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2 years ago

The x-intercept was substituted incorrectly

Mathematics

1 answer:

seraphim [82]2 years ago

4 0

Answer:

Step-by-step explanation:

let the eq. of parabola be

y=ax²+bx+c

points (-1,0),(2,0),(3,4) and (0,-2) lie on it.

0=a-b+c

0=4a+2b+c

subtract

3a+3b=0

a=-b

4=9a+3b+c

-2=0+0+c

c=-2

a-b-2=0

-b-b-2=0

-2b-2=0

b+1=0

b=-1

a=-b=-(-1)=1

eq. of parabola is

y=x²-x-2

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3 years ago

Is 3/5 and 1/10 closest to 0, 0.5, or 1

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3 years ago

The circumference of a dime is 56.52 mm find the diameter

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3 years ago

Read 2 more answers

The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progre

Rudik [331]

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : $a=-2$

Common difference : $d = 5 - (-2)$

$= 5 + 2$

$= 7$

nth term of an A.P. is

$a_n=a+(n-1)d$

where, a is first term and d is common difference.

$a_n=-2+(n-1)(7)$

According to the equation, $a_n>200$ .

$-2+(n-1)(7)>200$

$(n-1)(7)>200+2$

$(n-1)(7)>202$

Divide both sides by 7.

$(n-1)>28.857$

Add 1 on both sides.

$n>29.857$

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

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

Substituting n=30, a=-2 and d=7, we get

$S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]$

$S_{30}=15[-4+(29)7]$

$S_{30}=15[-4+203]$

$S_{30}=15(199)$

$S_{30}=2985$

Therefore, the sum of all the terms in the progression is 2985.

6 0

3 years ago

A supply company manufactures masks and ventilators for hospitals. To maintain hugh quality, the company should not manufacture

notsponge [240]

Answer:

20 masks and 100 ventilators

Step-by-step explanation:

I assume the problem ask to maximize the profit of the company.

Let's define the following variables

v: ventilator

m: mask

Restictions:

m + v ≤ 120

10 ≤ m ≤ 50

40 ≤ v ≤ 100

Profit function:

P = 10*m + 65*v

The system of restrictions can be seen in the figure attached. The five points marked are the vertices of the feasible region (the solution is one of these points). Replacing them in the profit function:

point Profit function:

(10, 100) 10*10 + 65*100 = 6600

(20, 100) 10*20 + 65*100 = 6700

(50, 70) 10*50 + 65*70 = 5050

(50, 40) 10*50 + 65*40 = 3100

(10, 40) 10*10 + 65*40 = 2700

Then, the profit maximization is obtained when 20 masks and 100 ventilators are produced.

4 0

3 years ago