Find the discriminant of the following quadratic equation and indicate the nature of the solutions. Then find the solutions to the quadratic equation. Make sure solutions are simplified! 8x² + 15x = 7x - 4 ​

Answer:

[tex]y = |x - 3|+ 5[/tex]

y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.

The ratio 120/150 represented in the simplest form is 4 : 5 .

The given ratio is 120 /150 .

Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.

The HCF of the number is 30. Hence the ratio in simplest form will be

120÷30 : 150÷30 = 4 : 5 .

By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.

Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.

Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.

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The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend.

Day      hybrids    total

Fri           5             9

sat                         63

sun         40            

we need to find number of hybrids in sat and total in sun.

Number of hybrids in sat = 5*7 = 35(ratios are equal)

Total in sum = 9*8 = 72.

Day      hybrids    total

Fri           5             9

sat          35           63

sun         40           72

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The value of 1/10 of 0.5 lies between 0.1 and 0.2

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Given:

Point on the number line to show the value that is 1/10 of 0.5

So, 1/10 of 0.5

= 1/10 x 0.5

= 0.05

Hence, the value of 1/10 of 0.5 lies between 0.1 and 0.2

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Answer:

answer. {-2187x}/{625}

Answer:

p=17

Step-by-step explanation:

P = 3n+2r+t -1

when n=3, r=2, and t=5?

we will just substitute for the values

p=3(3)+2(2)+5-1

p=9+4+4

p=9+8

p=17

;- The value for p is 17

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Answer:

D, 3216

Step-by-step explanation:

Calculators are great. I love calculators.

The simplest radical form of  √(11/(x + 4)) when x is 16 is; ¹/₁₀√55

Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.

We are given the expression of the surd as;

√(11/(x + 4))

We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;

√(11/(16 + 4))

= √(11/20)

Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;

√(55/100)

Square root of 100 is 10 and as such we now have;

√(55/100) = ¹/₁₀√55

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It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.

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The area of a bull's eye is equal to: B. 452.39 mm².

The area of a circle simply refers to the region enclosed or space occupied by a circle within its boundary, and in a two-dimensional plane.

Mathematically, the area of a bull's eye can be calculated by using this formula:

Area of bull's eye = πr²

Where:

r is the radius of a circle.

Note: The radius of the bull's eye is equal to 12 mm and π = 3.14159.

Substituting the given parameters into the formula, we have;

Area of bull's eye = π × (12)²

Area of bull's eye = 3.14159 × 144

Area of bull's eye = 452.39 mm².

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Answer:

182 minutes

Step-by-step explanation:

0.09x+5=21.38

         -5.   -5

0.09x=16.38

/0.09.   /0.09

  X=182

182 minutes

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The original function of y = -1/3|x| was translated 2 units to the right and 5 units up.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, the translation of a geometric figure (shape) to the right simply means adding a digit to the numerical value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure (shape) that is translated up simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.

In this scenario, the original function was shifted 2 units to the right and then shifted 5 units up to produce the new function as follows:

Original function (x, y)    →     New function (x + 2, y + 5)

y = -1/3|x|                         →        y = -1/3|x + 2| + 5

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{2 +1}{8 +4} \implies \cfrac{ 3 }{ 12 } \implies \cfrac{1 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y +1 = \cfrac{1 }{ 4 } ( x +4) \\\\\\ y+1=\cfrac{1 }{ 4 }x+1\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 4 }x \end{array}}[/tex]

Answer:

Step-by-step explanation:

it help by showinbng thta

Answer:

Step-by-step explanation:

15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4

cevaplar: 17, 19,21,23

Answer:

83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4

Answer:

Step-by-step explanation:

Ok:

1. Identify the thousandths digit

The numbers to the left of the decimal point are the ones and hundreds digits

The first number to the right of the point is the tenths digits

The second to the right of point i s the Hundreths

The third number to the right of point is the thounsandths which is what we are looking for!

2. Apply to problem!

1. 83.978 : Thousandths digit is 8

2. 78.934 : Thousandths digit is 4

3. 84.765 : Thousandths digit it 5

Extra tips and tricks writing as fractions!Ps: Some are not simplified!

1. 83.978= 83 978/1000 as fraction

2. 78.932= 78 932/1000 as fraction

3. 84.765= 84 765/1000 as fraction

The likelihood that the sample mean time required to finish the exam will be less than 47.5 minutes is 0.566.

Given;

The average amount of time needed to finish an exam is 45 minutes, with a standard deviation of 15 minutes. The average amount of time required for 100 randomly chosen pupils is calculated.

