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3 years ago

Indicate in standard form the equation of the line through the given points.

Mathematics

1 answer:

Molodets [167]3 years ago

7 0

Answer:

x-y=4

Step-by-step explanation:

(y+4)/(1+4) = x/5

(y+4)/5 = x/5

y+4 = x

-x+y= -4

x-y = 4

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A museum charges $10

Tanzania [10]

A piecewise function is a function that behaves differently in different intervals of its domain.

The piecewise function is:

f(x) = $10 if 0 < x < 6
f(x) = $15 if 6 ≤ x ≤ 18
f(x) = $20 if 18 < x

Here the given information for the function is:

The museum charges $10 for kids of 5 and under
The museum charges $15 for ages of 6 to 18
The museum charges $20 for ages larger than 18.

Then if we define x as the age of the person, the function f(x) that tells the cost of the ticket will be:

f(x) = $10 if 0 < x < 6
f(x) = $15 if 6 ≤ x ≤ 18
f(x) = $20 if 18 < x

So as you can see, depending on the value of x and in which interval it belongs, the function behaves differently.

If you want to learn more, you can read:

brainly.com/question/12561612

5 0

3 years ago

Which of the following is not a correct name for the line shown?

Talja [164]

Answer:

Step-by-step explanation:

The line can be named with small latin letters or with two large latin letters which represent two points lying on the line.

Consider all options:

A. Points V and X lie on the line, so you can name the line as VX (true option)

B. Points W and X lie on the line, so you can name the line as WX (true option)

C. p represents the line (small letter given on the diagram) - (true option)

D. You cannot name the line using point V and line p, so this option is false

3 0

3 years ago

Read 2 more answers

The answers To this I don’t understand

Nataly_w [17]

Answer:nvuycghg

Step-by-step explanation:

ngyufuf

6 0

3 years ago

A rectangular patio has an area of 91 fl. The length is 6 feet

puteri [66]

Answer:

Total area equation = tex]w(w+6)=91[/tex]

b/2 = 3

Dimensions of the patio: width = 7 feet, length = 13 feet

Step-by-step explanation:

The area of a rectangle is given the formula:

$A=wl$

where

$w$ is the width

$l$ is the length

We know from our problem that the area of the patio is 91 square feet, so $A=91$ . We also know that the length is 6 feet longer then the width, so $l=w+6$ .

Replacing values in our area equation

$A=wl$

$91=w(w+6)$

$w(w+6)=91$

Expanding the left side:

$w*w+6w=91$

$w^2+6w=91$

Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is $w$ , so its coefficient is 6. Now, half its coefficient or $\frac{b}{2} =\frac{6}{2} =3$ . Finally, $3^2=9$ .

To complete the square we need to add 9 to both sides of the equation:

$w^2+6w+9=91+9$

$w^2+6w+9=100$

Notice that the left side is a perfect square trinomial (both $w^2$ and 9 are perfect squares), so we can express it as:

$(w+3)^2=100$

Now that we completed the square, we can solve our equation

- Take square root to both sides

$\sqrt{(w+3)^2} =\pm\sqrt{100}$

$w+3=\pm10$

- Subtract 3 from both results

$w=10-3,w=-10-3$

$w=7,w=13$

Since length cannot be negative, $w=7$ is the solution of our equation.

We now know that the width of our rectangular patio is 7 feet, so we can find its length:

$l=w+6$

$l=7+6$

$l=13$

We can conclude that half the coefficient of the width is $\frac{b}{2}=3$ , the width of the patio is 7 feet, and its length is 13 feet.

7 0

3 years ago

Prove the polynomial identity.

Kaylis [27]

Answer:

Proven

Step-by-step explanation:

We prove the polynomial with factorization. We must first simplify the expression before we can factorize:

$(4\cdot{x^2}-2)\cdot{(4\cdot{x^2}-2)}-16\cdot{x^4}$

$16\cdot{x^4}-8\cdot{x^2}-8\cdot{x^2}+4-16\cdot{x^4}$

$4-16\cdot{x^2}$

4 is the common number and we can take it out of the expression:

$4\cdot{(1-4\cdot{x^2})}$

We can factorize further with the x term being zero. For this to be true we must have -2x and 2x to cancel out and therefore the expression is proven:

$4\cdot{(1-2\cdot{x})}\cdot{(1+2\cdot{x})}$

5 0

3 years ago