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2 years ago

A student says that the x-intercept of a line is (0,-10,). Is the student correct? Explain.

Mathematics

1 answer:

nataly862011 [7]2 years ago

5 0

Answer:

Yes, the student is correct

Step-by-step explanation:

Given

$(0,-10)$

Required

Does it represent the x intercept

At the x intercept, the value of x is 0.

So, the function $(x,y)$ becomes $(0,y)$

$(0,-10)$ can be compared to $(0,y)$

Hence, the student is correct

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The whole numbers a,b and c such that $a^2+b^2 = c^2$ are Pythagorean triples satisfying the Pythagorean theorem.

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3 years ago

Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients a, b, and c of the parabola equation

$a=4, b=-6, \:and \:c=-8$

2. You can apply this formula to find x-coordinate of the vertex

$x=-\frac{b}{2a}$ , so

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

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3 years ago

The perimeter of a rectangle is 42 cm and the area is 80 cm². Write an equation to model the situation and find the dimensions o

mafiozo [28]

Answer:

16cm by 5cm

Step-by-step explanation:

P=2(l+w)

A= wl

80 factorization: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.

you then would have to find 2 numbers that would add up to make 42.

When you try 16*2+5*2= 32+10= 42 cm as your perimeter.

16*5= 80 cm^2 as your area.

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3 years ago

A student says that the​ x-intercept of a line is ​(0,-10,​). Is the student​ correct? Explain.

A student says that the x-intercept of a line is (0,-10,). Is the student correct? Explain.