Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20? (4 points)

The vertex of the parabola `f(x)=2x²-4x+7` can be found by using the formula `-b/2a`. Here, `a=2` and `b=-4`.

Hence, `x=-b/2a = -(-4)/(2×2) = 1`.

Now, we can find the value of `f(1)` using the equation `f(x) = 2x² - 4x + 7`.

Putting `x=1`, we get `f(1) = 2×1² - 4×1 + 7 = 5`.

Therefore, the vertex of the parabola `f(x) = 2x² - 4x + 7` is `(1, 5)`.

The correct option is `(e) (1, 5)`.

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Using the equation of a circle, it is found that the value of y is -4.

Equation of the circle:

A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center.

The equation of a circle with (h, k) center and r radius is given by:

(x-h)² + (y-k)² = r²

Given,

The points (0, 5) and (0, −5) are the endpoints of the diameter of a circle.

The point (3, y) is on the circle, in quadrant 4.

Here we need to find the value of y.

The center is the midpoint of them, thus:

\(x=\frac{0+0}{2}=0\\ y=\frac{5-5}{2}=0\)

So, the midpoint is (0,0).

The diameter(twice the radius) is the distance between these two points, so:

\(2r=\sqrt{(0-0)^2+(5-(-5))^2}\)

=> 2r = √0+100

=> 2r = √100

=> 2r = 10

=> r = 5

Thus, the equation of the circle is:

=> x² + y² = r²

Apply the values,

=> x² + y² = 5²

=> x² + y² = 25

The point (3,y) is on the circle, in quadrant 4. This means that:

Replacing x by 3, we can find the value of y.

Quadrant 4 means that y < 0.

Then:

=> 3² + y² = 25

=> y² = 25 - 9

=> y² = 16

=> y = ±√16

=> y = - 4

The value of y is -4.

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Answer:

3000 ................,...

Answer:A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hope this helps.

I don't know for certain if you are trying to write this in standard form, graph it, or so forth. However, here is the standard form.

Standard Form:

\((x+2)^2+(y-2)^2=36\\\)

Hope this helps you!

After six months, your new balance sheet position shows that your equity is $2480, the market value of your shares is $3800, and you have a margin call if your equity is less than the maintenance margin.

To calculate your new balance sheet position, we need to consider the initial margin requirement, the maintenance margin, the purchase price, the current market price, and the number of shares purchased.

1. Calculate the total purchase price:
  The purchase price per share is $22, and you purchased 200 shares. Therefore, the total purchase price is $22 x 200 = $4400.

2. Calculate the initial margin amount:
  The initial margin requirement is 70%, which means you need to put down 70% of the total purchase price as a margin. So, the initial margin amount is 0.70 x $4400 = $3080.

3. Calculate the amount borrowed:
  To determine the amount borrowed, subtract the initial margin amount from the total purchase price: $4400 - $3080 = $1320.

4. Calculate the equity:
  Equity represents the portion of the investment that you own outright, which is the initial margin amount: $3080.

5. Calculate the maintenance margin:
  The maintenance margin is 40% of the current market value. Since the current market price is $19 per share, the maintenance margin is 0.40 x ($19 x 200) = $1520.

6. Calculate the market value of the shares:
  The market value of the shares is the current market price multiplied by the number of shares: $19 x 200 = $3800.

7. Calculate the new balance sheet position:
  a. Calculate the new equity:
     Since the market value of the shares is $3800 and the amount borrowed is $1320, the new equity is $3800 - $1320 = $2480.
  b. Compare the new equity with the maintenance margin:
     If the new equity is greater than or equal to the maintenance margin ($2480 >= $1520), your position is safe, and you don't need to take any action.
     If the new equity is less than the maintenance margin ($2480 < $1520), you have a margin call. This means you need to deposit additional funds to bring your equity back up to the initial margin requirement.

In summary, after six months, your new balance sheet position shows that your equity is $2480, the market value of your shares is $3800, and you have a margin call if your equity is less than the maintenance margin.

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The probability that he or she has a visa card is 40%.

Probability is a mathematical concept that describes the likelihood of an event happening. In this case, the event is the selected individual having a visa card.

Let's assume that the individual has a total of n cards and v of those are visa cards. The probability of the individual having a visa card is given by the formula:

P(Visa) = v/n

This formula expresses the ratio of the number of successful outcomes (having a visa card) to the total number of possible outcomes (having any type of card).

The probability is expressed as a decimal or a percentage. If the individual has 5 cards and 2 of them are visa cards, then the probability of them having a visa card is

=> 2/5 = 0.4 or 40%.

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Answer:

3

Step-by-step explanation:

slope = y2-y1/x2-x1

slope = (20-5)/(9-4)

slope = 15/5 = 3

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (9, 20)

m = \(\frac{20-5}{9-4}\) = \(\frac{15}{5}\) = 3

Answer:

x = 4

Step-by-step explanation:

In a parallelogram, the opposite sides are equal/congruent. This means that KL and JM are equivalent.

Step 1: Subtract 12x from both sides.

Step 2: Add 2 to both sides.

Step 3: Divide both sides by -5.

Therefore, x = 4.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

TU = 5.7 inches

Step-by-step explanation:

We solve using Tangent Secant Theorem

RS = 8in

ST = 4in

TU = ?

Using the Tangent Secant Theorem

TU² = RS × ST

TU = √RS × ST

Hence,

TU = √8in × 4 in

TU = √32 in²

TU = 5.6568542495 in

Approximately to the nearest tenth = 5.7 in

Therefore, TU = 5.7 inches

We have the following:

The points S(-2,6) and T(2,-4)

a.

the midpoint is:

replacing:

b.

the length is segment:

replacing:

The length is 10.8

(a) Laplace transform of `f(t) = e²t cosh² t` is `(s-2)/(s-2)² - 4`. (b) Laplace transform of `f(t) = tsin 6t` is `72/(s² - 36)³`. (c) Laplace transform of `f(t) = t³8 (t-1)` is `3/s⁴`.

Given the differential equation: `(d'y)/(dx²) + 4y = sec²(cx)`, `cis` a constant, find the constant `c` if the Wronskian, `W = 3` and find the solution of the differential equation.The Wronskian for a differential equation `y'' + p(x)y' + q(x)y = 0` is given by the equation:`W = Ce^(∫p(x)dx)`, where `C` is a constant.Substitute the values of `p(x)` and `q(x)` in the equation given:`y'' + 4y = sec²(cx)`On comparing with the general form of the differential equation `y'' + p(x)y' + q(x)y = 0`, `p(x) = 0` and `q(x) = sec²(cx)`.So, we get:`W = Ce^(∫p(x)dx)``W = Ce^(∫0 dx) = C``W = C` = 3Therefore, the constant `C` is 3.Now, we have to find the solution of the differential equation:`y'' + 4y = sec²(cx)`The characteristic equation for this differential equation is:`m² + 4 = 0`Solving the above equation we get:`m = ±2i`Therefore, the general solution of the differential equation is given by:`y = c1cos(2x) + c2sin(2x) + (1/8c)tan(cx)sec(cx)`Since `W = 3`, the solution of the differential equation is given by:`y = (3/8)tan(cx)sec(cx)`Hence, the solution of the differential equation is `(3/8)tan(cx)sec(cx)`.Laplace transform of (a) `f(t) = e²t cosh² t`, (b) `f(t) = tsin 6t`, (c) `t³8 (t-1)` is given below:(a) Laplace transform of `f(t) = e²t cosh² t` is `(s-2)/(s-2)² - 4`. (b) Laplace transform of `f(t) = tsin 6t` is `72/(s² - 36)³`. (c) Laplace transform of `f(t) = t³8 (t-1)` is `3/s⁴`.

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Answer:

85°C

Step-by-step explanation:

F = 185

Substitute the value of F in the formula.

C = \(\frac{5}{9}\) × (185 - 32)

C = \(\frac{5}{9}\) × 153

C = 85

∴ 185°F = 85°C

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.

Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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The formula for y = f(x - 14) in terms of the variable x is y = (1/3)(x - 14)^2. To sketch the graph, draw a parabola and shift it 14 units to the right.

(a) To get a formula for y = f(x - 14) in terms of the variable x, substitute (x - 14) for x in the given function f(x) = (1/3)x^2:
y = f(x - 14) = (1/3)(x - 14)^2
(b) To sketch a graph of y = f(x - 14) using graph transformations, consider that the original function f(x) = (1/3)x^2 is a parabola. The transformation f(x - 14) shifts the graph 14 units to the right. Unfortunately, I cannot provide or select a graph letter from A-E, as there are no graphs provided here. However, to sketch it on paper, draw a parabola and shift it 14 units to the right.

