Joe uses metal rods to make triangular frameworks in which each side has a different length. He buys metal rods which have lengths 1 meter, 2 meters, 3 meters etc and he always keeps one rod of each length in stock. This diagram shows one of Joe's triangular frameworks.

Check the picture attached.

a, b, c are all integers and c>b> a. That is, c is the longest side, a is the shortest side and a, b, c are whole numbers.

1. How many different triangular frameworks can Joe make which have a longest side 7 meters long? using the rods he has in stock? Show your work.
2. Investigate this situation for other values of c.
3. Write down any generalizations you can make.​

Answer:

It would be C

Step-by-step explanation:

A negative times a negative is a positive, and 7 x 4 is 28

Answer: 28 positive C

Step-by-step explanation:

it C

Answer:

27-[38-{46-(15-13-2)}]

27-(38-(46-0)

2-(38-46)

27-(-8)

27+8

35

Is this better

Answer:

0

27

Step-by-step explanation:

HOPE IT HELPS (◕‿◕✿)

Answer:

In triathlon an athlete swims 750meter in 15minutes cycles at an average speed of 40km/h for 30minutes and runs 5km at an average speed of 3meter/second find his average speed for the entire competition giving your answer in km/h

The average speed for the entire triathlon = 21.229 km/hr

Step-by-step explanation:

Calculate the distance covered and time taken in the first part of the Triathlon in Kilometers and hours respectively - Swimming

Distance 750 meters ⇒  750/100= 0.75Km

Time = 15 minutes ⇒  15/60      =  0.25 hours

Calculate the distance and time in Km and hours in the second phase:

Time is 30 minutes = 30/60 = 0.5 hours

Speed = 40km/hr

Distance = speed × time = 40km/hr × 0.5 = 20km

Calculate the distance covered and time taken in the last phase of the triathlon: Running

Runs 5 Km - this is the distance

5km = 5000m

Speed = 3 meters/sec

Time = Distance / speed

      = 5000 m / 3m/s

      = 1666.66666667 s

Convert to hours

1666.66666667 /3600 = 0.46 hours

Final step is to calculate the average speed:

Average speed = total distance travelled / total time taken

Total distance in Km = 0.75 km + 20 km + 5 km = 25.75 km

Total time taken = 0.25 hours + 0.5 hours + 0.46 hours = 1.21296296296 hours

Average speed of the athlete = 25.75 km / 1.21296296296 hours

                                             = 21.229 Km/hr

The average speed for the entire triathlon = 21.229 km/hr

Answer:

Here, we will use the formula from trigonometry which defines a radian

we know that an angle is a radian when the length of the radius of the circle is equal to the length of the arc formed

hence, if the radius is r and the arc is r, the angle (in radians) will be 1

if the radius is r and the arc is 2r, the angle in radians will be equal to:

length of arc / radius = 2r/r = 2 radians

I believe this will explain what is actually happening in these type of questions

So, the equation:

Θ(in radians) = s / r (where the length of arc is s and the radius is r)

π/4 = s / 12

s = 3π or 9.42 inches

Answer:

Kade

Step-by-step explanation:

.53 is bigger than .52

Answer:

a random order

Step-by-step explanation:

because if you just hit shuffle it will be a random order

Answer:

2/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]D. \: \boxed{x>-1.75}[/tex]

Step-by-step explanation:

[tex]3 + 4x > -5 \\ 4x > - 5 - 3 \\ 4x > - 7 \\ x > - \frac{7}{4} \\ \\ x > - 1.75[/tex]

♨Rage♨

Answer:

B. x > -2

Step-by-step explanation:

Answer:

One ruler cost 0.60

Step-by-step explanation:

7.50(1) + 1.80(3) + 4x = 20 - 4.70

7.50 + 5.40 + 4x = 15.30

12.90 + 4x = 15.30

4x = 2.40

x = 0.6

After Sophia eats a red grape, the number of red grapes remaining in her bag is given by (12/63) * x - (3/7), and the number of green grapes remaining is given by (16/63) * x - (4/7).

Let's assume that Sophia initially has x grapes in her bag.

We are given that 4/9 of the grapes in her bag are red. This means that (4/9) * x grapes are red, and (5/9) * x grapes are green.

Sophia picks out a red grape and eats it. This means that there are now (4/9) * x - 1 red grapes remaining in her bag, and (5/9) * x green grapes remaining.

We are also given that 3/7 of the remaining grapes in her bag are red. This means that (3/7) * ((4/9) * x - 1) grapes are red, and the remaining (4/7) * ((4/9) * x - 1) grapes are green.

To find the values, we can simplify the expressions:

Number of red grapes remaining: (3/7) * ((4/9) * x - 1)

Number of green grapes remaining: (4/7) * ((4/9) * x - 1)

Simplifying further:

Number of red grapes remaining: (12/63) * x - (3/7)

Number of green grapes remaining: (16/63) * x - (4/7)

So, the number of red grapes remaining is (12/63) * x - (3/7), and the number of green grapes remaining is (16/63) * x - (4/7).

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Answer:

no enough information

Answer:

7

Step-by-step explanation:

According to the question,

f(x)= 3x + 4 and g(x) = 5x - 10 are equal.

So,

3x + 4 = 5x - 10

- 2x = - 10 - 4

-2x = -14

2x = 14

x = 7

Answer:

-10

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

−10

Answer:

-10

Step-by-step explanation:

3(-2)-4=

-6-4=-10

:)

Answer:

Step-by-step explanation:

Start at the left side and work your way over.

3 x 1 + 9 should be easy.  3 x 1 = 3 then + 9 = 12

The question says to report the answer as a decimal so now is the perfect time to convert those fractions into decimals.

