The complete square for the binomial expression is x² + 15x + [ 15²/4 ].
Square of a binomial:→ The squaring of a binomial will always give a trinomial.
For example,
(a + b)(a + b) = (a + b)² = a² + 2ab + b²
(ax - b) (ax - b) = (ax - b)² = ax² - 2axb + b²
→ If a trinomial (ax² + bx + c ) is perfect square then
The formula for constant term c = [ b/2√a ]²
Here we have
x² + 15x + __ is a square of the expression
As we know constant term c = [ b/2√a ]²
=> Constant term of (x² + 15x + __) = [ 15/2√1 ]² = [ 15²/4 ]
Therefore the complete expression is x² + 15x + [ 15²/4 ]
Here divide and multiply by 2 with 15x
=> [tex]x^{2} + 2 (\frac{15x}{2}) (1) + (\frac{15}{2})^{2}[/tex]
The above expression is in the form of (a + b)² = a² + 2ab + b²
=> [tex]x^{2} + 2 (\frac{15x}{2}) (1) + (\frac{15}{2})^{2}[/tex] = [tex][x + \frac{15}{2} ]^{2}[/tex]
Therefore,
The complete square for the binomial expression is x² + 15x + [ 15²/4 ].
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100 POINTS
Find the focus. x^2 = 6y (please explain, I want to understand the solution)
The coordinate of the parabola's focus in the following equation, x2=6y, is (0,3/2)
What are Directrix and Focus?
What are a parabola's focus and directrix? Typically speaking, parabolas are the graphs of quadratic functions. They can alternatively be thought of as the collection of all points whose separation from the focus is the same as their separation from a certain line (the directrix).
What are the focus's coordinates?
The focus's coordinates f(0,a)
The equation that we have given is
x^2 = 6y
We are aware that the parabola's general equation is,
x^2 = 4ay
The axis of symmetry is a line that splits the parabola in half and runs through the focus.
We must ascertain the worth of
6y = 4ay
6 = 4a
a = 6/4 = 3/2
The focus' coordinate (0,3/2) is as a result.
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A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is A)Zero B)the same C)1/3 D)1/16
The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars is (D) 1/16.
The term Acceleration defined as the gravity at the surface of Mars is given by the formula
Gₙ = GM/R²
where
M refers mass of Mars
R refers radius of Mars
Here we need to find if we take a point which is at height 3 times the radius of Mars from its surface.
While we take the height 3 times the radius of Mars from its surface.
The it can be written as,
=> Gₙ = GM/(3R + R)²
When we expand it then we get.
=> Gₙ = GM/16R²
Therefore, the resulting gravity on the surface of the mars is 1/16.
So, the option (D) is correct.
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in a recent survey 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen find the probability that 8 of them favor building the health center
The probability of those that favors building the health center is 0.196
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.
According to the scenario, 70% of the community favoured in building a health centre.
Hence , p=0.7.
In order to find the probability, binomial theorem will be used as follows :
= 0.196
Hence, The probability is 0.196
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convert the following equation into standard form.
Y= -2x+6
Answer:
x = 3+y
Step-by-step explanation:
is your ans .................
Given f(x)=3x+4 find f(4)
Answer:
Step-by-step explanation:
To find f(4), you can substitute 4 for x in the equation f(x) = 3x + 4. This gives you:
f(4) = 3(4) + 4
= 12 + 4
= 16
Therefore, f(4) = 16.
An online streaming service charges a monthly fee as well as a one-time sign-up fee. The cost for this online streaming service is modeled by the following function where m represents the number of months the service is subscribed to and C(m) represents the total cost given that amount of time:
C(m) = 13m + 9
In the above function, what is the slope?
What is the y-intercept?
How do we interpret the slope of this function?
How do we interpret the y-intercept of this function?
The slope of the given line is 13 and the y - intercept of the line is 9.
What is equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
Consider, the given equation of line,
C(m) = 13m + 9
We have to find the slope and y - intercept of the given equation.
From the given equation the slope of the equation is 13 and the y - intercept is 9.
Consider, the general equation of line
y = mx + c
where,
m is the slope of line and
c is the y - intercept of the line.
