what are the solutions of x2-4x+5=0
please help!!

Answer:

x = 4y - 4/3

Step-by-step explanation:

Step 1: Write expression

3x + 4 = 12y

Step 2: Subtract 4 on both sides

3x = 12y - 4

Step 3: Divide both sides by 3

x = 4y - 4/3

The sample correlation coefficient (r) can be found using the following formula :r = (n(Σxy) − (Σx)(Σy)) / √[(nΣx2 − (Σx)2)(nΣy2 − (Σy)2)] .

Where n = number of data points,

Σxy = sum of products of paired scores,

Σx = sum of X scores

and

Σy = sum of Y scores.

Given data: Speed (Miles per our30 50 40 55 30 24 60 25 51 55

Miles per Gallon 28 24 24 23 30 32 21 35 26 25

To compute r, we first need to find

Σxy, Σx, Σy, Σx2, and Σy2

using the given data:Speed (x)

Miles per GallonΣx = 384 Σy = 278

Σxy = 14836

Σx2 = 19264

Σy2 = 7995

Now substituting the values in the formula we get:

r = (n(Σxy) − (Σx)(Σy)) / √[(nΣx2 − (Σx)2)(nΣy2 − (Σy)2)]

r = (10(14836) − (384)(278)) / √[(10(19264) − (384)2)(10(7995) − (278)2)]

r =  0.4253

Therefore, the sample correlation coefficient is 0.43 rounded to two decimal places and its interpretation is:For driving speeds between 24 and 60 miles per hour, higher speeds are associated with lower miles per gallon.Based on the computation of the sample correlation coefficient, it can be concluded that there is a moderate positive linear relationship between speed and miles per gallon.

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The solutions of the equation 20cosθ=-8 in the interval from 0 to 2π are 0.785 and 5.236, rounded to the nearest hundredth.

To solve the equation, we divide both sides by 20 to get cosθ=-0.4. The cosine function has a period of 2π, so all solutions of the equation can be found by adding multiples of 2π to the solution cosθ=-0.4.

The solutions in the interval from 0 to 2π are then cosθ=-0.4+2πk, where k is an integer. When k=0, we get cosθ=-0.4. When k=1, we get cosθ=-0.4+2π=0.785. When k=2, we get cosθ=-0.4+4π=5.236.

The solutions cosθ=-0.4 and cosθ=5.236 are both in the interval from 0 to 2π. When rounded to the nearest hundredth, these solutions are 0.785 and 5.236, respectively.

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From the rigid transformation that takes ABC to EDF, the coinciding parts based on congruency; are matched below.

When we say two triangles are congruent to each other, it means that the corresponding sides and corresponding angles of both triangles are equal.

Thus, if triangle ABC is congruent to triangle EDF, then we can say that;

Angle A ≅ Angle E

Angle B ≅ Angle D

Angle C ≅ Angle F

Segment AB ≅ Segment ED

Segment AC ≅ Segment EF

Segment BC ≅ Segment DF

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Answer:

670000

Step-by-step explanation:

67 * 10^4

67 * (10*10*10*10)

= 670000

Answer:

670,000

Step-by-step explanation:

You'd do 10^4 first which is 10,000.

Then multiply 10,000 by 67.

67*1 is 67. Add the 4 zeros and you get...

670,000

Answer:

x=42

Step-by-step explanation:

Just do 24/32 on calculator to get .75

Then multiply .75 by 56, the side you are looking for to get 42

Answer:

\(1 \frac{3}{14}\)

Step-by-step explanation:

\(\frac{3}{7} (2\frac{5}{6}) \\= \frac{3}{7} ( \frac{17}{6} )\\= \frac{17}{14} \\=1 \frac{3}{14}\)

Answer:

0.109375

Step-by-step explanation:

Answer:

\(^7/_{64}\)

Step-by-step explanation:

\(56\div512={^5^6}/_{512}\)

Look for the \(GCF\) of \(56\) and \(512\)

we find that it's \(8\)

\(56\div8=7\\512\div8=64\)

our fraction in simplest form is \(^7/_{64}\)

Answer:

1/4

Step-by-step explanation:

answer key lang sakalam

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Answer: 26,104

Step-by-step explanation:

106 + (106+39) = 251

251 x  104 = 26,104

Answer:

Same question ?

