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2 years ago

A technology company produces two types of calculators.

Mathematics

1 answer:

lubasha [3.4K]2 years ago

7 0

10 ≤ x ≤ 30, x < 2y, x < 40.

Solution:

Given x is the number of graphing calculators produced daily and

y is the number of scientific calculators produced daily.

Step 1: A company produce atleast 10 and not more than 30 graphing calculators per day.

⇒ 10 ≤ x < 30

Step 2: Each day, the number of graphing calculators cannot exceed twice the number of scientific calculators produced.

⇒ x < 2y

Step 3: The number of scientific calculators cannot exceed 40 per day.

⇒ x < 40

Hence, the constraints are 10 ≤ x ≤ 30, x < 2y, x < 40.

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Alex has 520 yards of fencing to enclose a rectangular area.

Pavlova-9 [17]

Perimeter =2w+2L= 520.
We can solve this by understanding that the area is maximized by a square
Therefore L=w.

p=2w+2w=520=4w
w=130

Area

A=wL=130(130)= 16900 square yards

6 0

2 years ago

Read 2 more answers

Solve the equations by factoring: x^2−3x−40=0 4x^2−81=0

Alja [10]

Answer:

see explanation

Step-by-step explanation:

Given

x² - 3x - 40 = 0

Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)

The factors are - 8 and + 5, since

- 8 × 5 = - 40 and - 8 + 5 = - 3, thus

(x - 8)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 5 = 0 ⇒ x = 5

------------------------------------------------------

Given

4x² - 81 = 0 ← this is a difference of squares and factors in general as

a² - b² = (a + b)(a - b), thus

4x² - 81

=(2x)² - 9²

= (2x + 9)(2x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = - $\frac{9}{2}$

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = $\frac{9}{2}$

8 0

2 years ago

Read 2 more answers

The table shows the temperature (y) at different altitudes (x).

Shtirlitz [24]

Answer/Step-by-step explanation:

2. Using two pairs of values, (0, 59) and (2,000, 51),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{51 - 59}{2,000 - 0} = \frac{-8}{2,000} = -\frac{1}{250}$

3. The y-intercept is the value of y when x = 0. Thus, x = 0, when y = 59. Therefore,

y-intercept (b) = 59

4. To write an equation in slope-intercept form, simply substitute m = -¹/250, and b = 59, in $y = mx + b$

✅ $y = -\frac{1}{250}x + 59$

5. Substitute x = 5,000 in $y = -\frac{1}{250}x + 59$ .

$y = -\frac{1}{250}(5,000) + 59$

$y = -20 + 59$

$y = 39$

At an altitude of 5,000 ft, temperature would be 39°F

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2 years ago

Aubrey's coach asks her to bring 5 liters of water to practice.

fenix001 [56]

Answer:

Step-by-step explanation:

This is because a liter is 1000 milliliters, so multiplying the amount of liters to the milliliters you would get 5000, you would then divide that by 500 since a bottle would contain that much, giving you 10 bottles

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2 years ago

What is the equation of the line connecting (1,5) and (4,14)?

german

To find the slope of the line:
(y2-y1)/(x2-x1)
(14-5)/(4-1)=(9)/(3)=3

Only one of your 4 possible answers has 3 as a slope. However, plugging in each point into the y=mx+b equation, the y-intercept consistently comes out as 2..
y=mx+b
14=3(4)+b b=2
5=3(1)+b b=2
y=3x+2
If there is a consistent, positive slope (from your question, this does not seem to have a quadratic as an option), 3x+5 is not even a viable solution because x=1 when the y-value is 5 (and thus no other x value {0} could have a y-value of 5). It seems as though you have a typo on your hands. Hopefully this helps?

3 0

2 years ago