Rafael rented a truck for one day. There was a base fee of 15.95, and there was an additional charge of 74 cents for each mile driven. Rafael had to pay 220.19 when he returned the truck. For how many miles did he drive the truck?

The weights of meteorite A and meteorite B are 69 tons and 23 tons respectively.

It is given in the question that the weight of meteorite A is 3 times the weight of meteorite B.

Also, the sum of their weights is 92 ​tons.

We have to find the weights of meteorite A and meteorite B.

According to the data given in the question,

Let the weight of meteorite B be x and,

The weight of meteorite A be 3x

Hence, we can write an algebraic equation,

3x + x = 92 tons

4x = 92 tons

x = 92/4 tons

x = 23 tons

Hence, 3x = 3*23 = 69 tons.

To learn more about  algebraic equation, here:-

https://brainly.com/question/953809

#SPJ1

The most appropriate choice for trigonometric function will be given by -

sin 45° =  [tex]\frac{1}{\sqrt{2} }[/tex]

cos 45° =  [tex]\frac{1}{\sqrt{2} }[/tex]

tan 45° =  1

cot 45° =  1

sec 45° =  [tex]\sqrt{2}[/tex]

cosec 45° =  [tex]\sqrt{2}[/tex]

What are trigonometric functions?

Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.

There are six trigonometric functions-

[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]

[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]

[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]

[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]

[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]

Here,

The diagram of the square has been attached with this answer

∠ABC = 90° [Side of a square is 90°}

∠BAC = [tex]\frac{90}{2}[/tex]

          = [tex]45[/tex]°

Side of square = 1 unit

Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side

                                                    = [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]

                                                    = [tex]\sqrt{2}[/tex] units

From [tex]\Delta[/tex] ABC,

sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

           = [tex]\frac{BC}{AC}[/tex]

           = [tex]\frac{1}{\sqrt{2} }[/tex]

cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]

           = [tex]\frac{AB}{AC}[/tex]

           = [tex]\frac{1}{\sqrt{2} }[/tex]

tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]

           = [tex]\frac{BC}{AB}[/tex]

           = [tex]\frac{1}{1}[/tex]

           = 1

cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]

           = [tex]\frac{AB}{BC}[/tex]

           = [tex]\frac{1}{1}[/tex]

           = 1

sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]

           = [tex]\frac{AC}{AB}[/tex]

           = [tex]\frac{\sqrt{2} }{1}[/tex]

           = [tex]\sqrt{2}[/tex]

cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]

           = [tex]\frac{AC}{BC}[/tex]

           = [tex]\frac{\sqrt{2} }{1}[/tex]

           = [tex]\sqrt{2}[/tex]

To learn more about Trigonometric functions, refer to the link:

https://brainly.com/question/1143565

#SPJ9

The missing digits are 0, 4, and 5 in descending order

The complete division operation is

    8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

From the question, we are to determine the missing digits in the division operation

From the diagram,

The first two digits of the divided were divided by the divisor, this resulted into a quotient of 8 and a remainder of 1.

The divisor is 6

Let the value of the first two digits be x

Thus,

x / 6 = 8 1/6

x/6 = 49 / 6

By comparison,

The first two digits is 49

Therefore,

The dividend of the division operation is 4,925

Now, we can complete the division operation

      8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

Hence, the missing numbers are 0, 4, and 5

Learn more on Division operation here: https://brainly.com/question/19318593

#SPJ1

The x value of 24 makes the equation to be true

The equation is given as

x/2 - 2 = x/4 + 4

Add 2 to all sides of the equation

So, we have

x/2 = x/4 + 6

Subtract x/4 from all sides of the equation

So, we have

x/2 - x/4 = 6

Multiply through by 4

So, we have

2x - x = 24

So, we have

x = 24

Hence, the value of x in the equation is 24

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

The length of metal flashing needed to be purchase is [tex]1\frac{5}{8}[/tex] feet's.

He needs 6 ½ feet of metal flashing to complete a household project.

He has two small pieces measuring 3 1/8 feet and 1 3 / 4 feet.