Step-by-step explanation:

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .

In the question ,

it is given that ,

the ratio is 25:18 , we need an equivalent ratio .

the ratio is 25:80 which can be written in fraction as 25/80 .

writing the factors of 25 and 80 .

= (5×5)/(5×16)

we can see that 5 is the common factor in both the numerator and the denominator .

= 5/16

which can be written as

= 5:16

the equivalent ratio is 5:16  .

Therefore , The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .

The given question is incomplete , the complete question is

Which of the following ratio is equivalent to  25:80 ?

(a) 2:5

(b) 8:5

(c) 16:5

(d) 5:16

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Answer:

70

Step-by-step explanation:

RU=20 (45-45-90 triangle)

use pythagorean theorum

20^2+b^2=73^2

evaluate

b^2=4929

sq root both side

rounded to nearest integer, side SU is 70

The two lines have different y-intercepts, so they are not coincident or vertical. Therefore, the graphs of the two lines must intersect. The answer is B) intersecting lines.

In mathematics, a line is a straight, one-dimensional figure that extends infinitely in both directions. It can be thought of as a series of points that are all in a straight line. A line can be described by its slope-intercept form equation, y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line represents its steepness or inclination, and is defined as the change in y divided by the change in x between any two points on the line. If the slope is positive, the line goes uphill as it moves from left to right; if the slope is negative, the line goes downhill as it moves from left to right. If the slope is zero, the line is horizontal.

Here,

The best way to determine whether the graphs of two lines are coincident, intersecting, parallel, or vertical is to find the slope of each line.

For the line that passes through (-4,5) and (0,0), the slope is:

m = (y2 - y1) / (x2 - x1) = (0 - 5) / (0 - (-4)) = 5/4

For the line that passes through (4,6) and (12,16), the slope is:

m = (y2 - y1) / (x2 - x1) = (16 - 6) / (12 - 4) = 1

Since the slopes of the two lines are different, we know that the lines are not coincident or parallel. To determine whether they intersect or are vertical, we need to examine their y-intercepts.

For the line that passes through (-4,5) and (0,0), the y-intercept is:

y = mx + b

0 = (5/4)(0) + b

b = 0

So the equation of this line is y = (5/4)x.

For the line that passes through (4,6) and (12,16), the y-intercept is:

y = mx + b

6 = (1)(4) + b

b = 2

So the equation of this line is y = x + 2.

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Answer:

the answer is 11.125

Step-by-step explanation:

Multiply the numbers

Evaluate the exponent

Divide the numbers

Multiply the numbers

Evaluate the exponent

Add the numbers

Solution: 89/8 or 11.125

HOPE THIS HELPS!!! :)

Step-by-step explanation:

remember the priorities :

first brackets

then exponents

then multiplications and divisions (from left to right)

then additions and subtractions (from left to right)

remember, a fraction is a division ...

10 + (2 × 3)² ÷ 4 × 1/2³ =

= 10 + 6² ÷ 4 × 1/2³ =

= 10 + 36 ÷ 4 × 1/8 =

= 10 + 9 × 1/8 =

= 10 + 9/8 =

= 10 9/8 = 11 1/8 = 89/8 = 11.125

There are 15 different 2-member committees that can be formed from the 6 members of the high school student council as per combination.

In mathematics, a combination is a way of selecting objects from a larger group without considering the order in which they are chosen. A combination is also known as a binomial coefficient or a choose function, and is denoted by the symbol "n choose k", where n is the total number of objects and k is the number of objects to be selected.

