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denis23 [38]
3 years ago
6

Find the zeros of the function by rewriting in intercept form.

Mathematics
1 answer:
Naddika [18.5K]3 years ago
8 0
The intercept form is y=a(x-p)(x-q) where p, q - the zeroes of a function.

1.
y=2x^2-4x \\
y=2x(x-2) \\
y=2(x-0)(x-2) \\
\hbox{the zeroes - }\boxed{x=0 \ and \ x=2}

2.
y=2x^2-11x-21 \\
y=2x^2-14x+3x-21 \\
y=2x(x-7)+3(x-7) \\
y=(2x+3)(x-7) \\
y=2(x+\frac{3}{2})(x-7) \\ y=2(x-(-\frac{3}{2}))(x-7) \\
\hbox{the zeroes - }\boxed{x=-\frac{3}{2} \ and \ x=7}
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If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height
Tju [1.3M]

Correct question :

If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height x, and side length x + 4. A rectangle with length of x + 3 and width of one-half x. (x + 4) + x + (x + 2) = one-half x + (x + 3) (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3) 2 (x) + 2 (x + 2) = 2 (one-half x) + 2 (x + 3) x + (x + 2) + (x + 4) = 2 (x + 3 and one-half)

Answer: (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3)

Step-by-step explanation:

Given the following :

A triangle with base x + 2, height x, and side length x + 4 - - - -

b = x + 2 ; a = x ; c = x + 4

Perimeter (P) of a triangle :

P = a + b + c

P =( x + 2) + x + (x + 4) - - - (1)

A rectangle with length of x + 3 and width of one-half x

l = x + 3 ; w = 1/2 x

Perimeter of a rectangle (P) = 2(l+w)

P = 2(x+3) + 2(1/2x)

If perimeter of each same are the same ; then;

(1) = (2)

(x + 2) + x + (x + 4) = 2(x+3) + 2(1/2x)

7 0
3 years ago
The value of the definite integral / 212x – sin(x) dx / 122x-sin(x) is
blondinia [14]

Hi there!

\boxed{= 70 + cos(12) - cos(2) \approx 71.26}

\int\limits^{12}_{2} {x-sin(x)} \, dx

We can evaluate using the power rule and trig rules:

\int x^n = \frac{x^{n+1}}{n+1}

\int x = \frac{1}{2}x^{2}

\int -sin(x) = cos(x)

Therefore:

\int\limits^{12}_{2} {x-sin(x)} \, dx = [\frac{1}{2}x^{2}+cos(x)]_{2}^{12}

Evaluate:

(\frac{1}{2}(12^{2})+cos(12)) - (\frac{1}{2}(2^2)+cos(2))\\= (72 + cos(12)) - (2 + cos(2))\\\\= 70 + cos(12) - cos(2) \approx 71.26

3 0
3 years ago
A rectangular painting by Leonardo da Vinci measured 62cm along its diagonal. If the painting has a height of 42 cm how wide is
IRINA_888 [86]

ANSWER

45.6cm to the nearest tenth.

EXPLANATION

The diagonal of the rectangular painting is 62cm.

The height of the painting is 42 cm.

The height of the painting h , the diagonal, and the width of the painting forms a right triangle with the diagonal being the hypotenuse.

From the Pythagoras Theorem,

{w}^{2}  +  {42}^{2}  = {62}^{2}

{w}^{2} = {62}^{2} -  {42}^{2}

{w}^{2}  = 2080

{w} =  \sqrt{2080}

w = 4 \sqrt{130}

The width of the painting is 45.6cm to the nearest tenth.

4 0
3 years ago
Please help im literally crying i cant fail this please ​
Gennadij [26K]
For the surface area u take the surface and multiply the length by the width which is in this cas 7x4 then multiply, 7x4 is equal to 28.

Hope this helped, tell me if I’m wrong
Brainliest would be nice
Thank you
3 0
2 years ago
Factor completely 20x3y + 30x2y2.
Alexxandr [17]
<span>10x2y(2x + 3y)

Each term has 10 in it. Plus each term has at least 2 x's and 1y. The parenthesis are what's left over. </span>
8 0
3 years ago
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