What are the solution's to the quadratic equation 9x2 4 group of answer choices?.

The substitution which should be made to rewrite given equation  4x⁴ + 21x² + 20 = 0 as a quadratic equation is U = x² .

The Quadratic Equations are the type of polynomial equations which has the highest degree of 2 ,

The quadratic equations are algebraic equation of the second degree in the variable x .

given equation is ⇒ 4x⁴ + 21x² + 20 = 0 ;

we have to make this equation as a quadratic equation ,

So , we substitute , U as x² in given equation ,

we get ;

⇒ 4(x²)² + 21x² + 20 = 0 ;

⇒ 4(U)² + 21U + 20 = 0  ;

the equation becomes as  ⇒ 4U² + 21U + 20 = 0  , which is a quadratic .

Therefore , the substitution of U = x² , should be used .

The given question is incomplete , the complete question is

What substitution should be used to rewrite  4x⁴ + 21x² + 20 = 0 as a quadratic equation ?

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Sum of first n natural numbers, i.e., n(n + 1)/2 is an example of sum of numbers.

Sum is defined as a way of putting all the things like numbers, quantities, etc. together. Alternate words used for sum are “all together, “put together,” and “total,” etc. For example, the sum of first five natural numbers. First five natural numbers are 1, 2, 3, 4, and 5, then sum of first five natural numbers is written as 1 + 2 + 3 + 4 + 5 = 15

Similarly, Sum of First n Natural Numbers :

We have to calculate the sum of the sequence of first n natural numbers. Consider the first n natural numbers as 1, 2, 3, 4,…., n. This represents an AP with first term a = 1 and last term l = n. As we know Sum formula for Arithmetic Progression, S = (n/2) (a + l)

= (n/2)(1 + n)

= n(n + 1)/2

Therefore, the sum of the first n natural numbers is given by n(n + 1)/2.

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Answer:The steps in solving the quadratic function 7x – 9 = 7x^2 – 49x by completing the square are as follows:

Add and subtract (49/2)^2 = (36) to the right-hand side of the equation to complete the square. This gives us:

7x - 9 = 7x^2 - 49x + 36

Factor out the coefficient of the x^2 term, which is 7, on the right-hand side of the equation. This gives us:

7x - 9 = 7(x^2 - 7x + 6)

Take the square root of the number inside the parenthesis and add and subtract it, to get:

7x - 9 = 7(x - 3.5)^2 - 2.25

Now we can add 9 to both sides of the equation to get:

7x = 7(x - 3.5)^2 + 0.75

Now we can divide both sides by 7 to get:

x = (x - 3.5)^2 + 0.75/7

Now we can solve the equation by taking the square root of both sides and adding and subtracting 3.5 to get:

x = 3.5 ± √(x^2 - 7x + 6)

Now we have our solutions, x = 3.5 + √(x^2 - 7x + 6) and x = 3.5 - √(x^2 - 7x + 6) which are the solutions of the quadratic equation.

Step-by-step explanation:

Answer:

56, 112, 16

Step-by-step explanation:

I just know

The average cost of the given question is $115.11.

Average Cost:

The average cost is the total cost of goods divided by the number of units produced or sold. It is used to determine the cost of each unit produced or sold. Without more information about your costs and the number of products you have produced or sold, it is not possible to determine the average cost.

To calculate the average cost of the product, you will need to subtract the gross margin percentage from 100% and then divide the result into the selling price.

First, convert the gross margin percentage to a decimal: 3% = 0.03

Then, subtract the gross margin from 1: 1 - 0.03 = 0.97

Finally, divide the selling price by the result: 111.55 / 0.97 = 115.11

So your average cost is $115.11

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Answer:

7

Step-by-step explanation:

La tasa unitaria de salvamentos por juego es de 7 salvamentos por juego. Esto se puede calcular dividiendo el número total de guardados (35) por el número de juegos (5): 35 guardados / 5 juegos = 7 guardados por juego.

The following triangles are congruent.

Yes AAA

The product of numbers , 3× 3×3×3 is equals to the eighty-one.

In mathematics, a product is a number or result that is obtained by multiplying two or more numbers together. So, 12 is the product of 3 and 4. For example product of 5 and 4 is represented by 5 × 4 = 20 , it is a multiplication expression. A multiplication expression has three parts, a multiplier ( i.e., 4) , a multiplicand ( i.e., 5), and the product ( i.e., 20). We have, a multiplication expression as 3×3×3×3. We can rewrite it in form 3¹× 3¹ ×3¹× 3¹ = 3¹⁺¹⁺¹⁺¹ = 3⁴ , it is an exponential form number. Therefore, results is equals to 81. So, the required product value is 81.

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Aditi and Kavita had 40 coins in total. the coin share b/w them is

x=25, y=15

Generally, Aditi and Kavita's original coin total is 40.

x+y=40

Aditi gave 10 coins to Kavita.

(x-10)*(y+10)=375

Now solving a system of equations using a calculator

x=25, y=15

x=35, y=5

Since Aditi had fewer than 30 coins when she started.

The correct proportion is

x=25, y=15

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CQ

Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.

How much coin did dey both have

On Solving we get that the zero of the polynomial "3x -9" is x = 3 .

The polynomial function is a type of function which involves only non negative integer powers or involves only positive integer exponents of a variable in an equation .

the polynomial function is given as : 3x-9 ;

to find the zeros of the polynomial we equate the given polynomial to zero(0) .

we get ; 3x - 9 = 0 ;

⇒ 3x = 9 ;

dividing both sides by 3 ,

we get ;

⇒ x = 3 .

Therefore , the zero is x = 3 .

The given question is incomplete , the complete question is

What is the zero of the polynomial "3x - 9" ?

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When Richter scale magnitude is less 3. 0 to 3. 9, the frequency of occurrence in the whole world will be over 100,000 per year.

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the change in distance between different seismographs and the epicenter of the earthquake). The original formula is: [tex]Mₗ = log_{10}(A) - log_{10}(A₀ ) = log_{10}( \frac{A}{ A₀}) \\ [/tex]. The classification starts with "small" for magnitudes between 3.0 and 3.9, where earthquakes generally begin to be felt, and ends with "major" for magnitudes greater than 8.0, where significant damage is expected. The National Earthquake Information Center now locates about 20,000 earthquakes worldwide each year, or about 55 per day.

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Answer:

One ft2 of sod costs $10.14 and one pot of ivy costs $0.24

Step-by-step explanation:

We can use the information provided to find the cost of one ft2 of sod and the cost of one pot of ivy.

To find the cost of one ft2 of sod, we can divide the total cost of sod by the total area of sod:

Cost of 1 ft2 of sod = (71 / 7) = $10.14/ft2

To find the cost of one pot of ivy, we can divide the total cost of ivy by the total number of pots:

Cost of 1 pot of ivy = (76 - 71) / (11 + 10) = $5 / 21 = $0.24/pot

So one ft2 of sod costs $10.14 and one pot of ivy costs $0.24

Keep in mind that these calculations only give approximate prices since it's not specified that the cost of ivy and sod is the same, but it's just an estimation based on the information that you provided.

10 is the least 2-digit number having 0 on one's place and 1 on ten's place.

There are just two place values in 2-digit numbers: the units place and the tens place. Every number with more than one digit has various digits, each of which is described by its place value. 2-digit numbers range in value from 10 to 99. In other words, the smallest and largest 2-digit numbers are 10 and 99, respectively. When a number has two digits, it is called a 2-digit number. 2-digit numbers have two digits and range from 10 to 99.

Any number between 1 and 9 can be used as the digit in the tens place. The placement of each digit in a number is known as place value. There is just one place value that matters when discussing 1-digit numbers, and that is the ones place.

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Always insert the x-coordinate first before the y-coordinate.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more integers, or coordinates. The spherical, cylindrical, and cartesian coordinate systems are the three most used ones. Both a cylinder-based coordinate system and a cartesian one will be examined in this chapter. Both horizontal and vertical coordinate systems are used to describe data. Vertical coordinate systems find data's relative height or depth, whereas horizontal coordinate systems locate data over the surface of the globe.

However, you can opt to trace your point in any co-ordinate as per the plot data. But the usual sequence is 1, 2, 3, 4 quadrant and x, y plane respectively.

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To calculate my grade in class 10 divide your total points by the total points possible.

Total points earned divided by total points possible

The maximum amount of points you may have obtained in the course is referred to as total points possible.

The total number of available points in a class with 50 participation points, 50 homework points, 100 essay points, and 200 test points is 400. If you received 330 points in this class, divide that number by 400 to get a quotient of 0.825, This is equivalent to an 82.5% grade, or a low B.

Divide the total by the number of entries to get a percentage. Divide the total by 30, for instance, if you have % grades for 30 activities. Your final grade is expressed as a percentage by the quotient.

