The graph of a quadratic function having the form f(x) = ax? + bx + c passes
through the points (0, -8), (3, 10), and (6,34). What is the value of the function
when x = -3?
Answers
Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
_____
The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
Related Questions
The fox population in a certain region has a continuous growth rate of 5% per year. It is estimated that the population in the year 2000 was 10,100 foxes.
a) Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).
b) Use your function from part (a) to estimate the fox population in the year 2008.
c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.
Answers
Answer:
P(t) = I × ( 1 +g)^t
14922
2013
Step-by-step explanation:
Given the following :
Growth rate (g) = 5% = 0.05
Initial population (I) = 10,100
Time (t) = t (t = 0 in year 2000)
A) population function P(t)
P(t) = I × ( 1 +g)^t
P(t) population in t years
I = inital population
g = growth rate
t = years after year 2000
B) Population Estimate in year 2008
2008 - 2000 = 8 = t
P(8) = 10,100 × ( 1 +0.05)^8
P(8) = 10,100 × (1.05)^8
P(8) = 10,100 × 1.4774554437
P(8) = 14922.299 = 14922
C.) Nearest whole year when population will reach over 18,400
18,400 = 10,100 × ( 1 +0.05)^t
18400 = 10,100(1.05)^t
1.05^t = 18400 / 10,100
1.05^t = 1.8217821
In(1.05^t) = ln(1.8217821)
(0.0487901)t = 0.5998152
t = 0.5998152 / 0.0487901
t = 12.293789
To attain a population of 18400 and over, the nearest whole year = 13 years
2000 + 13 = 2013
a process used to convert units and rates using a conversion factor and multiplication
Answers
Dimensional Analysis
If x * (x + 2) = 49, find x
Answers
Answer:
x = -8.07107, 6.07107
Step-by-step explanation:
Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Step 1: Write out equation
x(x + 2) = 49
Step 2: Distribute
x² + 2x = 49
Step 3: Subtract 49 on both sides
x² + 2x - 49 = 0
Step 4: Quadratic Formula
a = 1
b = 2
c = -49
x = -8.07107, 6.07107
Kathy found a job listed on an employment web site that pays a yearly salary of $27,630. What is
the biweekly salary based on this annual salary rounded to the nearest cent?
Do not include a dollar sign in your answer.
Answers
Answer:
1151.25
Step-by-step explanation:
You would divide $27,630 by 12 months.
You would then have her monthly salary. Since there are 4 weeks in a month, she has two pay periods. You would divide her monthly salary (2302.5) by two weeks, to get $1151.25
please help me on this
Answers
Answer:
Median
Step-by-step explanation:
A line that goes from the vertex of a triangle to the midpoint of the opposite side is a median.
What is the difference between law and scientific law.
Answers
Answer:
A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept, according to Kennesaw State University. ... However, Newton's law doesn't explain what gravity is, or how it works.
Step-by-step explanation:
Answer:
law is federal
Step-by-step explanation:
ik
Find the circumference given the area = 28.3 km². Use 3.14 for π as necessary. A. 18.9 km B. 20.8 km C. 21.4 km D. 37.8 km
Answers
================================================
Work Shown:
Use the given area A = 28.3 to find the radius r
A = pi*r^2
28.3 = 3.14*r^2
3.14*r^2 = 28.3
r^2 = 28.3/3.14
r^2 = 9.01273885350319 approximately
r = sqrt(9.01273885350319)
r = 3.00212239149292
---------
Which is then used to find the circumference
C = 2*pi*r
C = 2*3.14*3.00212239149292
C = 18.8533286185756
C = 18.9
Determine the value of
x isosceles triangle?
Answers
Answer:
x = 13ft
Step-by-step explanation:
The isosceles triangle is a polygon with three sides, two being equal and the other unequal.
The angles P and N will also be equal and the M other different.
