what is the solution for x^2 - 18x < -77

Answer:

$488.33 monthly savings

Step-by-step explanation:

Parent payment 30% of $21,800 is $6,540.

Subtract all payment from total cost.

21,800−6,540−5,600−3,800=5,680.

Split this into monthly payment by dividing 5,680 by 12 months.

5,680÷12= $488.33

The domain is actually the set of all "x" values, whereas the range is the set of all "y" values in an ordered pair.

Given,

What is the definition of the word "domain"?

Remember which of the following symbols corresponds to which ordered pair: (x, y).

If an x value has more than one y value connected with it, such as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2, a collection of ordered pairs is not a function.

Thus, the connection is referred to as a function if there is only one y value for every x value.

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A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.

To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:

force = m * g

where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).

force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs

The distance is the height to which the rock is lifted, which is 3 ft.

The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.

So,

Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs

So, the work done is 300 ft-lbs.

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32.56 is the expected weight for a bluegill fish that is 11 inches long.

Equation: What is it?

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation. Without them, one can still create an equation, such as 5 + 10 = 15. There are no variables in the equation below.

given expression:

In(Weight) = -5.28 + 3.44 In(Length)

So, we have to find 11 inches then

In(weight) = -5.28 + 3.44 x 11

               = -5.28 + 37.84

               = 32.56

Hence, 32.56 is the expected weight for a bluegill fish that is 11 inches long.

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The exponent or power that must be added to a base to produce a particular number is called the logarithm.

Indicated by the letter log n, the later class of logarithms, those with base 10, are referred to as common or Briggsian logarithms.

Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits. For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.

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The multiplicative inverse of 'a' is stipulate by a-1 or 1/a. on other side, the multiplicative inverse of a number is expounded as 1 divided by the number.

The multiplication inverse of 6 is 1/6.

hence, the multiplicative inverse of -6 is -1/6.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to define mathematical expressions.

The word 'inverse' concludes something opposite/contrary in effect, order, position. or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse formula is called that the multiply of a number and its reciprocal is 1.

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Answer:

x^2 + 6x + 9 and x^2 + 8x + 16 are examples of perfect-square trinomial

Step-by-step explanation:

1. x2 + 6x + 9

(x + 3)^2

= (x + 3)(x + 3)

= x2 + 6x + 9

2. x^2 + 8x + 16

x^2 + 8x + 16

= x^2 + 2(x)(4) + 4^2

= (x + 4)^2

Count 6 point from zero to the left side from zero for negative (-6) and for 5 count 5 points right from the zero on the number line.

A number line in mathematics is a horizontal straight line with numbers spaced equally apart along that line. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may also be left empty or blank. A number ladder is almost a vertical number line.

Number lines are frequently used in elementary and middle school to help students develop skills like counting, adding, and subtracting numbers. They are typically introduced in kindergarten.

Additionally, it is very easy to read number lines. The values provided enable kids to compare and visualise the relationships between the numbers shown on the line, despite the fact that it isn't a ruler and the space between the numbers isn't fixed. In turn, this promotes the growth of number sense.

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Answer:

Step-by-step explanation:

We can write this out as an equation and let x represent the number:

7x-5=0

Adding five on both sides gives us: 7x=5

Therefore, x=5/7

An ordered pair contains one point's coordinates. The name of a point in an ordered pair is (x, y).

The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates. The name of a point in an ordered pair is (x, y). The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates.

A set of ordered pairs is any pair of components that are wrapped in brackets and exist in a specific sequence. If there are two components, "a" and "b," the two distinct pairings are "(a, b)" (b, a). A and B are referred to as the first and second elements, respectively, in an ordered pair (a, b). The relationship between the input or domain and the output or range is described by the function rule. If and only if there is only one value in the range for each domain value, a relation is a function.

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Answer:

Below

Step-by-step explanation:

The answer can be found by   11/5 * 325

 here is how this comes about

    ratios

  325 is to 5 hours as 'd' is to 11 hours

325/5 = d/11     Multiply both sides by ' 11 '

11/5  * 325 = d     ( the equation above )

d = 715 miles

The simplified exponential expression 3^10×37^9/9^12 as a single power of 3 is given as follows:

3^70.

The exponential expression for this problem is defined as follows:

[tex]\frac{3^{10} \times (3^7)^{12}}{9^{12}}[/tex]

Applying the power of power rule, we have that:

(3^7)^12 = 3^(7 x 12) = 84.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

3^10 x 3^84 = 3^94.

For the denominator, we have that:

9^12 = (3²)^12 = 3^24.

When two terms with the same base and different exponents are divided, we keep the base and subtracted the exponents, hence:

3^94/3^24 = 3^(94 - 24) = 3^70.

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Substitution is a method for solving systems of equations by substituting the values from one equation into the other. To use substitution to determine if an ordered pair is the solution to a system of equations, first solve one of the equations for either x or y.

Then substitute this value into the other equation, and solve for the other variable. If the ordered pair you obtain is also found in both equations, then it is a solution to the system.

Take the equation set as an example.

2x + y = 5

3x – y = 1

To use substitution to determine if (2, 3) is a solution to this system, first solve one of the equations for either x or y:

2x + y = 5  ⇒ y = 5 – 2x

Add this value to the other equation after that:

3x – (5 – 2x) = 1  

⇒  5x = 6  

⇒ x = 6/5

Finally, substitute 6/5 back into either equation to find y:

2(6/5) + y = 5  

⇒ 12/5 + y = 5  

⇒  y = 10/5  

⇒  y = 2

Since (6/5, 2) is found in both equations, it is a solution to the system.

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Answer:

The slope is simply the gradient of the two points . use the gradient equation (Y2-Y1/X2-X1) to find the answer ;⁠)

Answer:

Step-by-step explanation:

Y = e−x

Answer: A negative exponential function or y = e−x, is otherwise known as exponential decay

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

Answer:

37500

Step-by-step explanation:

40%=$15,000

100%=?

100%×$15,000/40%

$1,500,000/40

=37500

The type of function always has an inverse is one to one.

In math function is referred as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we need to identify the type of the function always has an inverse.

As we all know that in each and every function has an inverse, here we have also know that but not every inverse will be a function.

Where as the inverse may fail the vertical line test.

Here we have identified that if the original function is a one-to-one function then its inverse will be a function.

Finally in a one-to-one function not only passes the vertical line test, then it also passes a horizontal line test.

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Answer:

2 ...

Step-by-step explanation:

since LM = 8

and LN = 10

therefore MN = LN - LM .

MN = 10 - 8 .

MN = 2

The number of solutions to an equation x₁ + x₂ + x₃ + x₄ = 17 are 1140

Consider given equation x₁ + x₂ + x₃ + x₄  = 17,

where x₁ , x₂ , x₃ and x₄ are non-negative integers.

As we know x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ the number of ones between the second and the third zero, and x₄ is the number of ones after the third zero.

This means, there is a 1-1 correspondence between the solutions and reorderings of 17 ones and 3 zeros.

So, the number of solutions to given equation would be,

n = ²⁰C₃

Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],

²⁰C₃ = 20! / (3! × (20 - 3)!)

²⁰C₃ = 1140

So, n = 1140

The possible number of solutions = 1140

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The complete question is:

How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17 where x₁ , x₂ , x₃ and x₄  are nonnegative integers?.

The logarithmic function

[tex] f(x) = log_{b}(x) [/tex] is represent the inverse of an exponential function f(x)= bˣ.

A logarithmic function involves logarithms. Its basic form is

[tex]f(x) = log_{a}(x) ,[/tex] , where a > 0. It is Log functions include natural logarithm (ln) or common logarithm (log). For example f(x) = ln(x). An exponential function is defined as a mathematical function in the form f(x) = aˣ , where “x” represent a variable and “a” is a constant number which is known as the base of the function and it's value always be greater than zero. Transcendental number e is mostly used as a base of exponential function base is f. We have, the logarithmic function

[tex]f(x) = log_{b}(x) [/tex] , is the inverse of an exponential function f(x) =bˣ, and which means that

[tex]y = log_{b}(x) [/tex], is bʸ = x. The expression bʸ = x is said to be the “exponential form” for the logarithm

[tex]y = log_{b}(x) [/tex].

