All categories

3 years ago

In the standard (x, y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,−8)?

1 answer:

4 0

$(3,7) \ and \ (4,-8)\\ \\ First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} } \\ \\m=\frac{-8-7}{4-3} = \frac{-15}{1}=-15 \\ \\Now \ use \ y = mx + b \ with \ either \ point \ to \ find \ b, \ the \ y-intercept \ : \\ \\ y=mx+b \\ \\7=-15*3+b\\ \\7=-45 +b \\ \\b=7+45\\ \\b=52 \\ \\ y= - 5x+52 \ is \ the \ answer
$

You might be interested in

A bag contains even and odd numbered balls in the ratio of 3:7, respectively. For each of the following, what is the probability

Gre4nikov [31]

Answer:

a) 0.425

b) 0.65

c) 0.575

Step-by-step explanation:

The ratio of even balls to odd balls is 3:7. That means if there are 3 even balls, then there are 7 odd balls. That makes a total of 10 balls, of which 30% are even and 70% are odd.

a) There are 240 balls, so originally, 72 are even and 168 are odd. 30 of the odd balls are renumbered by multiply by 4. An odd number times an even number is an even number, so 30 of the odd balls become even balls. So there are now 102 even balls and 138 odd balls. Therefore:

P(even) = 102 / 240

P(even) = 0.425

b) Originally, 70% of the balls are odd. Half of those are renumbered by multiplying by 6, so they become even numbers.

P(odd) = 0.5 (70%) = 35%

P(even) = 30% + 35% = 65%

A third of the even balls are renumbered by multiplying by 5, so they remain even numbers.

Therefore, P(even) = 0.65.

c) Originally, 30% of the balls are even. Half of those are renumbered by adding 3. An even number plus an odd number is an odd number, so:

P(even) = 0.5 (30%) = 15%

P(odd) = 70% + 15% = 85%

Next, half the odd balls are renumbered by adding 5. An odd number plus an odd number is an even number, so:

P(odd) = 0.5 (85%) = 42.5%

P(even) = 15% + 42.5% = 57.5%

Therefore, P(even) = 0.575.

8 0

3 years ago

Need to find the sum of 50

Bumek [7]

Answer:

4600

Step-by-step explanation:

This is an arithmetic sequence with common difference d between consecutive terms.

d = - 2 - (- 6) = 2 - (- 2) = 6 - 2 = 4

The sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [ 2a + (n - 1)d ]

where a is the first term

here a = - 6, d= 4 and n = 50, hence

$S_{50}$ = $\frac{50}{2}$ [ (2 × - 6) + (49 × 4) ]

= 25 ( - 12 + 196 )

= 25 × 184

= 4600

6 0

4 years ago

The quadratic function fhas a vertex at (3,4) and opens upward. The quadratic function g is shown below.

Alecsey [184]

Answer:

Option (C)

Step-by-step explanation:

Equation of the quadratic function having vertex at (3, 4) and opening upwards,

So the the minimum point of the function is (3, 4).

Therefore, minimum value of the function is 4 at x = 3.

y = (x - h)² + k [Here, (h, k) is the vertex]

g(x) = 2(x - 4)² + 3

Vertex of the parabola is (4, 3).

Since, leading coefficient is positive, parabola will open upwards.

Therefore, vertex will be the minimum point.

Minimum value of the function will be 3 at x = 4.

Minimum value of the function 'f' is greater than the minimum value of the function 'g'.

Option (C) will be the answer.

6 0

3 years ago

Ben has a cell phone plan that provides 200 free minutes each month for a flat rate of $39. For any minutes over 200, Ben is cha

faltersainse [42]

Answer:

$\left\{\begin{matrix}39 & x\leq 200\\ 39+(x-200)\times 0.35 & x>200\end{matrix}\right.$

Step-by-step explanation:

We are given that Ben has a cell phone plan that provides 200 free minutes each month for a flat rate of $39.

We are also told that For any minutes over 200, Ben is charged $0.35 per minute.

let x be the minutes used each month

So, if $x\leq 200$

So, coat will be $39

If $x>200$

So, Ben is charged $0.35 per minute

So, when $x>200$

So, charge = $39+(x-200)\times 0.35$

So, the piecewise functions accurately represents charges based on Ben's cell phone :

$\left\{\begin{matrix}39 & x\leq 200\\ 39+(x-200)\times 0.35 & x>200\end{matrix}\right.$

4 0

3 years ago

Read 2 more answers

Long division 5th grade I’m sorry if I’m asking a lot but I’m really new to this

Nuetrik [128]

Answer:

95.2

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers