find the slope line 2x + 5y = 21

The relationship of the battery represent a proportional relationship and the constant is 7.7 pounds.

From the information, 6 car batteries weigh 46.2 pounds. The weight per battery will be:

= 46.2 / 6

= 7.7 pounds

Also, rourteen car batteries weigh 107.8 pounds, the weight per battery will be:

= 107.8 / 14

= 7.7 pounds

The constant of proportionality is 7.7.

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Answer:

Okay, so let's make the variable x the 60% juice.

The equation:

0.60(x) + 1(120-x) = 0.7(120)

Multiply both sides by ten for easier calculation:

6x + 1200 - 10x = 840

Put x on one side and the numbers on the other:

-4x = -360

the negatives cancel out...

4x = 360

define x

x = 90

Step-by-step explanation:

Answer:

Step-by-step explanation:

so we need slope intercept form, which is  y=mx+b  ... just memorize this, you'll need it many many times

next we are told to find a line perpendicular to y= [tex]\frac{1}{8}[/tex]x+10

recall that the reciprocal of the slope will give us a perpendicular line with a sign change also.

then the slope m is:

m = -8

and we are given the point P(x1,y1) = (  -1,1)

now use the point-slope formula to find the equation to the line in the slope intercept form.

y-y1 = m(x-x1)

plug in our given info.

y-1 = (-8)(x-(-1))

y-1 = -8(x+1)

y-1= -8x -8

y = -8x -8+1

y=-8x-7

there is your slope intercept form of the equation  :)

The equation of the line that best describes the given table of ordered pair is y = x + 7

Equation of the line:

By using the slope and y intercept of the point, we can calculate the equation of the line as

y = mx + c

here m refers the slope and c refers the intercept.

Given,

Here we have the table of ordered pairs shows the coordinates of the two points on the graph of a line.

Now, we need to find the equation of the line that best suits this one.

In order to find the equation of the table, first we have to calculate the slope and the y intercept of the given table.

But in order to calculate the slope we need the points.

So, the point take has been taken by the table are

=> (-5, 2) and (0,7)

Now, the slope of the line is,

=> m = (0 - (-5))/ (7-2)

=> m = 5/5

=> m = 1

By looking into the point we have identified that the y intercept is 7,

Therefore, the equation of the line is

=> y = 1x + 7

=> y = x + 7

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Kala the trainer lasted 0.75 hours for each of the work out.

Let A represent plan A and B for plan B

On Wednesday there were 3 clients who did Plan A and 5 who did Plan B for a total of 6 hours. this is represented mathematically as

3A + 5B = 6 hours

On Thursday there were 9 clients who did Plan A and 7 who did Plan B for a total of 12 hours. this is represented mathematically as

9A + 7B = 12 hours

hence we have two system of equations with two unknown

9A + 7B = 12 hours

3A + 5B = 6 hours

solving the equation gives that A = B = 0.75 hours = 45 minutes

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The area of this triangle is 21 square units.

From the graph:

The length of the base = 4 + 3 units

= 7 units

The length of the height = 3 + 3

= 6 units

Area of the triangle = 1/2 b *h

= 1/2*7*6

= 1*42/2

= 42/2

= 21 square units.

Therefore the area of this triangle is 21 square units.

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The company's expected cash receipts for August from its current and past sales is $126220.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the sales for June, July, and August are $56000, $62000, and $52000 respectively.

The company collects 45% of sales in cash, therefore, for June month the cash collected by the company is,

June = 56000×45%

June =56000×45/100

June =25200

Therefore, the credit amount for June is,

56000 - 25200

=30800

The cash collected by the company for July is,

= 62000×45%

=  62000×45/100

= 27900

The company will also collect 60% of its credit from June sales in July, therefore, the total collected cash in July is,

July  = 27900 + 60% of 30800

July = 27900 + 60×30800/100

July = 46380

The remaining credit after July is,

62000-27900

= 34100

The cash collected for August is,

52000×45%

= 52000×45/100

= 23400

The company also collects cash credits in June and July. Therefore, The net cash collected by the company is,

August = 23400 + 30800×35% + 34100×60%

August = 23400 + 30800×35/100 + 34100×60/100

August = 23400 + 10780 + 20460

            = 54640

Therefore, the total cash collected by the company for august from its current and past sales is,

June + July + August

= 25200 + 46380 + 54640

= 126220

Hence, the company's expected cash receipts for August from its current and past sales is $126220.

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Part a; compounded semiannually (n = 2); CI =  $6,390.

Part b: compounded quarterly ( n = 4) ; CI =  $6,425

Part c: compounded monthly (n = 12): CI =  $6,450

Part d: compounded continuously; CI =  $6,467.

The compound interest is calumniated by formula.

