Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no
triangles
12 ft 7ft. 14 ft
A unique triangle
B many different triangles
C no triangles​

Answer:

Around 16 hours

(16 hours, 2.74 minutes)

Step-by-step explanation:

In 3 hours,

Rachel has managed: 3 ÷ 5/2 = 6/5

In 6 hours,

Jenna has managed: 6 ÷ 9 = ⅔

Till 9 am,

Thomas and Paul have been woking and maneged:

(9 ÷ 7) ÷ (9 ÷ 2) = 81/14

Total works done in first 9 hours:

6/5 + 2/3 + 81/14 = 1607/210

Remaining work:

15 - 1607/210

= 1543/210

Rachel, Paul and Thomas complete this remaining job together in next 't' hours

(t/2.5) + (t/2) + (t/7) = 1543/210

73t/70 = 1543/210

t = 7.0456621 hours

Or 7 hours 2.74 mins

Overall, it will take them around 9+7 = 16 hours to complete the task

They'll be done at 1600

Which is 4 pm

Final answer:

It will take them approximately 22 hours and 21 minutes to build 15 tractors. The tractors will be finished at around 10:21 PM.

Explanation:

To find out how long it will take them to build 15 tractors, we need to first calculate how many tractors each person can build in 1 hour. Jenna can build 1/9 of a tractor in 1 hour, Thomas can build 1/7 of a tractor in 1 hour, Rachel can build 2/5 of a tractor in 1 hour, and Paul can build 1/2 of a tractor in 1 hour.

Adding up the fractions, we get 1/9 + 1/7 + 2/5 + 1/2 = 85/126. Therefore, in 1 hour, all four of them can build 85/126 of a tractor. To build a total of 15 tractors, we need to find how many hours it will take to build 126/85 of a tractor.

Therefore, it will take them (126/85) × 15 = 22.35 hours to build 15 tractors. Since they started building at midnight, it will take them about 22 hours and 21 minutes, so they will finish building the tractors at around 10:21 PM.

Answer:

Step-by-step explanation:

Given the simultaneous equation

3x+4y=15. Equation 1

3x-y=30. Equation 2

Using elimination method

Sutract equation 2 from 1

Then, will have

3x-3x+4y--y=15-50. -×-=+

4y+y=-15

5y=-15

Divide Both sides by 5

y=-15/5

y=-3

From equation 2

3x-y=30

3x--3=30

3x+3=30

3x=30-3

3x=27

Divide both side by 3

x=27/3

x=9

Then, x=9 and y=-3

Answer:

x=7 y=-9

Step-by-step explanation:

Use a system of equations to solve.

3x-y=30 changes to y=-30+3x

This can then be substituted into the other equation.

3x+4(-30+3x)=15

solve for x

X=7

Now use 7 in the other equation.

y=-30+x(7)

y=-9

Answer:

Step-by-step explanation:

5-2(x-1)=12

5-2x+2=12

5+2-2x=12

7-2x=12

2x=7-12

2x=-5

x=-5/2

Answer: It is already a decimal???

Step-by-step explanation:

Option C: x = 5.5 is the value of x

Explanation:

Given that CD, AE, an BF are the medians of the triangle ABC

Also, given that [tex]AM = 4x - 5[/tex] and [tex]ME=x+3[/tex]

We need to determine the value of x.

Since, we know that the centroid divides the median in the ratio 2 : 1

Hence, we have,

[tex]AM=2\times ME[/tex]

Substituting the values, we get,

[tex]4x-5=2(x+3)[/tex]

Simplifying, we get,

[tex]4x-5=2x+6[/tex]

Subtracting both sides of the equation by 2x, we have,

[tex]2x-5=6[/tex]

Adding both sides of the equation by 5, we have,

[tex]2x=11[/tex]

Dividing both sides of the equation by 2, we get,

[tex]x=5.5[/tex]

Therefore, the value of x is 5.5

Hence, Option C is the correct answer.

Answer:

16.2

Step-by-step explanation:

Add the numbers together

Answer:

Avg. monthly expenses are $1,481.83

Step-by-step explanation:

Just took the test :)

Chandra's average monthly expenses are calculated by adding her total annual expenses for each category and then dividing by 12, yielding an average monthly expense of $1,481.83.

To calculate Chandra's average monthly expenses, we first need to sum up all the expenses for each month and then divide by the total number of months (12).

Adding all these up gives us the total annual expense:

$852 (cell phone) + $12,300 (rent) + $300 (gym) + $300 (internet) + $850 (auto insurance) + $1,440 (gas) + $1,740 (food) = $17,782 total annual expense.

To find the average monthly expense, we divide by 12:

$17,782 / 12 months = $1,481.83

Therefore, Chandra's average monthly expenses are $1,481.83.

Answer:

13 +13 +14 ensures he is getting the smallest amount so its 14

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

6+30=36

6^2=36

Answer:

the positive number is equal to  6.

Step-by-step explanation:

from the question which says A positive number is 30 less than its square. Find the number.

let the number be "n"

and the square of the number = n²

So, we have  the expression to be

n = n²-30

n ²-30 -n =0

Re-arrange the equation

n²-n-30=0

the factors of -30 are 5 and -6

so we have

(n+5)(n-6)=0

n+5 =0

n = -5

or

n-6 =0

n = 6

therefore the number can either be -5 or 6.

note we are asked to find the positive number , so the positive number is 6

Answer:

x=(-2/3)

Step-by-step explanation:

(9x+13)^2=49

√(9x+13)^2=√49

9x+13=7

9x+13-13=7-13

9x=-6

9x÷9=-6/9

x=-6/9

-6/9=-2/3

Answer:

x = -2/3; -20/9

Step-by-step explanation:

Answer:

(6, 2)

Step-by-step explanation:

Flipped is equivalent to mirrored, so on the other side of the y axis should be a mirrored point equally far from 0, which is -6 and the value for y should be the same: 2.

The coordinates (-6,2) when flipped on the y-axis become (6,2), as the process involves changing the sign of the x-coordinate while keeping the y-coordinate same.

The coordinates (-6,2) when flipped on the y-axis will become (-(-6),2), which makes it (6,2). To understand why, we can refer to the principle of reflection in mathematics. Reflection of a point about the y-axis implies changing the sign of the x-coordinate while keeping the y-coordinate same. Here, the x-coordinate is -6, and when we flip or reflect on the y-axis, it changes its sign. Therefore, -(-6) becomes +6. The y-coordinate remains the same. Hence, -6 2 flipped on the y axis becomes (6, 2).

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Answer:

Exact Form:

tan(x)=5/3

Decimal Form:

tan(x)=1.¯6

Mixed Number Form:

tan(x)=12/3 mixed number

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

It moves to the right 3 and up 2.

Answer:

Step-by-step explanation:

the answer would be 2/3

For the given triangle, the tan of angle A equals C.

Step-by-step explanation:

Step 1:

For the given triangle, the hiking route is represented by AB and the change in elevation is represented by BC.

So we need to calculate the value of BC for the given triangle

Step 2:

In the given triangle, the opposite side has a length of 'a' feet, the adjacent side has a length of 'b' feet while the triangle's hypotenuse measures 400 feet.

To calculate the opposite side of the triangle, we can use the sine of any angle in that particular triangle. The sine of a particular angle is the opposite side's length divided by the hypotenuse's length.

sin A = [tex]\frac{oppositeside}{hypotenuse}[/tex] .

Step 3;

The length of the opposite side = a,

The length of the hypotenuse side = 400 units.

[tex]\sin A=\frac{a}{400}, \sin 25^{\circ}=0.4226[/tex]. So

[tex]0.4226=\frac{a}{400}, a=0.4226 \times 400[/tex] = 169.04 feet.

So the change in elevation is 169.04 feet.

Answer:

The brand that is the best buy is D. Cousin Ben's Stuffing Mix 6 oz, because the cost per ounce is the lowest.

Step-by-step explanation:

For answering this question correctly, we need to calculate the cost per ounce to compare the four stuffing mix options available. Therefore,

Cost per ounce = Price/Number of ounces in the package

Proceeding with the calculations, we have:

A. Cook Top Stuffing Mix 6 oz. for $1.49. If we use the coupon the price would be $ 1.39.

Cost per ounce = 1.39/6

Cost per ounce = $ 0.23 (rounding to the next cent)

B. Cook Top Stuffing Mix 12 oz. for $2.99.  If we use the coupon the price would be $ 2.89.

Cost per ounce = 2.89/12

Cost per ounce = $ 0.24 (rounding to the next cent)

C. Saltridge Farms Stuffing Mix 6 oz. for $1.79.

Cost per ounce = 1.79/6

Cost per ounce = $ 0.30 (rounding to the next cent)

D. Cousin Ben's Stuffing Mix 6 oz. for $1.29.

Cost per ounce = 1.29/6

Cost per ounce = $ 0.22 (rounding to the next cent)

The brand that is the best buy is D. Cousin Ben's Stuffing Mix 6 oz, because the cost per ounce is the lowest.

The functions which will form the composite function G(F(x)) = 3(x + 1) are  F(x) = x + 1 and G(x) = 3x.

Given is a composite function,

G(F(x)) = 3(x + 1)

We have to find the functions G(x) and F(x).

G(F(x)) means that F(x) is substituted instead of x in G(x).

Let G(x) = 3x and F(x) = x + 1

In the composite function G(F(x)), F(x) = x + 1 is substituted in place of x in G(x).

So,

G(F(x)) = 3(x + 1)

Thus, F(x) = x + 1 and G(x) = 3x

Learn more about Composite Functions here :

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Final answer:

To find the composite function GF(x) from the given equation, identify the functions F(x) and G(x) and match them with the answer choices to determine the correct option, which is C.

Explanation:

The composite function GF(x) is calculated by substituting F(x) into G(x).

Identify F(x) and G(x) in the given equation, G(F(x)) = 3(x+1), which corresponds to F(x) = x+1 and G(x) = 3x.

Comparing them with the answer choices, the correct option is C. F(x) = 5x + 1 and G(x) = 3x.

Therefore, the composite function GF(x) is formed by F(x) = 5x + 1 and G(x) = 3x.

Answer:

Below.

Step-by-step explanation:

These reasons will probably be similar to the US conventions but not exactly the same ( I'm using the UK conventions).

1.  Given

2. Given.

3, Opposite sides of a parallelogram.

4. Opposite sides of a parallelogram.

5. This side is common to both triangles.

6.  The triangles are congruent  by 3 equal sides ( I think that is  SSS).

Answer:

1. P(N) =  3/5

2. P(R) =  2/5

3. P(N and R) = 1/4

4. P(N or R) = 3/4

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Number of students in a high school senior class = 500

Number of students that regularly wear a necklace = 300

Number of students that regularly wear a ring = 200

Number of students that wear a necklace and a ring = 125

2. What is P(N), the probability that a senior wears a necklace?

Let's recall the formula of probability:

Probability = Number of favorable outcomes/Total of possible outcomes

Substituting with the real given values:

P(N) = 300/500 = 3/5 (Dividing by 100 numerator and denominator)

P(N) =  3/5

3. What is P(R), the probability that a senior wears a ring?

Substituting with the real given values:

P(R) = 200/500 = 2/5 (Dividing by 100 numerator and denominator)

P(R) =  2/5

4. What is P(N and R), the probability that a senior wears a necklace and a ring?

Substituting with the real given values:

P(N and R) = 125/500 = 1/4 (Dividing by 125 numerator and denominator)

P(N and R) = 1/4

5. What is P(N or R), the probability that a senior wears a necklace or a ring?

P(N or R) = P(N) + P(R) - P(N and R)

Substituting with the real given values:

P(N or R) = 3/5 + 2/5 - 1/4

P(N or R) = 5/5 - 1/4

P(N or R) = 1 - 1/4

P(N or R) = 3/4

The probabilities are:

P(N) = 0.6
P(R) = 0.4

P(N and R) = 0.25

P(N or R) = 0.75.

Let's solve the given probabilities step-by-step using the provided information.

Step 1: Calculate P(N)

The probability that a senior wears a necklace, P(N), is calculated by dividing the number of students wearing a necklace by the total number of students.

Step 2: Calculate P(R)

The probability that a senior wears a ring, P(R), is calculated similarly by dividing the number of students wearing a ring by the total number of students.

Step 3: Calculate P(N and R)

The probability that a senior wears both a necklace and a ring, P(N and R), is given directly in the problem.

Step 4: Calculate P(N or R)

The probability that a senior wears either a necklace or a ring is given by the formula:

Answer:

a is correct

Step-by-step explanation:

Answer:

(52, 32 )

Step-by-step explanation:

Given the 2 equations

y = x - 20 → (1)

x + y = 84 → (2)

Substitute y = x - 20 into (2)

x + x - 20 = 84, that is

2x - 20 = 84 ( add 20 to both sides )

2x = 104 ( divide both sides by 2 )

x = 52

Substitute x = 52 into (1) for corresponding value of y

y = 52 - 20 = 32

Solution is (52, 32 )

1. D

2. D

3. c

4. A

5. C

I'm not 100% sure about these. Just letting you know.

Similar triangles may or may not be congruent.

1. The length of RS

Since U and V are the midpoints, then:

[tex]\mathbf{RS = 12 + 12}[/tex]

[tex]\mathbf{RS = 24}[/tex]

Hence, the length of RS is (d) 24

2. The value of x

This is calculated as:

[tex]\mathbf{SV = VT}[/tex]

So, we have:

[tex]\mathbf{2x = 11}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 5.5}[/tex]

Hence, the value of x is (d) 5.5

3. The value of y

This is calculated as:

[tex]\mathbf{WT = WR}[/tex]

So, we have:

[tex]\mathbf{3y = 15.9}[/tex]

Divide both sides by 3

[tex]\mathbf{y = 5.3}[/tex]

Hence, the value of y is (d) 5.3

4. The value of UW

This is calculated as:

[tex]\mathbf{UW = 2x}[/tex]

So, we have:

[tex]\mathbf{UW = 2 \times 5.5}[/tex]

[tex]\mathbf{UW = 11}[/tex]

Hence, the value of UW is (a) 11

5. The value of UV

This is calculated as:

[tex]\mathbf{UV = RW}[/tex]

So, we have:

[tex]\mathbf{UV = 15.9}[/tex]

Hence, the value of UV is (c) 15.9

Read more about similar triangles at:

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Step-by-step explanation:

A rational no. between 4.1 and √17=4.12

is 4.11 option a

Answer:

V=3,140in3

Step-by-step explanation:

Answer:

D) 8sqrt(2)

Step-by-step explanation:

h² = 8² + 8²

h² = 2(8²)

h = 8sqrt(2)

Answer: 0.18

Step-by-step explanation:

Answer:

B. Henry for the first one and A. Isebella for the second one

Step-by-step explanation:

Answer:

1. Henry

2. Isabella

Step-by-step explanation:

Answer:

192 cm^3

Step-by-step explanation:

Volume for rectangular prism is V=l*w*h

V=8*4*6=32*6=192

So volume is 192 cm^3

Answer:

96

Step-by-step explanation:

3^4 = 81

3 . 5 = 15

81+15 - 96

Answer:

96

Step-by-step explanation:

3^4=3*3*3*3=9*9=81

81+3*5=81+15=96