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2 years ago

The sum of three consecutive integers is 105. Find the smallest integer.

Mathematics

1 answer:

Rasek [7]2 years ago

3 0

Answer:

34.

Step-by-step explanation:

The three integers would be 34,35,36 because the sum of the three numbers is 105.

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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is

trasher [3.6K]

The function is graphed as shown below

Part A:

We use the formula $- \frac{b}{2a}$ to find the vertex of the function. A quadratic function of the form of $a x^{2} +bx+c$ and equating this form to the given function $- x^{2} +20x-75$ , we have
$b=20$ and $a=-1$ .

Substituting $a$ and $b$ into the vertex formula, we have
$x=- \frac{20}{2(-1)}=10$ , as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

$- x^{2} +20x-75=0$
$-( x^{2} -20x+75)=0$
$x^{2} -20x+75=0$
$(x-5)(x-15)=0$
$x=5$ and $x=15$ , as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos

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3 years ago

PLEASE HELPPP! Write the quotient<br> as a mixed number.<br> 32 divided by 5 = 6 R2

dmitriy555 [2]

Answer:

$6 \frac{2}{5}$

Step-by-step explanation:

6 is the whole number, while 2 is the numerator and 5 is the denominator.

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3 years ago

When a quadratic equation has a repeated solution it's called

Talja [164]

A blank root or a root of blank

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3 years ago

The area of a playground is 336 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of th

kondaur [170]

L=16
W=21

Set up a systems of equations:
x=length
y=width

xy=336
x+5=y

Use substitution to solve:
x(x+5)=336
x^2+5x=336

Solve using factoring:
x^2+5x-336=0
(x-16)(x+21)=0
x=16 and x= -21
Since length can't be negative, l=16

To find width, plug length into the first equation:
(16)y=336
y=21

So...
L=16
<span>W=21</span>

7 0

2 years ago

Read 2 more answers

12000 corn seeds and 92% grew how many plants. How many plants grew. Please explain your reasoning.

Vedmedyk [2.9K]

It's 11040 plants because 92 percent of 12000 is 11040. (Idk if this is the best reasoning but :/)

4 0

3 years ago

The sum of three consecutive integers is 105. Find the smallest integer.​

The sum of three consecutive integers is 105. Find the smallest integer.