we have
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
A quadratic equation in standard form is equal to
y=Ax^2+Bx+C
substitute the given values
(1,2)
2=A(1^2)+B(1)+C
2=A+B+C ------> equation 1
(2,-1)
-1=A(2^2)+B(2)+C
-1=4A+2B+C -------> equation 2
(3,-6)
-6=A(3^2)+B(3)+C
-6=9A+3B+C -------> equation 3
step 1
In the equation 1 isolate the variable A
A=2-B-C -------> equation 4
step 2
substitute equation 4 in equation 2 and 3
-1=4(2-B-C)+2B+C
-1=8-4B-4C+2B+C
-1=8-2B-3C
2B+3C=
Calculate the difference between 7.841 and 3.733
You have to subtract each value from rigth to left.
[tex]\begin{gathered} 007.841 \\ -03.733 \\ \text{ 4.107} \end{gathered}[/tex]The result for 7.841 minus 3.733 is 4.107
Simplify the equation 3( m- 5 ) + m
Answer:
4m-15 is the answer
Step-by-step explanation:
Hope this helps!!
Circle O has a center of (-1,5) and passes through the point (2,9) write the equation in center radius form and standard form
Firstly, calculate the radius r of the circle using distance between two points
[tex]\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}[/tex]Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle
[tex]\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}[/tex]The center radius form is
[tex]5^2=(x+1)^2+(y-5)^2[/tex]The standard form is
[tex]\text{ 25}^{}=(x+1)^2+(y-5)^2[/tex]A driver accelerates her car from rest to a velocity of 35.9 mi/hr in 8.2 seconds. What is the acceleration of the car?
The acceleration of the car will be 0.002 m / s².
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The velocity of the car = 35.9 m/hr
The time take by car = 8.2 seconds
Now,
Since, We know that;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.
So, Initial velocity = 0
And, Final velocity = 35.9 m / hr
= (35.9 / 3600) m/s
= 0.01 m / s
So, We get;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
⇒ Acceleration = (0.01 - 0) / 8.2
⇒ Acceleration = 0.01 / 8.2
⇒ Acceleration = 0.002 m / s²
Thus, The acceleration of the car will be 0.002 m / s².
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What did I do wrong? Need help with this equation
Solve the system
[tex]\begin{bmatrix}y=4x-8 \\ y=2\mleft(x-3\mright)^2-2\end{bmatrix}[/tex]Subtract the equations
[tex]\begin{gathered} y-y=4x-8-\mleft(2\mleft(x-3\mright)^2-2\mright) \\ 0=4x-8-2(x-3)^2+2 \\ 0=4x-8-2(x^2-6x+9)+2 \\ 0=4x-8-2x^2+12x-18+2 \\ 0=16x-24-2x^2 \\ 0=-2x^2+16x-24 \end{gathered}[/tex]Solve quadratic equation
[tex]\begin{gathered} 0=-2(x^2-8x+12) \\ 0=-2(x-2)x-6) \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \\ \text{For y} \\ y=4(2)-8=8-8=0 \end{gathered}[/tex]And
[tex]\begin{gathered} x-6=0 \\ x-6+6=0+6 \\ x=6 \\ \text{For y } \\ y=4(6)-8=24-8=16 \end{gathered}[/tex]Answer:
(2,0)
(6,16)
Nicole wants to buy a car for his brother. Nicole calculates the amount of the car as $121.80. The actual price of car is $100. What is the cars percent error?
Percent error of the car with actual value of $100 and expected value of the car is $121.80 is equal to 17.898%.
As given in the question,
Expected amount calculate by Nicole to buy a car = $121.80
Actual price of a car is equal to $100
To calculate a percent error we have,
Percent error = | (Actual value - Expected value ) / Expected value | × 100
= | ( 100 - 121.80 ) / 121.80| × 100
= | -21.80/ 121.80 | × 100
= | -0.17898 | × 100
= 17.898% error
Therefore, percent error of the car with actual value of $100 and expected value of the car is $121.80 is equal to 17.898%.