1/10 = 0.1

1/100 = 0.01

1/1000 = 0.001

The columns are the same as whole numbers ( tens, hundreds, thousands, etc) except they go in the opposite direction (to the right instead of left).

The first column after the decimal is the tens; second column is hundreds and so on.

Back to the problem.  So far we did the first 3 numbers and are at the number 12.

Now you will multiply 12 and 0.1.  This answer is 1.2 which just moves the decimal place one spot toward the left.

Next you are adding 2 to the above number.  2 + 1.2 = 3.2

Now you are multiplying this number and 0.01.  Again it is just moving the decimal to the left but by two steps this time.  You'll have to add a zero in front of the 3 in order to do this so you now have 0.032

Again we will add 2 to this number which will now give you 2.032

Multiply this number and 0.001 which again moves the decimal to the left but 3 spaces this time.  Again you'll have to add zeros in front of the 2 in order to do this.  You end up with 0.002032

Answer:5.7

Step-by-step explanation:

Answer: 5.7

Step-by-step explanation:

Answer:

1 with 3

2 with 5

3 with 2

4 with 1

5 with 4

Step-by-step explanation:

sorry if its wrong im not really good at this

Answer:

WHAT?

Step-by-step explanation:

Answer:

I think it’s step 2 where she distributed the exponents incorrectly but she got it right so since no explanation is really needed then I guess it’s step 2.

step 1 where she divided 5 on both sides. Step 3 is also correct since the answer is 0. so step 2 had the mistake.

Answer:

Step one.

Step-by-step explanation:

She needed to move all terms to the left side of the equation and simplify, she should have subtracted 245 from both sides and ended up with an equation that looked like this:

5(x+7)^2-245=0

Note: ^2 is a superscript.

Answer:

c

Step-by-step explanation:

Answer:

5a-7b+c

Step-by-step explanation:

Combine and don’t forget to keep the signs

The expression after combing the like terms is 5a - 7b + c.

Like terms in an expression is defined particularly for the expression involving sum of numbers including variables.

Or in other words, the term only differ by a numerical factor. Their coefficients can be added to get the answer.

For example in the expression, 32a + 5a + 3c + a, we can add all the three terms 32a, 5a and a to get 38a.

The given expression is,

6a - 4b - 2a + c - 3b + a

The terms involving 'a' are one like terms, 'b' are another like terms and 'c' are another.

Add together 6a, -2a and a. Also add -4b and -3b. Term including 'c' is only one term.

6a - 4b - 2a + c - 3b + a = (6a - 2a + a) + (-4b - 3b) + c

                                       = 5a - 7b + c

Hence the expression 6a - 4b - 2a + c - 3b + a can be added together by combining like terms to get 5a - 7b + c.

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Answer:

33/6 or 11/2 or 5.5

Step-by-step explanation:

One way to solve this is by using a calculator and spitting out a answer, but just in case you're not allowed to use a calculator, here's how you would do it on paper.

[tex]\frac{7}{6} +\frac{13}{3}[/tex]

The two denominators are different, so we have to make them the same by multiply either side (sometimes both) to make the denominator the same.

[tex]\frac{7}{6} +\frac{13}{3}*2\\\\\frac{7}{6} + \frac{26}{6}[/tex]

Now the denominators are the same. Since the denominators are the same, we can ignore the denominator for now and focus on the numerators.

26 + 7 = 33

The numerator is 33 when adding the two fractions together. Now, to make your fraction complete attach the denominator we ignored.

Your final answer is : [tex]\frac{33}{6}[/tex] or a simplified version [tex]\frac{11}{2}[/tex] or 5.5.

Answer:

Step-by-step explanation:

[tex]7/6 + 13/3\\\\\mathrm{Least\:Common\:Multiplier\:of\:}6,\:3:\quad 6\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\=\frac{7}{6}+\frac{26}{6}\\\\\mathrm{Apply\:the\:fraction\:rule}:\\\quad \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\\\\\frac{7}{6}+\frac{26}{6}=\frac{7+26}{6}\\\\=\frac{33}{6}\\\\\mathrm{Factor\:the\:number:\:}\:33=3\times\:11\\\\=\frac{3\times\:11}{6}\\\\\mathrm{Factor\:the\:number:\:}\:6=3\times\:2\\=\frac{3\times\:11}{3\times\:2}\\[/tex]

[tex]\\\mathrm{Cancel\:the\:common\:factor:}3\\=\frac{11}{2}\\\\= 5\frac{1}{2}[/tex]

Answer:

1. consecutive interior angles

2. alternate exterior angles

3. alternate interior angles

4. alternate interior angles

5. alternate exterior angles

6. consecutive interior angles

7. not sure but i think it's corresponding angles

8. alternate interior angles

9. alternate exterior angles

10. corresponding angles

Answer:

fuesgsnjfd

Step-by-step explanation:

hsfhbsafd

your welcome bro

Answer:

B

Step-by-step explanation:

Answer:

129

Step-by-step explanation:

ok my friend the 2 angles are the same

Answer:

129 degrees

Step-by-step explanation:

I believe alternate interior angles are identical angles.

Answer:

25/3x - 61/3

Step-by-step explanation:

Step 1: Write expression

3(2x - 7) + 1/3(7x + 2)

Step 2: Distribute

6x - 21 + 7/3x + 2/3

Step 3: Combine like terms

25/3x - 61/3

Answer:

3,000,000

Step-by-step explanation:

60,000,000x34%=20,400,000

60,000,000x29%=17,400,000

20,400,000-17,400,000=3,000,000

Answer:

225

Step-by-step explanation: