Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -7.5 and 5.4

Answer:

Well, in the local reservoir we have an initial amount of water A.

And per hour, the amount of water in the reservoir decreases by 500 gals.

So after t hours, the amount of water in the reservoir is:

W = A - 500gal*t

This is a linear equation, so the model that fits best in the given situation is a linear model.

Where the only thing that you need to take in mind, is that the domain of this model is restricted:

This is because we can not have a negative amount of water in the reservoir, so the maximum value of t accepted is:

W = 0 = A - 500gal*t

t = A/500 hours

So the domain of this linear relation is:

t ∈ {0h, A/500 }

Answer: lin

Step-by-step explanation:

Answer: 10x^4y^5

Step-by-step explanation:

5x^3y^1•2x^1y^4

5•2=10

x^3•x^1=x^4

y^1•y^4=y^5

10x^4y^5

If both are complementary then their sum will be 90°

[tex]\\ \sf\longmapsto m<A+m<B=90[/tex]

[tex]\\ \sf\longmapsto 2x-10+x-2=90[/tex]

[tex]\\ \sf\longmapsto 2x+x-10-2=90[/tex]

[tex]\\ \sf\longmapsto 3x-12=90[/tex]

[tex]\\ \sf\longmapsto 3x=90+12[/tex]

[tex]\\ \sf\longmapsto 3x=102[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{102}{3}[/tex]

[tex]\\ \sf\longmapsto x=34[/tex]

Now

[tex]\\ \sf\longmapsto <A=2x-10=2(34)-10=68-10=58[/tex]

Answer:

Step-by-step explanation:

Given the expression (8x² −15x)−(x² −27x) = ax² +bx, we are to determine the value of b-a. Before we determine the vwlue of b-a, we need to first calculate for the value of a and b from the given expression.

On expanding the left hand side of the expression we have;

= (8x² −15x)−(x² −27x)

Open the paranthesis

= 8x² −15x−x²+27x

collect the like terms

= 8x²−x²+27x −15x

=  7x²+12x

Comparing the resulting expression with ax²+bx

7x²+12x =  ax²+bx

7x² = ax²

a = 7

Also;

12x = bx

b =12

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a is equivalent to 5

The value of b minus a is 5

Since the expression is

[tex](8x^2 -15x)-(x^2 -27x) = ax^2 +bx[/tex]

Here we have to expand the left-hand side of the expression so it should be like

[tex]= (8x^2 -15x)-(x^2 -27x)\\\\= 8x^2 -15x-x^2+27x\\\\= 8x^2-x^2+27x -15x\\\\= 7x^2+12x[/tex]

Now

[tex]7x^2+12x = ax^2+bx\\\\7x^2 = ax^2[/tex]

a = 7

Also;

12x = bx

b =12

So,

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a should be 5

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Answer:

(1c times 9/5) +32

That is the way  to figure out °1c as 33.8°

Hope it helped

Answer:

$19.15

Step-by-step explanation:

$1=0.626

$1/0.626=£1

$11.99=$11.99/0.626

=$19.15

Answer:

Step-by-step explanation:

 £ 0.626  =$ 1

£1 = $ [tex]\frac{1}{0.625}[/tex]

£ 11.99 = [tex]11.99*\frac{1}{0.625}= \frac{11.99*1000}{0.625*1000}\\\\[/tex]

           [tex]= \frac{11990}{626}\\\\[/tex]

          = $ 19.15

19.15 - 16.95 = $2.2

Jane pays $2.20  more dollars that George

Answer:

[tex]\frac{14}{55}[/tex]

Step-by-step explanation:

note that

n! = n(n - 1)(n - 2) .... × 3 × 2 × 1

Given

[tex]\frac{8!9!}{5!12!}[/tex]

Cancel the terms from 8! ( 5 × 4 × 3 × 2 × 1 ) with the same terms from

5! ( 5 × 4 × 3 × 2 × 1 ) leaving

8 × 7 × 6 = 336 on the numerator

Similarly

Cancel the terms from 9! and 12!

leaving 12 × 11 × 10 = 1320 on the denominator, thus simplifies to

[tex]\frac{336}{1320}[/tex]

= [tex]\frac{14}{55}[/tex]

Answer: 58unit²

Step-by-step explanation:

We will take 1 square as 1 unit

We will count the number of squares in in this figure.

Total squares = 58

Area = 58unit²

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Answer:

0.07245

Step-by-step explanation:

Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).

Answer:

(B) 9π in²

Step-by-step explanation:

I’m going to assume that by 6 inches you meant 6π inches.

