Solve the following linear inequalities given in the first column and choose the appropriate results

Answer:

Step-by-step explanation:

Find the zero's of f(x)

Answer:

[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]

(one real zero and 2 complex zeros)

Step-by-step explanation:

Given polynomial:

[tex]f(x)= 2x^3-12x^2+20x-16[/tex]

According to the Factor Theorem, if f(4) = 0 then (x - 4) is a factor of the given polynomial.

[tex]\implies f(x)=(x-4)(ax^2+bx+c)[/tex]

Expand the brackets:

[tex]\implies f(x)=ax^3+bx^2+cx-4ax^2-4bx-4c[/tex]

[tex]\implies f(x)=ax^3+(b-4a)x^2+(c-4b)x-4c[/tex]

Compare coefficients with the given polynomial:

[tex]\implies a=2[/tex]

[tex]\implies -4c=-16 \implies c=4[/tex]

[tex]\implies (b-4a)=-12 \implies b-8=-12 \implies b=-4[/tex]

Substitute the found values of a, b and c:

[tex]\implies f(x)=(x-4)(2x^2-4x+4)[/tex]

To find the zeros of f(x), set the function to zero and solve for x:

[tex]\implies (x-4)(2x^2-4x+4)=0[/tex]

[tex]\textsf{Therefore},\: (x - 4) = 0\: \textsf{ and }\: (2x^2-4x+4)=0[/tex]

[tex]\textsf{To solve}\: (2x^2-4x+4)=0\: \textsf{ use the quadratic formula}[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(2)(4)} }{2(2)}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{-16}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{16 \cdot -1}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{16}\sqrt{-1}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm 4i}{4}[/tex]

[tex]\implies x=1 \pm i[/tex]

Therefore, the zeros of the function are:

[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]

(one real zero and 2 complex zeros)

Answer:

This needs more context im sorry

Step-by-step explanation:

The total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Since an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. The heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the length of the shorter base of each trapezoid is 1.5 centimeters, the radii of the hexagon, and the base of the trapezoid form a triangle of

So, the area of this triangle is A = 1/2bh

= 1/2 × 1. 5 cm × 2 cm

= 1.5 cm × 1 cm

= 1.5 cm²

Since there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A

= 6 × 1.5 cm²

= 9.0 cm²

So, the total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Learn more about area of a hexagon here:

https://brainly.com/question/369332

Answer:

[tex] \frac{4}{5} > \frac{1}{2} [/tex]

Step-by-step explanation:

[tex] \frac{4}{5} = 0.8[/tex]

[tex] \frac{1}{2 } = 0.5[/tex]

Answer:

6 times means 6 multiplied by

The sum of a number and 2 means x + 2

x = number

(2+x) × 6

Answer:

62.9 inches^3

Step-by-step explanation:

Find the area of both using the formulas then add them togther

r = radius = 4/2 = 2

h = height = ;cone = 3;cylinder = 4

cylinder volume = pie*2^2*4=50.3

cone volume = pie *2^2*3/3=12.6

total = 62.9 inches^3

Formula : V = πr²h/3

Fill in the values.

(3.14)(4)^(2)(6/3)

V=100.48 yd^3

Answer: A) an equilateral triangle inscribed in a circle

Step-by-step explanation:

       In the mathematical world, a compass is a mathematical tool used for drawing and constructing precise shapes. You have likely seen one of these before, I have attached a visual example of what one might look like.

       Out of these given options, the only one that utilizes a compass for one step in addition to drawing the circle itself is A:

          A) an equilateral triangle inscribed in a circle

Read more about using a compass here: https://brainly.com/question/27490907

Answer:

  1161

Step-by-step explanation:

We can solve this using what we know about multiples of 3 and 5. Multiplying the first number by 3 will give the value ...

  1?? × 3 = 38? . . . . where ? is an unknown digit

The two least significant digits in the first number must be ones that give 80-something when multiplied by 3. They will be between 80/3 = 26 2/3 and 90/3 = 30. The requirement that the least significant digit be odd* means the choices are 27 or 29.

When the first number is 127, its triple is 381. The 1 in the least significant digit is disallowed by the requirement that the 9 digits of these numbers be unique. (127 already has 1 as its most-significant digit.)

So, the first number is 129, making the second number be 3×129 = 387, and the third number be 5×129 = 645.

The numbers have the ratios ...

  129 : 387 : 645 = 1 : 3 : 5 . . . . . . . as required.

We note that the digits 1–9 are used exactly once each, as required.

The sum of the numbers is 1161.

_____

* Only odd numbers will give a product that ends in 5 when they are multiplied by 5. The requirement that the third number have a ones digit of 5 means the ones digit of the first number must be odd.

Answer:

B

Step-by-step explanation:

Remark

If the Hypotenuse and a corresponding leg in one right triangle = the Hypotenuse and corresponding leg of the second right triangle, then the triangles are congruent.

Answer

HL

Given data:

1. Determining the range of the line plot:

To determine the range of the data, we need to subtract the biggest value of the data (8) from the smallest value of the data (1).

Thus, 7 is the range.

2. Determining the mode of the line plot:

The mode of the data is the digit that has repeated the most. In this case, the digit "2" has repeated five times and has repeated the most.

Henceforth, "2" is the mode.

