All categories

3 years ago

I need help with this

Mathematics

1 answer:

evablogger [386]3 years ago

6 0

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

You might be interested in

What is the range? 5,10,5,4,5,10,3,10 Help me pls

Nady [450]

Answer: the answer is 7

Step-by-step explanation: the lowest number is 3 and the biggest one is 10 so you substract 10-3 and you get 7

8 0

3 years ago

Read 2 more answers

Which expression represents the number of feet that are in x yards?

AleksandrR [38]

we know that

$1\ yard=3\ feet$

Let

y-------> the number of feet that are in x yards

by proportion

Find the value of y

$\frac{3}{1} \frac{feet}{yard}=\frac{y}{x} \frac{feet}{yards} \\ \\y=3x\ feet$

therefore

the answer is the option C

$3x$

3 0

3 years ago

Read 2 more answers

4 x 15 = What is the product

Marysya12 [62]

Answer: 60

Step-by-step explanation: multiply four by 15 in this case take four 15's and add them all up

3 0

3 years ago

Read 2 more answers

Schaum earns (x4 + 16x) every month. His wife earns (3x4 + 11x) every

damaskus [11]

Given:

Schaum's earnings in a month = $x^4+16x$

His wife's earnings in a month = $3x^4+11x$

Where x is the number of working days in a month.

To find:

The total earnings in a month.

Solution:

We know that,

Total earnings = Schaum earnings + His wife's earnings in a month

$=x^4+16x+3x^4+11x$

$=(x^4+3x^4)+(16x+11x)$

$=4x^4+27x$

Therefore, the correct option is A.

7 0

3 years ago

Triangle RST has vertices R(−2, 2), S(1, 1), and T(−1, −3). Find the coordinates for the image of each vertex for the given rota

Vesnalui [34]

Answer:

A. $R'(-2,-2),S'(-1,1),$ and $T'(3,-1)$

Step-by-step explanation:

Given:

Vertices of triangle RST are $R(-2,2),S(1,1),$ and $T(-1,-3)$ .

Rotation is 90° about the center O(0,0). The rotation is counter-clockwise as the angle of rotation is positive.

Now, the co-ordinate rule for 90° rotation counter-clockwise is given as: $(x,y)$ → $(-y,x)$

$x$ and $y$ values interchange their places with $y$ becoming negative when interchanged.

So, $R(-2,2)$ → $R'(-2,-2)$

$S(1,1)$ → $S'(-1,1)$

$T(-1,-3)$ → $T'(-(-3),-1)$

⇒ $T(-1,-3)$ → $T'(3,-1)$

Therefore, the image of the vertices are $R'(-2,-2),S'(-1,1),$ and $T'(3,-1)$ .

6 0

3 years ago