Enter the correct answer in the box. Write the sum of √28x^6 + 4√7x^6 in simplest form, if x ≠ 0.

If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be:
y = a(x - 5/2)^2 + k
Substitute (1, -2): -2 = a(-3/2)^2 + k
-2 = 9a/4 + k
Substitute (2, -4): -4 = a(-1/2)^2 + k
-4 = a/4 + k
Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4.
So the equation is y = (x - 5/2)^2 - 17/4
Expanding: y = x^2 - 5x + 25/4 - 17/4
y = x^2 - 5x + 2 (This is the standard form.)

5 0

3 years ago

S is the midpoint of TV. TS = 4x - 7, and SV = 5x - 15. Find TS, SV, and TV.

jasenka [17]

Step-by-step explanation:

TS = 4x - 7

x = -7/4

SV = 5x -15

x = -15/5

= -3

TV = -7/4 + -3

= -3 3/4

= -4.75

8 0

1 year ago

Which is the midpoint of the segment joining (12, 2) and (-5, – 7)?

Rainbow [258]

Answer:

$m(x, y)=(\frac{7}{2} , -\frac{5}{2} )$

Step-by-step explanation:

Midpoint of line segment is calculated as

$m(x, y)=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$ -----------(1)

Here

$(x_1, y_1) = (12,2) \ \ and \ \ (x_2, y_2) = (-5, -7)$

Substituting values in equation (1)

$m(x, y)=(\frac{12-5}{2} , \frac{2-7}{2} )$

$m(x, y)=(\frac{7}{2} , -\frac{5}{2} )$

3 0

3 years ago

Factor the polynomial.<br><br> X2-13x+30

Svetllana [295]

Answer:

<h2> $\ \boxed{(x - 3)(x - 10)}$ </h2>

Step-by-step explanation:

${x}^{2} - 13x + 30$

Write -13x as a difference

${x}^{2} - 3x - 10x + 30$

Factor out x from the expression

$x(x - 3) - 10x + 30$

Factor out -10 from the expression

$x(x - 3) - 10(x - 3)$

Factor out x-3 from the expression

$(x - 3)(x - 10)$

Hope I helped!

Best regards!!

4 0

3 years ago

Derek owns a landscape business. He charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. Derek's earnings (in

luda_lava [24]

From the given problem statement alone, we can say that the equation relating the area of the lawn mowed and the earnings has a linear relationship. That is because there is a constant increase in the earnings per area which is $1 per 1000 square feet.

Therefore the equation must be in the form of:

y = m x + b

where,

y = is the total earnings

m = is the fee per area = 1 / 1000

x = is the area of the lawn

b = is the fixed fee = 30

Therefore the equation becomes:

y = 0.001 x + 30

Rewriting this in terms for x since we are to find the area:

x = (y – 30) 1000

when y = 204

x = (204 – 30) 1000 = 174,000 square feet

when y = 344

x = (344 – 30) 1000 = 314,000 square feet

when y = 450

x = (450 – 30) 1000 = 420,000 square feet

when y = 482

x = (482 – 30) 1000 = 452,000 square feet

when y = 504

x = (504 – 30) 1000 = 474,000 square feet

8 0

3 years ago