The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.

The actual roots ordered from least to greatest are
and
.

The radius of Ana's brother's circle in the blue car is 35 feet.

For the given question-

The total distance covered by the Ana's brother in the blue car = 220 feet.

Total distance = circumference of the circle.

circumference of the circle = 2 π r

r = radius of the circle.

π = 3.14

Thus,

220 = 2 x 3.14 x r

r = 220 / (3.14 x 2)

r = 35.03

r = 35 feet.

As a result, the radius of Ana's brother's circle in the blue car is 35 feet.

To know more about the radius of the circle, here

https://brainly.com/question/12908707

#SPJ4

The complete question-

The missing data from the question is given in diagram attached.

The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.

What is inequality?

In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.

According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].

Now, combine the two expressions as follows:

9<2x

[tex]2x\le45[/tex]

[tex]9 < 2x\le45[/tex]

Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].

Learn more about inequality from the following link:

https://brainly.com/question/24372553

#SPJ1

Answer: -19 49/50 ==> a

Step-by-step explanation:

(−5 2/5) ⋅ 3 7/10=

(−5 - 2/5) ⋅ (3 + 7/10)=

(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators

((-25-2)/5) ⋅ ((30+7)/10)=

-27/5 ⋅ 37/10 =

-27 ⋅ 37 / (5 ⋅ 10) =

-999/50=

(-950-49)/50=

-950/50 - 49/50=

-19 - 49/50=-19 49/50 ==> a

The height of the tower is 87.4870 feet

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The body of the calculation is contained in the attached file.

In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet

Learn more about angle of elevation: https://brainly.com/question/88158

#SPJ1

She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

To learn more about distance here:

https://brainly.com/question/15172156

#SPJ1

Answer: 21 c^16 + 24c^9+ 21 c^8

Step-by-step explanation: To multiply exponents with the same base, add them.

Answer:

3c^3(7c^8+8c+7)

=(3c^3)(7c^8+8c+7)

=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)

=21c^11 + 24c^4 + 21c^3

Step-by-step explanation:

Remember....  ^ is for power

Both  2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent

Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.

They are also known to be made up of some arithmetic operations, such as;

We have the equations;

2/3m=4 and -4m=24

Let's solve for m in the first equation

12m = 2

Divide both side by coefficient of m

m = 2/ 12  = 1/ 6

For the second equation

-4m = 24

Divide both sides by - 4

m = 24/-4

m = 6/ -1

Take inverse

m = 1/6

Hence, the equations are equivalent

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

The probability that you guess the combination correctly 0.00001.

We know that the probability of an event is (possible outcome/total outcome)

I will assume that repeats are allowed as in most combination locks so the number of possible codes

= 10⁵ = 100000

We also know that there is only one correct combination so the probability that you guess the combination correctly

= 1/10⁵ = 1/100000 = 0.00001

Orchestrating individuals, digits, numbers, letters in order, letters, and tones are instances of changes. Choice of menu, food, garments, subjects, and group are instances of combination.

To learn more about permutation and combination,

https://brainly.com/question/28065038

#SPJ4

[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]

The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:

40.01.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

Hence the quotient of the division is the numerator divided by the denominator.

In this problem, interpreting the blank variable as x, the fraction that represents the situation is:

x/40.01 = 1.

Applying cross multiplication, the numeric value of the variable x is obtained as follows:

x = 40.01 x 1

x = 40.01.

The complete problem asks for which number divided by 40.01 is close to 1.

More can be learned about fractions at https://brainly.com/question/1622425

#SPJ1

Lauren got 5 votes in class president election.

Number of votes Lisa got = 36

Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.

36 = x + 6x

Calculating the value of x from mentioned equation

36 = 7x

Rewriting the equation with 7 as denominator

x = 36/7

Performing division on Right Hand Side of the equation

x = 5.14

Rounding off the digits as number of votes will be whole number

x = 5

Based on the mentioned information, Lauren got 5 votes.

Learn more about equations -

https://brainly.com/question/21405634

#SPJ4

The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.

