Explain how linear equations can be used in temperature conversion.

Answer:

I sell 12 bracelets and 24 necklaces.

Step-by-step explanation:

The selling price of each bracelet is $2 and that of each necklace is $3.

I collect $96, selling a total of 36 jewelry items.

Let us assume that I sell x bracelets and y necklaces.

So, x + y = 36 ........ (1) and  

2x + 3y = 96 .......... (2)

Now, solving equations (1) and (2) we get, 3y - 2y = 96 - 72

⇒ y = 24

Hence, from equation (1) we get x = 36 - y = 36 - 24 = 12

Therefore, I sell 12 bracelets and 24 necklaces. (Answer)

Answer:

Part a) [tex]AC=135.95\ m[/tex]

Part b) [tex]BC=124.14\ m[/tex]

The diagram in the attached figure

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]

substitute the given values

[tex]53^o+61^o+m\angle C=180^o[/tex]

[tex]114^o+m\angle C=180^o[/tex]

[tex]m\angle C=180^o-114^o[/tex]

[tex]m\angle C=66^o[/tex]

step 2

Find the distance AC

Applying the law of sines

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

see the attached figure to better understand the problem

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}[/tex]

[tex]AC=\frac{142}{sin(66^o)}(sin(61^o))[/tex]

[tex]AC=135.95\ m[/tex] ---> rounded to the nearest hundredth

step 3

Find the distance BC

Applying the law of sines

[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}[/tex]

[tex]BC=\frac{142}{sin(66^o)}(sin(53^o))[/tex]

[tex]BC=124.14\ m[/tex] ---> rounded to the nearest hundredth

Step-by-step explanation:

I don't know if this helps, but none of the above.

first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)

P.S. but 83 degrees and 7 degrees would be complementary...

hope you at least know why i say none of the above

Answer:

800

Step-by-step explanation:

Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number

Answer:

832 --> ???

832 - we must round the underlined digit

832 --> ???

832 --> 800

The rounding rule is:

4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].

So with that rule, 832 becomes 800.

800 is your answer.

I hope this helps!

Question:

You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence.  What fraction of the fence did you paint?

Answer:

The fraction of the fence painted is [tex]\frac{1}{12}[/tex]

Solution:

Given that:

You have a 32-foot fence around a square garden. There are 4 equal sections

Find the length of each section:

4 sections = 32 foot

[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]

Find the length that is painted:

[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]

Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted

Find the fraction that that is painted:

Total length of fence = 32

[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]

Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted

The profit Haddie makes from selling scarves at a craft fair can be represented by the algebraic expression P = 12s - 25. Here, P represents profit, s represents the number of scarves sold, 12 represents the price of each scarf, and 25 represents the cost of booth rental.

The subject of the question deals with the concept of profit in a business transaction, which falls under Mathematics, specifically algebra and economics. It's a High School level problem since it involves creating a basic algebraic expression.

Haddie's profit can be determined by subtracting her costs (the booth fee) from her earnings (the sale of the scarves). She earns $12 for each scarf sold, represented as 12s (where s is the number of scarves sold), and she has a fixed cost of $25 for the booth rental.

Therefore, the expression for Haddie's profit, P, for selling s scarves is: P = 12s - 25. This expression represents the total amount Haddie will earn from selling s scarves after deducting her cost for the booth rental.

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Answer:

Option 1 is correct.

Step-by-step explanation:

Let there is a line A which is perpendicular to line L at point O.

Now, rotating line A about point O by 360° will give the plane R.

So, plane R is perpendicular plane to line L.

Again, let there is a line B which is perpendicular to line L at point P.

Now, rotating line B about point P by 360° will give another plane S.

So, plane S is perpendicular plane to line L.

Since line A and line B are parallel (As they are perpendicular to the same line L) so, plane R containing line A and plane S containing line B will also be parallel to each other.  

Hence, option 1 is correct. (Answer)

Answer: 11,056.1

Step-by-step explanation: Because you have to add the first 7

Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.

To find the total amount that Jerome has paid in interest over the 7 months, we need to sum up the interest paid each month. The interest for each month is calculated as follows:

[tex]\[ \text{Interest for the month} = \text{Previous balance} \times \text{APR} / 12 \][/tex]

Let's calculate the interest for each month:

1. For the second month:

 [tex]\[ \text{Interest} = \$2200.00 \times 0.18 / 12 = \$33.00 \][/tex]

2. For the third month:

[tex]\[ \text{Interest} = \$2189.00 \times 0.18 / 12 = \$32.84 \][/tex]

3. For the fourth month:

[tex]\[ \text{Interest} = \$2178.06 \times 0.18 / 12 = \$32.67 \][/tex]

4. For the fifth month:

[tex]\[ \text{Interest} = \$2167.16 \times 0.18 / 12 = \$32.51 \][/tex]

5. For the sixth month:

[tex]\[ \text{Interest} = \$2156.33 \times 0.18 / 12 = \$32.34 \][/tex]

6. For the seventh month:

 [tex]\[ \text{Interest} = \$2145.55 \times 0.18 / 12 = \$32.18 \][/tex]

Now, sum up these monthly interest amounts:

[tex]\[ \$33.00 + \$32.84 + \$32.67 + \$32.51 + \$32.34 + \$32.18 = \$195.54 \][/tex]

So, Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.

The ratio of time taken by Henry to time taken by Gavin is 3:5

Step-by-step explanation:

Time taken by Henry for each set = 36 minutes

Time taken by Gavin for each set = 1 hour

We will convert Gavin's time into minutes.

Time taken by Gavin for each set = 60 minutes

Ratio;

Time taken by Henry : Time taken by Gavin

[tex]36:60[/tex]

Dividing by 6

[tex]\frac{36}{6}:\frac{60}{6}\\6:10[/tex]

Dividing by 2

[tex]\frac{6}{2}:\frac{10}{2}\\3:5[/tex]

The ratio of time taken by Henry to time taken by Gavin is 3:5

Keywords: ratio, division

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Answer:

y+2=3/4(x-4)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-(-2))/(12-4)

m=(4+2)/8

m=6/8

m=3/4

----------

y-y1=m(x-x1)

y-(-2)=3/4(x-4)

y+2=3/4(x-4)

Answer:

3

Step-by-step explanation:

You want a number that if it is multiplied by 3 1/3 the result will be 10. Let the number be x

3 1/3 * x = 10                         Change to a mixed number

10/3 * x = 10                          Multiply by 3/10

(10/3)*x * 3/10 = 10 * 3/10     Combine

x = 10*3 / 10                          Simplify

x = 30/10 = 3

Answer:

3

Step-by-step explanation:

Answer:

1 liter × 0.2642 gallons liter × 33.817 fluid ounces gallon.

Step-by-step explanation:

Given:

1 gallon = 3.785 liters

We need to find how many fluid of ounce are there in 1 liter.

First we will find number of gallons in 1 liter.

We know that;

3.785 liters = 1 gallons

1 liters = number of gallons in 1 liter.

By using Unitary method we get;

number of gallons in 1 liter = [tex]\frac{1}{3.785}= 0.2642\ gallons[/tex]

Now we know that:

1 gallons = 128 fluid ounce

So 0.2642 gallons = Number of fluid ounce in 0.2642 gallons

Again by using Unitary method we get;

Number of fluid ounce in 0.2642 gallons = [tex]128 \times 0.2642\approx 33.817\ oz[/tex]

Hence we can say,

1 liter ×0.2642 gallons liter × 33.817 fluid ounces gallon.

Answer:

11/5

Step-by-step explanation:

5x-7=4

5x=4+7

5x=11

x=11/5

The required solution of the function at x = 4 is f(4) = 13.

Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,

f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13

Thus, the required solution of the function at x = 4 is f(4) = 13.

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Answer:

The midpoints of the given graph are ( - 1, 3 ).

Step-by-step explanation:

By the graph we have to given that the endpoints are  R ( -5, 4) and S (3, 2)-

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex]) and  ( [tex]x_{2}, y_{2}[/tex]  ) then the mid points C are-  

C = (  [tex]\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{2}[/tex] )

Here,

R ( - 5, 4 ) and S ( 3, 2 )

then the  midpoints C are-

C = ( [tex]\frac{ - 5 + 3}{2}[/tex] , [tex]\frac{4 + 2}{2}[/tex]

C= ( - 2/2 , 6/2 )

C = ( -1, 3 )

Hence the midpoints are ( - 1, 3 ).

Answer:

Step-by-step explanation:

[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]

Answer:

The equation to represent the distance traveled by Olive in here solar powered scooter can be given as:

D: [tex]m=30h[/tex]

Step-by-step explanation:

Given:

Speed of Olive's solar powered scooter = 30 miles/hour

[tex]m\rightarrow[/tex] miles traveled

[tex]h\rightarrow[/tex] hours of travel

To find the distance traveled by Olive.

Solution:

Distance traveled = [tex]Speed\ \times \ Time[/tex]

Thus, the equation to represent the distance traveled by Olive in here solar powered scooter can be given as:

[tex]m=30\times h[/tex]

∴ [tex]m=30h[/tex]

Option A and Option F

The expressions that represent the perimeter of rectangle are 4s + 1 and [tex]2(2s + \frac{1}{2})[/tex]

Solution:

From figure,

Length = s

Width = [tex]s + \frac{1}{2}[/tex]

The perimeter of rectangle is given as:

perimeter = 2(length + width)

Substituting the values we get,

[tex]perimeter = 2(s + s + \frac{1}{2})\\\\perimeter = 2(2s + \frac{1}{2})[/tex]

Thus option F is correct

On further simplification,

[tex]perimeter = 2(2s + \frac{1}{2})\\\\perimeter = 4s + 2(\frac{1}{2})\\\\perimeter = 4s + 1[/tex]

Thus Option A is correct

Jimmy can get -18 marks in the Mathematics competition based on his correct, incorrect, and unanswered answers.

To calculate the marks Jimmy can get, we need to consider the number of questions he answered correctly, incorrectly, and left unanswered. Since each question carries 10 marks for a correct answer and deducts 8 marks for a wrong answer, we can calculate his marks as follows:

To get the total marks, we add up his scores from each category:

Total marks = 30 - 48 + 0 = -18 marks.

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Answer:

  Yes

Step-by-step explanation:

2 × 2/3 = 4/3 yards of fabric needed for 2 scarves. This amount is less than 1 1/2 yards. The amount of fabric that Jessica has is more than 1 1/2 yards, so is more than enough.

Jessica can make 2 scarves.

Answer:

Brainly User: eletricblu3s@*********.com

Should college be free? It’s a classic question with a complicated and arguably unclear answer. The affordability of college education, as well as the current student debt crisis, is always one of the center-stage issues for presidential political seasons. In fact, many candidates build their platforms around college costs as a key issue.

As with any major decision, especially relating to higher education, there are pros and cons to consider. Let me help break down the positives and negatives of tuition-free college.

The PROS of Tuition-Free College

More Lower-Income Students Might Reach Graduation if There’s No Tuition

Some students drop out because they do not have the ability to pay for tuition all four years. Getting rid of tuition would eliminate this reason for not graduating. This would also serve to improve college graduation rates, as fewer students would feel the need to drop to part-time status or take a break from education for financial reasons.

Student Debt Will No Longer Crush the Younger Generations

If an American college student is able to graduate with less than $10,000 in student loan debt, they are considered lucky (the average is $37,000). However, students from other countries that don’t have tuition already have that luxury; most of their loans come from living expenses and books. Without the weight of student loan debt, more college graduates might buy houses rather than renting apartments. They might buy cars, spend more on healthy food, travel more: In essence, they could contribute more to the economy.

Students Might Have More Freedom to Choose a Major They Enjoy

Whether it is the influence of parents or knowing you need to pay loans back as quickly as possible, current students are often guided toward “practical” majors that have a more lucrative post-graduation income. If shelling out thousands upon thousands of dollars is no longer a factor, parents and students might feel more relaxed about studying for majors that don’t necessarily have a large paycheck associated with them. Interest and enjoyment from a field of study goes a long way in helping students stick with it and avoid burning out.

