find the slope of each line

[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 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]

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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.

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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.

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Answer:

3.46

Step-by-step explanation:

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

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

3.46

Hopes this helps please mark brainliest

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 :)

Answer:

5.8 cm

Step-by-step explanation:

the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:

4^2 + 4.2^2 = a^2

Simplify: 16 + 17.64=a^2

Simplify again: 33.64 = a^2

Square root both sides: 5.8 = a

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.

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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.

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Answer:

Step-by-step explanation:

12.5km

i made that up sorry

The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the​ population, A, of a country in​ millions, t years after 2003.

The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.

Here,

A = 384. 7e^0. 018t

513=384. 7e^0. 018t

513/384.7= e^0.018t

ln(513/384.7) = 0.018t

ln(513/384.7)/0.018 =t

t=15.9895575229 years

t=16 years

2003+16= 2019

In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.

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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.

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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.

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The complete question-

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

The answers are a) 29.55 ft, b)  23.08 feet and c)  45.05 feet

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.

Given is a figure, of two wires 1 and 2 attached to a pole and ground

Using trigonometric ratios, we have,

a) tan41° = Height of pole/34

Height of pole = tan41°x34

Height of pole = 29.55 ft

b) tan38° = (distance of wire 2 from the base of pole)/29.55

Distance of wire 2 from the base of pole = tan38°x29.55 = 23.08 feet

c) cos41° = 34/length of wire 1

Length of wire 1 = 34/cos41°

Length of wire 1 = 45.05 feet

Hence, The answers are a) 29.55 ft, b)  23.08 feet and c)  45.05 feet

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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.

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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.

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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

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.

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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).

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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.

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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

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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

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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.

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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 vertical asymptote is x=2 and horizontal asymptote is y = 0

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

There are three types is asymptotes:

Horizontal asymptote , Vertical asymptote and oblique asymptote.

in the expression 1/x-2, the horizontal asymptote is y=0 since the power of x in the numerator is less than that of denominator.

And the vertical asymptote is found by equation the denominator to zero

therefore x-2= 0

x= 2

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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;

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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.

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the correct format for a multiple regression equation is

ŷ= [tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex]

multiple regression: The relationship between a single dependent or criterion variable and multiple independent or predictor variables is typically explained by multiple regression. The constant term and multiple independent variables with their corresponding coefficients are used to model a dependent variable. The term "multiple regression" refers to the fact that it requires two or more predictor variables.

because, the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; and the maximum number of passengers.

thus, ŷ=[tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex] is the multiple regression equation.

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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.

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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].

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