A spinner simulation with an 8-section spinner and 7 trials would be appropriate.
Vince makes 75% of his free throws, so there is a 75% chance that he will make any given free throw. In order to simulate his free throw shooting and predict the probability that he will make 6 of his next 7 free throws, a spinner simulation with an 8-section spinner would be appropriate. The 8 sections would represent the possible outcomes of each free throw attempt: make or miss. The spinner would need to be spun 7 times to represent the 7 free throw attempts Vince will take. This simulation would allow Vince to see the probability of making 6 out of 7 free throw attempts based on his 75% success rate.
To learn more about probability, visit:
brainly.com/question/30034780
#SPJ4
Given the quantity of 3 x squared plus x minus 4, all over x minus 1, what are the domain and range? domain is x is all real numbers where x does not equal negative 1 comma range is y is all real numbers where y does not equal 1 domain is x is all real numbers where x does not equal 1 comma range is y is all real numbers where y does not equal negative 1 domain is x is all real numbers where x does not equal negative 1 comma range is y is all real numbers where y does not equal negative 7 domain is x is all real numbers where x does not equal 1 comma range is y is all real numbers where y does not equal 7
The domain and range are equal to: D. domain is x is all real numbers where x does not equal 1 comma range is y is all real numbers where y does not equal 7.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain represents the input values (x-values) to a function.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.
Translating the word sentence into an algebraic expression (function), we have;
Function = (3x² + x - 4)/(x - 1)
Function = (3x² + 4x - 3x - 4)/(x - 1)
Function = [(3x + 4)(x - 1)]/(x - 1)
Function = 3x + 4
Note: The domain is all real numbers except one (1) because one (1) would make the function to become undefined.
When x = 1, the range of this function are all real numbers except;
Range = 3x + 4
Range = 3(1) + 4
Range = 7
Read more on range here: https://brainly.com/question/28190802
#SPJ1
can someone pls explain this, I'm stuck
Answer:
A = 6
B = 4
C = 8
D = 10
surface area ❀
leftmost rectangle : 8 x 4 = 32
middle rectangle : 10 x 4 = 40
rightmost rectangle : 6 x 4 = 24
top and bottom triangles : (8 x 6) = 48
total = 32 + 40 + 24 + 48 = 144cm²
Step-by-step explanation:
not sure if its correct. but i tried.
The solution is
The measure of A = 6 cm
The measure of B = 4 cm
The measure of C = 8 cm
The measure of D = 10 cm
b) The net surface area of the triangular prism = 144 cm²
What is the surface area of the prism?
The surface area of the prism is calculated as
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
Given data ,
Let the measure of the side A = 6 cm
The measure of side B = 4 cm
The measure of side C = 8 cm
The measure of side D = 10 cm
The surface area of the triangular prism is = 2B + ph
The surface area A = ( 6 x 8 ) + ( 6 x 4 ) + ( 10 x 4 ) + ( 8 x 4 )
The surface area A = 48 + 24 + 32 + 40
The surface area A = 144 cm²
Therefore , the value of A is 144 cm²
Hence , the area of the triangular prism is 144 cm²
To learn more about triangular prism click :
https://brainly.com/question/9183590
#SPJ2
If triangle abc is rotated 90 degrees clockwise about the origin, what are the coordinates of b'?.
After rotating 90 degrees anticlockwise, B's new coordinates are (y, -x).
By switching the x and y coordinates and negating the new x coordinate, we can rotate a point (x, y) 90 degrees clockwise around the origin.
After rotating the triangle 90 degrees anticlockwise around the origin, note the new coordinates of B.
Let (x, y) be point B's coordinates.
Fllowing a 90° anticlockwise turn:
B'x, the modified x coordinate, will now be y.
B'y, the modified y coordinate, will now be -x.
Therefore, B's new coordinates are (y, -x).
Learn more about Rotation here:
https://brainly.com/question/1571997
#SPJ12
Which transformations can prove that figures are congruent?
Answer:
TranslationsRotationsReflectionsStep-by-step explanation:
Translations, rotations, and reflections can prove that figures are congruent because these transformations preserve angle measures and distances of the figures. These transformations are also called rigid motions.
Mrs. Crosland asked students to factor the expression 28x−8. The students offered the answers shown in the box.
Which student(s) offered answer(s) equivalent to the original expression?