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what is the 34th term of this seauence 1,9, 17,25,33
Answer : 34th term is 265
Given the following sequence
1, 9, 17, 25, 33
Firstly, we need to find the common difference of the series
Common difference = Larger number - lower number
Common difference = 9 - 1 = 8
17 - 9 = 8
25 - 17 = 8
33 - 25 = 8
Therefore, the common difference = 8
Tn = a + (n - 1 ) d
Where a = first term, n = no of terms, d = common difference
a = 1, n = 34, d = 8
T34 = 1 + (34 - 1) x 8
T34 = 1 + (33) x 8
T34 = 1 + 264
T34 = 265
Therefore, the 34th term is 265
How do you divide x by a fraction, or an example of dividing x by a fraction.
SOLUTION
Now this is how I can divide x by a fraction.
Let's divide x by
[tex]\frac{2}{3}[/tex]So
[tex]x\text{ divided by }\frac{2}{3}[/tex]Now to do this, change division to multiplication. When you do this, the fraction reverses. That is the number up will come down and the number down will go up.
So, this becomes
[tex]\begin{gathered} x\text{ divided by }\frac{2}{3} \\ x\times\frac{3}{2} \end{gathered}[/tex]x on its own means x over 1, that is
[tex]\begin{gathered} x\times\frac{3}{2} \\ \frac{x}{1}\times\frac{3}{2} \\ m\text{ultiplying we have } \\ \frac{3x}{2} \end{gathered}[/tex]So this is how to divide x by a fraction.
Two different squares have an areas of 36m° and 49m°
What is the difference of the lengths of their sides?
The difference of the length of two different squares having area of 36 square meters and 49 square meters is 1 m.
According to the question,
We have the following information:
Two different squares have an area of 36 square meters and 49 square meters.
We know that the following formula is used to find the area of square:
Area = side*side
Side*side = 36
Side = √36
Side = 6 m
Now, side of the another square:
Side*side = 49
Side = √49
Side = 7 m
Now, the difference in the length of the sides of these two squares:
7-6
1 m
Hence, the difference of the length of two different squares having area of 36 square meters and 49 square meters is 1 m.
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The amounts of plastic waste generated in a region during two years were 32,400,000 tons and 20,300,000 tons. What was the total plastic waste generated over these two years in the region, expressed in scientific notation? (5 points)
a
52.7 ⋅ 1014 tons
b
52.7 ⋅ 107 tons
c
5.27 ⋅ 107 tons
d
5.27 ⋅ 1014 tons
The correct option is C that is 5.27x10⁷ tons as represented by scientific notation that says, "A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10".
What is scientific notation?Numbers that are either too large or too small to be conveniently written in decimal form can be expressed using scientific notation. It is also known as standard form in the UK and scientific form, standard index form, and standard form. Using scientific notation, one can express extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. Due to its shorter length, increased efficiency, and straightforward magnitude indication, it is particularly helpful when expressing extremely large or extremely small numbers. Every real number can be expressed as the product of an integer power of ten and a decimal part.
Here,
32,400,000+20,300,000
The sum will be,
52,700,000 tons
In scientific notation,
5.27*10⁷ tons.
According to scientific notation that reads, "A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10," the correct option is C, which is 5.27x10⁷ tons.
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Naomi opened a savings account 7 years ago. the account earns 8% interest compounded monthly if the current balance is 1,000.00 how much did she despoit initially
survey of 100 shoppers, were asked whether they have access to a computer at home. and if they have a personal email account. A) what % of shoppers have an email account?B) what % of shoppers do NOT have computer access at home?
Answer:
A). 34%
B). 62%
Explanation:
Part A:
How many shoppers have an email account?
The answer is 32 + 2 = 34 shoppers have an email account.
What percent of the total shoppers are 34 shoppers?
We know the there are 100 shoppers in total ( 32 + 2 + 6 + 60 = 100); therefore, 34 shoppers is
[tex]\frac{34}{100}\times100\%=34\%[/tex]Hence, 34% of the shoppers have an email account.
Part B:
How many shoppers do not have computer access at home?
The answer is 2 + 60 = 62 shoppers do not have computer access at home.
Now, what percent of the total number of shoppers is 62 shoppers?
The answer is
[tex]\frac{62}{100}\times100\%=62\%[/tex]Meaning, 62% of the shoppers do not have computer access at home.
Hence, to summerise
A). 34%
B). 62%
What are the domain and range of g(x) = −4?
Answer:
look at attached image!
Step-by-step explanation:
Can someone please help me answer this?
