What is the nature of the roots of the quadratic equation â 3x² 10x 7 â 3 0?

Answer: The perimeter of a shape is the sum of all its sides.

From the diagram, we can see that the shaded shape is composed of a square and a rhombus.

The square has 4 sides of equal length, which is the same as the length of one of the diagonals of the rhombus.

The rhombus has 4 sides with two sides of equal length (the diagonals) and two sides of equal length (the parallel sides).

We can call the length of the diagonals of the rhombus as "d" and the length of the parallel sides of the rhombus as "s".

So, the perimeter of the shaded shape is:

Perimeter = 4s + 4d

It is not possible to find the perimeter with out knowing the length of the sides of the rhombus and the square.

Step-by-step explanation:

The number of trays of dog treats Jayden made is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of ounces in the mixture.

= 1 quart yogurt + 10 ounces of peanut butter + 6 ounces of honey

[ 1 quart = 32 ounces ]

= 32 + 10 + 6

= 48 ounces

Now,

Number of ounces in each tray = 16 ounces

The number of tray.

= 48/16

= 3

Thus,

The number of trays for dog treats is 3.

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The solution to the given linear inequality is given in graph.

What is linear inequality?

In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols "< and '>' represent strict inequalities, whereas  ‘≤’ and ‘≥’ represent slack inequalities. A linear inequality appears to be a linear equation, however there is a difference in the formula.

Graph for |2x + 2| ≤ 6 is in the image.

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Answer:

It is C

Step-by-step explanation:

Answer:

  9/4

Step-by-step explanation:

You want to simplify (6x^-2)^2(0.5x)^4.

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

We first work out the value of each set of parentheses, then form the product of the results.

  [tex](6x^{-2})^2(0.5x)^4=(6^2)(x^{-2\cdot2})(0.5^4)(x^4)=(36x^{-4})\dfrac{1}{16}x^4\\\\=\dfrac{36}{16}x^{-4+4}=\boxed{\dfrac{9}{4}}[/tex]

__

Additional comment

As you know, x^0 = 1, so the variable disappears when this is simplified.

The simplified form of each of the given expressions as required is as follows;

a. -2 + 5 = 3

b. (−4) • (6) = -24

c. 4 − (−3) = 4 + 3 = 7

d. 10 + (−2) − 7 = 10 - 2 - 7 = 1.

e. −5 − 3(2 − 6) = -5 -3(-4) = -5 + 12 = 7.

f. (3 − 3)(102 − 11) = (0) (91) = 0.

It follows from the task content that the given arithmetic operations are to be simplified.

The PEMDAS guidelines which prescribe the order of mathematical operations is used for the computation.

where;

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

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The c d f is (  1     : x≥4), b) mean is 2, c) the variance of x is 4/3 d) the value of f is 0.35 e) value of p is 0.375 and value of k is 1.4

a) F(x)=P(x ≤ x)=(  1     : x≥4

b) E(x)=∫^ (x)dx=2

c) ∫^4^0 x^ 2f(x)dx=4/3

d) f(x)=x/4,0<x<4)=0.35

e)P(1/2<X<2)=0.375

f)(p(x ≤ k)=F(K)=1.4

The pdf of x is
F(X)=1/4: 0<X<4
0 : otherwise


A) The c d f of x is
F(x)=P(x ≤ x)

=∫^ x f(t) αt
= ∫^ x1/4 αt
=1/4(t)^ x
=x/4,0<x<4
F(x)=(0: x≤0)        
      ( x/4:0<x<4)
     (  1     : x≥4)


B) We need, mean(x)
=E(x)=∫^ (x)dx

=1/4  ∫^4^ x dx
=1/4 (x^ 2/2)^ 4
=16/8
=2    

C) Here, E(X^2)          
=∫^4^0 x^ 2f(x)dx

=1/2∫^4^0 x^2 dx        
=1/4(x^ 3/3)^ 4^0
=16/3
Var(x)+E(X^2)-E^2(X)
=16/3-(2)^2
=4/3
       
d) F(1.4)=1.4/4   ∵   f(x)=(x/4,0<x<4)

