The vertex of the graph of y = 3x² + 2x + 1 is (-0.33, 1.33)
We know that the general form of a parabola is given by an equation y = ax² + bx + c.
the x coordinate of the vertex of the quadratic equation is given by the formula -b/(2a)
To find y-coordinate we substitute value of x in given quadratic equation and solve it for x.
Consider given quadratic equation y = 3x² + 2x + 1
Comparing given quadratic equation y = 3x² + 2x + 1 with y = ax² + bx + c we get, a = 3, b = 2 and c = 1
The x-coordinate of vertex would be,
-b/(2a)
= -2/(2 × 3)
= -2/6
= -1/3
= - 0.33
substitute x = -1/3 in given quadrtic equation in order to find the y-coordinate.
y = 3(-1/3)² + 2(-1/3) + 1
y = (-1)² - 2/3 + 1
y = 2 - 2/3
y = 4/3
y = 1.33
So, (-1/3, 4/3) is the vertex.
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What number is one more than 79?.
The number one more than 79 is 80.
Number:
Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits. In common parlance, a number is indistinguishable from the number it represents.
Greater than Number:
It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">", "equal to" is represented by "=", and "less than" is represented by "<".
According to the Question:
To better understand this question,
It can be expressed as 1 more than 79, 1 more than 79, 1 more than 79, 79 plus 1.
Thus,
1 more than 79 is the same as 79 plus 1. So the answer for 1 greater than 79 is calculated as:
Therefore,
1 + 79 = 80.
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Dee ued 2 1/3 cup of ugar for a cake recipe. If the amount of ugar the container hold i 3 time the amount he ued, doe the container hold more than, le than, or equal to 3 cup of ugar?
The container holds more than 3 cups of sugar, since it holds 3 times the amount used in the recipe.
To calculate the amount of sugar in the container, we need to first determine the amount used in the recipe. The recipe calls for 2 1/3 cups of sugar. This can be converted to a decimal by dividing by 3, resulting in 2.333 cups of sugar used in the recipe. Now that we know the amount used, we can calculate the amount the container holds.
1. 2 1/3 cups = 2.33 cups
2. 3 x 2.33 cups = 6.99 cups
The container holds 3 times the amount used, so we can multiply 2.333 cups by 3, resulting in 6.999 cups of sugar in the container. This is more than 3 cups of sugar, so the container holds more than 3 cups of sugar.
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Answer:
there's nothing there?
What is called equivalence?.
Equivalence is a relationship that exists between two statements such that if the two statements are both true or both false, then the affirmation of one and the negation of the other contradicts itself.
Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities. It can be represented by bars or equal signs. "Equivalence" relies on a specific relationship called an equivalence relationship. Any two elements are said to be equivalent if there is an equivalence relation between them. Also, in mathematics, equality is different from equivalent. The same means the same in all respects, and equivalent means similar but not identical. For example, 2 is said to be equal to 2, but it is equivalent to 1 + 1.
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two linear function are shown. Which function has the greater initial value y=3*+2
A function which has the greater initial value include the following: linear function A.
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
By critically observing the table of values for linear function A, we can reasonably and logically deduce that its y-intercept (initial value) is equal to 8 when the value of "x" is equal to zero (x = 0).
For linear function B, we would substitute the value of x with zero (0) as follows;
y = 3x + 2
y = 3(0) + 2
y = 0 + 2
y = 0.
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There i 64 inger in acquire the tenor and Soprano are in eparate row there are eight inger in each row there are four row of tenor how many row of Soprano are there
There are 4 rows of Soprano. The concept of algebraic manipulation is used to solve the problem.
Given the information that there are 64 fingers in total and 8 fingers in each row of the Tenor, I was able to determine that there are 32 fingers in the Tenor rows by multiplying 8 fingers/row x 4 rows.
Then, We subtracted the number of fingers in the Tenor rows (32 fingers) from the total number of fingers (64 fingers) to find the number of fingers in the Soprano rows, which is also 32 fingers.
Finally, We divided the number of fingers in the Soprano rows by the number of fingers per row (8 fingers/row) to find the number of rows of Soprano, which is 4 rows.
