The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.
What is the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x)=√x - 2 + 3.
The inverse function can be found as shown below,
f⁻(x) = √(y - 2) + 3 (Replace x by y)
x = √(y - 2) + 3
solve the equation as shown below,
x - 3 = √(y - 2)
Squaring both sides,
(x - 3)² = [√(y - 2)]²
x² + 9 - 6x = y - 2
x² + 9 - 6x + 2 = y
y = x² - 6x + 11 or y = (x - 3)² + 2
Thus, the inverse of the function is (x - 3)² + 2.
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is triangle ABC similar to CDE?
Answer:Yes
?=6
Step-by-step explanation:
they sare the same angle 55 and angle
Answer:
Triangle ABC is similar to triangle CDE
?=8
Step-by-step explanation:
We can set up a proportion: x/12=8/12. We can use cross multiplication to get 12x=96 which would x=8.
The triangles are similar since both of them have 55 degrees as one of the angle measures.
Brie bought a rug for her bedroom. The area of the rug measures 25 square feet. Her bedroom is ten feet wide and twelve feet long. Using the given measurements, what is the amount of her bedroom NOT covered by the rug
The area of bedroom rug is 15 square feet. the longer side measures 5 feet. his living room rug is twice as long and twice as wide as the bedroom rug.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in cm², also known as square centimeters.To learn more about square centimeters refer to:
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Is 5 an algebraic term?
5 is not an algebraic expression.
Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.
It follows that 5 cannot be an algebraic expression.
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?
Kadeesha left her house at time zero and drove for 3 minutes to the store, at a speed
of 1 blocks per minute. Then she stopped and went into the store for 3 minutes. From
there, she drove in the same direction at a speed of 2 blocks per minute until she got
to the bank, which is 6 blocks away from the store. She stopped at the bank for 5
minutes. Then she drove home at a speed of 3 blocks every minute. Make a graph of
showing the number of blocks away from home that Kadeesha is a minutes after she
leaves her house, until she gets back home.
Graph Stories (Level 1)
Jan 08, 3:36:47 PM
Watch help video
Click twice to plot a segment.
Click a segment to delete it.
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
Given :
At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.
after traveling six blocks at her normal speed of three blocks per minute
She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.
She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
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A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a $\heartsuit$
The probability that the top card is a suit of heart as calculated from the data given is found to be 4 / 663.
We are given that ,
The number of cards in the deck = 52
Number of 3's in the deck = 4
Number of 8's in the deck = 4
As because all the card deck's have 4 cards of same number in different suits.
Probability is calculated as ,
P = required outcome / Total possible outcomes
Therefore, when we can choosing cards without replacing them we get,
P(top card is a 3) = 4 / 52
P(second being 8) = 4 / 51
P(top card is a 3 and second 8)
=4/52 x 4/51
= 16 / 2652
= 4 / 663.
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Find the solutions of the quadratic equation 3x2−x+8=03x 2 −x+8=03, x, squared, minus, x, plus, 8, equals, 0.
The solutions of the quadratic equation 3x² − x + 8 = 0 are as follows;
x = 0.1667 + 1.6245i
x = 0.1667 - 1.6245i
How to solve the given quadratic equation?In Mathematics, the standard form of a quadratic equation is given by this mathematical expression;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
From the information provided above, we can logically deduce the following data values (parameters);
3x² − x + 8 = 0
Where:
a = 3b = -1c = 8Substituting the data values (parameters) into the quadratic formula, we have the following;
[tex]x = \frac{-(-1)\; \pm \;\sqrt{(-1)^2 - 4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;96}}{6}[/tex]
x = (1 ± √95)/6
x = (1 + √95)/6 = 0.1667 + 1.6245i
or
x = (1 - √71)/6 = 0.1667 - 1.6245i
In conclusion, i represents a complex number.
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Complete Question:
Find the solutions of the quadratic equation 3x² − x + 8 = 0.
