X2+5xy+6y2 challenge question

Answer:

the x intercepts of the parabola are -2.

After solving using quadratic equation we get,

x = 1.12 or x = -1.79

Given, 0=-8m-12m²+24

-8m-12m²+24 = 0

8m+12m²-24 = 0

12m²+8m-24 = 0

Now, taking 4 common from the expression

4(3m²+2m-6) = 0

3m²+2m-6 = 0

Now, applying Quadratic Formula

\(x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}\)

x = (-2 ± √4 + 72)/6

x = (-2 ± √76)/6

x = (-2 ± 8.72)/6

x = (-2 + 8.72)/6 or x = (-2 - 8.72)/6

x = 6.72/6 or x = -10.72/6

x = 1.12 or x = -1.79

Hence, x = 1.12 or x = -1.79

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Answer:

A. x + 9

Step-by-step explanation:

x² + 5x - 36 = (x + 9) (x - 4)

Step-by-step explanation:

Let's start by using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume of the cylinder, r is the radius of the cylinder, h is the height of the cylinder, and π is a mathematical constant (approximately equal to 3.14).

Since we are dealing with a drain pipe, we can assume that the height of the cylinder is fixed and does not change. Therefore, we can rewrite the formula as:

V = πr^2h = Ah

where A is the cross-sectional area of the cylinder.

Now, let's use the given information that the drain pipe can carry 36 litres per second. We know that the volume of water that passes through the pipe in one second is equal to 36 litres. We can therefore write:

36 = Ahv

where v is the velocity of the water flowing through the pipe. Since we are assuming that the height of the cylinder is fixed, we can simplify this equation to:

36 = Av

Now we need to determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second. Let's call the new diameter d2 and the old diameter d1. We can set up a proportion to solve for d2:

A1/A2 = d1^2/d2^2

We know that A1 and A2 are proportional to the volumes of water the pipe can carry, so we can write:

A1/A2 = 36/60

Simplifying this equation, we get:

A1/A2 = 3/5

Substituting in the formula for the cross-sectional area of a cylinder, we get:

πd1^2/4 / πd2^2/4 = 3/5

Simplifying further, we get:

d1^2/d2^2 = 3/5

Taking the square root of both sides, we get:

d1/d2 = sqrt(3/5)

Now we can solve for d2:

d2 = d1 / sqrt(3/5)

We want to know the percentage increase in the diameter, which we can find using the formula:

% Increase = (New Value - Old Value) / Old Value x 100%

Substituting in our values, we get:

% Increase = (d1 / sqrt(3/5) - d1) / d1 x 100%

Simplifying, we get:

% Increase = (1 / sqrt(3/5) - 1) x 100%

Using a calculator, we get:

% Increase ≈ 34.64%

Therefore, the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is approximately 34.64%.

The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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A) All x- and y-intercepts include the following:

x-intercepts: none.

y-intercept: 1.

B) The equation for vertical asymptote is x = 4 and the equation for horizontal asymptote is y = 0.

C) The domain and range of f are:

Domain = [-∞, 4) U [4, ∞]

Range = [0, ∞]

In Mathematics, the x-intercept is the point at which the graph of a function crosses or touches the x-coordinate and the y-value or value of "y" is equal to zero (0).

Part A.

Based on the graph of this rational function, the x-intercept and y-intercept include the following:

x-intercept: none.

y-intercept: 1.

Part B.

An equation that represents the vertical asymptote is x = 4 while the equation represents the horizontal asymptote is y = 0 because the line does not cross those points.

Part C.

By critically observing the graph of this rational function, we can logically deduce the following domain and range:

Domain = [-∞, 4) U [4, ∞] or {x|x ≠ 4}.

Range = [0, ∞] or {y|y ≥ 0}.

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Answer:

Step-by-step explanation:

This problem requires the use of the Pythagorean Theorem to find the lengths of the sides of a piece of property in the shape of a right triangle

Example:

Taylor finds a piece of property in the shape of a right triangle. She finds that the longer leg is 10 m shorter than twice the length of the shorter leg and the hypotenuse is 20 m longer than the longer leg. Find the lengths of the sides of the triangular lot.

