Four more than twice a number is less than negative fourteen. Solve the inequality for the unknown number. Solve the inequality for the unknown number.

By using the vertex and the given point, we will see that the graphed quadratic equation is:

y = -(x - 2)^2 + 4

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

Here the vertex is (2, 4), replacing that we get:

y = a*(x - 2)^2 + 4

Now we also can see that the line passes through the point (0, -8), replacing these values we get:

-8 = a*(0 - 2)^2 - 4

-8 = 4a - 4

-8 + 4 = 4a

-4 = 4a

-4/4 = a

-1 = a

The quadratic equation is:

y = -(x - 2)^2 + 4

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The number of students in the class after the changes here are 35.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The question tells us that 7 more juniors have joined this class, while 2 seniors have dropped the class. Then the ratio would be 5 : 2 from the question.

This would give us the ratios as

From here we would have to cross multiply

2(3x + 7) = 5(2x - 2)

6x + 14 = 10x - 10

6x - 10x = -10 - 14

- 4x = -24

x = 6

Put the value of x in both equations

3x + 7 = 3 x 6 + 7

= 25

2x - 2 = 2 x 6 - 2 = 10

25 + 10 = 35

The number of students that are in the class is given as 25

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Step-by-step explanation:

you made a typo.

since we are using only the digits 1, 3, 6 and 9, the list has to start

1, 3, 6, 9, 11, 13, 16, 19, 31, 33

it has to continue with

36, 39

we can skip the 40s and 50s and have then

61, 63, 66, 69

we can skip the 70s and 80s and have then

91, 93, 96, 99

that means we have 20 (5×4) numbers for the first 100.

we would have the corresponding 20 numbers in the 100s. like 101, 103, ...

but we have to skip 101, 103, 106, 109, because they contain 0.

so, it is only 16 numbers in the 100s.

there are none in the 200s.

then again 16 in the 300s. and the 600s and 900s.

so, we have

20 + 4×16 = 84 numbers in the first 1000.

then we have

16 in each the 1100s, the 1300s, the 1600s and 1900s.

and we have none in the 2000s.

so, in total we have

84 + 4×16 = 84 + 64 = 148 numbers to write.

angle bcd is 140. see explanation in image

The number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.

Given that soccer player = 11

We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players

Out of 11 player, we have to pick one captain and one alternate captain

nCr ways

nCr = n!/r!(n-r)!

Here n = 11 and r = 2

= 11C2

= 11!/2!(11-2)!

= 11! / 2!.9!

= ((11x 10 x 9!)/2!.9!)

= (11 x 10)/2

= 110/2

= 55

Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

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Answer:1. 8

2. 16

Step-by-step explanation:

Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

Answer:

6.6

Step-by-step explanation:

you subtract 6.6 from both sides to cancel it out on one side

Hopes this helps please mark brainliest

Answer:

The first measurement is known as the "P-R interval" and is measured from the beginning of the upslope of the P wave to the beginning of the QRS wave. This measurement should be 0.12-0.20 seconds, or 3-5 small squares in duration.

Step-by-step explanation:

...

Answer:

200

Step-by-step explanation:

Answer:

y = -0.5x + 7

Step-by-step explanation:

Equation of a Line is y = mx + c

where m is the slope and c is the y-intercept

Given two lines are Perpendicular

Then [tex]m_{1} m_{2} =-1[/tex]

So we given Line whose Equation is y = 2x +8

Then [tex]m_{1} =2[/tex] (Coefficient of x)

Since the Line we want is Perpendicular to that line

Then [tex]m_{1} m_{2} =-1[/tex]   ,  [tex]2m_{2} =-1 , m_{2} =\frac{-1}{2}[/tex]

So the Equation of the required Line is y = -0.5x +c

Since the Line passes through (2 , 6) , Then y = 6 when x = 2

By substitution , 6 = -0.5*2 + c  ,   6 = -1 + c

Then c = 6+1 =7

Then the Equation will be y = -0.5x + 7

Answer:   y= -1/2x+7

Step-by-step explanation: use the point slope form and use the -1/2x like the slope because the perpendicular lines are negative reciprocals.

To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

Unit conversion is the expression of the same function in a new unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles to kilometers/feet, or another length measurement. A conversion factor is a numerical equation that allows for the equal conversion of feet to another dimensional analysis unit.

A conversion factor is a number that is used to multiply or divide one set of units into another. When converting to an equivalent value, the proper conversion factor must be utilized. For example, to translate inches to feet, the correct conversion value is 12 inches equals 1 foot. The converting value for minutes to hours is 60 minutes equals 1 hour.

From the information given:

To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

The conversion factors are:

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Answer: 12⋅|x3|−512√⋅|3|

PLEASR GIVE BRAINLIEST THANK YOU VERY MUCH!!!

Answer:

Step-by-step explanation:

Given,

No. of nails the factory makes = 600

Time taken by the factory to make 600 nails = 3 minutes

So,

Time taken by the factory to make 1 nail = [tex]\frac{3}{600}[/tex] minutes

∴ Time taken by the factory to make 27000 nails

= ( [tex]\frac{3}{600}[/tex] × [tex]27000[/tex] ) minutes

= ( [tex]\frac{1}{2}[/tex] × [tex]270[/tex] ) minutes

= 135 minutes

Or,

As we know ,  [ 1 minute =  [tex]\frac{1}{60}[/tex] hour]

So, 135 minutes = [tex]\frac{135}{60}[/tex] hours

= 2.25 hours

Now, [1 hour = 60 minutes]

0.25 hours = [tex]\frac{1}{4}[/tex] hours

= [tex]\frac{1}{4}[/tex] × 60 minutes

= 15 minutes

Hence,

The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)

Answer:

2.25 hours or 2 hours 15 minutes

Step-by-step explanation:

600 nails / 3 minutes = 200 nails / minute

27,000 nails / 200 nails/minute = 135 minutes

1 hour = 60 minutes

135 minutes × 1 hour / 60 minutes = 2.25 hours

2.25 hours = 2 hours  + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes

Answer: 2.25 hours or 2 hours 15 minutes

The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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Answer:

x=0

Step-by-step explanation:

it is a straight line on the y axis making x=0

Answer:

Step-by-step explanation:

The maximum number of plants Sophie can have in each pot is 18.

Highest Common factor:

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

Here it is given that Sophie plants 36 violas, 54 sweet peas, and 72 fuchsias. She wants to plant them in pots.

So we have to find the maximum number of plants she could have in each pot.

For that, we have to find the Highest common factor of the given different-different plant she has.

HCF of 36, 54, 72 = 18

So the maximum number of plants she can pot is 18.

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The area of the parallelogram shown in this problem is of:

A = 432 units squared.

The area of a parallelogram of base b and height h is given by the multiplication of these two dimensions, as presented as follows:

A = b x h.

In this problem, these dimensions are given as follows:

(the height is perpendicular to the sides of the parallelogram, forming an angle of 90º, as is the case in this problem).

Hence the area of the parallelogram, applying the multiplication of the obtained base and height, is calculated by the multiplication of the base and of the height given as follows:

A = 27 x 16 = 432 units squared.

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Answer:

432

Step-by-step explanation:

The area of a parallelogram is the product of a side length (the base) and the perpendicular distance between that side and the opposite side (the height). In this case, we can use (line)DC as a base and (line)EG as the matching height, so the area is equal to

(DC) ∙ (EG) = 27 ∙ 16 = 432.

Answer:

x = -1

Step-by-step explanation:

8 - 3x - 12 = 2x + 1

-3x - 4 = 2x + 1

-5 = 5x

x = -1

The value of x in the equation 8-3(x+4)=2x+1 is -1.

Given equation 8-3(x+4)=2x+1

= 8-3x-12 = 2x+1

= -3x-4 = 2x+1

= -5x = 5

= x = -1

We will first solve the bracket which is -3(x+4) which will give us -3x-12 and then we will add this to 8 which will give us -3x-4. Next, we will move all the constants to one side and the terms with x to one side which will give us -5x=5. Finally, we will divide the whole equation by -5 and we will get the answer of x as -1.

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The probability that the retailer sells no more than one house in a month is 0.60.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes and how likely they are to happen. The analysis of events governed by probability is called statistics.

The given is a probability distribution. The probability density function or PDF of the probability is defined for the random variable x, where x ranges from 0 less than or equal to x less than or equal to 2 ie the range of x is from 0 to 2 with 0 and 2 inclusive.

x    :      0          1           2

p(x):   0.20    0.40     0.40

The probability that the retailer sells no more than one house in a month is given by

P(x less than or equal to one) = P(0) + P(1)

=0.20 + 0.40 = 0.60.

