Let the universal set be the set R of all real numbers and let A = {x ∈ R | 0 < x ≤ 2}, B = {x ∈ R | 1 ≤ x < 4} Then A ∪ B is

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

In accordance with the information presented in the statement, we find a parabola whose axis of symmetry is parallel to the y-axis. The location of the vertex is the midpoint of the segment between the focus and a point of the directrix.

V(x, y) = 0.5 · (- 3, 4) + 0.5 · (- 3, 2)

V(x, y) = (- 3, 3)

The distance between the focus with respect to the vertex (p) is:

D(x, y) = F(x, y) - V(x, y)

D(x, y) = (- 3, 2) - (- 3, 3)

D(x, y) = (0, - 1)

Which a distance equal to - 1.

The standard form of the equation of the parabola is based on this model:

4 · p · (y - k) = (x - h)²             (1)

Where (h, k) are the coordinates of the vertex.

If we know that (h, k) = (- 3, 3) and p = - 1, then the standard form of the equation of the parabola is:

- 4 · (y - 3) = (x + 3)²

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

The statement has typing and orthographical mistakes. Correct form is presented below:

What is the standard form of the equation of the parabola with a focus at (x, y) = (- 3, 2) and directrix at y = 4.

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The correct formula for the given trigonometric function is cos2θ = 1-2sin²θ

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given that, what is the correct formula for, cos2θ,

cos2θ = 1-2sin²θ

cos2θ = 2cos²θ-1

cos2θ = cos²θ-sin²θ

Hence, the correct formula for the given trigonometric function is cos2θ = 1-2sin²θ

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The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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Answer:  a

Step-by-step explanation: hope it helps.

The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

I believe its C i saw this yesterday somewhere not 100% sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

The greatest difference possible is 0.4

The decimal 0.4 is equivalent to 410 , so 0.4 is located between 0 and 1 . On a number line, divide the interval between 0 and 1 into 10 equal parts and place marks to separate the parts.

The greatest difference possible difference of two decimals to the hundredths place that are between 0 and 1 is 0.99

For us to get the difference possible difference, we will take the difference between the highest values and the lowest values between 1 and 10

Greatest values = 0.99999999999

Possible least value = 0.0000000001

Taking the difference:

Difference = 0.99999999999 - 0.0000000001

Difference = 0.9999999998

Convert to the nearest hundredth place

0.9999999998 to the nearest hundredth is 1.00. Since the value must be between 0 and 1, the required value will be 0.99

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Answer:

13.5

Step-by-step explanation:

We can use a ratio to solve

2        3

---- = ------

11        3+x

Using cross products

2(3+x) = 3*11

Distribute

6+2x = 33

Subtract 6

6+2x-6 = 33-6

2x = 27

Divide by 2

2x/2 = 27/2

x = 13.5

Now we have to,

→ solve for x

Then use a ratio to solve,

→ 2/11 = 3/3+x

Now see the further steps,

→ 2(3+x) = 3 × 11

→ 6+2x = 33

→ 2x = 33-6

→ 2x = 27

→ x = 27/2

→ x = 13.5

Hence, 13.5 is value of x.

Answer:

m∠AOC= 120°

, m∠BOD = 130°

m∠COE = 110°

m∠COD.= 60°

Step-by-step explanation:

Let's note that

AOF = COD= 60°

BOC = FOE= 70°

AOB = DOE= 50°

Given: m∠AOB=50°, m∠FOE=70°. m∠AOC

, m∠BOD,

m∠COE

m∠COD. = AOF = (360-(2(70)+2(50)))/2

AOF = (360-240)/2

AOF = 120/2

AOF = 60°= COD

COE = COD+DOE= 60+50= 110°

BOD = BOC + COD = 70+60= 130°

AOC = AOB + BOC = 50+70 = 120°

Answer:

55%, or C.

Step-by-step explanation:

There are 20 marbles in the bag. 9 of them are red, and 11 of them are another color. Percentages consist of a part of 100, so you would have to make your denominator (20) into a 100. To do this, simply multiply the 20 by 5. Since you did this with 20, you have to do it with your 11 non-red marbles as well. This would be 55. Put the two together, and you have 55/100. What is 55/100 in percentage form? 55%!

Hope this helped! :-D

Answer:

  a.  18.5 million

  b.  2002

Step-by-step explanation:

Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.

The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.

  A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5

The population in 2000 was 18.5 million.

We can solve for t to find the year in which the population reached 26.6 million:

  26.6 = 18.5·e^(0.1708t)

  26.6/18.5 = e^(0.1708t)

  ln(266/185) = 0.1708t

  t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000

The population will reach 26.6 million in the year 2002.

__

Additional comment

The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.

