Write the quadratic equation whose roots are 5 and 6 and whose leading coefficient is 5
(Use the letter x to represent the variable.)

Answer and Step-by-step explanation:

First, distribute the 2 to the 4x and 4.

[tex]\frac{8x + 8}{3}[/tex]

This can be the final answer, or you can have it as [tex]\frac{8x}{3} +\frac{8}{3}[/tex].

I'm not sure about the X =5, but I think it is saying that x is equal to 5, so we will plug 5 in to the equation.

[tex]\frac{8(5)}{3} + \frac{8}{3} \\\\\\ \frac{40}{3} + \frac{8}{3} \\\\\\ \frac{48}{3} = 16[/tex]

When x is equal to 5, 16 is the answer.

#teamtrees #PAW (Plant And Water)

The direction of inequality is reversed when you multiply or divide both sides by a negative value.

When expressions are compared using the operators "less than" (), "less than or equal to" (=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.

Example- x + 3 <= 10

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not.

The solution set of an inequality is the set of all solutions.

The solution set of example 1 is the set of all x <= 7. In interval notation, this set is (-inf, 7], where we use inf to stand for infinity.

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No, 9x2 42x 49 is not a perfect square trinomial.

Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."

No, 9x2 42x 49 is not a perfect square trinomial. A perfect square trinomial is a polynomial of the form a2 + 2ab + b2,

where a and b are numbers or variables.

9x2 42x 49 does not fit this pattern, as it does not involve two terms whose sum is multiplied by itself.

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a) This part is already complete I think..

b) This is a cuboid and lateral surface area of cuboid is: 2(lb +bh + hl)

= 2( 10 × 3 + 3 × 7 + 7 × 10)

= 2(30 + 21 + 70)

= 2 × 121 = 242 cm²

Now, the area of top & bottom: lb

= 2 × 10 × 3

= 60 cm²

Neglecting the top & bottom surface area of cuboid:

= 242 - 60

= 180 cm²

c) The total surface area us 242.. I have already done that part above...

__________________________

If i have done something wrong.. please lemme know :)

multiple 5x 3 3/4 then change to an improper fraction

Answer: its is 300 hope this helps Pls give me brainly

Step-by-step explanation: Remember that the tens place is two moves from the left of the decimal point (if it exists). To round to the nearest ten (nearest 10), we use the whole numbers place to determine whether the tens place rounds up or stays the same.

Solution steps:

Step 1: Locate and underline the ten place (0) and look to the right (3):

303

Step 2: The digit to the right (3) is 4 or below. So, we replace it by a 0 (zero), then we get 300 as the answer.

In short: 303 rounded to the nearest ten is 300.

Answer:

30/100 X $60= $18.

The original price will be $60 + $18 = $78.

Answer:

48

Step-by-step explanation:

I'm assuming all the points are on one line..

In that case you'd subtract the big segment (67) by the little segment (19) to get the other little segment

When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

The coordinate point's size is specified as (-3, -1).

The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)

Consequently, A"s coordinate would be (-6, -2)

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Answer:

To find the area of a trapezium you do 1/2(a + b)h

Step-by-step explanation:

When these equations are solved, the value of x is 4 and the value of y is 3. Therefore, the value of x + y = 7.

To solve the system of equations, we will use the elimination method.

First, we multiply the first equation by 3 and the second equation by 5.

3(3x + 5y = 9)

5(5x + 3y = 7)

Then, we add the equations together:

9x + 15y = 27

25x + 15y = 35

Now, we subtract the second equation from the first to eliminate the x terms:

-16y = -8

y = 0.5

Next, we plug this value for y into one of the original equations and solve for x:

3x + 5(0.5) = 9

3x = 8.5

x = 2.83

Finally, we plug the values of x and y into the original equation to verify that they are correct:

3(2.83) + 5(0.5) = 9

So, the value of x is 2.83 and the value of y is 0.5. Therefore, the value of x + y = 2.83 + 0.5 = 3.33.

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Therefore, the equation that best fits these scatter plot facts as the answer to this problem is y=661-0.1x.

The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.A scatter plot is a specific type of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that appear showing any associations between the data.

y=661-0.1x is the equation whose solution best fits this data.