Mean (μ) = 45

Standard deviation (σ) = 15

Here, σ/√n = 15/√100

                   = 1.5

To get the probability the sample mean time necessary to complete the examination is less than 47.5 minutes, we need;

P (x < 47.5) = P(z < (x-μ /σ/√n ) )

                  = P(z < 47.5 - 45/1.5)

                  = P(z < 17.5)

                  = 0.566

The probability the sample mean time necessary to complete the examination is less than 47.5 minutes is 0.566

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Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.

The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.

Hence, when  i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and  then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then  the independent variable in this experiment is the book given by me.

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The domain and range of the functions represented by the graph is equal to [-2, 2]. Also, the range of the functions represented by the graph is equal to [-2, 2].

The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent -1 unit.

By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:

Domain = [-2, 2].

Range = (-2, 2).

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The slope of the line that contains the the given points is 1/5 .

The slope of the line containing the two points (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

slope = (y₂ - y₁)/(x₂ - x₁)

In the question ,

it is given that the

line contains the points x [tex]=[/tex] -4 , y [tex]=[/tex] -3

and x = 1 , y = -2 .

we need two points to find the slope of the line

Substituting the values in the formula for slope ,

we get

slope = (-2 -(-3))/(1-(-4))

= (-2+3)/(1+4)

= 1/5

Therefore , The slope of the line that contains the the given points is 1/5 .

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The number of way in which bride can rank the three Djs out of 6 is 120.

There are several different ways we might rank the three DJs.

Therefore, we must identify the permutation P. (6,3).

ⁿPₓ = n!/(n - x)!

⁶P₃ = 6!(6-3)!

⁶P₃ = 6×5×4

⁶P₃ = 120

Thus, the number of way in which bride can select the three Djs out of 6 is 120.

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Considering the dimensions of the rectangular prism and it's volume, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:

V = l x w x h.

In the context of this problem, from the image, the dimensions are given as follows:

Then the polynomial expression regarding the volume of the prism is obtained as follows:

V(x) = 2x(x - 3)(2x - 5)

V(x)= 2x(2x² - 11x + 15)

V(x) = 4x³ - 22x² + 30x.

The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:

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Answer:

Step-by-step explanation: The constant growth for Plant A is two cm a month and the growth of Plant B is also two cm a month.

In relation, Plant B will also be 3cm taller than Plant A on any month so when Plant A is 49cm, Plant B is 52.

When Piece A's height is 49 cm then the Piece B's height will be 52 cm.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can see that Piece A's height increases by 2 cm each month and Piece B's height increases by 2 cm each month as well.

To find out what Piece B's height will be when Piece A's height is 49 cm, we need to find how many months it will take for Piece A to reach 49 cm.

From Month 1 to Month 2, Piece A's height increased by 2 cm, and from Month 2 to Month 3, Piece A's height increased by another 2 cm. Therefore, Piece A's height increases by 2 cm per month.

To go from 28 cm (Piece A's height in Month 3) to 49 cm, it takes 21 cm ÷ 2 cm/month = 10.5 months.

So 10.5 months after Month 3 is Month 13.5.

In Month 13.5, Piece A's height will be 49 cm and Piece B's height will be:

Piece B's height in Month 3 + 2 cm/month × (13.5 - 3 months)

= 31 cm + 2 cm/month × 10.5 months

= 52 cm

Therefore, when Piece A's height is 49 cm, Piece B's height will be 52 cm.

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a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².

b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².

Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:

df / dx = (df / du) · (du / dx)

a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:

F'(x) = [2 · g(x) + 6] · g'(x)

F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²

b) Now we proceed to expand the polynomial in its standard form:

F'(x) = [(2 / 3) · x³ + 7] · x²

F'(x) = (2 / 3) · x⁵ + 7 · x²

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The value of x is 22.5528.

Let ABC be the triangle , <A = 70, <B = 30 ,<C = 80.

Sum of angles in a triangle is 180.

70 + 30 + <C = 180

<C = 180 - 100

<C = 80.

Let sides be a = x , b = 12 and c = ?

According to sines law,

a/sin A = b/sin B = c/sin C

substitute a ,b,A,B values

a/sin A = b/sin B

x/sin 70 = 12/sin 30

x = 0.9397*12/1/2

= 11.2764*2/1

x = 22.5528.

Therefore the value of x is 22.5528.

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Answer:

2:1

Step-by-step explanation:

.5 kg : 250g

the units must be same at both sides

500g : 250g

{as 1 kg = 1000g}

by simplifying both sides

10g : 5g

2g : 1g

2:1

Answer:

x^5

Step-by-step explanation: