Write a quadratic equation in the form x^2+bx+c=0 that has the following roots: {-9,3}

Answer: y = -2/3x+4

Step-by-step explanation:

negative slope

y intercept (0,4)

4th answer choice.

Answer:

D.  

Step-by-step explanation:

It's really blurry but here's what I did

Pick two random points:

(0, 4) and (6,0) is what I picked personally.

Calculate slope: rise/run = [tex]\frac{0 - 4}{6 - 0} = \frac{-4}{6} = \frac{-2}{3}[/tex]

b is the y-int at 4 therefore your equation is [tex]y = \frac{-2}{3}x + 4[/tex]

The degree measure is which is equivalent to [tex]\frac{7 \pi}{11}[/tex] is 114.54°.

The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.

A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.

The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.

Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.

= [tex]$ \frac{7 \pi}{11} \times \frac{180}{\pi}[/tex]

= [tex]$ \frac{7 }{11} \times 180[/tex]

=[tex]$ \frac{1260}{11}[/tex]

= 114.54°

Therefore, the correct answer is 114.54°.

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Full question:

When the discriminant b² - 4ac is greater than zero and also a perfect square, the nature of roots of the quadratic equation ax² + bx + c = 0 will be real and distinct.

A perfect square means that the discriminant can be written as a product of two equal factors, for example (x+y)^2 = x^2 + 2xy + y^2. In this case the roots can be easily calculated by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this scenario, the square root of the discriminant will be a real number and not a complex number, and the equation will have two distinct solutions for x. This means that the graph of the equation will cross the x-axis twice.

It's important to notice that the values of a,b and c also play an important role in the nature of the roots.

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The equation's solution yields -4/3 for x. Rhoda is the wrong, for this reason.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions.

Equation given: 4(x-8)=7 (x-4).

Here is how to answer the given equation:

4x-32=7x-28

7x-4x=-32+28

3x=-4

x=-4/3

Kylie starts off with a first step that yields the result 4x-32=7x-28. Using a first step that yields 4x-8=7x-4, Rhoda uses.

The equation's solution yields -4/3 for x. Rhoda is the wrong, for this reason.

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There are 12 red counters and 18 blue counters in the bag.

We can use the formula for conditional probability to find the number of red and blue counters in the bag.

The probability of both counters being blue is:

P(blue and blue) = P(blue | blue) * P(blue) = (y/ (x+y)) * (y-1) / (x+y-1) = 57/100

We can then use this equation to find the value of y:

y = ((x+y) * 57/100) / ((x+y-1) * 100/57)

We can also use the equation:

P(red | blue) = P(red and blue) / P(blue) = P(red) * P(blue) / P(blue) = x * y / (x+y)

We can then use this equation to find the value of x:

x = (57 * (x+y)) / (100 - 57)

Now we have two equations with two variables:

y = ((x+y) * 57/100) / ((x+y-1) * 100/57)

x = (57 * (x+y)) / (100 - 57)

We can use the first equation to solve for y in terms of x and substitute into the second equation:

x = (57 * (x + (((x+y) * 57/100) / ((x+y-1) * 100/57)))) / (100 - 57)

Solving for x, we get x = 12 and y = 18

Therefore, there are 12 red counters and 18 blue counters in the bag.

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Therefore, the expression mR > 90°, mS + mT 90°, mR > mT and mR > mS comes out to be true for the solution to the right angle triangle problem.

Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides from ends to ends at such a single point. Three angles in the triangle combine to form a 180-degree angle.

Here,

An RST is a triangle.

This means that m∠R+m∠S+m∠T = 180° and m∠S+m∠T = 180° - m∠R.

It is given that mvR > m∠S + m∠T.

'- m∠R' '- (m∠S + m∠T)' 

The formula is changed to 180°-(mS + mT) and 180°-(mR + mS) by appending 180 degrees to both sides.

(m∠S + m∠T) - 180 degrees

The angle becomes 180° by multiplying m∠S + m∠T on both sides.

=>2(m∠S+m∠T) < 180°

=> m∠S+m∠T < 90°

M R > 90° because M ∠R + M∠ S + M ∠T = 180°.

Yet again, mvR > m∠S + mT.

=> "m∠R > m∠T," "m∠R > mS," etc.

This means that the first, second, third, and fifth options are correct.

The fact that m∠S = m∠T can only happen when m∠R=90° should be highlighted

This is why m∠S = m∠T is inaccurate.

Furthermore, there is not enough proof to prove that m∠S > m∠T.