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Answer:

The sine of the opposite angle

Answer: c=23

Step-by-step explanation: Honest guess

Answer:

Eva spends £35 in a month.

Step-by-step explanation:

We know that Eva gets £42 a month for her allowance and for every £5 she spends, she saves £1.

We are looking to find out how much money does she spend in a month.

To calculate this, we can use the following formula:

Spent money = Allowance - (Allowance / (5 + 1))

Plugging in the known values:

Spent money = 42 - (42 / (5 + 1))

Spent money = 42 - (42 / 6)

Spent money = 42 - 7

Spent money = 35

So, Eva spends £35 in a month.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The sides marked on the triangle are adjacent to and opposite the given angle. The mnemonic SOH CAH TOA is intended to remind you which trig functions relate which sides. The one applicable here is TOA:

  Tan = Opposite/Adjacent

Using the values on the diagram, we have ...

  tan(65°) = 18/y

Multiplying by y/tan(65°) gives ...

  y = 18/tan(65°)

  y ≈ 8.3935 ≈ 8.4

65 seats in 20th row.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.

Given,

No. of seats in 3rd row = 31

No. of seats in 6th row = 37

Seats increase at a constant rate

Let k is the rate of increment.

Difference between no. of seats = k × difference between no. of rows

Difference of seats in 3rd and 6th rows = k difference between the no. of rows

37 - 31 = k ×(6-3)

6 = 3k

k = 2

Thus, we can determine

Difference between the no. of seats is twice the difference between the no. of rows.

Difference between 6th and 20th row = 14 rows

Hence the difference between number of seats = 2 × 14 = 28 seats.

No. of seats in 20th row = No. of seats in 6th row + 28 seats

No. of seats in 20th row = 37 + 28 = 65

Hence, there will be 65 seats in 20th row.

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If 400 people attend the convention,

the food will last for 3 days.

Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant.  Sometimes, it is also known as inverse variation.

That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1

Given,

Food for 300 people will Last for 4 days.

Attending people = 400

Let the food for 400 will last for x days.

According to the question,

300 × 4 = 400 × x

x = 300 × 4 /400

x = 3

Hence, the food will last 3 days,

if 400 people attend the convention.

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The total amount in the bank after the specific number of years is;

9.  $476. 1

11. $7, 128. 8

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

9.Principal amount = $450

Interest rate = 1.45

Time = 5

Substitute the values into the formula

SImple interest = $450 ×1. 45× 5/100

Multiply the values, we get;

Simple interest, I = 2610/100

Divide through

Simple interest = $26. 1

Total amount = $450 + $26.1 = $476. 1

11. Principal amount = $5600

Interest rate = 3.9

Time = 7 years

Substitute the values

Simple interest = $5600× 3. 9 × 7/100

Multiply the values

Simple interest = 152,880/100

Simple interest = $1528. 8

Total amount = $7, 128. 8

Hence, the values are $476. 1 and  $7, 128. 8

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Answer:

sum of angles = 40 + (8x + 4) + (3x + 4) = 180

Collecting all similar terms, the equation above becomes

11x + 8 = 140 ---> x = 12

Therefore. angle S = 3x + 4 = 3(12) + 4 = 40

The solution for x in the equation given as x² = 1/4 is (b) x = ±1/2

From the question, we have the following parameters that can be used in our computation:

An equation

The equation as poorly stated in the question is represented as

x2=14

When written properly

We have the following representation

x² = 1/4

Solving further, we need to take the square root of both sides of the equation

So, we have the following representation

√x² = ±√1/4

Evaluate the exponents on the left-hand side

So, we have the following representation

x = ±√1/4

Evaluate the exponents on the right-hand side

So, we have the following representation

x = ±1/2

Hence, the solution is (b) x = ±1/2

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When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.