Answer:
sol y=5x+15 (see photo for calc)
A group of students was asked, "How many hours did you watch television last week?" Here are their responses. 15,14,20,17,6,11. Find the mean number of hours for these students.
The mean of these numbers is 13.83 hours (14 hours to the nearest whole number)
Here, we want to calculate the mean number of hours
To do this, we simply add all the numbers and divide by the count of the numbers
The count of the numbers is 6
Thus, we have the calculation as follows;
[tex]\frac{(15+14+20+17+6+11)}{6}\text{ = }\frac{83}{6}\text{ = 13.83}[/tex]help me please , for 20 points
Answer:
A
Step-by-step explanation:
First off we can see that there are 46 pencils - and 7 students - so we can divide the two
46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.
If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.
Now that we know that each student gets 6 pencils, we need to find out how many are left.
We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.
Manuel took a total of 20 quizzes over the course of 2 weeks. How many weeks of school will Manuel have to attend this quarter before he will have taken a total of 90 quizzes? Assume the relationship is directly proportional.
Manuel will attend the quarter in 9 weeks.
Given,
In the question:
Total taken quizzes is 90
Manuel took a total of 20 quizzes over the course of 2 weeks.
To find the how many weeks of school will Manuel have to attend this quarter ?
Now, According to the question:
Based on the given conditions :
Formulate:
Let the no. of weeks be x
Total quizzes = 90
Here, The relationship is directly proportional.
20/2 = 90/x
If the fraction is defined, the denominator cannot be equal 0.
Solve the equation:
10 = 90/x
10x = 90
x = 9
Hence, Manuel will attend the quarter in 9 weeks.
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What type of correlation intensity exists between these two variables (weak, moderate, strong)?
Answer:
As a rule of thumb, a correlation greater than 0.75 is considered to be a “strong” correlation between two variables. However, this rule of thumb can vary from field to field. For example, a much lower correlation could be considered strong in a medical field compared to a technology field.
Step-by-step explanation:
What is the least common denominator of 1/7 and 7/8?
Answer:
72/24. Solution: Rewriting input as fractions if necessary: 3/2, 3/8, 5/6, 3/1. For the denominators (2, 8, 6, 1) the least common multiple ( LCM) is 24. LCM (2, 8, 6, 1) Therefore, the least common denominator ( LCD) is 24. Calculations to rewrite the original inputs as equivalent fractions with the LCD: 1 1/2.
Step-by-step explanation:
Question 3 Part B (2.02, 2.04): The table of values represents a linear function
(x), where x is the number of weeks that have passed and g(x) is the balance
n the bank account.
Write the equation of the line in point slope form (1 point):
Write the equation of the line in slope-intercept form (1 point):
Write the equation of the line in standard form (1 point):
X
0
5
10
g(x)
$1,250
$750
$250
The point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
What is equation of line?
The algebraic form of representing set of points is known as the equation of line.
The point slope form is as follows:
[tex]y-y_{1}=m(x-x_{1})[/tex] ... (1)
Here, [tex]y_{1}[/tex] is [tex]y[/tex] co-ordinates, [tex]x_{1}[/tex] is [tex]x[/tex] co-ordinates, and [tex]m[/tex] is the slope.
Also, slope is given by the following expression:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Hence, equation (1) can be written as follows:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex] ... (2)
Consider the following points:
[tex](g(x_{1}),x_{1})=(1250,0)\\(g(x_{2}),x_{2})=(750,5)[/tex]
substitute values in equation (2).
[tex]y-1250=\frac{750-1250}{5-0}(x-0)\\y-1250=-100x[/tex]
On comparing the above equation with equation (1), the value of slope [tex]m=-100[/tex]
Now, calculate the slope intercept form.
The following form is known as the slope intercept form:
[tex]y=mx+c[/tex]
Here, [tex]c[/tex] is the [tex]y[/tex] intercept that the value of [tex]y[/tex] when [tex]x=0[/tex] .
Substitute the value of slope that is -100 and value of g(x) when x =0 that is 1250 for [tex]c[/tex] in the above equation.
[tex]y=-100x+1250[/tex] ... (3)
Standered form of a line is as follows:
[tex]Ax+By=C[/tex]
Here, A,B, and C are integeres.