PM ≅ MN
∠P ≅ ∠N
PN = 2x
because the line starting at M divides the triangle into two sections
26 = 2x
2x = 26
x = 26 /2
x = 13ft
8. Which of the numbers in each pair is farther to the left on the number line?
a. 305 and 17
b. 187 and 900
C. 16 and 46
d. 157,019 and 149,984
Answers
b. 900
c. 46
d. 157,019
I need help with b and d
Answers
Step-by-step:
add (-9) & (+10) to get (+1) : (-9+10 = 1)
= -4x + y2 + 1 - x + 3x - 4y2
combine (-4x) & (-x) to get (-5x) : (-4x+ (-x) = -4x-x = -5x)
= -5x + y2 + 1 + 3x - 4y2
combine (-5x) & (3x) to get (-2x) : (-5x + 3x = -2x)
= -2x + y2 + 1 - 4y2
combine (y2) & (-4y2) to get (-3y2) : (y2 + (-4y2)) = y2 - 4y2 = -3y2)
= -2x - 3y2 + 1 Or 1 - 3y2 - 2x (rearrange)
---
D) -4xy + 4y2 - y - 10 or -10 - 4xy - 4y2 (rearrange)
Step-by-step:
subtract 20 from 0 to get −20 (0-20 = -20)
= −20 − 5xy + 4y2 + 10 − y + xy
add (-20) & (10) to get (-10) : (-20+10 = -10)
= -10 -5xy + 4y2 - y + xy
combine (-5xy) & (xy) to get (-4xy) : (-5xy + xy = -4xy)
= -10 - 4xy + y2 - y or (-4xy + 4y2 - y - 10) (rearrange)
express 0.0706 to standard form
Answers
Answer: 706 x[tex]10^{-4}[/tex]
It can also be written as 7.06 x [tex]10^{-3}[/tex]
Answer:
Step-by-step explanation:
0.0706 * 10 (0) the zero is supposed to be on top of the 10
Reemu read 1·5 pages of a book. If she read further 40 pages,she would have read 7.10 pages of the book. How many pages are left to be read?
Answers
Answer:
Let total pages be x
ATQ,
(x/5)+40=7x/10
(x+200)/5=7x/10
Cross multiply
10x+2000=35x
10x-35x=-2000
-25x=-2000
x=2000/25
x=80 pages
Therefore pages left= 3/10 of pages
=3*80/10=24 pages
Answer:
(x/5)+40=7x/10
(x+200)/5=7x/10
Cross multiply
10x+2000=35x
10x-35x=-2000
-25x=-2000
x=2000/25
x=80 pages
Therefore pages left= 3/10 of pages
=3*80/10=24 pages
ther u is good person
if x=1 then (x-1)(x-2)= -3 -1 0 2
Answers
I used this other app to find out the answer it’s a app that helps you with mathematical problems
My question is 9 + 12n
Answers
Answer:
3(3 +4n)
OR
9 + 12n
Step-by-step explanation:
9 + 12n
Factorize it
3(3 +4n)
OR
The answer is the same.
Since we can't add a number with a number and letter. So in that case the answer is ;
9 + 12n.
Hope it helps!!Please mark me as the brainliest!!!Thanks !!!!
Rayée sold 3 desks at the local trade show. H paid $4.00 to rent the booth. He gave half of his revenue to the carpenter and was left with $185.50. At what price did he Rayen sell with each desk
Answers
Answer:
$125
Step-by-step explanation:
Given the following :
Number of desks sold = 3
Amount of rent paid = $4
Amount paid to carpenter = 1/2 of revenue
Amount left = $185.50
At what price did Ryan sell each desk?
If Rayee gave half of his revenue to the carpenter and then had $185.50 left,
The his revenue before paying the carpenter will be twice what he has left ($185.50 * 2) = $371
Hence, total revenue from the sale of 3 desk= ($371 + rent) = (371 + 4) = $375
Then each desk cost :
$375 / 3 = 125
$125
If ∠P measures 27°, ∠R measures 135°, and p equals 9.5, then which length can be found using the Law of Sines?
Answers
Answer:
r = 14,8
Step-by-step explanation:
Hope you can read my writing ;-)
The length that can be found using the Law of Sine rule is
r= 14.80 units
What is the lenght?Generally,
Generally, the equation for sin rule is mathematically given as
[tex]\frac{p}{sinP} = \frac{q}{sinQ} = \frac{r}{sinR}[/tex]
Where
p = 9.5 units
∠P = 27°
∠R = 135°
Therefore
[tex]\frac{9.5}{sin 27^0} = \frac{q}{sin Q} = \frac{r}{sin 135^0}[/tex]
[tex]\frac{9.5}{sin 27^0} = \frac{r}{sin 135^0}[/tex]
9.5 x 0.7071 = r x 0.4540
r = 14.80 units
Read more about length
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A gas that exerts a pressure of
215 torr in a container with a volume of
51.0 mL will exert a pressure of
torr when transferred to a
container with a volume of 18.5 mL.