Because of this, mS > mT is likewise incorrect.

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Step-by-step explanation:

what happen if a body is projected at an angle of 75 to the horizontal then it is a projector Once More with the same initial speed as an angle of 15 so he wants me to calculate the horizontal Range and I don't know have

Answer:

y > -14

Step-by-step explanation:

4y < 5y + 14

Subtract 5y from both sides of the < sign:

4y - 5y < 5y - 5y + 14

-y < 14

Divide both sides by -1:

y > -14 is the answer.

Note, in the last step, the sign flips because we are dividing by a negative

On the Richter scale is 1258.93 times as intense as a standard earthquake.

The Richter scale is a base-10 logarithmic scale, which means that each order of magnitude is 10 times more intensive than the last one. We have,

the an earthquake measuring 3. 1 on the Richter scale.

On Richter Scale, A = log(I/Iₛ)

here, A ---> amplitude

I --> intensity of earthquake

Iₛ ---> standard intensity of earthquake

As, A = 3.1

=> 3.1 = log(I/Iₔ)

Taking anti-logarithm both sides

=> 10³·¹ = I/Iₛ

=> 1258.93 = I/Iₛ

=> I = 1258.93 Iₛ

Therefore, the earthquake with measuring 3.1 on Richter scale is 1258.93 times as intense as a standard earthquake.

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The seven types of symmetry are Euclidean, Reflectional, Point reflection, Rotational, Translational, Glide reflection, Helical and Double rotation symmetry.

In math the term symmetry is defined as one shape is exactly like the other shape when it is moved, rotated, or flipped.

Here we need to identify the seven types of symmetry.

As per the definition of symmetry here we have identified the types of symmetry as are possible for a geometric object depend on the set of geometric transforms available and on what object properties should remain unchanged after a transformation.

They are listed as follows, Euclidean symmetries, Reflectional symmetry, Point reflection and other involutivity isometries, Rotational symmetry, Translational symmetry, Glide reflection symmetry, Helical symmetry and Double rotation symmetry.

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Answer:[-11, ∞]

The range of the function f(x) = 3x2 + 6x - 8 is [-11, ∞].

Step-by-step explanation:

Answer:

31.875 m

Step-by-step explanation:

We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.

The volume of the well is given by the formula for the volume of a cylinder:

V = πr^2h

where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).

V = π(1.5)^2(21) = 42.5π m^3

The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:

V = 1/3 πr^2h

where r is the radius of the base of the cone (4 m) and h is the height of the embankment.

V = 1/3π(4)^2h = 4/3πh m^3

Now we know that the volume of the embankment is equal to the volume of the well:

V = 42.5π m^3 = 4/3πh m^3

Then we can solve for h by dividing both sides by 4/3π:

h = 42.5π m^3 * 3/4π = 31.875 m

So the height of the embankment is 31.875 m.

1. On simplifying the radical expression √28 the result is 2√7.

2. On simplifying the radical expression √40 the result is 2√10.

3. On simplifying the radical expression √72 the result is 6√3.

4. On simplifying the radical expression √99 the result is 3√11.

What is a radical expression?

Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.

The first radical expression is -

√28

Take the LCM of 28.

The LCM is obtained as - 2 × 2 × 7.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 2√7.

Therefore, the expression is 2√7.

The second radical expression is -

√40

Take the LCM of 40.

The LCM is obtained as - 2 × 2 × 2 × 5.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 2√10.

Therefore, the expression is 2√10.

The third radical expression is -

√72

Take the LCM of 72.

The LCM is obtained as - 2 × 2 × 2 × 3× 3.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 6√3.

Therefore, the expression is 6√3.

The fourth radical expression is -

√99

Take the LCM of 99.

The LCM is obtained as - 3 × 3 × 11.

The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.

So, the simple form is 3√11.

Therefore, the expression is 3√11.

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The sum of given polynomials (m + n + 3) + (m + n + 4) is 2m + 2n + 7

A polynomial is an equation composed of more than two algebraic terms, particularly the sum of numerous terms containing different powers of the same variable(s)

The polynomials can be added by first organising them in standard form, then grouping like terms together, and lastly simplifying them.

Given the expression:

(m + n + 3) + (m + n + 4)

Now, we have to combine the like terms.

(m + m) + (n + n) + (3 + 4)

Add the coefficients of the same variable:

2m + 2n + 7

The sum of polynomials is 2m + 2n + 7

Complete question:

What is the sum of the polynomials (m+n+3)(m+n+4)

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Answer:

Step-by-step explanation:

Percentage of Phosphorus in Diphosphorus Trichloride is  36.8 %

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Formula of DiPhosphorus trichloride.

