Petrol costs $1.65 per litre. Calculate how much, correct to the nearest cent, the
petrol will cost Anne for a journey of 120km.

Answer:

xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8

Step-by-step explanation:

q+++

None of the expressions is equivalent to 78

The number is given as:

Number = 78

Next, we evaluate the expressions in the options using a calculator

2 × (10 × 3 + 32) = 124

2 × (13 + 32) = 90

(10 × 3 + 32) =62

2 × (10 × 3 + 3) = 66

None of the options equals 78

Hence, none of the expressions is equivalent to 78

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Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.

If:

AB = BA = [3    0]

                 [0    3]

Then:

AB = BA = 3 [1    0]

                    [0    1]

This can be further written as:

AB = BA = 3I₂

And again as:
A (¹/₃ B) = I

This then allows us to either write this as:

A⁻¹ = ¹/₃ B

Or:

B⁻¹ = ¹/₃ A

In conclusion, option A is correct.

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The domain and the range of f(x) = -25x + 50 are the set of all real numbers

The function is given as:

f(x) = -25x + 50

The above function is a linear function.

All linear functions have their domain and range to be the set of all real numbers

Hence, the domain and the range of f(x) = -25x + 50 are the set of all real numbers

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The acute angle is 40.40 degrees

The cosine of the angle is given as:

cos(x) = 0.7620

Take the arc cos of both sides

[tex]x = \cos^{-1}(0.7620)[/tex]

Evaluate the arc cos

x = 40.359

Approximate

x = 40.40

Hence, the acute angle is 40.40 degrees

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Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of  [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.

First part;

Following the transformation (x, y) → (3•x, 2•y), the images are;

A'(9, 10), B'(15, 6), C'(6, 4)

Second part;

The distance between points A and B is 2•√2 which is different from the distance between the image A' and B' which indicates that the transformation is a non rigid transformation.

First part;

The given points are;

The given transformation is presented as follows;

(x, y) → (3•x, 2•y)

Therefore, the images are;

A(3, 5) → A'(3 × 3, 2 × 5) = A'(9, 10)

B(5, 3) → B'(3 × 5, 2 × 3) = B'(15, 6)

C(2, 2) → C'(3 × 2, 2 × 2) = C'(6, 4)

Second part;

Length of AB = √((5-3)² + (3-5)²) = 2•√2

Length of A'B' = √((15-9)² + (6-10)²) = 2•√13

Given that the length of AB ≠ the length of A'B' then we have;

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The points of the image are (9, 10), (15, 6) and (6, 4) and the resulting image is a nonrigid motion.

The points are given as:

A = (3, 5)

B = (5, 3)

C = (2, 2)

The transformation is given as:

(x, y) ⇒ (3x, 2y)

So, we have:

A' = (9, 10)

B' = (15, 6)

C' = (6, 4)

Hence, the image of the transformation is (9, 10), (15, 6) and (6, 4)

See attachment for the image

Also, the resulting image is a nonrigid motion.

This is so because the lengths of the image and the preimage are not equal

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Answer: [tex]\frac{1}{4}[/tex]x - y = 2

Step-by-step explanation:

    Standard form is Ax + By = C where A, B, and C, are integers.

   Given:

y - 1 = 1/4(x - 12)

  Distribute:

y - 1 = [tex]\frac{1}{4}[/tex]x - 3

  Add 3 to both sides of the equation:

y  + 2 = [tex]\frac{1}{4}[/tex]x

  Subtract y from both sides of the equation:

2 =  [tex]\frac{1}{4}[/tex]x - y

   Apply the reflexive property:

[tex]\frac{1}{4}[/tex]x - y = 2

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

We have:

[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]

Find the common ratio:

[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]

[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]

Substitute:

[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]

[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]

The expression is -1/6 x (-1/5) = 1/30.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given:

negative 1 over 6 multiplied by negative 1 over 5.

As per the data,

if -1/6 is multiplied with -1/5 then the resultant value will be

=-1/6 * -1/5

= 1/5*6

=1/30

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Answer:

28

Step-by-step explanation:

Answer:

6 mm

Step-by-step explanation:

So, the area he needs to fill isn't really important, you don't need to calculate it. What is necessary is the individual dimensions of that area (width/length). The width and the length must be divisible by the lengths of the tiles. This is so you don't need to cut anything. For example let's say the area needed to be filled was 15 mm (width) by 10 mm (length). If I chose 3mm square tiles, it could perfectly fill up the width, but when it came to the length there would be a small 1 mm gap. And you would need to cut one of the square tiles, so it would have a length of 1 mm. In this case the 15mm was divisible by 3, but the 10 mm wasn't. So using this logic, it can't be the 4 mm square tile since 150mm / 4 mm = 37.5. It can be the 6m since 150mm / 6mm = 25 and 180 mm / 6mm = 30. It can't be the 8 mm since 150 mm / 8mm = 18.75 mm

Answer:

Step-by-step explanation:

Comments

AE = AT = 7                                                  Given

AT is a perpendicular bisector of OS        Property of a circle

AE is a perpendicular bisector of BR        Property of a circle

ER = 1/2 BR = 48/2 = 24                              Property of a bisector

TS = ER                                                        Property of a bisector and chord

TS = 24                                                        ER = 24 so TS = 24

AS^2 = TS^2 + TA^2                                   Pythagorean Theorem + rt angle

AS^2 = 24^2 + 7^2                                      Substitute values

AS^2 = 576 + 49                                         Combine

AS^2 = 625                                                 Take sqrt of both sides

√AS^2 = √625                                  

AS = 25

Answer

AS = 25

The amount in pounds of Type A coffee used is 36 pounds.

