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The solutions to the equation 10x⁴ + 30x³ + 35x² as required in the task content are; 0, (-3 + i√5)/2, and (-3 - i√5)/2.

It follows from the task content that the given equation is; 10x⁴ + 30x³ + 35x² = 0.

Hence, to find all the solutions of the equation, one must factorise the expression on the left hand side so as to obtain the factors as follows;

10x² (x² + 3x +3.5) = 0

Hence, we have;

10x² = 0; x = 0 OR

x² + 3x +3.5 = 0.

Hence, it follows from the quadratic formula that the roots/zeroes of x in the equation above can be evaluated as follows;

x = {-b±√(b²-4ac)}/2a

hence, by comparison, we have;

x = {-3±√(9-14)}/2

x = (-3 ± √-5)/2

x = (-3 ± i√5)/2

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Answer:

x = 3, y = -9

Step-by-step explanation:

plug y=4x-21 into 7x+y=12 to get

7x + (4x-21) = 12 -> 11x -21 = 12 -> 11x = 33 -> x = 3

plug x=3 into y=4x-21 to get

y = 4(3) - 21 = 12 - 21 = -9

The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represents the number of months and y represents the total charge.

Scenario 1: DesTunes charges adults $15 per month.

Hence:

y = 15x

Scenario 2: DesTunes charges students a $20 sign-up fee and $5 per month, hence;

y = 5x + 20

The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20

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Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

C1(x) = C2(x).

Hence:

22 + x = 14 + 3x

2x = 8

x = 4.

4 movies would cause the two plans to have an equal monthly cost.

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Answer:

The answer is 7 for C.

Step-by-step explanation:

7+7=14 and 7x7=49

The diamond just asks for numbers that make up a pattern for the two given numbers.

Answer:

6

Step-by-step explanation:

Possibly 6 but if not let me know

Answer:

6

Step-by-step explanation:

the h's cancel out

Answer:

x = 11

m<H = 39°

Step-by-step explanation:

m<G = 6x - 15

m<H = 3x + 6

complementary angles = angles that add up to 90

6x - 15 + 3x + 6 = 90

9x = 99

x = 11

m<H = 3x + 6, plug in 11 as x

3 * 11 + 6

= 33 + 6

m<H = 39°

Answer:

I could be wrong, but I think you got right in the beginning 107°, but go with your gut feeling. Wish you the very best <3

Answer: x=73 degrees, z=73 degrees, y=107 degrees

Step-by-step explanation:

y=107 degrees because y and 107 degrees are congruent angles

z=x because z and x are congruent angles

x+y=180 ==> x and y are supplementary angles that are placed on a straight line(the straight line is 180 degrees and is called a straight angle.)

x+107=180

x=73 degrees

z=x

z=73 degrees

The factor that is not a possible confounding factor is B. the expected sales for the year 2014.

A confounding factor is a third variable that influences or explains both the independent and dependent variables.

The independent variable here is the year while sales are the dependent variable.

However, confounding factors could include the number of new buildings constructed in 2013, which was not factored in by the architectural company and the state of the economy in 2013.

Thus, the expected sales for the year 2014 cannot be a confounding variable for the decreased sales in 2013 because it cannot explain the 2013 performance.

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A. the number of new buildings constructed

B. the expected sales for the year 2014

C the state of the economy

Answer: 27.185

Step-by-step explanation:

Hi there!

If you just want to add 27+0.185, the answer is 27.185.  

You just have to add 27+0.185 (what I think of for this question is just adding the 27 to it).

Hope this helps! Have a great day!

Answer:

Undefined

Step-by-step explanation:

Plugging in 3 for x and 4 for y we get:

6(3) + 4(4) = 36

multiplying we get

18 + 16 = 36
34 = 36

which is not true.

if this was helpful pls give me brainliest <3

Answer:

steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts

Answer:

3×8 =24

24÷2=12

Area of triangle=12m²

Step-by-step explanation:

3×8 =24

24÷2=12

The dimensions of floor is 500 cm by 212.5 cm

Multiply the width and length of each rectangle to find its area. The areas of each rectangle are then added up to determine the total area. In the event that your room is L-shaped, for instance, this can be split into two rectangles. Additionally, this method still works in a complicated room.

500 cm by 212.5 cm

Given :

The main arena hall has dimensions 200 m by 85 m.

On a large diagram on the office wall the scale is 1:40.

Length of arena hall = 200 m

Scale is 1:40

So, the length of the floor =

Since 1 m = 100 cm

So, 5 m = 100*5 = 500 cm

Width of arena hall  = 85 m

So, width of floor =[tex]\frac{85 * 1}{40}[/tex]  =  2.125m

Now 1 m = 100 cm

So, 2.125 m = 212.5 cm

Thus the dimensions of floor is 500 cm by 212.5 cm

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Rawr!~ Allow me to help you today!

Answer:

[tex]V=\frac{2}{5}[/tex] cubic units!

Step-by-step explanation:

Step 1: Draw the carton (Carton is in the image)

Step 2: Calculate the volume V

[tex]V=LWH[/tex]

[tex]V=\frac{8}{3}[/tex] × [tex]\frac{1}{8}[/tex] ×[tex]\frac{6}{5}[/tex]

[tex]V=\frac{2}{5}[/tex] cubic units

I hope this helps you! <3

AshTheNeko

Answer:

172 kilowatts.

Step-by-step explanation:

Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹

People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹

Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.

Answer:

The Ratios, Rate and unit rate are used to solve many real-world problems.

Step-by-step explanation:

As a ratio is a comparison of two numbers or measurements.

A rate is also a ratio in which the two terms are in different units.

A unit rate means a rate for one of something

Answer:

7/10 = 0.7 = 70%

25/100 = 0.25 = 25%

56/100 = 0.56 = 56%

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

To work out the lowest common multiple, we first:

7, 14, 21, 28...

14, 28...

The common multiples of 7 and 14 are 14, 28 etc, but the LEAST (or lowest) common multiple is 14.

Hope this helps.

Jane is 2x+3 years old. (answer)

In this case, we can use Kay as the base/foundation in this problem. Kay is x years old. Mary is twice as old as Kay, making Mary 2 times x or 2x. We are solving for Jane. Jane is 3 years older than Mary, who we know is 2x. We can add on 3 years making the final expression for Jane's age: 2x+3. Since we do not know Kay's age, or x, we cannot solve this problem any further.

Answer:

Answers below

Step-by-step explanation:

To find per 20 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 40 (to get miles per 20 min)

=  20 miles / 160 minutes

_____________________________________________

To find per 15 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 30 (to get miles per 15 minutes)

= 15 miles / 120 minutes

_____________________________________________

To find miles per minute

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 8 (to get miles per minute)

= 0.125 miles / 1 minute

_____________________________________________

To find miles per hour

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 15 (to get miles per hour)

= 7.5 miles / 60 minutes

Answer:

Volume V ≈ 1481.3269 cubic inches

Step-by-step explanation:

Volume V of a cylinder is given by the formula

V = πr²h  where r = radius of the base of the cylinder and h the height

Here we are given the diameter, d = 5.9375 inches

Radius r = d/2 = 5.9375/2 = 2.96875 in

Height h = 53.5 in

V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches

Answer V ≈ 1481.3269 cubic inches

When given 3 meters of cloth and it is to be divided in a ratio of 3:7 then one part will have 0.9 meters  and the other will have 2.1 meters.

The first thing to do is to find the denominator of the ratio by summing the two numbers in the ratio:

= 3 + 7

= 10

The first part of the cloth would be:
= 3 / 10 x 3 meters

= 0.3 x 3 meters

= 0.9 meters

The second part of the cloth would be:

= 7 / 10 x 3 meters

= 0.7 x 3

= 2.1 meters

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Answer:

4/9

Step-by-step explanation:

Answer:

Options 2-5

Step-by-step explanation:

1. False, since the designs aren't identical.

2. True, both circles have a radius of 1.

3. True, you can translate the circles in Diego's design up to that they are all tangent to each other to make Elena's design.

4. True, both circles have diameter 10.

5. True, simlar logic to 2 and 4

The value of x is -160.

An equation in which the power of any variable is not more than one is called a linear equation.

Here, we are given a linear equation as follows-

5 × x + 860 = 2 × x + 380

⇒ 5x + 860 = 2x + 380

Let us solve the given equation-

Subtracting 2x from both sides, we get

5x - 2x + 860 = 2x - 2x + 380

3x + 860 = 380

Subtracting 860 from both sides-

3x + 860 - 860 = 380 - 860

3x = -480

dividing both sides by 3,

3x/3 = -480/3

x = -160

Thus, the value of x comes out to be -160.

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Answer:

x> - 4

Step-by-step explanation:

In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them.

Answer:

$ 850.25

Step-by-step explanation:

I will assume anything over 40 hours is 'overtime'

total pay will be

   regular pay    +   overtime pay

 17.90 * 40 hr    +   (17.90 * 1.5)(5hr) = $ 850.25

Step-by-step explanation:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.

b. The  number of successes in the Washington sample were 4740 .

The number of  failures in the Washington sample is 1,260

c. the 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement "Employers should be required to pay men and women the same salary for the same job" is 0.018 to 0.068.

(b) Number of successes and failures in the Washington sample:

Total number of respondents in the Washington sample: 6,000

Percentage who agreed with the statement: 79%

Number of successes = 79% of 6,000

= 0.79 * 6,000

= 4,740

Number of failures = Total - Number of successes

= 6,000 - 4,740

= 1,260

(c)

confidence interval = (p1 - p2) ± Z * √((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

p1 = Proportion of successes in the Washington sample

p2 = Proportion of successes in the Atlanta sample

n1 = Size of the Washington sample

n2 = Size of the Atlanta sample

Z = Z-score for the desired confidence level = 1.96

confidence interval = (0.79 - 0.74) ± 1.96 * √((0.79 * (1 - 0.79) / 6000) + (0.74 * (1 - 0.74) / 4800))

confidence interval = 0.05 ± 1.96 * √((0.79 * 0.21 / 6000) + (0.74 * 0.26 / 4800))

confidence interval = 0.05 ± 1.96 * √(0.00013815 + 0.0001244583)

confidence interval = 0.05 ± 1.96 * √(0.0002626083)

Lower bound of the confidence interval (DC - Atlanta)

= 0.05 - 0.0317226549

=  0.018

Upper bound of the confidence interval (DC - Atlanta)

= 0.05 + 0.0317226549

= 0.068

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