Example 3: The following data was collected by a taxi driver who was interested in how much fuel he used on different journeys. Length of journey 100 250 150 180 220 (miles) 300 Fuel Used (liters) 24 59 44 50 59 97 Estimate how much fuel would be needed for a 200-mile journey.​

According to the solving the dimensions of the triangles are as follow:

a . 29

b. 58

c. 57

A mathematical space's dimension is defined informally as the smallest number of coordinates required to specify any point within it. Thus, a line has a dimension of one since only one coordinate is required to identify a point on it - for example, the point at 5 on a number line.

2-D shapes really had no thickness and they can only be measured on two sides. Two-dimensional objects include the square, circle, rectangle, and triangle.

x=length of the shortest side

2x=length of another side

x+28=length of the third side

144=x+2x+x+28

144=4x+28

144-28=4x

116=4x

x=116/4

x=29 feet (one side)

Putting the value of x to find second side

2x=58 feet (second side)

x+28= 57 feet (third side)

the perimeter of the triangle = sum of all the sides

                                                = 29+58+57

                                                =144

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Answer:

[14 -4 8]

Step-by-step explanation:

[4+10 -6+2 8+0]

[14 -4 8]

Answer: .17 m/h

Step-by-step explanation: One centimeter is .01 meters/one hundredth of a meter, so you just need to move the decimal two digits to the right to convert.

Answer:

y   [tex]\leq[/tex] -6.5

Step-by-step explanation:

2(9+y) [tex]\leq[/tex] 5

(distribute)

18 + 2y [tex]\leq[/tex] 5

(isolate variable)

2y  [tex]\leq[/tex] 5 - 18

(simplify)

2y  [tex]\leq[/tex] -13

(isolate variable)

y   [tex]\leq[/tex] -6.5

This could be wrong, but I think your answer is [tex]x=-2x^3+\frac{900^{\circ \:}x-360^{\circ \:}}{9}[/tex]

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Hope this helps!

Have a great day and God bless! :)

23$ is the total cost .

What is cost and example?

the total cost = 13$ + 10$= 23$ because he losses a hour in work .

13$ and additionally spending 10$ in carnival .

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the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.

We are given that:

Cost of 48 buttons = $ 6

48 buttons = $ 6

Divide both sides by 48:

1 button = $ 6 / 48 = $ 1 / 8

Now, the cost of 4 dozen buttons will be:

4 dozen buttons = 12 × 4 = 48

So, the cost will be 4 6 only.

For $ 27, the organizers can buy:

Number of buttons = 27 ÷ 1 / 8

Number of buttons = 27 × 8

Number of buttons = 216 buttons.

Therefore, the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.

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Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.

Given,

The distance between the two players = 10yards

The angle from each player to the goalie is 64° and 75°, respectively

We have to find,

the distance from the farthest soccer player to the goalie.

In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:

∠A = 180-(∠B+∠C)

∠A = 41°

Using Sine rule

AC/Sin B = BC / Sin A

AC = 10yrd*Sin75°/Sin41°

AC = 14.723 yards

The farthest distance is of 14.723 yards.

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So the change of rate of x is -1/3 .

The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given that object is decreasing at constant rate of 2 units per second so we have [tex]y = 2x^2 + 1[/tex]

[tex]\frac{dy}{dt} = 4x \frac{dx}{dt}[/tex]

given dy/dt = -2

when x = 3/2

-2 = 4(3/2) dx/dt

-2 = 6 dx/dt

dx/dt = -2/6

         = -1/3

Hence the change of rate of x is -1/3 .

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Expressions in component form for the position vectors having the  polar coordinates are:

a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j

b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j

c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j

Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.

The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.

Let the +x and +y represent, respectively, the unit vectors represented by I and j.

(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.

    -12 cos(40)i + 12sin(40) j

     = -9.19i + 7.71j

(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.

     3cos(40) i + 3 sin(40) j

      = 2.29i + 1.92j

(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.

    -24cos(48)i - 24sin(48) j

    = -16.059i - 17.83j

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I understand that the question you are looking for is:

Obtain expressions in component form for the position vectors having the following polar coordinates.

(a) 12.6 m, 130° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= m

(b) 3.60 cm, 70.0° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= cm

(c) 24.0 in., 206° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= in.

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

4 • ((2x • (2x - 1)) -  (2x - 1))  = 0

The rule says: To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x-1)  and the exponents are :

         1, as  (2x-1), is the same number as  (2x-1)1

and   1, as  (2x-1)  is the same number as  (2x-1)1

The product is therefore,  (2x-1)(1+1) = (2x-1)2

 4 • (2x - 1)2  = 0

4.2      Solve  :    (2x-1)2 = 0

 (2x-1) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means:   2x-1  = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Answer:

x = 1/2.

Step-by-step explanation:

4 (2x (2x - 1) - 1 (2x - 1)) = 0

(2x (2x - 1) - 1 (2x - 1)) = 0

(2x - 1) is common to both parts.

(2x - 1)(2x - 1) = 0

2x - 1 = 0

x = 1/2.

