what is the length, x, of the diagonal line drawn? round to the nearest tenth if necessary

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

Answer:

A is the answer

Step-by-step explanation:

Answer:

The required answer must be X = -8

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer:

That is negative x and negative y values - so its Quadrant III.

Step-by-step explanation:

Answer:

Quadrant III

Step-by-step explanation:

That's the only quadrant with all negatives.

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

The measure of angle GPE, considering the two tangents that intersect, is given as follows:

m < GPE = 27º.

The two-secant theorem states that when two secant lines of a circle intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.

Hence the equation is given as follows:

y = (far arc - near arc)/2.

The parameters for this problem are given as follows:

Hence angle GPE is the angle of intersection of the two secant segments, given as follows:

m < GPE = (97 - 43)/2

m < GPE = 27º.

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Answer:

33.20% probability that the sample mean would differ from the population mean by greater than 1 gallon

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

The weight gain among your friends compare to the national average is 1.46.

\(\bar_x\) =  average of weight gain = 16.2

μ = population average = 15

σ = standard deviation = 2.6

n = sample size = 10

To compute the test statistic, first we will choose the correct method.

Test statistics have different method to calculate but often is z-test and t-test, for this test we will use t-test because is ideal for the sample size is under 30. So,

t = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}\)

= \(\frac{16.2 - 15}{\frac{2.6}{\sqrt{10}}}\)

= 1.459

= 1.46

Thus, the weight gain is 1.46 among your friends comparing to the national average.

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The unit vector orthogonal to the plane can be found by taking the cross product of the vectors p-q and p-r. The vector should have a positive y-component if the cross product points in the positive y direction.

To find a unit vector orthogonal to the plane through the points p, q, and r, with a positive y-component, we will use the cross product of two of the vectors. The cross product of two vectors is a vector perpendicular to both of them. First, we will create vector p-q, which is a vector from point p to point q. We can do this by subtracting the coordinates of point q from the coordinates of point p. Next, we will create vector p-r, which is a vector from point p to point r. We can do this by subtracting the coordinates of point r from the coordinates of point p. Finally, we will take the cross product of the two vectors. This will give us a vector orthogonal to the plane through the three points. If the vector has a positive y-component, then it is the unit vector orthogonal to the plane that we are looking for.

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The number of lights L that are on after t minutes of the stage shows is,

A. L = (1/2)t + 10.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, When the show starts, 10 lights are on which is a constant in out function.

Every 30 seconds or (1/2) a minute 1 more light comes on.

∴  The function best models the number of lights that are on after t minutes of the stage shows is,

L = (1/2)t + 10.

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Answer:

-75 0 25 50

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

√36+√64

√36=6

√64=8

6+8

14

THANK YOU

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Answer: c. 9

Step-by-step explanation:

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

y = -2/3x + 3

Step-by-step explanation:

Parallel lines have the same slope so we already know

y = -2/3x + b

Solve for b using the point given

-1=-2/3(6)+b

-1+4=b

b=3

y = -2/3x + 3

the mode of this data is 7

Answer:

Mode: 7

Step-by-step explanation:

To find the mode, you have to find the number the appears the most.

2, 3, 4, 4, 5, 5, 7, 7, 7

Highlight the number that appears the most

2, 3, 4, 4, 5, 5, 7, 7, 7

Seven is the mode because it appears three times.

Have a wonderful day! :)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Pink Friday, this is the solution:

As we reviewed before, these are the steps to find out the solution:

Step 1: Calculate the length of the legs of the isosceles right triangle HDC

Hypotenuse = 12√3

Leg 1 = x

Leg 2 = x

Using the Pythagorean Theorem, we have:

(12√3)² = x² + x²

144 * 3 = 2x²

432 = 2x²

Dividing by 2 at both sides:

432/2 = 2x²/2

216 = x²

Square root at both sides:

√216 = √x²

14.7 = x

In consequence,

• HC = 14.7 m = 6√6 m

• CD = 14.7 m = 6√6 m

Step 2: Now we calculate the centroid of triangle RDO, as follows:

This is an equilateral triangle, therefore:

RD = DO = RO

Let's recall that the centroid is always located in the interior of the triangle. The centroid is located 2/3 of the distance from the vertex along the segment that connects the vertex to the midpoint of the opposite side.

Thus, if CD = 14.7, then

MC = 6√6/2

MC = 3√6 or 7.35m or 7.4 m (rounding to the next tenth)

Answer:

67% Of 88=60

23% Of 294=75

18% Of 92=20

8% Of 458=45

Step-by-step explanation:

67% of 88 is the Best Estimate of 60 because its equal to 58.59.

23% of 294 is the Best Estimate of 75 because it equals to 67.62

18% of 92 is the Best Estimate of 20 because it equals to 16.56

8% of 458 is the Best Estimate of 45 because it equals to 36.64.

Hope This Helps. !!

Answer:

75%

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

There are four scoops, and three of them are mini chocolate chips. 3/4=75/100. Therefore, 75%

Answer: $5289.35

Step-by-step explanation:

Since the cars have an average mileage of 6.78 miles per gallon and the race is 500 miles, the number of gallons each car will take will be:

= 500/6.78

= 73.75 gallons

Since they're 44 cars, the total gallons of fuel will be:

= 44 × 73.75

= 3245 gallons

Since the fuel cost is $1.63 per gallon, the total fuel cost, will be:

= $1.63 × 3245

= $5289.35

Answer:

A-  The sun

Step-by-step explanation:

Your welcome , have a good day take care and be safe

Answer: A, The sun :)

Answer: 97

Step-by-step explanation:

394 / 4 = 98.5, so the 4 numbers must be around 98.5.

97 + 98 + 99 + 100 = 394

Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Hi there!

\(\large\boxed{\frac{1}{18}}\)

1/3x = 6

Begin by multiplying both sides by 3 to cancel the fraction:

1/x = 18

Take the reciprocal of both sides:

x = 1/18

Answer:

1/18

Step-by-step explanation:

I N E E D P O I N T S :O)