In mathematics, a permutation is an arrangement of objects in a specific order. The number of possible permutations of a set of n distinct objects is given by n!, which is the product of all positive integers up to n.

The number of different 2-member committees that can be formed from a group of 6 members is given by the combination formula:

C(6, 2) = 6! / (2! * (6 - 2)!) = 15

where C(n, r) represents the number of combinations of r items that can be selected from a group of n items.

Therefore, there are 15 different 2-member committees that can be formed from the 6 members of the high school student council to attend the rally in Washington D.C.

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

Explanation:

Take away the four white small squares on the left side. To balance things out, you have to add 4 black squares to the right side.

Also, take away the two white long rectangles from the right side. To balance this out, you have to add 2 gray long rectangles to the left side.

You should have:

From here you'll group up the 10 black squares so that you'll have 2 black squares per gray rectangle.

This means the solution is 2.

-------------------------------------

If you're curious about the algebraic way to solve, then you could do this:

3x-4 = -2x+6

3x+2x = 6+4

5x = 10

x = 10/5

x = 2

This method doesn't require us to use the visual model.

Answer:

6)a. π(16²)x = 62,731.3

b.

\(x = \frac{62731.3}{\pi( {16}^{2} )} = 78\)

c. The height is 78 cm.

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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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer: 8,064

Step-by-step explanation:

12 times 3 = 36

36 times 7 = 252

252 times 4 =1,008

1,008 times 8 = 8,064

Answer:

$1.20

Step-by-step explanation:

Just divide $3.60 by 3. If that's the price of 3 boxes, dividing it by 3 will estimate it to how much 1 box will cost.

Answer:

$1.20 per box

Step-by-step explanation:

Hope this helps :)

Yes, this confidence interval provide evidence of an association between development of cancer and taking finasteride.

The likelihood that a parameter will fall between two values around the mean is shown by a confidence interval. Confidence intervals quantify how confident or uncertain a sampling technique is. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Here,

Yes, this confidence interval shows a connection between using finasteride and a higher risk of developing cancer.

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Answer:

5*7=35 square units

Step-by-step explanation:

area of parrelogram =B×h

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The option B is correct option. Thus, the Study design is used is a Case control study.

According to the statement

we have given that the incident cases of MI diagnosed in the emergency rooms of several hospitals is 500 and compared to 1,000 other subjects who visited the same emergency rooms for reasons other than cardiovascular and respiratory diseases.

And we have  to find that the all these type of reports are formed which study method in medical science.

So, For this purpose, we know that the

A case control study is a  study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls).

This study is perfectly match with the given condition.

So,

Case-control study is used in it by the below written way:

The study design relies on hospital-based recruitment of cases (persons with an MI) and controls (other patients in the emergency room who did not have cardiovascular and respiratory diseases which may be associated with air pollution). The exposure under investigation is a time-dependent measure of exposure to high-density automobile traffic in the days preceding the emergency room visit.

So, The option B is a correct option. The Study design is used is a Case control study.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

The effect of exposure to high-density automobile traffic either as a bicyclist or pedestrian was compared to minimal or no exposure to automobile traffic. It is hypothesized that direct exposure to automobile traffic has an effect on acute myocardial infarction (MI). This association was studied with 500 incident cases of MI diagnosed in the emergency rooms of several hospitals and compared to 1,000 other subjects who visited the same emergency rooms for reasons other than cardiovascular and respiratory diseases. All subjects were asked to report the amount of time that they spent exposed to high-density traffic over the past month prior to their hospital visit.

What type of study design is this?

A) Cross-sectional

B) Case-control

C) Retrospective cohort

D) Prospective cohort

E) Randomized clinical trial

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Answer:

∠5≈∠1 - corresponding angles

m∠6+m∠5=180° - supplementary angles

i hope this helps!

Answer:

D is correct.

0 is greater than -2.

-1 is greater than -2.

5 is greater than -2.

-3 is smaller than -2.

Hope this helps!