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Alekssandra [29.7K]
3 years ago
5

Write a quadratic function f whose zeros are 6 and -5 .

Mathematics
2 answers:
Iteru [2.4K]3 years ago
7 0

Answer: f(x) = x² - x - 30

Step-by-step explanation:

Here's a really simple way.

Quadratic equations are the product of two first order equations such as

f(x) = (x + A)(x + B)

intercepts mean the function result is zero, which means that either

(x + A) = 0 or (x + B) = 0

if x + A = 0 then x = - A

if x + B = 0 then x = -B

So all we have to do is to negate the numbers and add x to make the factor

Long story short, this example looks like this

(x - 6)(x + 5) = x² - x - 30

dexar [7]3 years ago
4 0

Answer:

so ez

Step-by-step explanation:

HI IM INDIAN AND STUDING IN 10TH GRADE U?

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Adam and Tom share a sum of money in the ratio 18:17
Digiron [165]

x = total amount split between Adam and Tom.

since we know the total amount split between both in a 18 : 17 ratio is "x", let's divide "x" by (18 + 17) and distribute accordingly to get the amount of each.

\stackrel{Adam~received}{18\cdot \cfrac{x}{18+17}}\qquad \qquad \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that Adam got "5" more}}{ \stackrel{Adam}{18\cdot \cfrac{x}{18+17}}~~ = ~~\stackrel{Tom}{17\cdot \cfrac{x}{18+17}~~ + ~~5} }\qquad \implies \qquad \cfrac{18x}{35}~~ + ~~\cfrac{17x}{35}+5

\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{18x}{35} \right)~~ = ~~35\left( \cfrac{17x}{35}+5 \right)}\implies 18x~~ = ~~17x+175\implies \boxed{x =175} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}}\implies \cfrac{17(175)}{35}\implies \blacktriangleright 85 \blacktriangleleft

5 0
2 years ago
Let f(x)=x^3-x-1
alexira [117]
f(x) = x^3 - x - 1

To find the gradient of the tangent, we must first differentiate the function.

f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1

The gradient at x = 0 is given by evaluating f'(0).

f'(0) = 3(0)^2 - 1 = -1

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

y = -x + c

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

f(0) = (0)^3 - (0) - 1 = -1

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}
6 0
3 years ago
Find the inverse.. ASAP
Evgen [1.6K]
Answer :
F-1(x)=-x/4-7/4


This is right
Go get help to sum sites!!!!!

8 0
3 years ago
A town has a population of 32,000 in the year 2002; 38,400 in the year 2003; 46,080 in the year 2004; and 55,296 in the year 200
NeTakaya
The point is to find the growth rate. The compound formula is:

P=A(1+ growth rate)ⁿ, where A is the initial Value & P the new value after n years:
P₂₀₀₃ =P₂₀₀₂ (1+ growth rate)¹ (the period "n" from 2002 to 2003 being 1 year)

38400 = 32000(1+growth rate)¹
38400 / 32000 - 1= growth rate & growth rate = 1/5 = 0.2
You will balso find the same growth rate for:
P₂₀₀₄ = P₂₀₀₃(1+ growth rate)¹
P₂₀₀₅ = P₂₀₀₄((1+ growth rate)¹
between 2015 & 2002 THERE ARE 14 YEARS:

P₂₀₁₅ = P₂₀₀₂(1+0.2)¹⁴ & P₂₀₁₅ = 32000(1+02)¹⁴ = 410,854
8 0
3 years ago
If 100 treats will feed 15 dogs (each dog is given the same number of treats), how many dogs can be fed with 40 treats?
Lisa [10]

Answer: 6 dogs

Step-by-step explanation:

If 100 treats will feed 15 dogs, then that means that the number of treats that each dog requires is:

= 100/15

= 6.67 treats

If 6.67 treats will feed one dog then the number of dogs that will be fed by 40 is:

= 40 / 6.67

= 6 dogs

4 0
3 years ago
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