Assume that the number of moles and the
temperature remain constant.
Answers
Step-by-step explanation:
According to Boyle's Law :
[tex]p _1v _1 = p _2v _2[/tex]
[tex]v _2 = \frac{p _1v _1}{p _2} = \frac{215 \times 51}{18.5} = 592.7ml[/tex]
The pressure exert in a container is 592.70 torr.
To find The pressure exert in a container.
What is Molarity?Molarity is defined as the moles of a solute per liters of a solution. Molarity is also known as the molar concentration of a solution.
Given that :
pressure([tex]P_{1}[/tex])=215 torr
volume ([tex]v_{1}[/tex])=51.0 mL
volume([tex]v_{2}[/tex])= 18.5 mL
[tex]P_{2}[/tex]=?
Number of moles and the temperature remain constant.
By the use of "Boyle's law" :
[tex]P_{1} V_{1} =P_{2} V_{2} \\\\215*51=P_{2} *18.5\\\\P_{2} =\frac{215*51}{18.5} \\\\P_{2} =592.70 torr[/tex]
So, the pressure exert in a container is 592.70 torr.
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Write the expression in exponential form.
[tex] \sqrt{10} [/tex]
Answers
When we use an exponent of 1/2, it is the same as a square root. The more general rule is
[tex]\sqrt{x} = x^{1/2}[/tex]
In this case, we plug in x = 10.
The use of a fractional exponent is handy when you want to deal with things like cube roots on a calculator. This is because
[tex]\sqrt[3]{x} = x^{1/3}[/tex]
Many calculators don't have a button labeled [tex]\sqrt[3]{}[/tex] but they have the button [tex]x^y[/tex] to allow fractional exponents.
Which expression is equivalent to (3^4 • 5^4)^-3
A. 1/15^3
B. 15^-48
C. 1/15^12
D. 15^5
Tania chose B as the correct answer, How did she get that?
Answers
3^4*5^4 = (3*5)^4 = 15^4
Raise this to the exponent -3 and we get
(3^4*5^4)^(-3) = (15^4)^(-3) = 15^(4*(-3)) = 15^(-12)
The last step is to use the rule
x^(-k) = 1/( x^k )
So,
15^(-12) = 1/( 15^12 )
The answer is actually choice CIt seems like Tania multiplied all the exponents to get 4*4*(-3) = 16*(-3) = -48, but you only multiply the inner and outer exponents together as I did when I went from (15^4)^(-3) to 15^(-12)
The quotient below is shown without the decimal point. Use number sense to place the decimal point correctly. 370 ÷ 2.5 ÷ 1.6 = 925
Answers
Answer:
92.5
Step-by-step explanation:
When you would look at this you would just see that there are if you divide 370 by 2 and 2 again you will not get a small number so the only logical answer is 92.5
The number would be 92.5
First, we have to convert decimal to fraction
370/(25/10 * 16/10)
now, reduce the expression to the lowest term
370/4
reduce the fraction
185/2
=92.5
What are Decimals?
In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator
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Solve the equation
(If possible please show work)
Answers
Answer:
x = 0
Step-by-step explanation:
First, distribute the -4 to the parentheses:
-4 + 3x = 2x - 4(1 - 3x)
-4 + 3x = 2x - 4 + 12x
Then, add like terms:
-4 + 3x = 14x - 4
Solve for x:
3x = 14x
0 = 11x
0 = x
Answer:
x=0
Step-by-step explanation:
We are given the following equation and asked to solve. We must solve for x by isolating x on one side of the equation.
-4 + 3x= 2x-4(1-3x)
First, distribute the -4. Multiply each term inside the parentheses by -4.
-4+3x=2x + (-4*1) + (-4*-3x)
-4+3x= 2x -4 + (-4*-3x)
-4+3x= 2x-4+12x
Combine like terms on the right side of the equation. The terms 2x and 12x can be added.
-4+3x= (12x+2x)-4
-4+3x=14x-4
Next, subtract 3x to both sides of the equation.
-4+3x-3x=14x-3x-4
-4= (14x-3x)-4
-4= 11x-4
Next, add 4 to both sides of the equation.
