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4 years ago

Which function is a horizontal translation of the parent quadratic function

Mathematics

1 answer:

alexandr1967 [171]4 years ago

8 0

Answer:

Step-by-step explanation:

Given f(x) then f(x + a) represents a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Thus

g(x) = (x - 4)² represents a horizontal translation to the right of f(x) by 4 units.

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What is the value of c such that X^2+14x+c, is a perfect-Square trinomial?

Slav-nsk [51]

I hope this helps you

8 0

3 years ago

The concentration C (in mg/dl), of an antibiotic in a patient’s bloodstream per hour, t, is given by: c(t) = (50t)/(t^2+25) In o

NARA [144]

Answer:

Step-by-step explanation:

Functions

The problem describes a function that expresses the concentration of an antibiotic in mg/dl vs time in hours as:

$\displaystyle c(t)=\frac{50\ t}{t^2+25}$

We need to find the first value of t such that

$\displaystyle c(t)\geq 4$

It means that

$\displaystyle \frac{50\ t}{t^2+25}\geq 4$

Operating with the inequality

$\displaystyle 50\ t\geq 4\ t^2+100$

Rearranging and dividing by 2, we have a polynomial inequality:

$\displaystyle 2t^2-25t+50\leq 0$

Factoring

$\displaystyle 2(t-10)\left (t-\frac{5}{2}\right )\leq 0$

There are two possible values for t, both valids because they are positive

$\displaystyle t=\frac{5}{2}=2.5, \ t=10$

We need to find the first value, i.e.

$t=2.5 \ hours$

Now for the graphic method, we plot the graph for the function and a horizontal line at c=4 to find the values of t.

The graph is shown in the image provided below. We can see both values where the funcion and C=4 intersect. Both values coincide with the previously analitically found values

4 0

3 years ago

How do you solve this

fiasKO [112]

(((x + y) / 3) + (1 / x)) / (5 + (15 / x))
The best way is to make it one fraction.
Multiply by ((3x/3x) / (3x/3x)) to remove the other fractions.
((x(x + y)) + 3(1)) / (5(3x) + 3(15))
(x^2 + xy + 3) / (15x + 45)
Then factor to simplify
(x^2 + xy + 3) / (3(x + 15))

4 0

3 years ago

A vender sold a combined total of 131 sodas and hot dogs. The number of hot dogs sold was 31 less than the number of sodas sold.

puteri [66]

Answer:

81 sodas and 50 hotdogs

Step-by-step explanation:

131 = x + x - 31

131 + 31 = x + x - 31 + 31

162 = x + x

x = 81

131 = 81 + (81 - 31)

131 = 81 sodas + 50 hot dogs

5 0

3 years ago

A store manager wishes to investigate whether there is a relationship between the type of promotion offered and the number of cu

sveticcg [70]

The answer would be D.

5 0

3 years ago