For a polynomial function y = f(x), where f(1/3)=0, one of the factor would be

Answer:

x < 5

Step-by-step explanation:

7x + 5 < 3x + 25

Subtract 3x from each side

7x-3x + 5 < 3x-3x + 25

4x+5 < 25

Subtract 5 from each side

4x +5-5 < 25-5

4x < 20

Divide by 4

4x/4 < 20/4

x < 5

Answer

x<5

Step-by-step explanation:

7x + 5 < 3x + 25

you would subtract 3x from both sides

Leaving you with 4x+5< 25

next you would subtract 5 from both sides

leaving you with 4x<20

Then you would divide both sides by 4

leaving you with x <5

Hoped this helped

:)

Answer: If the function is: f(x) = (x^2−3x−10)/(x−5) The function has no holes.

If the function is f(x) = x^2−3x−10/x−5 then the hole is at x = 0 (the left side goes up, and the right side goes down, as the numerator is a negative number)

Step-by-step explanation:

I am not shure of what is the function, as you used no parentheses in it, so i will solve it for two different functions:

We have the function:

f(x) = (x^2−3x−10)/(x−5)

We want to find the "hole", this means that we want to find the value of x where the denominator is equal to zero.

If you look at the function, is easy to think that in x = 5 the denominator will be equal to zero, but we need to prove it.

First, we need to see if the numerator part is also zero when x = 5.

so

5^2 - 3*x - 10 = 25 -15 - 10 = 0

Ok, let's find the other root of the quadratic function:

x^2 - 3*x - 10 = (x - 5)*(x - b) = x^2 - (b + 5)*x + (b*5)

then we have: (b + 5) = 3 and b*5 = -10

then b = -2, this means that we can write the numerator part as:

x^2 - 3*x - 10 = (x - 5)*(x + 2)

then our function is:

f(x) =   (x - 5)*(x + 2)/(x - 5) = x + 2

This function has no holes.

Now, if the function actually is:

f(x) = x^2−3x−10/x−5

Then we have an x on the denominator of the third term of the equation, this denominator is 0 only when x = 0

Answer:

x =2                x = -4

Step-by-step explanation:

-5|x + 1|+ 3 = -12

Subtract 3 from each side

-5|x + 1|+ 3-3 = -12 -3

-5|x + 1| = -15

Divide each side by -5

-5/-5|x + 1| = -15/-5

|x + 1| = 3

Since this is an absolute value, we have two solutions one positive and one negative

x+1 = 3     x+1 = -3

Subtract 1 from each side

x+1-1 = 3-1     x+1-1 = -3-1

x =2                x = -4

Answer:

the answer is c

Step-by-step explanation:

Answer:

First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

First system: 3x-2y=3; 6x-4y=1

From the first equation: y = (3x - 3)/2

Using this value of y in the second equation:

6x - 6x + 6 = 1

6 = 1 -> System has no solution

Second system: 3x-5y=8; 5x-3y=2

From the first equation: x = (8 + 5y)/3

Using this value of x in the second equation:

5*(8 + 5y) - 9y = 6

40 + 25y - 9y = 6

16y = -34 -> y = -2.125

x = (8 - 5*2.125)/3 = -0.875

This system has one solution

Third system: 3x-2y=8; 4x-3y=1

 From the first equation: x = (8 + 2y)/3

Using this value of x in the second equation:

4*(8 + 2y) - 9y = 3

32 + 8y - 9y = 6

y = 26

x = (8 + 2*26)/3 = 20

This system has one solution

Fourth system: 3x-6y=3; 2x-4y=2

  From the first equation: x = 1 + 2y

Using this value of x in the second equation:

2*(1 + 2y) - 4y = 2

2 + 4y - 4y = 2

2 = 2

This system has infinite solutions

Fifth system: 3x-4y=2; 6x-8y=1

  From the first equation: x = (2 + 4y)/3

Using this value of x in the second equation:

2*(2 + 4y) - 8y = 1

4 + 8y - 8y = 2

4 = 2

This system has no solution

Answer:

see below

Step-by-step explanation:

f(x) = x^2 – 2x – 3

To find the roots, set the equation equal to zero

0  = x^2 – 2x – 3

Factor, what two numbers multiply to -3 and add to -2

-3 * 1 = -3

-3 + 1 = -2

0 = (x-3)( x+1)

Using the zero product property

x-3 =0   x+1 =0

x=3          x=-1

Answer:

3

Step-by-step explanation:

cuz i said so lol

Answer:

x = 20°

Step-by-step explanation:

4x + 10 = 90

4x = 80

x = 20

Answer:

[tex] \boxed{x\degree = 20\degree} [/tex]

Step-by-step explanation:

Two Angles are Complementary when they add up to 90° (a Right Angle).

