Juan is trying to factor x² + 7x+3 and makes the following table.

- see picture-

Juan concludes that x² + 7x+3 cannot be factored using integers.

a. Is Juan correct?

b. Comment on Juan's strategy and improve it if possible.

Answer:  m= -1/2

Step-by-step explanation:

Hope the gif loads to help you but if not thats the answer.

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Step-by-step explanation:

let's start at the origin (0, 0).

from there we increase x by 1. what is y ? 2.

so, we see, for every increase of x by 1, y increases by 2.

that makes the slope 2.

and therefore, the right equation is

y = 2x

remember, the slope is always the factor of x, when we have a pure "y =" on one side of the equation.

surface area=total area of rectangle

the base total Surface area

=(LW+lw)2

=(8×4+6×3)2

=(32+18)2

=50×2

=100cm²

surface area of a rectangle

4×12

48cm²

SA of another rectangle

5×12

60cm²

Sa of contact base

8×12=96cm²

sa of height rectangle

10×12

120cm²

Sa of another rectangle

6×12

72cm²

area of the top=3×12

36cm²

total area=100cm²+48cm²+60cm²+96cm²+120cm²+72cm²+36cm²

sa=532cm² is the answer

hope it was helpful.

please mark brainliest

All three components of the fire triangle are usually present whenever and wherever surgery is performed. The fire triangle consists of three elements: fuel, heat, and oxygen.

In the context of surgery, nitrous oxide can be considered as a source of the fuel component of the fire triangle. Nitrous oxide is commonly used as an anesthetic in surgery, and it is highly flammable. It can act as a fuel for fire if it comes into contact with a source of ignition, such as sparks or open flames.

Therefore, it is important for healthcare professionals to be aware of the potential fire hazards associated with the use of nitrous oxide in surgical settings and take appropriate safety precautions to prevent fires.

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Vertical angles are opposite angles that share only a vertex.

When two lines intersect, we have two sets of vertical angles.

Linear pairs are two angles that form a straight line; when two lines intersect, we have two linear pairs.  

If we know one of the angles formed when two lines intersect, we know that the angle opposite it, the vertical angle, has the same measure.

We also know that the angle beside it, that forms a linear pair, will be supplementary with it (add to 180); this means we can find its measure by subtracting from 180.

The remaining missing angle will be the same as this supplementary angle, since they are vertical angles.

Answer:

Tn=a+(n-1)d

Tn=29+(n-1)9

Tn=29+9n-9

Tn=20+9n

Tn=20+9 (21)

T21=580

Step-by-step explanation:

a=first term

d=common difference

Tn=a+(n-1)d .....general formula for an arithmetic number pattern

Answer:

Step-by-step explanation:

I assume the 8 is the question number and the sequence is

29,38,47...

This is an arithmetic sequence as any term minus the previous term is a constant, called the common difference, which in this case is 47-38=38-29=9. An arithmetic sequence has the form

an=a+d(n-1)

Where an=nth term, a=initial term, d=common difference, and n=term number.

In this case a=29 and d=9 so

an=29+9(n-1)

an=9n+20, then the 21st term is

a(21)=9(21)+20

a(21)=189+20

a(21)=209

So the 21st term is 209.

Answer:

MAR = 71°

Step-by-step explanation:

MAE 23°+ EAR 48°= MAR71°

To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.

Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:

P(z < 2.67) ≈ 0.9960

P(z < -0.15) ≈ 0.4404

To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:

P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)

≈ 0.9960 - 0.4404

≈ 0.5556

Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.

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The measure of side length x in the smaller triangle is 27.

The figure in the image is two similar triangle.

From the diagram:

Leg 1 of smaller triangle DQ = 39

Leg 2 of the smaller triangle DC = x

Leg 1 of larger triangle DB = 26 + 39 = 65

Leg 2 of the larger triangle DR = ( x + 18 )

To determine the value of x, we take the ratio of the sides of the two triangle since they similar:

Hence:

Leg 1 of smaller triangle DQ : Leg 2 of the smaller triangle DC = Leg 1 of larger triangle DB + Leg 2 of the larger triangle DR

DQ : DC = DB : DR

Plug in the values

39 : x = 65 : ( x + 18 )

39/x = 65/( x + 18 )

Cross multiplying, we get:

39( x + 18 ) = x × 65

39x + 702 = 65x

65x - 39x = 702

26x = 702

x = 702/26

x = 27

Therefore, the value of is 27.

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To find the point on the hyperbola xy = 8 that is closest to the point (3, 0), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Let's denote the coordinates of the point on the hyperbola as (x, y). Substituting the given coordinates (3, 0) and the equation of the hyperbola xy = 8 into the distance formula, we get:

Distance = √[(x - 3)² + (y - 0)²]

Now, we need to minimize this distance. Since the distance is squared, we can minimize the square of the distance, which is:

Distance² = (x - 3)² + y²

To minimize this expression, we can take its derivative with respect to x and y and set them equal to zero. Let's differentiate Distance² with respect to x and y:

d(Distance²)/dx = 2(x - 3)

d(Distance²)/dy = 2y

Setting these derivatives equal to zero, we have:

2(x - 3) = 0 => x = 3

2y = 0 => y = 0

Therefore, the point on the hyperbola xy = 8 that is closest to the point (3, 0) is (3, 0).

Note that the distance from (3, 0) to any point on the hyperbola xy = 8 is always the same, which means the hyperbola is equidistant from the point (3, 0).

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Answer:

one solution..........

The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.

The work done in lifting the lower end of the chain to the ceiling can be calculated using the formula for work, which is given by:

Work = force x distance

In this case, the force is the weight of the chain, which is 25 lb, and the distance is the length of the chain, which is 10 ft.

So, the work done in lifting the lower end of the chain to the ceiling is:

Work = 25 lb x 10 ft

Work = 250 ft-lb

Therefore, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.

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The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

To find the work done in lifting the lower end of the chain to the ceiling, we need to consider the average weight of the chain as it is being lifted.

1. First, find the weight per foot of the chain:Weight of chain = 25 lbLength of chain = 10 ftWeight per foot = (25 lb) / (10 ft) = 2.5 lb/ft2.

Determine the average weight being lifted:Since you're lifting the chain from one end, the average weight you're lifting is half of the chain's total weight.

Average weight = (25 lb) / 2 = 12.5 lb3. Calculate the work done:Work done = Force x DistanceForce = Average weight = 12.5 lbDistance = Length of chain = 10 ftWork done = (12.5 lb) x (10 ft) = 125 ft-lb

So, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

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According to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

The natural logarithm, often denoted as ln(x), is a mathematical function that represents the logarithm to the base e, where e is the mathematical constant approximately equal to 2.71828.

To find out how long it will take for 300 grams of Mercury 203 to decay, we can use the exponential decay model.

The general formula for exponential decay is given by:

A(t) = A₀ * e^(-rt),

where A(t) represents the amount of the substance at time t, A₀ is the initial amount, r is the decay rate, and e is the base of the natural logarithm.

In this case, we have the initial amount A₀ = 300 grams and the decay rate r = 0.01481 (1.481% written as a decimal).

We want to find the time t when the amount A(t) is equal to zero. Substituting these values into the formula, we have:

0 = 300 * e^(-0.01481t).

To solve for t, we can divide both sides of the equation by 300 and take the natural logarithm of both sides:

ln(0) = ln(e^(-0.01481t)),

0 = -0.01481t.

To isolate t, we divide both sides by -0.01481:

0 / -0.01481 = t,

t = 0.

Therefore, according to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

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Answer:

8,010,005

Step-by-step explanation:

eight million ten thousand and five

hope this helps

Answer:

Step-by-step explanation:

The attached graph is NOT a function, since it doesn't pass the vertical line test.

If a vertical line cuts the graph more than once, then this relation is not a function.

The length of the segment indicated is: 4.6 when rounded to the nearest tenth.

To find the length of the segment, we begin by adopting the Pythagoras theorem, where the length of the longest side is given as

x² = y² + z²

From this diagram,

y = 38.8/2 = 7.76

z = 9

x = ?

9² = 7.76² + z²

81 = 60.22 + z²

81 - 60.22 = z²

20.78 = z²

z = √20.78

= 4.55

So, the length of x = 4.55

The full length can be gotten by multiplying by 2 to give 9.1

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The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In this context, an equation that models the situation is given by:

y = mx + c

340 = 28x + 102

28x = 340 - 102

28x = 238

x = 238/28

x = 8.5 gallons of gasoline.

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The volume of the triangular prism is 112 cubic meters (m³).

To find the volume of the triangular prism, we need to multiply the area of the triangular base by the height of the prism. The formula for the volume of a prism is V = base area * height.

First, let's calculate the area of the triangular base. We can use the formula for the area of a triangle, which is A = 1/2 * base * height.

The base of the triangle is given as 4m, and the height is given as 7m. Plugging these values into the formula, we get:

Base area = 1/2 * 4m * 7m = 14m²

Now, let's find the height of the prism, which is given as 8m.

