What is the distance between three and 11 on the number line

Answer:

Discriminant = 9.

Step-by-step explanation:

Discriminant

[tex]\boxed{b^2-4ac}\quad\textsf{when}\;ax^2+bx+c=0[/tex]

[tex]\textsf{when $b^2-4ac > 0 \implies$ two real roots}.[/tex]

[tex]\textsf{when $b^2-4ac=0 \implies$ one real root}.[/tex]

[tex]\textsf{when $b^2-4ac < 0 \implies$ no real roots}.[/tex]

Given function:

[tex]x^2+x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned} \implies b^2=4ac&=(1)^2-4(1)(-2)\\&=1-4(-2)\\&=1+8\\&=9\end{aligned}[/tex]

Therefore, the discriminant of the given function is 9.

As the discriminant is greater than zero, this implies that there are two real roots.

If Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

The number of lemon limes in the bag = 2 lemon-lime

Number of watermelon in the bag = 3 watermelon

Number of grape gumballs in the bag = 5 grape gumball

Sample space is the set of all the possible outcomes the experiment

Here there are 2 lemon-lime, 3 watermelon and 5 grape gumball

Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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Answer:Option B is the correct answer

Draw the graph of x-axis which is lesser than 5 .

What is  Graph inequality ?

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Answer:

its was 100.6

Step-by-step explanation:

i hope this helps

Answer:

31

Step-by-step explanation:

800/25=32

992/32=31

Answer:

£31

Step-by-step explanation:

let me know if you want a through explanation

Part 1

Relative maxima are where the function changes from increasing to decreasing.

Part 2

None, see above.

Part 3

Relative minima are where the function changes from decreasing to increasing.

Part 4

None, see above.

According to the given equation (y = (3/4)x -2) the value of y for x:

Y = {-5 , -2 , 1 , 4}

A coordinate plane is just a two-dimensional plane that is created when two number lines cross. These number lines include the x-axis, a horizontal number line, and indeed the y-axis, a vertical number line.

In a coordinate plane, which is a two-dimensional number line, the vertical line is known as the y-axis and the horizontal line as the x-axis, as you might recall from pre-algebra. These parallel lines cross one another at their zero points. The origin is where we start from.

Equation:

y = (3/4)x -2

X = {-4 , 0 , 4 , 8}

for each value of x the value of the y :

For x = -4

y = (3/4)x -2

y = (3/4)(-4) -2

y = -5

For x = 0

y = (3/4)x -2

y = (3/4)(0) -2

y = 0 -2

y = -2

For x = 4

y = (3/4)x -2

y = (3/4)(4) -2

y = 1

For x = 8

y = (3/4)x -2

y = (3/4)(8) -2

y = 6 -2

y = 4

According to the given equation (y = (3/4)x -2) the value of y for x:

Y = {-5 , -2 , 1 , 4}

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968 / 10

To divide by the move the coma one place to the left

968/10 = 96.8

We need to find the point given the domain and range of the relation:

For domain and range, the result includes the number. Hence, the end values are given by the points.

For point C:

(-6,4)

Because point c is on quadrant two, where x is negative and y is positive.

Also, it takes the higher y value.

For point D:

(6,3)

Because point D is on quadrant 1, where x is positive and y is also positive.

Let us divide 6 by 1/4

6/1 ÷ (1/4)

6/1*4/1 (Turning the second fraction upside down and multiplying it by the first fraction)

24 (Multiplying)

The answer is 24.

Answer:

Step-by-step explanation:

Since there are four 1/4 in 1 then you have to multiple 6*4= 24!

Albert floating in hot air balloon and Isabelle standing at ground are 29 meters far apart from each other.

What is hot air balloon?

A hot air balloon is a lighter in weigh than air. It is an object made up of an envelope-like bag that holds heated air. A wicker basket, gondola, or capsule suspended below transports people and a heat source, typically an open flame produced by burning liquid propane. A capsule also carries passengers in some long-distance or high-altitude balloons.

Lets understand with the help of a right angle triangle, The point from where the hot air balloon taken off be point A, and the point where Isabelle is standing is point B, and the point where the balloon is point C.

The AB= distance between Isabelle and the point from where hot air  balloon taken off = base of the imagined triangle,

AC = height at which hot air balloon is floating = perpendicular of the imagined triangle

BC = distance between Isabelle and hot air balloon = Hypotenuse of the imagined triangle

Applying Pythagoras theorem,

(BC)² = (AC)² + (AB)²

(BC)² = (20)² + (21)²

BC = 29

Hence Albert and Isabelle are 29 meters far apart.

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25(8+ x)=14

25*8+ 25x =14

200+ 25x= 14

25x=14-200

25x = -186

x = -186/25

x= -7.44

The equation of a line in 2 point form is

So, inputting the points, we have

So, the equation of our line is y = x + 4

The real length of the ship in centimeters is  800000 cm and the real length of the ship in meters is 8000 m

Ratio is a comparison tool for like-kind amounts. A:B or a/B is the ratio formula for two numbers, a and b. A ratio is considered to be in proportion when two or more ratios are equal. Fractions form the foundation of the ratio and proportion concepts. The primary pillars on which many other mathematical notions are built are ratio and proportion. When comparing heights, weights, distances, or times, or when adding ingredients to a recipe, for example, ratio and proportion can be used to solve a variety of everyday problems. Ratios are created by dividing two amounts, and proportions are created when two ratios are equivalent. Different ways, such as x: y or x/y, can be used to express a ratio.

The real length in cm

= 8 000 meters in cm

= 800000 cm

The real length

= 8000 m

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Answer:

6.5ft

Step-by-step explanation:

[tex]A=s^{2} \\42.25=s^{2} \\\sqrt[2]{42.25}=\sqrt[2]{s} \\6.5=s[/tex]

Answer:

6.5ft

Step-by-step explanation:

Given the following expression:

You need to follow the steps shown below in order to solve the exercise:

1. Since you know the value of "x", you must substitute it into the given equation:

2. Now you must solve the multiplication:

3. Finally, you need to solve the addition in order to find the value of the expression. Therefore, you get that the result is the following:

The answer is:

1)

Note that the more people work together the less time they spend.

This is a question about Proportions, Inverse variation. So let's set the ratios and the proportion given these data.

So we can write out the following ratios:

So, it would take 8 hours for Adam to do it alone.

The probabilities that have been calculated here are:

The probability that he is a smoker = 0.08 + 0.16

= 0.24

The given probability that has been calculated is 0.24.

The probability that he does not have lung disease = 0.16 + 0.73

= 0.89

The probability that he has lung disease given that he is a smoker

= 0.08 / 0.08 + 0.16

= 0.08 / 0.24

= 0.333

The probability here is calculated to be 0.333

The probability that he has lung cancer given that he does not smoke

= 0.03 / 0.03 + 0.73

= 0.03 / 0.76

= 0.0395

The given probability here is 0.0395

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The value of the width is 13.5 cm which is the correct answer would be option (C).

The volume of the rectangular prism is the product of the base area and the height.

Given that the volume of a rectangular prism is 6,142.5 cm³. The height is 16.25 cm and the length is 28 cm

The volume of the rectangular prism

V = Length × Width × Height

6,142.5 = 28 × Width × 16.25

Apply the multiplication operation,

6,142.5 = 455 × Width

Width = 6,142.5 / 455

Apply the division operation, and we get

Width = 13.5 cm

Hence, the value of the width is 13.5 cm.

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Answer: 85 cm

Step-by-step explanation:

Given: A small toy rocket is launched from a 48-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula

Required: To find out how long will it take the rocket to hit the ground.

Explanation: When the rocket hits the ground its height h=0. Hence

which gives

Since time can't be negative. Hence t=4 seconds.

Final Answer: t=4 seconds.

On comparing the given expressions we get-

[tex]9^{-2} < (\frac{1}{9}) ^{-1}[/tex]

[tex](\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}[/tex]

[tex]9^{-1} > 9^{-2}[/tex]

Here, we are given 3 pairs of expression. Let us evaluate them one by one.

[tex]9^{-2}[/tex] _ [tex](\frac{1}{9}) ^{-1}[/tex]

The negative exponent means that the base is the reciprocal raised to a positive power. Thus, [tex]9^{-2}[/tex] can be written as- [tex](\frac{1}{9}) ^{2}[/tex] = 1/81

similarly, [tex](\frac{1}{9}) ^{-1}[/tex] can be written as- [tex](9}) ^{1}[/tex] = 9

Thus, the expression becomes-

1/81 _ 9

clearly we can see that 1/81 < 9

Now, we have [tex](\frac{1}{9}) ^{-1}[/tex] _ [tex](\frac{1}{9}) ^{-2}[/tex]

As shown above, the expression can be simplified as-

[tex](9) ^{1}[/tex] _ [tex](9) ^{2}[/tex]

9 _ 81

clearly we can see that 9 < 81

Next, we have- [tex]9^{-1}[/tex] _ [tex]9^{-2}[/tex]

we can write this as-

1/9 _ 1/81

Clearly, 1/9 > 1/81

Hence, we have solved the given inequalities.

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The equation of a line is given by

where m is the slope of the line and (x1,y1) is a point where the line passes through.

In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is

We know that the line we are looking for is parallel to the line

we notice that this line in written in the slope-intercept form

then its slope is 13.

Since the line is parallel to the one we are looking for, our slope is also 13.

Using the point (9,12) and the slope the equation of the line is

now we have to write in the slope-intercept form

Therefore the line is

For this case we have the following function given:

We also know that the domain is given by:

and in order to find the range we need to use the domain given:

So then the range for this case would be given by:

Let f(x) be a function; thus, the reflection across the y-axis of f(x) is given by f(-x).

Therefore, in our case,

Simplifying,

Thus, the answer is g(x)=x^3-8x^2+9x+11, the first option (top to bottom).

Answer:

dihuyyh

Step-by-step explanation:

Answer:

3a x 7a= 21a^2

Step-by-step explanation:

7a x 13a=91a^2

We will first sketch the problem

Let x be the vertical distance above the ground

Using the trigonometric ratio;

cross-multiply