A = P(1 + r/100n)∧nt

In which,

A  = amount after compounding

P = principal amount  ($20,000 )

n = number of time principal amount compounded in a year.

t = total time in years (7 years)

r= rate of interest (4%)

Part a; compounded semiannually (n = 2)

A = P(1 + r/100n)∧nt

A = 20,000(1 + 4/200)∧(2x7)

A = 26390

CI = A - P

CI =  26,390 -  20,000

CI =  $6,390.

Part b: compounded quarterly ( n = 4)

A = 20,000(1 + 4/400)∧(4x7)

A = 26425

CI = A - P

CI =  26,425 -  20,000

CI =  $6,425

Part c: compounded monthly (n = 12)

A = 20,000(1 + 4/1200)∧(12x7)

A = 26450

CI = A - P

CI =  26,450-  20,000

CI =  $6,450

Part d: compounded continuously.

P = P₀e∧rt

P = (20,000)(2.72)∧(0.04 x 7)

P = 20,000 x 1.32

P = 26,467

CI =  26,467 - 20, 000

CI =  $6,467.

Thus, the for compounded continuously is $6,467.

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The expression to represent the average rate of Priya is (5.6×2)÷13 and the average rate is approximately  0.86 miles per hour .

Laura jogs for 2 hours at the rate of 5.6 miles per hour.

Distance travelled = speed × time

= 5.6 × 2

= 11.2 miles

Priya jogs the same distance in 13 hours.

Now to calculate the average rate of Priya we haver to divide the total distance travelled by the total time taken to complete the journey.

Average rate of Priya:

= 11.2 / 13

= 0.86153

≈ 0.86 miles per hour

You will be better able to appreciate the pace of a journey if you are aware of average speed. The speed may occasionally fluctuate while travelling. The need of determining the average speed then increases in order to estimate how quickly the trip will be completed.

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The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))= -38

Given that,

All real numbers x are defined by the functions r and s.

r(x) =2x+1

s(x) =-2x²-2

We have to find the expression

r( s(-3))

Take the functions,

r(x) =2x+1

s(x) =-2x²-2

Now, Take

r( s(-3))

Substitute s function first

r(-2(-3)²-2)

r(-2(9)-2)

r(-18-2)

r(-20)

Now substitute r function

2(-20)+2

-40+2

-38

Therefore, The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))=-38=

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Answer:

  (a)  68 grams

  (b)  42.5%

Step-by-step explanation:

You mix 100 g of 35% copper with 60 g of 55% copper to form an alloy. You want to know the number of grams and the percentage of copper in the mixture.

The total amount of copper is ...

  0.35·(100 g) +0.55·(60 g) = 35 g + 33 g = 68 g

There are 68 grams of copper in the resulting mixture.

The percentage of copper in the mixture is ...

  (68 g)/(100 g + 60 g) × 100% = 68/160 × 100% = 42.5%

The resulting mixture is 42.5% copper.

By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is equal to 120.7°

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

In order to determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property. Mathematically, the exterior angle property can be used to model triangle EFG (ΔEFG) and this is given by:

m<G = m<E + m<F

Substituting the given parameters into the formula, we have;

m<G = 84.3° + 36.4°.

m<G = 120.7°.

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For the given composite function, then values of

(a) 63x + 8

(b) 63x + 56

(c) 81x + 80

(d) 49x

Composite functions:

An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)) is known as composite functions.

Given,

Here we have the functions f(x) = 9x + 8 and g(x) = 7x

Now, we have to find the composite function of each.

(a) The composite function is written as,

=> f(g(x)) =f(7x)

=> f(7x) = 9(7x) + 8

=> f(g(x)) = 63x+ 8

(b) The composite function is written as,

=> g(f(x))

=> g(f(x)) =g(9x + 8)

=> g(9x + 8) = 7(9x + 8)

=> g(9x + 8) = 63x + 56

(c) The composite function is written as,

=>  f(f(x))

=> f(9x +8) = 9(9x + 8) + 8

=> f(9x + 8) = 81x + 72 +8

=> f(9x + 8) = 81x + 80

(d) The composite function is written as,

=> g(g(x))

=> g(7x) = 7(7x)

=> g(7x) = 49x

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The bicycles which the shop should build to minimize the average cost per bicycle is 25 bicycles

Average cost function:

This is a quadratic function, So

Average cost is minimum when

x = - b / 2a

= -(-0.1) / 2(0.2)

= 0.1 / 0.4

x = 1/4

Number of bicycles which should to minimize average cost per bicycle = minimum average cost × total cost

= 1/4 × 100

= 25 bicycles

Therefore, the number of bicycles which will minimize the average cost function is ,25 bicycles.

Complete question:

Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+3.799, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

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Step-by-step explanation:

area of parallelogram = length × height

780 = 26 × height

height = 780/26 = 30cm

The expression we get after measuring prq is 5610x²+ 891x+33.

Given that,

p is 33, r is 17x+1 and q is 10x+1

We have to find the measure of prq.

