The value of b is 14
The value of c is 65
Step-by-step explanation:
The quadratic equation ax² - bx + c = 0, where a = 1 has two roots
Their sum = bTheir product = c∵ The quadratic function is g(x) = ax² + bx + c
∵ a = 1
∴ g(x) = x² + bx + c
∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)
∴ g(x) = 0
∴ x² + bx + c = 0
∵ The general form of the quadratic equation is x² - bx + c = 0,
with sum of roots b and product of roots c
- Compare them
∴ x² - (-b) + c = 0
∵ -b = the sum of the two roots
∴ -b = (-7 + 4i) + (-7 - 4i)
- Add like terms
∴ -b = (-7 + -7) + (4i + -4i)
∴ -b = -14 + 0
∴ -b = -14
- Multiply both sides by -1
∴ b = 14
The value of b is 14
∵ c is the product of the two roots
∴ c = (-7 + 4i)(-7 - 4i)
- Remember (a + b)(a - b) = a² - b²
∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²
∵ (-7)² = 49
∵ (4i)² = 16i²
∵ i² = -1
∴ (4i)² = -16
∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65
∴ (-7 + 4i)(-7 - 4i) = 65
∴ c = 65
The value of c is 65
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An airliner is 9.34 feet wide. The airline wants to install 5 seats in each row. The seats are each 1.46 feet wide. Rounded to the nearest tenth, about how much space would be left for the aisle?
About 2.0 feet space will be left for aisle.
Step-by-step explanation:
Width of airliner = 9.34 feet
Width on one seat = 1.46 feet
Seats to install = 5
Width of 5 seats = 5*1.46 = 7.3 feet
Space left for aisle = Width of airliner - width of 5 seats
[tex]Space\ left\ for\ aisle=9.34-7.3\\Space\ left\ for\ aisle=2.04\ feet[/tex]
Rounding off to nearest 10th
Space left for aisle = 2.0 feet
About 2.0 feet space will be left for aisle.
Keywords: multiplication, subtraction
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To find the space left for the aisle, we first calculate the total seat width (5 seats × 1.46 feet/seat) and subtract it from the airliner width (9.34 feet), resulting in 2.0 feet of space for the aisle when rounded to the nearest tenth.
Explanation:To calculate the available space for the aisle in an airliner, we first determine the total width consumed by the seats. Since each seat is 1.46 feet wide and there are 5 seats in a row, we multiply the width of one seat by the number of seats:
1.46 feet/seat × 5 seats = 7.3 feet
Next, we subtract the total width of the seats from the total width of the airliner to find the space left for the aisle:
9.34 feet (total width) - 7.3 feet (width of seats) = 2.04 feet
Therefore, rounded to the nearest tenth, there would be approximately 2.0 feet of space left for the aisle.
f(x) 3x^2+x-3 g(x)=x^2-5x+1 find f(x)-g(x)
Answer:
2x² + 6x - 4
Step-by-step explanation:
f(x) - g(x)
= 3x² + x - 3 - (x² - 5x + 1) ← distribute
= 3x² + x - 3 - x² + 5x - 1 ← collect like terms
= 2x² + 6x - 4
Answer:
f(x) - g(x) = 2x² - 4x - 2
Step-by-step explanation:
f(x) = 3x² + x - 3
g(x) = x² - 5x + 1
f(x) - g(x)
3x² + x - 3 - x² - 5x + 1
3x² - x² - 5x + x - 3 + 1
= 2x² - 4x - 2
f(x) - g(x) = 2x² - 4x - 2
Solve the system of linear equations by addition
x+y=-9
x+y=5
Answer:
No Solution.
Step-by-step explanation:
x+y=-9
x+y=5
------------
x+y=-9
-(x+y)=-5
---------------
x+y=-9
-x-y=-5
-------------
0=-14
: Create a story or context for this number sentence
50 1/2 divided by 1/4 + 202
Answer:
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
Step-by-step explanation:
Given:
[tex]\frac{50\frac{1}{2}}{\frac{1}{4}}+202[/tex]
The Story can be created as :
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
3/10 11/12 5/8 in Oder from least to greatest
Answer: 5/8 11/12 3/10 I think
Step-by-step explanation:
Find common denominators (LCM is 120).