Compare the given equation C(m) = 13m + 9 with, y = mx + c
⇒ m = 13 and c = 9
Hence, the slope of the given line is 13 and the y - intercept of the line is 9.
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State the degree and leading coefficient of the polynomial in one variable. If it is not a polynomial in one variable, explain why.
n+8
degree =
leading coefficient =
Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.
So, the degree of the polynomial is 1 and the leading coefficient is 1.
Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.
What is the slope of the line?
-3
3
-1
1
By analyzing the given line mathematically, we get the required slope of the line as 3.
What is Slope ?A line's steepness and direction can be expressed as a value called slope. It is frequently represented in variable format by the letter m. Its gradient or rate of change are other names for a line's slope.
The rise over run or slope formula, often known as the vertical change in y divided by the horizontal change in x, To determine the change in y over the change in x, the slope formula requires two points, (x1, y1) and (x2, y2).
As from the Line,
Two points = (1,2), (2,5)
(x1, y1) = (1,2)
(x2,y2) = (2,5)
Using two point we can calculate slope as
= [tex]\frac{y2-y1}{x2-x1}[/tex]
Putting the points in the formula, we get:
[tex]\frac{5-2}{2-1}[/tex]
= 3
Hence, we get the required slope as 3.
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Given a2 = 7 and a5 = −56 of a geometric sequence, what is the recursive equation for the nth term? a an = 2(an − 1), a1 = 3.5 b an = 2(an − 1), a1 = −3.5 c an = −2(an − 1), a1 = 3.5 d an = −2(an − 1), a1 = −3.5
Answer: an=-2(an-1), a1=3.5
Step-by-step explanation: took the quiz and got it right
An = -3.5(-2)ⁿ⁻¹ and -3.5 are the Nth and first terms of the above sequence, respectively.
What is Geometric sequence?Every term in a geometric series is obtained by multiplying the term before it by the same number. Aₙ = a₁ rⁿ⁻¹ is the general phrase for it. The common ratio is denoted by the number r.
Given a₂ = 7 and a₅ = −56 for a geometric sequence.
From the general formula of geometric sequence's nth term
Aₙ = a₁ rⁿ⁻¹
Thus
A₂ = 7 = a₁ r²⁻¹ = a₁ r
A₅ = -56 = a₁ r⁵⁻¹ = a₁ r⁴
comparing both equations
A₂/ A₅ = a₁ r / a₁ r⁴
=> -7/56 = 1/r³
=> r³ = -8
=> r = -2
putting this value of r in equation 1
a₁ = -7/2
Hence, for the nth term of the sequence
Aₙ = -7/2(-2)ⁿ⁻¹
Therefore, the Nth term and the first term of the given sequence are Aₙ = -3.5(-2)ⁿ⁻¹ and -3.5 respectively.
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8.
supplementary angles. IfAnswer:
Do u like m&m because I do
The balance on Howard Gessner’s American Express card on August 1 is $543.27. In August, he charges an additional $201.25 of purchases, has returns of $89.22, and makes a payment of $300. If the finance charges are calculated at 1.5% per month on the unpaid balance, find the balance on September 1.
Mathematically, the balance on Howard Gessner's American Express card on September 1 is $360.63.
How do we determine the balance?The ending balance on September 1 is determined using the mathematical operations of addition, subtraction, and multiplication (for the finance charge).
The finance charge is the interest and other fees paid for borrowing credit.
The finance charge is always based on a percentage, called the annual or monthly percentage rate (APR or MPR).
In this situation, the monthly percentage rate is applied to the unpaid balance (multiplication) at the end of August, to determine the finance charge, which is added to the unpaid balance to compute the September 1 balance.
August 1 Balance = $543.27
Purchases 201.25
Returns (89.22)
Payments (300.00)
Unpaid balance $355.30
Finance charge 5.33 ($355.30 x 1.5%)
September 1 Balance $360.63
Thus, using mathematical operations, the balance on September 1 is $360.63.
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Solve the inequality for x.
2(4x+9) ≤5x+3
Digital watches of a certain brand are advertised to have an average lifetime of 800 days. A customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised. A random sample of 50 watches is obtained from the manufacturer and the lifetime of each watch is recorded. In particular, one obtains the sample mean
X
ˉ
=738.44
days and sample variance
S 2
=1459.24
days squared from this sample of digital watches. 1. Explain why the test statistic
ζ= S/ 50
X
ˉ
−μ
has a normal distribution despite the experimenter being unaware of the distribution of the population of digital watches. 2. Devise an appropriate hypothesis test to determine whether the given customer is willing to purchase a digital watch. 3. Conduct the hypothesis test of 2 . at a significance level of
α=0.05
(1) The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.
(2) There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.
Test the hypothesis that the client is prepared to buy a watch unless it can be shown that the average lifespan is shorter than what is claimed using a significance level of α=0.05.
Given that,
Sample size (n)=50
Sample mean (x−)=738.44
Sample standard deviation (S)=38.2 where (S)2=1,459.24
The null and alternative hypothesis are,
H(0): μ≥800
vs
H(1): μ<800
(1) In the given question we have to explain why the test statistic has a normal distribution despite the experimenter being unaware of the distribution of the population of digital watches.
The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.
(2) In the given question we have to devise an appropriate hypothesis test to determine whether the given customer is willing to purchase a digital watch.
Then test statistic becomes,
t = x−μ/(s/√n)
t = 738.44−800/(38.2/√50)
t = −61.56/5.40229
t = −11.40
Here the test is one tailed (left tailed) at α=0.05
Then degrees of freedom=(n-1)=(50−1)=49
Thus P-value becomes,
P-value = <0.00001
The P-value is less than or equal to α=0.05
Then we reject the null hypothesis H(0).
We use excel command to find the P-value we get,
=T.DIST( x, deg _freedom, TRUE)
=T.DIST(-11.40 , 49,TRUE)
=<0.00001
There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.
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The right question is given below:
Find x
NOTE: Angles not necessarily drawn to scale.
Answer:
148 degrees
Step-by-step explanation:
b/c a line is 180 degrees and the angle given is 32 so 180- 32= 148
and the line is bisected at point p so it is 148 because of alternate interior angles.
Can someone help me with this real quick?
Answer:
y = 5
Step-by-step explanation:
the line is horizontal and has always y = 5
using the least-squares regression line, calculate the predicted value and residual value for the data point where the non-native grass biomass is equal to 35 and the coastal sage scrub biomass is equal to 20. give your answers precise to three decimal places.
By using the least-squares regression line the equation will be y = 1.518x + 0.305.
Let us find the value of slope and y-intercept that suits the data y = mx + b
And then , we have to find the value of x² ,∑x,∑y,∑x²,∑xy also N
Then, we have to calculate the slope m
m = n∑(xy) - ∑x ∑y / n ∑(x²) - (∑x)²
= 5 X 236 -26 X 41 / 40 - 676
= 249 / 164
= 1.5183
Then , we hace to calculate the intercept b
b = ∑y - m∑x / n
= 41 - 1.5183 X 26 / 5
= 0.3049
After this we have to assemble it in the equation of line
y =mx + b
Therefore ,
y = 1.518x + 0.305
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No. of coffee sales (undred)
2
18
S
10
15
20
Temperature (°C)
25
30
Describe the relationship between the temperature and the coffee
sales
0
As the temperature decreases, the number of coffee sales
decreases
As the temperature increases, the number of coffee sales
increases
As the temperature increases, the number of coffee sales
decreases
D
There is no trend between the temperature and the number of
coffee sales
LT
The relationship between the temperature and the coffee sales is if the temperature decreases then the number of coffee sales decreases.
So, option a is correct.
What is meant by temperature?The SI unit of temperature according to the International System of Units is Kelvin, indicated by the sign K. The Kelvin scale is widely recognized or used in research and engineering. However, the global standard for measuring temperature is the Celsius or Fahrenheit scale. The unit of measurement known as temperature can be expressed on a number of scales, including the Fahrenheit and Celsius systems. Temperature depicts the direction in which heat energy spontaneously moves, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).
The relationship between the temperature and the coffee sales is if the temperature decreases then the number of coffee sales decreases.
Hence, option a is correct.
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Write a quadratic function in standard form whose graph passes through (-5,0), (0,-8), and (4,0)
The quadratic equation y = (2 / 5) · x² + (2 / 5) · x - 8 contains the points (- 5, 0), (0, - 8) and (4, 0).
How to derive the equation of a parabola
In this problem we find the case of a parabola, parabolae are defined by quadratic equations of the form:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficients.x - Independent variable.y - Dependent variable.First, write the points associated with the parabola:
(x₁, y₁) = (- 5, 0), (x₂, y₂) = (0, - 8), (x₃, y₃) = (4, 0)
Second, create a system of linear equations:
25 · a - 5 · b + c = 0
c = - 8
16 · a + 4 · b + c = 0
Third, resolve the system by numerical methods:
(a, b, c) = (2 / 5, 2 / 5, - 8)
Fourth, write the resulting quadratic equation:
y = (2 / 5) · x² + (2 / 5) · x - 8
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Franco said 9.37×0.1=93.7 is he correct
Answer:
No, Franco's calculation is incorrect.
Step-by-step explanation:
No, Franco's calculation is incorrect. The correct answer is 9.37 x 0.1 = 0.937.
When multiplying a decimal number by a decimal number, the decimal point in the product should be placed so that the number of decimal places in the product is equal to the sum of the number of decimal places in the factors. In this case, the number 9.37 has two decimal places, and the number 0.1 has one decimal place. Therefore, the product of 9.37 x 0.1 should have a total of 2 + 1 = 3 decimal places.
To obtain the correct answer, we need to multiply 9.37 x 0.1 using standard long multiplication:
Copy code
9.37
x 0.1
0.937
Therefore, the correct answer is 0.937, not 93.7 as Franco stated.
Answer:
No. This is incorrect.
Step-by-step explanation:
9.37 × 1 = 9.37
Times by 1 the number stays the same.
If you multiply by 0.1 the decimal will move one place and the 9.37 should get smaller! The sentence in the problem shows 93.7 which is bigger.
9.37 × 10 = 93.7
9.37 × 0.1 = 0.937
A subscription to a program normally costs $36 but is on sale for 25% off. A 7% tax is added at checkout. What is the total cost? $28.89 $45.59 $9.00 $27.00
Answer:
$28.89
Step-by-step explanation:
he subscription is on sale for 25% off, so the cost is $36 - (25% * $36) = $36 - $9 = $27.
Then, a 7% tax is added at checkout, so the total cost is $27 + (7% * $27) = $27 + $1.89 = $28.89.
Therefore, the total cost is $28.89.
Answer:
Step-by-step explanation:
36 will be 27 and 7% of 27 should be added 1,89 so 28,89
What is 9/12 in simplest form? A 2/3 B 3/4 C 12/16 D 10/13
3/4 is 9/12 in simplest form.
What is 9/12 in simplest form?The simplest form of 9/12 is 3/4.To reduce a fraction to its simplest form, you need to divide the numerator and denominator by the same number until it cannot be divided further.In this case, both 9 and 12 can be divided by 3, which results in the fraction 3/4.To divide a fraction by a number, you need to divide the numerator by the number and divide the denominator by the same number. For example, if you divide 9/12 by 3, you would get 3/4.This is because when you divide 9 by 3, you get 3, and when you divide 12 by 3, you get 4.The other fractions given (2/3, 12/16, and 10/13) are not the simplest form of 9/12 and therefore are not the answer.The simplest form of 9/12 is 3/4.To learn more about simplifying fractions refer to:
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WILL GIVE BRAINLIEST!
The aquarium has one fewer redfish than blue fish. 60% of the fish are blue. How many blue fish are in the aquarium? Show your work.
Answer:
There are 3 blue fish in the aquarium.
Step-by-step explanation:
Let the total number of fish be denoted by T, total number of blue fish be B and total number of red fish be R
We can write, T = B + R
Since the aquarium has one fewer redfish than blue fish, R = B - 1
So,
T = B + (B - 1) = 2B - 1
As 60% of total fish is blue, we can write
60% of T = B
or, (60/100) x T = B
or, 3/5 x T = B
or, 3/5 x (2B - 1) = B
or, 6B - 3 = 5B
or, 6B - 5B = 3
or B = 3
Therefore, there are 3 blue fish in the aquarium.
No. of red fish, R = B - 1 = 3 - 1 = 2
The restaurant has 25 boxes of ketchup.
Each box has 250 packets of ketchup.
How many packets of ketchup does the restaurant have?
Answer: 6,250
Step-by-step explanation: As the equation states there are 25 boxes with 250 packs of ketchup take the 25 boxes and multiply the 250 packets
250x25=6,250
determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. X = 0, 1, 9P( X = x ) | 0.41 | 0.6 | 0.06
Since the probabilities lie exclusively between 0 and 1 and the sum of probabilities is equal to 1 , therefore the yes , the distribution is discrete probability distribution.
As the probabilities range from 0 to 1, and the sum of probability equals 1.
Discrete probability distribution is a sort of probability distribution that provides all potential values of a discrete random variable along with the related probabilities. In other words, a discrete probability distribution describes the possibility of each potential value of a discrete random variable occurring.
Some common discrete probability distributions are geometric distributions, binomial distributions, and Bernoulli distributions. This page defines a discrete probability distribution, as well as its formulas, types, and numerous instances.
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y=-3x+2 and 6x+2y=10
There is no solution to the given system of equations which is the correct answer would be an option (A).
The system of equations is given in the question as:
y = -3x+2 and 6x+2y = 10
These are two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
The first equation, y = -3x + 2, has a slope of -3 and a y-intercept of 2.
The second equation, 6x + 2y = 10, can be rewritten in slope-intercept form as y = -3x + 5. This has a slope of -3 and a y-intercept of 5.
Since both equations have the same slope, they are parallel to each other. This means that they will never intersect, and there is no solution to this system of equations.
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The question seems to be incomplete the correct question would be:
Which statement is true about this system of equations?
y = -3x+2 and 6x+2y = 10
A. there is no solution
B. there is one solution
C. there is many infinite solutions
10, 12, 11, 13, 14, 12, 13, 14, 13, and 12 find the mean.
The mean of the given data is 12.4
What is mean?The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values.
Given that, a data, 10, 12, 11, 13, 14, 12, 13, 14, 13, and 12
Arranging the data in ascending order, 10, 11, 12, 12, 12, 13, 13, 13 14, 14
The sum is = 10+12+11+13+14+12+13+14+13+12 = 124
Total number of data = 10
Mean = sum of the numbers/ total numbers of data
Mean = 124/10
Mean = 12.4
Hence, the required mean is 12.4
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What is the answer for identifying the slope and Y intercept for this graph ?
find the value of x in this problem
Answer: x=22
Step-by-step explanation:
Based on the given figure, we can tell that 2x and 44 are vertical angles. Vertical angles are congruent to each other, so we can set them equal to each other.
2x=44 [divide both sides by 2]
x=22
Therefore, x=22.
What’s the remainder
177R[?]
52 9234
The remainder when 9234 is divided by 52 is 30
the quotient is 177 R 30
What is quotient, in math?Division is onw of the mathematical operators that is applied in sharing.
The quotient is the result of dividing two numbers by each other, the number being divided is the dividend while the number dividing is the divisor.
As in the case of 9234 is being divided by 52, the dividend is 9234, while the divisor is 52 the result of the division is the quotient.
the division is done to get
9234 / 52
= 177 30/52
the remainder from the division involving 9234 and 52 is 30, the mixed number is 177 30/52
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in a homicide case different witnesses picked the same man from a line up. the line up contained 5 men. if the identifications were made by random guesses, find the probability that all witnesses would pick the same person. round to seven decimal places.
Rounding to seven decimal places, the probability that one individual would be selected by all witnesses is 0.0000128.
Six different witnesses chose the same individual from a lineup in a homicide case. There were 5 guys in the lineup. The likelihood that each of the six witnesses would choose the same person if the identifications were done based just on guesswork.
P = 1 ÷ 5 is the likelihood that a witness will choose a certain individual at random.
The likelihood that all seven witnesses would select the same subject is P = [tex](\frac{1}{5})^{7}[/tex]= 0.0000128.
Simply put, the probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes to determine how likely they are if we are unclear about how an event will turn out.
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