If there are 64 fingers in total and 8 fingers in each row of the Tenor, then there are 8 fingers / row x 4 rows = 32 fingers in the Tenor rows.
Since there are 64 fingers in total and 32 fingers in the Tenor rows, then there are 64 fingers - 32 fingers = 32 fingers in the Soprano rows.
Therefore, there are 32 fingers / 8 fingers/row = 4 rows of Soprano.
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What is the quadratic polynomial whose sum and the product of zeroes is 2 â…“ respectively?.
Zero of the quadratic polynomial whose X²+3X+2 are -2 and -1.
Sum of zeros ( alpha + beta) = -3
Product of zeros ( alpha × beta) = 2.
Quadratic polynomial = X²-(alpha + beta)X+ Alpha× beta = X²-(-3)X+2.
= X²+3X+2 is the required quadratic polynomial.
A = 1 , b = 3 , C = 2
X²+ 3X +2
X² + 2X+ X + 2
X(X+2) +1 ( X+2)
(X+2). ( X+1)
X+2 = 0. X+1 = 0
X = -2. X= -1
Zero of the quadratic polynomial whose X²+3X+2 are -2 and -1.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
Find a quadratic polynomial, the sum, and the product of whose zeroes are -3 and 2 respectively. hence find the zero
What is sin 45 simplified?.
Under Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle.
One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.
The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
To determine a right triangle's unknown angle or sides, utilize the sine function. The sine function for any right triangle with an angle, let's say ABC, will be:
Opposite/hypotenuse = Sin
According to the trigonometric table, the value of Sin 45=[tex]\sqrt[/tex]2/2 which can be simplified as [tex]\sqrt{2} /2[/tex]×[tex]\sqrt{2} /\sqrt{2} =2/\sqrt[]{2}[/tex][tex]=1/\sqrt{2}[/tex]
Simplified value of Sin 45=1/[tex]\sqrt{2}[/tex]
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Anyone who helps w this page gets brainliest
The required coordinates of point Q are (-46/13, 50/13) lie on line PR.
What is a line?A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
Let the coordinate of Q be (x, y)
Given PR with P(-6, -6) and R(-2, 10), it is on PR such that the ratio of PO to PR is 5:8,
Apply the Section formula.
x = mx₂ + nx₁ / m + n ; y = my₂ + ny₁ / m + n
m = 5 and n = 8
Put the values in the section formula along with points.
x = 5 × -6 + 8×-2 / 5 + 8 ; y = -6×5 + 8 × 10 / 8 + 5
x = -46/13 ; y = 50/13
Thus, the required coordinates of point Q is (-46/13, 50/13) lie on line PR.
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Amy flicks the spinner 200 times and it comes up gray 157 times. Do you think Amy's spinner is fair? Explain.
The percentage of getting grey is 78.5%. Amy's spinner is fair.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Amy flicks the spinner 200 times and it comes up grey 157 times.
The percentage of the grey comes up 157 times will be calculated as:-
P = 157 / 200
P = 0.785 x 100
P = 78.5%
Amy's spinner is fair.
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If You Are Measuring The Electrical Potential Difference From A Rectangular \( 9 \Mathrm{~V} \) Battery, Which Setting Should You
A battery is a nice illustration. Atoms have had their electrons chemically removed in batteries. Because the positive ions and electrons are stored at the opposing ends of the battery, there is a potential difference between the two ends.
What is Rectangular?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral a term that refers to a quadrilateral whose angles are all equal or a parallelogram with a right angle. A square is an irregular shape with four equal sides. A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.To learn more about Rectangular, refer to:
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
A sixth grade class is going on a field trip. The school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.
Identify which list below shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots if there are an equal number of each type of sack lunch and students are randomly selecting their lunch. Use this information to mark the probability on the number line.
Answer: List 2
Mark the midpoint between 1/6 and 1/2 (see diagram below)
======================================================
Explanation:
There are 3 meats (ham, turkey, bologna) and 2 vegetables (carrots, celery).
This gives 3*2 = 6 different combos of meat plus a vegetable. This is where we can only pick one of each type.
The 6 different combos are shown in list 2
List 1 is not correct because you can choose one vegetable only, and not have both.
