is two hours. Since his reading pace doesn't change, we just have to look for an answer that has a difference of two answers. The only answers that have a difference of two hours are A, D, and E.

To find the time periods during which Marco reads the same number of pages as he reads between 11 a.m. and 1 p.m., we need to solve the equation P(t) = 350 - 45t for t using the value of 260 pages read between 11 a.m. and 1 p.m. The time periods are from 9 a.m. to 11 a.m., and from 1:30 p.m. to 3:30 p.m.

To find the time periods during which Marco reads the same number of pages as he reads between 11 a.m. and 1 p.m., we need to determine the values of t that make P(t) = 350 - 45t equal to the number of pages read between 11 a.m. and 1 p.m. which is 350 - 45(2) = 260 pages.

Substituting this value into the equation, we get:

P(t) = 350 - 45t = 260

Solving for t, we have:

t = (350 - 260) / 45 = 2

So, Marco reads the same number of pages during the time period from 9 a.m. to 11 a.m., and also during the time period from 1:30 p.m. to 3:30 p.m.

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Answer:

A. (0,0) is a solution to n=m and to n=4m.

Step-by-step explanation:

The solution to the system is the point where the lines intersect. The lines do intersect: they are distinct and not parallel.

(x, y) = (0, 0) is the point of intersection

The solution point (0,0) satisfies both the system of equations n=m and n=4m, making statement A correct. The other statements are incorrect since (0,0) exists on both lines, which are not equivalent and not parallel.

The system of equations n=m and n=4m indeed has the solution point (0,0). To verify if the provided solution is correct, we can substitute the values into both equations. Substituting into the first equation, we get 0=0, which is true. Substituting into the second equation, we also get 0=0, which is true as well.

Given this assessment, the correct statement is A. (0,0) is a solution to n=m and to n=4m. The other options can be disregarded as follows: B is incorrect because (0,0) exists on both lines; C is incorrect because the two equations are not equivalent; D is incorrect because the lines intersect, proving they are not parallel.

Answer:

Length of wire = 50 ft

Step-by-step explanation:

In the figure below AB is the telephone pole and C is the point on the ground where wire is anchored.

so we have

AB= 45 ft

∠ACB= 64°

Let is assume the length of the wire be x ft

now in Δ ABC

[tex]sin C = \frac{AB}{AC}[/tex]

we can plug AB= 45, ∠C= 64°and AC=x

so we have

[tex]sin(64)[/tex]°[tex]=\frac{45}{x}[/tex]

[tex]xsin(64)[/tex]°[tex]=45[/tex]

[tex]x=\frac{45}{sin(64)}[/tex]

now we have sin 64°=0.8988

[tex]x=\frac{45}{0.8988}[/tex]

[tex]x=50.07[/tex] ft

rounding to nearest foot

x= 50 ft

Final answer:

To find the length of the wire attached to a telephone pole at a 64-degree angle, we use the tangent function, resulting in an approximate wire length of 22 feet to the nearest foot.

Explanation:

The question asks how long a wire is if it's attached to the top of a 45-foot telephone pole and anchored to the ground, with an angle of elevation of 64 degrees.

To solve this, we can use trigonometry, specifically the tangent function, because we know the opposite side (height of the pole) and are trying to find the hypotenuse (length of the wire).

The tangent of an angle in a right triangle is the opposite side divided by the adjacent side. In this scenario, the angle of elevation is 64 degrees and the opposite side (height of the telephone pole) is 45 feet.

To find the length of the wire (hypotenuse), we use the formula: length of wire = opposite side / tan(angle), which translates to length of wire = 45 / tan(64 degrees).

Using a calculator, we find that tan(64 degrees) is approximately 2.05.

Therefore, the length of the wire is approximately 45 / 2.05, which equals about 21.95 feet.

To the nearest foot, the wire would be 22 feet long.