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3 years ago

What number is represented by 4x²+17x+2 if x=10?

Mathematics

1 answer:

Fynjy0 [20]3 years ago

4 0

Answer:

at x = 10, $4x^{2} + 17x + 2 = 572$

Step-by-step explanation:

The given equation is $4x^{2} + 17x + 2$

Here, lets substitute the value of x = 10

So, the equation simplifies to ,

$4 \times (10)^{2} + 17(10) + 2$

= (4 x 100) + 170 + 2 = 400 + 170 + 2

= 572

So, at x = 10, $4x^{2} + 17x + 2 = 572$

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An equation of a hyperbola is given.

siniylev [52]

Answer:

The vertices are $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

The foci are $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$ .

The asymptotes are $y=2x,\:y=-2x$ .

b) The length of the transverse axis is 6.

c) See below.

Step-by-step explanation:

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$ is the standard equation for a right-left facing hyperbola with center $\left(h,\:k\right)$ .

The vertices $\:\left(h+a,\:k\right),\:\left(h-a,\:k\right)$ are the two bending points of the hyperbola with center $\:\left(h,\:k\right)$ and semi-axis a, b.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ and vertices $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

For a right-left facing hyperbola, the Foci (focus points) are defined as $\left(h+c,\:k\right),\:\left(h-c,\:k\right)$ where $c=\sqrt{a^2+b^2}$ is the distance from the center $\left(h,\:k\right)$ to a focus.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ $c=\sqrt{3^2+6^2}= 3\sqrt{5}$ and foci $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$

The asymptotes are the lines the hyperbola tends to at $\pm \infty$ . For right-left hyperbola the asymptotes are: $y=\pm \frac{b}{a}\left(x-h\right)+k$

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ and asymptotes

$y=\frac{6}{3}\left(x-0\right)+0,\:\quad \:y=-\frac{6}{3}\left(x-0\right)+0\\y=2x,\:\quad \:y=-2x$

b) The length of the transverse axis is given by $2a$ . Therefore, the lenght is 6.

c) See below.

4 0

4 years ago

Which shows the equation of the line containing the point (4, 6) and having a slope of 4 in slope-intercept form?

shutvik [7]

Answer:

y=4x-10

Step-by-step explanation:

See attached image

8 0

2 years ago

Find the area of the shaded regions round the hundredth if needed.

inn [45]

1. Find the area of the circle. You know the radius = 10 in. Use
$a = \pi {r }^{2}$
2. Find the area of the (I'm assuming) equilateral triangle. Use the 30-60-90 rule to determine the length of half one of the edges, since you already know the hypotenuse of the 30-60-90 triangle. Multiply that value by 2 to get the length of one side. Then use
$a = \frac{ \sqrt{3} }{4} {l}^{2}$
to find the area, where l = length of one side.

3. Subtract the area of the equilateral triangle from the area of the circle to find the area of the shaded region.

Hope this helps. Let me know if you're confused!

7 0

4 years ago

The formula for the circumference, C, of a circle with given radius, r, is C = 2nr.

LekaFEV [45]

Answer:

C. 22

Step-by-step explanation:

C = circumference

n (pi) = 22/7

r = 3 1 /2

Plug in the numbers for each variable.

C = 2x (22/7) x (3 1/2)

Change the mixed number inIto an improper fraction by multiplying 3 x 2 and adding the 1 which gives us 7 over 2 because 2 is our denominator so, 3 1/2 = 7/2. It also helps to have 1 as the denominator for 2.

C = (2/1) x (22/7) x (7/2)

Lastly, just multiply the numerators across which give us 308 then multiply the denominators across which gives us 14, so then we divide 308 by 14 and get 22.

6 0

3 years ago

Find the y-intercept of the following equation.

Dafna1 [17]

Answer:

(0,12)

Step-by-step explanation:

y = -3x^2 – 4x + 12

To find the y intercept, let x=0

y = -3(0) -4(0) +12

y=12

The y intercept is (0,12)

6 0

4 years ago