The diagram shows triangle ABC, with AB = xcm, AC = (x+2)cm, BC = 2square root7cm and angle CAB = 60°.
(i) Find the value of x.​

Answer:

Her wage on the 8th day is $105 ⇒ answer d

Step-by-step explanation:

* Lets explain how to solve the problem

- The average of set of data = The sum of data/the number of data

- The sum of data = the average of set of data × the number of data

∵ Cindy worked for 15 consecutive days

∵ She is earning an average wage of $91 per day

∴ Her total earning = 91 × 15 = $1365

∵ Her average earning during the first 7 days is $87 per day

∴ Her total earning in the first 7 days = 87 × 7 = $609

∵ Her average earning during the last 7 days is $93 per day

∴ Her total earning in the last 7 days = 93 × 7 = $651

- Her total earning in the 14 days is the sum of the earning in the

 first 7 days and the earning during the last 7 days

∵ Her total earning in the 14 days = 609 + 651 = $1260

∵ Her total earning in the 15 days is $1365

- To find her wage on the 8th day subtract her wage of the 14 days

  from her wage of the 15 days

∴ Her wage on the 8th day = 1365 - 1260 = $105

* Her wage on the 8th day is $105

Answer:

Step-by-step explanation:

-3x -2 = 19

+3x +3x

-2 = 19 + 3x

-19 -19

-21 = 3x

Divided by 3

-7 = x

Answer:

16

Step-by-step explanation:

The sum of 3 and 13 would look like this as an equation, 3 + 13 = ? Just add 3 to 13 and you get 16 as your answer.

x + 300 = 450 is the correct answer. This is becuause the unknown amount, x, is how much she put in the bank. $450 is her total, so it would be equal to 450. If she already had 300, you need to firgure out what she added to 300 to make the answer 450, so the correct answer is x + 300 = 450.

Answer:

Option B. $72, because the price of each pack is $8

Step-by-step explanation:

Looking at the double number line we have that

The price of 2 packs of spaghetti is $16

The price of 4 packs of spaghetti is $32

The price of 6 packs of spaghetti is $48

The price of 8 packs of spaghetti is $64

To find out he units rate, divide the price by the number of packs

[tex]\$16/2=8\frac{\$}{pack}[/tex]

Find out what is the price of 9 packs of spaghetti

Multiply the unit rate by 9

[tex]8\frac{\$}{pack}(9\ packs)=\$72[/tex]

therefore

The price of 9 spaghetti packs is $72

Answer:

B. 72

Step-by-step explanation:

LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOL

When a line passes through two points on a plane, according to Euclidean geometry, that line is on the same plane as the points-the correct statement is Statement C.

In the context of the four statements given about a line passing through two points on a plane, only Statement C is correct. According to Euclidean geometry, specifically the concept of a plane, if a line passes through two points on a plane, the line is indeed on the same plane as the points. To further clarify this mathematical rule, you can picture a page of a book as the plane, and any line drawn between two points on the page is considered to be on the same plane as the points.

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The correct statement is Statement C: The line is on the same plane as the points.

The correct statement regarding a line passing through two points on a plane is Statement C: The line is on the same plane as the points. A line that passes through two points on a plane is always on the same plane as those points. Since a plane is a flat surface that extends infinitely in all directions, any line that lies on the same plane as the points will also lie on that plane.

For example, if we have two points A and B on a flat table, any line that passes through those points will also lie on the table itself, and thus, on the same plane as the points.

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Answer:

The answer to your question is: -17°C

Step-by-step explanation:

Data

Initial temperature = 7°C at 3:00 pm

Temperature drops 6°C every hour

Temperature at 7:00 pm

Process             Temperature

3:00                          7°C

4:00         -6°C           1°C      

5:00         -6°C          -5°C

6:00         -6°C          -11°C

7:00          -6°C          -17°C

The required value of the given expression would be fraction -9 17/72.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The expression is given in the question

⇒ (4 3/4) × 5/6 × ( -2 1/3)

We have to evaluate the given expression,

⇒ (4 3/4) × 5/6 × ( -2 1/3)

⇒ (4 3/4) × 5/6 × (-1)(2 1/3)

⇒ (4 + 3/4) × 5/6 × (-1)(2 + 1/3)

⇒ (19/4) × 5/6 × (-1)(7/3)

⇒ 85/24 × (-7/3)

Apply the multiplication operation,

⇒ -665/72

Apply the division operation,

⇒ -9.236111

⇒ -9 17/72

Therefore, the required value of the given expression would be fraction -9 17/72.

