Question 1

Find the value of x.
2x
(3x + 25)
X

Answer:

A+B=C

Step-by-step explanation:

you to put more information in the question

The steps are;

Let us assume the quadratic equation x² - 2x + 1 = 0

To solve this by factoring;

Step 1: We will first look for two numbers such that if added will give the coefficient of x and if multiplied will give the product of the constant andthe coefficient of x²

For the given equation, the two values are -1 and -1

The quadratic equation becomes;

x² - 1x - 1x + 1 = 0

x² - x - x + 1 = 0

(x²-x)-1(x-1) = 0

Step  2: Factorize the common value from both brackets

x(x-1)-1(x-1) = 0

x-1 = 0 and x - 1 = 0

x = 1twice

The given steps are the ways you can solve quadratic equations in one variable using factoring method

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The volume of a cube whose edge is 6 cm long is 216

Answer:

943

Step-by-step explanation:

21| 1000

   | ----------

       47 | 13

21-13=8

1000+8=1008

21|9999

  |---------

     476|3

9999-3=9996

1008,1029,...,9996

let n be number of terms

a=1008,d=21,l=9996

9996=1008+(n-1)21

9996-1008=(n-1)21

8988=(n-1)21

n-1=8988/21

n-1=428

n=428+1=429

again 15|1000

            |---------

                66|10

15-10=5

1000+5=1005

15|9999

  | ---------

      666|9

9999-9=9990

1005,1020,...,9990

a=1005,d=15,l=9990

let n be number of terms.

9990=1005+(n-1)15

9990-1005=(n-1)15

8985=(n-1)15

n-1=8985/15

n-1=599

n=599+1=600

21=3×7

15=3×5

L.C.M.=3×5×7=105

105)1000(9

      -945

     ____

         55

105-55=50

1000+50=1050

105)9999(

     -945

   ---------

         549

       - 525

        -------

            24

        -------

9999-24=9975

1050,1155,...,9975

let n be number of terms.

d=105

l=a+(n-1)d

9975=1050+(n-1)105

9975-1050=(n-1)105

8025=(n-1)105

n-1=8925/105

n-1=85

n=85+1=86

so there are 86 multiples of 21 and 15

(A∪B)=A+B-(A∩B)

multiples of 21 or 15=429+600-86=1029-86=943

Answer:

Step-by-step explanation:

Let's start by reading the problem since it maybe is a bit confusing at first.

The product of 8

Now we know that it starts with 8 multiplied by another number. We do not know that number yet, so let's put 8 * () and fill in the parentheses later.

So far, our equation is:

8()

.. And the sum of 4 and a number

So, 4 + n

We can enter that into our equation

8(4+n)

The next line says "..Is 112"

So, the solution to our equation is 112

Our equation becomes:

8(4+n)=112

Answer:

5/9

Step-by-step explanation:

complement means not choosing an orange  

P( not choosing orange) = (apple and fruit) / total

                                          = (4+6) / (4+6+8)

                                          =10/18

                                           = 5/9

Answer:

the answer is C. 5/9

Step-by-step explanation:

correct on egde 2023 (btw im from the future and the rona is still a thing)

The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.

Given data;

A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.

We need to get the probability that the mpg for a randomly selected compact car would be more than 30.

Therefore;

Mean = μ = 31

Standard deviation = σ = 1.2

Let;

P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)

               = P(Z > -0.833)

               = 0.797

Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.

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Answer:

M=(-3)

Step-by-step explanation:

Take two points on the line

(5,1) and (2,2)

the equation to find M is y2-y1/x2-x1

2-5=(-3)  2-1=1

(-3)/1=(-3)

Hope this helps =3

The dependent variable in this experiment is the level of anxiety as measured by a standardized measure of anxiety before and after the interventions or waitlist period.

The dependent variable in this experiment is the standardized measure of anxiety that was administered to participants before and after the interventions or waitlist period.

The dependent variable is what is being measured or observed to determine the effectiveness of the two interventions (cognitive-behavioral therapy and mindfulness-based stress reduction program) for anxiety.

Therefore,  The researchers are trying to find out how the interventions affect anxiety, so anxiety levels are the outcome or result of the intervention and therefore the dependent variable.

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The equation of the line passing through the point (-1,2) with slope m is y = mx + m-2. This is a general equation of the line and we can find different equations by putting different values of m.

We know that when a point and slope of the equation are given, an equation can be written as

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

which is known as the slope-point form

where m is the slope of the equation

y1 is the  y coordinate of the given point

x1 is the x coordinate of the given point

In the given question, y1 = 2 and x1 = -1

Substituting the value of coordinates in the slope point equation, we get

\(\frac{y-2}{x-(-1)} = m\)

\(\frac{y-2}{x+1}=m\)

y-2 = mx + m

y = mx + m-2

Hence, the equation of the line passing through the point (-1,2) with slope m is y = mx + m-2.

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What is the equation of the line passing the point (-1, 2) with a slope m?

Answer:

You can either use substation or you can use elimination on both of the problems

Step-by-step explanation:

Answer:

x²+y² = 25

Step-by-step explanation:

Attached Picture...

Answer:

Step-by-step explanation:

The area of the square is 144 \(cm^{2}\).

Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.

We know, both these perimeters are equal. Hence,

4x = 3(x+4)

To further simplify the above equation.

4x = 3x + 12

x = 12

Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:

Area = \((side)^{2}\)

Area = 12 * 12

Area = 144 \(cm^{2}\)

Hence, the Area of the Square is 144 \(cm^{2}\)

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Answer:

2272.03

Step-by-step explanation:

A 13ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, then the foot of the ladder will be moving away from the wall at a rate of 4 ft/s when the top is 5 ft above the ground.