[tex] = > x\degree + (3x + 10)\degree = 90\degree \\ \\ = > x\degree + 3x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree = 90\degree - 10\degree \\ \\ = > 4x\degree = 80\degree \\ \\ = > x\degree = \frac{80}{4} \degree \\ \\ = > x\degree = 20\degree [/tex]

Answer:

The correct option is;

105 band members

Step-by-step explanation:

The 5 values are

Minimum value = 80

Q₁ = 90

Q₂ = 105

Q₃ = 115

Maximum value = 130

Whereby the horizontal axis indicates the number of band members is a school, while the 5 values of the box plot are the percentiles of the schools in Orange County and also that the lines are graduated in increments of 5, we have that the median = 105 which is the 50% mark, therefore;

50% of high schools in Orange County have more than 105 band members.

Answer:

The answer would be 105

Step-by-step explanation:

I got this right on Khan Academy <33

Answer:

8a^3.

Step-by-step explanation:

(a+b)^3=a^3+b^3+3a^2b+3ab^2

(a-b)^3=a^3-b^3-3a^2b+3ab^2

(a+b)^3+(a-b)^3=2a^3+6ab^2

According to the question

(a+b)^3+(a-b)^3+6a(a^2-b^2)

Put in the value

=2a^3+6ab^2 +6a^3–6ab^2

=8a^3

In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as,  8a³

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given that,

A algebraic identity,

(a + b)³ + (a - b)³ + 6a(a² - b²)

It is known that,

(a + b)³  = a³ + b³ + 3ab(a + b)

(a - b)³  =  a³ - b³ - 3ab(a - b)

So, now we can substitute expressions

(a + b)³ + (a - b)³ + 6a(a² - b²)

a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) +  6a(a² - b²)

a³ + b³ +  3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²

8a³

Hence, the simplest form is 8a³

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Answer:

i hope this helps you

Answer & Step-by-step explanation:

[tex]\frac{1}{4}(x+5)^2-1=3[/tex]

Add 1 to both sides.

[tex]\frac{1}{4}(x+5)^2=4[/tex]

Multiply both sides by 4.

[tex](x+5)^2=16[/tex]

Take the square root of both sides.

[tex]\sqrt{(x+5)^2} =\sqrt{16}[/tex]

[tex]x+5=4[/tex]

Subtract 5 from both sides.

[tex]x=-1[/tex]

Answer: ŷ = 0.07X + 5.2

Step-by-step explanation:

Given the following :

Number of citations 5 - 7.5 - 10 - 15 - 20

Outputs Residuals 3 - - 6 - - 10 - 5 - - 6

Using the online regression calculator :

Line of best fit is represented by the equation:

ŷ = 0.06897X + 5.2069

ŷ = 0.07X + 5.2

From the line equation:

y = mx + c

With 0.07 = slope of gradient(m)

Intercept (c) = 5.2 (point where the line of best fit intersect the y_axis

x and y are values of x and y respectively

Answer:

2

Step-by-step explanation:

x^0+ y^0

Let x = 3 and y = 2

3^0 + 2^0

Raised to the 0 power is 1

1 + 1

2

Answer:

the answer is 1, this is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The words "two iles a month" tells us that the expression represened by those words is the "2x" part of the equation. x represents the number of months. The .5 part tells us that he began this process with a half mile.

Answer:

y = - 4(x + 3)² + 7

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

From the graph (h, k ) = (- 3, 7 ), thus

y = a(x + 3)² + 7

To find a we require a point on the graph other than the vertex

Using (- 2, 3) , substitute into the equation

3 = a(- 2 + 3)² + 7

3 = a + 7 ( subtract 7 from both sides )

a = - 4

Thus

y = - 4(x + 3)² + 7 ← in vertex form

Answer:

x = -6

Step-by-step explanation:

-4x - 3(2x + 8) = 36

-4x - 6x - 24 = 36

-10x = 60

-x = 6

x = -6

Answer:

[tex]x = - 6[/tex]

Step-by-step explanation:

[tex] - 4x - 3(2x + 8) = 36 \\ - 4x - 6x - 24 = 36 \\ - 10x = 36 + 24 \\ - 10x = 60 \\ \frac{ - 10x}{ - 1 0} = \frac{60}{ - 10} \\ x = - 6[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

21.66666667

Step-by-step explanation:

3x-4(0)=65

3x=65

x=21.66666667

You replace y wil 0 when you are sovling for x

Answer:

Check below please

Step-by-step explanation:

A quadrilateral is a polygon with four sides.

Then let's plot it, check it below.

1) Since 5 line segments were given for a quadrilateral, one of them is an interior one. In this quadrilateral, a rhombus. We have a diagonal, id est a line segment between non-consecutive points.

2) Let's calculate the area of this rhombus. Since this polygon is made up of two triangles let's find it using Heron's Formula, not very popular. But equally valid, also we don't have the height nor angles.