More People Would Go to College

By negating the large bill of a college education, we could see an increase in the number of students able to attend college. This then creates a more well-educated workforce and a population that has better critical thinking skills. This could lead to more innovation in all areas of society. This would also help people with financial need to earn an education

Answer:

[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]

Step-by-step explanation:

Given equation of line:

[tex]9x+5y=3[/tex]

To find the equation of line perpendicular to the line of the given equation and passes through point (4,-7).

Writing the given equation of line in standard form.

Subtracting both sides by [tex]9x[/tex]

[tex]9x-9x+5y=3-9x[/tex]

[tex]5y=3-9x[/tex]  

Dividing both sides by 5.

[tex]\frac{5y}{5}=\frac{3}{5}-\frac{9x}{5}[/tex]  

[tex]y=\frac{3}{5}-\frac{9x}{5}[/tex]  

Rearranging the equation in standard form [tex]y=mx+b[/tex]

[tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex]  

Applying slope relationship between perpendicular lines.

[tex]m_1=-\frac{1}{m_2}[/tex]

where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of perpendicular lines.

For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex]can be found by comparing [tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex] with standard form.

∴ [tex]m_2=-\frac{9}{5}[/tex]

Thus slope of line perpendicular to this line [tex]m_1[/tex] would be given as:

[tex]m_1=-\frac{1}{-\frac{9}{5}}[/tex]

∴ [tex]m_1=\frac{5}{9}[/tex]

The line passes through point (4,-7)

Using point slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex](x_1,y_1)\rightarrow (4,-7)[/tex] and [tex]m=m_1=\frac{5}{9}[/tex]

So,

[tex]y-(-7)=\frac{5}{9}(x-4)[/tex]

Using distribution.

[tex]y+7=(\frac{5}{9}x)-(\frac{5}{9}\times 4)[/tex]

[tex]y+7=\frac{5}{9}x-\frac{20}{9}[/tex]

Subtracting 7 to both sides.

[tex]y+7-7=\frac{5}{9}x-\frac{20}{9}-7[/tex]

Taking LCD to subtract fractions

[tex]y=\frac{5}{9}x-\frac{20}{9}-\frac{63}{9}[/tex]

[tex]y=\frac{5}{9}x+\frac{(-20-63)}{9}[/tex]

[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]

[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]

Thus, the equation of line in standard form is given by:

[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]

Answer:

v = 1/2(1 + i√23) ,  1/2(1 - i√23).

Step-by-step explanation:

-2v^2 - v + 12 =  -3v^2 + 6

-2v^2 + 3v^2 - v + 12 - 6 = 0

v^2 - v + 6 = 0

This will not factor so we could use the quadratic formula to solve it:

For the equation ax^2 + bx + c = 0 the roots are:

x = [ - b +/-  sqrt(b^2 - 4ac) ] / 2a.

So here we have:

v = [-(-1) +/- sqrt((-1)^1 - 4*1*6)] /  2

v = [ 1 +/- sqrt (-23)] / 2

= 1/2 +  i√23/2 ,    1/2 -  i√23/2

= 1/2(1 +  i√23) ,  1/2(1 -  i√23).

Answer:

The equation representing the statement is [tex](x-1)+x=6[/tex].

Step-by-step explanation:

Given:

Distance from Sue house to Gill house = 6 miles.

Let the distance from Gill to Taco Town restaurant be 'x'.

Also Given:

Sue lives 1 mile closer to Taco Town restaurant than Gill does.

Hence Distance from Sue to Taco Town restaurant will be = [tex]x-1[/tex]

We need to write the equation for the below statement.

the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.

Framing in equation form we get;

[tex](x-1)+x=6[/tex]

Hence the equation is [tex](x-1)+x=6[/tex].