This can be determined using the formula Rate = Distance/Time. Since we know that the top of the ladder is slipping down at a rate of 2 ft/s, we can calculate the rate at which the foot of the ladder is moving away from the wall. The distance between the top of the ladder and the foot of the ladder is 8 ft (13 ft - 5 ft). Since the top of the ladder is moving down 2 ft/s, the foot of the ladder must be moving away from the wall at a rate of 4 ft/s.

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The area of the region bounded by

\[y=\frac{7}{(4+x)^2}+\frac{5}{7+x^2},\ y=0,\ x\ge5\]is 0.0188 (rounded to four decimal places).

Here's how to get the solution:

We are asked to find the area of the region bounded by the two curves.

The curves intersect at (5, 0) because x can not be less than 5.

They meet again at the point x ≈ 1.281.

Now, we must find the integrals for both functions in the given range.

We'll call the first function "f (x)" and the second "g (x)."

f(x) = 7 / (4 + x)² + 5 / (7 + x²)

g(x) = 0

The area between the two curves is obtained by finding the integral of the difference of the two functions.

The area is given by:

\[\int_{5}^{1.281} [f(x) - g(x)] dx\]

Since there is no point of intersection beyond x ≈ 1.281, we will use this value for the limit of integration.

Integrating:

\[\begin{aligned} &\int_{5}^{1.281} [f(x) - g(x)] dx \\ =& \int_{5}^{1.281} \left[\frac{7}{(x+4)^2}+\frac{5}{x^2+7}-0\right] dx \\ =& -\left[\frac{7}{4+x}+\sqrt{7}\tan^{-1}\left(\frac{x}{\sqrt{7}}\right)\right]_{5}^{1.281} \\ =& 0.0188. \end{aligned}\]

Thus, the area of the region is 0.0188.

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Answer:

The first one

Step-by-step explanation:

We simplify this inequality to x>4. This means it is moving past the four to the right with an open dot

\(\boxed{\boxed{\pink{\bf \leadsto Option \ A \ is \ correct . }}}\)

For the number line refer to the attachment :

A linear inequality is given to us . And we need to find the correct number line. So the given linear inequality is :-

\(\bf \implies 5x + 3 > 4x + 7 \\\\\bf\implies 5x - 4x > 7 - 3 \\\\\bf\implies \boxed{\red{\bf x > 4 }}\)

This implies that the value of x is Greater than 4 . That is the inequality can have all the values more than 4. So when we see the given number lines we see that the first number line represents all values greater than 4 .

Answer:

they are vertical angles

Step-by-step explanation:

Answer:

elsa can do 150 in 3 minutes.

so together they can do 450 in 3 minutes, or 150 in 1 minute

they would need two minutes

Answer:

4.5 minutes long to do their job.

Answer:

The equation is y=2

Step-by-step explanation:

Well if it has a slope of 0 this means that its a horizontal line

the point (-5, 2)

The x is -5 and the y is 2

so y=2

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

the point -5 is the vertex on the graph because it is the y-intercept.

Step-by-step explanation:

Answer:-16

dsfgdsggsgdsgsdg

The glasses of water he drinks in one hour is 1/3 of a 10-ounce glass water

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

Amount of water = 4/5 of a 10-ounce glass water

Time to drink this water = 2 2/5 hours

To calculate the amount he drank in one hour, we make use of the following equation

Amount of water = Amount of water/Time to drink this water

Substitute the known values in the above equation, so, we have the following representation

Amount of water = (4/5)/(2 2/5)

Evaluate the quotient

Amount of water = 1/3

Hence, the amount is 1/3 of a 10-ounce glass water

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Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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The solution to the equation is; x =± √-56/3 - 5

Completing the square is a mathematical technique used to manipulate a quadratic expression (i.e. an expression of the form ax^2 + bx + c) into a specific form in order to solve for the variable x. The goal of completing the square is to rewrite the quadratic expression in the form (x + p)^2 + q, where p and q are constants.

We have the equation;

y = 3x^2 + 30x + 71

Thus;

x^2 + 10x + 71/3

When we complete the square we have;

(x + 5)^2 + 71/3  = 0

(x + 5)^2 = -71/3 + 5

(x + 5)^2 = -56/3

x + 5 = ± √-56/3

x =± √-56/3 - 5

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Answer:

$2.25 is the cost of one pretzel

Step-by-step explanation:

6p/13.50

p=2.25

Points scored by Adam, Bethany and Charles are 25, 17 and 30 respectively.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

Adam scored 8 more points than Charles,

And Bethany scored 5 more points than Adam.

Also, total score is 72.

Let points scored by Adam is x,

Then point scored by Charles = x-8,

And point scored by Bethany = x+5.

Since, total score = 72

x + x-8 + x+5 = 72

3x - 3 = 72

3x = 75

x = 25

Points scored by Adam is x = 25,

Point scored by Charles = x-8 = 17,

And point scored by Bethany = x+5 = 30.

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One method for choosing the value of the exponential smoothing parameter is to find the value that would have yielded the best forecast for a set of past data.

This method is also known as optimizing the smoothing constant, and it can be done using a variety of statistical techniques and software packages. The goal of optimizing the smoothing constant is to find the value that minimizes the mean squared error (MSE) of the forecasted values compared to the actual values. This involves trying different values of the smoothing constant and comparing the resulting MSEs. The value that produces the lowest MSE is considered the best choice for the smoothing constant. Overall, choosing the right value for the smoothing constant is essential for accurate forecasting, and optimizing the value through statistical techniques is an important step in the forecasting process. The optimal value can vary depending on the data and the specific forecasting model being used, so it is important to experiment with different values to find the best one.

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