What is the nature of the roots for the given quadratic equation 5x 2 − 2x − 3 0?.

The inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99 ≤ 11.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Therefore, the inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99g ≤ 11.

where a= Apple

g = grape.

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Algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations.

Algebraic expressions: An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. For example, 3x + 2y is an algebraic expression that contains the variables x and y and the operations of addition and multiplication.

Algebraic equations: An algebraic equation is a statement that shows two algebraic expressions are equal. For example, 3x + 2y = 12 is an algebraic equation that shows the left-hand side (3x + 2y) is equal to the right-hand side (12).

To write an algebraic expression or equation, you need to follow these steps:

Identify the numbers and variables in the problem.

Write the problem using mathematical symbols and operations.

Use the correct order of operations (PEMDAS) to simplify the expression or equation.

Use the equal sign (=) to write the equation.

For example, if you are given the problem "Three times a number plus two times another number equals 12", you can write the algebraic equation as:

3x + 2y = 12

In this equation, x and y are the variables and 3 and 2 are the coefficient. The equation represents the relationship between x and y and it can be used to solve for one of the variables if the other one is known.

Therefore, In short, algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations. To write an algebraic expression or equation, you need to identify the numbers and variables in the problem, use mathematical symbols and operations, use the correct order of operations and use the equal sign (=) to write the equation.

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A triangle with a right angle is a 3 4 5 triangle.

A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.

The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.

So the right angle triangle is a triangle with sides of 3, 4, and 5.

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Answer: You multiply the 2 given numbers together

Step-by-step explanation: I hope this helped!

The formula for finding the axis of symmetry for a quadratic function in standard form is y = a (x-h)² + k

The term axis of symmetry in math is defined as an imaginary straight line that divides a shape into two identical parts hereby creating one part as the mirror image of the other part.

Here we need to identify the formula for finding the axis of symmetry for a quadratic function in standard form.

According to the definition of axis of symmetry, the general formula is written as

Here the quadratic equation in vertex form is written as,

=> y = a (x-h)² + k

Here the values (h, k) refers the vertex of the parabola.

And here we have also given that the axis of symmetry formula is x = h.

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Step-by-step explanation:

a function with a single input variable x is usually defined like

y = f(x) = expression in x

to "solve" it means either to have a value for x and then calculate y.

or to have a value for y and find the corresponding value for x, so that f(x) = y. this usually involves finding and using the inverse function of f(x).

the details depend on the functions and operations used in the function expression.

Step-by-step explanation:

the area of a rectangle is

length × width.

so, it's simply a problem of multiplying 2 fractions.

it is

2 3/5 × 3 1/4

first we need to convert the numbers into true fractions.

2 3/5 = (2×5 + 3)/5 = 13/5

3 1/4 = (3×4 + 1)/4 = 13/4

the beauty of a multiplication (compared to addition) is that we don't need to bring the fractions to the same denominator. we can simply calculate with what they are.

you remember,

a/b × c/d = (a×c)/(b×d)

therefore,

13/5 × 13/4 = (13×13)/(5×4) = 169/20 =

= (8×20 + 9)/20 = 8 9/20

the area of the rectangle is 8 9/20 in²

The standard deviation of the sampling distribution of a sample proportion using the formula σ^p=√p(1−p)N σ p ^ = p ( 1 − p ) N. The standard deviation of the sampling distribution of a sample proportion is about 0.054.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Checkpoint 4 will be higher than Checkpoint 3 by 108.

In our question, it is given that the Checkpoint 4 value is -99 and the Checkpoint 3 value is -207.

We will use Subtraction. What is Subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller. For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes. This can be expressed as a subtraction formula: 9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.

Subtracting the value of Checkpoint 3 from Checkpoint 4, we get:

Checkpoint  - Checkpoint 3 = -207 -(-99)

= -207 + 99 = 108.

Therefore Checkpoint 4 will be higher than Checkpoint 3 by 108.

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The equation -3p + (1/8) = (- 1/4) holds true for p = 0.125.

The equation is as follows:

-3p + ( 1/8 ) = ( - 1/4 )

The denominators of the two terms are different on the left-hand side of the equation.

The LCM of 1 and 8 is therefore 8.

Therefore,

- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )

- 24p / 8 + 1 / 8 = - 1 / 4

( - 24p + 1 ) / 8 = - 1 / 4

Add 8 to both sides of the equation now.

We get,

[ ( - 24p + 1 ) / 8 ]

× 8 = ( - 1 / 4 ) × 8

- 24p + 1 = - 8 / 4

- 24p + 1 = - 2

Add 1 to each side of the equation, then

- 24p + 1 - 1 = - 2 - 1

-24p = - 3

Subtract 24 from each side of the equation now.

- 24p / 24 = - 3 / 24

- p = ( - 1 / 8 )

On each side of the equation, multiply by -1.

( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 ) ( - 1 )

p = 1 / 8

p = 0.125

The equation will be true for p = 0.125.

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Answer:

f=32

Step-by-step explanation:

11f = 352

11x32=352

Answer:

[tex] \sf \: f = 32[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of f.

The equation is,

→ 11f = 352

Then the value of f will be,

→ 11f = 352

→ f = 352 ÷ 11

→ [ f = 32 ]

Hence, the value of f is 32.

Answer:

A, C, E

Step-by-step explanation:

No, 45 and 36 are not a Co-prime numbers, because the two numbers have a common prime factor i.e., 9 .

A co-prime number is a number that has exactly one common divisor, which is 1. This means that a pair of numbers is co-prime if their greatest common divisor is 1. Consider x and y are two positive integers, they are called relatively prime if and only if their only common divisor is 1, so gcd(x, y) = 1. There are two numbers 45 and 36. First we determine the divisors of both numbers, then check the greatest common divisor. So, the factors of 45 are 1,3,5,9,15,45.

=> 45 = 1× 3×3× 5

and factors of 36 are 1, 3,2,4,6,9,12,36

=> 36 = 1×2×2×3×3

Now, greatest commen factor between 45 and 36 is 9, i.e., gcd(45,36) = 9 ≠ 1. Therefore, 45 and 36 are not co-prime numbers.

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Complete question:

Are 45 and 36 a Coprime number?.

A possible tape diagram that shows the proportion of muffins with and without chocolate is one that displays 1/4 or 10 flavors with chocolate and 30 flavors without chocolate.

This is a simple diagram that uses segments of a tape to illustrate fractions.

It is known 25% of the flavors have chocolate, but let's calculate the exact number:

40/100 = 0.4 x 25= 10 flavors have chocolate and therefore 30 flavors do not have chocolate.  

Based on this, here is the diagram (green shows the chocolate flavors):

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The tip left by the family at the restaurant is 18.48% of the total bill.

To determine the percentage of the tip, we need to divide the amount of the tip by the total bill, and then multiply by 100 to get the percentage.

The amount of the tip can be calculated by subtracting the cost of the bill from the total amount paid: $49.77 - $42 = $7.77

So the percentage of the tip is:

$7.77 / $42 x 100 = 18.48%

Therefore, the tip left by the family at the restaurant is 18.48% of the total bill.

The percentage is a relative term that expresses a number as a fraction of 100. It is commonly used to express a proportion or rate in terms of a hundred. For example, 45% is equal to 45 out of 100, or 0.45. The percentage can be used to represent any ratio, such as a ratio of two numbers, a fraction of a whole, or a proportion of a total.

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Yes, Y = -3x + 10 is a linear function.

A linear function is a function that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The equation Y = -3x + 10 can be written in this form, with m = -3 (the coefficient of x) and b = 10 (the constant term).

Linear functions represent straight lines on a graph, and their slope and y-intercept can be used to determine the characteristics of the line, such as its direction and position. In this case, the slope of the function is -3, which means that for every unit increase in x, there is a corresponding decrease of 3 units in y. The y-intercept of this function is (0,10), which means that the line crosses the y-axis at the point (0, 10)

In summary, Y = -3x + 10 is a linear function because it can be written in the form of y = mx + b, and it represents a straight line on a graph.

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Answer: (9.5, 24)

Step-by-step explanation:

10x + 7y = 263           (1)

4x + 8y = 230              (2)

Multiply (1) by 4 and (2) by 10:

40x + 28y = 1052             (3)

40x + 80y = 2300              (4)

Do (4) - (3):

52y = 1248

y = 24

x = 9.5

(x, y) = (9.5, 24) :>

the required equation is 5x - 6y + 5z = 7

Given that;

points : (1, 4,4) and (-4, 1,2).

mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]

⇒ midpoint : ( -3/2, 3/2, 3 )  

                       x₀    y₀    z₀

Direction vector n = [-4-(1)], [  1-4], [ 2-4]

⇒ Direction vector n = < -5, -3, -2 >

General equation plane : n(x-x₀, y-y₀, z-z₀) = 0

so we substitute

⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0

⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0

⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0

⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0

⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2

⇒ 5x - 6y + 5z = 7

Therefore, the required equation is 5x - 6y + 5z = 7

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Answer:Answers below

Step-by-step explanation:

The average age of the zebras at the zoo can be found by adding up all of the ages and dividing by the number of zebras.

In this case, the ages of the zebras are 8, 11, 17, 7, 19.

To find the average age, we add up all of the ages: 8 + 11 + 17 + 7 + 19 = 62

Then we divide by the number of zebras (5): 62/5 = 12.4

So, the average age of the zebras at the zoo is 12.4 years old.

To find the standard deviation, we first need to find the variance.

The variance is the average of the squared differences from the mean.

We can find the variance by taking each value, subtracting the mean, squaring the result, and dividing by the number of zebras.

The standard deviation is the square root of the variance

So, the standard deviation of the zebras age is difficult to calculate by hand, but we can use a calculator to find the standard deviation, which is approximately 4.345 years.

Rounding to the nearest tenth:

The average age is 12.4 years old

The standard deviation is 4.3 years

For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is, 18/60.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Total number of tossing a number cube = 60

Here, Number of times greater than 4 comes up = 10 + 8 (frequency of is 10 and frequency of 6 is 8)

Hence, Number of times greater than 4 comes up = 18

Thus, Probability of getting number greater than 4

=  (frequency of getting 5 and 6) / (total number of trials)

Hence, Probability of getting number greater than 4  = 18 / 60                                                                      

Therefore, For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

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The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.

