write the following quadratic equation to standard form and find a,b,c

1) 2x²=3x
2)4x²-10=5
3)3(x²-4x)=2(x+2)
4)3x(x+2x)=11
5)6x(x-8)=2x²+4​

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is [tex]y = (3x)^{\frac{1}{2} }[/tex]

⇒ [tex]y^{2} = 3x[/tex] ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

[tex]y^{2} - y - 6 = 0[/tex]

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = [tex]\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx[/tex]

= [tex]\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}[/tex]

= [tex][\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} }  }{3}] - [13.5 - 18 - 6 + 12][/tex]

= 6 - 1.5

= 4.5 sq. units. (Answer)

Part A: The type of the quadrilateral of the rooftop is a square

Part B: The length of one side of the rooftop is 19 m

Step-by-step explanation:

Let us revise some notes about quadratic expression

The area of a rooftop can be expressed as 9x² + 6x +1

The rooftop is a quadrilateral

We need to find the type of the quadrilateral and the length of

one side of the rooftop

∵ The area of the rooftop = 9x² + 6x +1

- Check if 9x² + 6x +1 is a perfect trinomial

∵ [tex]\sqrt{9x^{2}}=3x[/tex]

∵ [tex]\sqrt{1}=1[/tex]

∵ [tex](3x)(1)(2)=6x[/tex]

∴ 9x² + 6x +1 = (3x + 1)²

∴ 9x² + 6x +1 is a perfect square trinomial

∵ Perfect square trinomial can represent the area of a square

∴ The quadrilateral is a square

Part A: The type of the quadrilateral of the rooftop is a square

∵ The area of the rooftop is 9x² + 6x +1

∵ 9x² + 6x +1 = (3x + 1)²

∵ Area of the rooftop = 361 m²

∴ (3x + 1)² = 361

- Take square root for both sides

∴ 3x + 1 = 19

∵ The area of a square = (side)²

∵ The area of a square = (3x + 1)²

∴ 3x + 1 is the length of the side of the square

∵ 3x + 1 = 19

∴ The length of the side of the square is 19 m

Part B: The length of one side of the rooftop is 19 m

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Answer:

n = 12 + 19

Step-by-step explanation:

Flip the equation around like this: 12 + 19 = n

Then you are going to add: 12 + 19 = 31

So, n = 31

Hope this helps

-Amelia

There are 120 professors at the university

Step-by-step explanation:

At one really small university:

We need to find how many professors are at the university

Assume that the number of people the university is 100%

∵ 53% of the people in the university are undergraduates

∵ 37% of the people in the university are graduates

∵ There are 100% people in the university

- To find the rest subtract the sum of the undergraduates and

   graduates from 100%

∵ The rest = 100% - (53% + 37%)

∴ The rest = 100% - 90%

∴ The rest = 10%

∴ The rest is 10% from 1200 people in the university

∵ The rest are going for their doctorate

∴ The rest is the number of the professors in the university

∵ The rest is 10% from 1200 people in the university

∴ The number of professors = 10% × 1200

∵ 10% = 10 ÷ 100 = 0.1

∴ The number of professors = 0.1 × 1200

∴ The number of professors = 120

There are 120 professors at the university

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Answer:

8.1 gallons of gas

Step-by-step explanation:

240/9=216/x

simplify 240/9 into 80/3,

80/3=216/x

cross product

3*216=80*x

648=80x

x=648/80

x=8.1

Answer: X= 4

Step-by-step explanation:

24+0.44x=19+1.69x exp equation like:

24+44x/100=19+169x/100

Multiply left and right side of equation with 100

2400+44x=1900+169x

2400-1900=169x-44x

500=125x

x=500/125

x=4

The solution of the equation is 4.

To solve the equation 24+0.44x=19+1.69x, we want to collect like terms and isolate the variable x on one side. This type of equation is a linear equation, not a quadratic equation, since the highest power of x is one. First, let's move the terms containing x to one side and the constant terms to the other side:

Subtract 1.69x from both sides: 24 - 19 = 1.69x - 0.44x

Combine like terms: 5 = 1.25x

Divide both sides by 1.25: x = 5 / 1.25

Solving for x gives us: x = 4

Answer:

8p + 56 + 16q

Step-by-step explanation:

To distribute, we must multiply all numbers/terms inside the paranthesis by '8.'

So:

8(p) = 8p

8(7) = 56

8(2q) = 16q

So your expression would be 8p + 56 + 16q  ^-^

Answer:

[tex]\rm{8p+56+16q[/tex]

Step-by-step explanation:

Hi there!

The Distributive Property states that

a(b+c)=ab+ac

Let's use this property to simplify our expression:

[tex]\rm{8(p+7+2q)[/tex]

[tex]\rm{8p+56+16q[/tex]

Thus, [tex]\rm{8p+56+16q[/tex] is our final answer.

[tex]\star\star[/tex]Hope it helps! Enjoy your day!

[tex]\bold{GazingAtTheStars(:}[/tex]

Answer:

The variables are 'p' and 'c'.

The inequality is: [tex]10p+4c\geq100[/tex]

The graph is plotted below.

Three possible solutions are: (0, 25), (10, 0) and (5, 20)

Step-by-step explanation:

Let the number of pizzas sold be 'p' and number of cookies sold be 'c'.

Given:

Price per pizza = $10

Price per cookie = $4

Minimum amount to be earned = $100

Price for 'p' pizzas sold = [tex]10p[/tex]

Price for 'c' cookies sold = [tex]4c[/tex]

As per question:

[tex]10p+4c\geq100[/tex]

Also, number of pizzas and cookies can't be negative. So,

[tex]p\geq0,c\geq0[/tex]

Plotting the above inequalities on a graph using DESMOS.

The region that is common to all the above inequalities is the solution region and is shown in the graph below.

The solution region also includes all the points on the line.

So, the three possible combinations of solutions can be any 3 points in the solution region. One such combination is:

(0, 25), (10, 0) and (5, 20)

Answer:

13.5

Step-by-step explanation:

2/3=9/x

2x=9*3

2x=27

x=27÷2

x=13.5

Final answer:

There are 13.5 cups of vegetables in the soup.

Explanation:

If the ratio of chicken to vegetables in a soup is 2:3, and there are 9 cups of chicken, we can find the number of cups of vegetables by setting up a proportion. According to the ratio, for every 2 cups of chicken, there are 3 cups of vegetables. Since we have 9 cups of chicken, we want to know how many cups of vegetables correspond to this amount.

Write the ratio of chicken to vegetables as a fraction: 2/3.

Set up a proportion where 2 cups of chicken is to 3 cups of vegetables as 9 cups of chicken is to x cups of vegetables.

2/3 = 9/x

Cross multiply to solve for x: 2x = 9 × 3

2x = 27

Divide both sides by 2 to solve for x: x = 27/2

x = 13.5

Therefore, there are 13.5 cups of vegetables in the soup.

Answer:

Its no Solution

Step-by-step explanation:

If you use elimination both 7x and the 4y will be 0 and you'll get

0=-26 and 0=-2

So

No Solution

sorry for my hand writing

A) exponential is the right answer.

Step-by-step explanation:

The formula used for increase after same number of time is:

[tex]A_t = A_0(1+r)^t\\Here\\A_0\ is\ the\ initial amount\\r\ is\ the\ rate\\and\\t\ is\ time[/tex]

We are given

A_0 = 35000

r = 3%

[tex]A_t = 35000(1+0.03)^t\\A_t = 35000(1.03)^t[/tex]

The function is an exponential function is the value of t can be put equal to 1,2,3,4..... which will increase the final output exponentially

Hence,

A) exponential is the right answer.

Keywords: Functions, Exponential function

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Answer: For number one it's decreasing

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

(∛5)^7

= (5 ^ 1/3)^7

= 5^(7/3)

The cube root of five to the seventh power can be rewritten as a rational exponent as five to the seven thirds power. This is achieved by making the denominator of the exponent the index of the radical and the numerator the power of the radicand.

In mathematics, radical expressions can be rewritten as expressions with rational exponents. In your case, the cube root of five to the seventh power, is represented as [tex]5^(^7^/^3^)[/tex], which is your rational exponent form. So the answer is C: five to the seven thirds power.

To convert a radical expression to an expression with a rational exponent, the denominator of the exponent becomes the index of the radical, and the numerator of the exponent becomes the power of the radicand. In this case, the cube root is the index, which is 3, and the power of the radicand (five) is 7. Hence, five to the seven thirds power.

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The sum of three consecutive odd integers is 76 less then seven times the middle number. The three integers are 17, 19 and 21 respeectively

Since each consecutive odd integer is separated by a difference of  2

Let "n" be the first integer

n + 2 be the second integer

n + 4 be the third integer

Given that the sum of three consecutive odd integers is 76 less then seven times the middle number

Which means,

The sum of ( n, n + 2, n + 4) is equal to 76 less than seven times the middle number ( 7(n + 2))

That is,

n + n + 2 + n + 4 = 7(n + 2) - 76

3n + 6 = 7n + 14 - 76

4n = 68

n = 17

So we get:

First integer = n = 17

Second integer = n + 2 = 17 + 2 = 19

Third integer = n + 4 = 17 + 4 = 21

Thus the three consecutive odd integers are 17, 19 and 21 respeectively

Answer:

1152? 36÷32=1152 I think?

