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Answer:

67.98°

Step-by-step explanation:

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19/12

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Explanation:

Use the triangle inequality theorem to set up these three inequalities

If you were to apply substitution and solve for x, then you'd get these solutions in the order presented shown above

We'll ignore the third inequality. It's not very useful because we were already told that x > 0.

The first two inequalities combine to get 3/4 < x < 11/2

This is the range of possible x values so that triangle ABC is possible.

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

If we want angle CAB (or angle A for short) to be the largest of the triangle, then side BC must be the longest of the three sides.

The rule is: the largest angle is always opposite the longest side. This applies to triangles only.

Since BC is the longest side, this means BC > AB and BC > AC

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

Let's focus on the first inequality

BC > AB

x+7 > x+4

7 > 4

That's true regardless of what we pick for x. So BC is always longer than AB.

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

Now onto the second inequality

BC > AC

x+7 > 4x

7 > 4x-x

7 > 3x

3x < 7

x < 7/3

Now recall that we found earlier x > 3/4 or 3/4 < x

Combine 3/4 < x and x < 7/3 to get the compound inequality 3/4 < x < 7/3

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

Notice the middle part of that compound inequality is x and BC = x+7

If we were to add 7 to all three parts of the compound inequality, then we'll determine exactly the possible range of lengths for segment BC.

3/4 < x < 7/3

3/4+7 < x+7 < 7/3+7

3/4 + 28/4 < x+7 < 7/3 + 21/3

31/4 < x+7 < 28/3

31/4 < BC < 28/3

The length of segment BC is between 31/4 units and 28/3 units, excluding both endpoints. Those are the values of m and n in that order.

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

The last step is to compute n-m

n-m = (28/3) - (31/4)

n-m = (112/12) - (93/12)

n-m = (112-93)/12

n-m = 19/12 which points us to choice D.

Side note: 7/3 - 3/4 = 28/12 - 9/12 = (28-9)/12 = 19/12

Answer:

Refer to below!

Step-by-step explanation (a):

[tex]\rightarrow \dfrac{10^{3} \times 10^{4} }{10^{5} } \\\\\\ \rightarrow \dfrac{10^{3 + 4} }{10^{5} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ] \\\\\\ \rightarrow \dfrac{10^{7} }{10^{5} } \\\\\\[/tex]

[tex]\rightarrow 10^{7 - 5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}] \\\\\rightarrow 10^{2}[/tex]

Step-by-step explanation (b):

[tex]\rightarrow \huge{\text{(}{10^{4} \times \dfrac{10^{12} }{10^{7} }\huge{\text{)}[/tex]

[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{12 - 7} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]

[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{5} }\huge{\text{)}[/tex]

[tex]\rightarrow \huge{\text{(}{10^{4 + 5} }\huge{\text{)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]

[tex]\rightarrow{10^{9} }[/tex]

Step-by-step explanation (c):

[tex]\rightarrow \huge{\text{(}\dfrac{10^{5} }{10^{3} } }\huge{\text{)}[/tex]

[tex]\rightarrow \huge{\text{(}10^{5 - 3} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]

[tex]\rightarrow 10^{2} }[/tex]

Step-by-step explanation (d):

[tex]\rightarrow \dfrac{10^{4} \times 10^{5} \times 10^{6} }{10^{3} \times 10^{7} }[/tex]

[tex]\rightarrow \dfrac{10^{4 + 5 + 6} }{10^{3 + 7} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]

[tex]\rightarrow \dfrac{10^{15} }{10^{10} }[/tex]

[tex]\rightarrow 10^{15 - 10} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]

[tex]\rightarrow 10^{5} }[/tex]

Step-by-step explanation (e):

[tex]\rightarrow \dfrac{(10^{5})^{2} }{(10^{2})^{3} }[/tex]

[tex]\rightarrow \dfrac{10^{5 \times 2} }{10^{2 \times 3} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^{2} )^{5} = a^{2 \times 5} = a^{10} ][/tex]

[tex]\rightarrow \dfrac{10^{10} }{10^{6} }[/tex]

[tex]\rightarrow {10^{10 - 6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]

[tex]\rightarrow {10^{4}[/tex]

Answer:

by using pythagoras theorem

[tex] {h}^{2} = {p}^{2} + {b }^{2} \\ {28}^{2} = {17}^{2} + {es}^{2} \\ {28}^{2} - {17}^{2} = {es}^{2} \\ {es}^{2} = 495 \\ es = \sqrt{495} \\ es = 3 \sqrt{55} [/tex]