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Final answer:

The expression 4 3/4 * 5/6 * -2 1/3 evaluates to -665/72 after converting mixed numbers to improper fractions and then multiplying the numerators and denominators. The result is in its simplest form.

Explanation:

The question involves evaluating a mathematical expression with mixed numbers and fractions and writing the answer in its simplest form. To solve this, we first convert mixed numbers to improper fractions. The expression given is 4 3/4 * 5/6 * -2 1/3. First, convert the mixed numbers:

Now multiply the improper fractions:

Multiply the numerators: 19 * 5 * (-7) = -665
Multiply the denominators: 4 * 6 * 3 = 72
Therefore, the result is -665/72. This is already in its simplest form as the numerator and denominator have no common factors.

Good evening ,

______

Answer:

[tex]\frac{183-97i}{89}[/tex]

____________________

Step-by-step explanation:

(11-19i)/(8-5i)

=(11-19i)(8+5i)/(8-5i)(8+5i)

=(88+55i-152i+95)/(8²+5²)

=(183-97i)/89.

:)

Answer:

9

Step-by-step explanation:

Answer:

slope = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (4, 0) and (x₂, y₂ ) = (- 2, 8)

m = [tex]\frac{8-0}{-2-4}[/tex] = [tex]\frac{8}{-6}[/tex] = - [tex]\frac{4}{3}[/tex]

Answer:

x³

Step-by-step explanation:

Differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

[tex]\frac{1}{4}[/tex] [tex]x^{4}[/tex], then

[tex]\frac{d}{dx}[/tex] ( [tex]\frac{1}{4}[/tex] [tex]x^{4}[/tex] )

= 4 × [tex]\frac{1}{4}[/tex] [tex]x^{4-1}[/tex] = x³

Answer:

x^3.

Step-by-step explanation:

Algebraic differentiation:

If y = ax^n , dy/dx = an x^(n-1), so

y = x^4 / 4

  = (1/4)x^4  

dy/dx = (1/4 * 4) x(4-1)

= x^3.

Answer:

[tex]y>-3x+6[/tex]

Step-by-step explanation:

First find the equation of the "boundary line" that separates the two sections of the plane. It is very simple to find its slope_y-intercept form from the graph.

We can find the slope of the boundary line by examining the two points where it intersects the axes: It crosses the y-axis at (0,6) (0 for x, 6 units for y)

and also crosses the x axis at (2,0) (2 unites for x and 0 for y)

That means that from the y intersect crossing, in order to arrive at the x intersect crossing, one has to go:

2 units to the right (this is called "run")

and 6 units down (this is called "rise", but should be considered as a negative value because instead of "rising" is going down)

Therefore, the slope of the boundary line is: [tex]slope = \frac{rise}{run} = \frac{-6}{2} = -3[/tex]

We also see that the y-intercept is = 6 (the point at which the line crosses the y-axis.

Then, we can write the equation of the boundary line as:

[tex]y = -3 x + 6[/tex]

Now, the set of (x,y) points that are highlighted in the picture are those "ABOVE" the boundary line, that is those points where the y-value is greater than those defined by the boundary line. Since the boundary line is drawn with a dotted line, that indicates that those values corresponding to (x,y) values in the line itself should NOT be included.

We therefore arrive at an inequality that does not contain an equal sign (to preclude the actual (x,y) values in the line to be included). and which indicates that we want all the (x,y) points on the plane which have y-values greater than those define by the boundary line. That is:

[tex]y>-3x+6[/tex]

1.0730000000000000000000000000

I searched it up

Answer:

infinite solutions

Step-by-step explanation:

Given

- 6(n - 8) = 4(12 - 5n) + 14n ← distribute parenthesis on both sides

- 6n + 48 = 48 - 20n + 14n, that is

- 6n + 48 = 48 - 6n ( add 6n to both sides )

48 = 48 ← True

This indicates that the equation is true for any value of n

Answer:

This is a very classical type of equation in which, the solution is basically any number and it is known as an "Identity". So it has infinite solutions

Step-by-step explanation:

-6(n-8) = 4(12-5n)+14n

-6n-6*(-8) = 4*12+4*(-5n) + 14n

-6n+48=48-20n+14n

-6n+48=48-6n

-6n+48=48-6n

-6n +6n + 48 -48 = 48 -48 - 6n + 6n

0 = 0

Answer:

54 hundreds

Step-by-step explanation:

Answer:

18 cherries

Step-by-step explanation:

45 lemon pieces

40 lemons=16 cherries

5 lemons=2 cherries

18x^4+72x^3 is the answer to your question

Answer: 9x^2(2x^2+8x)

2x^2 8x

9x^2. 18x^4 72x^3

18x^4 + 72x^3

Step-by-step explanation:

Answer: -4xy + 2x

Step-by-step explanation:

4xy - 8xy = -4xy

4x - 2x = 2x

Answer:

2x - 4xy    or     2x(1 - 2y)

Step-by-step explanation:

Simplify 4xy-2x+4x-8xy

We can start by rearranging the expression;

4xy-8xy -2x + 4x

Then we add or subtract numbers with the same variable

-4xy + 2x

We can further factorize the above since 2x is common between the two numbers, so we will factor out 2x

2x(-2y + 1)

This can be re-write as;

2x(1 - 2y)

A) Because the 80 is by itself that would be the start up fee.

B) We are told x is the number of months. Since the X is being multiplied by 30, we know that would be the total monthly cost. This is being added to the 80, which does not have an exponent, so we know this is a single cost, which would be the start up fee.

C) Copying the same format as the given equation above, change the numbers:

f(x) = 20 + 35x

D) I used the same format as the first equation, which meant replacing the start up cost from the original one ( 80) with the start up of the new one (20). Then I changed the monthly cost from the original one (30) with the monthly cost of the new one (35).

E) Replace x in each equation with 8 and calculate the cost of each:

80 + 30(8) = 80 + 240 = $320

20 + 35(8) = 20 + 280 = $300

The second club (club B) is the cheaper option for her.

Answer:

B. 7 hours

Step-by-step explanation:

Since the question states "at this rate" , this could be worked out by using simple proportion.

120miles = 3hours

280miles = ?

(280x3)/120 = 7 hours

It will take 7 hours to drive 280 miles.

Speed shows us how quickly or slowly an item is moving by converting distance to time. It gives the amount of time it took to travel a certain distance divided by the distance travelled.

Speed is inversely correlated with time and directly correlated with distance. As a result, distance equals speed times time, and time equals distance divided by speed; as speed rises, distance travelled will shorten, and vice versa.

Given:

Distance = 120 miles

Time= 3 hours

Now, using

speed= Distance / time

speed = 120/ 3

speed= 40 miles / h

Now, for distance 280 miles

time= Distance / speed

time = 280 / 40

time = 7 hours

Hence, it will take 7 hours to drive 280 miles.

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Answer:

24

Step-by-step explanation:

6/(7/28)

6/(1/4)

6 * 4/1

6 * 4

24

Answer: YES!

Step-by-step explanation:

IF you can divide it in 4 it is!

Answer:

No

Step-by-step explanation:

A perfect cube is something that is multiplied by itself 3 times.

For example, 8 is a perfect cube because 2×2×2 = 8

27 is a perfect cube because 3×3×3 = 27

64 is a perfect cube because 4×4×4 = 64

No number can be multiplied by itself three times to equal 48

Therefore its not a perfect square.

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Answer:

x = 10

Step-by-step explanation:

First you need to add like terms (x + x), which would give you 2x.

2x + 2 = 22

Then subtract 2 from both sides, causing it to cancel out one side, and 22 - 2, on the other side:

2x + 2 = 22

      -2     -2

22 - 2 is 20, giving you:

2x = 20

Then divide both sides by 2:

2x/2 = 20/2

And you should get x = 10 as your answer.

Answer:

about 7.4 miles

exact is 7.44 miles

Step-by-step explanation:

0.62×12=7.44

Answer:

8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

4[tex]\sqrt{2}[/tex] + 7[tex]\sqrt{2}[/tex] - 3[tex]\sqrt{2}[/tex]

Factor out [tex]\sqrt{2}[/tex] from each term

= [tex]\sqrt{2}[/tex](4 + 7 - 3) = 8[tex]\sqrt{2}[/tex]

Answer:

B. Triangles are similar if two corresponding angles in each triangle are the same measure.

Step-by-step explanation:

If two pairs of corresponding angles are congruent, then that makes the triangles similar to each other, by the Angle-Angle Similarity Postulate.

* This is definitely a genuine statement!

I am joyous to assist you anytime.