What are the solutions of x² - 5x+7=0?
OA. x =
OB. x =
5+3² or x = 5-3i
2
2
5+√2 or x = 5-√2
3
3
5+i√2
2
O C. x =
O D. x = 5+√3
2
or x =
5-i√2
2
or x = 5-i√3
2

Answer: To find the solution of a system of equations, we can either use substitution or elimination method.

For this system of equations, we can use the substitution method:

First, we solve one equation for one of the variables. For example, we can solve the first equation for y: y = -2x - 4

Then, we substitute this expression of y into the second equation and solve for x: 1/2x + 6 = -2x - 4

We can simplify this equation by adding 2x to both sides: 1/2x + 2x + 6 = -4

And then by adding 6 to both sides: 1/2x + 2x + 12 = 2

And then by multiplying both sides by 2: x + 4x + 24 = 4

And then by simplifying: 5x = -20

Finally, we find x = -4

Now that we have found x, we can substitute it back into one of the equations to find y:

y = -2(-4) - 4 = 8 - 4 = 4

So the solution of the system of equations is x = -4 and y = 4

We can check that this solution satisfies both equations.

Step-by-step explanation:

Value of expression 1: 176

Value of expression 2: 32

Are they equivalent? No

Equivalent expressions are expressions that work the same way even though they look different. They have the same value for all values of the variables. They can be transformed into each other using the rules of algebra, such as the commutative, associative, and distributive properties.

Since the value of y is 2

Expression 1: 4y (y + 20)

To evaluate 4y (y + 20), substitute y = 2 into 4y (y + 20). That is:

4*2 (2 + 20) = 8(2+20) = 8(22) = 176

Expression 2: 4y + 24

To evaluate 4y + 24, substitute y = 2 into 4y + 24. That is:

(4*2) + 24  = 8 +24 = 32

Since the value of expression 1 is not equal to the value of expression 2. Thus, they are not equivalent.

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Answer:

1250 in savings

Step-by-step explanation:

Answer:

[tex]C = \dfrac{1}{3} L[/tex]

Step-by-step explanation:

Number of cups of flour/number of loaves = constant, k

We can see this ratio is constant throughout the table

6/2 =9/3 = 15/5 = 3

Therefore the equation can be written as

C/L = 3

or

C = (1/3)L

where C is the number of cups needed to make L loaves

The statement which is not true for the given number line is |a| > b, option(a).

What is a number line?

A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

For the given question,

Point a is to the left of 0, so it is a negative number.

So taking the modulus of a, we get the positive value of a.

But since a is closer to 0 than b, if the positive value of a is less than b.

For example if a = -4 and b is 6

|a| = |-4| = 4 < b

So |a| < b

Therefore the incorrect statement is option(a), |a| > b.

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An ellipse's equation is (x - h)2/a2 + (y - k)2/b2 = 1.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

According to our question-

c is the distance between the center and the focus, and a and b are the distances from the center to the vertices, respectively, in the formula c2 = a2 - b2.

Therefore, we have 12 = 42 - b2.

As a result, 1 = 16 - b2, or b2 = 15.

The final equation is therefore written as x2/16 + y2/15 = 1.

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1) The equation is true for n = $12.30

2) 24 fluid ounces is equivalent to 3 cups.

Here we want to see for which values of n is the equation:

3n = $36.90

true.

To get that,we need to isolate the variable n. To do so, we can divide both sides by 3.

n = $36.90/3

n = $12.30

That is the value of n.

We want to write 24 fluid ounces as cups, we know the relation:

1 fluid ounce = 0.125cups.

Then we can just do the change of units as follows:

24 fluid ounces = 24*(0.125 cups.) = 3 cups.

So there are 3 cups on 24 fluid ounces.

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The range for the given domain is {4, -5, -1, 44}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Here set A is the domain and the images of the elements of set A is range.

Given the function,

f(x) = x² - 5

Domain is {-3, 0, 2, 7}

Domain is the values of x and range is the value of f(x).

If x = -3, f(x) = (-3)² - 5 = 4

If x = 0, f(x) = 0² - 5 = -5

If x = 2, f(x) = 2² - 5 = -1

If x = 7, f(x) = 7² - 5 = 44

So the range is {4, -5, -1, 44}

Hence the set {4, -5, -1, 44} is the range of the function given.

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The  slope of the line with the points (-2/3,-3) and (-1.5,-5/7) is 2.743.

The concept that will be used is the slope. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The slope of  the line passing through the points9 x1 y1) and (x2, y2 ) can be written as :

m= (y2 - y1)/(x2 -x1)

x1 = -2/3 , y1 = -3

x2 = -1.5 , y2 = -5/7

Then substitute the values,

Then the slope = [ (-5/7+3) / (-1.5+2/3 )]

= (16/7)/(-5/6)

=2.743

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Chanice's approximate displacement is 8.60 km as she rides her scooter 7 kilometers north. She has lunch and then travels 5 kilometers east.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides. The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse.

Here,

To find the length of one missing side in a triangle, you can use the Pythagorean Theorem:

a² + b² = c²

7² + 5² = c²

49 + 25 = c²

74 = c²

√74 = c

c ≈ 8.60 km

8.60 km is Chanice's approximate displacement as she drives her scooter 7 kilometres north. She stops for lunch and then drives 5 kilometres east.

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Answer:

The percentage of increase in price is 175%. To calculate this, you can subtract the cost price (in this case, $1) from the selling price ($2.75) to find the profit ($1.75). Then divide that profit by the cost price and multiply by 100 to express it as a percentage.

$2.75 - $1 = $1.75

$1.75/$1 * 100 = 175%

If you want to calculate the percentage increase in price, use the formula:

Percentage Increase = (New Price - Original Price) / Original Price x 100

In this case, the original price is $1 (the price of buying the cards) and the new price is $2.75 (the price of selling the cards). So, plugging these values into the formula:

Percentage Increase = (2.75 - 1) / 1 x 100 = 175%

The percentage increase in price is 175%.

On solving the provided question, we can say that perimeter of the quadrilateral  the value of x =0.8333333333.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Here quadrilateral sides are 3x+2, x, 2x+5, 6x-17

To find the perimeter of a quadrilateral,

we need to add all the lengths of four sides,

i.e., the perimeter of ABCD Quadrilateral = sum of lengths of all sides

                         = AB +BC + CD + DA.

                         = 3x+2+x+ 2x+5+6x-17

                         = 12x+(7-17)

                        = 12x-10

      Simplifying

 12x + -10 = 0

Reorder the terms:

-10 + 12x = 0

Solving

-10 + 12x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.

-10 + 10 + 12x = 0 + 10

Combine like terms: -10 + 10 = 0

0 + 12x = 0 + 10

12x = 0 + 10

Combine like terms: 0 + 10 = 1

12x = 10

Divide each side by '12'.

x = 0.8333333333

Simplifying

x = 0.8333333333

so the value of x =0.8333333333

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if u can't do this then ur in the matrix and a failure to life

Answer:

1)a=8,b=6,c=4

2)a=4,b=9,c=14

3)a=12,b=12,c=24

Answer:

-1/4

Step-by-step explanation:

perpendicular slopes are negative reciprocals

the negative reciprocal of 4 is -1/4

So on solving the provided question, we can say that the mathematical expression will be as follows, z-12, 17xy, 4x+75.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +. In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

x - 6 + z  = 9-6+5 = 8

5*(x+y) = 5*(9 + 10 ) = 95

2x + z = 2*9 + 5 = 23

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Answer:

Step-by-step explanation:

[tex]\cfrac{s}{31}=24[/tex]

Multiply both sides by 31.

[tex]\cfrac{31s}{31}=24\times\:31[/tex]

[tex]\boxed{s=744}[/tex]

-Hope this helps!

Answer:

s = 744

Step-by-step explanation:

Now we have to,

→ find the required value of s.

The equation is,

→ s/31 = 24

Then the value of s will be,

→ s/31 = 24

→ s = 24 × 31

→ [ s = 744 ]

Hence, the value of s is 744.

Concluding that there is an effect when in reality no effect exists is known as a: Standard error.

The approximate standard deviation of a statistical sample population is known as the standard error (SE) of a statistic.

By utilizing standard deviation, the standard error is a statistical concept that assesses how accurately a sample distribution represents a population. In statistics, the difference between a sample mean and the population's actual mean is known as the standard error of the mean.

The difference between the population's computed mean and one that is widely regarded as correct is described by the standard error.

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The unit rate of the number of pages penny reads per hour is; 56 pages per hour

A unit rate is also called unit ratio and it describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Now, we are told that;

Number of pages penny reads = 14 pages

Time he takes to read the 14 pages = 1/4 hours

Thus, applying the concept of unit rate gives;

Unit rate = 14/(1/4)

Unit rate = 14 * 4/1

Unit rate = 56 pages per hour

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0.3221469052

I hope its right

Answer:

The expression G³-h² + 8, when g = 3 and h = 5, evaluates to:

3³ - 5² + 8 = 27 - 25 + 8 = 10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

3^3=27,

5^2=25,

27-25=2,

2+8=10

Based on the changes that occurred in Ariel's bank account, the missing values are -$223.75, -$1.40, and -$4.40.

The missing values from the given table of the changes that occurred in Ariel's bank account balance is determined as follows:

Week 4 change:

Change = -$41.40 - $182.35

Change =  -$223.75

Week 5 balance: this is obtained from the sum of the change and the balance of the previous week:

Balance = -$41.4 + $40

Balance = -$1.40

Week 6 change:

Change = -$5.80 - (-$1.4)

Change  = -$4.40

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The requried equation model for the age of Jenna and her sister is given as y = x + 4.

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

here,

A variable can be used in an expression that represents a real-world situation where one value is unknown, not stated or can change.
Let the age of the Jenna sister be x,
According to the question,
Jenna[y] is four years older than her sister,
So,
y = x + 4

Form above expression
When her sister is of 4 years,
Jenna age,

y = 4 + 4
y = 8 years

Thus, the requried equation model for the age of Jenna and her sister is given as y = x + 4.

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A. The given relation is a function, but is not one-to-one. A possible domain for the inverse is given as follows: x ≥ 4.

B. The inverse function is given as follows: [tex]f^{-1}(x) = \sqrt{0.5(x + 8)} + 4[/tex]

C. The composition of the function with it's inverse results in x, hence they are inverse.

The quadratic function for this problem is defined as follows:

y = 2(x - 4)² - 8.

The classifications regarding function and one-to-one are given as follows:

The inverse can only be obtained when the function is one-to-one, hence a possible domain is given as follows:

x ≥ 4.

(as the vertex is at x = 4).

To obtain the inverse, first we must exchange the variables x and y, hence:

x = 2(y - 4)² - 8.

Now we must isolate the variable y, as follows:

2(y - 4)² = x + 8

(y - 4)² = 0.5(x + 8)

[tex]\sqrt{(y - 4)^2} = \sqrt{0.5(x + 8)}[/tex]

[tex]y - 4 = \sqrt{0.5(x + 8)}[/tex]

[tex]f^{-1}(x) = \sqrt{0.5(x + 8)} + 4[/tex]

The composition of the two functions is given as follows:

[tex](f \circ f^{-1}(x)) = 2(\sqrt{0.5(x + 8)} + 4 - 4)^2 - 8)[/tex]

[tex](f \circ f^{-1}(x)) = 2(\sqrt{0.5(x + 8)})^2 - 8[/tex]

[tex](f \circ f^{-1}(x)) = x + 8 - 8[/tex]

[tex](f \circ f^{-1}(x)) = x[/tex]

As the composition results in x, they are inverses.

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Answer:

Step-by-step explanation:

Answer:

1 microgram per day = 0.000000001/86400 kilograms per second

The probability that the teenager picked at random is male and their favorite hobby is playing video games is given as follows:

1/16.

The definition of a probability is that it is calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired and the total outcomes for this problem are given as follows:

Of the 14 males, 2 have playing videogames as their favorite hobby, hence the number of desired outcomes is given as follows:

2.

Then the probability is calculated as follows:

p = 2/32

p = 1/16.

The probability was simplified as the quotient of 32 and 2 has a result of 16.

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The total number of whole number between -4 and 6 are 7 that are 0,1,2,3,4,5,6.

Whole numbers are the complete set of natural numbers plus '0'. Examples include: 0, 11, 25, 36, 999, 1200, and so on. Learn more about numbers by clicking here.

Integers supplement this set of numbers because they include negatives, but otherwise follow the same rules. As a result, all whole numbers are integers (because they are all positive integers), but not all integers are whole numbers (because some are negative).

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On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = -1 < y < 1

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x) -1 < y < 1

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Solving the provided question, we can say that the exponential growth is the positive form of the exponential decay model that will be as the = > y = [tex]1500(.82)^t[/tex]

The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.

here,

we can say that the exponential growth is the positive form of the exponential decay model

that will be as the = > y = [tex]1500(.82)^t[/tex]

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