----------
Look through list 2 and circle the options that say "ham, carrots" and "turkey, carrots". There are 2 items that are circled. This is out of 6 total.
We arrive at the probability 2/6 = 1/3
The fraction 2/6, aka 1/3, is located at the halfway point between 1/6 and 1/2. This is because 1/6+1/2 = 1/6+3/6 = 4/6, which divides in half to get 2/6.
See the diagram below.
PLSSSHELP ASAP Determine which integers in the set S:{−40, −10, 20, 40} will make the inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty false.
S:{−40, −10}
S:{−10, 20}
S:{20, 40}
S:{−40, 40}
Answer:
C) S: {20, 40}
Step-by-step explanation:
Given inequality:
[tex]\dfrac{1}{5}(m-5)\leq \dfrac{1}{10}(m-20)[/tex]
To solve the inequality, multiply both sides by 10:
[tex]\implies \dfrac{10}{5}(m-5)\leq \dfrac{10}{10}(m-20)[/tex]
[tex]\implies2(m-5)\leq m-20[/tex]
Expand the left side:
[tex]\implies 2m-10 \leq m-20[/tex]
Subtract m from both sides:
[tex]\implies m-10 \leq -20[/tex]
Add 10 to both sides:
[tex]\implies m \leq -10[/tex]
Therefore, the true solution set to the given inequality are values of m that are less than or equal to -10.
Therefore, the integers in the given set that make the inequality false are the values of m that are greater than -10:
S: {20, 40}The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +8.00 µC; the other two have identical magnitudes, but opposite signs: q2 = -5.00 µC and q3 = +5.00 µC.
(a) Determine the net force (magnitude and direction(measured counter clockwise from the x-axis)) exerted on q1 by the other two charges
(b) If q1 had a mass of 1.50 g and it were free to move, what would be its acceleration?
(a) The net force equation on q1 is 10.6N towards q2. (b) The acceleration of q1 would be 6.8x10^7m/s^2.
a) The Coulomb's law equation for the force between two charges q1 and q2 is given by:
F = k(q1q2)/r2
Where k is the Coulomb's constant and r is the distance between the two charges.
Using this equation, the force on q1 due to q2 can be calculated as:
F12 = (8.99x109 N m2/C2)(8.00x10-6C)(-5.00x10-6C)/(1.00m)2
F12 = -44.8x10-6 N
Similarly, the force on q1 due to q3 can be calculated as:
F13 = (8.99x109 N m2/C2)(8.00x10-6C)(5.00x10-6C)/(2.00m)2
F13 = 55.2x10-6 N
The net force on q1 can be calculated as the vector sum of F12 and F13:
F1 = F12 + F13
F1 = 10.6N towards q2
b) The acceleration of q1 can be calculated using Newton's second law of motion:
F = ma
a = F/m
Where m is the mass of q1.
Therefore, the acceleration of q1 can be calculated as:
a = (10.6N)/(1.50g)
a = 6.8x107m/s2
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Pleas help me I need the answers asap. The reason why I have 3 copy's of the same question is to show the multiple choices.
The solution for the equations is at x = -1 and y = -3.
2: the system of equations has the same slope and the same y-intercept so the system of equations has infinitely many solutions.
What are linear equations?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given the equations,
-2x + 4y = -10
2x + 2y = -8
adding both the equations so -2x and +2x will be eliminated
-2x + 4y + 2x + 2y = -10 - 8
6y = -18
y = -18/6
y = -3
substitute the value of y in equation 2x + 2y = -8
2x + 2(-3) = -8
2x = -8 + 6
x = -1
2: Given equations y = -x + 5 .........(1)
y + x = 5 .........(2)
equation 2 can be written as,
y = -x + 5
so both the equations have the same slope and the same value of y-intercept,
so the line overlaps each other and has infinitely many solutions.
Hence the solution s at x = -1 and y = -3.
2: Equations have infinitely many solutions.
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The length of my living room is 24 feet.the width of my living room is 1/2 the length.what is the area of my living room
Answer: 24 x 1/2(24) = 288
Step-by-step explanation:
Half of 24 is 12.
Multiply 24 by 12 = 288
O is the centre of the circle, work out the value of X.
Answer:
69
Step-by-step explanation:
The central angle is twice the inscribed angle. So the angle that is behind the one equal to 2x is equal to x. We know that the opposite angles in a circle add up to 180. Therefore, we can solve for x:
[tex]x + x + 42 = 180$^{\circ}$\\\\2x = 180$^{\circ}$ - 42$^{\circ}$\\\\2x = 138$^{\circ}$\\\\x = 69$^{\circ}$[/tex]
what is the circumfrence of this circle r = 2 km
Answer:12.57
Step-by-step explanation:
Given that radius of the circle= 2km
as we know the formula of circumference of the circle as
Circumference of the circle= 2* pi * radius
circumference of the circle = 2*pi*2
= 2* 22/7*2
=88/7
=12.57
At which points are the functions y = f(x) and y = g(x) equal? What are the x-values of the solution?
The correct option regarding the solution to the system of equations is given as follows:
It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.
Hence the x-value of the solution is given as follows:
x = 3.
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.
Missing InformationThe complete problem is given as follows:
If x=3 is a solution to f(x)=x²-x and g(x)=2x, why is it also a solution to f(x) = g(x)
(1 point)
O It is a solution to f(x) = g(x) because it is the x-intercept of the two graphs
O it is a solution to f(x) = g(x) because it is the y-intercept of the two graphs.
O It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect
O it is a solution to f(x) = g(x) because both graphs are positive at x = 3.
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What are the factors of 9x2 24x 16 *?.
Answer:81, 384
Step-by-step explanation:
9x2 is 18
you can count 9+9 which would be the same as 9*2. 24x16 is 384.
A chef bought 1.48 kilograms of almonds and 8.74 kilograms of pecans. How many kilograms of nuts did the chef buy in all?
I need help!!
Answer:
10.22 kilograms
Step-by-step explanation:
you do 1.48+8.74=10.22
The chef bought 10.22 kilograms of nuts in total.
To find the total amount of nuts the chef bought, we add the number of almonds to the number of pecans:
1.48 kg + 8.74 kg = 10.22 kg
So the chef bought 10.22 kilograms of nuts in total.
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The population of a small town is decreasing at a rate of 7% per year. If the towns population is 12,259 now, what will be the population in 10 years? Around to the nearest whole number
The population of the town after 10 years will be, 5933
What is decrease rate?The decrease rate of a value measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.
Given that, the population of a small town is decreasing at a rate of 7% per year. If the town's population is 12,259 now,
The decrease rate =
A = P(1-r)ⁿ
A = final population
P = initial population
r = rate
n = time
A = 12259(1-0.07)¹⁰
A = 5933
Hence, the population of the town after 10 years will be, 5933
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find the size of QRS.
8 cm
12 cm
4 cm
Q
R
P
The size of QRS in the given figure 15 cm.
How to find the size of QRS?A fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean theorem, also referred to as Pythagoras' theorem. According to this definition, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
step1
We know
PS=8cm
PQ=12cm
QR=4cm
because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.
a² + b² = 4² (add in values)
8² + 12² +4²
64 + 144 +16=224
find the square root of 224= 15
Size of QRZ =15 cm
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The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500. The price that is 3 standard deviations above the mean is $ . The price that is 2 standard deviations below the mean is $ . The percentage of buyers who paid between $16,500 and $17,500 is % The percentage of buyers who paid between $17,000 and $18,000 is %. The percentage of buyers who paid less than $16,000 is %.
The price that is 3 standard deviations above the mean is $18,500. The price that is 2 standard deviations below the mean is $15,500.
The percentage of buyers who paid between $16,500 and $17,500 is approximately 13.6%.
The percentage of buyers who paid between $17,000 and $18,000 is approximately 34.1%.
The percentage of buyers who paid less than $16,000 is approximately 2.3%.
It's important to note that these values are approximate and based on the assumption that the prices paid for the car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500. It's also worth mentioning that these percentages are based on the standard normal distribution table which assumes a normal distribution with a mean of 0 and a standard deviation of 1.
I hope this helps :)
How do you multiply 3 mixed fractions?.
To multiply mixed numbers, first change them to improper fractions. Next, simplify, or reduce, the fractions by removing common factors. Then multiply the numerators, and multiply the denominators. Simplify, or reduce the answer if possible. Finally, if the answer is an improper fraction, you can change it back to a mixed number.
Now, According to the question:
A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
To multiply mixed numbers, first change them to improper fractions. Next, simplify, or reduce, the fractions by removing common factors. Then multiply the numerators, and multiply the denominators. Simplify, or reduce the answer if possible. Finally, if the answer is an improper fraction, you can change it back to a mixed number.
Here's an example of a multiplication problem with three mixed numbers:
[tex]3\frac{1}{3}[/tex] × [tex]5\frac{1}{4}[/tex] × [tex]1\frac{1}{2}[/tex]
= 10/3 × 21/4 × 3/2
By Simplification, we have:
=> 105/4
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What are the rules for plotting a graph?.
There are various rules for plotting a graph which includes having scale over X and Y axis.
The options for vertical bar charts are shown below. For horizontal bar charts, swap out "vertical" for "horizontal" and "horizontal" for "vertical."
1. A title ought to be at the top of the graph.
2. The vertical axis' scale has to be consistent and set to 0.
3. Utilise horizontal gridlines.
4. Each bar's definition ought to be listed on its label.
5. The label for the horizontal axis should include a description of the qualitative variable that the bar chart represents. In the event if the labels on each individual bar are sufficiently illustrative, a horizontal axis label is not required.
6. It should say "Count" or "Frequency" on the vertical axis.
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Adam has a points card for a movie theater.
• He receives 60 rewards points just for signing up.
• He earns 12.5 points for each visit to the movie theater.
•He needs at least 160 points for a free movie ticket.
Answer:
60+12.5x=160
12.5x=100
x=8
Step-by-step explanation:
Which answer best describes the quadratic formula?
Group of answer choices
A formula that can determine the sides of a right triangle
A formula that can solve quadratic equations in standard form
A formula that can solve linear equations
A formula that can solve quadratic equations in vertex form
Flag this Question
Question 21 pts
Select each quadratic expression that is in standard form.
Group of answer choices
LaTeX: 4x^2+8x-2x+104 x 2 + 8 x − 2 x + 10
LaTeX: -3x^2+5x-9− 3 x 2 + 5 x − 9
LaTeX: 5x^2-3+2x5 x 2 − 3 + 2 x
LaTeX: \frac{3}{5}x^2-6x+100000003 5 x 2 − 6 x + 10000000
The quadratic formula is an algebraic formula that provides the solutions to a quadratic equation. A quadratic equation is an equation of the shape ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula gives the values of x that satisfy the equation and is expressed as:
x = (-b ± √ (b^2 - 4ac)) / (2a)
In other words, the quadratic formula provides a method for finding the two roots of a quadratic equation, even if the equation cannot be solved by factoring or other methods.
The formula works for all quadratic equations and is a widely used tool in mathematics and various scientific and engineering fields.
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Please answer this question with decent explanation. Thank you.
Answer: Transversal
Step-by-step explanation:
Altitude is in the triangle as it has vertexes shown by the line, Hypotenuse is the longside of the triangle which is shown, and the legs, every single triangle has legs, which leaves us with transversal which means a straight line that cuts a parrel line. Which isn't shown so that's the answer. Have a good day ;)
7
If f(x)=√x-5 and g(x) = -x², what is the value of g(f(9))?
A 4
C 16
B -14
D 2
Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.
What is a function?
A relation known as a function connects members of one set in a specific way to those of another set.
Given, f(x)=√x-5 and g(x) = -x²
here, g(f(x)) = g(√x-5 )
= - (√x-5)²
So, g(f(9)) = - (√9 - 5)²
= - (3-5)²
= -4
Hence, Option (a) is correct.
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Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.
What is a function?a mathematical phrase, rule, or law that establishes the link between an independent variable and an outcome variable (the dependent variable). An input and also an output are linked by a function. It functions similarly to a machine with an input or an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
Given, f(x)=√x-5 and g(x) = -x²
here, g(f(x)) = g(√x-5 )
= - (√x-5)²
So, g(f(9)) = - (√9 - 5)²
= - (3-5)²
= -4
Hence, Option (a) is correct.
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