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Using proportions, the amounts are given as follows:

a) Number of weeks: 17.

b) Number of fortnights: 8.5.

a) Number of days studied: 51.

b) Number of hours studied: 102.

A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures in the context of a problem.

Using a calendar, the number of weeks between these two dates is of:

17.

A fortnight is composed by two weeks, hence the number of fortnights is:

17/2 = 8.5.

You studied 3 days a week, hence the number of days studying was of:

17 x 3 = 51 days.

You studied 2 hours a hence, hence the number of hours studying was of:

51 x 2 = 102 hours.

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It is possible to determine a line's direction and steepness by looking at its slope.

Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

A line's basic formula in gradient intercept form is y=mx + b. It is rewritable in point-slope form.

When y-b is equal to m(x-0), the location is the y-intercept (0,b).

The basic equation for a line with m=slope and (k,h) a position on the line is y-h=m(x-k).

By determining y and adding constant variables, the equation can be recast in slope-intercept form.

Y = mx-mk + h, where h-mk = b is the y-intercept in this form.

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The statement that describes the x-intercept of the graph is: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.

The x-intercept of a linear relationship between variable x and y can be described as the value of x when the value of y is zero.

On a graph, the x-intercept is the point on the graph where the line intercepts the x-axis. The value of y at this point is 0.

in the graph that shows a linear relationship between the number of monthly payments made and the remaining balance left on a loan, the line intercepts the x-axis at 60.

Therefore, it means: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.

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The probability that exactly 10 people will show up is 0.230

Let X measure the number of people (out of 12) who show up for a flight. For each passenger

we have a 90% chance of showing up, so X is a binomial random variable with n = 12 and p = 0.90.

(b) Everyone gets a seat when X ≤ 10. We have to find the probability when exactly 10 people show up for the flight , so we use the binomial probability for P(10)

∴ P(10) = [tex]C^{n} _{x} p^{x}(1-p)^{n-x}[/tex]

P(10) = 0.230

So , the probability that exactly 10 people show up for the flight is 0.230 .

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Answer:

0.14 (It would be divided by 10).

Step-by-step explanation:

Originally, our factors were 0.36 and 4. After modifying our problem, our factors are now 0.36 and 0.4. Comparing the original factors with the modified, we can see that there was no change done to 0.36. 4, on the other hand, has been divided by 10 ( [tex]0.4 = \frac4{10}[/tex] ).

We can rewrite [tex]0.36 \times 0.4[/tex] as [tex]0.36 \times 4 \times \frac1{10}[/tex]. Since we know 0.36 x 4 = 1.4, we can replace 0.36 x 4 with 1.4 in our modified problem, giving us [tex]1.4 \times \frac1{10}[/tex], which shows us that the product has now been divided by 10 as one of its factors was divided by 10.

Conclusion: Modifying one of the factors of a product using multiplication/division would also multiply/divide (respectively) the product by the same number.

Answer:

x= 3.4

x+2= 5.4

x+3= 6.4

Step-by-step explanation:

Just figured it out :)

Answer:

x = 41.5

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2x + 9 + x + 13 + x - 8 = 180 , that is

4x + 14 = 180 ( subtract 14 from both sides )

4x = 166 ( divide both sides by 4 )

x = 41.5

⇒The sum of the interior angles of a triangle is 180°

⇒Meaning (2x+9)°+(x-8)°+(x+13)°=180°

⇒Simplify the above equation to find the value of x.

⇒[tex]2x+x+x+9-8+13=180\\4x+14=180\\4x=180-14\\4x=166\\\frac{4x}{4} =\frac{166}{4} \\x=41.5[/tex]

∴ x=41.5

Stratified random sampling was the technique employed by Homer to choose his sample.

Given case;

Homer Simpson is fascinated with the proportion of the different sprinkled colors on lard lad doughnuts. Homer buys three of each type of donut they produce and counts the sprinkles on them to perform his research.

The method did homer use to select his sample is stratified random sampling. Because each variety is a stratum.

From there 3 3 samples are collected.

Stratified random sampling:

A crucial aspect of the sampling strategy known as stratified random sampling is the stratification of a population into smaller subgroups known as strata. During stratified random sampling, the strata are created based on the shared traits or features of the participants, such as level of education or income. Numerous uses and advantages of stratified random sampling include examining life expectancy and population demography.

The terms proportionate random sampling and quota random sampling are also used to describe stratified random sampling.

The method did homer use to select his sample is stratified random sampling.

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