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Your cars average acceleration in that time is 12.21m/s^2

The given parameters are

Initial velocity, u = 8.9 m/s

Final velocity, v = 35.76 m/s

Time, t - 2.2 seconds

The average acceleration is calculated using

v = u + at

So, we have

35.76 = 8.9 + 2.2a

Evaluate the like terms

26.86 = 2.2a

Divide by 2.2

a = 12.21

Hence, your cars average acceleration in that time is 12.21m/s^2

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Answer:

Solution

e^{3}\approx 20.085536923e

3

≈20.085536923

Answer:

z = 1

Step-by-step explanation:

-z + 7 = 6

    -7    -7

             -1    

So, basically add -7 on both side (or the kcf method) which cancels out on on the right side but makes -1 on then notice how the -z/-1 = a positive because a negative divided by a negative is a positive so its positive one.

How to check?

just replace -z with -1 and put -1 + 7 = 6 which makes this answer correct.

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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The time taken by the bug will be 5 seconds and the formula used to calculate time is T = D/S.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

S = D/T or T = D/S

where T is time, D is distance, and S is speed.

If a bug travels 5 meters across the floor if it is traveling 1 meter/second. Then the time taken by the bug will be

T = 5/1

T = 5 seconds

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Answer:

uhm 0 degrees

Step-by-step explanation:

The value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.

Simply put, inverse trigonometric operations are the opposites of the fundamental trigonometric parameters sine, cosine, secant, cosecant, tangent, and cotangent.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The inverse trigonometric expression is given below.

⇒ sin⁻¹(sin 17°)

We know that the value of sin⁻¹(sin θ) is θ.

Then the value of the inverse trigonometric expression will be

⇒ sin⁻¹(sin 17°)

⇒ 17°

Thus, the value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.

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Answer:

She can buy 3

Step-by-step explanation:

The algebraic expression for the coordinates of each endpoint of a line segment whose midpoint is the origin is Endpoint 1: (-x₂, -y₂) and Endpoint 2: (x₂, y₂). The values of x₂ and y₂ determine the specific coordinates of the endpoints.

To determine the algebraic expression for the coordinates of each endpoint of a line segment whose midpoint is the origin, we can use the midpoint formula. Let's denote the coordinates of the endpoints as (x₁, y₁) and (x₂, y₂).

Since the midpoint is the origin, the coordinates of the midpoint are (0, 0). According to the midpoint formula, the coordinates of the midpoint are the average of the coordinates of the endpoints:

x₁ + x₂ = 2 * 0 = 0

y₁ + y₂ = 2 * 0 = 0

Simplifying these equations, we get:

x₁ + x₂ = 0

y₁ + y₂ = 0

We have two variables and two equations, so we can solve this system of equations to express one variable in terms of the other.

Solving for x₁, we get:

x₁ = -x₂

Solving for y₁, we get:

y₁ = -y₂

Therefore, the algebraic expression for the coordinates of each endpoint is:

Endpoint 1: (-x₂, -y₂)

Endpoint 2: (x₂, y₂)

The coordinates of the endpoints depend on the value of x₂ and y₂, which can be any real numbers.

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\(\red{\leadsto}\:\)\(\textsf{area of a trapezium} \)\(\sf=36cm² \)

\(\green{\leadsto}\:\)\(\textsf{parallel sides }\)\(\sf \;are\: 10.5 cm \:and \;9.5 \;cm \)

\(\green{ \underline { \boxed{ \sf{Area \:of\: trapezium = \dfrac{1}{2} \times(sum \:of\:parallel\:sides)\times h }}}}\)

Putting Values :-

\(\begin{gathered}\\\implies\quad \sf 36 = \frac{1}{2} \times(10.5 +9.5 )\times h \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 36 = \frac{1}{\cancel{2}} \times(\cancel{20} )\times h \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 36 =10\times h \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf h =\frac{36}{10} \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf h = 3.6 cm \\\end{gathered} \)

Therefore, distance between the two parallel sides = 3.6 cm

The radius of the hemisphere is approximately 28.0 inches to the nearest tenth.

To find the radius of a hemisphere with a volume of 45,729 in³, we'll use the formula for the volume of a sphere, since a hemisphere is half of a sphere. The volume of a sphere (V) is given by:

V = (4/3)πr³

Since we're dealing with a hemisphere, we'll adjust the formula accordingly:

V = (1/2)(4/3)πr³

Given the volume of the hemisphere is 45,729 in³, we can set up the equation:

45,729 = (1/2)(4/3)πr³

Now, we'll solve for r (the radius) to the nearest tenth:

1. Multiply both sides by 2:
91,458 = (4/3)πr³

2. Multiply both sides by 3/4:
68,594 = πr³

3. Divide both sides by π:
21,841 ≈ r³

4. Take the cube root of both sides:
r ≈ 28.0

So, the radius of the hemisphere is approximately 28.0 inches to the nearest tenth.

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