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3 years ago

What is the minimum point of the equation x^2+19=9x

Mathematics

1 answer:

azamat3 years ago

3 0

Answer:

The minimum point is (4.5, -1.25).

Step-by-step explanation:

x^2+19=9x

= x^2 - 9x + 19 = 0

Convert to Vertex form:

(x - 4.5)^2 - 4.5^2 + 19 = 0

= (x - 4.5)^2 - 1.25.

The minimum point is (4.5, -1.25).

You might be interested in

Move triangle ABC so it lies on top of triangle DEF, triangle GHI, and triangle JKL. How many units do you have to move triangle

dusya [7]

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the diagram of coordinates of the three triangles are not given.

A general explanation is as follows:

First, record the coordinates of the corresponding points of the three triangles.

For instance; In triangles ABC, DEF and GHI; A, D and G are corresponding points.

Now, assume the coordinates are:

$A = (1,1)$

$D = (1,5)$

$G= (-2,1)$

Point D is 4 points to the right of A;

i.e.

$D =(1,1+4) = (1,5)$

Hence, ABC will be moved 4 units right to lie on DEF

Similarly, point G is 3 units down of A

i.e.

$G =(1-3,1) = (-2,1)$

Hence, ABC will be moved 3 units down to lie on GHI.

5 0

3 years ago

Find the number C(10,6)

EastWind [94]

Answer:

210.

Step-by-step explanation:

Combination formula is

$nCr = \frac{n!}{r!(n-r)!}$

Then, we have that n = 10 and r=6:

$C(10,6) = \frac{10!}{6!(10-6)!}$

$C(10,6) = \frac{10!}{6!4!}$

To simplify calculus, we are going to use that n! = (n-1)!n = (n-2)!(n-1)n and so on.

$C(10,6) = \frac{6!*7*8*9*10}{6!4!}$

$C(10,6) = \frac{7*8*9*10}{4!}$

$C(10,6) = \frac{5040}{4*3*2*1}$

$C(10,6) = \frac{5040}{24}$

$C(10,6) = 210.$

5 0

2 years ago

5x=4y make x the subject

oee [108]

Answer:

$x = \frac{4y}{5}$

Step-by-step explanation:

$5x = 4y\\\rule{150}{0.5}\\\frac{5x=4y}{5}\\\\\boxed{x = \frac{4y}{5}}$

Hope this helps.

4 0

2 years ago

H(t)=(t+3)

Anarel [89]

Answer:

Step-by-step explanation:

h(t) = (t + 3)² + 5, -5 ≤ t ≤ -1

The average rate of change is the change in h over the change in t.

(h(-1) − h(-5)) / (-1 − (-5))

= ((-1 + 3)² + 5 − ((-5 + 3)² + 5)) / (-1 + 5)

= (4 + 5 − 4 − 5)) / 4

= 0

3 0

3 years ago

Rewrite the equation in vertex form. then find the vertex of the graph. y=-3x^2-5x+1

amm1812

Answer: y = -3(x + $\frac{5}{6}$ )² + $\frac{37}{12}$ , $(-\frac{5}{6}$ , $\frac{37}{12})$

Step-by-step explanation:

First, you need to complete the square:

y = -3x² - 5x + 1

-1 -1

y - 1 = -3x² - 5x

y - 1 = -3(x² + $\frac{5}{3}x$

y - 1 + -3( $\frac{25}{36}$ ) = -3(x² + $\frac{5}{3}x$ + $\frac{25}{36}$ )

↑ ↓ ↑

$\frac{5}{3*2}$ = $(\frac{5}{3*2})^{2}$

y - 1 - $\frac{25}{12}$ = -3(x + $\frac{5}{6}$ )²

y - $\frac{12}{12}$ - $\frac{25}{12}$ = -3(x + $\frac{5}{6}$ )²

y - $\frac{37}{12}$ = -3(x + $\frac{5}{6}$ )²

y = -3(x + $\frac{5}{6}$ )² + $\frac{37}{12}$

Now, it is in the form of y = a(x - h)² + k where (h, k) is the vertex

Vertex = $(-\frac{5}{6}$ , $\frac{37}{12})$

8 0

3 years ago