Find the value of the missing coefficient a in the equation y = a(x - 3)(x + 5) if the graph goes through the point (1, -6)

Plz help I will mark brainliest

Answer:

(a) Amplitude = 4

(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period

(c)

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

Step-by-step explanation:

Given

[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]

Rewrite the function as:

[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]

Solving (a): The amplitude

A cosine function is represented as:

[tex]f(x) = A\cos[B(x - C)] + D[/tex]

Where:

[tex]|A| \to Amplitude[/tex]

So, in this equation (by comparison):

[tex]|A| = |-4|[/tex]

[tex]|A| = 4[/tex]

The amplitude is 4

Solving (b): The period (T)

This is calculated as:

[tex]T = \frac{2\pi}{B}[/tex]

By comparison:

[tex]B =3[/tex]

So:

[tex]T = \frac{2\pi}{3}[/tex]

Solving (c): The shift

The phase shift is C

The vertical shift is D

By comparison:

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

Answer:

Yes

Step-by-step explanation:

875 roses / 7 plants per row

875 / 7 = 125 rows, which is a whole number, meaning nothing is left over

Answer:

[tex]2x + 8[/tex]

Step-by-step explanation:

Area of triangle equal

[tex] \frac{b \times h}{2} = a[/tex]

where b is the base and h is the height.

Plug in what we know.

[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]

Multiply 2 by both sides.

[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]

Divide 6x by both sides.

[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]

Answer:

No, you cannot have a negative distance.

Step-by-step explanation:

No, you cannot have a negative distance.

Let's say you were asked for the absolute value of -4. How many units is -4 away from 0? The answer would be 4. There is no negative distance from 0.

Hope this helps, please mark brainliest! :)

Answer:

Table could be first x = 2, y = 4, then x = 4, y = 8. It is proportional because both (x,y) values equal 1/2. The equation is x = 1/2y. Last, the table could be the same, or you could do first, x = 6, y = 12, then x = 12, y = 24, because they still equal 1/2.

Step-by-step explanation:

Explanation:

P(T = 1) is the notation that means "The probability of getting exactly one tail". The table shows 3/8 in the bottom row, under the "1" in the top row. So that's why P(T = 1) = 3/8

Or it might make more sense to say P(one tail) = 3/8 so we don't have too many equal signs going on.

Answer:

Mary's friend Larry is taller by 15cm.

Step-by-step explanation:

First look for the bigger number.

Then subtract the smaller number from the bigger number.

Answer:

D. 5 + c

Step-by-step explanation:

( - 5 - c ) ( - 1 )

use distributive property ; to multiply -5 and - c by -1.

Answer:

C ,D , E just follow it . thank me later if its right

Answer:

E

Step-by-step explanation:

(10+7)(50+1)

=17×51

=867

Answer:

option B : 31.4 cm

Step-by-step explanation:

Given radius , r = 5cm

Circumference = [tex]2 \pi r[/tex]

                       = 2 x 3.14 x 5

                       =10 x 3.14

                       = 31.4 cm

Answer:

b. 31.4

Step-by-step explanation:

The radius of the circle can be plugged into C=(pi)2r. So 5x2= 10 and 10x(pi)= 31.4

Your Answer is in the above image.

[tex]h(-3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]

Step-by-step explanation:

[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]

[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]

[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]

[tex]h(2) = \frac{ 8 - 1}{4} [/tex]

[tex]h(2) = \frac{7}{4}[/tex]

[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]

[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]

[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\ h(3) - h( - 2) =-2 + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-2}{1}+ \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16}{8} + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16+11}{8} \\ h(3) - h( - 2) = \frac{-5}{8} \\ - \frac{5}{ 8} [/tex]

Answer:

24

Step-by-step explanation:

the perimeter is all sides added up

therefore to solve for "z"

3z + 3z + 4z + 3 + 4z + 3 = 118

simplify

14z + 6 = 118

isolate z by first subtracting 6 from both sides and then dividing by 14 for both sides

z=8

plug z into side CB as AD and CB are congruent

3(8)

=24

Answer:

Step-by-step explanation:

Answer:

acute triangle

Step-by-step explanation:

First find the other angle

The sum of the angles is 180

x+65+60  = 180

x + 125 = 180

x = 180-125

x = 55

All three angles are different so all three side lengths are different

All the angles are less than 90 so all the angles are acute

This is an acute scalene triangle

Answer:

im is 55 so the only correct option is c

Step-by-step explanation:

hope this helps! have a great day!!

