Quadratic Functions graph

Answer: The answer is x < 5/2 and x > -5.

Step-by-step explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

[tex]5-2x > 0*3\\5-2x < 5*3[/tex]

[tex]-2x > 0-5\\-2x < 15-5[/tex]

[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.

The relative frequency of students who are not seniors at this high school will be 82.96%.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

P = a/b × 100

A local high school has 1,203 students with 367 freshmen, 382 sophomores, 249 juniors, and 205 seniors.

Then the relative frequency of students who are not seniors at this high school will be

P = 998/1203 × 100

P = 0.82959 × 100

P = 82.959%

P ≈ 82.96%

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Answer:

3,n-1>9

3>n2+9

3>n11 is ans

Answer:

=  -10

Step-by-step explanation:

p + (-q) - 2 = x

if:

p = -3

q = 5

then:

-3 + (-5) - 2 = x

we know that:

+(-) = -

then:

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

x = -10

The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

It is defined as the combination of constants and variables with mathematical operators.

We have given an expression:

= P + (-q) - 2

Plug p = -3

q = 5

= -3 + (-5) - 2

= -3 - 5 - 2

= -10

Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

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Answer:

Answer:

x = 12

Step-by-step explanation:

m∠S + m∠T = 180

8x + 7x = 180

15x = 180

x = 12

does this help?

The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be [tex]N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )[/tex].

Suppose X has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma,[/tex]then,

the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]

Symbolically, we write it as:

[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]

A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.

The mean and standard deviation of the x sampling distribution for each of the following sample sizes.

If N=41

[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )[/tex]

If N=130

[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )[/tex]

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According to the function transformations, the value of h is -2

The complete question is in the attachment

The functions are given as:

[tex]f(x) = (2.5)^x[/tex]

[tex]g(x) = (2.5)^{x-h[/tex]

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

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Answer:H=-2

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

9+51 = 60

(51/3) ÷ (60/3) = 17/20

(17/20)% = 85%

Step-by-step explanation:

Revin imediat...... ✨.

Alexa's proof is incorrect. She made an error in her counterexample.

"It is a quadrilateral whose all angles measure 90°, opposite sides are parallel and equal in length."

"It is a parallelogram whose all sides are equal in length and all angles measure 90° "

"It is quadrilateral whose opposite sides are parallel and equal in length."

"It is a special kind of example that disproves a statement. "

For given question,

Alexa wants to use an indirect proof to prove that all rectangles are not squares.

We know that, to prove a theorem indirectly, we assume the hypothesis is false, and then arrive at a contradiction. It follows the that the hypothesis must be true.

Alexa first assumes that all rectangles are squares.

Then she provides counterexample as shown in the given diagram.

The diagram represents the parallelogram not a rectangle.

This means  she made an error in her counterexample.

Therefore, Alexa's proof is incorrect. She made an error in her counterexample.

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Answer:

slide - translate

Step-by-step explanation:

you slided them both as neither of the figures changed

By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.

By physics we know that both the angle of incidence and the angle of reflection are same. Thus, we have a geometric system formed by two proportional right triangles:

5.6 ft / 4 ft = h / 100 ft

h = (5.6 ft × 100 ft) / 4ft

h = 140 ft

By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.

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The value of the composite function f(g(x)) is 5x + 2

Composite functions are functions inside another function. Given the following functions:

f(x) = 5√x+1 - 2

g(x) = x² - 1

Determine the composite function f(g(x))

f(g(x)) = f(x² - 1)

f(x² - 1) = 5√x² - 1+1 - 2

f(x² - 1) = 5√x² + 2

f(x² - 1) = 5x + 2

Hence the value of the composite function f(g(x)) is 5x + 2

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Answer:

5.0

Step-by-step explanation:

0.16÷0.03220=4.9689

=5.0

Answer: 1

Step-by-step explanation:

[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]

Answer:

The decrease in price is $61.92

The sale price is $196.08

Step-by-step explanation:

24% × 258 = 61.92

258 decrease 24% =

258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08

i ) 3(2x - 3) = 4(2x + 4)