The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;

d² = (x₂ - x₁)² + (y₂ - y₁)²

The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;

[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2

[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2

[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)

72 + 32 = 104

Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]

ΔABC is a right triangle

The slopes of the equation of the lines of the sides of the triangle are;

Slope of side AB = (5 - (-1))/(6 - 0) = 1

Slope of side BC = (3 - 5)/(-4 - 6) = 0.2

Slope of side AC = (3 - (-1))/(-4 - 0) = -1

Therefore;

[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]

Which gives;

Learn more about the Pythagorean theorem in mathematics here:

https://brainly.com/question/343682

#SPJ1

Answer:

Step-by-step explanation:

12.5km

i made that up sorry

A graph of the given mathematical expression (x = -6) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.

Read more on number line here: brainly.com/question/17325155

#SPJ1

The slope of the given graph x^2 = ln (xy) at the point (1, e) is e

We have been given a graph x^2 = ln (xy) and a point (1, e)

Differentiate the given graph on both sides

d/dx x^2 = d/dx (ln (xy))

⇒ 2x = 1/xy × d/dx (xy)

⇒ 2x × xy = x.dy/dx + y.dx/dx

⇒ 2x^2y = x.dy/dx + y

⇒  2x^2y = x.dy/dx + y

⇒ 2x^2y - y = x.dy/dx

⇒ (2x^2y - y)/x = dy/dx  … (1)

The slope at the point (1, e)

m = dy/dx at x = 1, y = e

Substitute the values in Equation (1)

⇒ m = (2(1)^2 (e) - e)/1

⇒ m = (2e - e)/1

⇒ m = e/1

⇒ m = e

Hence, the slope of the given graph is e.

To know more about slope here

https://brainly.com/question/3420555

#SPJ9

As function f(x) is not completely right i assume it to be like f(x)= 10x-200.

Acc. to which the answer is  -350.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X.

Main Body:

f(x)= 10x-200

f(4)= 10*4-200

    = 40-200

    =-160

g(x)= 25[tex]x^{2}[/tex]+90

g(2)= 25*(2)² +90

     = 25*4+90

     =190

So, f(4)-g(2) = -160-190

     = -350

Therefore the answer is -350.

to learn more about function click on the link below

https://brainly.com/question/11624077

#SPJ13

The solution set for the given equations is x = 4.

What is a set?

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.

Here,

we put the value of x in the given equation and justify our answer

when we x=4, we get

5x−5=15

5(4) - 5 = 15

20 - 5 = 15

15 = 15

Hence, the solution set for the given equations is x = 4.

To learn more about the sets from the given link

https://brainly.com/question/856690

#SPJ1

Answer: f(x)=-.5x-1

Step-by-step explanation:

I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5

Hope this helps :)

The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).

The slope of a line is defined as the gradient of the line.

Given that line passes through the points (-2,10), (10 -14)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -2, y₁ = 10

x₂ = 10, y₂ = -14

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]

⇒ y - 10 = (-24)/(12 )[x +2]

⇒ y - 10 = -2(x +2)

⇒ y = -2x - 4 + 10

⇒ y = -2x + 6

Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).

Learn more about the Slope of the Line here:

brainly.com/question/14511992

#SPJ1

The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Given,

In the question:

A leading coefficient of 1, and zeros of 4 and 3 + i.

To find the polynomial function of least degree having only real coefficients.

Now, According to the question;

The function has 4 and 3 + i .

As, i's roots

So, 3 - i is also its root a leading coefficient of 1 .

So, The function of polynomial is :

f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]

To solve the function;

f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Learn more about Polynomial Function at:

https://brainly.com/question/12976257

#SPJ1

The sampling method used in this scenario is random Systematic random sampling

Systematic random sampling

Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.

If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.

To learn more about the sampling method, visit:

https://brainly.com/question/20849477

#SPJ4

An equation of slope-intercept form describing this relationship. Use ordered pairs of the form​ the equation, y = 640x + 4760

Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.

Leran more about Slope intercept here

https://brainly.com/question/19824331

#SPJ4

1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.

2. 9(x + 3) = 9x + 12 ; This is true for no values of x.

3. 4(2x + 3) = 12 + 8x ; True for any values of x.

Given,

The equations;

1. 3x + 9 = -4.5x + 20

2. 9(x + 3) = 9x + 12

3. 4(2x + 3) = 12 + 8x

We have to find whether each equation is true for all, one or no values of x.