Rearrange equation (3) as follows:
[tex]y=-100x+1250\\100x+y=1250[/tex]
Hence, the point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
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Answer:
Step-by-step explanation:
the scatter plot below was constructed using data on length and inches (x) of several alligators and weight in pounds (y)right if you sent this describing the relationship between weight and length for these alligators
Answer
We are told that the relationship describing the weight and length, for alligators.
The length in inches is presented on the x-axis and the weight in pounds is presented on the y-axis.
The observations about this include
- From the scatterplot, we can see that the more the length of the alligator (that is, as x increases), the weight of the alligator also increases (that is, y increases too).
- This points to a direct relationship between the length of alligator and the weight of the alligator.
- Small alligators weigh light weights and longer alligators are heavy.
Hope this Helps!!!
The expression -7y is a ____. (20 Points!!) (Please help!)
Term
Constant
Variable
Answer:
constant
Step-by-step explanation:
-7y is a contant
Mr. March sells popcorn at his theater. He uses 3 3/4 cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn.
The equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
Given, Mr. March sells popcorn at his theater.
He uses 3(3/4) cups of unpopped corn to make 15 bags of popped corn. We have to write an equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn.
Now, according to the question
3(3/4) cups = 15 bags
15/4 cups = 15 bags
1 cup = 4 bags
So, in 'c' cups he will make, 4c bags
therefore, 4c = b
Hence, the equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
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Which is the smallest ratio? 2 3 to 4, 3, 10:12, 2 to 1 03 to 4 em O 10:12 2 to 1
Answer:
2/3
Explanation
Given the following:
3 to 4, 2/3, 10:12 and 2 to 1
First let us express them as percentage. The smallest percentage will be the smallest ratio;
3 to 4 = 3/4 * 100
3 to 4 = 75%
2/3 = 2/3 * 100
2/3 = 66.7 %
10:12 = 10/12 * 100
10:12 = 1000/12
10:12 = 83.3%
2 to 1 = 2/1 * 100
2 to 1 = 200%
Since the lowest percent id 66.7%, hence the smallest ratio will be 2/3
PLEASE HELP 3x^2 - 3x - 18
Answer: 3(x-3)(x+2) is the solution
Step-by-step explanation:
Common factor
Use the sum-product pattern
Common factor from the two pairs
Rewrite in factored form
Answer:
x1,2= 3;-2
Step-by-step explanation:
3x^2 - 3x - 18=0
Counting discriminant: (-3)^2-4*3*-18=225
X1,2= 3+-√225/2*3= 3+-15/6=3;-2
X1=3, x2=-2
3. Evaluate:
Suppose you want to buy something for $60, and you have
$15 saved up so far. Then your grandmother calls and says she
will chip in for your purchase. She doesn't tell you the amount
of money she will give you yet, so you just consider it x
dollars. Write the expression that represents the equation.
The expression that represents the equation is x + 15 = 60
The total money needed to buy something is $60
And the saved up amount is $15
The amount of money that the Grandmother contributes is x
The saved up amount and the grandmothers contribution is equal to the total amount required to purchase
We need to write the expression that represents the equation.
x + 15 = 60
Therefore, the expression that represents the equation is x + 15 = 60
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3(2y + 3) + 6(3y – 1) = 1 – 7y
Answer:
y = - [tex]\frac{2}{31}[/tex]
Step-by-step explanation:
3(2y + 3) + 6(3y - 1) = 1 - 7y ← distribute parenthesis and simplify left side
6y + 9 +18y - 6 = 1 - 7y
24y + 3 = 1 - 7y ( add 7y to both sides )
31y + 3 = 1 ( subtract 3 from both sides )
31y = - 2 ( divide both sides by 31 )
y = - [tex]\frac{2}{31}[/tex]
I’m confused because I don’t know how to answer this question
SOLUTION:
We are to find the domain of the given exponential function shown;
The domain of exponential functions is all real numbers.
So the correct option is D
What is 39/75 simplified into its smallest fraction
Answer:13/25
Step-by-step explanation:
I need to find x. if m
Given:-
[tex]\angle BCD=51[/tex]To find the value of x.
Since the corresponding opposite angles are equal and also the sum of angles inside a triangle is 180 degrees. we get,
[tex]\begin{gathered} 14x+4+55+51=180 \\ 14x+110=180 \\ 14x=180-110 \\ 14x=70 \\ x=\frac{70}{14} \\ x=5 \end{gathered}[/tex]So the required value of x is 5.