[tex]6x - 9 = 8x +1 6 \\ \\ 6x - 8x = 16 + 9 \\ \\ - 2x = 25 \\ \\ x = - \frac{25}{2} .[/tex]

ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)

[tex]2x + 4 + 5x + 25 = 4x - 32 + 2x - 4 \\ \\ 7x + 29 = 6x - 36 \\ \\ 7x - 6x = - 36 - 29 \\ \\ x = - 65.[/tex]

2. 3x /4 - 7 /4 = 5x + 12

[tex] \frac{3x}{4} - \frac{7}{4} = 5x + 12 \\ \\ \frac{3x}{4} - 5x = 12 + \frac{7}{4} \\ \\ \frac{3x - 20x}{4} = \frac{48 + 7}{4} \\ \\ \frac{ - 17x}{4} = \frac{55}{4} [/tex]

cancel 4 from both sides

[tex] - 17x = 55 \\ \\ x = \frac{ - 17}{55} .[/tex]

3. x +7 - 8x/3 = 17/6 - 5x/8

[tex]x + 7 - \frac{8x}{3} = \frac{17}{6} - \frac{5x}{8} [/tex]

put x = 4

[tex]4 + 7 - \frac{ 8\times 4}{3} = \frac{17}{6} - \frac{5 \times 4}{8} \\ \\ 11 - \frac{32}{3} = \frac{17}{6} - \frac{20}{8} \\ \\ \frac{33 - 32}{3} = \frac{68 - 60}{24} \\ \\ \frac{1}{3} = \frac{8}{24} \\ \\ \frac{1}{3} = \frac{1}{3} .[/tex]

L.H.S. = R.H.S.

4. Let 3 consecutive integers : x , x+1 , x+2

As per the question : 2x + 3(x+1) + 4(x+2) = 56

9x + 11 = 56

Transpose 11 to RHS

9x = 45

Divide both sides by 9

x = 5 ,

x + 1 = 5 + 1 = 6

x + 2 = 5 + 2 = 7

Numbers are 5 , 6 and 7 .

5. Let the age of Jane’s younger sister is x.

Age of Jane will be x + 6

As per the question, after 10 years the sum of their ages will be 50.

After 10 years,

age of Jane = x + 16

age of her younger sister = x + 10

Therefore,

x + 16 + x +10 = 50

2x + 26 = 50

2x = 24

x = 12

Thus, the present age of Jane’s younger sister is 12 years.

And of Jane’s is 12 + 6 = 18 years.

6. Let the breadth of rectangular swimming pool be x metres.

Then, its length = (2x + 2) metres.

We know that the Perimeter of a rectangle

= 2(Length + Breadth)

= 2(2x + 2 + x) = 6x + 4

According to the given condition, we have

6x + 4 = 154

6x = 154 − 4

6x = 150

[Dividing both sides by 6]

x = 25

Thus, breadth = 25 m and

length = 25 × 2 + 2 = 52 m .

7. Let the digit in ten's .

Place be x and the digit in the one's place be y.

x − y = 5 ⟶ (i)

Two digit number = 10x + y

Two digit after reversing the digits = 10y + x

According to question ,

10x + y + 10y + x = 99

11x + 11y = 99

x + y = 9 ⟶ (ii)

On adding (i) and (ii),

2x = 14

x = 7

Putting the value of x in equation (i)

x − y = 5

y = 2

Number = 10x + y

=72 .

8. Let the speed of the steamer in still water be x km/h.

Then , the speed downstream = (x+2) km/h

and the speed upstream = (x−2) km/h

Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream

4(x + 2) = 5(x − 2)

4x + 8 = 5x − 10

4x − 5x = − 10 − 8

[Transposing 5x to LHS and 8 to RHS]

−x = −18 or x = 18 km/h .

9. Let the number of notes of different denomination be x.

∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.

Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x

Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x

Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x

As per the question

Total amount = 400000

200x + 150x + 50x = 400000

400x = 400000 , x = 1000

No of Rs 100 notes = 2x = 2 × 1000 = 2000

No of Rs 50 notes = 3x = 3 × 1000 = 3000

No of Rs 10 notes = 5x = 5 × 1000 = 5000 .

10. Let the age of the man be x

Then age of his son becomes (x − 24)

2 years later from now,

Age of man will be = x + 2

and age of his son will be = (x − 24 + 2) = x − 22

According to question,

2(x − 22) = x + 2

i.e., 2x − 44 = x + 2

i.e., x = 46

Therefore ,

Present age of man = 46 years

And present age of his son = 46 − 24 = 22 years .

The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have given a table:

Time     height

2                8

4               12

6                16

8               20

10              24

The slope of the line = (12-8)/(4-2) = 4/2 = 2

The value of the slope is positive we can say,  the height of water increases as time passes.

Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

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the answer is A: The height of the water increases 2 inches per minute.

hope this helped :)

The probability of getting a heart from the first deck and then a diamond on the second deck will be 6.25%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The probability of getting a heart from the first deck = 13/52.

And the probability of getting a diamond from the second deck = 13/52.

So, The probability of getting a heart from the first deck and then a diamond on the second deck will be,

Probability = (13/52) × (13/52) = 0.0625 = 6.25%

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The best counterargument: the margin of error is quite small compared to the change year over year, so it is a significant issue.

In statistics, the margin of error refers to half the confidence interval. It measures how much of a random sample does not fall within the confidence interval as the number of samples taken increases indefinitely.

As, the temperature rises by 0.09 degree.

So, the difference between margin error and increase is higher which is

= 0.13- 0.09

=0.04

Hence, The margin of error is quite small compared to the change year over year, so it is a significant issue.

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Answer:

insectistics a category variable also called various validity variable is a variable that can take on a limited as usually fixed number two possible values assigning each into visual or other unit of the vision 2 a particular group aur nominacle category of the basis some qualitative

Answer:

BEC = C. 50

BCD = A. 120

Step-by-step explanation:

BEC

65 + 65 = 130

180 - 130 = 50

BCD = 180 - 60 = 120

BEC is 50

From the slope, it is possible to classify the lines as parallel.

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

The lines are classified as parallel when they have the same slope. You will have perpendicular lines when one line is the negative reciprocal of the second line. If the lines intersect, none of the previous conditions presented are met.

The given equations are:

6x-2y=-2 (1)

y=3x+12 (2)

First, you should write the equation 1 in the standard form.

-2y=-6x-2

-y=-3x-1

y=3x+1

Therefore, the slope for equation 1 is m=3.

After that, you should indicate the slope for equation 2. Thus, m also is 3.

As, both equations present the same slope (m=3). The lines are parallel.

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Answer: The Product(?) of their slopes is 3, so the lines are parallel

Step-by-step explanation:

summary of what the other person said

Answer:

$5067,12

Step-by-step explanation:

14,73*43*8

The required money Priscilla will earn in 8 weeks is $5067.12.

As mentioned in the question, Priscilla works 43 hours a week for eight weeks. If she makes $14.73 per hour,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the amount earned be x,
According to the condition,
x = 8 × 43 × 14.73
x =  $5067.12.

Thus, the required money Priscilla will earn in 8 weeks is $5067.12.

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Answer:

value of car depreciate each year = $2000

y + 2000x = 16,500

slope of line = -2000

No, not proportional

Step-by-step explanation:

Value of depreciation of an object is given by :-

Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]

according to question ;

total cost = $16500

scrap value = $500

estimated life = 8 years

therefore,

depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000

now,

let the value of car after 'x' years be 'y'

therefore linear equation showing the relation of x and y is

y + 2000x = 16500

The graph of a linear equation is a line.

If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.

If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.

here equation is of type,

y = mx +c, thus it is not linear.

also in the equation y = mx +c,

'm' is the slope of line

therefore by comparing the equation,

y +2000x = 16500

y = -2000x + 16500

slope is - 2000

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Answer:

D

Step-by-step explanation:

Original area = x * x  =  x^2

New area =   x ( x +3.5) = x^2 + 3.5x    <====the underlined is the increase in area