If the circumference of a circle is 6π inches, then it’s radius will be half of 6 (because the circumference of a circle is [tex]2\pi r[/tex]).

[tex]6\div2=3[/tex]

So the radius is 3.

Now that we know the radius, we can find the area by using the equation [tex]\pi r^2[/tex].

[tex]\pi 3^2\\\pi9\\9\pi[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

2πr = 6, r = 3/π

πr² = π(3/π)² = 9/π in.²

Answer:

Step-by-step explanation:

Volume of the can is expressed as Length *Breadth* Height.

If the area of the can base is Length * Breadth

Volume of the can = area of the base of the can * Height

Given parameters

Volume of the can V = 3416.32cm³

Height of the can h = 17cm

Required

Area of the base of the can

Substituting the given parameters into the formula we have;

V = Ah

A = V//h

A = 3416.32/17

A = 200.96cm²

Hence, the area of the base of the can is 200.96cm²

Answer:

The load weight is 2.29 N

Step-by-step explanation:

We note that  at equilibrium, the sum of the moment and the sum of forces about a point is zero, therefore, we have;

∑M =0

∑F = 0

The parameters given are;

The distance of the load from the hinge = 35 cm

The distance of the load from the spring balance = 15 cm

The applied force on the spring balance = 4 N↑

The direction of the applied force on the spring balance = Upwards

Let the weight of the load = W↓

The direction of the weight of the load = Downwards

We use downward negative and upward positive coefficients for the forces

We take moment about the hinge as follows;

Sum of moments equals zero gives;

4 × (35 - 15) - W × 35 = 0

∴ 4 × (35 - 15) = W × 35

4 × 20 = W × 35

W = 4 × 20/35 = 2.29 N

The weight of the load = 2.29 N.

Answer:

The load weight is 2.29 N

hope it helps

Answer: Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

Step-by-step explanation:

Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function. Trigonometric functions have a periodic nature. As opposed to tangent and cotangent, which have period, sine, cosine, secant, and cosecant all have period 2.

Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. By using geometry to study astronomy, the field first appeared in the Hellenistic civilization during the third century BC. The earliest documented tables of values for trigonometric ratios (sometimes called trigonometric functions) such as sine were developed by mathematicians in India, while the Greeks concentrated on chord calculation.

Geodesy, surveying, celestial mechanics, and navigation are just a few of the fields where trigonometry has been used historically. The various identities of trigonometry are well recognized.

These trigonometric identities are frequently used to simplify, discover a more practical form for, or solve equations involving trigonometric expressions.

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complete question:

Explain what is meant by the period of a trigonometric function. what are the periods of the six trigonometric functions?

Answer:

classified info jk juss use a mf calculater

Step-by-step explanation:

Answer:

your inequality signs are correct so i'll skip those

-2.06, .9803

.67, .7486

Step-by-step explanation:

1.)

To do this one you need to standardize x by subtracting the mean and dividng by the standard deviation

(1000-3262)/1100= -2.056 which i will round to -2.06

with this as our z value use the table to find the associated probability

.9803

2.)

Same process

(4000-3262)/1100=.67

which has a probability of .7486

Answer:

Both ends go down

Step-by-step explanation:

The end behavior of the function are Both ends go down. Therefore, Option C is true.

Given that,

The function is,

[tex]f (x) = - 2 (x - 17)^4[/tex]

Now the given function is defined at x → ∞,

f (x) = - 2 × ∞

f (x) → - ∞

As x goes to -∞

f(-∞) = -2(-∞)⁴

= -2 (∞)

= -∞

So, Both ends go to  -∞, or go down

Hence, The end behavior of the function are Both ends go down.

Therefore, Option C is true.

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Step-by-step explanation:

1.answer is 6.9667738478

2 answer is 42.872454448

3answer is 14.1339764202

4answer is 0.0857449089.

Answer:

x = 0

y = -2

Step-by-step explanation:

2304.06 is written in expanded form

4 is unit place. So, 4 *10⁰ = 4 * 1 = 1    {Any integer to the power of 0 is 1}

x = 0

6 is hundredth place = 6 * 1/100 = 6*10⁻²

y= -2

Step-by-step explanation:

the absolute value simply removes a negative sign, if there is one. if there is no negative sign, it leaves the argument untouched.

so, we need to calculate the argument first :

2b + 4 = 2×-8 + 4 = -16 + 4 = -12

|-12| = 12

that's it.