(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)

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Answer:

C ≈ 49.64 cm

Step-by-step explanation:

Step-by-step explanation:

Given

radius (r) = 7.9 CM

Circumference

= 2πr

= 2 * 3.14 * 7.9

= 49.6 cm

Hope it will help :)

Answer:

192 cubes

Step-by-step explanation:

the box has a volume of 32cm x 24cm x 16cm = 12,288 cubic centimeters.

each cube has a volume of 4^3cm, or 64cc. so the box will hold 12,288/64 = 192 cubes.

Answer:

i think its d

Step-by-step explanation:

im not sure, im sorry if its wrong, but it makes about as much sense as i can squeeze out of it.

Answer:

i hope this helps

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

calculator

Answer:

That would be y = 2x.

Answer:

sorry I can't answer this question

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Money offered to Michelle per annum in Job A = $1700

Number of years she will work in job A = 5

Percentage of earnings per annum for her retirement plan = 6.60%

Money she will earn will be the simple interest at the end of 5 years.

We know that :

\(\color{plum}{ \tt{Simple \: interest = \frac{Principle \ \: \times \: Rate \: \: \times \: \: Time}{100} }}\)

Principal = $1700

Rate = 6.60%

Time = 5 years

Which means :

\( = \frac{1700 \times 6.60 \times 5}{100} \)

\( = \frac{56100}{100} \)

\( = \color{plum}\$561\)

We also know that :

\(\color{plum}\tt \: Amount = Principal + Interest \)

Amount Michelle will earn at the end of 5 years for her retirement plan :

\( = 1700 + 561\)

\( =\color{plum}\bold{\$ 2261}\)

2261 can be rounded off to 2260.

Therefore, Michelle will earn $2260 at the end of 5 years for her retirement plan.

Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

Marvin Co. sells a total of 12 flashlights and 84 pens

Price of pen sold by Marvin Co. = $6

Price of flashlight sold by Marvin Co. = $10

Total sales = $624

Let the number of flashlights be x and the number of pens be y

Formulating the equations:

10x + 6y = 624

It is given that customer bought 7 times as many pens as flashlights, therefore:

y = 7x

Putting y = 7x in the equation we get,

10x + 6(7x) = 624

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12 and the number of pens sold is 84

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Answer:

$3.20

Step-by-step explanation:

If 4 peaches cost 1.28, then 1 peach would cost $1.28/4, or $0.32. Now that we know how much 1 peach cost, we can multiply that by 10 to get $0.32*10, which is $3.20.

Answer:

Step-by-step explanation:

To find the value of sec(145°), we first need to find its reference angle in the range 0° to 90°. The reference angle is the acute angle between the terminal side of the given angle and the x-axis.

To find the reference angle of 145°, we can subtract the nearest multiple of 90° (which is 90° itself) from 145°:

reference angle = 145° - 90° = 55°

Now we can use the definition of the secant function:

sec(θ) = 1/cos(θ)

To express sec(55°) in terms of secant of a positive acute angle, we need to find the cosine of 55°. We can use a scientific calculator to get:

cos(55°) ≈ 0.5736

So we have:

sec(145°) = 1/cos(145°) = 1/cos(55°) ≈ 1.742

Therefore, sec(145°) can be written in terms of the secant of a positive acute angle as sec(55).

According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

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Answer:

x>7

Step-by-step explanation:

Let's solve your inequality step-by-step.

7(x−8)>−7

Step 1: Simplify both sides of the inequality.

7x−56>−7

Step 2: Add 56 to both sides.

7x−56+56>−7+56

7x>49

Step 3: Divide both sides by 7.

and answer is x>7 your welcome:)

Answer:

x > 7

Step-by-step explanation:

7(x-8) > -7

7x -8(7) > -7

7x-56>-7

7x-56+56>-7+56

7x>49

x>7

Hope this helps!!!

Answer:

answer is D

x = -4±√4^2 - 4(3)(5)

               2(3)

Step-by-step explanation:

ax^2 + bx + c = 0

3x^2 + 4x + 5 = 0

x = -b ±√b^2 - 4ac

             2(a)

x = -4±√4^2 - 4(3)(5)

               2(3)

Answer:

The last choice is correct.

Step-by-step explanation:

Use only the coefficients and the constant, a, b & c. not the variable x.

Answer:

i will say methods try yourself:

How to Determine Maximum Value

How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:

How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).

How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...

How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.

How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.Since the term with the x2 is negative, you know there will be a maximum point.

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The product of the integer numbers 235 and 617 is rounded off only one non-zero digit will be 200,000.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The integer numbers are shown below.

235 and 617

The product of the integer numbers will be given as,

⇒ 235 × 617

⇒ 144,995

If the integer number is rounded off, then the integer number will be

⇒ 145,000

⇒ 150,000

⇒ 200,000

The product of the integer numbers 235 and 617 is rounded off only one non-zero digit will be 200,000.

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