Mr. Hanson needs to multiply the number of students (32) by the number of pencils required per student (36) to find out he needs to purchase a total of 1152 pencils for the school year.

Mr. Hanson needs to calculate the total number of pencils required for his class for the entire school year. With 32 students and the need for each student to have 36 pencils, the calculation is straightforward:

Multiply the number of students by the number of pencils each student requires.

32 students imes 36 pencils per student = 1152 pencils.

Therefore, Mr. Hanson needs to purchase 1152 pencils in total.

By having this quantity of pencils, Mr. Hanson ensures that each student has a pencil for each week of the school year, contributing to a well-prepared classroom environment.

Answer:

Step-by-step explanation:

points that lie on an axis do not lie in any quadrant.  

So point A lies in the  positive x-axis

The origin (0,0) does't lie on any quadrant.

Origin is the point that lies on both x-axis and y-axis

Answer:

So the value of u is [tex]24[/tex] degree.

Step-by-step explanation:

Given;

Three angle [tex]2u[/tex] , [tex](u+18)[/tex] degree and [tex]90[/tex] degree in a Triangle.

We know;

Addition of three angle in a triangle is equal [tex]180[/tex] degree

[tex]2u+u+18+90=180[/tex]

[tex]3u=180-90-18[/tex]

[tex]3u=72[/tex]

[tex]u=\frac{72}{3}[/tex]

[tex]u=24[/tex]

∴ The value of u is [tex]24[\tex] degree.

Answer:

29 feet

2.6 seconds

Step-by-step explanation:

h(t) is a downwards parabola, so the maximum is at the vertex.

t = -b / (2a)

t = -40 / (2×-16)

t = 1.25

h(1.25) = -16(1.25)² + 40(1.25) + 4

h(1.25) = 29

When the ball lands, h(t) = 0.

0 = -16t² + 40t + 4

0 = 4t² − 10t − 1

t = [ -(-10) ± √((-10)² − 4(4)(-1)) ] / 2(4)

t = (10 ± √116) / 8

t = (5 ± √29) / 4

t is positive, so:

t = (5 + √29) / 4

t ≈ 2.6

Answer:

15 3/4 pounds

Step-by-step explanation:

4.5*3.5=15.75

Percent uncertainty is calculated by dividing the uncertainty value by the average value and then multiplying by 100 to get a percentage. In the example of a 5-lb apple bag with a 0.3-lb uncertainty, the percent uncertainty is 6%. If the bag's weight is halved but uncertainty remains unchanged, the percent uncertainty increases.

The question provided presents a situation requiring the calculation of percent uncertainty for the weight of bags of apples. The percent uncertainty is calculated as the uncertainty value divided by the average value, multiplied by 100 to convert it to a percentage.

For example, if a 5-lb bag of apples has an uncertainty of 0.3 lb, the percent uncertainty would be (0.3 lb / 5 lb) × 100%, which equals 6%. If the weight of the bag were to be halved while the absolute uncertainty remains the same, the percent uncertainty would increase.

This is because the same absolute uncertainty represents a larger proportion of a smaller number, thus increasing the percent uncertainty when converted into a percentage.

The algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three" is [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]

Given statement is "the quotient of negative eight and the sum of a number and three"

To write the algebraic expression, follow these steps:

Let "n" be the number

The expression "negative eight" is equivalent to -8

Now look at the statement "the sum of a number and three"

"The sum of a number and three" is equivalent to n + 3

Now put all the statements together:

Quotient means you are dividing. So use division

"The quotient of negative eight and the sum of a number and three" = [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]

Answer: Square

Step-by-step explanation: It has 4 equal sides that are all the same length.

The shape with four equal right angles and sides of the same length is a square, a fundamental concept in Euclidean geometry discussed in middle school mathematics.

The shape that has right angles and sides that are the same length is a square. In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). To identify a square, you can look for these two characteristics. .

The understanding of similar triangles is relevant when considering shapes and their properties, such as when using the properties of similarity to prove that two right triangles are similar based on their equal angles.

Answer:

Thomas still has 1 3/5 suitcases available for his own belongings.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of souvenirs bought by Thomas = 6

Space that each souvenir takes of Thomas suitcase = 1/15

Number of Thomas suitcases = 2

2.  How much room is left for his own belongings in his suitcases?

Let's find out how much space the souvenirs take:

Number of souvenirs * Space that each souvenir takes

6 * 1/15 = 6/15 = 2/5 (Dividing by 3 the numerator and the denominator)

The souvenirs take 2/5 of one suitcase.

Now, we can calculate the room that is left for Thomas' belongings.

2 Suitcases - 2/5 for the souvenirs

2 - 2/5 = 10/5 - 2/5 = 8/5 = 1 3/5

Thomas still has 1 3/5 suitcases available for his own belongings.