Here, b is called the base (of the logarithm) and it should be positive constant.

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Complete question:

What function is

[tex]f(x)= log_{b}(x) ?[/tex]

Answer:

(f∘g)(x) = 2x + 12

Step-by-step explanation:

(f∘g)(x) =

f(g(x)) =

2(g(x)) + 4 =  ==> substitute g(x) for x in f(x) = 2x + 4

2(x + 4) + 4 =  ==> substitute x + 4 for g(x)

2x + 2*4 + 4 =  ==> use distribution property on x and 4

2x + 8 + 4 = ==> simplify

(f∘g)(x) = 2x + 12

According to the question A line has a slope of -3 and includes the points (9, 4) and (8, t) then the value of t is 7

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is typically used to signify slope.

tan θ = Δy/Δx

the solution is -

Considering a line with a slope of -3 and also the point (9, 4), we could use the point-slope form of either a line to find the equation of a line:

y - 4 = -3(x - 9)

y = -3x + 27 + 4

y = -3x + 31

We are given some other point on the line (8, t) we can try substituting it in the equation above:

t = -3(8) + 31

t = -24 + 31

t = 7

And hence, the value of the t is 7.

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The true statement is D)Census. It's pretty easy to survey all the students at a high school.

All units or participants in the target population under the survey are statistically compiled as part of the census method's process.

Population in this context refers to the total collection of observations associated with a specific study.

For instance, if university students are asked for input on the teaching staff, the latter group will be considered the study's population.

The targeted population is used to choose the various sample entities. With this approach, a predetermined number of observations that come from a bigger pool of populations are statistically analyzed.

Different types of sample methodology can be used, including basic random sampling, systematic sampling, cluster sampling, stratified sampling, and more.

By the above observations, we can conclude that This given situation is a Census as we can survey it among a collection of people that is the batch of senior students and it is easy to survey as there will be a few members of seniors in a school.

Therefore,

The true statement is D)Census. It's pretty easy to survey all the students at a high school.

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Answer: [tex]16x^2-102x+77[/tex]

Step-by-step explanation:

1) distribute

[tex](-8x+7)(4x+2)\\-32x^2-16x+28x+14\\-32x^2+12x+14[/tex]

2) distribute

[tex](-8x+7)(6x-9)\\-48x^2+72x+42x-63\\-48x^2+114x-63[/tex]

3) solve

[tex](-32x^2+12x+14)-(-48x^2+114x-63)\\(-32x^2+12x+14)+(48x^2-114x+63)\\16x^2-102x+77[/tex]

Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero.

Equations of the form a x +b y = 0; where a and b are real numbers, and a ,b ≠ 0, is also linear equations in two variable.

Since the solution of linear equation in two variable is a pair of numbers (x,y), we can represent the solutions in a coordinate plane.

To draw graph , we need to find some points

y =-3x

for  y =-3x ,lets substitute value and check,

x=0

then y =0

x=1

then y =-3

x=2

then y =-6

x=3

then y =-9

x=-1

then y =3

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Lana has 5 apples and her friend has 10 times as many as her So her friend will have 50 apples.

Here times mean The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the time sign or the dimension sign.

So if Lana has 5 apples

her friend has 10 times as many as her

By using the unitary method

The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.

The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.

5 time 10

50 apples

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Yes. Zero is a real value of x.

Given,

Real value of x;

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

How do you discover the true worth?

The influence of price level changes is subtracted from the nominal value of a good, service, or time-series data to create real value, which provides a more accurate view of economic trends. A deflator is used to alter the nominal value of time-series data, such as GDP and incomes, in order to produce real values.

Here,

The real value of x includes 0.

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Answer:

400!

Simple Step-by-step explanation:

40x10

=400

Sorry for being late <3