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To prove that if KB = (p ⇒ q)∧(r∨s)∧(¬p)∧(¬ ⇒ ¬t)∧(¬q∨t)∧(¬p∧r ⇒ u)∧(w∨t), then KB |= (u ∧ w) using resolution, we can start by assuming the negation of the conclusion, (¬u ∨ ¬w)

Then use the resolution to derive the empty clause, which would mean that our assumption is false and therefore the conclusion is true.

Here is one possible sequence of resolution steps:

step 1: Assume ¬u

step 2: ¬p∧r ⇒ u (from KB)

step 3: ¬p∧r (by resolution with step 2)

step 4: ¬p (from KB)

step 5: r (by resolution with step 3)

step 6: ¬q∨t (from KB)

step 7: t (by resolution with step 5)

step 8: ¬ ⇒ ¬t (from KB)

step 9: (by resolution with step 7)

step 10: p ⇒ q (from KB)

step 11: q (by resolution with step 9)

step 12: ¬q∨t (by resolution with step 6)

step 13: t (by resolution with step 7)

step 14: w∨t (from KB)

step 15: w (by resolution with step 13)

step 16: ¬u ∨ w (by resolution with steps 1 and 15)

step 17: (by resolution with steps 10 and 16)

Since we have derived the empty clause, our assumption (¬u ∨ ¬w) is false, and we have proven that KB |= (u ∧ w) by resolution.

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The difference between the largest 7-digit and the smallest 8-digit number is 1.

The aim is to find the largest 5-digit and the smallest 8-digit numbers, and then we need to determine the difference between these two values.

Let's start by finding the smallest 8-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.

Thus, we can create the required 8-digit smallest number with 0 and 1.

Hence, the smallest 8-digit number is 10000000.

Now, we will discover the largest 7-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 7-digit number with the digit 9.

Thus, the largest 7-digit number is 9999999.

Now, find the difference between these two values.

So, we can determine the difference between the smallest 8-digit number and the largest 7-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒10000000 - 9999999

⇒1

Hence, 1 is the difference between the smallest 8-digit and the largest 7-digit numbers.

--The given question is incomplete; the complete question is

"What is the difference between the largest 7-digit number and the smallest 8-digit number?"--

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The shortest side of the right-angle triangle is its base therefore the shortest side is XY.

There are various different kinds of triangles that exists for example there is an isosceles triangle, right angle triangle equilateral triangle acute angle triangle, obtuse angle triangle hey and many more many. So in a right angle triangle the size of each side is different. As we know that the side opposite to the right angle is known as hypotenuse which is the longest side of the rightangle triangle and the adjacent side the hypotenuse is called base which is the shortest side of a right-angle triangle XYZ.

Also the sum of all the interior angles of a triangle should be equal to 180 degrees.

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C is calculated from solving simultaneous equation generated, the value of C is equal to 10

The information from the problem helps to derive the equations which are solved simultaneously to get A and B then substituted to solve for C

A + A + B = 17and A + B + B = 13 are the given equations

2A + B = 17

A + 2B = 13

solving with calculator will result to

A = 7 and B = 3

substitution to solve for C

and C = A + B

C = 7 + 3

C = 10

hence c is equal to 10

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Step-by-step explanation:

answer is 567

Answer: D , Y + 4 = 2/3 (x-5)

Step-by-step explanation: Since the equation has to be parallel, both equations need to have the same slope; in this case it is 2/3. Then, you can plug in the point into the equations to ascertain if it’s a true statement or a false statement.

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

θ = 30 °

terminal point = cos 30° , sin30°

= (underroot 2 , 1/2 )

tan30° = 1/ underroot 3 = underroot3/3

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

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The mirror image of (3,2) in X-axis => (-3,-2), Y-axis => (3,-2).

The term mirror image of the point is a reflected duplication that appears identical but in reverse.

Here we have given points (3,2).

And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is the same from the origin O (0, 0) and the same from both axes as of the point (3,2).

As we all know that (3,2) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.

And we all also know that In the second quadrant, here the x-coordinate of any point (x, y) is negative.

Therefore, while we looking into the given graph we have identified that the mirror image is (-2, 3).

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The triangles ΔUVW are ΔUKL discovered to be similar by AA Similarity theorem.

Similar triangles are defined as triangles that have the same shape, but then their sizes may differ. Thus, if two triangles are said to be similar, then it means that their corresponding angles are congruent and  also their corresponding sides are in equal proportion

There are three triangle similarity theorems, namely; Angle-Angle (AA), Side-Angle-Side (SAS) or Side-Side-Side (SSS).

Now, looking at the given image, we see that ∠UVW ≅ ∠UKL because they are both corresponding angles.

Similarly, we can say that ∠UWV ≅ ∠ULK because they are corresponding angles.

Thus, ΔUVW is similar to ΔUKL by AA similarity theorem.

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The ladder will now reach 21.7 ft.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is that a 45-foot ladder is placed against the side of a house so that it reaches 27 feet in height. Cooper grabs the ladder by its base and pulls it 4 feet farther away from the house.

Refer to the image attached. We can write in ΔCEB as -

EB² = 45² - 27²

EB² = (45 + 27)(45 - 27)

EB² = 72 X 18

EB² = 1296

EB = √1296

EB = 36 ft

Now -

AB = AE + EB = 36 + 4 = 40

From ΔDAB, we can write -

BD² = 45² - 40²

BD² = (45 + 40)(45 - 40)

BD² = 95 X 5

BD² = 475

BD = 21.7 ft

Therefore, the ladder will now reach 21.7 ft.

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Time-series Plot graph is the best choice for determining the change in the stock market over time.

The term stock exchange refers to several exchanges where shares of publicly traded companies are bought and sold. Such financial activities are conducted through formal stock exchanges and over-the-counter (OTC) markets that operate under a specific set of regulations.

Other major stock exchanges in the world are Tokyo Stock Exchange (Japan), Shanghai Stock Exchange (China) and London Stock Exchange (UK). Stock exchanges are considered capital markets as they provide long-term financing for companies.

A time series chart, also known as a time series chart or time series graph, is a data visualization tool that plots data points at successive time intervals. Each point on the chart corresponds to both time and quantity being measured.

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The measure of ∢1 is 40 degrees.

What is the measure of angle?

The measure of an angle is a numerical value that represents the amount of rotation of one ray around a common endpoint, called the vertex, compared to another ray. The measure of an angle is usually measured in degrees (°).

The measure of an angle can be found by using the following formula:

Measure of ∢1 = 180 - (measure of ∢2 + measure of ∢3)

In this case, we are given the measures of ∢2 and ∢3:

∢2 = 102 degrees

∢3 = 38 degrees

So, we can substitute these values into the formula:

Measure of ∢1 = 180 - (102 + 38) = 180 - 140 = 40 degrees

Therefore, the measure of ∢1 is 40 degrees.

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Answer:

$0.40

Step-by-step explanation:

4% = 0.04

10 times 0.04 = $0.40

So, sale tax is $0.40

To write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8.

To write 3 more than 5, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 5 + 3 = 8.

This notation means that we are adding 3 to 5, which results in 8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is 8.

Another way to write 3 more than 5 is to use the phrase "5 plus 3". This phrase indicates that we are adding 3 to 5 to get 8.

Therefore, In short, to write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8. This means that we are adding 3 to 5, resulting in 8. It can also be written as "5 plus 3", indicating the same operation.

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Step-by-step explanation:

the ratio is 25/50 (25 kg in 50 minutes).

as a ratio is basically a fraction (just with a special meaning), we can simplify it as a "normal" fraction :

25/50 = 1/2

in other words, the hippo can eat 1 kg in 2 minutes.

now the answer to the question is easy :

how many minutes to eat 60 kg ?

remember, when we multiply one part of the fraction by a factor, we need to multiply the other post by the same factor to keep the overall value.

so, 60 kg = 60×1 kg

we multiply the numerator by 60, therefore, we need to multiply the denominator by 60 too. and we get

1/2 × 60/60 = 60/120

it takes the hippo 120 minutes to eat 60 kg.

Therefore , the solution of the given problem of parallelograms comes out to be Figure 2 and Figure 4 are of the same area.

A simple quadrilateral with two sets of equal spacing is known as a parallelogram in Euclidean geometry. Both set of opposite ends are straight and equal in a particular type of quadrilateral termed as a parallelogram. Parallelograms come in four varieties, three of which are exclusive. The four different shapes are rhombuses, parallelograms, squares, and rectangles. A quadrilateral is a parallelogram if it has two sets od parallel sides. In a parallelogram, all cross-sectional lengths of the opposing angles and angles are equal.

Here,

Given :

Four parallelogram are given with different area we have to find the

parallelogram area equal is :

We observe from the given image ,

We get

Figure 2 and Figure 4 are of the same area.

Therefore , the solution of the given problem of parallelogram comes out to be Figure 2 and Figure 4 are of the same area.

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