P₂Cl₃

Molar mass of the compound = 31 * 2 + 35.5* 3 = 168.5

Percentage of Phosphorus in the compound is = (62/168.5) *100 = 36.8 %

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The equation of the directrix for the parabola y = 18 · x² - 4 · x + 41 is y = 2935 / 72.

In this question we find the case of the equation of a parabola in standard form:

y = a · x² + b · x + c

Where:

This equation must be changed into vertex form:

y - k = C · (x - h)²

Where:

Where the vertex constant is:

C = 1 / (4 · p)

Where p is the distance between focus and vertex.

And the equation of directrix is:

y = k - 1 / (4 · C)

First, write the quadratic equation in standard form:

y = 18 · x² - 4 · x + 41

Second, use algebra properties until vertex form is obtained:

y = 18 · [x² - (2 / 9) · x + 41 / 18]

y = 18 · [x² - (2 / 9) · x + 1 / 81] + 18 · (367 / 162)

y = 18 · (x - 1 / 9)² + 367 / 9

y - 367 / 9 = 18 · (x - 1 / 9)²

Third, find the equation of the directrix:

y = 367 / 9 - 1 / (4 · 18)

y = 2935 / 72

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Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

The subscription has a one-time fee of $30 plus $9 per month, so the total cost per month is $9 + $30 = $39.

Emani plans to spend $210 or less from her summer job on this subscription, so we can write an inequality to represent this situation:

$39x <= $210

Where x is the number of months Emani will be able to purchase the subscription.

To solve for x, we need to divide both sides of the inequality by $39:

x <= (210/39)

x <= 5.38

So Emani will be able to purchase the subscription for a maximum of 5 months, if she wants to spend $210 or less from her summer job.

Note: This is an approximation, since x can't be a decimal. And if you round down to 5 months she will be able to spend $195.

Therefore, Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

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The subscription has a one-time charge of $30 and a monthly fee of $9, making the monthly cost total $9 + $30 = $39 for the subscription.

We can create an inequality to symbolize this circumstance since Emani intends to spend no more than $210 from her summer job on this subscription:

$39x <= $210

Emani will have the option to buy the subscription for x months.

Divide both parts of the inequality by $39 to find the value of x:

x <= (210/39)

x <= 5.38

The graph of the inequality x - 6y > 18 is plotted and attached

Inequality are graphed considering the table of values formed by assigning several values for x

x - 6y > 18

rearranging the equation will result to

x - 18 > 6y

y < x/6 - 3

for x = -6, y < -6 / 6 - 3 = -4

for x = 0, y < 0 / 6 - 3 = -3

for x = 6, y < 6 / 6 - 3 = -2

Table of value

x      y

-6    -4

0      -3

6      -2

the equation: y < x/6 - 3 will have a dashed line and shading is below the line because it has a less than sign

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Answer:

25

Step-by-step explanation:

(-4 + 9) x (8 - 3)

= (5) x ( 5)

= 25

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(-4 + 9) \times (8 - 3)}\\\\\mathsf{-4 + 9 = \boxed{\frak 5}}\\\mathsf{8 - 3 = \boxed{\frak 5}}\\\\\mathsf{= (-4 + 9) \times (8 - 3)}\\\mathsf{= 5\times5}\\\mathsf{= 25}[/tex]

[tex]\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{25}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Based on the unit rate, Brand X costs $0.10 per fluid ounce less than Brand Y.

The unit rate refers to the ratio of one value to the whole.

The unit rate is the average of the values of the data set.

We can compute the unit rate by dividing the total value by the number of units.

The total cost of Brand X for 5 fluid ounces = $3.25

The unit cost of Brand X per fluid ounce = $0.65 ($3.25/5)

The total cost of Brand Y for 8 fluid ounces = $6.00

The unit cost of Brand Y per fluid ounce = $0.75 ($6.00/8)

The difference in the unit cost of Brand X and Brand Y = $0.10 ($0.75 - $0.65)

Thus, we can state that Brand Y costs more than Brand X per unit.

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Step-by-step explanation:

always remember :

the sum of all angles in a triangle is always 180°.

so, in triangle EFD

180 = E + F + D = 37 + 105 + D

D = 38°

since we know that the combination (sum) of B and D is 90° (right angle),

B + D = 90

B + 38 = 90

B = 52°

and now we look at the triangle ABC and its angles to get A, which then in turn gets us I of the triangle A(BD)I.

