The function "g" is defined as g(x)=5x+a, where "a" is a constant. If g(4)=31, what is the value of "a"?

Write a rule for the linear function in the table.

JulijaS [17]

Answer:

I guess that you want to know the transformations:

We start with:

f(x) = y = 4*x + 3

a)the transformed function is:

f(x) = y = -4*x - 3

So the sign changed.

This means that we go from (x, y) to (x, - y)

This is a reflection over the x-axis which changes the sin of the y component.

b) Now we go to f(x) = 4*x + 3

So the coefficient in the leading term changed.

This is a horizontal contraction:

A horizontal contraction of factor K for the function g(x) is: g(K*x)

In our case, we have:

f(K*x) = 4*(k*x) + 3 = x + 3

4*k*x = x

4*k = 1

k = 1/4

Then the transformation is an horizontal contraction of scale factor 1/4.

6 0

2 years ago

Uma is paid $12.25 for each chair she decorates. Last week she

Luda [366]

Answer:

$514.50

Step-by-step explanation:

7+4+2+8=21

$12.25x21=$514.50

6 0

2 years ago

What is the missing number in the synthetic division problem below?

Crank

Given:

A synthetic division problem.

To find:

The missing number it in the given synthetic division problem.

Solution:

The given synthetic division problem is:

$3|\overline{3\quad -2\quad 2\quad 4}\\$

$\quad 6\quad 8\quad 20\\$

$\overline{3\quad 4\quad ?\quad 24}$

In synthetic division, we need to add first and second row to get the bottom row.

$3+0=3$

$-2+6=4$

$4+20=24$

Similarly,

$2+8=10$

Therefore, the missing value in the given synthetic problem is 10. Hence, the correct option is C.

6 0

2 years ago

The area of triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is k

n200080 [17]

Answer:

The value of a will be $a=-\frac{1}{2}$

Step-by-step explanation:

Start by graphing the parabola and the three points of the triangle. These points are at intersections of y=a(x-1)(x-4) and the axes

so the y = 0 points are (1,0) and (4,0).

The x = 0 intersection is when y=a(-1)(-4) or (0,4a)

The base and height of this triangle are

The base would be the distance between the y=0 intersections and the height would be the y value of the other vertex.

Hence, base=3 units and height = 4a units. Thus, area can be calculated as

$A = \frac{1}{2}\times b\times h =\frac{1}{2}\times 3\times 4a = 3$

$a=\frac{1}{2}$

∵ the parabola opens downward therefore a will be negative.

hence, $a=-\frac{1}{2}$

3 0

2 years ago

PLATO: Type the correct answer in each box. The vector is first dilated by a factor of 2.5 and then rotated by pi/2 radians. If

yawa3891 [41]

Answer:

a = -1, b = -2.5

Step-by-step explanation:

Rule for the dilation of a vector $\binom{x}{y}$ by a scale factor of k is,

(x, y) → (kx, ky)

BY using this rule for a vector $\binom{-1}{4}$ by a scale factor of 2.5

$\binom{-1}{4}$ → $\binom{-2.5}{1}$

Followed by the rotation by 90° Or $\frac{\pi }{2}$ radians,

Rule for rotation of a vector by 90° is,

(x, y) → (-y, x)

By this rule vector $\binom{-2.5}{1}$ will become,

$\binom{-2.5}{1}$ → $\binom{-1}{-2.5}$

If we represent this vector by $\binom{a}{b}$ ,

Then a = -1 and b = -2.5 will be the answer.

5 0

3 years ago

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