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3 years ago

How many integers are between 5/3 and 30/7?

Mathematics

1 answer:

devlian [24]3 years ago

4 0

first off, let's convert the "improper" fractions to mixed,

$\bf \cfrac{5}{3}\implies 1\frac{2}{3}\qquad \qquad \qquad\qquad \qquad \cfrac{30}{7}\implies 4\frac{2}{7}\\\\ -------------------------------\\\\ 1\frac{2}{3}\text{\textemdash\textemdash\textemdash}\boxed{2}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{3}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{4}\text{\textemdash\textemdash}4\frac{2}{7}$

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Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ

Ahat [919]

Answer:

D. $f(x) = 2\cdot x^{2}-4\cdot x -16$

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

$4\cdot a -2\cdot b + c = 0$ (Eq. 1)

(4, 0)

$16\cdot a + 4\cdot b +c = 0$ (Eq. 2)

(0,-16)

$c = -16$ (Eq. 3)

Then,

$4\cdot a - 2\cdot b = 16$ (Eq. 4)

$16\cdot a + 4\cdot b = 16$ (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

$a - 0.5\cdot b = 4$ By Eq. 4 (Eq. 4b)

$a = 4 + 0.5\cdot b$

Then,

$16\cdot (4+0.5\cdot b) + 4\cdot b = 16$ (Eq. 4b in Eq. 5)

$64 + 12\cdot b = 16$

$12\cdot b = -48$

$b = -4$

The remaining coeffcient is:

$a = 4 + 0.5\cdot b$

$a = 4 + 0.5\cdot (-4)$

$a = 2$

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is $f(x) = 2\cdot x^{2}-4\cdot x -16$ . Thus, the right answer is D.

6 0

3 years ago

The new set of tires you will need for your car cost $320 you have $80 saved how much will you need to save each month to buy th

SOVA2 [1]

$80/month 320-80=240, then 240/3=80

5 0

3 years ago

I need help please!!!!

zaharov [31]

Answer:

Step-by-step explanation:

The equations are all in point-slope form with a slope of 6/5. The points used are (-1, -2), (-2, -1), and (1, 2). It seems point (1, 2) best matches a point on the graphed line. Choice C is the best. (In the attached graph, choice C is the red line.)

_____

<em>Additional comment</em>

The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

The equation might be easier to see if the point chosen were one at a grid intersection, such as (-4, -4) or (6, 8).

8 0

2 years ago

Sammy served food to a group at a restaurant. The total cost of the food was $62.00. The sales tax is 6% of the cost of food. Th

Phoenix [80]

$62 total food amount
6% tax
20% of original cost of food for tip

62x0.06= 3.72
62x0.2= 12.4

62+12.4+3.72= $78.12

the total cost of the group is $78.12

5 0

3 years ago

Read 2 more answers

Write one number that is a factor of 13.

maw [93]

Answer: 1 and 13

Step-by-step explanation: To find the factors of 13, begin by dividing 13 by 1 which gives us 13. This tells us that 1 and 13 are factors of 13.

13 is a prime number which means it only has two factors which are 1 and 13.

3 0

3 years ago

Read 2 more answers