180 = A + B + C = A + 52 + 83

A = 45°

and that means for A(BD)I

180 = A + (B + D) + I = 45 + 90 + I

I = 45°

FYI : that means that the total triangle is an isoceles triangle (both legs are equally long : AB = DI).

a) The equation would be 25 + 16x = 201.

b) Kallik was a member of the club for 11 years.

What is an equation?

An equation is a mathematical statement that shows the equality of two expressions. It consists of two expressions separated by an equal sign (=), and the goal is to find the values of the variables that make the equation true. Equations can be used to model real-world situations, to describe relationships between variables, or to solve problems.

a. Let's call the number of years that Kallik was a member of the club "x". The equation to model the membership fees can be written as follows:

25 + 16x = 201

b. To solve for the number of years, we can subtract 25 from both sides of the equation:

16x = 176

And then divide both sides by 16:

x = 11

So Kallik was a member of the club for 11 years.

Hence,

a) The equation would be 25 + 16x = 201.

b) Kallik was a member of the club for 11 years.

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So,  the y-intercept of the equation 3x + y = -1 is the point (0, -1).

The y-intercept of a linear equation in the form of y = mx + b is the point at which the line crosses the y-axis, which is the point (0, b). In the equation 3x + y = -1, the y-intercept is the point at which y = -1 and x = 0, which can be found by solving for y when x = 0:

3(0) + y = -1

y = -1

So the y-intercept of the equation 3x + y = -1 is the point (0, -1). This means that the equation of the line passes through the point (0, -1) on the Cartesian plane.

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According to the given statement, 3x^3y^4 represents the length of the room.

Its length w is calculated using the formula h = A/w if you have an area A and a width w. Its length can be determined using the formula h = P/2w if you know its perimeter (P) and width (W). The length is given by h = (d2w2) if the diagonal d and width w are present.

Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.

The area of a square box is length x width, so that we can set up the calculation:

length x (2x³y²) = 6x6y8

To find the length of the court, we can divide both sides by 2x³y²:

length = (6x6y8) / (2x³y²)

so the length of a room is represented by 3x^3y^4

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The complete question is -

Oscar's rectangular room has an area of 6x^6y^8 square units. If the width of Oscar's room can be represented by 2x^3y^2, which of the following represents the length of the room?​

(a)3x^2y^4

(b)3x^3y^4

(c)12x^9y^10

(d)12x^18y^16

Using Pythagoras theorem, The height of the television is 56.65 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

d² = (ax)² + (bx)²

= x² (a² + b²)

⇒ x = √(d²/a²+b²)

length = a . √(d²/a²+b²)

width = b. √(d²/a²+b²)

with an aspect of 16:9,

has an advertised size of 65 inches,

a = 16, b = 9, d = 65

length = 56.65 inches

width = 31.87 inches

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Answer:

[tex]6\frac{3}{4}[/tex] and [tex]3\frac{1}{8}[/tex]

Step-by-step explanation:

I don't know what benchmark fractions are but here's what I did

[tex]4\frac{7}{8} + 1 \frac{7}{8} = 5 \frac{14}{8} = 6 \frac{6}{8} or 6\frac{3}{4}\\5\frac{3}{8} - 2\frac{1}{4} = 5\frac{3}{8} - 2\frac{2}{8} = 3\frac{1}{8}[/tex]

The first question is straight forwards since the fractions have the same denominator, so its simply adding and simplification.

The second questions needs you to find a common denominator (8) and swap the fraction to that of 8 before subtracting

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Kelly pours 1/3 litre of fruit punch into each glass at a party for her chess team.

What does the division do?

divides left-hand operands into right-hand operands while performing a division operation in mathematics.

For instance, 4/2 = 2.

She combined the prescribed amounts of 1 2/5 litres of cranberry juice and 1 3/5 litres of pineapple juice.

The appropriate response to the aforementioned situation would be

⇒ 1 2/5 + 1 3/5

fractionalizing mixed numbers

⇒ 7/5 + 8/5

Consider the LCM in the previous equation.

⇒ (7 + 8)/5

⇒ 15/5

⇒ 3

She then divided the fruit punch equally among the nine cups.

3 litres of fruit punch must now be divided among 9 glasses.

3/9, therefore, equals 1/3 litres of fruit punch.

She, therefore, fills each glass with a third of a litre of fruit punch.

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