Responses
only Danny
only Danny
only Irene
only Irene
both Carlos and Danny
both Carlos and Danny
both Carlos and Irene
both Carlos and Irene
Both Carlos and Irene offered answers equivalent to the original expression.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is
28x − 8.
The prime factors of 28 is 2 and 7.
Rewrite 28 as the product prime factors:
28 = 7 × 2 × 2.
The prime factors of 8 is 2.
Rewrite 8 as the product prime factors:
8 = 2 × 2 × 2.
Replace 28 = 7 × 2 × 2 and 8 = 2 × 2 × 2 in the given expression:
28x − 8
= (7 × 2 × 2) x − (2 × 2 × 2)
Taking common 2
= 2[ (7 × 2)x − (2 × 2)] = 2(14x − 4)
Again taking common 2:
= 2× 2[ 7x − 2]
= 4(7x − 2)
Thus 2(14x − 4) and 4(7x − 2) is the equivalent expression of 28x − 8.
To learn more about factor, click on below link:
https://brainly.com/question/18674832
#SPJ1
what is the inequality:the sign below the troll for driving on alligator alley. Passenger cars troll:2.50. write an inequality to represent the number of times someone can drive on alligator alley with $15.
Answer:
2.5n ≤ 15
Step-by-step explanation:
Let n = number of times
Each toll is $2.50, so the toll for n trips is n times $2.50, or 2.5n.
The total amount of money available is $15, so 2.5n must be less than or equal to 15.
Inequality:
2.5n ≤ 15
(In case you're asked next, here is the solution of the inequality:
Divide both sides by 2.5.
2.5n/2.5 ≤ 15/2.5
n ≤ 6
A person can drive up to 6 times with $6.)
Which is not a test for similarity 1⃣ SSS 2⃣ SAS 3⃣ AAA 4⃣ ASA?
From the given options ASA is not a test for similarity. Hence option D is the correct answer.
Theorem for similarity of triangles states that we can say two triangles are similar if their corresponding angles are same and the corresponding sides are same. And a result of that their corresponding remaining sides and angles will be also equal.
Hence the possible similarity postulates for two triangles to be similar are AAA(angle angle angle) SAS(side angle side),SSS(side side side)
Therefore the correct option is D. angle side angle (ASA) is the one which does not fall under similarity test.
Learn more about similarity :
https://brainly.com/question/21247688
#SPJ4
The following three shapes are based only on squares, semicircles,
and quarter circles. Find the perimeter and the area of each shaded
part. Give your answer as a completely simplified exact value
in terms of 7 (no approximations).
ABCD is 8cm
Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.
Definition of accuracy-The accuracy formula provides accuracy as a difference of error rate from 100%. To find accuracy we first need to calculate the error rate. And the error rate is the percentage value of the difference of the observed and the actual value, divided by the actual value.
Given: A study of the accuracy of fast food drive-through orders, one restaurant had 37 orders that were not accurate among 333 orders observed. Significance level-0.05
Explanation: Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.
Let a be the population proportion of the orders that were not accurate.
Then according to the claim we have,
[tex]H_{o} :[/tex] [tex]p[/tex] = [tex]0.10[/tex]
[tex]H{a} :p[/tex] ≠ [tex]0.10[/tex]
Since the alternative hypothesis is two-tailed so the hypothesis test is a two-tailed test.
For example,
n = 333
The proportion of the orders that were not accurate = [tex]p{'}[/tex][tex]=\frac{37}{333}[/tex] ≈[tex]0.112[/tex]
Test statistics for population proportion:-
Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.
Let a be the population proportion of the orders that were not accurate.
Then according to the claim we have,
[tex]H_{o} :p=0.10[/tex]
[tex]H_{a} :p[/tex] ≠ [tex]0.10[/tex]
Since the alternative hypothesis is two-tailed so the hypothesis test is a two-tailed test.
For example,
n = 333
The proportion of the orders that were not accurate = [tex]p^{'} =\frac{37}{333}[/tex] ≈ [tex]0.112[/tex]
Test statistics for population proportion:-
[tex]z=\frac{p-p'}\sqrt{p(1-p)/\sqrt{n}[/tex][tex]=\frac{0.112-0.10}\sqrt{0.10(0.90)}/ {333}[/tex] ≈ [tex]0.75[/tex]
By using the standard normal distribution table,
The p-value : [tex]2(z > 0.75)=2.55[/tex]
Since the p-value is greater than the significance level (0.05), so we do not reject the null hypothesis.