Note: Same answer to question 14040097, answered by me.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 8x - 6y - 4 = 0 by adding 8x + 4 to both sides

- 6y = 8x + 4 ( divide all terms by - 6 )

y = - [tex]\frac{4}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{4}{3}[/tex] and y- intercept c = - [tex]\frac{2}{3}[/tex]

To find the x- intercept let y = 0 in the equation and solve for x

- 8x - 0 - 4 = 0 ( add 4 to both sides )

- 8x = 4 ( divide both sides by - 8 )

x = - [tex]\frac{1}{2}[/tex] ← x- intercept

The width of the rectangles is 4.

Step-by-step explanation:

Given that two rectangles have same width. So, let be the two rectangles [tex]R_{1}[/tex] and [tex]R_{2}[/tex] and width of rectangle is ‘x’. So, according to question, we have  

Length of one rectangle , [tex]R_{1}[/tex] = x + 1

Length of other rectangle, [tex]R_{2}[/tex] = x + 2

But we also know that,

                  [tex]\text { Area of rectangle } = \text { Length } \times \text { width }[/tex]

So,  then the area for one rectangle,

                [tex]\text { Area of rectangle } R_{1} = x \times(x+1)[/tex]

Similarly,

                [tex]\text { Area of rectangle } R_{2} = x \times(x+2)[/tex]

So, according to question,

                [tex]\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}[/tex]

                [tex]x \times(x+2) = 4+x \times(x+1)[/tex]

Now, by solving the above equation, we get

                [tex]x^{2}+2 x = 4+x^{2}+x[/tex]

                [tex]x = 4[/tex]

So, from the above equation, we found that width of the rectangle is 4.

Answer:

m = - 8 ± 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

m² + 16m - 8 = 0 ( add 8 to both sides )

m² + 16m = 8

To complete the square

add ( half the coefficient of the m- term )² to both sides

m² + 2(8)m + 64 = 8 + 64

(m + 8)² = 72 ( take the square root of both sides )

m + 8 = ± [tex]\sqrt{72}[/tex] = ± [tex]\sqrt{36(2)}[/tex] = ± 6[tex]\sqrt{2}[/tex]

Subtract 8 from both sides

m = - 8 ± 6[tex]\sqrt{2}[/tex]

Equation: 1.15 c = 40

Solution: $34.78

Step-by-step explanation:

The given is:

We need to write an equation that can be used to find c, and then

find the value of c

∵ The cost of the printer cartage = $c

∵ The computer game costs 15% more than a printer cartridge

- That means add the cost of the cartage by 15% of it to find the

   cost of the computer game

∴ The cost of the computer game = c + 15% × c

∵ 15% = 15 ÷ 100 = 0.15

∴ The cost of the computer game = c + 0.15 c

- The two terms of c (1 + 0.15)

∴ The cost of the computer game = $1.15 c

∵ The cost of the computer game = $40

- Equate the two expressions of the cost of the game

∴ 1.15 c = 40

The equation that can be used to find c is 1.15 c = 40

Solve the equation to find c

∵ 1.15 c = 40

- Divide both sides by 1.15

∴ c = $34.78

The cost of the printer cartridge is $34.78

Equation: 1.15 c = 40

Solution: $34.78

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Answer:

26.

Step-by-step explanation:

15% of 29.90 is 3.90

26+3.90= 29.90

The price of Mr Johnson's lunch bill before the 15% tip paid is $26.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

In order to determine the price before the tip, divide the lunch bill by the percentage tip.

Price before the tip = lunch bill / ( 1 + percentage tip)

29.90 / 1/15 = $26

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Answer: 6x^2-9x-20

Step-by-step explanation:

(3x+4)(2x-5)

6x^2-15x+6x-20

6x^2-9x-20

Answer:

2 milion

Step-by-step explanation:

2,000 x 2,000= 4,000,000

4,000,000÷ 2= 2,000,000

Half the number of square root of a number is 2k is [tex]2k^2[/tex].

Let's break down the problem step by step to find half of the number. We start with the given information: the square root of a number is [tex]2k[/tex]. Our goal is to find half of this number.

Let the number be [tex]x[/tex]. The problem tells us that the square root of [tex]x[/tex] is [tex]2k[/tex].

We write this mathematically as:
[tex]\sqrt{x} = 2k[/tex]

To find [tex]x[/tex], we square both sides of the equation to remove the square root:
[tex]x = (2k)^2[/tex]

Simplify the right side:
[tex]x = 4k^2[/tex]

Now, we need to find half of [tex]x[/tex]. Half of [tex]x[/tex] is:
[tex]\text{Half of } x = \frac{x}{2} = \frac{4k^2}{2}[/tex]

Simplify the fraction:
[tex]\frac{4k^2}{2} = 2k^2[/tex]