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almond37 [142]
2 years ago
11

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and poin

t C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
How far would Pete walk if he went from A to B to C? yards

The direct distance from A to C is more than yards.

The inequality w < represents the distance, w, that Pete might save by taking the direct path.
Mathematics
1 answer:
Nana76 [90]2 years ago
3 0

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

<h3>What is inequality?</h3>

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

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Given f(x) = 3x^3+ kx – 11, and x – 1 is a factor of f(x), then what is the value<br> of k?
STatiana [176]

let's recall the remainder theorem.

we know that (x-1) is a factor, that means x -1 = 0 or x = 1.

since we know that (x-1) is a factor, then dividing the polynomial by it will give us a remainder of 0, which correlates with saying that f(1) = 0, in this case, so we can simply plug in "1" as the argument, knowing it gives 0.

f(x)=3x^3+kx-11\\\\[-0.35em]~\dotfill\\\\\stackrel{0}{f(1)}=3(1)^3+k(1)-11\implies \stackrel{f(1)}{0}=3+k-11\implies 0=-8+k\implies 8=k

7 0
2 years ago
Express 73/5as a decimal.
Assoli18 [71]

Answer:

as a fraction it could be 3/5

Step-by-step explanation:

but as a decimal it would be 0.6

7 0
3 years ago
What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10
jasenka [17]

<u>Answer:</u>

 The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

<u>Solution: </u>

The given expression is (2 x-3 y)^{10}

As per binomial theorem, we know,

(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now x^{5}\times y^5 will be the 6 term where k =5

Now, \mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}

So, the coefficient of x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right.

10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252

The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

6 0
3 years ago
3. In the expression 362 + 6, what will be the place value of the first digit of the quotient?
Hunter-Best [27]

Answer:

B. It will be the tens place because 6 is greater than 3.

Step-by-step explanation:

Since the question said "quotient," then I believe we have 362 ÷ 6 and not "362 + 6."

If we work on the quotient we have

60\frac{1}{3}

Obviously, the first digit in the quotient is 6 and it takes the place of tens.

Looking at the options, option B fits the most because 6 is actually greater than 3.

Therefore, the answer is option B, It will be the tens place because 6 is greater than 3.

4 0
3 years ago
Find the angle of RMQ.
faust18 [17]

Answer:

22

Step-by-step explanation:

since there is a bisector that makes the two angles equal. you first need to find x then with x you can add the angles to get the biggest angle witch is RMQ

2x+1 = 4x-9

1=2x-9

10=2x

5=x

x=5

RMQ=2x+1+4x-9

RMQ=2(5)+1+4(5)-9

RMQ=10+1+20-9

RMQ=11+11

RMQ=22

RMQ=16

8 0
3 years ago
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