Answer:

4-12x

Step-by-step explanation:

opening the brackets;

(-6×-2/3)- 12x

-2×-2 -12x

4-12x

Answer:

4 - 12x

Step-by-step explanation:

We can find an equivalent expression by distributing

-6(-⅔+2x)

Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )

-6 * -⅔ = 4

-6 * 2x = -12x

We would be left with 4 - 12x

Answer:

-3

Step-by-step explanation:

My knowledge ;D

Answer:

A

Step-by-step explanation:

42-14=28

Answer:

A. 42 and 14

Step-by-step explanation:

first number = x

second number = y

x - y = 28

3x - x = 28

(y is now x because it says the second number is whatever x was, but three times less)

x = 14

3(14) - (14) = the original number, 28

Answer:

,(i) answer is 203,918

(ii)answer is227,306.36

9514 1404 393

Answer:

  B

Step-by-step explanation:

In order for the matrix to represent the equations, the coefficients in the equations need to match the terms in the matrix. That is only the case for choice B.

__

Details are important in math.

Answer:

345

Step-by-step explanation:

Answer:

[tex]P(T = 1) = \frac{3}{8}[/tex]

Step-by-step explanation:

The table, along with the relative frequency chart, state that the probabilities are:

[tex]P(T = 0) = \frac{1}{8}[/tex]

[tex]P(T = 1) = \frac{3}{8}[/tex]

[tex]P(T = 2) = \frac{3}{8}[/tex]

[tex]P(T = 3) = \frac{1}{8}[/tex]

Find the probability P(T=1)

As given by the table, and by the relative frequency chart, [tex]P(T = 1) = \frac{3}{8}[/tex]

Answer:

100/8 = 12.5 (s)

Step-by-step explanation:

hmm bro

Answer:

[tex]{ \boxed{ \tt{formular : { \bf{ \green{time = \frac{distance}{speed} }}}}}} \\ time = \frac{100}{8} \\ { \boxed{time = 12.5 \: seconds}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Answer:

3x4 +x3+ 15x2+30x-14

Step-by-step explanation:

Answer:

$3.53 per lb of salami

Step-by-step explanation:

0.75 lb of salami for $2.65

The price per of salami will be :

0.75 lb = $2.65

1 lb = x

Using cross multiplication :

0.75 * x = $2.65 * 1

0.75x = $2.65

Divide both sides by 0.75

0.75x / 0.75 = $2.65 / 0.75

x = $3.533

This means that :

The price per unit of salami is $3.53

Answer:

0.75 lb of salami for $2.65 is $3.53 per lb of salami.

Answer:

s(8) = 1162

Step-by-step explanation:

We are told that the acceleration is;

a(t) = 18t + 16

Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.

v(t) = ∫a(t) = ∫(18t + 16)

v(t) = 9t² + 16t + c

We are told that at t = 0, v(0) = 16

Thus;

9(0)² + 16(0) + c = 16

c = 16

Thus;

v(t) = 9t² + 16t + 16

Also, the velocity is the first derivative of distance. Thus;

S = ∫v(t) = ∫9t² + 16t + 16

S = 3t³ + 8t² + 16t + c

At t = 0, s(t) = 10. Thus;

10 = 3(0³) + 8(0²) + 16(0) + c

c = 10

Thus;

s(t) = 3t³ + 8t² + 16t + 10

At t = 8;

s(8) = 3(8³) + 8(8²) + 16(8) + 10

s(8) = 1162

Hello,

As somebody has distroyed my question, (may be he have not understood ?)

i will reply to y=(√x)+5

[tex]\displaystyle \boxed{\dfrac{d^n y}{dx^n} =(-1)^n*n!! *\dfrac{1}{2^n} *x^{-\frac{2n+1}{2} }\\}\\y'=\dfrac{1}{2} *x^{-\frac{1}{2}} \\\\y''=-\dfrac{1}{4} *x^{-\frac{3}{2}} \\...\\[/tex]

Answer:

D

Step-by-step explanation:

the domain of the function is the boundaries in the X condition. using the graph we see X starts at 2 and ends at 7 so the domain is

[tex]2 \leqslant x \leqslant 7[/tex]