Which statement about the polynomial function g(x) is true?

1If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

2If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

3If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

4If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

Answer:

2⁶

Step-by-step explanation:

law of indices states multiplication of powers in and out of bracket 3×2=6

[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The value is 64}[/tex]

A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?

[tex] {p}^{2} > {p}^{2} \: \: and \: \: p {1}^{2} - \: p {2}^{2} \: < \frac{1}{3} [/tex]

Step-by-step explanation:

HOPE ITS HELP

Answers for different section are given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

  f(x) = -x² - 4x + 6

1.    If we take -1 common from the given function, we get

                     f(x) = -1 (x² + 4x - 6)

                    f(x) = -1 (x² + 4x) + 6

     Thus, first block contains -1 and second block contains 4.

2.   Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².

                f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6

                f(x) = -1 ( x² + 4x + 2²) +4 + 6

Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.

3. Then we factorize the bracket and simplify outside the bracket;

               f(x) = -1 (x + 2)² + 10

Thus, first block contains -1, second block contains 2 and third block contains 10.

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Answer:

x = 0 y = -5

x = 3 y = 4

Step-by-step explanation:

x² + y² = 25

y - 3x = -5

-----------------------

y = 3x-5

x² + y² = 25

x² + (3x-5)² = 25

(3x-5)(3x-5) = 9x² -15x -15x + 25

x² + 9x² -15x -15x + 25 = 25

x² + 9x² -15x -15x = 0

x² + 9x² - 30x = 0

10x² - 30x = 0

x(10x-30)=0

x = 0

10x-30=0

x = 3

y - 3x = -5

y - 3(0) = -5

y = -5

y - 3(3) = -5

y - 9 = -5

y = 4

Answer:

(4,3) and (0,-5) are both solutions where we have (x,y).

Step-by-step explanation:

Here are simplified steps:

https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input

Symbolab is an excellent tool for just most math.

Answer:

Step-by-step explanation:

(√6 - √2)/4

Answer:

see below

Step-by-step explanation:

To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.

The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.

D (2,2)

You could also see this on a graph, see image.

E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.

E is (-1,1)

Then we are able to calculate the slope of DE and BC.

To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.

Slope of DE:

(2-1)/(2--1)

= 1/3

Slope of BC:

(0--2)/(3--3)

=2/6

=1/3

The slopes of BC and DE are equal, so the segments are parallel.

(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)

Answer:

the answer is 5

Step-by-step explanation:

if you plug in everything, then the equation is the square root of 2 to the 3rd power minus 7 plus the absolute value of 4.

So first 2 to the third power is 8

Then the absolute value of negative 4 is 4

So 8-7 is 1

The square root of 1 is 1

1 plus 4 is 5, the answer is 5

Answer:

5m-3

Step-by-step explanation:

Answer:

5m-3

Step-by-step explanation:

a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].

c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given points represent on the graph is;

x = 0 , y = 0

x = 120 , y = 0

x = 60 , y = 40

The standard equation is;

[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]

Substitute the value as;

[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)

The above equation  in the standard form is found as;

[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]

c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

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Answer:

2x³ + 2x

Step-by-step explanation:

(x² + x³ + x² + x) - (x² - x³ + x² - x)

= x² + x³ + x² + x - x² + x³ - x² + x

Gathering like terms...

x³ + x³ +x² + x² -x² - x² + x + x

= 2x³ + 2x

The difference of the polynomials is 2(x³+x).

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given are two polynomials (x² + x³ + x² + x) and (x²-x³+x²-x), we need to find the difference,

So,

(x² + x³ + x² + x) - (x²-x³+x²-x)

= x² + x³ + x² + x - x²+x³-x²+x

= 2x²-2x²+x³+x³+x+x

= 2x³+2x

= 2(x³+x)

Hence the difference of the polynomials is 2(x³+x).

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Answer:

Surface area of the composite figure = 508cm²

Step-by-step explanation:

Composite figures :- A composite shape is a 2D shape that is made from a combination of other basic 2D shapes and polygons. These shapes include squares, rectangles, triangles, circles.

Surface area of cuboid = 2(LB + LH + BH)

There are 2 cuboids in the question therefore solving them separately,

L = 12cm

B =  2cm

H = 10cm

putting these values in the above formula,

SA of bigger cuboid = 2(12×2 + 12×10 + 2×10)

                  SA           = 328cm²

L = 8cm

B =3cm

H = 6cm

SA = 2(8×3 + 8×6 + 3×6)

SA = 2×90

SA = 180cm²

now surface area of whole figure,

SA of bigger cuboid + SA of smaller cuboid

     328cm²   +    180cm²

       508cm² answer

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Answer:

[tex]x(x^2+2)[/tex]

Step-by-step explanation:

Since x is the only common term, you factor that part out using the distributive property.

Solution:

Detailed explanation:

Hii! Let's factorise this expression!