Hence, we conclude that the accuracy rate appears to be acceptable and satisfactory.
To learn more about accuracy rate visit:
brainly.com/question/18882142
#SPJ4
select all the true: ninety-six golf balls were picked up at the driving range and placed into two buckets. one bucket has twenty-eight more balls then the other bucket. how many gold balls are in each bucket?
The number of golf balls that are in each bucket would be = bucket X = 62, bucket y = 34
What is division?Division is one of the major arithmetic operation that is used to know the number of groups that can be placed under data sets when shared.
The number of golf balls that are picked up at driving range = 96
The number of buckets present= 2( X and y)
Bucket X = 28 + a
Bucket y = a
To calculate for each bucket first find a.
But 96 = 28+ a+ a
96 = 28 + 2a
2a = 96- 28
2a = 68
a = 68/2 = 34
Bucket X = 28+34 = 62
Bucket y = 34.
Learn more about range here:
https://brainly.com/question/26098895
#SPJ1
What is set in math 6?
Set is a collection of unique objects. The objects are unique, that is there is no repetition in set, making it distinct from a group. A set is well defined.
In mathematics, the objects belonging to a set are called the elements of that particular set.
These elements will be listed in a pair of curly brackets. For example, A is a set of first ten natural numbers, that is its elements are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. According to the notation
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
To know more on sets
https://brainly.com/question/8053622
#SPJ4
Why is the AAA similarity test not necessary?
Knowing merely angle-angle-angle (AAA) does not work, because it can result in triangles that are similar but not congruent.
A set of triangles must have equal sides and angles in order for them to be congruent. The sides of the triangles may or may not be equal in the case of a triangle with all of the corresponding angles equal, or the AAA condition. Only if the two triangles are similar would the congruence be true for two triangles with identical respective angles.
So, knowing merely angle-angle-angle (AAA) does not work, because it can result in triangles that are similar but not congruent.
To learn more about AAA Theorem link is here
brainly.com/question/29887944
#SPJ4
10.Rohan's maid has two children of same age. Both of them have equal number of dresses. Rohan on his birthday, plans to give both of them same number of dresses. What can you say about the number of dresses each one of them will have after Rohan's birthday? Which Euclid's axiom is used to answer this question?
Answer:
Step-by-step explanation:
Rohan is a generous person who cares deeply for his maid and her two children. On Rohan's birthday, he plans to give both of them the same number of dresses. This situation can be solved using Euclid’s axiom that states “things which are equal to the same thing are also equal to one another”. Therefore, after Rohan's birthday each child will have an equal number of dresses as they were given an identical amount from him.
This kind gesture by Rohan demonstrates his commitment towards taking care of those around him and providing fairness in all situations possible - it serves as a reminder that we should always strive for equality among people regardless of their backgrounds or social statuses in life! By following this axiom, everyone can benefit from having access to resources no matter what their circumstances may be; thus creating a more equitable society overall.
The act done by Rohana is praiseworthy and must serve as an example for others too so they understand how important it is treat everyone equally regardless if they belong to different castes or classes in our society! We should take measures like these on regular basis so that true justice prevails everywhere without any discrimination whatsoever- this would make sure everybody has access basic necessities such us clothes just like Rohana provided his maid's kids with new sets on his own birthday!
How do you graph a slope of 3?
The graph of a slope of 3 is a straight line.
What is a slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass. Any two distinct places along the line can be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the "vertical change" to the "horizontal change" in each case. The difference between the line's y and x coordinate changes is known as the slope of the line.Here, let us graph a line with slope = 3Let us assume the co-ordinates
[tex](x _1, y_1) = (2,1)\\(x _2, y_2) = (5,10)\\\\\text{We know} ,\\\\m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m = \frac{10-1}{5-2} \\[/tex]
m = 9/ 3
m = 3 (Refer image for graph)
To learn more about slope, refer:
https://brainly.com/question/16949303
#SPJ4
A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are $7, $8, $8, $15, $15, $16, $17, $18, and $20, which word or phrase best describes this kind of advertising?
accurate
inaccurate
inaccurate and misleading
accurate, but misleading
The word or phrase no which best describes this kind of advertising is inaccurate.
The correct answer option is option B
What is mode?Mode refers to a statistical data which occurs most in a given set of data.
Advertisement can be defined as a commercial solicitation by a producer to the public in order to buy his product.
Given data:
$7, $8, $8, $15, $15, $16, $17, $18, and $20
$8 appeared twice$15 appeared twiceHence, it can be said that the mode of the most popular meals is not $8
Therefore, using $8 as a kind of advertisement for the mode of most popular meals is inaccurate
Read more on mode:
https://brainly.com/question/12047942
#SPJ1
What is the median of 10?
The required median of the first ten natural numbers is 5.5.
The median is the number in the middle of a list of numbers in ascending order, from lowest to highest.
The median is the middlemost element if the total number of elements in the list is odd, and the median is the average of the middlemost two values if the total number of elements in the list is even.
The list of the first 10 natural numbers is: 1,2,3,4,5,6,7,8,9,10
Here is the total number of elements in the list is even.
And the two middlemost elements are 5 and 6.
The required median is: 5+6 /2 = 11/2 = 5.5
Hence, the required median of the first ten natural numbers is 5.5.
To know more about median visit: brainly.com/question/28060453
#SPJ4
In the blank alo write the reaon for your anwer a rational number P by Q i aid to be in a lowet form if P and Q have no Dah
P/Q is in the lowest form as the when the HCF is 1 and if we divide it by 1 P/Q remains same so it is the lowest form ,if P and Q have no common factor other than 1.
What is rational number?It is possible to express rational numbers in the form p/q, where p and q are integers and q≠0.
What is lowest form of Rational number?If there is just one other common factor between the denominator and numerator of a rational number, that number is said to be in its lowest form. In other words, if the HCF of a and b is 1 and a and b are relatively prime, then we can state that a rational number a/b is considered to be in its simplest form.
as described in the above contion in order to reduce any rational number to its lowest form we need to divide both numerator and denominator by the HCF of p,q . suppose if the HCF of p,q is 1 then divide p and q 1 won't change the value of the rational number.
so, now it is shown that the given rational number can't be further deduced and hence we conclude that a rational number is in lowest form when HCF of its numerator and denominatior is equal to 1.
To know more about rational number click on below link:
https://brainly.com/question/24398433#
#SPJ4
Complete question:
Write the reason why a rational number written in the form of p/q is said to be in lowest form if P and Q have no common factor other than 1.
What is the nature of the roots of the quadratic equation √ 3x² 10x 7 √ 3 0?
The nature of the roots of a given quadratic equation √3x²+10x+7√3=0 is real and distinct because of the value of b²-4ac>0.
where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0
Given quadratic equation is √3x²+10x+7√3=0 on comparing with the standard form of a quadratic equation ax²+bx+c=0. Hence a=√3,b=10,
and c=7√3
Now b²-4ac=10²-4×√3×7√3=100-28×3=16>0.
here the value of b²-4ac is greater than 0.
We know if the value of b²-4ac then the roots of the given equations are real and distinct.
To know more about the quadratic equations-related questions click on the below link:
brainly.com/question/1863222
#SPJ4
Am I doing this right please help
The correct solution of the given function is g'(t)=20 for some t in the interval. The correct option is (B).
Definition of function- Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in sciences.
Given that g(10)= 220, g(0)=20
Explanation: A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
So putting values in condition of differentiation for increasing function we get:
=[tex]\frac{g(10)-g(0)}{10-0}[/tex]=[tex]\frac{220-20}{10}[/tex]=[tex]\frac{200}{10}[/tex]=20
The correct solution for given function is g'(t) = 20 for some t in the interval.
Learn more about function here:
brainly.com/question/28303908
#SPJ4
What is meant by rigid transformation?
Rigid transformation is a type of geometric transformation in which the shape of an object is preserved. It includes translations, rotations, and reflections, but does not include any scaling, shearing, or any other kind of distortion. In other words, rigid transformations preserve the distances between points in an object.
Transformations – what are they?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.
A transformation example is what?A dramatic change in look or form is referred to as a transformation. An important event, such as acquiring your driver's license, starting college, or getting married, may cause your life to alter. A metamorphosis is a significant, abrupt change.
To know more about transformation visit:
https://brainly.com/question/8568509
#SPJ4
What is the solution to the system of linear equations?
Answer:
(0,2)
Step-by-step explanation:
The equations must be derived from the graph:
First, find the slope of f(x):
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] let [tex](x_1,y_1)=(-3,3)[/tex] and [tex](x_2,y_2)=(3,1)[/tex]
[tex]m=\frac{(1)-(3)}{(3)-(-3)}\\m=\frac{-2}{6}\\m=-\frac{1}{3}[/tex]
Then use [tex]y-y_1=m(x-x_1)[/tex]
[tex]y-3=-\frac{1}{3}[x-(-3)]\\y-3=-\frac{1}{3}x-1\\y=-\frac{1}{3}x+2\\f(x)=-\frac{1}{3}x+2[/tex]
For g(x), let:
[tex](x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)[/tex]
[tex]m=\frac{(2)-(0)}{(0)-(-3)}\\m=\frac{2}{3}[/tex]
[tex]y-0=\frac{2}{3}[x-(-3)]\\y=\frac{2}{3}x+2\\g(x)=\frac{2}{3}x+2[/tex]
Now, to solve for x, allow the two expressions written in terms of x equal each other.
[tex]-\frac{1}{3}x+2=\frac{2}{3}x+2\\(-\frac{1}{3}x+2)+\frac{1}{3}x=(\frac{2}{3}x+2)+\frac{1}{3}x\\2=x+2\\(2)-2=(x+2)-2\\x=0[/tex]
To solve for y, substitute 0 for x in f(x):
[tex]y=-\frac{1}{3}x+2\\y=-\frac{1}{3}(0)+2\\y=0+2\\y=2[/tex]
So, the solution to this system of equations would be the ordered pair (0,2). This solution is seen on the graph as the intersection of the two lines.
Help help meeeeee help meee please asap please !!??
Step-by-step explanation:
12 boxes * 8 candies = 96 total
divided among 30 kids:
each kid gets 3 pieces with (96 - (30 *3)) = 6 remaining.
What is the symbol of linear inequality?
There are four types of symbols that are used to represent linear inequalities.
What is the definition of inequality symbol?
A quick way to compare distinct quantities is to utilise inequality symbols. "Greater than," "less than," "greater than or equal to," and "less than or equal to" are the four inequality symbols. Thus, the phrase "5 is greater than 2" may be represented as "5>2."
What does inequality simply means?
Inequality is a relationship between two expressions or values that is not equal to each other.
There are four symbols of inequalities:
>: greater than
<: less than
≥: greater than or equal to
≤: less than or equal to
≠: not equal to
To learn more about inequality symbol visit the link:
https://brainly.com/question/30092326
#SPJ4
What is the median of the following 3 4 5 3 6 7 2?
To find the median of a set of numbers, you first need to put the numbers in order from smallest to largest. Once the numbers are ordered, the median is the middle number in the list.
In this case, the ordered list of numbers is: 2, 3, 3, 4, 5, 6, 7.
The median of this list is 4.
The mathematical median is what?Sorting all the data points and selecting the central one are required to determine the middle number (or if there are two middle numbers, taking the mean of those two numbers). Example: The number 4 is in the middle when the numbers are grouped (1, 4, 7), making it the median of the numbers (4, 1 and 7).
How can you determine a median?By summing up the center values and dividing them by two, you may obtain the mean and, from there, the median.
To know more about median visit:
https://brainly.com/question/21396105
#SPJ4
For what values of k the roots of the quadratic equation 9x 2 )+ 3kx 4 0 are equal?
The value of k is ±4 so that the roots of the quadratic equation 9x² + 3kx +4 are equal
A second-degree polynomial equation, which must contain at least one squared component, is what is known as a quadratic. Quadratic equations is another name for them. The quadratic equation's general form is as follows: ax² + bx + c = 0
Quadratic equation, ax2 + bx + c = 0 has equal roots if (b2 - 4ac) = 0
Hence in quadratic equation, 9x2 + 3kx +4 = 0 has equal roots if
(3k)² - 4×9×4 = 0
Hence 9k² = 144 or k² = 16 or k = ±4
In order for the roots of the quadratic equation 9x2 + 3kx + 4 to be equal, the value of k must be 4.
To learn more about the Roots click here :
brainly.com/question/12029673
#SPJ4
Purchasing 5 bananas and a $3.50 pineapple costs the same as purchasing 7 bananas and a pear that costs 90 cents. What is the cost of each banana?
Answer:
$0.52
Step-by-step explanation:
the pear is 0.90 and the total for the 5 bananas and one pineapple is 3.50
3.50-0.90=2.6 2.6/5=$0.52
Which triangles must be congruent? two isosceles triangles, each with both legs 40 inches long. two isosceles triangles, each with a base 40 inches long. two right triangles, each with both legs 40 inches long. two right triangles, each with a hypotenuse 40 inches long.
Answer:
(c) two right triangles, each with both legs 40 inches long
Step-by-step explanation:
You want to know which pair of triangles are congruent, given their descriptions.
Congruent trianglesThere are basically 4 theorems that allow you to claim congruence of triangles:
AAS, ASA, SAS, SSS
A fifth one applies to right triangles only: HL.
These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.
ChoicesAn isosceles triangle with only one or two sides defined is not sufficient.
A right triangle with only the hypotenuse defined is not sufficient.
A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.
What is the nature of the roots of the quadratic equation 9 x2 6x =- 9?
The nature of the roots of the quadratic equation x² - 6x + 9 = 0 are real and equal
Given that :
The quadratic equation x² - 6x + 9 = 0
To find :
The nature of the roots of the quadratic equation x² - 6x + 9 = 0
x² - 6x + 9 = 0
Find discriminant of the equation
Comparing the given Quadratic equation x² - 6x + 9 = 0 with the general equation ax² + bx + c = 0 we get
a = 1 , b = - 6 , c = 9
The discriminant of the quadratic equation
= b² - 4ac
= (-6)² - 4* 1*9
=36 - 36
=0
Find nature of the roots of the quadratic equation
Since the discriminant of the quadratic equation = D = 0
Hence the roots of the quadratic equation x² - 6x + 9 = 0 are real and equal
To learn more about the Discriminant click here :
brainly.com/question/15884086
#SPJ4
PLEASE HELP I WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!
Use mathematical induction to prove that 1 + 2 + 3 + … + n = (1/2) n (a1 + an).
Use the result to find the sum of 1 + 2 + 3 + ... + 500.
Answer:
See below for proof.
[tex]S_{500}=125250[/tex]
Step-by-step explanation:
Given arithmetic series:
1 + 2 + 3 + … + nTherefore:
[tex]S_n=1+2+3+...+(n-2)+(n-1)+n[/tex]
[tex]S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)[/tex]
[tex]S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))[/tex]
Let:
a = first term = 1d = common difference = 1n = nth termTherefore:
[tex]S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)[/tex]
Reverse the order:
[tex]S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a[/tex]
Add the two expressions for Sₙ:
[tex]2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)[/tex]
Therefore, the term (2a + (n – 1)d) has been repeated n times:
[tex]2S_n=n(2a+(n-1)d)[/tex]
Divide both sides by 2:
[tex]S_n=\dfrac{1}{2}n(2a+(n-1)d)[/tex]
[tex]S_n=\dfrac{1}{2}n(a+a+(n-1)d)[/tex]
Replace a with a₁ (first term) and a + (n – 1)d with aₙ (last term):
[tex]S_n=\dfrac{1}{2}n(a_1+a_n)[/tex]
To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:
a₁ = 1aₙ = 500n = 500Therefore:
[tex]\implies S_{500}=\dfrac{1}{2}(500)(1+500)[/tex]
[tex]\implies S_{500}=250(501)[/tex]
[tex]\implies S_{500}=125250[/tex]
In a certain school, there are 180 students, 110 study french, 88 studied German and 65 Study Spanish . 40 students Study both french and German, 38 Study German only , 20 study french and Spanish , 25 study German and Spanish .
find the number of students who study
1. all 3 languages
2. Spanish only
3. none of the languages
4. at least one language
Answer:
1. 38 = 88 - (10 + x + 25)
38 = 88 - 35 - x
x = 53 - 38
x = 15
There are 15 students who study 3 languages2. Spanish only = 65 - (5 + 15 + 10)
= 65 - 30
= 35
There are 35 students who study Spanish only3. x = 180 - (65 + 25 + 38 + 15 + 5 + 10 + 35)
x = 180 - 193
x = -13
There are 13 students who studied none4. 65 + 38 + 35
= 138
There are 138 students who studied one language onlyStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-At a real estate agency, an agent sold a house for $375,000. The commission rate is 6.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The real estate agency made $24,375 on the house. The agent earned $6,093.75 in commission.