3/10 = 36/120
11/12 = 110/120
5/8 = 75/120
Now, we can put them from least to greatest.
3/10, 5/8, 11/12
______
Best Regards,
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is this a function ?
Answer:
No
Step-by-step explanation:
For the relation to be a function
Each value of x from the domain ( values on left ) must map to exactly one unique value of y in the range ( values on the right )
Here x = 0 → 0 and 1 ( that is 2 values from the range )
Thus this does not represent a function
If you buy a home and make a relatively small down payment, what happens to the monthly payments and total payment for you loan?
Answer:
Both monthly payment and total payment will increase.
Step-by-step explanation:
If I buy a home and make a relatively small down payment, then the due payment will be more.
If I pay for my home through a bank and I fix the number of installments to pay back the due amount after down payment (say, monthly installment for 5 years), then the amount of installment payment will definitely increase if my down payment is less.
Again, if the down payment is less, the remaining amount to pay back will rise and the bank calculates interest on the remaining amount to pay. Therefore, the amount of interest will rise in value and finally the total payment after interest for my loan will increase. (Answer)
The price of a toaster increase 10% to $40. What is the original price of the toaster before the increase?
Answer:
36.36
Step-by-step explanation:
We can express 10% as a decimal by multiplying it by (1/100), resulting in 0.1. Therefore, adding 0.1 of the original price, or x, to the price will result in 40, so x+0.1*x=40
= 1.1x
Dividing both sides by 1.1, we get that x, or the original price, is $36.36 (approximately).
At the market, 8 apples cost $4dollar. How much do 9 apples cost?
Answer: $4.50 for 9 apples
Step-by-step explanation: To find out how much it is for 1 apple, we need to find the unit price of 1 apple which is the cost per apple.
Since we know that it costs $4 for 8 apples, to find the cost for 1 apple, we need to divide 8 into $4 or 4 divided by 8 which is 0.5 of 50 cents per apple.
Since we know that it costs 50 cents per apple, to find the cost for 9 apples, we will need to multiply .50 by 9.
(.50) (9) = 4.50
Therefore, it will cost $4.50 for 9 apples.
Ratio question. Someone please help me!
Answer:
b is the right answer
Step-by-step explanation:
because the ratio of 98÷10=9.8
when we did the ration of 1078÷110=9.8
we can say that both ratio is same.
Answer: [tex]\frac{98}{10}[/tex] ; x = 110
Step-by-step explanation:
Since the ratio of weight to mass is constant , it implies:
[tex]\frac{490}{50}[/tex] = [tex]\frac{1078}{x}[/tex]
490x = 1078 X 50
490x = 53900
x = 53900/490
x = 110
Therefore the ratio of weight to mass will be :
1078/110
98/10
could someone help with this inequality?
20≥−3.2(c−4.3)
thanks >o
The solution of inequality would be -
c ≥ 1.95
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
We have the following inequality -
20 ≥ −3.2(c − 4.3)
It is given that -
20 ≥ −3.2(c − 4.3)
−3.2(c − 4.3) ≤ 20
-3.2c + 13.76 ≤ 20
-3.2c ≤ 20 - 13.76
-3.2c ≤ 6.24
c ≥ 1.95
Therefore, the solution of inequality would be -
c ≥ 1.95
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what is half of 7 minutes and 24 seconds
Step-by-step explanation:
7 minutes are 7*60=420 seconds
420+24=444
444:2=222 seconds
222 seconds are 3minutes and 42 seconds
Answer:3.7 is half of 7 minutes and 24 seconds
Step-by-step explanation:
There are 450 children that attend a high school. Of those students. 23%
are in the marching band. How many students are not in the marching
band?
Answer:
The number of students not in the marching band is 346.5
Step-by-step explanation:
Given as :
The total number of children that attend a high school = 450
The percentage of students in the marching band = 23 %
Let The number of students not in the marching band = x
Now ,
∵ The percentage of students in the marching band = 23 %
∴ The percentage of students not in the marching band = 100 % - 23 % = 77 %
So, The number of students not in the marching band = 77 % of the total number of students in the school
I.e The number of students not in the marching band = 77 % × 450
Or , The number of students not in the marching band = [tex]\frac{77}{100}[/tex] × 450
∴ The number of students not in the marching band = 346.5
And The number of students in the marching band = 450 - 346.5 = 103.5
Hence The number of students not in the marching band is 346.5 Answer
What are the possible values of the missing term of the geometric sequence 6,....,13.5?
Answer:
THE ANSWER IS 1.5
Step-by-step explanation:
13.5 is the 3rd and last value. 6 is the first value.
The formula you need to use is an= 3r^n-1
13.5=3r^3-1
THE REASON YOU USE 3 IS BECAUSE IN TOTAL THERE ARE 3 TERMS AND WE ARE SOLVING FOR ONE MISSING TERM.
Now we bring 3 over to 13.5 to get r alone because we are solving for r
13.5/3 =r^2
Now we want to get rid of the square root. So we...
√13.5/3 =√r^2
The final answer is 1.5=2
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
Answer:
5 more weeks
Step-by-step explanation:
5 more weeks if he already sold 15. 10 more weeks if you exclude the 15 he already sold.
F=9/5c+32 a is there a constant of proportionality? Explain your reasoning
yes because in a standard form that that equation is in, it'd be y=mx=b. the m represents the constant of proportionality or the rate of change. another name for it is the slope. in this case, the 9/5 is the m & c is x. meaning that, there is one & it is 9/5
5p = 1/15
what does p equal?
Answer:
(:5) 5p=1/15 (:5)
p=1/3
Answer:
p= .3333333
Step-by-step explanation:
Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.
Answer:
Number of songs played in commercial are 7 and Number of songs played in movie are 5.
Step-by-step explanation:
Let Number of songs played in commercial be x
and Number of songs played in movie be y.
Total number of songs played =12
Hence,
[tex]x+y=12\ \ \ \ equation \ 1[/tex]
Also
Cost for songs played in commercial = $50
Cost for songs played in movie = $130
Total Money earned = $1000
Hence,
[tex]\$50x+\$130y=\$1000[/tex]
Dividing by 10 on both side we get;
[tex]\$5x+\$13y=\$100\ \ \ \ equation \ 2[/tex]
Now multiplying equation 1 by 5 we get;
[tex]5x+5y=60 \ \ \ \ equation \ 3[/tex]
Now Subtracting equation 3 from equation 2 we get;
[tex](5x+13y=100)- (5x+5y=60)\\8y=40\\y=\frac{40}{8}=5[/tex]
y = 5
x + y = 12
x + 5 = 12
x = 12 - 5
x = 7
Hence, Number of songs played in commercial are 7 and Number of songs played in movie are 5.
A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students?
4:14
4:10
2:7
2:5
Answer:
2:7
Step-by-step explanation:
There are 4 boys and 14 total students. That ratio is 4:14, and to find the simplest form you divide both numbers by the greatest common factor, which is 2. That leaves you with 2:7, the final answer.
Answer: simple just put boys=4ovrwhole class =14 put it in fraction 4/14 simplify you get 2/7
Step-by-step explanation:
Find 4(6a−5)−(9a+1).
Answer:
15a-21
Step-by-step explanation:
could be wrong though
The system of equations is graphed on the coordinate plane.
y=x−1y=−2x−4
What are the coordinates of the solution to the system of equations.
Answer:
(-1,-2)
Step-by-step explanation:
Hope it helps!
Answer:
the correct answer is (-1,-2)
Step-by-step explanation:
write an equation that is not a linear function explain why it is not linear
Answer:
x=y^2
Step-by-step explanation:
cause the definition of equation is one x correspond to one y,but one y can correspond to 2 x,
the picture I give to you a x correspond to 2 y
The function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
According to the question,
A nonlinear equation is given as,
y = x²
Now plotting the curve,
When we see that the relationship does not contain a straight line, and has a varying rate of change are nonlinear functions.
So this function is not linear.
Thus, the function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
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I need the answer and if you could please explain step by step
Umm sir where is the Graff we need it to solve the problem
Answer:
we need a graph to solve this. please provide the graph and we will be happy to help you!
Step-by-step explanation:
The expression x2 - 36y2 is equivalent to
Answer:
(x + 6y)(x - 6y)
Step-by-step explanation:
The expression x² - 36y² can be factored.
Since the expression is a difference (subtraction) between two numbers that are square (x² = x*x and 36y² = 6y*6y), the factoring can be done as a "difference of squares".
The rules is generalized as: [tex]x^{2} - y^{2} = (x - y)(x+y)[/tex]
To factor x² - 36y², take each square roots for each of the numbers and add and subtract between them.
x² - 36y²
= (√x² + √36y²)(√x² - √36y²)
= (x + 6y)(x - 6y)
[tex] \frac{1}{3}x - 5 + 171 = x[/tex]
Answer:
x=249
Step-by-step explanation:
1/3x-5+171=x
1/3x+166=x
166=x-1/3x
166=2/3x
x=166/(2/3)
x=(166/1)(3/2)
x=498/2
x=249
What is the simplified form of 2n ^ 2/3 * 3n^ 3 / 4
Answer: N^5/2 thats the answer thank you :)
Marty ordered three extremely accurate and scientific water-balloon launchers from a mail order catalog (one for himself and two for his friends). The total price including shipping charges was $50. If the total shipping cost was $5, how much did each launcher cost?
Answer:
The price of each launcher is $ 15 .
Step-by-step explanation:
Given as :
The total price of three water balloon launchers including shipping charges = $50
The cost of the three shipping = $ 5
So, The price of water balloon launchers excluding shipping charges = $50-$5 = $ 45
Now,
∵ The price of 3 balloon launcher = $45
∴, The price of 1 balloon launcher = [tex]\frac{45}{3}[/tex] = $15
Hence The price of each launcher is $ 15 . Answer
use the rational exponent property to write an equivalent expression for
[tex] \sqrt[5]{n ^{4} } + 3 - 12[/tex]
Using the rational exponent property, an equivalent expression for[tex]\(x^{3/4}\[/tex] can be written as[tex]\(\sqrt[4]{x^3}\).[/tex]
Explanation:The rational exponent property states that for any real number a and positive integer[tex]\(n\), \(a^{m/n} = \sqrt[n]{a^m}\)[/tex] . Applying this property to the given expression[tex]\(x^{3/4}\[/tex] ), where (m = 3) and (n = 4), we can rewrite it as [tex]\(\sqrt[4]{x^3}\)[/tex] . This is derived by taking the fourth root of [tex]\(x^3\),[/tex] which is equivalent to raising [tex]\(x^3\)[/tex] to the power of[tex]\(1/4\).[/tex]
To further understand this, consider the original expression [tex]\(x^{3/4}\).[/tex] This represents the fourth root of [tex]\(x^3\)[/tex] , as the numerator 3 indicates the power to which x is raised, and the denominator 4 indicates the root. Expressing it as [tex]\(\sqrt[4]{x^3}\)[/tex] provides a clearer representation of the same mathematical concept, emphasizing the fourth root of [tex]\(x^3\).[/tex]
In mathematical notation, the rational exponent property is a useful tool for simplifying expressions involving fractional exponents. It allows us to transform expressions between radical form and exponent form, providing flexibility in mathematical manipulations and aiding in the understanding of the underlying concepts.
What is the equation of a line in slope intercept form that passes through the points (-4,3) and (-2,4)
Answer:
y=1/2x+5
Step-by-step explanation:
y-y/x-x for slope
4-3/-2-(-4) 1/2
Answer:
y= --2/4+5
Step-by-step explanation:
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer in the box.
y = 17.5 when x = 5
Step-by-step explanation:
When two variables are in direct proportion i.e. change in one variable causes change in other variable it can be expressed mathematically as:
y∝x
when the proportionality symbol is removed a proportionality constant is introduced
So,
[tex]y = kx[/tex]
Putting y = 7 and x = 2
[tex]7 = k * 2\\k = \frac{7}{2}\\k = 3.5[/tex]
So the expression will be:
[tex]y = 3.5x[/tex]
Now putting x = 5
[tex]y = 3.5 * 5\\y = 17.5[/tex]
Hence,
y = 17.5 when x = 5
Keywords: Proportion, variables
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