Therefore, the length of metals for him to purchase can be calculated as follows;

The length he has = 3 1 / 8 + 1 3 / 4

The length he has = 25  /8 + 7 / 4

The length he has =  25 + 14/ 8

The length he has = 39 / 8 feet

Therefore

length required to purchase =  [tex]6\frac{1}{2} - \frac{39}{8}[/tex]

length required to purchase = [tex]\frac{13}{2}-\frac{39}{8}[/tex]

length required to purchase =  [tex]\frac{52-39}{8}[/tex]

length required to purchase = [tex]\frac{13}{8}[/tex] feet

Therefore,

length of metal flashing required to be purchase = [tex]\frac{13}{8}[/tex] feet = [tex]1\frac{5}{8}[/tex] feet

learn more on length in feet's here:https://brainly.com/question/17720533

#SPJ1

Answer:

2x + 14

Step-by-step explanation:

8 + 2(x + 3) = 2x + 14

2x + 14 = 2x + 14

0 = 0; True

All real numbers

0.6054 is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree.

What are examples and probability?

this is binomial with parameter n=21 and p=0.39

a)

probability = P(X<=5)= ∑x=0x     (nCx)px(1−p)(n-x)    =  0.1124

b)

probability = P(X=8)= (nCx)px(1−p)(n-x)    =    0.1763

c)

probability = P(8<=X<=13)= ∑x=x1x2     (nCx)px(1−p)(n-x)    =  0.6054

Learn more about probability

brainly.com/question/11234923

#SPJ9

    There are 14 girls and 19 boys in the chess club.

    Let x be girls and y be boys in the chess club. First, we need to write the system.

    We know there are 33 students in total.

x + y = 33

    We also know there are five more boys than girls in the club.

x + 5 = y

x + y = 33

x + 5 = y

    First, we will solve for y with substitution:

x + y = 33

x + (x + 5) = 33

2x = 28

x = 14

    Now, we will plug in this x-value:

x + y = 33

(14) + y = 33

y = 19

           There are 14 girls and 19 boys in the chess club.

Based on Jaylen's equation and the distance, as well as the time, the missing values are:
                 Distance                               Time minutes

                      2.89                                        24.0

                       3                                             24.9

                     4.34                                          36.0

                       6                                             49.8

The missing values can be found by Jaylen's equation where y is the Time in minutes and x is the distance.

With a time of 24 minutes, the distance is:

24 = 8.3x

x = 24/8.3

= 2.89

With a distance of 3, time would be:

= 8.3x

= 8.3 (3)

= 24.9 minutes

With a time of 36 minutes:

= 36 / 8.3

= 4.34  

With a distance of 6, the time is:

= 6 x 8.3

= 49.8 minutes

Find out more on missing values at https://brainly.com/question/14695415

#SPJ1

Answer:

"What is 180 lbs to kg?" is the same as "What is 180 pounds to kilograms?" or "What is 180 pounds to kg?" or "What is 180 lbs to kilograms?" Here we will show you how to convert 180 lbs to kg.

There are 0.45359237 kilograms per pound and there are 2.204622622 pounds per kilogram. Therefore, you can get the answer to "180 lbs to kg?" two different ways. You can either divide 180 by 2.204622622 or multiply 180 by 0.45359237. Therefore, the answer is

Step-by-step explanation:

81.6466

Answer:

f(4) = 8

Step-by-step explanation:

Hello!

You can find f(4) by substituting 4 for x in 3x - 4.

The value of f(4) is 8.

Answer:

Step-by-step explanation:

h(x)=-2x-3 h(6)

Answer:

1_y=3(0)-5

y=0-5

y=-5

(0,-5)

2_y=3(-1)-5

y=-3-5

y=-8

(-1,-8)

3_y=3(2)-5

y=6-5

y=1

(2,1)

Step-by-step explanation:

The solution of the equation 11kx+13kx= 6 is x = 1/(4k)

The given equation is 11kx+13kx = 6

To solve this equation first we have to take x as common and rearrange the equation, so we can group the like terms together

x(11k+13k) = 6

Add the like terms in the equation

x(24k) = 6

Move 24k to the right hand side of the equation

x = 6/(24k)

Here we have to simplify the value of x, for that we have to divide 6 by 24k in the equation

x = 1/(4k)

Hence, the solution of the equation 11kx+13kx= 6 is x = 1/(4k)

Learn more about solution of the equation here

brainly.com/question/14603452

#SPJ1

Circle A and Circle B's connection

Circle A's size is more significant than Circle B's size.

As a result, circle A's radius exceeds circle B's radius.

The connection between segments

1.

Let M be the location where Segment QT and ER intersect.

Additionally, tangents from an outside point to a circle have identical lengths.

QM = ME———— (1)

MT=MR————(2)

Including (1) and (2)

MR + ME = QM + MT

Q T=ER

2.

Tangents from an exterior point to a circle have identical lengths.

We may write the following segments are equal using this property.

UP=U Q

ZC=ZR

VC=VS

NR=NS

KC=K T

What are Tangents?