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Answer: B. 45/100 & D. 9/20

Step-by-step explanation:

100-55=45

45/100 works

45/5 = 9

100/5 = 20

9/20 is a simplified 45/100

Answer:

By using the Pythagorean theorem, the sides form a right triangle:

36^2 + 15^2 = 39^2

Here it is . Sorry for bad handwriting

Answer:

1) c. AD || CE

2) solve them both first:

3y + 1 = 6x + 4                2y + 1 = x - 9

3y = 6x + 3                     2y = x - 10

y = 2x + 1 .                      y = 1/2x - 5

Parallel lines should have the same slope and they are definitely not the same line, so both A and C are eliminated

Perpendicular slopes should be negative reciprocals of each other. If they were negative reciprocals one slope would be either -2 or -1/2, which means that they're not perpendicular either.

The answer is D, neither parallel nor perpendicular.

3) to find the midpoint of a line, add the x coordinates and divide by 2 and add the y coordinates and divide by 2.

[tex](\frac{-6+1}{2},\frac{1+8}{2} )\\\\=(\frac{-5}{2},\frac{9}{2} )\\\\=(-2\frac{1}{2} ,4\frac{1}{2} )[/tex]

The answer is D.

4) d. GB || HC

5) d. 345.6

[tex]A=2\pi rh\\\\A=2\pi (5)(11)\\\\A=2\pi (55)[/tex]

A ≈ 345.58 ≈ 345.6

6) first change the other equation (4x + 2y = 10) to slope-intercept form:

2y = -4x + 10

y = -2x + 5

because the line must be parallel, it has to have a slope = -2

That automatically eliminates all answers except for D, so you don't even have to do the work to make the other equation.

7) best bet is a. EH and BC are coplanar, but I'm really not sure

8) d. DB and HF

9) first change the other equation (4x - 6y = 15) to slope-intercept form:

-6y = -4x + 15

y = 2/3x - 5/2

slope of the perpendicular line should be -3/2

y = -3/2x + a

9 = -3/2(6) + a

9 = -9 + a

a = 18

y = -3/2x + 18

which is the same as y - 9 = -3/2(x - 6), which is A

Answer:

Add 3 to both sides of the equation

Solution:

The first step is to basically realize that all it's asking you to do is to find a way to make the expression on the left ([tex]x^2 - 8x + 13[/tex]) into an expression that is a perfect square. So what number should you add to both sides such that [tex]x^2 - 8x + (13 + j)[/tex] can be factored into [tex](x-p)^2[/tex] ? Well, we can approach it like this:

Since [tex](x-p)^2[/tex] can be turned into [tex]x^2 -2px + p^2[/tex], and our original form was [tex]x^2 - 8x + (13 + j)[/tex], we quickly realize that [tex]-2px = -8x[/tex]. From there, we can easily tell that [tex]p = 4[/tex]

Plug this into our last value [tex]p^2[/tex] to get 16. Therefore, if we compare this with our original equation again [tex]x^2 - 8x + (13 + j)[/tex], we notice that 13 + j = 16.

Thus, j = 3 for the last answer.

Add 3 to both sides of the equation.

Note: With more practice, you will quickly gain enough intuition to notice that [tex]x^2 - 8x + 13[/tex] is very close to [tex]x^2 - 8x + 16[/tex] which can be factored into [tex](x-4)^2[/tex]. But for now, the solution above will suffice. I hope this helps :))

The arc length AB of the given circle = 11.16 m.

In the given circle,

Radius (r) = 8 m

Sector angle (θ) = 80 degree

We have to find arc length AB

Since we know that,

A curve contains an arc. A circle is the most common example of an arc, yet it may also be a section of other curved forms like an ellipse.

We also know that,

Length of arc of circle = (θ/360)x2πr

                                     = (80/360)x2x3.14x8

                                     = 11.16 m

Hence,

Required arc length of AB = 11.16m

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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.

A few more constant examples are :

The number of days in a week represents a constant.

Substitute:

m*o+b=18

m+b=20

Apply Zero Property of Multiplication:

b=18

m+b=20

Substitute into one of the equations:m+18=20

Rearrange unknown terms to the left side of the equation:m=20-18

Calculate the sum or difference:m=2

The solution of the system is:

b=18

m=2

The answer is b=18 m=2

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Answer:

70%

Step-by-step explanation:

20-6=14.

14/20=0.7

0.7=70%

(tip, multiply the decimal by 100 to find percents. 0.7×100=70