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2 years ago

25. Save the simultaneous equations 2x-y=4;x+y=5

Mathematics

1 answer:

Helen [10]2 years ago

3 0

Answer:

x = 3

Step-by-step explanation:

2x - y = 4

x + y = 5

y = 5 - x

2x - (5 - x) = 4

2x + x - 5 = 4

3x = 9

x = 3

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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

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

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3 years ago

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Step-by-step explanation:

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2 years ago

the sales tax rate for a community is 6.75%. If you purchase an item for $500, how much will you pay in sales tax?

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3 years ago

(05.08) Solve for x: 2 over quantity x minus 2 plus 7 over quantity x squared minus 4 equals 5 over x. (2 points) x = negative 4

Oxana [17]

Answer:

Step-by-step explanation:

The best way to do this is to use your LCM and eliminate the fractions. To find the LCM you have to use all the denominators as a multiplier so the denominator in each term cancels out. We will first factor the x-squared term to simplify and see what 2 factors are hidden there.

$x^2-4$ factors to (x + 2)(x - 2). That means that our 3 denominators that make up our LCM are x(x+2)(x-2). We will mulitply that in to each term in our rational equation, canceling out the denominators where applicable.

$x(x+2)(x-2)[\frac{2}{(x-2)}+\frac{7}{(x-2)(x+2)}=\frac{5}{x}]$

In the first term, the (x-2) will cancel leaving us with

x(x+2)[2] which simplifies to

$x^2+2x[2]$

In the second term, the (x+2)(x-2) cancels out leaving us with

x[7].

In the last term, the x cancels out leaving us with

(x+2)(x-2)[5] which simplifies to

$x^2-4[5]$

Now we will distribute through each cancellation:

2x²+4x;

7x;

5x²-20

Putting them all together we have

2x² + 4x + 7x = 5x² - 20

Combining like terms gives us a quadratic:

3x² - 11x - 20 = 0

Factor that however you find it easiest to factor quadratics and get that

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3 years ago

7. Mrs. Molina's dog weighs 33.7 pounds. Ms. Curtis's dog

Anarel [89]

Answer:

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Step-by-step explanation:

33.7 x 3.4 = 114.58

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3 years ago

25. Save the simultaneous equations 2x-y=4;x+y=5​

25. Save the simultaneous equations 2x-y=4;x+y=5