=0.35


e)P(1/2<X<2)
=F(2)-F(1/2)

=2/4-1/2/4
=1/2-1/8=3/8              
=0.375

F) let R=35th percentile

so, we must have,
p(x ≤ K)=0.35           ∵  (p(x ≤ k)=F(K)
=K/4=0.35                    =k/4
k=1.4

Complete Question is given below

1. let x be a random variable with pdf . a) find the c d f f(x). b) find the mean of x. c) find the variance of x. d) find f (1.4). round to 3 decimal places. e) find P(1/2<X<2). f) find THE 35TH PERCENTILE.

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Answer:

hope I'm right-

Step-by-step explanation:

first row: 0.3

second row: 0.2

last row: 0.1

Answer:

No, you cannot fold the figure in half so that one side matches the other.

Step-by-step explanation:

The figure does not have any symmetry, so it cannot be folded in half so that one side matches the other.

There are 10,000,000 (10 million) 7-digit combinations. A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations

A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations:

n!/(r!(n-r)!)

where n=10 (the number of possibilities for each digit) and r=7 (the number of digits).

10!/(7!(10-7)!) = 10!/7!3! = 10!/(7!3!) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5 x 3 x 2 x 1 x 3 x 2 x 1) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5 x 3 x 2 x 1) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5) = 10 x 9 x 8 x 7 x 6 x 5/7 = 10 x 9 x 8 x 7 x 6 = 10,000,000 (10 million)

Therefore, there are 10 million 7-digit combinations.A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations

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If you have 25 members and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

In the given question,

If you have 25 members and wish to pick a president, secretary, and treasurer, then we have to find how many ways can we choose the officers, if individual members may hold more than one office.

We have a total of 25 members.

They have a total of 3 positions president, secretary, and treasurer.

When the one position of president was filled then there were left 24 members for the secretary position.

When the one position of secretary was filled then there were left 23 members for the treasurer position.

So the possible ways to fill the position are found by multiplying 25,24 and 23. So

Possible ways=25*24*23

Possible ways=13,800

Hence, if you have 25 members, and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

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Jace should visit the theator 18 times for earning a free movie ticket.(inequality)

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The stages of resolving inequities are as follows:

Let x be the number of visit in the theator to get at least 1 movie ticket

so the inequation is :

50 + 14.5*x > 310

x > 17.93

Jace should visit the theator 18 times for earning a free movie ticket.

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Answer:

([tex]-\frac{7}{12}[/tex],-1)

Step-by-step explanation:

A. Liam sets a goal to score a 720 on the GMAT test in October.

B. Liam develops an action plan to study for a month and take a practice test. After studying for a month, he takes a practice test and scores 40 points higher than he did on his first practice test.

C. Based on the average test scores of students at his target schools, Liam decides he wants to earn a 710 on the GMAT.

D. To achieve his goal, Liam will spend one hour each weeknight and three hours every Saturday and Sunday studying GMAT practice questions. He will also review progress regularly to ensure that he is on track to achieve his goal.

E. Finally, Liam will appraise his performance by comparing his scores on practice tests with his goal score of 710. If he finds that he is not making enough progress, he may adjust his study schedule or seek additional help.

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8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

We can begin solving the problem by using the proportion:

(18 muffins) / (15 muffins) = (x muffins) / (7 muffins)

where x represents the number of Susan's muffins that weigh the same as 7 of Tom's muffins. To solve for x, we can cross-multiply and then divide:

18 muffins * 7 muffins = 15 muffins * x

x = (18 * 7) / 15

x = 8.4

Therefore, 8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

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The equation of graph in slope intercept form with inequality is

y < -2x + 6.

What is slope - intercept form of line?

The slope intercept equation can be used to determine a straight line's general equation from its slope and the location of its y-axis intersection.

Y = mx + b is the slope intercept form equation.

One formula for figuring out a line's equation is the slope-intercept formula. A line with slope m and a y-intercept of b has a slope-intercept formula of y = mx + b. Any point on the line can be found at (x, y).