Answer:

(y^2 + 6)(y^2 - 6)

Step-by-step explanation:

First, substite variable x for y^2:

FOR x = y^2:

y^4 - 36

= (y^2)(y^2) - 36

= (x)(x) - 36

= x^2 - 36

Now, use the formula a^2 - b^2 = (a + b)(a - b):

x^2 - 36

= x^2 - 6^2

= (x + 6)(x - 6)

Finally, since the expression is factored for x, not y, substite y^2 in for x:

(x + 6)(x - 6)

= (y^2 + 6)(y^2 - 6)

[tex]= (y^2 + 6)(y^2 - 6)[/tex]

Answer:

2w-12

Step-by-step explanation:

Jose = 2x(Maria's weight) -12

j = 2w -12

Answer:

1:1000

2,100 kg

Step-by-step explanation:

A linear scale of 1:10 means a volume scale of 1:1000.

The ratio of the volumes is model:real = 1:1000.

The mass is proportional to the volume.

The real car has a volume 1000 times the volume of the model, so its mass is also 1000 times the mass of the car.

mass of real car = 1000 × 2.1 kg = 2100 kg

Answer:

C 5.55

Step-by-step explanation:

253/60 = 4.21

80/60 = 1.33

4.21 + 1.33 = 5.55

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well, we can take a peek at this from the standpoint of moving from the right towards 0, but never getting there.

[tex]e^{-\frac{5}{x}}\implies \cfrac{1}{e^{\frac{5}{x}}}\qquad \qquad \stackrel{x = 1}{\cfrac{1}{e^{\frac{5}{1}}}}\implies \cfrac{1}{e^5}\qquad \qquad \stackrel{x=0.000001}{\cfrac{1}{e^{\frac{5}{0.000001}}}}\implies \cfrac{1}{e^{500000}}[/tex]

as "x" is moving towards 0, the denominator is becoming larger and ever larger, whilst the numerator is remaining the same, thus the fraction is become ever smaller, going towards = 0.

Answer:

9

Step-by-step explanation:

Raising a number to the second means multiplying that number.  3 * 3 = 9

height = 10m

hope it helps...!!!

y = -1.5(x) + 0.5

slope:

⇒ (y2-y1)/(x2-x1)

⇒ (5-(-1))/(-3-1)

⇒ 6/-4

⇒ -1.5

equation:

⇒ y -(-1) = -1.5(x-1)

⇒ y + 1 = -1.5(x) + 1.5

⇒ y = -1.5(x) + 0.5

Answer: 150 kilometers

Step-by-step explanation:

if it's 30 units of 5 kilometers then you multiply it

5x30=150

Step-by-step explanation:

a circle with r=6 so the area for the circle is π*r^2

and the area for the rectangle in the meddle is 18*12 which 12 is the height of the rectangle

and the area for that shape equals the area for the circle plus the area for the rectangle

A proportion is a mathematical comparison between two ratios.

A ratio is a comparison between two numbers.

For instance, the ratio of apples to bananas in a fruit basket is 1 apple to 2 bananas:

This is proportional to the ratio of apples to bananas in another fruit basket, which is 2 apples to 4 bananas:

To write a proportion from this information, we can compare the ratios by makign them equal to each other:

We're given:

$118 per week is one ratio:

$472 per 4 weeks is another ratio:

Now, set them equal to each other to create a proportion:

Therefore, the proportion is [tex]\dfrac{118}{1}=\dfrac{472}{4}[/tex].

67 miles

On Monday, Jullo ran 39 miles.

On Tuesday, he ran 24 miles.

On Wednesday, he ran 4 miles.

Finding the total miles:

Total miles ran on Monday, Tuesday, and Wednesday = 39 + 24 + 4

                                                                                            = 67 miles

Answer:

The probability for A  is 1-0.1 is 90%

P(A)=90%

P(NOT B)=30%

P(A AND B)=0.9+0.7/2=1.6/2=80%

p(a and b) may be a little off.

Answers:

=======================================================

Work Shown:

P(A) = 1 - P(not A)

P(A) = 1 - 0.1

P(A) = 0.9

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

P(not B) = 1 - P(B)

P(not B) = 1 -0.7

P(not B) = 0.3

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

P(A and B) = P(A)*P(B) only when A and B are independent

P(A and B) = 0.9*0.7

P(A and B) = 0.63

Answer:

1.2kl

Step-by-step explanation:

1000grams=1kilogram

700+500=1200

so 1.2kilograms

Answer:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent. Using labels: If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF  

Step-by-step explanation:

qwe

Answer:

Step-by-step explanation:

Te processing fee was applied to the discounted price.

The discounted price is

Amount of fee is

Answer:

c. 15

Hope it helpz~

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Answer:

6 Hours

Explanation:

Linear Equation: mx+b=y

x variable: Hour

Hourly Fee: $15(x)

(Initial) Rent Fee: $25

Balance: $100

Equation:

15x+25=100

15x+25-25=100-25 -- Separate the constant terms from the x by subtracting 25 from both sides.

15x=100

15x/15=100/15 -- Isolate the x variable by dividing 15 from both sides.

x=6.6.. -- Round down to 6 (not 7) because you can't afford to snowboard for 7 hours with less than $15.

x=6 Hours

answer: 6 hours

Step-by-step explanation:

I did this on a paper

First of all, subtract 5 from both sides:-

13-5<z+5-5

13-5<z

8<z

Since 8 is less than z, z is greater than 8:-

[tex]\bigstar{\boxed{\pmb{z > 8}}[/tex]

Hence, all the numbers greater than 8 will make this inequality true.

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Let's solve your inequality step-by-step.

13<z+5

Step 1: Flip the equation.

z+5>13

Step 2: Subtract 5 from both sides.

z+5−5>13−5

z>8

Answer:

z>8

Step-by-step explanation:

He can find the area of the individual shapes the backyard is made up of, then take the sum.

A composite figure is made up of different shapes and hence their area might be difficult to determine.

In order to determine the area of such a complex shape, the area of the individual shapes is first determined and then sum up. The sum of their areas will give  the area of the composite figure

For your neighbour, he can find the area of the individual shapes the backyard is made up of, then take the sum.

Learn more on area of composite figure here: https://brainly.com/question/21135654

a) The preparation of the bank reconciliation statement on August 31 for Cullumber Company is as follows:

Balance as per bank statement            $16,780

Add uncredited deposits of 17,220

       Check #705 overstated                         36

Less uncashed checks                            (5,780)

Adjusted bank statement balance of $28,256

b) The preparation of the necessary adjusting entries on August 31 is as follows:

Debit Cash $2,050

Credit Accounts Receivable (EFT deposits) $2,050

Debit Accounts Receivable (R. Dubai) $197

Credit NSF charges $187

Credit Service charges $10

Debit Bank service charges $27

Credit Cash $27

Bank reconciliation is the comparison of an entity's records with those of its bank, to uncover any differences between these two sets of records of bank transactions.

Bank reconciliation is carried out by the preparation of a bank reconciliation statement, which outlines the deposits, withdrawals, and other activities affecting a bank account for a specific period.

Cash balance per books on August 31, 2021 = $26,420

Bank statement balance = $16,780

1. Uncredited deposit = $17,220

2. EFT deposits = $2,050

3. Outstanding checks:
Check #673 = $1,230

Check #710 = $2,330

Check #712 = $2,220

Total outstanding checks = $5,780 ($1,230 + $2,330 + $2,220)

4. NSF charge = $187

Service charge = $10

5. Bank service charges = $27

6. Check #705 overstated = $36 ($173 - $137)

Balance as per Cash Book        $26,420

EFT deposits                                $2,050

Less:

NSF charge                 187

Bank service charges 27                (214)

Adjusted cash book balance $28,256

Learn more about bank reconciliation statements at https://brainly.com/question/15525383

Answer:

A. $5,448

B. $102,800

If you need the rest of the parts:

C. $4,500

D. $20,500

E. $68,000

The income tax of $5,448.

The taxable income is $102,800

The tax that is imposed on all people and corporations is called income tax. The amount of individual income taxes is determined by the individual's income. Because the burden is assumed to fall on the payers, it is typically characterised as a direct tax. Corporate income tax is charged on net profits, which are determined as the difference between allowable costs and receipts.

From the graph,

it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.

Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.

His taxable income is $102,800 as shown in the graph below.

Learn more about Income tax here:

brainly.com/question/30157668

#SPJ2

Answer:

Draw line a through points A and B. Draw line b through point C and parallel to line a. Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'. It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees

Answer:

the cost of 9 articles is 40.5