A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:

As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):

Utilizing the differentiation principles, determine the gradient function's derivative.

To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate

Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).

Circle's Tangent

A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.

Geometric Tangent

Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.

Learn more about Tangent https://brainly.com/question/19064965

#SPJ1

Sebastian has solved the expression wrongly and the correct answer will be 536.

We are given the expression:

(87 × 8) - (4 × 40)

We need to simplify the expression.

For this, we need to follow the rule of PEMDAS.

So, we get that:

696 - 160

= 536

Sebastian has simplified it wrong as he has not followed the rule of PEMDAS and first subtracted 4 from 8.

Therefore, we get that, Sebastian has solved the expression wrongly and the correct answer will be 536.

Learn more about expression here:

https://brainly.com/question/24734894

#SPJ1

Answer:

$46.64

Step-by-step explanation:

convert 6% to .06

multiply that by 44

you get 2.64.

add that to 44 to get a final ansewr of 46.64 dollers

The value of the fraction given as - 1 3/4 - (-8 1/3) - (- 4 1/4) will be 10 5/6.

It should be noted that a fraction is simply used to represent the numbers that aren't whole.

Based on the information given, the fraction is illustrated as:

= - 1 3/4 - (-8 1/3) - (- 4 1/4)

Note that (-) × (-) = +

Therefore,

= - 1 3/4 - (-8 1/3) - (- 4 1/4)

= - 1 3/4 + 8 1/3 + 4 1/4

The LCM of the denominator is 12

= - 1 9/12 + 8 4/12 + 4 3/12

= 12 7/12 - 1 9/12

= 10 10/12

= 10 5/6

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

Answer: The answer is a scale factor of 6

Step-by-step explanation:

5 feet is 60 inches, and on the drawing the closet is 10 inches while the real closet is 5 feet, so just divide 60 by whatever gets you 10.

Answer:

A = 1

B = 5

Step-by-step explanation:

Answer:

16

Explanation:

It states the answer in the question. Unless you meant something else?

Hope this helps!

Have a good day :)

Answer: He shared 16.

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

It is given to us that the expression is -

[tex]x^{2} -5x+8[/tex] ----(1)

We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.

The given expression from (1) is -

[tex]x^{2} -5x+8[/tex]

This expression is in the form of [tex]ax^{2} +bx+c[/tex]

Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get

[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)

Equation (2) can also be represented as -

[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]

[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)

We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].

So, we can derive that -

[tex]a=\frac{5}{2}[/tex]

and, [tex]b=\frac{7}{4}[/tex].

Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

To learn more about complete the square method visit https://brainly.com/question/4822356

#SPJ9

Step-by-step explanation:

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.

What are Trigonometric Identities?

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.

Given that the value of tan(x) = -4/3 and x is in quadrant 2.

In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,

\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}cos(2x)=

1+tan

2

(x)

1−tan

2

(x)

Since the value of tan(x) is known, substitute the value in the identity,

\begin{gathered}\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\\end{gathered}

cos(2x)=

1+(−

3

4

)

2

1−(−

3

4

)

2

cos(2x)=

1+(

9

16

)

1−(

9

16

)

cos(2x) = (-7/9) × (9/25)

Cancelling 9 from the numerator and the denominator,

cos(2x) = -7/25

Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.

Learn more about Trigonometric Identities:

https://brainly.com/question/13094664

Answer:

24

Step-by-step explanation:

the equation is 6s^2, where s=2. This equals 24

Answer:

Step-by-step explanation: area of one square 2x2 right, then you multiply to get 4 then x6 because of the six sides to a cube then you get 24

Answer : 3500

Reasoning 2589+2920+3500=9009

Then 9009/3 = 3003

Round 3003 to 3000 and there's your answer

Based on the given expression; there are three terms;

and one coefficient; 7

A term refers to any value (variable or constant) or expression separated from another term by a space or an appropriate character or symbol, in an overall expression.

Coefficient refers to be a constant by which an algebraic term is multiplied.

f + 15 + 7g

There are three terms in the expression;

From the task given above,

The coefficient of 7g is 7

Also the coefficient of f is 1.

Therefore, the terms in the expression are f, 15 and 7g.

Read more on terms and coefficients:

https://brainly.com/question/11988485

#SPJ1

Answer:

Step-by-step explanation:

The graph starts at 70 and decreases by 5 temp after 15 mins

70

65               o

60                                      o

55                                                            o

50

45

40

35

30

25

20

15

10

5                 i                      i                     i

0   5   10   15   20   25   30   35   40   45   50

                      time