The following expressions are polynomials:

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

Describe polynomials.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers.

Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

These expressions are now:

A. 6y^2 + 5x

B. (7x^2 + 8) / 4x

C. (y^2 + 3x ^1/3) / 4

D. (7y^2 + 9x) / 4

Here, we can observe that there are just two polynomial expressions.

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

The non-polynomial expressions include,

B. (7x2 + 8/ 4x) contains a variable in the numerator.

C. (y2 + 3x 1/3) / 4 - This exponent has a fractional exponent.

Consequently, the polynomial expressions are,

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

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The required number of Peppermint candies in each bag is 8.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of peppermint candies be x in each bag,
Butterscotch candies in 5 bags = 5 × 4 = 20 candies
Peppermint candies in 5 bags = x × 4 = 4x candies

According to the quesiton, Altogether, the bags contain 52 candies.
20 + 4x = 52
x = 8

Thus, the required number of Peppermint candies in each bag is 8.

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Answer:

.125%

Step-by-step explanation:

Answer:

To find the percent of tourists buried up to their neck in sand, you can divide the number of buried tourists by the total number of tourists and multiply by 100.

12 buried tourists / 9,600 total tourists = 0.00125

0.00125 x 100 = 0.125 or 12.5%

So, 12.5% of the tourists were buried up to their neck in sand.

The slope intercept form of the equation of the line graphed on the coordinate plane below will be y=-3x -1.

As we know, The slope intercept form of a straight line is y=mx + c, where m is the gradient which is the Tanθ where θ is the angle between the line and the x-axis. And C is the interception point on the y-axis.

To find the gradient, we can calculate Δy/Δx. From the graph given we can take two points on the line with the coordinates (1,-4) and (0,-1). From this, we can calculate the gradient :

⇒[tex]\frac{(y2-y1)}{(x2-x1)}[/tex]

⇒[tex]\frac{(-1)-(-4)}{0-(1)}[/tex]

⇒-3

And , from the figure we can see the line is intersecting the y-axis -at -1.

So, putting the values in y=mx+c will give us y=-3x -1

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Answer:

£1885.71

Step-by-step explanation:

Reducing by 30% is doing this: 100% - 30% = 70% = 0.7

Reducing a price by 30% is the same as multiplying the price by 0.7

Adding 17.5% is doing this: 100% + 17.5% = 117.5% = 1.175

Adding 17.5% to a price is the same as multiplying the price by 1.175

Let the original price be x.

1.175 × 0.7 × x = £1551

x = £1551/(1.175 × 0.7)

x = 1885.71

Answer: £1885.71

The initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink based on the query we have;

The roller skating rink's fees are comprised of a skate rental fee and an hourly rate.

Skating for two hours will cost you a total of $9.50.

Five hours of skating will cost you $18.50 in total.

Skating's overall cost and its duration in hours are related in a linear fashion.Let 'x' be the number of hours spent skating, and 'y' denote the overall cost;

The equation has the form y = mx + b.

Where;

m = The linear relationship's rate of change

b = The starting point (y-intercept)

X = 2 and Y = 9.50

Consequently, we can write;

9.50 = 2·m + b..(1) (1)

X = 5 and Y = 18.50

Consequently, we can write;

18.50 = 5·m + b..(2) (2)

Equation (1) minus equation (2) results in;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

m = 3.0 is the rate of change.

Likewise, we have;

We obtain from equation (1);

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The starting point is 3.50.

As a result, the initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

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By applying the division formula, the number of times the ferry crossed the river would be 6 times.

To divide something means to split it into two or more equal pieces, areas, classes, categories, groups, or divisions. Dividing something means to give each component to a separate group, or to create equal parts from the whole. When doing division, the resulting value may or may not be an integer. The final result may occasionally be expressed as a decimal.

To calculate the division, we can use this following formula:

Dividend ÷ Divisor = Quotient + Remainder.

Where:

Dividend = the number, which is being divided

Divisor = the number, which divides the number (dividend) into equal parts

Quotient = the result of the division operation

Remainder = the leftover number in the division operation.

In this case, we are given that:

Dividend = 150

Divisor = 25

Thus, the number times the ferry crossed the river would be:

= 150 ÷ 25

= 6

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Answer:

Nabila has $25 dollars.

Hasan has $19 dollars.

Tarek has $50 dollars.

Step-by-step explanation:

Let's say Hasan has "x" dollars at first. The question tells us that Nabila has six more dollars than Hasan has. This means that Nabila has "x + 6" dollars. The last given information is that Tarek has two times what Nabila has. So, Tarek has "2x + 12" dollars, basically.

Then, we can add up all these amounts to find out the result for each person.

We found what is "x". This means that we actually found the answer.

Hasan had "x" dollars so he has $19 dollars.

Nabila had "x + 6" dollars so she has $25 dollars.

Finally, Tarek had "2x + 12" dollars or two times of what Nabila has so he has $50 dollars.