Finally, we can calculate the volume using the formula:

V = base area * height = 14m² * 8m = 112m³.

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The probability that the mean time for the sample of 100 returns for this year is greater than 92 is 0.0764.

The term probability in math refers the possibility of occurring the event.

Here we have given that Bones brothers & associates prepare individual tax returns. Over prior years, bones brothers has maintained careful records regarding the time to prepare a return.

And we need to find the probability that the mean time for the sample of 100 returns for this year is greater than 92

As per the given question, we know the following values,

=> mean,μ=90

=> population standard deviation,σ=14

=> sample size ,n=100

Then the standard error is 1.4

Therefore, the z value is obtained by the z table is 0.9236.

Then the resulting probability is calculated.

=> 1 - 0.9236

=> 0.0764

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Answer:

b. interaction effect

Step-by-step explanation:

In a regression model, the interaction effect is present when a predictor variable changes the effect of another predictor variable on the outcome.

In a regression model, the interaction effect exists when one predictor variable impacts the outcome of another predictor variable differently than when examined individually. It refers to the interaction between two or more predictor variables and their influencers on an outcome or response variable. For example, in a regression model, studying and having a quiet place may individually contribute to a better score on a test, but perhaps studying in a quiet place provides a significantly better effect than the sum of those two effects separately. This would be considered an interaction effect.

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==================================================

Work Shown:

A = 2+i

O = -4, this is the letter 'oh' not to be confused with the number zero

P = -i

S = 2+4i

A-O+P+S = (2+i) - (-4) + (-i) + (2+4i)

A-O+P+S = (2+i)  + 4 + (-i) + (2+4i)

A-O+P+S = (2+4+2) + (i-i+4i)

A-O+P+S = 8+4i

the perimeter of the triangle is 10.2ft (option A)

Given:

A triangle with two angles and a side opposite one of the angles is given

To find:

the approximate length of the vinyl needed

The triangle is right-angled and isosceles as the base angles are equal. To get the approximate length of the vinyl needed, we will be assuming the whole triangle is the table top and vinyl will cover the whole of it

We will use Pythagoras theorem to get the longest side:

Hypotenuse² = opposite² + adjacent²

The two legs are equal since the base angles are equal

opposite = adjacent = 3 ft

Hypotenuse² = 3² + 3²

Hypotenuse² = 9 + 9 = 18

Hypotenuse = √18

Hypotenuse = 4.24

The perimeter of the triangle = Length of the outer edges of the tabletop

The perimeter of the triangle = 3ft + 3ft + 4.24 ft = 10.24 ft

From the options, the perimeter of the triangle is 10.2ft (option A)

3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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The speed of the car is approximately 74.4 mph, given the wheel radius of 11 inches and rotation speed of 550 rpm.

To find the speed of a car in miles per hour, given the radius of its wheels and their rotational speed in revolutions per minute (rpm), we need to convert the rotational speed to linear speed and then convert it to miles per hour.

To convert the rotational speed to linear speed, we can use the formula v = ω * r, where v represents linear speed, ω represents angular speed in radians per minute, and r represents the radius of the wheel. Since the rotational speed is given in rpm, we need to convert it to radians per minute by multiplying it by 2π/60.

In this case, the radius of the wheels is 11 inches, and the rotational speed is 550 rpm. To convert the rpm to radians per minute, we multiply by 2π/60, which gives us an angular speed of 57.8 radians per minute. Then, we use the formula v = 57.8 * 11 to find the linear speed in inches per minute.

To convert the linear speed from inches per minute to miles per hour, we need to perform two additional conversions. First, we divide the linear speed by 12 to convert it from inches per minute to feet per minute. Then, we divide by 5,280 to convert it from feet per minute to miles per minute. Finally, we multiply by 60 to obtain the speed in miles per hour.

In summary, to find the speed of the car in miles per hour, we use the formula v = ω * r to convert the rotational speed to linear speed. Then, we convert the linear speed from inches per minute to miles per hour by dividing by 12, dividing by 5,280, and multiplying by 60.

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Answer:

y = 3x + 1

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

Answer:

156

Step-by-step explanation:

Hey There!

The angle that is equal to 156 and the angle labeled x are corresponding angles meaning that they are congruent angles. Therefore x=156

Answer:

To find the x intercept, set y=0 . The x intercept is (4,0) . To find the y intercept, set x=0 . The x intercept is (0,12) .

Step-by-step explanation:

I believe the answer is A. (4,0) (0,-12)

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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Answer:

$2720

15%= 480

3200-480=

$2720