Take the,

p is 33, r is 17x+1 and q is 10x+1

Now,

prq

By multiply we get an expression

Multiplying each term to each other.

(33)(17x+1) (10x+1)

1st multiply 33 to 17x+1

(561x+33) (10x+1)

Now multiply each 561x with 10x+1 and 33 with 10x+1

5610x²+ 561x+ 330x+33

Adding 561x and 330x

5610x²+ 891x+33

Therefore, The expression we get after measuring prq is 5610x²+ 891x+33.

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Answer:

0

Step-by-step explanation:

3.5m + 2.5 = 79.5 is the equation that could be used to determine m, the number of miles in the taxi ride.

Given in question,

Pick-up fee = $2.50

Fee per mile = $3.50

Total fare = $79.50

Let the no. of miles = m

Fee for m miles = 3.50m

Equation, 3.50m + 2.50 = 79.50.

Hence, the equation is 3.50m + 2.50 = 79.50.

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Answer:yes its 15

Step-by-step explanation:

The polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.

Given:

polynomial function s(x) if s(−5)=−4 .

x = -5 when substitute in s(x) the output is -4 which is not equal to zero so

x+5 is not a factor of s(x) is correct.

The factor theorem tells you that a polynomial f(x) has a factor (x - k) only when f(k)=0 . So if s(-5) is not 0, we can draw the conclusion that (x+5) is not a factor of s(x).

Therefore the polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.

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Answer:

x=47

Step-by-step explanation:

Sum of all three angles of a triangle is 180 degrees

We know one angle which is 51 degrees

The second is 73 degrees since it’s corresponding angle is 73 degrees

73+51=124

Now subtract this from 180

180-124=56

We can set x+9 equal to this

X+9=56

  -9.  -9

x=47

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The amount that the patient is receiving, in mcg/min, using proportions, is of:

1008 mcg/min.

A proportion represents a unit rate relative to a total amount, and this unit rate is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

Considering than an hour has 60 minutes, the amount infused each minute is given as follows:

40.5/60 = 0.675 mL/min.

The rate of milligrams per milliliters is given as follows:

400/250 = 1.6 mg per mL.

Hence the number of mg received per minute is:

1.6 x 0.675 = 1.08 mg per minute.

1 mg equals 1000 mcg, hence the number of mcg received per minute is:

1.08 x 1000 = 1008 mcg/min.

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Answer:25/.2

Step-by-step explanation:

i think this is right

Answer:

The answer would be 4 7/24

Step-by-step explanation:

We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount.

The LCM (least common multiple) for your question would be 24, so you would multiply in order to get the fractions to have a common denominator of 24, while keeping the same value.

Answer:no

Step-by-step explanation:

No because 2 5's in x

Order of the tiles D, C, E, A

A square root of a number is a value of a number(other than the original number) that when multiplied by itself gives the original number. A square root of a number will be in the form of a².

Here are some examples of the square root of a number

√4 = 2 [ since 2 × 2 = 4 ]

√9 = 3 [ since 3 × 3 = 9 ]  

Here we have

1. √90 - √40

2. (√35 - √42) / (√5 - √6)

3. 2√27 - √48  

4. (√54 -√24)/√18 - √8  

Each problem can be solved as given below

1. √90 - √40

= √9 × 10 - √4 × 10  

= 3√10 - 2√10

= √10 = 3.16227

2.  (√35 - √42) / (√5 - √6)  

= (√5 × √7 - √7 × √6 ) / (√5 - √6)  

= √7 [√5 - √6 ] / (√5 - √6)  

= √7  = 2.64575

3. 2√27 - √48  

= 2√9×3 - √16×3

= 6 √3 - 4√3

= 2√3 =  3.46410

4. (√54 -√24)/√18 - √8  

= (√9×6 - √4×6)/√9×2 - √4×2 )

= (3√6 - 2√6)/3√2 - 2√2 )  

= (√6) / √2 )

= 1.73205

The resultant decimal numbers are

3.16227, 2.64575, 3.46410, and 1.73205.

And the order of the decimal numbers is

1.73205 < 2.64575 < 3.16227 < 3.46410

Therefore,

Order of the tiles D, C, E, A

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Answer:

choose 3rd option

Step-by-step explanation:

Answer:

[tex]\frac{2x\sqrt{3y}}{{3y}}[/tex]

Step-by-step explanation:

Apply fractional law for squares:

[tex]\sqrt{\frac{4x^2}{3y}} = \frac{\sqrt{4x^2}}{\sqrt{{3y}}}[/tex]

Then simply:

[tex]\frac{2x}{\sqrt{{3y}}}[/tex]

Rationalize denominator:

[tex]\frac{2x}{\sqrt{{3y}}} \cdot \frac{\sqrt{{3y}}}{\sqrt{{3y}}} = \frac{2x\sqrt{3y}}{{3y}}[/tex]