Nick is driving from Brookville to Kansas City, a distance of more than 325 miles, to watch the Bengals play the Chiefs in the playoffs. After driving 75 miles, Nick stops for gas. Write and solve an nequality to determine how much farther Nick has to drive to reach Kansas City.
The distance that Nick has to drive to reach Kansas will be at least 250 miles.
How to illustrate the inequality?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 ≥ < > ≤.
Since Nick is driving from Brookville to Kansas City, a distance of more than 325 miles and after driving 75 miles, Nick stops for gas.
An inequality to determine how much farther Nick has to drive to reach Kansas City will be:
x > 325 -75
x > 250
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Type the correct answer in each box. Sharon tracks the number of cupcakes she sells each day for a week. The numbers of cupcakes she sold are 23, 25, 32, 35, 36, 25, and 27. The mean of her sales over the week is , and the median is . Reset Next
The mean of her sales over the week is 29 and the median is 27.
What is mean?The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey. The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean.
Here,
To find the mean you need to sum all daily sales and then divided by the number of days. If we called daily sales as xi and the number of days evaluated as N, we have that the mean can be expressed as
mean = (∑xi)/N ⇒ media = (23 + 25 + 32 + 35 + 36 + 25 + 27 )/7
⇒mean = 29.
To find the mediana you have to put the number of sales in increasing orden and then look which is the number in the middle of the serie. So
23 - 25 - 25 - 27 - 32 - 35 - 36
⇒median = 27.
Summarizing, the mean of the sales is 29 and the median 27.
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Pls help due in 5 mins
The given algebraic equation can be written in many ways as shown.
What is algebraic equation?The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
Solution:-
-5x-15+25x-30
it can be written as
-5(x+3-5x+6)
20x-45
5(4x-9)
and also
-5(9-4x)
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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].
First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]
*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up
[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]
Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].
Both have the same factor is [tex]-5[/tex].
Use the distributive property to find the equation that is equivalent.
[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]
So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]
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(X-5)-1 substitute the 9 for x and evaluate
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
The definition of a linear equation.A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.
Here,
Given : (X-5)-1
Thus,
after substituting the value of x with 9
We get,
=> (X-5) -1
=>(9-5)-1
=> 4 -1
=> 3
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
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Match the solution to its expression.
The equivalent values to the given expressions are -
2/3 and 3/7 respectively.
What is expression?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 are two expressions as -
1/3 + 1/3
5/7 - 2/7
The given expression are -
1/3 + 1/3
(1 + 1)/3
2/3
5/7 - 2/7
(5 - 2)/7
3/7
Therefore, the equivalent values to the given expressions are -
2/3 and 3/7 respectively.
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A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25
Selecting ball number 25 has no chance of happening.
Explain about the probability?Probability is only the likelihood that something will occur. When we don't know how something will turn out, we might discuss the likelihood of various outcomes or the potential of one. Statistics is the scientific study of events that conform to a probability distribution.
It is predicated on the likelihood that something will take place. The rationale for probability serves as the theoretical probability's essential tenet. A coin has a 12% chance of landing on its head, for instance, when it is flipped.
Probability is a statistic that is used to indicate the likelihood or potential for an event to occur. Both fractions from 0 to 1 and percentages from 0% to 100% can be used to indicate probabilities.
In 25th Ball it is 0
Because there is no 25th ball
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50PTS 50 PTS (DONT explain just answer please)
Answer: 17
Step-by-step explanation:
Answer:
x = 17°
Step-by-step explanation:
The given angles are,
→ 6x + 8
→ 4x + 2
Now we have to,
→ find the required value of x.
Forming the equation,
→ (6x + 8) + (4x + 2) = 180°
{As two angles in a straight line is 180°}
Then the value of x will be,
→ (6x + 8) + (4x + 2) = 180°
→ 6x + 4x + 8 + 2 = 180°
→ 10x + 10 = 180°
→ 10x = 180° - 10
→ x = 170/10
→ [ x = 17° ]
Hence, the value of x is 17°.
