What is the solution to this system of equations?

Answer:

40

Step-by-step explanation:

plugging in a and b will get us:

\(2^{2} + 6^{2} = c^{2}\)

4 + 36 = \(c^{2}\)

40 = \(c^{2}\)

c= \(\sqrt{40\\\)

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

Direct V:

y=3x

y=(2/7)x

-0.5x=y

Not direct V:

y=2.2x+7

x=-1

y=4

Step-by-step explanation:

That was the answer on edge2020 :))

Direct variation usually conform to the general formula : \(y = kx \) where k is the proportionality constant. Hence sorting the equation into tbe appropriate category :

Direct variation :

y = 3x

y = (2/7)x

y = -0.5x

Non - direct variation :

y = 2.2x + 7

y = 4 and x = - 1

Therefore, only three of the expressions exhibit direct variation while the other three do not.

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By doing a change of units, we know that he will need 40 pint jars to hold the whole volume of sauce.

We know that Joe makes tomato sauce to sell at a craft fair, and we know that he did make that sauce in 5-gallon batches.

We want to see how many jars do he need to hold these 5 gallons, so we need to perform a change of units.

Remember the relation:

1 gallon  = 8 pints.

So, for each gallon, he will need 8 pint jars, then for the 5 gallons, he will need:

5*8 pint jars = 40 pint jars.

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Answer:

2.6

I am pretty sure this is right.

Answer:

x = ± \(\sqrt{8}\) - 2

Step-by-step explanation:

x² + 4x = 4

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 4 + 4

(x + 2)² = 8 ( take square root of both sides )

x + 2 = ± \(\sqrt{8}\) ( subtract 2 from both sides )

x = ± \(\sqrt{8}\) - 2

Answer:

1 rubber cost is 0.59

Step-by-step explanation:

The computation of the cost of one rubber is shown below:

Given that

6 pencil cost = 1.68

3 pencils and 1 rubber cost = 1.09

based on the above information

one pencil cost is

= 1.68 ÷ 3

= 0.56

Now

3(0.56) + 1 rubber = 1.09

So, 1 rubber cost is 0.59

Answer:

7π

Step-by-step explanation:

SO first find the area of the whole circle

which has a radius of 3

a=πr^2

So 3^2=9

9π

Now the two circles which are the same in area due to having the same radius

so if you plug in the 1 for radius the answer would just be π or 1π

now multiply that by 2 becuase there are 2 identical circles

π*2=2π

Now subtract

9π-2π=7π

Answer:

Step-by-step explanation:

area of unshaded circle:

A=π*r^2=π*1=π

we have 2 circles so the area of both circles are 2π

area of the large circle is A(l)=Π*3^2=Π*9=9Π

area of the shaded region: A(s)=9Π-2Π=7Π

Answer:

0.26599

Step-by-step explanation:

When given a random number of samples, we solve using this z score formula

z = (x-μ)/σ/√n

where x is the raw score = 268

μ is the population mean = 266

σ is the population standard deviation = 16

n = 25

For x > 268

z = 268 - 266/16/√25

z= 2/16/5

z = 0.625

Probability value from Z-Table:

P(x<268) = 0.73401

P(x>268) = 1 - P(x<268)

P(x>268) = 1 - 0.73401

P(x>268) = 0.26599

The probability that the average pregnancy length of the women in the study is more than 268 days is 0.26599

Given data:

The original coordinate of T is (-2, 6).

The coordinate of T after reflection on y-axis is,

T

Answer:

Tommy has 12 slices

Step-by-step explanation:

1. You have 4 cakes, and it says to cut it into thirds.

2. So, each cake gets cut into three pieces.

3a. Now you have 12 pieces (or slices!) of cake.

3b. From cutting the cakes into three pieces, you could also just multiply the 4 cakes by 3 (the number of slices), and you would get 12, the answer.

Step-by-step explanation:

9/11=0.81818181....

the digits that repeat is 81

Answer:

.81 repeating

Step-by-step explanation:

9/11 = 0.81 repeating.

Answer:

x = 16

Step-by-step explanation:

Step 1: We know DF - DE = EF

9x - 39 - 47 = EF

Step 2: Simplify

9x - 86 = EF

Step 3: Set the equation equal to 3x + 10

9x - 86 = 3x + 10

6x = 96

x = 16

Therefore x is equal to 16

Answer:

58

Step-by-step explanation:

DE + EF = DF

47+ 3x+10 = 9x-39

Combine like terms

57 +3x = 9x-39

Subtract 3x from each side

57+3x-3x = 9x-3x-39

57 = 6x-39

Add 39 to each side

57+39 = 6x-39+39

96 = 6x

Divide by 6

96/6 = 6x/6

16 =x

We want the length of EF

EF = 3x+10

     = 3*16 +10

    = 48+10

   = 58

An exponential equation that passes through the points (2,1.8) and (5,14.4) is y = (0.6708)2ˣ

Exponential equation:

If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation

y = abˣ

and solving for a and b.

In general, you have to solve this pair of equations:

y1 = abˣ¹ and y2 = abˣ²

Given,

The points (2,1.8) and (5,14.4).

Here we need to find the exponential equation that passes through the points.

This yields the following pair of equations:

1.8 = ab²

14.4 = ab⁵

If you divide the second equation by the first, you get

b³ = 14.4/1.8

b³ = 8

b = ∛8

b = 2

so b = 2. It's possible for b to also be equal to -2, but in this case, assume it's positive.

Now, we can substitute this value for b in either equation to get a. It's easier to use the first equation, so:

1.8 = a² x (2)²

1.8 = a²  x 4

a²  = 1.8/4

a²  = 0.45

a = √0.45

a = 0.6708

Therefore, the exponential form of the equation is,

y = (0.6708)2ˣ

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Answer:

x = 2

Step-by-step explanation:

2x - 3 = 9 - 4x

6x - 3 = 9 (added 4x to both sides)

6x = 12 (added 3 to both sides)

x = 2 (divided 12 by 6)

hope this helps :)

The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term  \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.

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The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:

Branch of Santosh & Co. Chennai

For the year ended December 31, 2018

Sales revenue            $40,300

Cost of goods sold         4,200

Gross profit                 $36,100

Expenses:

Office expenses $36,000

Salaries                    3,600

Total expenses         $39,600

Loss                             $3,500

An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.

The profit or loss is the difference between the total revenue and the total expenses for the accounting period.

Credit sales at branch 40,000

Office expenses by Head office 36,000

Cash remittance to branch for petty cash 9,000

Goods sent to Branch 7,200

Salaries paid by head office 3,600

Debtors 31.12.2018 30,000

Petty cash on 31.12.2018 16,200

Cash sales at branch 300

Stock of 31.12.2018 3,000

Sales revenue   $40,300 ($40,000 + $300)

Cost of goods sold $4,200 ($7,200 - $3,000)

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Answer:

Domain { -5,2,7,-2}

Step-by-step explanation:

The domain is the input values, in this case the x values

Domain { -5,2,7,-2}

Answer:

Option C is the correct option.

Step-by-step explanation:

Domain is the set of all values of x

{( -5 , 6 ) , ( 2 , -8 ) , ( 7 , 12 ) , ( -2 , -8 )

⇒ { - 5 , 2 , 7 , - 2 }

Hope I helped!

Best regards!

Answer:

I will prefer the cone having volume 21.21 cubic inches.

Step-by-step explanation:

A cup of ice cream holds ice cream = 21.21 cubic inches

Since volume of a cone = Capacity of the cone to hold the ice cream

Volume of an another cone having radius (r) = 1.5 inches and height (h) = 3 inches will be,

         V = \(\frac{1}{3}(\pi)(r^{2} )(h)\)

           = \(\frac{1}{3}(\pi )(1.5)^{2}(3)\)

           = 7.069

           ≈ 7.07 cubic inches

Since the volume of the second cone is less than the first cone, I will prefer the first cone with volume = 21.21 inches³

Answer: 8 flips

Step-by-step explanation:

Step-by-step explanation:

sin(30°)cos(45°) + cos(30°)sin(45°)=1+√3/2√2

Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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The volume of the figure with two rectangular prisms would be 1, 728 ft ³

.

To find the volume of the figure with the two rectangular prisms, you can find the volume of the individual rectangular prisms and then add them up.

Volume of rectangular prism 1:

= Length x Width x Height

= 19 x 12 x 6

= 1, 368 ft ³

Volume of rectangle prism 2:

= Length x Width x Height

= 10 x 12 x 3

= 360 ft ³

The volume of the entire figure is then :

= 1, 368 + 360

= 1, 728 ft ³

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The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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Answer: 7

Step-by-step explanation:

\(x+3=10 \\ \\ x=7\)

The value of the car after 5 years is $11,809.8.

It is simply the monetary worth of something.

The purchased cost of car is $20,000.

Every year 10% of car value decease.

The formula for the value of car after t years is given by

Car value = 20,000 * (0.9)^t

To find car value after five years, substitute t=5

i.e.  car value = 20,000 * (0.9^5) = 11,809.8.

$11,809.8 is the value of the car after 5 years.

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Answer:

7 lawns

Step-by-step explanation:

Given:

⇒ Total cost of trip = airfare + transportation + 4 x food

                                = 198 + 56 + (4 x 45)

                                = $434

Given:

⇒ Amount to make from mowing lawns = total cost of trip - savings

                                                                  = 434 - 189

                                                                  = $245

Therefore, he needs to make $245 from mowing lawns to have enough money to pay for the trip.

Given:

⇒ number of lawns = amount needed ÷ amount earned per lawn

                                = 245 ÷ 35

                                = 7

So he needs to mow 7 lawns to have enough money to pay for the trip.

Answer:

7 lawns

Step-by-step explanation:

Let us do this. replace l with lawns mowed and replace day with 4 since the trip is a 4-day trip.

What is 198 + 56?

254.

35l + 189 must be equal to or more than 45(4) + 254.

(45 x 4) + 254 = 180 + 254 = 434

434 - 189 = 245

35l = 245

35/35 = 245/35

l = 7

He has to mow 7 lawns.

Answer:

Step-by-step explanation:

Pour répondre à ces questions, nous devons utiliser la réciproque du théorème de Pythagore, qui établit que si le carré de la longueur du côté le plus long d'un triangle est égal à la somme des carrés des longueurs des deux autres côtés, alors le triangle est rectangle.

a. Pour calculer la longueur AC, nous pouvons utiliser le théorème de Pythagore. Dans le triangle rectangle ABC, l'hypoténuse est AC et les côtés sont AB et BC. Selon le théorème de Pythagore, nous avons :

AC² = AB² + BC²

AC² = 10² + 8²

AC² = 100 + 64

AC² = 164

AC ≈ √164

AC ≈ 12,81 cm

Donc, la longueur AC est d'environ 12,81 cm.

b. Pour déterminer si le triangle ABC est rectangle, nous devons vérifier si la réciproque du théorème de Pythagore est satisfaite. Si la somme des carrés des longueurs des deux côtés les plus courts est égale au carré de la longueur du côté le plus long, alors le triangle est rectangle.

Dans notre cas, nous avons AB = 10 cm, BC = 8 cm et AC ≈ 12,81 cm. Vérifions si la réciproque du théorème de Pythagore est satisfaite :

AB² + BC² = 10² + 8² = 100 + 64 = 164

AC² ≈ 12,81² ≈ 164,16

Nous pouvons voir que AB² + BC² ≠ AC², donc la réciproque du théorème de Pythagore n'est pas satisfaite. Par conséquent, le triangle ABC n'est pas un triangle rectangle.

The graph of the piece-wise function in this problem is given by the image shown at the end of the answer.

A piece-wise function is a function that has different definitions, based on which interval the input value of the function belongs to.

In this problem, the function has three definitions, given as follows:

Hence the graph is defined as follows:

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