Length and width of book is 5.91 inches and 2.36 inches respectively

Solution:

Given that a book is 15 centimeters long and 6 centimeters wide

To find: length and width of book in inches

From given question,

Length of book = 15 cm

Width of book = 6 cm

The conversion factor used is:

1 cm = 0.393701 inches

Therefore, length of book in inches is:

[tex]15 \text{ cm} = 15 \times 0.393701 \text{ inches }= 5.905515 \text{ inches }[/tex]

Rounding off rules:

First look at the digit to immediate right of rounding off digit

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

On rounding to nearest hundredth, ( two decimal places )

[tex]5.905515 \text{ inches } = 5.91 \text{ inches }[/tex]

Width of book in inches:

[tex]6 \text{ cm} = 6 \times 0.393701 \text{ inches } = 2.362206 \text{ inches }[/tex]

On rounding to nearest hundredth, we get 2.36 inches

Final answer:

The book measures approximately 5.91 inches in length and 2.36 inches in width.

Explanation:

To convert the dimensions of the book from centimeters to inches, we use the conversion factor that 1 inch is equal to 2.54 centimeters.

The length of the book in inches is calculated as follows:

Similarly, the width of the book in inches is:

Therefore, the book measures approximately 5.91 inches in length and 2.36 inches in width.

C(x) = 4x³+7x²-14x-6

Step-by-step explanation:

Given that the amount of water used in normal days is given by the equation;

W(x) = 5x³ +9x²-14x +9 -----(i)

The amount of decrease in water used is modeled by the equation;

D(x)= x³+2x² +15--------(ii)

To get the function C(x) that models the water used by the car wash on shorter day you subtract equation (ii) from equation(i)

 5x³ +9x²-14x +9

-  x³+2x² +15

-------------------------

4x³+7x²-14x-6

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Answer:

C(x) = 4x³ + 7x² − 14x - 6

Step-by-step explanation:

In a shorter day the water used by the car wash is computed as the difference between the original usage and the decrease, that is:

C(x) = W(x) - D(x)

Replacing with data:

C(x) = 5x³ + 9x² − 14x + 9 - (x³ + 2x² + 15)

C(x) = 5x³ + 9x² − 14x + 9 - x³ - 2x² - 15

C(x) = (5-1)x³ + (9-2)x² − 14x + (9-15)

C(x) = 4x³ + 7x² − 14x - 6

Step-by-step explanation:

4x > 36-4

4x > 32 (divide both sides of the inequality by 4 )

4x ÷ 4 > 32 ÷ 4

x > 8

Final answer:

To determine the solution set of the inequality 4x + 4 > 36, subtract 4 from both sides to get 4x > 32 and then divide by 4 to find x > 8. Any number greater than 8 is part of the solution set.

Explanation:

To find which number is in the solution set of the inequality 4x + 4 > 36, we need to solve for x by performing a series of steps:

Subtract 4 from both sides of the inequality to get 4x > 32.

Divide both sides of the inequality by 4 to solve for x, resulting in x > 8.

Thus, any number greater than 8 is in the solution set of the given inequality.

Answer:

The answer is 50.

Step-by-step explanation:

The answer is 50 because, the line that the Exterior angle is on is equal to 180. So you take the two interior angels and add them. Then subract that from 180 and you get 50.

Hope this helps :))

Answer:

The correct answer is 110°.

Step-by-step explanation:

The Exterior Angle Theorem states, "the exterior angle of a triangle is equal to the sum of its non-adjacent angles".

This means we would add 50 + 60 to get 110°.

Or we could look at the exterior angle and the adjacent angle to it. The two angles form a supplementary angle - this equals 180°. To find our answer this way, we subtract the known angle form 180:

180 - 70 = 110°

Hope this helps,

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Answer:

12 square units.

Step-by-step explanation:

I just took the test.

The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Solution:

Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall

A small tree in her back yard is about 7 times as the shurd

To find: height of tree

From given information,

Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]

Given that small tree in her back yard is about 7 times as the shurb

So we get,

height of tree = 7 times the height of shrub

[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]

Therefore on solving we get,

[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]

Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Answer:

D

Step-by-step explanation:

Using the rule of logarithms

log x - log y = log([tex]\frac{x}{y}[/tex])

Given

[tex]log_{7}[/tex]([tex]\frac{n}{2}[/tex])

= [tex]log_{7}[/tex] n - [tex]log_{7}[/tex] 2 → D

Answer:

yoink im eating them points nomnomnom

Step-by-step explanation: