What is the shape of the graph of an absolute value function?

Given condition will be represented by linear equation 5x+10y=90.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Total trail hiked=90miles

mountain trail=5mile

canal-trail=10mile

x represent the number of times Maria hiked the mountain trail, and  y represent the number of times Maria hiked the canal trail

Therefore,

Linear equation will be 5x+10y=90

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If tangent of x degrees equals four-thirds, and measures of triangle is 10. 5 units, and NM measures 2b units then the value of b is equals to seven. So, last option is correct, b = 7 here.

Right angled triangle : A triangle is defined as a regular polygon, with three sides and the sum of any two sides is always greater than the third side. Right angled triangle is one type of triangle. When the angle between a pair of sides is equal to 90 degrees it is called a right-angle triangle. See in above figure ∆LMN is a right angled triangle with m∠LMN = 90° . Also, we have m∠MLN = x° so, m∠LNM = 180° - 90° - x° = 90° - x° ( Since, sum of interior angles of triangle = 180°)

Length of side LM = 10.5

length of side, NM = 2b

tangent of x, tan x = 4/3

We have to determine the value of b. For considering angle x° as centre point then

base of triangle = LM = 10.5

As we know Tangent of any angle is equals to ratio of perpendicular/base.

so, tan x = 4/3 = LM/NM

=> 4/3 = 2b / 10.5

=> 4× 10.5 = 2b × 3

=> b = 42.0/6

=> b = 7

So, the required value is 7.

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yea seven is right. just finished

The finance charge is. s= 80/3 m.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The price of a stove is s dollars.

Pedro makes 10% down payment for a two year installment purchase.

The monthly payment is m dollars.

Also, 2 years= 24 month

Then, the finance charge is

s x(1- 10%) / 24 = m

m= s ( 1- 0.10) / 24

24m = 0.9s

s= 24m/ 0.9

s= 80/3 m

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Answer:

4

Step-by-step explanation:

6n - n = 5n

13 + 7 = 20

5n = 20

20/5 = 4

n = 4

Answer:

n = 4

Step-by-step explanation:

To solve this, we first have to get the n's on one side:

[tex]6n - 7 = n + 13[/tex]

↓ add 7 to both sides

[tex]6n = n + 20[/tex]

↓ subtract n from both sides

[tex]5n = 20[/tex]

Then, we can divide by 5 on both sides to solve for n.

[tex]n = 4[/tex]

The plant is 17/4 inches above the ground

Pam plants the seed 5 1/2 inches below the ground

After a period of one month, the tomato plant has increased to 9 3/4 inches

Therefore the height of the tomato plant above the ground can be calculated by subtracting the height of the seed below the ground from the height of the plant after one month.

9 3/4 - 5 1/2

39/4 - 11/2

= 17/4

Hence the plant is 17/4 inches above the ground

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Step-by-step explanation:

Using a proportion:

5.5 liters * 1,000 milliliters/liter = 5,500 milliliters

Conversion method:

1 liter = 1,000 milliliters

So, 5.5 liters = 5.5 liters * 1,000 milliliters/liter = 5,500 milliliters

The graph for the given piecewise function is as provided in image.

What is piecewise function?

A piecewise function is a function f(x) which has different definitions in different intervals of x. The graph of a piecewise function has different pieces corresponding to each of its definitions. The absolute value function is a very good example of a piecewise function. Let us see why is it called so. We know that an absolute value function is f(x) = |x| and it is defined as:

f(x)=(x if x≥0 ,

     -x  if x><0)

We should read this piecewise function as

f(x) is equal to x when x is greater than or equal to 0 and

f(x) is equal to -x when x is lesser than 0.

Given piecewise function

f(x)=(3x-5  if x<=-1

       -2x+3 if -1<x<4

        2      if x>=4)

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The value of the variable 'a' by solving the given equation 3a²- 21 = 27 is given by :

option B. a = plus or minus 4.

As given in the question,

Given equation is equal to :

3a²- 21 = 27

Express the given equation in the given form of ax² =c which is equal to :

3a²- 21 = 27

Add 21 on both the side of the equation we get,

⇒3a² -21 + 21 = 27 + 21

⇒ 3a² = 48

Now divide both the side by 3 we get,

⇒ 3a² / 3 = 48 / 3

⇒ a² = 16

Take square root both the side we have,

⇒ a = √ 16

⇒ a = ± 4

Therefore , the solution of the given equation 3a²- 21 = 27  is  given by :

option B. a = ±4.

The above question is incomplete, the complete question is:

Solve the following equation by first writing the equation in the form

ax² =c

3a²- 21 = 27

A. a = 4

B. a = plus-or-minus 4

C. a = plus-or-minus 16

D. a = 16

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All real numbers except {x = 4} denote the solution set.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = (4⁢x + 8/6⁢x − 24)

The given function is -

y = (4⁢x + 8/6⁢x − 24)

Domain is the set of values for which the given function is defined. The given function is not defined for -

6x - 24 = 0

6x = 24

x = 4

So, all real numbers except {x = 4} denote the solution set.

Therefore, all real numbers except {x = 4} denote the solution set.

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The total amount with Siobhan is given by the equation S = $ 8.33

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount with Siobhan be represented as S

Let the amount with Priya be represented as P

Let the amount with James be J = $ 7.00

And , Priya makes 40% more than James

So , P = ( 40 / 100 ) x P + P

Substituting the values in the equation , we get

The amount with P = ( 0.40 ) ( 7 ) + 7

The amount with Priya P = 2.8 + 7

The amount with Priya P = $ 9.80

Now ,

Siobhan makes 15% less than Priya

So , the amount with Siobhan S = P - ( 15/100 )P

Substituting the values in the equation , we get

The amount with Siobhan S = 9.80 - ( 0.15 )( 9.80 )

On simplifying the equation , we get

The amount with Siobhan S = 9.80 - 1.47

The amount with Siobhan S = $ 8.33

Hence , the amount with Siobhan is $ 8.33

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Under division, the set of polynomials is not closed. In that, they are closed under addition, subtraction, and multiplication, polynomials constitute a system like the system of integers.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The word polynomial is pronounced as "many terms" since it comes from the Greek words "poly," which means "many," and "nominal," which means "terms." A polynomial is not infinite, although it can have any number of terms.

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Answer:

no solution

Step-by-step explanation:

Since you are using substitution, you will plug in one of the variables using one of the equations.

y=x+4

x-y=8

put the y from above into the y below

x-(x+4)=8

Now, solve the equation

x-x-4=8

Put x's together

-4=8

-4 does not equal 8, so this system of equations has no solution

The quotient is 2x^2 + 4x + 5.

The given polynomial is 2x^3 - 3x -10.

As we can see that the given polynomial is a three-degree polynomial but the second degree term is missing, so we can write the polynomial as 2x^3 + 0x^2 - 3x -10.

The divisor is (x-2).

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x) (2x^2) = 2x^3

Thus, we multiply the divisor (x-2) by 2x^2 which gives 2x^3 - 4x^2

Now we subtract this from the polynomial which gives 4x^2 -3x -10.

Repeating the same we multiply the divisor by 4x which gives 4x^2 - 8x. Subtracting the same from 4x^2 -3x -10, we get 5x - 10.

Now we multiply the divisor with 5 to get 5x - 10. Subtracting it from the remaining polynomial 5x -10 leaves the remainder 0.

Thus, we get the quotient as  2x^2 + 4x +5.

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They are both quadrilaterals and they both have equal and parallel opposite sides.

Rectangles and parallelograms both have four sides, and thus are quadrilaterals.

Quadrilaterals

The definition of a quadrilateral is a 2-D shape with 4 sides and 4 angles. Rectangles and parallelograms both fall under this category. So, they both have all the attributes listed in the definition.

This means 3 shared attributes of rectangles and parallelograms are:

Opposite Sides

Rectangles and parallelograms also have unique relationships between opposite sides. Remember that opposite sides are directly across from each other and not adjacent. In both shapes, opposite sides are parallel. This means that if the sides were to continue forever, they would never intersect. Also, opposite sides are equal. By this, I mean that the lengths of opposite sides are equal. Another way to say this is that opposite sides are congruent.

2 and 3 has a multiplicative inverse of -3 and 2, which is 2. A number that, when multiplied by the inputted number, produces the result 1 is said to be the multiplicative inverse of that number.

When a number is multiplied by another, the result is 1, this is known as the multiplicative inverse of the original number . It is the reciprocal of a number per multiplicative inverse definition. A-1 or is used to denote the multiplicative inverse of a number "a".

According to the multiplicative inverse property, a multiplies with its reciprocal, 1/a, to get 1, for any number a. It follows that 1/a is a number's multiplicative inverse. The multiplicative inverse of 5, when applied to the integer 5, is 1/5, according to this characteristic. Dividing 1 by a real number yields the multiplicative inverse of that number. One fifth (1/5, or 0.2) and one-quarter (0.25, or 1 divided by 0.25, respectively) are examples of reciprocals.

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Answer:

-49.5

Step-by-step explanation:

3x + 96 = x - 3

2x + 96 = -3 (-x both sides)

2x = -99 (-96 both sides)

x = -49.5 (/2 both sides)

The answer of 10 more than 24 is 34.

The answer of 10 more than 24 is 34 which can be derived using simple mathematical calculations.