Answer:

C. 4

Step-by-step explanation:

Use the slope formula:

\(m=\frac{y2}{x2} -\frac{y1}{x1}\)

m = the slope.

Substitute the values into the formula:

\(\frac{9}{3} -\frac{-7}{-1} =\frac{?}{?}\)

Solve:

\(\frac{9}{3} -\frac{-7}{-1} =\frac{16}{4}\)

Simplify 16/4:

\(\frac{16/4}{4/4} =\frac{4}{1}=4\)

Answer:

The Answer in Exact Form:

-3/22

In Decimal Form:

-0.136

Step-by-step explanation:

-\(\frac{3}{2}\)÷5\(\frac{1}{2}\)=-3/22

the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy is 0.814

Probability is a measure of the likelihood of a particular event occurring, expressed as a number between 0 and 1. It is a mathematical tool used to quantify the likelihood of an event occurring, or the likelihood of a proposition being true.

Step 1: Calculate the probability that an applicant is trustworthy:

P(trustworthy) = 95% = 0.95

Step 2: Calculate the probability that an applicant is untrustworthy:

P(untrustworthy) = 100% - 95% = 5% = 0.05

Step 3: Calculate the probability that the lie detector correctly identifies a trustworthy applicant as trustworthy:

P(trustworthy applicant correctly identified) = 65% = 0.65

Step 4: Calculate the probability that the lie detector incorrectly identifies a trustworthy applicant as untrustworthy:

P(trustworthy applicant incorrectly identified) = 15% = 0.15

Step 5: Calculate the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy:

P(job applicant rejected under suspicion of dishonesty was actually trustworthy) = P(trustworthy applicant correctly identified) x P(trustworthy) + P(trustworthy applicant incorrectly identified) x P(trustworthy)

= 0.65 x 0.95 + 0.15 x 0.95

= 0.814

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Answer:

It's C.

Step-by-step explanation:

Did the test

The inequality is y/9 - x > 21.

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), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

x less than the quantity y divided by 9 is more than 21.

Now, writing the mathematical Inequality for the given statement is

x less than the quantity y divided by 9

y/9 -x

and, more than 21.

y/9 - x > 21

Hence, the inequality is y/9 - x > 21.

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Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).

The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..

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Answer:

c. 1 and 14

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

i did the quiz

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

2(30) + 2x = 245

Step-by-step explanation:

As u know a rectangle has four sides, two equally long sides and two equally short sides. If each of the short sides are 30, that means 30 times 2 adding the 2 missing long sides would equal 245. So the long sides are going to be represented with x in this equation:

2(30) + 2x = 245

To make sure our equation is right, lets try solving it:

2(30) + 2x = 245

60 + 2x = 245

subtract 60 from both sides

2x = 185

x = 92.5

Now put 92.5 in the equation instead of x to confirm:

2(30) + 2(92.5) = 245

60 + 185 = 245

245 = 245

\(\text{In}~ \triangle ABC,\\\\~~~~~~~~\sin 45^{\circ} =\dfrac{BC}{AC} \\\\\implies \dfrac 1{\sqrt 2} = \dfrac{BC}{6\sqrt 2}\\\\\\ \implies BC= 6\\\\\text{Now, In}~ \triangle BCD\\\\~~~~~~\cos 60^{\circ} = \dfrac{BD}{BC}\\\\\ \implies \dfrac 12 = \dfrac{x}{6}\\\\\\\implies x = \dfrac 62\\\\\\\implies x = 3\)

Answer:

x = 3

Step-by-step explanation:

using the sine ratio in right triangle ABC and the exact value

sin45° = \(\frac{1}{\sqrt{2} }\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{BC}{6\sqrt{2} }\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

BC × \(\sqrt{2}\) = 6\(\sqrt{2}\) ( divide both sides by \(\sqrt{2}\) )

BC = 6

using the cosine ratio in right triangle BCD and the exact value

cos60° = \(\frac{1}{2}\) , then

cos60° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BD}{BC}\) = \(\frac{x}{6}\) = \(\frac{1}{2}\) ( cross- multiply )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

the unit rate is 10 cents

Step-by-step explanation:

divide $1.00 and 10 which is $0.10 or 0.1

Answer:

18

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

In order to grow, a plant needs all the radient energy that it can get.

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:  The first one (-3,6)

Step-by-step explanation:

Both linear functions meet at (-3,6).

You can graph both linear functions on the Desmos graphing calculator website to verify your answer.

The height of the bridge is  442.23m.

In the question ,

it is given that

time taken(t) to reach the pebble from bridge to the water = 9.5 sec

the initial velocity(u) = 0    ....as the ball was at rest ,

the acceleration(a) is the gravity = 9.8 m/s

let s be the distance between bridge and water , which means the height of the bridge = h

Now by the second equation of motion , we have

h = u*t + (1/2)*a*t²

Substituting the values of u, a, t from above , we get

h = 0*9.5 + (1/2)*9.8*(9.5)²

h = 0 + (1/2)*9.8*90.25

h = 0 + 884.45/2

h = 884.45/2

h = 442.225

h ≅ 442.23

Therefore , if a pebble dropped from a bridge strikes the water exactly 9.5 sec then the height of the bridge is 442.23m .

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Answer:

15 : 13

Step-by-step explanation:

Girls : Boys

15 : 13

Answer:

8

Step-by-step explanation:

2x² + 3x - 6

plug in x with 2

2(2)^2+3(2)-6

2(4)+6-6

8+6-6

14-6

8

The number of days it will take the virus to grow from 90 to 410 is 15 days.

The growth rate of the virus is calculated as follows;

growth rate = (200 - 90) / 5

growth rate = 22 per day

The number of days it will take the virus to grow from 90 to 410 is calculated as follows;

growth = 410 - 90

growth = 320

Number of days = 320 / 22/day = 14.55 ≈ 15 days

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Answer: 286/19, 15.052632 and 1

                                                     15

                                                        19

Calculate; 858/57

You can see the division procedure, below.    

   \(\bf{\red{ \ \ \ \ \ 1 \ 5 }} \\ \bf{57 \ |\overline{8 \ 5 \ 8}}\\ \bf{ \ \ \underline{ - \ 5 \ 7}}\\ \bf{ \ \ \ \ \ 2 \ 8 \ 8}\\ \bf{ \ \ \underline{- \ 2 \ 8 \ 5}}\\ \bf{\ \ \ \ \ \ \ \ \ \ \ 3}\)

Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

The volume of the solid generated is V=8π and 32/5π

Given functions are  x=y²,  x=2  and  y=0

The equation y=x² is a parabola opening to right and has a vertex at  O(0,0)

and another y=0 is the x-axis and  x=2  is a line parallel to the y-axis

The region bounded by the above will be formed once their intersection points are known.

y²=2⟹y=±√2

OFB is bounded by  O(0,0), F(2,0) and  B(2,√2)

Let  V be the volume of solid generated when the region  OFB  is revolved around line x=2.

\(V=\pi \int\limits^2_0 {x^4} \, dx \\\)

V=π[x⁵/5]²₀

V=π[(2)⁵/5]

V=32/5 π.

\(V=\pi \int\limits^4_0 {(2^2)_2-(\sqrt{y}^2)_3 } \, dy\\\\ V=\int\limits^4_0 {(4-y)} \, dx\)

V=8π.

when the shaded region revolves the bout x-axis:

\(V=\pi \int\limits^b_a {y^2} \, dx \\\\V=\pi \int\limits^2_0 {y^2} \, dx =\pi \int\limits^2_0 {x^4} \, dx =\pi [\frac{1}{5}.x^5]_0^2\\\\ V=\pi [\frac{32}{5}-0]\)

V=32/5

when the shaded region revolves the bout y-axis:

\(V=\pi \int\limits^c_d [(x^2)_2-(x^2)_1} \, dx \\V=\pi \int\limits^4_0 [(2^2)_2-(\sqrt{y} ^2)_1} \, dy \\V=\pi \int\limits^4_0 {(4-y)} \, dy =\pi [4y-\frac{1}{2}y^2]_0^4\)

V=π[16-8]

V=8π

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