Answer:

-2 + 2i

Step-by-step explanation:

[tex](1 + i)^{3}[/tex]

i = [tex]\sqrt{-1}[/tex]

[tex](1 + \sqrt{-1})^3[/tex]

[tex][(1 + \sqrt{-1})(1 + \sqrt{-1})] (1 + \sqrt{-1})[/tex]

distribute the first 2 expressions

(1 + 2[tex]\sqrt{-1}[/tex] - 1 ) [tex](1 + \sqrt{-1})[/tex]

distribute

1 + 2[tex]\sqrt{-1}[/tex] - 1 +

combine like terms

-2 + 2 [tex]\sqrt{-1}[/tex]

which is -2 + 2i

Answer:

Rs 400

Step-by-step explanation:

Let us assume that the cost price of the article = x

Selling price = S.P

Cost price = C.P

Loss = %Loss × C.P(percentage loss × Cost Price)

S.P = C.P - Loss

In the question, Loss = 20%

S.P = x - 20x/100

Find the Lowest Common Multiple

S.P= 100x - 20x/100

S.P = 80x/100.........Equation 1

In the question, we are told if the article was sold for RS 160 more, it would have made a profit of 20%

Profit = %profit × C.P(percentage profit × Cost Price)

S.P = C.P + Profit

In the question, profit = 20%

S.P = x + 20x/100

Find the Lowest Common Multiple

S.P= 100x + 20x/100

S.P = 120x/100.........Equation 2

Hence,

Equation 2 - Equation 1 = Rs 160

= 120x/100 - 80x/100 = 160

= 40x/100 = 160

Cross multiply

40x = 100 × 160

40x = 16000

x = 16000/40

x = Rs 400

Since x = Cost price, the cost price of the table = Rs 400

Answer:

Divide by -8.

Step-by-step explanation:

48 is a multiple of 8, an we are trying to isolate p, so you should divide both sides by +/- 8.

Answer:

Step-by-step explanation:

You would do 48 divided by -8, and your answer would be -6

And just to clarify, -8 times -6 = 48. (You can use a calculator if still unsure)

Answer:

67.02

Step-by-step explanation:

[tex]\\ \sf\longmapsto b^2x^2+a^2y^2[/tex]

[tex]\\ \sf\longmapsto b^2(asin\Theta)^2+a^2(bcos\Theta)^2[/tex]

[tex]\\ \sf\longmapsto b^2a^2sin^2\Theta+a^2b^2cos^2\Theta[/tex]

[tex]\\ \sf\longmapsto a^2b^2(sin^2\Theta+cos^2Theta)[/tex]

[tex]\\ \sf\longmapsto a^2+b^2(1)[/tex]

[tex]\\ \sf\longmapsto a^2b^2[/tex]

Answer:

Take a look at this: https://brainly.com/question/14269575?referrer=searchResults

Step-by-step explanation:

Answer:

Step-by-step explanation:

So we know that there are 213 oranges and Theresa fills each bag with 3 oranges, so we can represent each bag as 3x. She keeps filling until she reaches 51 oranges.

First. let's write this as an equation, She is starting with 213 oranges and filling x bags with 3 oranges to the point she has less than 51 oranges.

213 - 3x < 51

Now add 3x to both sides,

213 - 3x + 3x < 51 + 3x

213 < 51 + 3x

Now we subtract 51 from both sides,

213 - 51 < 51 - 51 + 3x

162 < 3x

Now we divide both sides by 3,

162/3 < 3x/3

We find the answer,

54 < x

x > 54 bags

Answer:

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

To solve for the variable, we must isolate the variable, which is x.

[tex]\sqrt{x+4} -3=1[/tex]

3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.

[tex]\sqrt{x+4} -3+3=1+3[/tex]

[tex]\sqrt{x+4} =1+3[/tex]

[tex]\sqrt{x+4} =4[/tex]

The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.

[tex](\sqrt{x+4})^2 =4^2[/tex]

[tex]x+4=4^2[/tex]

Evaluate the exponent.

4^2= 4*4=16

[tex]x+4=16[/tex]

4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.

[tex]x+4-4=16-4[/tex]

[tex]x=16-4[/tex]

[tex]x=12[/tex]

The solution to this equation is x=12.

Answer:

94.33

Step-by-step explanation:

add up all numbers then input into a percentage calculator

Percentage of flu vaccine has been given 94.33%

Percentage is defined as ratio expressed as a fraction of 100.

The physician have total 1500 flu injections

300 shots given in September,

450 shots given in October,

and 665 shots given in November,

Total flu vaccine has been given = 300+450+665 = 1415

Percentage of flu vaccine has been given = (1415/1500)×100%

Percentage of flu vaccine has been given = 0.9433×100%

Percentage of flu vaccine has been given = 94.33%

Hence, percentage of flu vaccine has been given 94.33%

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Answer:

32

Step-by-step explanation:

If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.