Ali and Steve share some sweets in the ratio 2 : 7

A quadratic pattern has a second term equal to 1,a third term equal to -16 and a fifth term equal to -14

chubhunter [2.5K]

Given are several terms in a quadratic pattern:

a1 = ?
a2 = 1
a3 = -16
a4 = ?
a5 = -14

let:

x y
1 ?
2 1
3 -16
4 ?
5 -14

considering the 2nd term and 3rd term, we can determine a quadratic function:

y = -17x + 35

therefore,

a1 = 18
a4 = -33

7 0

2 years ago

Shanelle already has $137 from babysitting. She needs at least $625 for a new tablet. Which inequality best represents this scen

kap26 [50]

Answer:

t + 137 ≥ 625

Step-by-step explanation:

Shanelle already have in her possession the sum of $137 from babysitting. She requires at least $625 for a new tablet. t is the remaining amount she needs to get the new tablet.

She already has $137 and to get the tablet she needs at least $625 . This means she needs nothing less than or equal to $625 to get the tablet. Recall t is the remaining amount needed to add to what she has to be able to reach the least amount required to purchase a tablet. Therefore , the sum of t and the amount of money already in her possession should be equal to or greater than $625.

To get the new tablet,

t + 137 ≥ 625

5 0

2 years ago

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believ

olga_2 [115]

Answer:

Value of v that minimizes E is v = 3u/2

Step-by-step explanation:

We are given that;

E(v) = av³L/(v-u)

Now, using the quotient rule, we have;

dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²

Expanding and equating to zero, we have;

[3av³L - 3av²uL - av³L]/(v - u)² = 0

This gives;

(2av³L - 3av²uL)/(v-u)² = 0

Multiply both sides by (v-u)² to give;

(2av³L - 3av²uL) = 0

Thus, 2av³L = 3av²uL

Like terms cancel to give;

2v = 3u

Thus, v = 3u/2

5 0

2 years ago

Which graph represents the solution set for the inequality StartFraction one-half EndFraction x is less than or equal to 18.x ≤

Mrrafil [7]

Answer:

A number line from 0 to 60 in increments of 6. A point is at 36 and a bold line starts at 36 and is pointing to the left. ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- When solving an inequality, there are some important points:

# If the inequality is x > a, then it represented on the number line by

a ray with empty small circle as end starts at a and pointed to

the right (⇒ ∞)

# If the inequality is x ≥ a, then it represented on the number line by

a ray with bold small circle as end starts at a and pointed to the

right (⇒ ∞)

# If the inequality is x < a, then it represented on the number line

by a ray with empty small circle as end starts at a and pointed to

the left (⇒ -∞)

# If the inequality is x ≤ a, then it represented on the number line by

a ray with bold small circle as end starts at a and pointed to the

left (⇒ -∞)

* Lets solve the problem

∵ 1/2 x ≤ 18

- Multiply both sides by 2

∴ x ≤ 36

- To represent it draw a number line from 0 to 60 and the counted

by 6 as 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

- Draw a ray with bold end starts at 36 and pointed to the left

∴ A number line from 0 to 60 in increments of 6. A point is at 36 and

a bold line starts at 36 and is pointing to the left.

3 0

2 years ago

Read 2 more answers

HELP ASAP In two or more complete sentences, Explain how you would find the equation of a parabola, given the coordinate of the

kvasek [131]

In the general case in Cartesian coordinates, you would use the definition of a parabola as the locus of points equidistant from the focus and directrix. The equation would equate the square of the distance from a general point (x, y) to the focus with the square of the distance from that point to the directrix line.

Suppose the focus is located at (h, k) and the equation of the directrix is ax+by+c=0. The expression for the square of the distance from (x, y) to the point (h, k) is ...
(d₁)² = (x-h)²+(y-k)²
The expression for the square of the distance from (x, y) to the directrix line is
(d₂)² = (ax+by+c)²/(a²+b²)

Equating these expressions gives the equation of the parabola.
(x-h)²+(y-k)² = (ax+by+c)²/(a²+b²)

When the directrix is parallel with one of the axes, one of the coefficents "a" or "b" is zero and the equation becomes much simpler. Often, it would be easier to make use of the formula (for a directrix parallel to the x-axis):
y = 1/(4p)*(x -h)² +k
where the (h, k) here is the vertex, the point halfway between the focus and directrix, and "p" is the (signed) distance from the focus to the vertex. (p is positive when the focus is above or to the right of the vertex.)

4 0

2 years ago