From graph we can see that the graph passing through the points (3, 0) and (0, 6).

We have to find the slope intercept form of line.

First to find the slope of the line.

m = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{6-0}{0-3}=\frac{6}{-3} = -2[/tex]

Slope of the line is -2.

Now consider, the point -slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = -2, (x_1, y_1) = (3, 0)[/tex]

⇒

[tex]y-0=-2(x-3)\\y=-2x+6[/tex]

Hence, the equation of graph in slope intercept form with inequality is

y < -2x + 6.

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Answer:

6/8 = 9/12

Step-by-step explanation:

6/8 = 3/4

9/12 = 3/4

So, the answer is

6/8 = 9/12

Therefore , the solution of the given problem of number line comes out to be option D is correct .

The number line, a representation of real numbers integers in visual form, is a tool for teaching mathematics. An intensity line is depicted by it. Every actual number is used to represent a point just on real number, or every precise number is used to represent a position. The separations between increments on a number line are equation. The numbers on a line can only be replied in the manner indicated by those numbers. The number's intended usage will be determined by the question it answers.

Here,

Given :

Because multiplying two negative integers together

results in a positive number,

the meaning of -16 is not -4.

as a result: -4 will turn into 16

So, option D is correct .

Therefore , the solution of the given problem of number line comes out to be option D is correct .

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The percent of adults who are developmentally disabled by the criterion of an IQ score below 70 is approximately 2.28%

We can use the standard normal distribution in order to find the probability of an IQ score below 70.

We know the mean IQ score is 100 and the standard deviation is 15, so we can use the formula:

z = (70 - 100) / 15

z = -2

Using a normal probability table, we find that the probability of a score less than -2 is approximately 0.0228.

Therefore, we get that approximately 2.28% of adults are considered developmentally disabled by the criterion of an IQ score below 70.

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Suitable choices are (1), (2), (7), and (8). In a plane, lines that are consistently spaced apart from one another are referred to as parallel. Parallel lines don't ever intersect.

Given:

A and B are parallel lines.

Think of a | b and 'd' as a transversal,

Statements

Reasons

1. [tex]$\angle B X Z=\angle A Z P=58^{\circ}$[/tex]

Corresponding angles are equal

[tex]$\therefore \mathrm{m} \angle 2=58^{\circ}$[/tex]

2. [tex]$\angle B Y C=\angle X Y Z=(4 x-10) \cdot$[/tex] Vertically opposite angles are equal

Now, consider a | b and ' c ' be a transversal then,

Statements

Reasons

1. [tex]$\angle X Y Z=\angle Q Z U=(4 x-10)^{\circ}$[/tex]

Corresponding angles are equal  [tex]$\therefore \mathrm{m} \angle 1=(4 x-10)^{\circ}$[/tex]

2. [tex]$\angle P Z A+\angle P Z Q+\angle Q Z U=180^{\circ}$[/tex]

Sum of angles on a straight line is [tex]$180^{\circ}$[/tex]

3. [tex]$58^{\circ}+(3 x-1)^{\circ}+(4 x-10)^{\circ}=180^{\circ} \quad$[/tex]

Substitution property

4. [tex]$47^{\circ}+7 x=180^{\circ}$[/tex]

Combining like terms

5. [tex]$7 x=180^{\circ}-47^{\circ}$[/tex]

Subtraction property of equality

[tex]$\therefore 7 x=133^{\circ}$[/tex]

6. [tex]$x=19^{\circ}$[/tex]

Division property of equality

Plug in x = 19

in [tex]$(3 x-1)^{\circ}$[/tex]

and [tex]$(4 x-10)^{\circ}$[/tex]

we get [tex]$(3 x-1)^{\circ}=(3(19)-1)^{\circ}=56^{\circ}$[/tex]

[tex]$(4 x-10)^{\circ}=(4(19)-10)^{\circ}=66^{\circ}$[/tex]

So, [tex]$(3 x-1)^{\circ} \neq(4 x-10)^{\circ}$[/tex]

Hence, options (1), (2) , (7) and (8) are correct.

