Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 12x+ 9 = 5

The solution for the given equation is C) [tex]x=\frac{-1+-\sqrt{33} }{4}[/tex]

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is

[tex]x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}[/tex].

So, the solution for the equation [tex]2x^{2} +x-4=0[/tex] is

[tex]x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}[/tex]

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Answer:

97 R=26

Step-by-step explanation:

Answer:

In feet: [tex]\boxed{158,892 \textrm{ feet}}[/tex]

In miles: [tex]\boxed{\textrm{ 3.11 \;miles}}[/tex]

Step-by-step explanation:

A diagram really helps here and so I have drawn one for your understanding

From the diagram we see that Point A refers to the location of the plane when it is 50 miles away from the airport at am altitude of 30,500 feet

In a 2D coordinate system where x refers to the horizontal distance from the airport value and y refers to the altitude,
=> Point A has coordinates (50, 30500)

When the plane is 20 miles away from the airport, the altitude has dropped down to 18000 feet

This location is represented as point B(20, 18000)

The horizontal distance traveled by the plane is 50 - 20 = 30 miles

The vertical distance traveled by the plane(drop in altitude) is 30,500 - 18,000 = 12, 500

These two form the legs of a right triangle with the actual path of descent as the hypotenuse of the right triangle (see figure)

The distance c traveled by the plane is the distance from Point A to Point B which can be computed using the Pythagorean theorem given the two legs of the right triangle

The general formula is :

[tex]\mbox{\large c = \sqrt{a^{2} + b^{2}}}[/tex]

where c is the length of the hypotenuse, a and b are the lengths of the other two sides

We have a = 12, 500 feet and b = 30 miles

Convert miles to feet to get same units:

a = 12, 500 feet

b = 30 miles = 30 x 5280 feet = 158400

[tex]\mathbox{ c = \sqrt{158400^{2} + 12500^{2}}}[/tex]

[tex]c = \sqrt{25090560000 + 156250000}[/tex]

[tex]c = \sqrt{25246810000}[/tex]

[tex]\mathrm{c = 158,892.45 \;feet}\\[/tex]

[tex]\mathbox{ \textrm{c = 158,892 feet (to the nearest foot)}}[/tex]

So the distance traveled by the plane is 158, 992 feet (to the nearest foot)

This works out to 158992/5280 miles = 30.11 miles which is pretty close to 3.09

Maybe you are required to answer in feet and not in miles.

I don't know

Answer:

hey

Step-by-step explanation:

Andrew's training plan can be modeled by an exponential function, and Sebastian's training plan can be modeled by a linear function. So, correct option is c) .

A linear function is a mathematical function that maps a set of inputs to a set of outputs in such a way that the output is proportional to the input. In other words, if the input changes by a certain amount, the output changes by a constant factor.

The equation of a linear function has the form:

y = mx + b

where x is the input variable, y is the output variable, m is the slope of the line, and b is the y-intercept. The slope represents how much the output changes for each unit change in the input, and the y-intercept represents the output value when the input is zero.

Linear functions are represented by straight lines on a graph. If you plot the input and output values for a linear function on a graph, the resulting points will form a straight line. The slope of the line represents the rate of change of the output with respect to the input, and the y-intercept represents the initial value of the output.

In Andrew's training plan, the weight he lifts is increasing by a constant percentage each week, which is characteristic of exponential growth. In Sebastian's training plan, the weight he lifts is increasing by a constant amount each week, which is characteristic of linear growth.

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The complete question is:

Andrew and Sebastian are training for a weightlifting competition. In order to prepare, each of them has created their own personal training plan as follows:

Which of the following statements are true?

a) Andrew and Sebastian both increase the weight they lift each week by the same amount.

b) Andrew's training plan can be modeled by a linear function, and Sebastian's training plan can be modeled by an exponential function.

 c) Andrew's training plan can be modeled by an exponential function, and Sebastian's training plan can be modeled by a linear function. 

d) Andrew increases the weight he lifts each week by equal factors, and Sebastian increases the weight he lifts each week by equal differences

e)  Andrew increases the weight he lifts each week by equal differences, and Sebastian increases the weight he lifts each week by equal factors.

Answer:

252 dollars

Step-by-step explanation:

so $3,500 * 2.4% is $84 * 3 gives you $252

Answer:

Step-by-step explanation:

when does this come into play? what year??

Therefore, the seamstress used 200 + 200 - 179 = 221 buttons for her recent mending.

As per the data given in the above question are as bellow,

The data provided are as bellow,

There are 35 buttons remaining in a package in the equipment of a seamstress.

She repaired some things and used 14 of another box.

How many buttons did the seamstress use for her most recent repair if both boxes initially had 200 buttons?

The seamstress had

200 - 35 = 165 buttons

left in her first box after using some of them.

So she had

165 + 14 = 179 buttons in total.

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On solving the provided question, we can say that Length of rectangle = 50 m and Area of rectangle = 300 m.sq and the breadth of the garden is 6 m.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Length of rectangle = 50 m and Area of rectangle = 300 m.sq

Since, Area of rectangle = length x breadth

Therefore, Breadth = 300/6

Thus, the breadth of the garden is 6 m.

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Answer:

3(x)+4-8

find x.

Step-by-step explanation:

The ratio of the cost in dollars of the materials to the sale price in dollars is 0.4:1

The cost of the materials for one porch swing is $100 and the sale price of the swing is $250.

To find the ratio of the cost of the materials to the sale price, we divide the cost of the materials by the sale price as follows -

$100 ÷ $250 = 0.4

So, the ratio of the cost of the materials to the sale price is 0.4:1.

This means that for every $1 in the sale price, $0.4 is spent on materials or we can say that 40 cents of every dollar go towards materials.

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The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

The correct option is A.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

Mahek owns a holiday tree farm.

There are currently 800 trees on the property.

Each year, 20% of the trees are harvested and sold,

and 200 seedlings are planted.

a₁ = 800

The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

Hence, aₙ = 0.20aₙ₋₁ + 200

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The exposure time when x = 560 is: 13.66 hour

A method of simulating the relationship between two sets of variables is quadratic regression. The outcome is a regression equation that may be applied to the data to generate predictions. The formula for the equation is: y = ax² + bx + c, where a ≠ 0. Situations that may be approximated by quadratic functions include tossing a ball, firing a cannon, jumping from a platform, and striking a golf ball. Researchers may find the quadratic model to be a useful tool for data analysis in identifying the combined impact of success objectives on academic accomplishment. We anticipate that future studies on the impact of academic performance objectives will frequently use the quadratic model to analyse their data.

Given that,

T = 0.0002x² - 316x + 127.9

exposure time = T

Now, calculate exposure time when x = 560

So, T = 0.0002x² - 0.316x + 127.9

T = 0.0002×(560)² - 0.316 × (560) + 127.9

T = 62.72 - 176.96 + 127.9

T = 13.66 hour

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If a triangle has one side of 7 meters and another side of 12 meters, the other side is approximately 13.928 meters long.

A triangle is a three-sided polygon that has three angles and three sides. The sides of a triangle are connected by its angles, and the sum of the angles of a triangle is always equal to 180 degrees. The length of the sides of a triangle affects the size of its angles, and the size of its angles affects the length of its sides.

Now, in the case of a triangle where one side is 7 meters and another side is 12 meters, the length of the third side can be calculated using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be written as

=> a² + b² = c²,

where a and b are the lengths of the two sides, and c is the length of the hypotenuse.

Using the Pythagorean theorem, we can find the length of the third side of the triangle. Let's call the length of the third side "x". So,

=> x² = 7² + 12² = 49 + 144 = 193.

Taking the square root of both sides, we get

x = √(193) = 13.928.

So, the third side of the triangle is approximately 13.928 meters long.

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Using the graph, the solution of 1/4 (25x + 3/5) = -2.5 - 3/8x is the point of intersection which is

The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions of systems of equations.

Finding all of these intersections or common solutions is what it means to solve a system.

Examining the attached graph the point of intersection is  (-0.4,-2.35) and this is hence the solution.

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Answer:

4:5

Step-by-step explanation:

Answer:

80% shining

20% not shining

The probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]. Option E is correct.

Let Y be the discrete random variable that counts the number of face cards in a seven-card hand drawn from a standard 52-card deck. The possible values for Y are 0, 1, 2, 3, 4, 5, 6, and 7.

The number of ways to get Y face cards in a seven-card hand is given by the binomial coefficient C(7, Y), where C(7, Y) represents the number of combinations of 7 things taken Y at a time.

The probability of getting Y face cards in a seven-card hand is given by:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

where [tex](12/52)^Y[/tex] represents the probability of drawing Y face cards and [tex](40/52)^{(7-Y)}[/tex] represents the probability of drawing the remaining 7-Y cards from the 40 non-face cards.

Thus, the probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

Y = 0, 1, 2, ..., 7

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Answer:

-96188148454815460181518484413

The x-value of the intersection point of the lines is ( d - b)/(a-c).

Intersection of lines

Given the equation of a line communicated as;

y = ax +b and;

y = cx + d.

Comparing the two lines, we will have:

ax + b = cx + d

Make x the subject of the method:

ax - cx = d = b

x (a-c) = d - b

x = ( d - b)/(a-c)

Thus the x-worth of the intersection point of the lines is ( d - b)/(a-c)

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Answer:

17

a. 5^4 = 625

b. 3^4 = 81

18

a. log base 10000 , 10 = -4

b. log base 2, 1/2 = -1

19. Inverse represent opposite functions, when you plug one into the other using variables, the result should be x.

Step-by-step explanation: Remember that when converting, use the base of the log function as the base of exponent. The answer to the log function represents the value of the exponent. Hope this helps!

the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

In the superposition theorem, the voltage across any element in a linear circuit is equal to the sum of the voltages caused by each source acting independently. In other words, in a linear circuit, each source is treated as the only source, and the other sources are replaced with their internal resistances.

With the resistance value of 8 ohms, we can calculate the voltage across the circuit using the superposition theorem.

First, consider [tex]I_{1}[/tex] as the only source, and set [tex]I_{2} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{1} = i1 * R = 6 A * 8 ohms = 48 V[/tex]

Next, consider [tex]I_{2}[/tex] as the only source, and set [tex]I_{1} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{2} = i2 * R = 4 A * 8 ohms = 32 V[/tex]

Finally, the voltage across the circuit ([tex]V_{0}[/tex]) is the sum of the voltages found in steps 1 and 2.

[tex]V_{0} = V_{1} + V_{2} = 48 V + 32 V = 80 V[/tex]

So, the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

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There is a 0.99% chance of getting the first 2 white and the last 2 black if you draw 4 balls without replacement from a bag containing 10 white and 20 black balls.

If there are W white balls and B black balls in a bag, and you are drawing 4 balls without replacement, the probability that the first 2 selected are white and the last 2 black can be calculated as follows:

[tex]P(WWBB) = (W/ (W + B)) * ((W-1) / (W + B - 1)) * (B / (W + B - 2)) * ((B-1) / (W + B - 3))[/tex]

So, for example, if there are 10 white balls and 20 black balls, then the probability of getting the first 2 white and the last 2 black is:

[tex]P(WWBB) = (10 / 30) * (9 / 29) * (20 / 28) * (19 / 27) = 0.0099[/tex]

This means that there is a 0.99% chance of getting the first 2 white and the last 2 black if you draw 4 balls without replacement from a bag containing 10 white and 20 black balls.

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Answer: A, 4[tex]\sqrt{14}[/tex]

Step-by-step explanation:

18^2-10^2=224

[tex]\sqrt{224}[/tex] =4[tex]\sqrt{14}[/tex]

Answer: 4 √ 14

Step-by-step explanation:

Pythagorean theorem is (a^2 + b^2 = c^2)

Step 1. (10^2) + (x^2) = (18^2) {we divided the 20 by 2 to get one right triangle for the pythagorean theorem.}

Step 2. 100 + x^2 = 324

Step 3. x^2 = 224

Step 4. x ≈ 15 (rounded to the nearest whole number) (x = 14.9666295)

Step 5. Eliminate the wrong choices. B and D are both eliminated, because they are whole numbers, and they don't match the answer we got.

Step 6. Find the square root. 2 √ 106 is ≈ 20.59126, which isn't equal to our 14.966, .

Step 7. With all but one answer remaining, the answer would be 4 √ 14, and we can double-check. (14.9666295 = 14.9666295.)

The following data represent the dividend yields of a random sample of 28 publicly traded stocks. The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

The term "trade shocks" refers to changes in the amount of commodities and services exchanged globally as well as in international pricing that result in net profits or losses from trade. It has to do with changes in international marketplaces that frequently occur independently of national influences. Conventional wisdom is that terms-of-trade shocks are a significant contributor to business cycles in developing and underdeveloped nations. This viewpoint is founded in great part on the examination of calibrated business-cycle models.

(a) From the given table it is shown that,

0,3.58,0.37/2, (0.69+0.85)/2, (2.11 + 2.49)/2

The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

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Not every possible subset is a valid word. The longest "word" seen on Sesame Street was a string of all 26 letters of the alphabet. "ALONG" is a valid subset because it can be found in the English dictionary, and it is a recognized English word.

(a) No, not every possible subset is a valid word. For example, the subset "zxy" is not a valid English word.

(b) The longest "word" seen on Sesame Street was a string of all 26 letters of the alphabet.

(c) "ALONG" is a valid subset because it can be found in the English dictionary, and it is a recognized English word. However, "GALLON" is not a valid subset because it is not a recognized word in the English language. This is because the letters are not arranged in the correct order, and there is no recognized word in the English language with this arrangement of letters.

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Answer:

Non-linear

Step-by-step explanation:

y = 10/x is non-linear!

Because a linear equation is an equation of a straight line, which means the degree of a linear equation must be 0. In this case, the degree of variable y is 1; the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not linear.

Assuming,

Question: what is the simplest form of the expression  [(X/6) + X³] * (1/2) ?

Solution:-

The simplest form of the expression  [(X/6) + X³] * (1/2) is,

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

[(X/6) + X³] * (1/2)

To simplify the expression [(X/6) + X³] * (1/2),

we can first simplify the two expressions in the parentheses:

(X/6) + X³ = X/6 + X³

(1/2) * (X/6 + X³) = X/12 + X³/2

So the simplified form of the expression [(X/6) + X³] * (1/2) is X/12 + X³/2.

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The expressions when evaluated are √(81/49) = 9/7 and (2/5)² = 4/5

From the question, we have the following visible expressions that can be used in our computation:

√(81/49) and (2/5)²

Solving (a), we have

√(81/49)

Take the square roots

This gives

√(81/49) = 9/7

The expression cannot be further evaluated

Solving (b), we have

(2/5)²

Evaluate the exponents

This gives

(2/5)² = 4/5

The expression cannot be further evaluated

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