Here,

1. 3x + 9 = -4.5x + 20

Solve for x;

3x + 4.5x = 20 - 9

7.5x = 11

x = 11/7.5

x = 1.47

Then,

This is true for one value of x.

2. 9(x + 3) = 9x + 12

Solve using distributive property;

9x + 27 = 9x + 12

9x - 9x = 12 - 27

0 = -15

This is true for no values of x.

3. 4(2x + 3) = 12 + 8x

Use distributive property and solve;

8x + 12 = 12 + 8x

8x - 8x = 12 - 12

0 = 0

True for any values of x.

Learn more about values of x here;

https://brainly.com/question/29473237

#SPJ1

At b= 24 will complete the square in the expression x^2 + bx + 144.

What is perfect square trinomial?

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.

Consider the given expression

x^2 + bx + 144

For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.

Here, c = 144

√144 = 12

So, b√c = 2(12) = 24

The expression becomes,

x^2 + 24x + 144 = (x + 12)^2

This is the perfect square.

Hence, b = 24  will complete the square in the expression x^2 + bx + 144.

To know more about the perfect square trinomial, click on the link

https://brainly.com/question/12759977

#SPJ1

There are 6984 inverse proportional relationships and the direct proportional relationships are 97/72.

Given that:

Kelly has 97 apples, and Jason has 72.

The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.

Y/X = k

Substitute the given X and Y values ​​and solve for k.

Suppose, Y = 97, X = 72

then k = 97/72

Distinguish a proportional relationship from other relations, including an inverse relationship (XY = k or Y = k/X).

An inverse proportional relationship is one in which two quantities vary inversely with respect to each other. We say that the variable Y changes inversely with X if

Y = k/X

Substitute the given X and Y values ​​and solve for k.

Suppose, Y = 97, X = 72

then k = 97 x 72

=> k = 6984

Hence, there are 6984 inverse proportional relationships and direct proportional relationships are 97/72 between Kelly which has 97 apples, and Jason which has 72.

To learn more about the proportional relationship visit: https://brainly.com/question/7096655

#SPJ9

The expression can be expanded as 125/64

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

To solve this problem, we need to evaluate the expression given;

For this, we can find the cube of the numerator and cube of the denominator.

(5/4)³ = 125/64

The solution to the problem is 125/64

Learn more on evaluating an expression here;

https://brainly.com/question/4344214

#SPJ1

The value of x will be 15 and the value of y will be 4.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.

x / ( x + 5 ) = 18 / ( 18 + 6 )

x / ( x + 5 ) = 18 / 24

24x = 18x + 90

6x = 90

x = 15

The value of y will be calculated by considering the two left-hand triangles.

12 / ( 12 + y) = 15 / 20

240 = 180 + 15y

15y = 60

y = 60 / 15

y = 4

Therefore, the value of x will be 15 and the value of y will be 4.

To know more about similarities follow

https://brainly.com/question/24184322

#SPJ1

Answer:

3.46

Step-by-step explanation:

[tex]\sqrt{21-9}[/tex]

[tex]\sqrt{12}[/tex]

3.46

Hopes this helps please mark brainliest

The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15

General equation of quadratic is

f(x) = a[tex]x^{2}[/tex] + bx + c

and Standard form is

f(x) =a [tex](x-h)^{2}[/tex] + k

where h , k are coordinates of vertex

and x , y represent some point on the graph.

By replacing f(x) with y in standard equation we get

y = a[tex](x-h)^{2}[/tex] + k

Put value of x , y , h , k from the graph.

h = -2

k = 7

x = 0

y = 9

9 = a (4) + 7

a = 2

Now put value of a in standard equation

f(x) = 2 [tex](x + 2)^{2}[/tex] + 7

f(x) = 2[tex]x^{2}[/tex] + 4x + 15

To know more about quadratic equation

https://brainly.com/question/27953127

#SPJ1

The area of the triangle is A. 17.5yd².

Using this formula to find the area

Area = 1/2 ( b × h)

Where:

b = base = 5

h = Height = 7

Hence,

Area = 1/2 (5 ×7)

Area = 1/2 (35)

Area = 1× 35/2

Area = 35/2

Area = 17.5yd²

Therefore the correct option is A.

Learn more about area here:https://brainly.com/question/25292087

#SPJ1