Any help is appreciated<3
A jewelry shop is offering a percent discount on the original price of a jade pendent. The original price of the pendant was $200.
Let d represent the percent discount, written as a decimal. Write an equation to find the discount price, y dollars, of the pendant.
An equation to find the discount price, y dollars, of the pendant is y=2d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The original price of the pendant was $200.
Let d represent the percent discount, written as a decimal.
The discount price, y dollars, of the pendant.
y=d% of 200
y=d/100 ×200
y=2d
Therefore, an equation to find the discount price, y dollars, of the pendant is y=2d.
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What is the minimum value of 2x^2 3x 5?
The minimum value of the given quadratic equation is 31/8. Solved using graph method to find a minimum value that is c - b^2/4a.
By graphing the equation and locating the minimum point on the graph, you may visually determine the minimum value. The graph's vertex will have the lowest y-value. When you have a graphing calculator that can perform the majority of the work for you, this is very simple.
A graph makes it simple to determine the minimum value of a quadratic equation. One can use the graph to identify the minimum point of the quadratic equation and to find the minimum value in a visual way. If the quadratic equation is written as [tex]y= ax^2 + b*x + c[/tex]one can follow the equation that says the minimum value is min = c- (b^2/4a) to obtain the minimum value of the quadratic equation.
Given Quadratic equation is y = 2x^2 + 3x + 5
a = 2 , b =3 ,c = 5.
Minimum value = c - (b^2/4a)
= 5 - 9/8
=31/8.
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dentify the relationship between angles x and y
the x & y angles are alternate angles.
What is alternate angles?The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.
Here, we have,
from the given figure , we get,
the x & y angles are alternate angles.
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Please help me! Find the circumference of the circle
Answer:
convert to cmthen write the perimeter of the circle and solveDuring two games, the number of points scored by a basketball team Increased from 75 to 87. By what percentage
did the number of points scored increase?
The percentage of increase in the number of points is 16 %
What Does Percent Mean?
A ratio or figure stated as a fraction of 100 is called a percentage. The percent marker is frequently used to indicate it,%
given the data,
The basketball team's total point total was 75.
The basketball team's enhanced point total was 87.
The difference between the basketball team's total points scored and its increased points are the increase in points.
The increase in points = 87 - 75
= 12 points
So, the percentage increase in points = ( increase in points/number of points scored by the basketball team ) x 100
The percentage increase in points = ( 12 / 75 ) x 100
= 0.16 x 100
= 16 %
Therefore, the percentage increase is 16 %
Hence, the percentage of increase in the number of points is 16 %
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
The distance between the girl and her bike is 25.00 ft.
What is distance?Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.
The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.
Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.
Therefore, the distance between the girl and her bike is 25.00 ft.
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does the order of the quantities in an inequality matter
The order of the quantities in an inequality matters. Therefore, it is true.
How to illustrate the inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.
Therefore, the order matters.
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A rectangle has a perimeter of 16 centimeters. The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters. If x represents the length of a side of the rectangle, then the rectangle's area is represented by x(8-x) square centimeters. Suppose a square is constructed to have the same area as this rectangle. The length of a side of the square is represented by centimeters. What is the range of possible perimeters of the square? Round answers to the nearest hundredth of a centimeter.
The range of possible perimeters of the square=10.583
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
A rectangle has a perimeter of 16 centimeters.
The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters.
let, x represents the length of a side of the rectangle,
then the rectangle's area is represented by x(8-x) square centimeters.
i.e. area of square = 8x-x^2
the side = √x(8-x)
perimeter= 4×√x(8-x)
Hence, the range of possible perimeters of the square=10.583
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Given: 2x−43=2
Prove: x = 5
Select from the drop-down menus to correctly complete the proof.
Statement Reason
2x−43=2 Given
2x−4=6
Choose...
2x = 10
Choose...
x = 5
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Given : 2x-4=6
To prove x =5
Thus,
We have to find the value of x
=> 2x =10
=> x =10/2
=> x =5
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
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I really need help on this question
Step-by-step explanation:
2×4=8
8×2/3
8×2=16
16×3=48
ans = 48
Using long division convert 1/4 to a decimal
Using long division convert 1/4 to a decimal
To convert a fraction into a decimal, we'll just divide the numerator by the denominator:
4√1
we'll divide 1 by 4.
1 divided by 4 equals 0
0
4√1
To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top
0.
4√1.0
Now we can divide 10 by 4, 10 divided by 4 equals 2.
0.2
4√1.0
Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.
0.2
4√1.0
-8
______
2
Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.
0.2
4√1.00
-8
________
20
20 divided by 4 equals 5.
0.25
4√1.00
-8
______
20
Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.
0.25
4√1.00
-8
______
20
20
________
0
So 1/4 is equal to 0.25.
Subject: Angles In a Circle
I need help with finding out how to get 5, d,e and f and getting the points
Step-by-step explanation:
please see the attachment
Given that $x$ is a positive integer less than 100, how many solutions does the congruence $x 13 \equiv 55 \pmod{34}$ have
There are three solutions to the congruence x+13=55 (mod 34).
What is congruence?Two figures are considered to be 'congruent' if they can be put exactly over each other. When you set one slice of bread on top of the other, you'll see that they're both the same shape and size. The phrase "congruent" refers to having exactly the same form and dimension. When two things or forms superimpose on each other, they are said to be congruent. Their shapes and sizes are identical. Line segments with the same length and angles of the same measure are congruent in the case of geometric forms.
Here,
something equaling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21
do you mean x+13=21 (mod 34) ?
clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100
The congruence x+13=55 (mod 34) has three solutions.
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I WILL MARK BRAINLYEST AND 40 POINTS
Describe a meal that you could put together that provides 4 servings of both a main course and a side dish. Explain how you know that it will not exceed the weight limit of the box
The total number of servings of chicken the food bank can provide is 70 servings.
What is per unit?Per-unit is a technique of expressing a quantity's value in terms of a base or reference quantity. Each system variable or quantity in a per-unit system is normalized in relation to its own base value.
Two chickens make up the main course of a plate of food, according to the table's content. Each chicken served by the food bank weighs 12.6 ounces. 110.9 pounds of chicken are available at the food bank (1,774.4 ounces of chicken)
Thus,
The mass of chicken per serving = 2 × 12.6 = 25.2 oz/serving
The total number of servings of chicken the food bank can provide = (The quantity of chicken the food bank has)/(The mass of chicken per serving)
∴ The total number of servings of chicken the food bank can provide = (1,774.4 oz)/(25.2 oz/serving) ≈ 70.413
Given that the servings are in whole numbers, we have;
therefore, To the nearest whole number, the food bank can offer a maximum of 70 servings of chicken.
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The function f open argument x close argument varies inversely with x and f open argument x close argument equals 0.5 when x
The value of function f(x), when x=2.4 is f(x)=0.00625.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
If the function f(x) varies inversely with x, then this function is of the form -
f(x)=a/x
where a is unknown number.
Since f(x)=0.5 when x =0.3, then -
0.5 = a/0.3
a = 0.5 × 0.3
a = 0.15
So, the function now becomes -
f(x) = 0.15/x
Substituting for x = 2.4 -
f(2.4) = 0.15 / 2.4
= 15/240
= 1/16
= 0.00625
Therefore, f(x) value is obtained as 0.00625.
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The function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?
PLEASE HELP ME
6.
Dom is selling pizza at Hoopfest to help him raise money to go on a road trip. He wants each topping to increase the total price at a rate of $1.25. When someone ordered a 3-topping pizza the price was $16.25. Write an equation to represent this data.
Answer : if each topping is 1.25 then multiply that by 3 because there's 3 toppings on the pizza and if the total was 16.25 the original price of the pizza is 12.5. I hope this was the answer you were looking for a good luck :)
Step-by-step explanation:
What is adjacent angle Class 7?
In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.
Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:
Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.
Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.
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