-4+4=11x-4+4
-4+4=11x
0=11x
Finally, divide both sides of the equation by 11.
0/11= 11x/11
0/11=x
0=x
The solution to the equation -4 + 3x= 2x-4(1-3x) is x=0
Calculate the total percentage of the shaded
region in both circles.
Answers
Answer:
80%
Step-by-step explanation:
Total area is the area of two circles. Each circle if accepted as a unit, in total it equals to 2 units.
Shaded area:
1 + 3/5 = 8/5Percentage of shaded area compared to total:
8/5 ÷ 2 = 4/5 = 0.8 =80%Answer: 80% of all region is shaded
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.
Answers
Answer: n> or equals to 3
Step-by-step explanation:
Find explanation on the attachment
1.2.41
Yuson used her calculator to solve the equation x-
- 8 = 3. She entered the following on her screen and got an incorrect answer. How
could she use parentheses to find the correct answer? Explain. What is the correct answer?
Answers
Answer:
[tex]x - (-8) = 3[/tex]
[tex]x = -5[/tex]
Step-by-step explanation:
Equation
[tex]x - -8 = 3[/tex]
Solving (a): Using Parenthesis
The equation can be rewritten by putting -8 in a parenthesis as follows;
[tex]x - (-8) = 3[/tex]
Solving (b): The correct answer
[tex]x - (-8) = 3[/tex]
Start by opening the bracket
[tex]x + 8 = 3[/tex]
Subtract 8 from both sides
[tex]x + 8 - 8 = 3 - 8[/tex]
[tex]x = 3 - 8[/tex]
[tex]x = -5[/tex]
Hence, the correct solution is [tex]x = -5[/tex]
domain and range of a function
Answers
Answer:
The domain of a function is the set of all possible inputs for the function. The range of a function is the set of all possible outputs for the function.
Step-by-step explanation:
The area of a rectangle is 560 cm^2. The length is 3 more than twice the width. Find the dimensions of the rectangle.
Answers
Let the width be x.
Then,length = 2x + 3
Area of rectangle = 560 [ Given ]
⇒ l × b = 560
⇒ ( 2x + 3 ) x = 560
⇒ 2x² + 3x - 560 = 0
⇒ 2x² + 35x - 32x - 560 = 0
⇒ x ( 2x + 35 ) - 16 ( 2x + 35 ) = 0
⇒ ( x - 16 ) = 0 and ( 2x + 35 ) = 0
⇒ x = 16 and x = -35/2 [ Ignore negative number ]
★ Width = x = 16 cm
★ Length = 2x + 3 = 2 × 16 + 3 = 32 + 3 = 35 cm
(-4) + (-5) =
I’m confused
Answers
Austin prepared 20 kilograms of dough after working 5 hours. How many hours did Austin work if he prepared 36 kilograms of dough? Assume the relationship is directly proportional.
Answers
Answer: 9 hours
If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4. Knowing this information, it would only make sense that Austin worked for 9 hours to prepare 36 kg of dough.
This is because 36/4=9.
Please mark brainliest and rate! Thank youu
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Austin prepared 20 kg of dough in 5 hours. Now you see he made 4 kg of dough in a hour, wanna know how? divide 20 to 5 = 4
Now thats done, ill show you the steps of how i got the answer 9.
So we will use that 4 we got from 20 divided by 5 and divide 36 by that 4 and we will get our answer!
--> 20÷5 = 4
36÷4= 9
For each problem, find the missing value using the Pythagorean Theorem
Answers
Answer: [tex]\sqrt{66}[/tex]
Step-by-step explanation:
The Pythagorean Theorem says that a^2 + b^2 = c^2 where a and b are the two legs.
In this care leg 1 is 4 and leg two is the square root of 50. So we will square them to find c which is the hypotenuse.
4^2 + [tex]\sqrt{50} ^2[/tex] = C^2
16 + 50 = c^2
66 = c^2
c =[tex]\sqrt{66}[/tex]
X-21=6 what does x equal??
Answers
Answer:
The answer is 27
Hope this helps
Answer:
x=27
Step-by-step explanation:
What you need to do is isolate the x or in other words have the x be alone on one side of the equal sign. To do this you would need to add 21 to both sides because you need to cancel out -21 with the opposite which would be positve 21. After that the x should be by itself and then finally add 21 to 6 to complete solving for x.