Answer:

84

Step-by-step explanation:

7x5x4x3= 84

Step-by-step explanation:

Answer:

I have completed it also

Step-by-step explanation:

what the person ontop of me said it correct

The length of the unknown side of the right triangle is 13

A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.

between the right triangle's angles and sides.

The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.

Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.

[tex]\sqrt{(12)^2+(5)^2}=13[/tex]

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The percentage of bags that Kia still has to make for the contest is 36 %.

We are given that:

Kia has to make 14 bags out of 25 bags.

Now, she has already made 5 gift bags.

The number of bags she still has to make = 14 - 5 = 9

Now ,we need to find the percentage of 9 from the total of 25 so to get the percentage of bags that Kia still has to make.

So, we get that:

Percentage = 9 / 25 × 100 %

Percentage = 9 × 4 %

Percentage = 36 %

Therefore, we get that, the percentage of bags that Kia still has to make for the contest is 36 %.

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Answer:

Bread

Step-by-step explanation:

Answer:

5x-30

Step-by-step explanation:

x+15+4x-45

5x+14-45

5x-30

The pair of triangles is similar with the ASA similarity condition

The figure that completes the question is added as an attachment

From the figure, we have the following properties:

This means that the pair of triangles is similar with the ASA similarity condition.

Since the triangles share the same point

So, the transformation to carry the triangles onto one another is dilation

Hence, the pair of triangles is similar with the ASA similarity condition

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Answer:

the standing line is the "Y line"

the line laying down is the "X line"

wherever the line touches on the y and x line is where it intercepts

for the x it intercepts at 25 since it touches the x line between 20 and 30

for the y line it intercepts at - 55 since it touches the y line in between - 50 and - 60

In the given statement is:

In simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.

If Y depends on X then the regression line is Y on X.

Y is dependent variable and X is independent variable. If X depends on Y, then regression line is X on Y and X is dependent variable and Y is independent variable. The regression equation Y on X is Y = a + bx, is used to estimate value of Y when X is known.

What is Simple linear regression?

Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.

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If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.

Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).

If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be

x = X + h and y = Y + k

If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.

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We get the number of elements in the set B will be 62.

The universal set is A consists of the primary one hundred positive integers.

Set B is a subset of A.

One possibility is that B consists of the primary 62 positive integers.

Then only, the greatest quantity that may be shaped through the sum of any factors of set B is 123.

The number of elements in set B is equal to  62.

We also can selectively interchange one or more elements of B and and add them in complement of B

In most of these instances the number of elements in set B might be 62.

Therefore, we get the number of elements in the set B will be 62.

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Step-by-step explanation:

the slope-intercept form :

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

but we have the slope and a point.

so, we can start with the point-slope form and then transform it :

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is the given point.

so, we have

y - 3 = 4(x - -4) = 4(x + 4) = 4x + 16

y = 4x + 19

and that's it.

The identify each representation's associated average rate of change. The average rate of change for the functions r, q, p is 5, 5, 7/3 over the range [0.3].

Given that,

We have to find over the range [0, 3], calculate each function's average rate of change. The identify each representation's associated average rate of change.

The equation for f(x) average's rate of change across [a,b] is

m=[tex]\frac{f(b)-f(a)}{b-a}[/tex]

The function provided is

r(x)=x²+2x-5

r(0)=(0)²+2(0)-5=-5

r(3)=(3)²+2(3)-5=9+6-5=15-5=10

Now,

m₁=[tex]\frac{r(3)-r(0)}{3-0}[/tex]

m₁=[tex]\frac{10+5}{3}[/tex]

m₁=15/3

m₁=5

It is clear from the graph that q(0)=2 and q(1)=3.

Now,

m₂=[tex]\frac{q(1)-q(0)}{1-0}[/tex]

m₂=[tex]\frac{3+2}{1}[/tex]

m₂=5/1

m₂=5

It is evident from the above table that s(0)=-2 and s(3)=5.

Now,

m₃=[tex]\frac{s(3)-s(0)}{3-0}[/tex]

m₃=[tex]\frac{5+2}{3}[/tex]

m₃=7/3

Therefore, The average rate of change for the functions r, q, p is 5, 5, 7/3.

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Answer:

Step-by-step explanation:

disribute it

Answer: A.  D.

Step-by-step explanation:

A.

x-b-3<0

x-b-3+3<0+3

x-b<3   (yes)

B.

0>b-x+3

0+x>b-x+3+x

x>b+3

x-b>b+3-b

x-b>3   (no)

C.

x<3-b

x+b<3-b+b

x+b<3   (no)

D.

-3<b-x

-3+3<b-x+3

0<b-x+3

0+x<b-x+3+x

x<b+3

x-b<b+3-b

x-b<3    (yes)

Answer:

A and D

Step-by-step explanation:

Option A

[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Option B

[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]

Option C

[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]

Option D

[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.

Answer: A is the same and equivalent

B is different not equivalent

C is the same and equivalent

Step-by-step explanation:

I'm on Edmund

Answer:

150 degrees

Step-by-step explanation:

Vertical angles