Type A coffee costs Susan $5.45 per pound, and type B coffee

costs $4.05 per pound.

Therefore,

Let x = the number of pounds of Type A coffee.

total pounds = x + 3x

total cost = 5.45(x) + 3x(4.05)

633.60 =  5.45(x) + 3x(4.05)

633.60 =   5.45x + 12.15x

633.60 = 17.6x

divide both sides by 17.6

x = 633.60 / 17.6

x = 36

Pounds of Type A coffee used = 36 pounds

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Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.

According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.

Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.

Thus, the complete statement is: RQ ≅ RT.

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Answer: [tex]y=x+2[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{0-2}{-2-0}=1[/tex]

since the y-intercept is 2, the equation is [tex]y=x+2[/tex]

Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

A linear equation o line can be expressed in the form y = mx + b.

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:

So, the slope m can be calculated as:

[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]

Solving:

m= -58

Considering point 1 and the slope m, you obtain:

11.5= -58×0.1 +b

11.5= -5.8 + b

11.5 + 5.8= b

17.3= b

Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

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Answer:

Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:

2 · x² - 9 · x + 2 = - 1

2 · x² - 9 · x + 3 = 0

d = (-9)² - 4 · (2) · (3)

d = 81 - 24

d = 57

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

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False, An exponential growth function represents a quantity that has a constant doubling time.

What does an exponential growth function represent?

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Answer:

The temperature decreased by 28%

Step-by-step explanation:

How did the temperature change if :

At first it decreased by 60%

Then increased by 80%

Assume that the temperature before decreasing is 100%

∵ The temperature before decreasing = 100%

∵ It decreased by 60%

→  Before decreasing  :  decreasing  :    after decreasing

→  100%                         :  60%              :    100% - 60% = 40%

∴ The temperature after decreasing = 40%

Assume that the temperature after decreasing is 100%

∵ The temperature after decreasing = 100%

∵ It increased by 80%

By using the ratio method

→  After decreasing  :  increasing  :    after increasing

→  100%                      :  80%             :   100% + 80% = 180%

→  40%                        :                       :   x%

By using cross multiplication

∴ 100% × x% = 40% × 180%

- Divide both sides by 100%

∴ x% =

∴ x% = 72%

∵ At first the temperature = 100%

∵ At last the temperature = 72%

∵ The first the temperature > the last the temperature

∴ The decreasing in temperature = 100% - 72% = 28%

The graph doesn't show a function as C. No; the graph fails the vertical line test.

It should be noted that a graph is the diagrammatic representation of data.

In this case, the graph doesn't show a function as the graph fails the vertical line test.

The vertical line test is a visual way that's uses to determine if the curve is a graph of the function.

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The inequalities represented by the graph are; y > -1 and y <= -x.

The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.

However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.

Ultimately, the graph represents the inequalities y > -1 and y <= -x.

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Answer:The inequalities represented by the graph are; y > -1 and y <= -x.

What are the inequalities described by the graph?

The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.

However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.

Ultimately, the graph represents the inequalities y > -1 and y <= -x.

Step-by-step explanation:

The probability that he rolls a 4 and flips a head is 1/12

Probability determines odds that a random event would happen. The odds of the random event happening lie between 0 and 1.

The probability that he rolls a 4 and flips a head = (number of sides that is a 4 / total number of sides) x (number of sides that is a head / total number of sides)

(1/6) x (1/2) = 1/12

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Answer: 1/12

Step-by-step explanation:

just say the answer

Answer:

Answer:

1/6

Step-by-step explanation:

Solution:

The given equation is:y=x/6 -5

arranging the equation :x/6-y=5

Given,

Coefficient of x=1/6

coefficient of y=-1

So,

Slope(m)=-(Coefficient of x/coefficient of y))

= -(1/6 / -1) {minus divided by - becomes plus }

1 by 6 whole divide by 1

= 1/6 ans✓

Answer:

12

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.

Using the Pythagorean theorem, it follows that KN = 12.

The area of the rectangle URST is 135 mm². so the option C is correct.

Congruent rectangles have the same lengths of sides, same measures of angles and same areas and same perimeters

The Rectangle ABCD is congruent to rectangle URST

Given; Rectangle ABCD ≅ rectangle URST

AB = UR , BC = RS , CD = ST , AD = UT

AB = 9 millimeters

UR = 9 millimeters

We know that, The area of any rectangle = l × w,

In rectangle URST

∵ UR = 9 millimeters

∵ RS = 15 millimeters

- Assume that UR = l and RS = w

The area of rectangle URST = UR × RS

The area of rectangle URST = 9 × 15 = 135 millimeters²

Hence, The area of rectangle URST is 135 mm²

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The probability of selecting a black sock is 1/4.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.  It is more likely that an event will occur if its probability is higher.

Number of white socks=20

Number of black socks=10

Number of red socks=6

Number of purple socks=4

Total number of socks=20+10+6+4

                                     =40

Probability of getting a black sock=Number of black socks/Total number                                                                                                        of socks

                                                         =10/40

                                                         =1/4

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The probability that none of them are spades is c(39,5) / c(48,5).

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final result of an experiment. Getting a Head whilst tossing a coin is an event.

Simple chance is the calculation of an outcome or the chance of an event ever taking place. Coverage companies use possibility statistics to determine the possibility of having to pay out a declaration. A simple chance is calculated by way of dividing a particular outcome by all of the feasible outcomes.

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