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3 years ago

Fill in the table using this function rule

2 answers:

8 0

This one isn't too hard, just plug in each value!

x = -1
y = -4(-1) + 3
y = 7

x = 0
y = -4(0) + 3
y = 3

x = 1
y = -4(1) + 3
y = -1

x = 2
y = -4(2) + 3
y = -5

Misha Larkins [42]3 years ago

6 0

Answer:

1st blank: 7

2nd blank: 3

3rd blank: $-1$ .

4th blank: $-5$ .

Step-by-step explanation:

We have been given a function formula $y=-4x+3$ . We are asked to fill in the given table.

We will substitute the given x values in our given formula to solve for y as:

$y=-4x+3$

$y=-4(-1)+3$

$y=4+3$

$y=7$

1st blank: 7

$y=-4x+3$

$y=-4(0)+3$

$y=0+3$

$y=3$

2nd blank: 3

$y=-4x+3$

$y=-4(1)+3$

$y=-4+3$

$y=-1$

3rd blank: $-1$

$y=-4x+3$

$y=-4(2)+3$

$y=-8+3$

$y=-15$

4th blank: $-5$ .

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The area of a rectangular piece of cardboard is represented by

Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

$A = wl$

w(2w + 3) = 9

From this, we get that:

$l = 2w + 3, A = 9$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

In this question:

$w(2w+3) = 9$

$2w^2 + 3w - 9 = 0$

Thus a quadratic equation with $a = 2, b = 3, c = -9$

Then

$\Delta = 3^2 - 4(2)(-9) = 81$

$w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5$

$w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3$

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0

3 years ago

Find the area of the figure.

Contact [7]

area of rectangle= 8*13=104m^2

base of the Triangle= 13 -(4+4)=5

area of Triangle = 5*6/2=15m^2

area of shaded shape =104-15= 89m^2

7 0

3 years ago

Q6. (15 points) IQ examination scores of 500 members of a club are normally distributed with mean of 165 and SD of 15.

melamori03 [73]

Answer:

a) 0.8413

b) 421

c) $P_{95} = 189.675$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 165

Standard Deviation, σ = 15

We are given that the distribution of IQ examination scores is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(IQ scores at most 180)

P(x < 180)

$P( x < 180) = P( z < \displaystyle\frac{180 - 165}{15}) = P(z < 1)$

Calculation the value from standard normal z table, we have,

$P(x < 180) = 0.8413 = 84.13\%$

b) Number of the members of the club have IQ scores at most 180

n = 500

$\text{Members} = n\times \text{P(IQ scores at most 180)}\\= 500\times 0.8413\\=420.65 \approc 421$

c) P(X< x) = 0.95

We have to find the value of x such that the probability is 0.95

$P( X < x) = P( z < \displaystyle\frac{x - 165}{15})=0.95$

Calculation the value from standard normal z table, we have,

$P(z < 1.645) = 0.95$

$\displaystyle\frac{x - 165}{15} = 1.645\\\\x = 189.675$

$P_{95} = 189.675$

8 0

3 years ago

Simplify the following expression.

HACTEHA [7]

Remember that exponentioal rule
x^m times x^n=x^(m+n)
therefor
7^4 times 7^-6=7^(4-6)=7^(-2)
remember the other rule
x^-m=1/(x^m) so
7^-2=1/(7^2)=1/49
answe ris A

5 0

3 years ago

John is looking at the eagle on top of a building The height of the building is 120 ft Approximately how many feet is Jack away

bearhunter [10]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete. A similar question is attached and is solved.

Solution:

A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, isosceles, equilateral and right angled triangle.

A right angled triangle is a triangle with one angle equal to 90 degrees. The longest side of a right angled triangle is known as the hypotenuse. Trigonometric identities is used to show the relationship between the angles and sides of a right angled triangle, i.e.:

sinθ = opposite/hypotenuse; cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent

From the image:

let the distance from jack to the base of the building be x, hence:

tan60 = x / 60

x = 60 * tan60 = 104 ft.

8 0

3 years ago