All we need is the semi-perimeter, (half of the Perimeter (2P) and plug it in the formula:

[tex]\bigtriangleup ABD semi-perimeter:\frac{6+8.5+7.5}{2} \therefore s=11\\Area \:\bigtriangleup ABD=\sqrt{11(11-6)(11-8.5)(11-7.5)}=\frac{5\sqrt{77}}{2} \approx21.94 cm\\\\\bigtriangleup \:BCD\: semi-perimeter:\frac{4.5+5+7.5}{2} \therefore s=8.5\\\\Area \bigtriangleup BCD=\sqrt{8.5(8.5-4.5)(8.5-5)(8.5-7.5)}=\sqrt{119}\approx 10.90[/tex]

[tex]Area\: of\: Rhombus\: ABCD=21.94+10.90=32.84 cm^2[/tex]

3) Well, now we need to trace a triangle whose area is 32.84 cm^2. From the classical formula for Area of Triangles we can write:

[tex]\frac{b*h}{2}=32.84 \therefore b*h=65.68[/tex]

Let's find out two values one for the base and another for height. Since 65.58 can be divided both by two and three, it is divisible by 6.

So

[tex]65.58 : 6 =10.93\\b=6\\h=10.93[/tex]

Answer:

47/73

Step-by-step explanation:

There are 73 people who like tea. 47 are women, 26 are men. This means that the probabili that the person chosen is a women is 47 out of the 73.

Answer & Step-by-step explanation:

We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.

Answer:

Step-by-step explanation:

Without the variable x, your "f(x) = 3(18)*" is not a function.  If you meant

f(x) = 3(18)^x, then the domain is "the set of all real numbers," and the range is (0, infinity).

the initial value is 3:  f(0) = 3(18)^0 = 3(1) = 3

The solution is: statements accurately describe the function f(x) = 3(18)* are:

The domain is all real numbers.

The initial value is 3.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Without the variable x, your "f(x) = 3(18)*" is not a function.

If you meant

f(x) = 3(18)^x,

then the domain is "the set of all real numbers,"

and the range is (0, infinity).

the initial value is 3:  

f(0) = 3(18)^0 = 3(1) = 3

Hence, The solution is: statements accurately describe the function f(x) = 3(18)* are:

The domain is all real numbers.

The initial value is 3.

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The complete question is:

A certain element has a half life of 4.5 billion years.

You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock?

Answer:

Age of rock = 7.82 billion years

Step-by-step explanation:

For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.

We are given that;

fraction remaining = 30% = 0.3

Thus;

0.3 = 0.5n

To find n, we have to use the log function;

log 0.3 = n log 0.5

-0.5229 = -0.301 n

n = -0.5229/-0.301

n = 1.737

We are given that;

Half life = 4.5 billion years

So, 1.737 half lives would give;

1.737 × 4.5 = 7.82 billion years

So, age of rock = 7.82 billion years

Answer:

B, The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

1. Rearrange the first equation to isolate either x or y.

x = -y + 24

2. Plug this new equation into the second equation to find the value of y.

3(-y + 24) + 5y = 100

-3y + 72 + 5y = 100

2y + 72 = 100

2y = 28

y = 14

3. Plug the value of y back into the other equation to find the value of x.

x = -14 + 24

x = 10

There are fourteen 5-point questions and ten 3-point questions.

Answer:

b)  The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

edgen2020

Answer:

See explanation

Step-by-step explanation:

[tex]9x(-2y+5x)-4xy(6x-3y)[/tex]

By the distributive property this is equal to:

[tex]9x(-2y)+9x(5x)-4xy(6x)-4xy(-3y)=\\\\-18xy+45x^2-24x^2y+12xy^2[/tex]

Hope this helps!

Answer:

slope = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 4)

m = [tex]\frac{4-3}{2+2}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

32°

Step-by-step explanation:

Given:

∠DMQ = 58º

In this circle, the radius is DM. Since AD is tangent to the circle M, at point D, and the angle between a tangent and a radius is 90°

Therefore, ∠MDQ = 90°

The total angle in a triangle is 180°. Since we have the values of ∠MDQ and ∠DMQ, ∠DQM will be calculated as:

180 = ∠DMQ + ∠MDQ + ∠DQM

Solving for ∠DQM, we have:

∠DQM = 180 - ∠DMQ - ∠MDQ

∠DQM = 180 - 90 - 58

∠DQM = 32°

The measure of ∠DQM is 32°

Answer: I got b., no solutions

Step-by-step

3x-5y=15

6x-10y-30x

times the top by-10 and the bottom by 10

-30x+50=-150

60x-50=300

crossing out the 50's cause they cancel out. also, subtract the others -30-60 giving -90x. and -150-300= -140

-90x=-450

divide  -450 by -90

x=5.

Put 5x in either equation. Either one you do. it cancels out the answer in the equation. then you would subtract and get zero. divide and still get zero.

Sounds really confusing but hope it helps. Please give me a brainliest. Thanks :)

Answer:

3/4 using equation y2-y1/x2-x1

Step-by-step explanation:

Use the equation y2-y1/x2-x1

x1, y1  x2, y2

(16,12) (0,0)

0-12/0-16= -12/-16= 3/4