The value of a is ( x - 5 ) factor of f (x) = x ³ - 3x² + ax -10 is found to be 8 .
What is a factor of an equation ?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.
Let f (x) = x ³ - 3x² + ax -10 be the given polynomial.
By factor theorem, ( x - 5 ) is the factor of f (x) , if f ( 5 ) = 0
Therefore,
f ( 5 ) = 3 ( 5 )² + a ( 5 ) - 10 = 0
125 - 75 + 5a - 10 = 0
5a = -40
a = -8
Hence, a = -8
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Mrs.Vernon paid $72 interest for a 2-year loan at 9% annual interest. How much money did she borrow?
Vernon borrowed an amount of $400.
What is Interest Rate?Interest rate is the amount a borrower has to pay which is also a percentage of the principal amount, which is the amount loaned. Annual interest rate is this amount which the borrower has to pay once in an year.
Let the money Vernon borrowed = x
Annual interest rate = 9%
Interest paid for 1 year = x × 9%
Interest paid for 2 years = x × 9% × 2
Interest paid for 2 years is given as $72.
⇒ x × 9% × 2 = 72
x × 18% = 72
x × (18/100) = 72
0.18 x = 72
x = 72/0.18
x = 400
Hence the money Mrs. Vernon borrowed is $400
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**What is the value of x in the function
p(x) = 9x - 2 such that p(x) = -3?
Answer:
x = -1/9
Step-by-step explanation:
p(x) = 9x - 2
9x - 2 = -3
9x = -1
x = -1/9
3 3/8 T = ? lb
math question
Answer:
6,750 pounds
Step-by-step explanation:
3 3/8 tons = ? pounds
there are 2,000 pounds in 1 ton so:
3 3/8 * 2,000 = 6,750 pounds
What is the nth root theorem?
Answer:
The nth root theorem is a mathematical principle that states that, for any positive integer, it will have n nth roots!
An nth root of x is equivalent to saying [tex]\sqrt[n]{x}[/tex]. To elaborate, if you want to know how many 2nd roots that 1 has, through this theorem you will know it has 2 of these roots (-1 and 1). This applies for all numbers!
hope this helps :)
It reflects off the mirror and strikes a wall 9.5m away at point P. By what distance does the laser spot on the wall move if the mirror is rotated by 10??
As per the tangent formula, the distance does the laser spot on the wall move if the mirror is rotated by 10 is 2.9m
While we looking into the given question we have identified the following values,
Previous distance = 9.5
And the angle = 30 degrees
Rotated angle = 10 degrees
And the distance is considered as x.
Then as per the tangent formula, it can be written like the following,
=> tan 30/9.5 = tan 10/x
When we apply the tangent value, then we get,
=> 0.5773/9.5 = 0.1763/x
When we perform the cross multiplication, then we get,
=> 0.5773x = 9.5 x 0.1763
=> 0.5773x = 1.6749
Then the value of x is obtained as,
=> x = 1.6749/0.5773
=> x = 2.9012
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Which expression is equivalent to 18-(8* q) ? .
A (8q) - 18
B (18 - q) * 8
C (18 - 8) * c
D 18 - (0 * 8)
Answer:
the way you typed that is kinda confusing but the answer is
[tex]18 - 8q[/tex]
Sheila is making accessories for the soccer team. She uses 675.22 inches of fabric on headbands for 46 players and 3 coaches. She also uses 443.44 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each
Answer:
232.88
Step-by-step explanation:
I used a calculator on this so it must be correct
Pam need $6321 for her first year of college tuition each of her two grandfather said they would match what she saves she has seven years before she goes to college how much does Pam need to save on her own each year to have enough for her first year with the help of her two grandfathers Pam needs to save blank dollars each year
to have enough.
Pam needs to save $905 per year for seven years to have enough for her first year with the help of her two grandfathers.
How Much Money Must Be Saved Every Year?Pam needs to save $903 each year to have enough for her first year of college tuition with the help of her two grandfathers.
To calculate this, we first need to add up the total amount of money Pam's two grandfathers are offering to contribute:
Grandfather 1: $6321
Grandfather 2: $6321
Total Contribution: $12642
We then subtract this total contribution from the total cost of tuition for the first year:
Tuition: $6321
Total Contribution: -$12642
Total Amount Needed: $6321
Finally, we divide this total amount needed by the number of years Pam has to save:
Total Amount Needed: $6321
Years: 7
Amount Needed to Save Each Year: $903
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What is the median for the following observations 5 8 6 9 11 4?
The median of 5,8,6,9,11,4 is 7.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
Here we have to find the median of 5,8,6,9,11,4.
Arranging the given data/observations in ascending order:-
4, 5, 6, 8, 9, 11
Here we can see that there are 6 numbers given
so, n= 6
Where the number of terms is even.
We know that the formula to find the value of the median whose n value is given,
Median= {(n/2 +1 )th term +(n/2)th term} / 2
We can now substitute the value of n in the above formula, we get
Median= {(6/2+1) +(6/2)} / 2
We can now simplify the above step, we get
Median= 3rd observation + 4th observation / 2 = 6+8/2 = 7
Therefore, the median of 5,8,6,9,11,4 is 7.
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Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval
Answer:
[tex]-10<x<-8[/tex]: Increasing[tex]-2<x>0[/tex]: Increasing[tex]8<x<10[/tex]: Neither[tex]3<x<7[/tex]: Neither[tex]-8<x<-5[/tex]: NeitherStep-by-step explanation:
A function is increasing if the graph is going up.
A function is decreasing if the graph is going down.
Two substances, a and z, were studied in a lab. Substance a can be broken down by a chemical change. Substance z cannot be broken down by a chemical change.
As per the concept of rate of change, the substance A and z are compound to each other.
Th term rate of change is defined as the speed at which a variable changes over a specific period of time.
Here we have given that there are two substances an z are given.
And we need to find the conclusion about the substances.
While we looking into the given question we have identified that there are two substances are given A and Z.
And we also know that substance A can be broken down by a chemical change. But the substance Z can't be broken down by a chemical change.
While we looking into to this condition, we know that the substance A is going to react on Z.
Therefore, the here A is and compound and Z is an element.
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Help me pls I need this to be answered fast!!!-.-
Answer:
36 feet
Step-by-step explanation:
If one inch in the drawing equals 3 feet, then the 12-inch length of the wing would correspond to 12(3 feet). This means the final length of the wing will be 36 feet from tip to tip.
.Write an expression equivalent to -3 + 2/3y - 4 - 1/3y
Answer:
−7+y/3 is the same as that, but simplified.
Answer:
y/3-7
Step-by-step explanation:
The answer is the solved equation of -3+2/3y-4-1/3y.
Subtract 4 from -3 to get -7
= -7+2/3y-1/3y
Combine 2/3y and -1/3y to get 1/3y
-7+1/3, or just y/3-7.
Are the whole numbers closed under division justify with example?
The division of the whole numbers is not closed under property as the division of whole number is not always a whole number.
A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation then we say that the set is “closed under the operation.” The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division that is a ÷ b is not always a whole number.
For example, 5 and 8 are whole numbers, but 5÷8 is not a whole number.
Therefore, closure property does not exist for division of whole numbers.
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which of the following statements is true? a.) simulations utilize certain rules to get estimates closer to theoretical probability. b.) using a sample size of 20 or less can be representative in simulations. c.) to achieve theoretical certainty, trials of chance should be repeated. d.) simulations are based on trials of chance that mimic real-life events.
The statement which is true: (Option D.) Simulations are based on trials of chance that mimic real-life events.
Simulations are designed to closely mimic real-life events by using trials of chance. These trials are repeated in order to get estimates closer to theoretical probability. However, a sample size of 20 or less can still be representative in simulations.The Power of Simulations: Using Trials of Chance to Predict Real-Life OutcomesSimulations are a powerful tool used to predict the outcomes of real-life events. They are based on trials of chance that are repeated multiple times to get estimates closer to theoretical probability.
Simulations rely on random sampling, which means that a sample size of 20 or less can still be representative of a larger population. This makes simulations a useful tool for understanding outcomes in situations where data is limited or unavailable. By using simulations to predict outcomes, researchers can gain a better understanding of their target population and make informed decisions.
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what does it mean when a company's corporate spread tightens
A corporate (or credit) spread is the extra interest a lender demands to make up for the extra risk they take on by financing the business.
Companies borrow money from their investors through the use of bonds, which are debt instruments. Better performance and low-risk perceptions for businesses cause bond spreads to narrow. The corporate spread decreases when people have favorable and low-risk impressions about the company issuing the bond since it is the extra interest paid over the interest from US Treasury bonds.
A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.
Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.
Spreads that are getting tighter indicate a company's assessment of risk is getting better. This is because investors have enough faith in the business to invest in it in exchange for reduced spreads. Strong financial statements, improved loan servicing, or a generally stable market impression could all be to blame for this.
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A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.
Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.
Suppoe the giver confidence level i 85%, what i the correponding z critical value?
The corresponding Z critical value for the given 85% confidence level is 1.440.
What is Z critical value?The Z critical value or known as Z-score is used if the sampling distribution is normal, or close to normal. Z-score is used when the population standard deviation is known or when we have larger sample sizes.
To determine the Z critical value, we can use Z-table or a calculator. To be able to find Z-score in Z-table, first, we need to look at the left side column of the Z-table to get the value corresponding to one decimal place of the Z-score. For example, the whole number and the first digit after the decimal point. Then, look up for the remaining number across the table (on the top).
In this case, based on the Z-table, the corresponding Z critical value for the given 85% confidence level is 1.440.
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How do I find a unique number in an array?
The simplest way to get unique number from an array is by putting all numbers of the array into hashmap's key and then print the keySet
How do we find a unique number in an array?an array is a collection of elements or numbers of the same data type.There are more than one way to find unique elements or number from an array:
1.By using hashing
2. By using nested loop
3. By using sorting
4. By putting all the elements in the hashmap's key
But the simplest way to get unique number from an array is the fourth method. And this is done by putting all the number from the array into the hashmap's key, we then print the key set.
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What are the 2 formulas for a rectangular prism?
The 2 formulas of rectangular prism are Volume = Length x Width x Height cubic units and Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.
An item with three dimensions is a rectangular prism. It will therefore have its own volume and surface area. We need to know the dimensions of a prism's sides or edges in order to compute its volume and surface area. Let l, w, and h represent the dimensions of the rectangular prism. Below are the supplied formulas.
The 2 formulas of rectangular prism are
Volume of rectangular prism:
Volume = Length x Width x Height cubic units
Surface area of rectangular prism:
Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units
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the question is in the pic
I think it could be 1.5 kilometers.
The distance is 1,500 m but you have to convert it so probably 1.5 km.
Which inequality is true when the value of d is -13?
(A) -d-5≥5
(B) d−5≥−5
(C) −d−5≤5
(D) d−5≤−5
please answer asap
By using linear inequation, it can be calculated that -
Option A and D is true when d is -13
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by
>, <, ≥, ≤
A one degree inequation is known as linear inequation.
Here, four sets of linear inequations are given
For option A
-d - 5 ≥ 5
-d ≥ 5 + 5
-d ≥ 10
d ≤ -10
-13 is satisfied here
For option B
d - 5 ≥ -5
d ≥ -5 + 5
d ≥ 0
-13 is not satisfied here
For option C
-d - 5 ≤ 5
-d ≤ 5 + 5
-d ≤ 10
d ≥ -10
-13 is not satisfied here
For option D
d - 5 ≤ -5
d ≤ -5 + 5
d ≤ 0
-13 is satisfied here
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please help me with this problem
Answer:
0.84 m^2
Step-by-step explanation:
Long: 1200 millimeter = 1.2 meter
Wide: 700 millimeters = 0.7 meter
Area of rectangle: L x W
1.2 x 0.7 = 0.84 m^2
A power company serves 17,000
customer's homes in a town. The
population of the town is decreasing by
about 3% every year. Which function
would represent the number of
homes,"H", the company will serve after
"n" years.
Answer:
2nd
Step-by-step explanation:
p=17000
r = -0.03
Hn)= p×(1+r)^n
H(n)= 17000(1+-0.03)^n
40 POINTS!
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
A. (6, 0)
B. (0, 5)
C. (1, 4)
D. (1, 5)
The best estimate of the solution to the system of equations will be (1, 4). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
2x + 3y = 12 ...1
4x + 2y = 10 ...2
Divide the equation 2 by 2, then we have
2x + y = 5 ...3
Subtract equation 3 from equation 2, then we have
2x + 3y - 2x - y = 12 - 5
2y = 7
y = 3.5
y ≈ 4
Then the value of 'x' is calculated as,
2x + 3.5 = 5
2x = 1.5
x = 0.75
x ≈ 1
The best gauge of the answer for the arrangement of conditions will be (1, 4). Then, at that point, the right choice is C.
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help please
- the line 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis. Determine the value of a.
The value of a if the lines 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis is; a = 13
How to solve the equation of a line?The general form of the equation of a line in slope intercept form is given as;
y = mx + c
where;
m is slope
c is y-intercept
We are given two equations of two lines as;
Line 1; 5x - ay + 26 = 0
Line 2; 3x - y + 2 = 0
Now, since they both intercept each other at the y-axis, it means that at the point of intersection, the value of x will be 0.
Thus, line 2 equation becomes;
3(0) - y + 2 = 0
y = 2
Putting 2 for y in line 1 equation gives;
5(0) - a(2) + 26 = 0
2a = 26
a = 26/2
a = 13
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please help as soon as possible!
Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.
Drag and drop the choices into the boxes to correctly complete the table.
corresponding
alternate interior
alternate exterior
none of these
The correct matching of the lines is given below.
Corresponding ⇒ Diagram C and Diagram E
Alternate interior ⇒ Diagram D
Alternate exterior ⇒ Diagram A
None of these ⇒ Diagram B
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The corresponding angles are represented by diagrams C and E.
The alternate interior angles are represented in diagram D and the alternate exterior in diagram A.
None of these is represented by diagram B.
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Is reflection congruent or similar?
What is set Give 5 examples?
A set is a collection of unique objects. There is no repetition of elements in a set. It is well defined. The number of elements can be finite or infinite.
Five examples of set are :
(1) Set of vowels in English alphabets
V = { a, e, i, o, u }
(2) Set of integers
Z = { ..., -2, -1, 0, 1, 2, ... }
(3) Set of natural numbers
N = { 1, 2, 3, ... }
(4) Set of natural numbers less than 10
A = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
(5) Set of months with number of days is 30
M = { April, June, September, November }
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What is a zero measurement?
The quantity or complete absence of the thing being measured is represented by the zero point.
Ex. Because the zero point is set arbitrarily and does not indicate the complete absence of temperature, the Fahrenheit scale is an interval scale.
What exactly is a random zero point?Zero degrees on either scale is not a "true" zero because it is an arbitrary number. The absence of temperature does not occur at the zero point; It's just a random number on the scale. Other examples of common interval scales include: Age and SAT scores (one is culturally determined).
Which scale has a point at zero?In addition, on a ratio scale, the distance between two variables is also the same. Furthermore, a proportion scale has a genuine zero point, meaning the worth of zero isn't erratic.
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your class collected more than 410 cans of food for th eannual food drive in the first week, 185 cans were collected.how many cans c of food were colected in the second week?
The number of cans collected in the second week would be 225 cans.
A can of food is a container that holds a prepared food product, such as vegetables, fruits, beans, or soups. Canned foods are shelf-stable, meaning they can be stored for long periods of time without spoiling. They are often used as a convenient and easy-to-store source of food, especially in emergency situations.
To find out how many cans of food were collected in the second week, you need to subtract the number of cans collected in the first week from the total number of cans collected. In this case, the number of cans collected in the second week would be:
410 cans - 185 cans = <<410-185=225>>225 cans.
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