Did you see that both terms, x^3 and 2x, have an x in common? That's what we are going to factor out, by dividing x^3 and 2x by x.

x^2+2 is what we obtain.

Now, this can't be the end of the process. We also need to put parentheses around x^2+2.

(x^2+2)

Next we put that x we factored out a short while ago outside the parentheses.

x(x^2+2). Did you get it?

________

Hope I helped, best wishes & happy studies!
Please reach out if any queries arise. Thankyou!!

_______

Answer:

Step-by-step explanation:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

For example, "whatis.com" could be a domain with records for "www.whatis.com" and "www1.whatis.com,"

[tex]\log_7(x+9)-\log_710=\log_77\qquad(x > -9)\\\log_7\dfrac{x+9}{10}=1\\\dfrac{x+9}{10}=7\\x+9=70\\x=61[/tex]

A real-life example of a hidden variable would be age in research that checks the correlation between shirt sizes in grade school and reading ability.

In a research that checks whether student shirt sizes (independent variable) have an impact on reading ability, it is found that students with high shirt sizes are better at reading.

A hidden variable here is age. Students who are older will more likely have a higher shirt size and better reading comprehension.

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Answer:

1st option

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 2, 1 ) and r = 3 , then

(x - (- 2) )² + (y - 1)² = 3² , that is

(x + 2)² + (y - 1)² = 9 ← expand factors using FOIL

x² + 4x + 4 + y² - 2y + 1 = 9

x² + 4x + y² - 2y + 5 = 9 ( subtract 9 from both sides )

x² + 4x + y² - 2y - 4 = 0 , that is

x² + y² + 4x - 2y - 4 = 0 ← in general form

Answer:

[tex]\textsf{1)} \quad x^2+y^2+4x-2y-4=0[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies (x-(-2)^2+(y-1)^2=3^2[/tex]

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

Expand and simplify:

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

[tex]\implies x^2+4x+4+y^2-2y+1=9[/tex]

[tex]\implies x^2+y^2+4x-2y+5=9[/tex]

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

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Step-by-step explanation:

To multiply the fractions, like

[tex] \frac{1}{4} \times \frac{1}{9} [/tex]

Multiply the top,

then multiply the bottom.

[tex] \frac{1}{4} \times \frac{1}{9} = \frac{1 \times 1}{4 \times 9} = \frac{1}{36} [/tex]

Try to use a calculator if you aren't arithmetic heavy, but I suggest you to try to remember them because they are going to be helpful for courses like Algebra, Calculus, Statistics, etc.

To divide fractions, like

[tex] \frac{ \frac{1}{5} }{ \frac{1}{8} } [/tex]

You take the top number,

[tex] \frac{1}{5} [/tex]

Then you flip the bottom number,

[tex] \frac{8}{1} [/tex]

Then multiply the two

[tex] \frac{1}{5} \times \frac{8}{1} = \frac{8}{5} [/tex]

And that is your answer. Comment if you need more clarification

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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Step-by-step explanation:

find the Lcm of 15 and 10 which is 30

multiply the 2fractions by the LCM

8/15*30=16

3/10*30=9

add the products and put them all over the Lcm

(16+9)/30

=25/30 which is equivalent to 5/6 when you divide both the numerator and the denominator by 5

Question:

A fair die is tossed.

Find the probability of obtaining an even number

Answer:

sample space=(1,2,3,4,5,6)

number of favourable outcomes=3

Event A= (outcome is even)

             = (2,4,6)

Total number of outcomes=6

Thus, P(even number)=3/6

                                      =1/2

Question 2:

A drawer contains 10 identical handkerchiefs of which 2 are white, 5 are blue, and 3 are pink. A handkerchief is drawn at random. what is the probability that it is white or pink?

Answer:

total number of outcomes=10

P(the handkerchief is white or pink)=2+3/10

                                                          =5/10

                                                          =1/2

Answer:

b. 66

c.56

a 0

Step-by-step explanation:

????????????????????????

Answer:

Midpoint is the average of the two points. Find it as follows:

Answer:

A

Step-by-step explanation:

5/44=0.11kg

Answer:

I think A

Step-by-step explanation:

I think A would be the answer.

Have a nice day !

Answer:

15, 20, 25

Step-by-step explanation:

added in the picture

Answer:

x>0

Step-by-step explanation:

points exist on the right of the graph so the domain is x>0

Answer:

1. Statement C is not true.

2. Option B is correct

3. Option C is correct

4.Option C is correct

Step-by-step explanation:

1. There are 5 Platonic solids : The tetrahedron, cube

,octahedron, dodecahedron ,icosahedron.

therefore statement C is incorrect.

2. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

12 - 18 + F= 2

F = 8.

3. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

V - 30 + 12 = 2

V = 20.

4. Probability is the number of favourable or unfavourable event divided by total events.

therefore denominator always greater than numinator.

so [tex]\frac{8}{7}[/tex] cannot represent the probability

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