Learn more about range and modes:

Answer:

Range = 7

Mode = 2

Step-by-step explanation:

Question (a)

Range = Highest value - Lowest value

           = 8 - 1

           = 7

Question (b)

The mode is the most common value that appears in the data.

From inspection of the line plot, we can see that 2 is the most common value (the value that appears the most in the data set).

Answer:

d+d+1+d+5+4+12+24/6

Step-by-step explanation:

add the numbers and divide them by 6

Answer:

3d + 432

Step-by-step explanation:

= d ÷ 4 + d + 1 ÷ 12 + d + 5 ÷ 24

= d + d + d + 1 + 5 ÷ 4 ÷ 12 ÷ 24

= 3d + 6 ÷ 0.013888.....

= 3d + 432

Please mark BRAINLIEST

Answer:

-(10)^-1 = A. -1/10

y^-5/x^-3 for x = 2 and y = -4. C. -1/128

Is the number written in scientific notation, if not explain, 5.1 x 10^-8? A. Yes; the number is written in scientific notation

What is the number written in standard notation 5.71 x 10^-3? D) 0.00571

Suppose that the diameters of different types of hairs are 1.7 x 10^-4 cm, 1.4 x 10^-3 cm, 1.2 x 10^-5 cm, and 1.9 x 10^-4 cm? What is the order of the hairs from least to greatest's diameter? B. 1.2 x 10^-5, 1.7 x 10^-4, 1.9 x 10^-4, 1.4 x 10^-3

What is the expression written using each base only once (-4) ^-6 (-4) ^7? B. -4

Find the simplified form of the expression. Give your answerer in scientific notation.

(3 x 10^6) (8 x 10^-4) B. 2.4 x 10^3

What is the simplified form of the expression (m^7) ^2? D. m^14

What is the simplified form of the expression t^8 (t^10) ^0? C. t^8

What is the simplified form of the expression (3q^2) ^4?

D. 81q^8

What is the simplified form of the expression (3xy^3) ^2(xy) ^6? A. 9x^8 y^12

I am not sure but according to my calculation answer of no.1 may be 67. And I am in 8 grade so I couldn't solve others. So sorry !!

Answer:

Equation: y=mx+b

sorry for taking so long! :)

AC) y=-1, because it is remaining constant and the slope is zero, the y intercept is -1.

AB) The slope is 1 and the y intercept is 1.

So, y=x+1

BC) The slope is -6. The y intercept is harder to find. You can use this equation however;

y-y(1)=m(x-x(1)

y-5=-6(x-4)

y=-6x+29

Step-by-step explanation:

I take it this is meant to be a multiplication, right ?

not a "function of function", which would be symbolized by a little empty circle.

to multiply 2 function means basically the same as to add, subtract or divide 2 functions : to apply the arithmetic operation in both expressions.

(f×g)(x) = (-2x² + 4x)(x² + 18x + 77) =

= -2x⁴ - 36x³ - 154x² + 4x³ + 72x² + 308x =

= -2x⁴ - 32x³ - 82x² + 308x

Answer:

See attached image.  82 and 98 degrees.

Step-by-step explanation:

On attached document.

Answer:

1000/5=200?

There are five prizes?

Each one has an equal amount?

Answer:

no

you can subsitute x = -5 into y= 5x+9 and the ans should be -16 instead of -10

so it does not satisfy

Hello!

In order to see whether or not a point satisfies an equation, just plug in the values:-

Instead of y, plug in 10:-

10=5x+9

Instead of x, plug in -5:-

10=5(-5)+9

Solve:-

10=-25+9

10=-16

See? We have a false statement.

Hence, this point does not satisfy the inequality.

I hope it helps you.

If you have any queries regarding my answer, please comment :)

[tex]\bf{CupcakeRealm8701~:)}[/tex]

[tex]1000000000 \times 43000000 = 43000000000000000[/tex]

Answer: 7.4.

Step-by-step explanation: To find the area of a triangle, you need the base, height, and then divide the results by two.  The following is done below:

A = h x b / 2, where h is the height, b is the base, and A is the area of the triangle.

A = 3.7 x 4 = 14.8.  

Next, 14/8 / 2 = 7.4.

Therefore, 7.4 is your answer.

Hope this helps! :)

Answer: 6.9

Step-by-step explanation:

Solve for the hypotenuse in the smaller triangle 5.83

Solve for x²= 9² - 5.83² = 81 - 33.99

X² = 47.01

A quadrilateral is a four sided figure. It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure

A quadrilateral is a four sided figure. The images are not shown here so we don't know what the dimensionof each figure is.

It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure and find the area of the two triangles in order to obtain the area of the orginal figure.

Learn more about  quadrilateral: https://brainly.com/question/13805601

Answer:

A 31.3

Step-by-step explanation:

just took the test

Answer:

27.0m^2

Step-by-step explanation:

Use the formula A = 0.5 * a * b * sin (x)

this formula is used for obtuse angles where a & b are the sides (12,7) and x is the angle between them.

Fill in the blanks:

A = 0.5 * 12 * 7 * sin (40)

use demos scientific calculator

A= 26.99

round up

27.0 m^2

Answer:

24

Step-by-step explanation:

Perimeter of a shape = sum of all lengths of sides

⇒ Perimeter of a rectangle = (2 × width) + (2 × length)

From inspection of the rectangle:

⇒ Perimeter = (2 × 4) + (2 × 8)

                     = 8 + 16

                     = 24