What are the roots of the polynomial equation? x² + 7x + 12 = 0 Enter your answers in the boxes. x1= x2=
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.. (x +3)(x +4) = 0
By the zero-product rule, the roots are
.. x1 = -4
.. x2 = -3
x= -3, -4
Related Questions
anyone wants to help?
Answers
The y-intercept is 1/3.
This is because this is written in slope intercept, which is defined as:
y = mx + b
With the slope being m and the y intercept being b. 1/3 is being added to -2/9x, and therefore by the rules of the formula it's the y intercept.
As a quick background on a y intercept, it's where the line crosses the y axis. It can be positive, or negative, and the coordinates never have an x value.
Hope this helps!
What is the domain of the square root function graphed below?
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From the graph, we see the least value of x is 3. x can be any value greater than or equal to 3.
The domain is
[tex] x \ge 3 [/tex]
Answer:
x greater than or equal to 3
Step-by-step explanation:
got it right on quiz
Your doctor told you to eat 25 grams of fiber each day.
You had 4 grams of fiber for breakfast.
What percent of the 25 grams of fiber have you eaten so far?
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two numbers have a difference of 0.7 and a sum of 1 what are the numbers
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0.85 - 0.15 = 0.70
0.85 + 0.15 = 1
0.85 and 0.15 is your answer
hope this helps
{x-y = 0.7
add both equations
2x = 1.7
x = 0.85
x+y = 1
y = 1-x
y = 1-0.85
y = 0.15
Which expression is equivalent to i^233
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divide 233 by 4 to find the remainer: 233÷4=58, remainder is 1
so the result is i
i^233=(i^4)^58×i=1^58×i=i
Answer: the answer is i
Step-by-step explanation:
A cube has a surface area of 486 square meters. What is the volume of the cube.
Answers
a=486/6=81
s=sqrt(81)=9
v=9^3=729
the volume of the cube is 729cm^3
aequals486/6=81
sequalssqrt(81)=9
vequals9^3=729
the volume of the cube is 729cm^3
Standard form............
Answers
Ninety-eight = 98
six-tenth = 0.6
98 + 0.6 = 98.6
98.6 is your answer
Hope this helps
To see how costly it would be for other people to complete a similar cycling tour, you decide to work out two averages and compare.
Group A
Person 1: $500
Person 2: $600
Person 3: $900
Person 4: $450
The average amount spent by members of cycle group A was $
Group B
Person 1: $700
Person 2: $500
Person 3: $680
Person 4: $500
The average amount spent by members of cycle group B was $
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Is y = 0 the asymptote of all functions of the form f(x) = ab^x? Explain your reasoning.
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Final answer:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. Functions of the form f(x) = ab^x do not have y = 0 as an asymptote.
Explanation:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. In order for a function to have y = 0 as an asymptote, the limit of the function as x approaches infinity or negative infinity would need to be 0. For example, the function f(x) = 1/x has y = 0 as an asymptote because as x approaches infinity or negative infinity, the function approaches 0. However, functions of the form f(x) = ab^x do not have y = 0 as an asymptote because as x approaches infinity or negative infinity, the value of the function either approaches infinity or approaches 0, depending on the values of a and b.
Consider the expression 4n3 + 3n2 + 2n + 1. What is the coefficient of n2?
Answers
hope it helps
Answer:
Coefficient of n² is 3.
Step-by-step explanation:
Given : 4n³ + 3n² + 2n + 1.
To find : What is the coefficient of n².
Solution : We have given 4n³ + 3n² + 2n + 1.
Coefficient : A numerical or constant quantity placed before and multiplying the variable in an algebraic expression
Example : 4 in 4x² .
In 4n³ + 3n² + 2n + 1.
Coefficient of n² is 3.
Therefore, Coefficient of n² is 3.
The bus will leave Norfolk, VA at 6:00 a.m. on Thursday. The distance from Norfolk to New York City is 350 miles. The average speed of the bus is 50 miles per hour. 1.Determine how long it will take the charter bus to arrive in New York City. Represent the distance traveled every hour in a table of values.
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A table would look something like this:
0 1 2 3 4 5 6 7
0 50 100 150 200 250 300 350
Hope you can read it and this helps
What is the b in 8b=5.6
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Explanation: Since we are doing multiplication (8 * b) we would now do the inverse operation which is dividing. First, it's 5.6 divided by itself so we can cross that out, then 8 divided by 5.6 = .7
If we put 8 * .7 in a calculator, sure enough, it comes out as 5.6
Two sides of an isosceles triangle have lengths of 6 inches and 15 inches, respectively. What is the length of the third side?
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The radius of a circle can be found by dividing the circumference of the circle by 6.28. What is the radius of a circle that has a circumference of 17.27 feet?
0.36 ft
2.75 ft
10.99 ft
2.58 ft
HELP ME!!
Answers
circumference ÷ 6.28 = radius
The circumference here is 17.27 feet :
circumference ÷ 6.28 = radius
so
17.27 ÷ 6.28 = 2.75
The radius of the circle is 2.75 feet.
Anthony ‘s family went out to dinner. They left at the. Time 5:05 pm any they returned home at 6:52p.m
How long was Anthony ‘s family gone
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Rachel opened a savings account 6 years ago. The account earns 8% interest, compounded monthly. If the current balance is $1,000.00, how much did she deposit initially?
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A rectangle has a perimeter of 48 feet and a length of 14 ft which equation can you solve to find the width
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Answer: 2n + 28 = 48
Step-by-step explanation: Got it right on TTM
does 3/4 have the same value as the expression 4 ÷ 3 answer
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i don’t know how to do this. can someone please help me :)
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.. surface area = 2*(end area) +(lateral area)
.. = 2*(π*r^2) +(2π*r*h)
.. = 2π*r*(r +h)
.. = 2*3.14*(8 in)*(8 in +8 in)
.. = 3.14*256 in^2
.. ≈ 803.8 in^2
The 3rd selection is appropriate.
Write a story problem to represent 5 divided by 1/4
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Hope this helps!
The problem can be seen below, we will see that the quotient between the given numbers is 20.
How to write the problem?Here we want to divide 5 by 1/4.
An example of this can be: Assume that you have $5, and you want to buy pieces of wood (to make little houses for birds) such that each piece costs $(1/4).
How many pieces can you buy?
To solve this, we need to take the quotient between 5 and (1/4), this gives:
[tex]\frac{5}{1/4} = 20[/tex]
You can buy 20 pieces.
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A local hamburger shop sold a combined total of 712 hamburgers and cheeseburgers on Tuesday. There were 62 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?
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There are 62 more cheeseburgers than hamburgers
let cheeseburers = c
let hamburgers = h
h + 62 = c
c + h = 712
Plug in h + 62 for c
(h + 62) + h = 712
2h + 62 = 712
2h + 62 (-62) = 712 (-62)
2h = 650
2h/2 = 650/2
h = 325
There are 325 hamburgers sold on Tuesday
c = 325 + 62
c = 387
There are 387 chesseburgers sold on tuesday (in case you were wondering)
hope this helps
Final answer:
To find how many hamburgers were sold, we set up an equation and solve for H, the number of hamburgers. After forming the equations, simplifying, and solving, it turns out that 325 hamburgers were sold on Tuesday.
Explanation:
The student is asking how many hamburgers were sold on Tuesday given that a total of 712 hamburgers and cheeseburgers were sold, with there being 62 more cheeseburgers sold than hamburgers. To solve this, we can set up an equation. Let's denote the number of hamburgers sold as H and the number of cheeseburgers as C. According to the problem,
C = H + 62 and H + C = 712.
By substituting the first equation into the second, we get:
H + (H + 62) = 712
Simplifying, we have
2H + 62 = 712
Subtracting 62 from both sides, we get-
2H = 650
Dividing both sides by 2, we find -
H = 325
Therefore, 325 hamburgers were sold on Tuesday.
the Jackson family went out to dinner
the price of the meal was 43.45
the sales tax was 7% of the price of the meal
the tip was 15% of the meal and sales tax.
how much money did the smith family pay for the meal, including tax and tip?
Answers
Answer: Amount that the Smith family need to pay for the meal including tax and tip = 53.47.
Step-by-step explanation:
Since we have given that
Price of the meal = 43.45
Rate of sales tax = 7%
Amount becomes after the sales tax is given by
[tex]\frac{7}{100}\times 43.45\\\\\frac{304.15}{100}\\\\=3.0415\\\\\text{Amount}=43.45+3.0415=46.4915[/tex]
Rate of tips over meal and sales = 15%
Amount of tips is given by
[tex]\frac{15}{100}\times 46.4915\\\\=0.15\times 46.4915\\\\=6.974[/tex]
So, Amount becomes
[tex]46.4915+6.974\\\\=53.465\\\\=53.47[/tex]
Hence, Amount that the Smith family need to pay for the meal including tax and tip = 53.47.
The cost of a television is $429.99 after sales tax is added. If the sales tax is 7.5%, what was the cost of the television before sales tax was added? (A) $377.74 (B) $389.46 (C) $397.74 (D) $399.99 (E) $459.27
Answers
The original cost of the television before a 7.5% sales tax was added, which made the total $429.99, is optionD. $399.99.
The question is asking to find the original cost of a television before sales tax was added. Given that the final cost after including the 7.5% sales tax is $429.99, we need to find the price before this tax was applied. To calculate this, we first convert the percentage to a decimal, which is 0.075, and then create an equation to represent the relationship between the original price (let's call it x) and the total cost with tax. The equation would be x + 0.075x = $429.99. This is equivalent to 1.075x = $429.99. Solving for x gives us the original price of the TV before tax.
To solve for x, we would divide both sides by 1.075, which is the combined total of the original price and the tax. x = $429.99 / 1.075. This calculation gives us the original price of the TV, which turns out to be $399.99, which is option (D).
The vertices of triangle ABC are A(−6,−3) and B(2,−3). Which coordinates of the third vertex allow the triangle to have an area of 24 square units?
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The third vertex C of triangle ABC with vertices A(-6,-3) and B(2,-3) and area 24 square units can have coordinates (0,3) or (0,-9).
Explanation:
Given the vertices of triangle ABC are A(−6,−3) and B(2,−3). The coordinates of point C will form the third vertex of the triangle. The distance from A to B is the base of the triangle and can be calculated as follows: AB = sqrt[(2 -(-6))^2 + ((-3) - (-3))^2] = 8 units. The area of a triangle is calculated by the formula: 1/2*base*height=area. Given that the area of the triangle ABC is 24 square units, we can set up the following equation: 1/2*8*height=24. Solve for height to get the y-coordinate of point C as 6 units above the line AB (which lies on y = -3), for C(0,3) or 6 units below line AB for C(0,-9). Therefore, the third vertex C can be at coordinates (0,3) or (0,-9) for the triangle to have an area of 24 square units.
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You may use any word processing program or Web 2.0 tool to present your argument, but you must include the following: A summary of your argument. The summary should begin with the argument statement you chose. In addition, provide at least three reasons why the method you chose is better than the other method and at least three reasons why the other method is not better. This summary can have a lot of opinion in it and should be persuasive and argumentative. A list of at least two resources used. Resources may include interviews with professionals and/or URLs of websites. Remember, you may gather ideas from research, but you must explain the ideas yourself.
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In summary, an effective argumentative essay includes a clear thesis statement followed by logically structured reasons supported by a mix of well-researched evidence and personal knowledge, ensuring a persuasive and objective argument.
Students tasked with creating an argumentative essay must focus on developing a persuasive argument. The essay should begin with a summary of the argument that clearly states the main thesis. Following this, at least three reasons should be provided to support why the adopted approach is superior, using logical and persuasive evidence, such as statistics, expert opinions, and relevant examples. Contrary to this, the reasons why the alternative method is less effective should also be articulated. The Rule of 3 is a strategic approach where the contentions made to support an opinion are outlined in three clear points, enabling a structured and convincing argument to be presented.
To successfully make an argument in a position paper, it is crucial to provide a paragraph for each reason, starting with a clear topic sentence and backed by well-researched evidence. This can include research findings, personal knowledge, and a variety of evidence to ensure the argument is perceived as objective. An informal approach may also be used to frame the debate, maintaining relevance and ensuring engagement with the topic.
Finally, it's vital to use reliable resources to supplement the argument. A combination of research from credible sources and well-prepared reasoning constructs an objective and persuasive document that clearly distinguishes the author's ideas from those presented in the referenced texts.
a $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
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Now we multiply that with starting funds and get
4000* 1.05^4 = 4862.03
To calculate the balance in the account after 4 years, use the compound interest formula.
Explanation:To calculate the balance in the account after 4 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the balance after the specified time period
P is the principal amount (initial deposit)
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal is $4,000, the interest rate is 5% (written as 0.05), the interest is compounded annually (n = 1), and the time period is 4 years (t = 4). Plugging in these values, we get:
A = $4,000(1 + 0.05/1)^(1*4)
A = $4,000(1.05)^4
A = $4,000(1.2155)
A ≈ $4,862.20
The balance in the account after 4 years is approximately $4,862.20.
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A hot air balloon descends at a rate of 320 ft per minute for 3 minutes use integers to calculate represent the balloons total change in altitude
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320 (feet per minute) / 1 (minute) = x (feet per minute) / 3 (minutes)
1) Divide: 320/1 = 320.
2) Multiply: 320 x 3= 960.
The balloon that descends at a rate of 320 feet/minute (so, every minute, it descends 320 feet) descends a total of 960 feet in 3 minutes.
The balloon's total change in altitude is -960
Need help with number 9 please, thanks.
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Jessie set up a lemonade stand for three days. On Saturday she sold 10 and 2/3 gallons of lemonade. On Sunday she sold 3 and 1/3 gallons mor3 than she sold on Saturday. On Monday she sold 2 and 2/3 gallons less than she sold on Sunday. How many gallons of lemonade did jessie sell on Monday
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Jessie set up a lemonade stand for three days.
On Saturday she sold 10 and 2/3 gallons of lemonade = 10+2/3 = 32/3 gallons
On Sunday she sold 3 and 1/3 gallons more than she sold on Saturday
Lemonade sold on Sunday = 32/3 + 3 and 1/3 gallons
= 32/3 + 10/3 = 42/3 gallons = 14 gallons
On Monday she sold 2 and 2/3 gallons less than she sold on Sunday
Lemonade sold on Monday = 14 - 2 and 2/3 gallons
= 42/3 - 8/3 = 34/3 gallons
Therefore, Jessica sold 11 and 1/3 gallons of lemonade on Monday
how do you solve each absolute value by graphing
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I like to subtract one side of the equation from the other, so the solutions are where the graph crosses the x-axis (the resulting function value is zero).
It can be useful to find the "turning point" of each absolute value expression (where its value is zero) and graph that and some points on either side.