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The equation of a sphere if one of its diameters has endpoints: (-6, 4, 0) and (0, 0, 6) will be (x+3)2+(y-2)2+(z-3)2=22

d2 = (xf-xi)2 + (yf-yi)2 +(zf-zi)2

d2 = (-6-0)2+(4-0)2+(0-6)2

d2=36+16+36=88

d=sqrt(88)

The radius is half the diameter

r=d/2

r=sqrt(88)/2

Use the center equation to get the diameter's middle.

(xf-xi)/2, (yf-yi)/2, (zf-zi)

(-6-0)/2, (4-0)/2, (0-6)/2

(-3,2,-3) Center

Apply the sphere equation now.

(x-xc)2+(y-yc)2+(z-zc)2=r2

(x+3)2+(y-2)2+(z-3)2=(sqrt(88)/2)2

(x+3)2+(y-2)2+(z-3)2=88/4

(x+3)2+(y-2)2+(z-3)2=22

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The median of the data set when Ms. Aniston asked seven students in her class to collect pet food cans for a local animal shelter will be C. 7

When everything is written out, the median is essentially the center number. So, using your line plot, you should write each number down as many times as a dot appears above it.

This would be 6, 6, 7, 7, 8, 9, for this issue. The fourth number would be the center since there are seven total. Out of these numbers, the 7 comes fourth in ascending order, giving you your answer.

Therefore, it should be noted that based on the information, the correct option is C.

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Complete question

Ms. Aniston asked seven students in her class to collect pet food cans for a local animal shelter. The dot plot shows the number of food cans collected by each student. Each dot represents one student.

What is the median of the data set?

A. 6

B. 9

C. 7

D. 8

Answer:

1 and - 2

Step-by-step explanation:

f(0) is asking what is the value of y when x = 0

locate x = 0 ( the origin), go vertically up the y- axis to meet the line at (0, 1)

then f(0) = 1

f(x) = 5 is asking what is the value of x when y = 5

locate y = 5 on the y- axis, go horizontally across to meet the line at (- 2, 5 )

then f(x) = 5 when x = - 2

The value of x in simplest radical form is 8√3.    

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root.  

The radical and root of a number are the same thing.      

Here we have

Given triangle is a right-angled triangle

From trigonometric ratios,

Sin θ = [ Opposite side ]/[ Hypotenuse ]

=> Sin 30° = [ Opposite side ]/[ 16 ]  

As we know, Sin 30° = 1/2

=> [ Opposite side ]/[ 16 ] = 1/2

=> Opposite side = 8 units      

By the Pythagorean theory,

Hypotenuse² = Opposite side² + Adjacent side²  

=> 16² = 8² + x²  

=> 256 = 64 + x²

=> x² = 192  

=> x = √64 × 3  

=> x = 8√3      

Therefore,

The value of x in simplest radical form is 8√3.

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The slope of the given coordinate points is -2. Therefore, option D is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (2, -8) and (-4, 4).

Here, substitute (x₁, y₁)=(2, -8) and (x₂, y₂)=(-4, 4) in slope formula, we get

m= (4+8)/(-4-2)

m= 12/(-6)

m= -2

Therefore, option D is the correct answer.

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Answer: 6 + 2x

Step-by-step explanation:

Combine like terms:

= 6 + 2x

The resulting religion Islam belongs to the class monotheism.

Monotheism is the class of religion where they believe in only one God.

Monotheism is the belief that there is one and only supreme power that is referred to as the universal God.

Given that according to Muslim tradition, the prophet Muhammad received his revelations from the only true God, whose name is Allah.

So there is only one God Allah that Islam believes in.

So Islam is a monotheistic religion.

Hence Islam is a monotheism.

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The log function is also called Logarithmic functions.

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Answer: 4

Step-by-step explanation:

y wouldn't it be 4

so 2+2=4

ex: ii + ii = iiii (2+2 = 4)

Answer:

4

Step-by-step explanation:

2+2= 4

1+1=2 and 1+1=2

so if you add it together

you get 4