To find 10 more than 24, you can add 10 to the original number 24.

10+ 24 = 34

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 24 is 34.

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Answer:

The maximum height = 14 ft, and the time caught at 5 ft high = 1.5 seconds

Step-by-step explanation:

Used desmos.

The figure has an image of right triangle and the dimensions are solved to get

The right triangle's sides are solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

From the question it can be deduced that

opposite = 12 ft

adjacent = b

hypotenuse = c

Using tan, TOA the adjacent is solved

tan 30 = Opposite / Adjacent

tan 30 = b / 12 ft

b = 12 / tan 30

b = AC = 20.784 ft

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 20.784 / c

c = 20.784 / cos 30

c = AB = 24 ft

< A + < B + < C = 180 (angles in a triangle)

30 + < B + 90 = 180

< B = 60

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Adrian need to invest $2041.88,  to the nearest hundred dollars for the value of the account to reach $3900 in 14 years.

Let principal amount is x

And interest is y

Then, according to question

X + y = 3900    --------------eq(1)

and formula of interest

I = (P*t*R)/ 100

Y = (x * 14 * 6.5) / 100   ----------------------eq(2)

3900 – x = (x * 14 * 6.5) / 100  from eq(1) and eq(2)

390000 – 100x = 91x

191x = 390000

X = 2041.88

So, therefore principal amount = $2041.88

and interest = $1858.12

You can earn interest on interest by using compound interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

You get interest based on the amount you deposit when you add money to a savings account or other account of a similar nature. For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily. The account balance plus any interest that has accrued but has not yet been paid out are used by the bank to determine your daily interest earnings.

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The study of statistics rests on two major​ concepts probability which  is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions

Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.

Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.

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The area of the given triangle is 130.7 cm^2.

What are Triangles?

Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorized into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorized into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now,

Area of a right angle triangle =1/2*base*height

here a=base and let h=height

h^2=b^2-a^2

=23^2-15^2

h^2=304

h=17.43cm

therefore

area=1/2*15*17.43

Area of the triangle=130.7cm^2

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The solution is k = -257.57

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: k/6.3 + 99.8 = 55.9

We have to find the solution to k.

By applying simplification in the given equation we get the solution to k

k/6.3 + 99.8 = 55.9

k + 99.8 × 6.3 =  55.9 × 6.3

k + 628.74 = 352.17

k = 352.17 - 628.74

k = 276.57

Hence, the solution is k = 276.57.

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Answer:

Step-by-step explanation:

(0.7}

The point estimate from a confidence interval can be found by taking the midpoint of the interval.

The formula for the point estimate is (lower bound + upper bound) / 2. For example, the 95% confidence interval for a sample mean of 25 is (23, 27). The point estimate for this sample mean is (23 + 27) / 2 = 25. This point estimate is the best estimate of the true population mean.

In essence, the point estimate is the best guess of the population mean given the data. It is calculated by taking the midpoint of the confidence interval, which is the range of values that is believed to contain the population mean with a certain degree of confidence. The point estimate is usually the most reliable estimate and is used to make decisions in statistical analysis.

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a. The fraction of the cup of juice that remained in the jug is 0

b. the total amount of juice in the 3 glasses is 1 cup of juice

c. The total amount of juice in the four glasses is 2 cups of juice

d. no juice was left in the jug after the 4 glasses have been poured

The total amount of juice is deduced from the problem to be 2 cups of juice

Total amount of juice poured out

= 1 cup was shared among three glasses + 1cup of juice in the fourth glass

= 1 cup + 1cup

= 2 cups of juice hence nothing is left in the jug

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The replacement approach refers to determining any variable's value from one equation in terms of another variable. Considering that, the point where the function crosses = (0, 7). The correct answer is c. (3,3).

Considering that the function's intersection point is now = (0, 7) As a result, the point must fulfil the function. We have to check whether these pairs satisfy equation 2x + y = 7 or not.. So, we will put these pairs one by one.

A) (0,7) x=0 & y=7

Than

2×0+7=7

7=7 so, it satisfies.

B) (1,5) x=1 & y=5

Than

2×1+5=7

2+5=7

7=7 so, it satisfies

C) (3,3) x=3 & y= 3

Than

2x3+3= 7

6+3 = 7

9= 7 so, it does not satisfies.

D) (2,3) x=2 & y= 3

Than

2x2+3 = 7

4+3= 7

7=7 so, it satisfies.

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Answer: In a parallelogram, opposite angles are congruent, which means they have the same measure. So, if angle g has a measure of (4x - 16)°, then angle h also has a measure of (4x - 16)°. Therefore, the measure of angle h is (4x - 16)°.

So, the answer is 88°.

Step-by-step explanation:

Answer: The vertex of the parabola is (2, -6)