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ehidna [41]
3 years ago
10

The length of a rectangle is five times its width.

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:let

Length =L

Width =W

L=5W

Perimeter(p)=2L+2W

P=10W+2W

84=12W

Divide both sides by 12

W=7m

L=5*7=35m

Hence, the length and width are 35m and 7m respectively

Step-by-step explanation:

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florida received 15 inches of rainfall in 3 months of the year. If the state receive 4.25 each month until the end of the year,
kherson [118]
Since there are 12 months in there year and there have already been 3 months there are 9 left

we need to multiply 4.25 by 9 and then add the first 15 inchess

4.25 times 9 = 38.25+15 = 53.25

Florida will recieve 53.25 inches of rain

I hope I've helped!

3 0
3 years ago
Orthogonalizing vectors. Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, a
jeka57 [31]

Answer:

\\ \gamma= \frac{a\cdot b}{b\cdot b}

Step-by-step explanation:

The question to be solved is the following :

Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if b \neq 0. Recall that given two vectors a,b  a⊥ b if and only if a\cdot b =0 where \cdot is the dot product defined in \mathbb{R}^n. Suposse that b\neq 0. We want to find γ such that (a-\gamma b)\cdot b=0. Given that the dot product can be distributed and that it is linear, the following equation is obtained

(a-\gamma b)\cdot b = 0 = a\cdot b - (\gamma b)\cdot b= a\cdot b - \gamma b\cdot b

Recall that a\cdot b, b\cdot b are both real numbers, so by solving the value of γ, we get that

\gamma= \frac{a\cdot b}{b\cdot b}

By construction, this γ is unique if b\neq 0, since if there was a \gamma_2 such that (a-\gamma_2b)\cdot b = 0, then

\gamma_2 = \frac{a\cdot b}{b\cdot b}= \gamma

6 0
3 years ago
PLS SOMEONE HELP ME
garik1379 [7]
Here are your answer's:

Number three would goes with "no relationship"...…
Number one would goes with "<span>causation</span>".....
Number two goes with "correlation"...…

<u>Correlation is the relationship between more than two things which is why it would go with number to because literacy rates go with the increase of doctors. Causation is like a cause and effect so in this case the cause would be a increase of the population and the effect would be more people who don't have jobs. No relationship would go with number three since how snowfall doesn't have anything to do with personal income. (which is how much a person makes) </u>

Hope this helps!
7 0
3 years ago
Solve the quadratic for x, then enter the numerical value of your solution. (If there are two solutions, either one will work.)
xz_007 [3.2K]

Answer: X= -1 OR X= 11

Step-by-step explanation:

Step 1 : Equate ( x-5)² since it occurred twice, hence the reason 2 is added in front of (x-5)²

= (x-5)²

= (x-5)(x-5)

= (x²-5x-5x+25)

= (x²-10x+25)

Step 2: multiply the result by two since it occurs twice and also bring the equation

= 2 (x²-10x+25) +7 = 79

= 2x²- 20x+50+7 = 79

= 2x²- 20x+57 =79

Step 3: most quadratic equation are always equal to zero, let's make this one equal to Zero by subtracting 79 from both sides

= 2x²-20x+57-79 = 79-79

= 2x²-20x-22=0

Step 4: divide the equation by a common number to get the least coefficient of the three coefficients

Dividing the three by 2

(2x²-20x-22)/2 = x²- 10x- 11

Step 5: Factorise completely

Sub step 1 : the first term in the equation is X² which makes the first term coefficient 1; the second term in the equation is -10x which makes the second term coefficient -10, the constant has a coefficient of -11

Sub step 2: multiply the coefficient of the first term (1) and the constant (-11) which gives us (-11)

1*-11 = -11

Sub step 3: Get two numbers in such a way that the addition of the first number and the second number gives the second coefficient in the quadratic equation and the multiplication of the two numbers will give us the product of the first coefficient and the constant.

And the two numbers is +1 and -11, the sum of the two numbers will give us -10 and the product will give us -11.

Step 6: slot the two numbers (+1, -11) into the equation by making themr replace the second coefficient

x²-10x-11=0

= x²+x-11x-11 =0

Step 7: split the equation into two and Factorise further

= (x²+x)(-11x-11) =0

= x(x+1)-11(x+1) = 0

= x+1= 0 or x-11 =0

Step 8 split them into individual equation

= x+1= 0.

Subtract 1 from both sides

= X+1-1=0-1

= x= -1

Or X should be

= x-11=0

Add 11 to both sides

= X-11+11 = 0+11

= x= 11

6 0
3 years ago
Pvc pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. find the probability that a r
Tema [17]
The probability that the sample mean is within 2 standard deviations on the high side and 1 standard deviation on the low side is about 0.8186.

5 0
3 years ago
Read 2 more answers
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