The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,
⇒ f (x) = x³ + 4x² - 7x - 10
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
For a polynomial,
A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Now, We know that;
The standard polynomial is given by:
⇒ f (x) = a (x - p) (x - q) ...
Where, 'a' is leading coefficient and p, q, .. are zeroes.
Here, A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Hence, The polynomial is,
⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)
⇒ f (x) = (x + 5) (x + 1) (x - 2)
⇒ f (x) = (x + 5) (x² - 2x + x - 2)
⇒ f (x) = (x + 5) (x² - x - 2)
⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10
⇒ f (x) = x³ + 4x² - 7x - 10
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find the area of a triangle with height 6 1/2cm and base 3 1/4cm
Answer:
10,5625
Step-by-step explanation:
S (triangle) = 1/2 * a * h
a= 3 1/4 = 3.25
h = 6 1/2= 6.5
=> S= 10,5625
the triangular region shows the number of possible walnuts, x, and number of possible chocolate chips, y, a baker can use in a recipe.which combination of walnuts and chocolate chips can the baker use?
28 walnuts and 20 chocolate chips are the combinations that the baker can use.
X stands for the total number of possible walnuts and y stands for the number of potential chocolate chips.
From the graph we can see:
a) 25 chocolate chips and 33 walnuts
Specifically, points (33,25) on the graph are outside the shaded region or the feasible region.
Therefore, it cannot be a solution.
b) With 10 chocolate chips and 45 walnuts.
i.e., the coordinate point (45,10) also lies outside the shaded area, making it impossible for this to be a solution to the problem.
c) The given problem will have an answer at point (28,20), which is located inside the shaded area.
d) with 12 chocolate chips and 55 walnuts.
Point (55, 12) is not a viable solution because it lies outside the shaded area.
Hence, 28 walnuts and 20 chocolate chips in combination are the ones baker can use.
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The full question is:
The triangular region shows the number of possible walnuts, x, and the number of possible chocolate chips, y, a baker can use in a recipe.
Which combination of walnuts and chocolate chips can the baker use?
A. 33 walnuts and 25 chocolate chips
B. 45 walnuts and 10 chocolate chips
C. 28 walnuts and 20 chocolate chips
D. 55 walnuts and 12 chocolate chips
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 3(m∠Y) − 70°. Find m∠Y.
The value the angles Y is 40° if ∠S and ∠Y are complimentary, as stated in the previous sentence.
Do you mean complimentary or complimentary?Complement or "favorable" refers to "offering a compliment." In the context of goods or services offered as a favor, it can also signify "free." The term "complementary" means to emphasize or enhance the positive aspects of that other person or object.
Angles that add up to 90 degrees are said to have complementary angles.
As a consequence, the value of factor y will be determined using the information provided:
x + y = 90°
3y - 70° + y = 90°
Collect like terms
3y + y = 90° + 70°
4y = 160°
y = 160/4
y = 40°
Angle y has a value of 40°.
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A dog trainer compared mean numbers of lessons for two
groups of dogs to learn a new trick.
Answer ASAP will give brainliest
A true statement on the mean number of lessons for the dogs is The mean number of lessons for group A is greater than the mean for group B by 1 MAD.
How to prove the mean number ?The difference in the mean number of lessons between the two groups being Group A and Group B is :
= Mean number of lessons Group A - Mean number of lessons Group B
= 5 - 3
= 2
The mean absolute deviation for Group B is 2. The mean number of lessons of group A related to this is :
= 2 / 2
= 1
This shows that the mean number of lessons for group A is greater than the mean for group B by 1 MAD.
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The full question is:
Mean number of lessons Mean Absolute Deviation (MAD)
Group A 5
Group B 3
2
2
Which statement about the data is true?
A. The mean number of lessons for group A is greater than the mean for group B by 1 MAD
B. The mean number of lessons for group A is greater than the mean for group B by 2 MAD
C. The MAD for group A is more than the MAD for group B
D. On average, the dogs in group B required more lessons than the dogs in group A
What are x and y i don't know
Answer:
Step-by-step explanation:
Perimeter of the rectangle= 42 cm
Length= x
Breadth= y
2(x+y)= 42
x+y= 42/2= 21 (Let it be the first equation)
Perimeter of the triangle= 36 cm
x+y+2y-3= 36 cm (Let it be the second equation)
Substitute equation 1 in 2.
x+y+2y-3= 36
⇒ 21+2y-3= 36
2y= 36-21+3
2y= 18
y= 18/2
y= 9
x+y= 21
x+9= 21
x= 21-9
x= 12
∴ the values of x and y are 12 and 9 respectively.
Keenan paid $25 for his cell
phone bill in January. If each
month's bill increases by 5%.
what is the total he will
pay that year?
Answer:
1.25
Step-by-step explanation:
To get your answer first multiply the $25 by 5% then you will get 1.25 as your answer.
Answer:
Step-by-step explanation:
It can be modeled by the equation:
y = x + 0.05x
So, Keenan pays about $398.02
Geometric number between 12 and 8.
Answer:
9.79
Step-by-step explanation:
12 × 8 and root of that is 9.7979589
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 9 people took the trip. She was able to purchase coach tickets for $120 and first class tickets for $980. She used her total budget for airfare for the trip, which was $6240. How many first class tickets did she buy? How many coach tickets did she buy?
Let's call the number of first-class tickets Sarah purchased x. Then the number of coach tickets purchased is 9 - x.
The total cost of the first-class tickets was x * $980 and the total cost of the coach tickets was (9 - x) * $120.
The total budget for airfare was $6240, so we can set up the following equation:
x * $980 + (9 - x) * $120 = $6240
Solving for x, we get:
x = 5
So, Sarah purchased 5 first-class tickets and 9 - x = 4 coach tickets.
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Francesca wants to
convert 1 foot to centimeters. Use what you
know about customary units to explain how she
can do this.
One foot is equal to 12 inches in the customary system.
What is customary system ?The customary system is a system of measurement used primarily in the United States, and it includes units of measurement such as inches, feet, yards, miles, ounces, pounds, and gallons, among others. The system is also known as the English system or the U.S. customary system, and it is based on historical English units of measurement.One inch is equal to 2.54 centimeters in the metric system. Therefore, to convert 1 foot to centimeters, Francesca can multiply 12 (inches in a foot) by 2.54 (centimeters in an inch) to get 30.48 centimeters.
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Denise has $250 in her checking account. Each time she buys a bottle of water, she spends $2. If Denise buys
x bottles of water, how much money will remain in her account?(1 نقطة)
After buying x bottles of water, the money will remain in her checking account is equals to the $(250 - 2x). So, the correct answer is option (b).
We have Denise has a checking account.
The amount on her checking account = $250
The price of each water bottle = $2
Number of boltes bought by Denise = x
Let the total remaining money after the spend by Denise on water bottles be " $y". Total cost of x bottles = number of bottles × cost of one bottle
= x× $2 = $ 2x
We have to determine the value of y. The money remaining in her account = total amount in her checking account - spends money
=> y = $ 250 - $2x
which is a two variable linear equation, when we know that how many bottles she buy, i.e., value of x then we will determine the value of y. So, the required value is $ 250 - $2x .
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Complete question:
Denise has $250 in her checking account. Each time she buys a bottle of water, she spends $2. If Denise buys
x bottles of water, how much money will remain in her account?
a) $ 250 + $2x
b) $ 250 - $2x
c) $250
Classify each statement about the function f(x)=2x3+8 as true or false.
The domain of the function is all real numbers.
The range of the function is (0, [infinity]).
The y-intercept is (0, 0).
The center of symmetry is (0, 8).
TRUE .The domain of the function is all real numbers.
FALSE , The range of the function is (0, [infinity]).
FALSE, The y-intercept is (0, 0).
FALSE , The center of symmetry is (0, 8).
True. The function f(x) = 2x^3 + 8 can take any real number as input and produce a real number as output.
False. The range of the function is all real numbers greater than or equal to 8, i.e., [8, [infinity]).
False. The y-intercept of the function is (0, 8), meaning that when x = 0, the output of the function is 8.
False. The function f(x) = 2x^3 + 8 does not have a center of symmetry, as it is an odd degree polynomial.
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What is the value of the angle marked with x?
Answer:
146
Step-by-step explanation:
becuase it's parallel, so x = 146
Express each of the following in m/second.
(a) 65cm/second
(b) 367km/hour
(c) 1000cm/min
(d) 86km/min
Answer:
you can see the above explanation
Step-by-step explanation:
thank you for this question
Find the number that makes the ratio equivalent to 2:6.
6:
18 is the number that makes the ratio equivalent to 2:6
How to find the number that makes the ratio equivalent to 2:6?Equivalent ratios are ratios that have the same value, but may have different numerator and denominator values. They are related to each other by multiplication or division of both the numerator and denominator by the same non-zero value.
For example, the ratios 2/4 and 1/2 are equivalent ratios because both represent the same fraction (1/2) and therefore have the same value.
In this case we have:
2:6 = 6: x
2/6 = 6/x
2 * x = 6 * 6
2x = 36
x = 36/2
x = 18
Thus, the number that makes the ratio equivalent to 2:6 is 18
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find the domain of each expression 25/y-9
The domain of the equation A = 25/ ( y - 9 ) is y < 9 or y > 9 and the interval notation is ( -∝ , 9 ) ∪ ( 9 , ∝ )
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 25/ ( y - 9 ) be equation (1)
when y = 0 , the equation is undefined
So , the domain of the function will be y < 9 or y > 9 and the interval notation is ( -∝ , 9 ) ∪ ( 9 , ∝ )
Hence , the domain is ( -∝ , 9 ) ∪ ( 9 , ∝ )
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5
Copy the diagram and write in the size of all the other angles.
Work out the unknown angles a, b and c
(It’s question 5)
In the diagram, one line is transversal of two parallel lines, so the value of a is 113°, value of b is 67° and value of c is 67°.
The parallel lines are what?On a plane, lines that are parallel to one another never cross or come together. They are always parallel and equally spaced apart from one another. Parallel lines are lines that do not intersect. Lines are referred to as parallel if they never intersect and do not have a common intersection.
One line crosses two parallel lines in the diagram.
Angle an is the 113°'s vertically opposite angle.
Therefore, the angle's value is 113°.
Here, a and b have the same side interior angles since a line is transversal to two parallel lines.
So, a + b = 180°
⇒ 113° + b = 180°
⇒ b = 180° - 113°
⇒ b = 67°
And c is vertically opposite angle of b
So, the value of angle c = 67°
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Need help ASAP will give brainilest to the CORRECT ANSWER
Answer:
First Two Options
Step-by-step explanation:
Ernest took a total of 12 quizzes over the course of 4 weeks. How many weeks of school will Ernest have to attend this quarter before he will have taken a total of 30 quizzes? Solve using unit rates. __weeks
The number of weeks for taking 30 Quizzes will be 10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Ernest took a total of 12 quizzes over the course of 4 weeks. The number of weeks required to take 30quizzes will be calculated as;-
12 quiz = 4 weeks
1 quiz = 4 / 12 weeks
30 quiz = ( 4 x 30 ) / 12 week
30 quiz = 10 week
Therefore, there will be 10 weeks total for taking the 30 quizzes.
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Please halp
Tysm for it ^-^
The standard form of the Polynomial is [tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
given:
The zeroes are 5/2 (multiplicity 2), 3 (multiplicity 1) and 0 (multiplicity 4.)
So, the standard form is
(x- 5/2)² (x-3) [tex]x^4[/tex] = 0
(x² + 25/4 - 10x) (x-3) [tex]x^4[/tex] = 0
(x³ + 25x /4 - 10x² - 3x² -5/4 + 30x) [tex]x^4[/tex] = 0
[tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0
Thus, the Standard form
[tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0
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using all digits 3247 make the smallest number
To form the smallest number, use the smallest digits first. The smaller digits are on the left. The larger digits are on the right.
Consider this smaller example of 23 vs 32.
Sin Cos Tan
Geometry
Answer:
[tex]\sf Sin \ A = \dfrac{30}{50}\\\\\\Cos \ A = \dfrac{40}{50}\\\\\\Tan \ A = \dfrac{30}{40}[/tex]
Step-by-step explanation:
Trigonometric ratios:1)
[tex]\sf Sin \ A = \dfrac{opposite \ side \ of \ \angle \ A}{hypotenuse}[/tex]
[tex]\sf =\dfrac{BC}{AC}\\\\=\dfrac{30}{50}[/tex]
[tex]\sf \sf Cos \ A = \dfrac{adjacent \ side \ of \ \angle \ A}{hypotenuse}[/tex]
[tex]\sf = \dfrac{AB}{AC}\\\\= \dfrac{40}{50}[/tex]
[tex]\sf \sf Tan \ A = \dfrac{opposite \ side \ of \ \angle \ A}{adjacent \ side \ of \ \angle \ A }[/tex]
[tex]\sf = \dfrac{BC}{AB}\\\\= \dfrac{30}{40}[/tex]
please help mybe easy????????????????????????????HELPPPP
Answer:
138
Step-by-step explanation:
720 - all the angles added up gives you the missing angle
Answer:
x = 138°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × (6 - 2) = 180° × 4 = 720°
sum the interior angles and equate to 720°
x + 85° + 135° + 125° + 85° + 152° = 720°
x + 582° = 720° ( subtract 582° from both sides )
x = 138°
Renata and her family go through an average of more then 15 cans of sparkling water each day. They buy cases of 24 cans at $3. 5 a case. Write an inequality for the number of cases they go through in 30 days.
The number of cases they go through in (x > 18.75 ) 30 days is greater than 18.75.
In this problem, Renata and her family go through an average of more than 15 cans of sparkling water each day. This means that in 30 days, they will go through a total of more than 15 * 30 = 450 cans of sparkling water.
They buy the sparkling water in cases of 24 cans each, and each case costs $3.5. To calculate the number of cases they need to buy, we divide the total number of cans they need by the number of cans in each case.
450 cans ÷ 24 cans per case = 18.75 cases
Since they need to buy more than 18.75 cases, we use the inequality symbol ">" to express this as:
x > 18.75
where x represents the number of cases of sparkling water they go through in 30 days.
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A ferris wheel is 50 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.
Answer: The height of a person on the ferris wheel can be modeled by the function:
h = 50 * cos(pi * t / 120) + 1
where t is the number of minutes since the wheel started turning, and pi represents the mathematical constant pi. The function takes into account the diameter of the ferris wheel (50 meters), the initial height of the platform (1 meter), and the fact that the wheel completes 1 full revolution in 4 minutes (120 seconds).
Step-by-step explanation:
Use the expression 32.6/10 - 5 x 8 - 9.16 to create an expression that has the value of 43. Make sure your expression includes parentheses. PLEASE ANSWER ASAP!!! THIS IS FOR HOMEWORK, IF U GET IT RIGHT I WILL MAKE U BRAINLIEST AND U WILL GET 30 POINTS!!!!!!!!!
The expression 32.6/10 - 5 x 8 - 9.16 + 88.9 has the value of 43.
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.
Let's the expression to be found be "y".
An expression that, when evaluated, gives us a value of 43 is required.
Start by manipulating the given expression to isolate the value of "y".
Use the order of operations (PEMDAS) to simplify the expression -
32.6/10 - 5 × 8 - 9.16
3.26 - 40 - 9.16 (since 5 × 8 = 40)
-45.9
So the value of the given expression is -45.9.
To make the expression equal to 43, add a constant term to it -
y = 32.6/10 - 5 × 8 - 9.16 + 88.9
Evaluate this expression -
y = 3.26 - 40 - 9.16 + 88.9
= 43
Therefore, the expression obtained is 32.6/10 - 5 x 8 - 9.16 + 88.9.
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4/7 of the girls the chicken nuggets,whereas 40% of the boys like the chicken nuggets.How many total students like chicken nuggets?What percents of the entire students body is this?
The percentage of students who like chicken nuggets is 97%, which is equivalent to 97 students.
How many students liked the chicken nuggets?To better understand this question, let's simplify some of the information given:
4/7 out of the girls liked the chicken nuggets = 0.57 or 57% of the girls
40% of the boys liked the chicken nuggets = 0.40
Based on this information, it can be concluded that 97% of students liked chicken nuggets. Moreover, if the population includes 100 students, this percentage will be equivalent to 97 students.
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Ella sees 7 beetles when she weeds her garden. Each beetle has 6 legs.
How many legs are there on all 7 beetles?
Check your work. How many legs are there on 7 beetles? ➡
legs on 7 beetles.
Step-by-step explanation:
Each beetle has 6 legs with 7 beetles
So 6 legs 7 times would be 6x7
And 6 multiplying by 7 is 42
In 7 beetles there are 42 legs.
in order to gauge student opinion on his grading procedures, the professor divides the class into two groups: undergraduate students and graduate students. he then takes random samples from each group. this is an example of
This is an example of stratified sampling.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.For this problem, we have that the population was divided into groups, hence either cluster or stratified sampling was used.
As an equal proportion of each group was sampled instead of the entire group, stratified sampling was used.
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In circle Q with the measure of minor arc PR= 48°, find mZPSR.
S
A
R
р P.
The proportion of minor arc ZPSR is equivalent to 48 degrees.
Given a circle Q with focus Q and minor curve PR with a proportion of 48 degrees, the objective is to find the proportion of ZPSR, the focal point that compares to the minor circular segment PR.
Since the focal point and the circular segment length of a circle are corresponding, the proportion of ZPSR can be found by partitioning the proportion of the minor curve PR by 360 degrees and afterward duplicating by the all out number of degrees all around, which is 360.
The recipe for the focal point comparing to a minor circular segment is given by:
mZPSR = (mPR/360) × 360
Subbing the given worth of mPR = 48, we get:
mZPSR = (48/360) × 360
= (1/7.5) × 360
= 48
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Brown's Car Repair charges $45 to tow the car plus $55 an hour to fix a car. Which expression shows how to find out how much a repair will cost ?
The expression shows how to find out how much a repair will cost is 45 + 55x
How to determine the linear expressionFrom the question, we have the following parameters that can be used in our computation:
Brown's Car Repair charges $45 to tow the car $55 an hour to fix a car.Using the above as a guide, we have the following:
Total charges = Tow + Rate per hour * x
Substitute the known values in the above equation, so, we have the following representation
Total charges = 45 + 55x
Hence, the expression is 45 + 55x
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