The equation of the parabola is y = 1/5( x + 2 )² + 8.
When x = 18 the value of y is 88 and the average rate of change between x = - 2 and x = 18 is 4.
The general equation of the parabola is given as:
y = a(x – h)² + k where ( h, k ) is the vertex of the parabola.
We have, the vertex as ( - 2, 8 ) and the parabola passes through ( 8, 28 ).
Then,
y = a(x – h)² + k
28 = a( 8 - (-2) )² + 8
28 = a(10)² + 8
28 - 8 = a(10)²
100a = 20
a = 20/100 = 1/5
Therefore, the equation of the parabola will be:
y = a(x – h)² + k
y = 1/5( x + 2 )² + 8
Now, when x = 18:
y = 1/5( x + 2 )² + 8
y = 1/5( 18 + 2 )² + 8
y = 1/5( 20 )² + 8
y = 80 + 8 = 88
Now, the change between x = - 2 and x = 18:
Then,
y = f(18) = y = 1/5( 18 + 2 )² + 8 = 1/5(20)² + 8 = 88
And;
y = f( - 2) = 1/5( -2 + 2 )² + 8 = 1/5(0)² + 8 = 8
Therefore the average rate of change between x = - 2 and x = 18 will be:
= [ f(18) - f(-2) / ( 18 - (-2) ) ]
= ( 88 - 8 ) / 20
= 80/20
= 4
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Zach can buy a dozen pencils for $1.89, 24 pencils for $3.60, or 36 pencils for $5.49. What is the best buy?
To know which one is the best option we have to divide the cost in the number of pencils so:
[tex]\frac{1.89}{12}=0.16[/tex]the second option is:
[tex]\frac{3.60}{24}=0.15[/tex]the thert option is:
[tex]\frac{5.49}{36}=1.16[/tex]So the best option is the second option
what is the answer to a negative 4 divided by a positive 6?
The expression given as negative 4 divided by a positive 6 has a value of -2/3
How to evaluate the expression?From the question, the expression is given as
negative 4 divided by a positive 6
Rewrite the expression properly
This is rewritten as follows
-4 divided by +6
This can be represented as
-4/6
There are no like terms in the above expression
So, we have the following equation
-4/6 = -4/6
Divide 4 and 6 by a common factor
The common factor is 2
So, we have
-4/6 = -2/3
The expression cannot be further simplified
So, we have the following equation
-4/6 = -2/3
Hence, the value of the expression is -2/3
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The expression given as "negative 4 divided by a positive 6" has a value of that is -2/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
From the problem, the expression is given as;
"negative 4 divided by a positive 6"
Rewrite the expression properly then;
-4 divided by +6
This can be express as;
-4/6
There are no like terms in the expression
So, we have the equation;
-4/6 = -4/6
Divide 4 and 6 by a common factor;
The common factor is 2
-4/6 = -2/3
So, we have the equation;
-4/6 = -2/3
Hence, the value of the expression will be; -2/3
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find the solution to the following system by substitution x + y = 20 y = 3x 8
Based on the substitution method, the solution of the system of the equation is x = 3 and y = 17.
Substitution method:
Substitution method is the way of finding the value of any one of the variables from one equation in terms of the other variable.
Given,
Here we have the system of equations
x + y = 20
y = 3x + 8
Now we need to find the solutions for these equation using the substitution method.
From the given details we know that the value of y is defined as 3x + 8.
So, we have to apply these value on the other equation in order to find the value of x,
x + (3x + 8) = 20
4x + 8 = 20
4x = 20 - 8
4x = 12
x = 3
Now apply the value of x into the other equation in order to find the value of y,
y = 3(3) + 8
y = 9 + 8
y = 17
Therefore, the solution of the equation is x = 3 and y = 17.
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Please help me I need this done fast I will give brainliest to whoever answers first
Consider that a standard quadratic equation is given by,
[tex]y=ax^2+bx+c[/tex]The curve passes through the point (-5,0),
[tex]\begin{gathered} 0=a(-5)^2+(-5)b+c \\ 0=25a-5b+c \\ c=-25a+5b\ldots\ldots\ldots(1) \end{gathered}[/tex]The curve passes through the point (3,0),
[tex]\begin{gathered} 0=a(3)^2+(3)b+c \\ 0=9a+3b+c \end{gathered}[/tex]Substitute value from equation (1),
[tex]\begin{gathered} 0=9a+3b+(-25a+5b) \\ 0=-16a+8b \\ b=2a\ldots\ldots\ldots(2) \end{gathered}[/tex]The curve passes through the point (4,9),
[tex]\begin{gathered} 9=a(4)^2+(4)b+c \\ 9=16a+4b+c \end{gathered}[/tex]Substitute tha values from (1) and (2),
[tex]\begin{gathered} 9=16a+4(2a)+(-25a+5(2a)) \\ 9=16a+8a-25a+10a \\ 9=9a \\ a=1 \end{gathered}[/tex]Substitute in equation (2),
[tex]\begin{gathered} b=2(1) \\ b=2 \end{gathered}[/tex]Substitute the values in equation (1),
[tex]\begin{gathered} c=-25(1)+5(2) \\ c=-25+10 \\ c=-15 \end{gathered}[/tex]Substitute the values of a, b, and c, in the standard equation,
[tex]\begin{gathered} y=(1)x^2+(2)x+(-15) \\ y=x^2+2x-15 \end{gathered}[/tex]This is the equation of the given parabola.
Therefore, option B is the correct choice.
help meeeeeeeeeeeeeeeeeeeeeee
how do I know where which choices below go into the correct blanks for number 1-4?
For 1, we have the following triangle:
Using the cosine function to get the hypotenuse we get:
[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:
[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]Therefore, the value of the remaining side is 7.
-10 is no less than 2 times a number plus 14
Let the number be x.
Then according to the question,
[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]Thus, the number should be greater than or equal to -12.
Find LM if LN = 137mm.
4. (A.20) Natasha and her friends go out for ice cream. They decide to create their own ice cream, which costs $1.60 plus 8 cents per topping. If x represents the number of toppings on the ice cream, then which'equation describes y, the total cost for the ice cream?A. y = 0.08 + 1.60)x B. y = .08 + 1.60x C. y = 1.60 +.08x D. y = 8x + 1.60
Answer:
C. y = 1.60 +.08x
Explanation:
The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x
So, the total cost for the ice cream is represented by the equation:
y = 1.60 +.08x
This not a test btw ! But can you please help me with this !
Using elimination:
[tex]\begin{gathered} (A)-3(B)\colon \\ 6x+12x-3y+3y=-4-15 \\ 18x=-19 \end{gathered}[/tex]Therefore, the answer is:
B) Multiply A by 1 and B by -3
ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points
To find:
We need to find two points on the linear equation y-1=0 and to plot those points on graph.
Step by step solution:
We know that:
General coordinate of any two points on line y = 1:
= (x, 1)
So let us assume any two random points on the line:
= (1,1) and (2,1)
We will now mark them on the graph:
Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
the rational number :
-1 ³/₄ is located as point 1
14/8 is located as point 5
1.125 is located as point 6
-0.875 is located as point 4
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here,
the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.
the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.
the rational number 1.125 is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th of the gap between 1 and 2.
the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.
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Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.45. See the figure below.
If the monthly cost for 22 HCF is $45.78, what is the monthly cost for 19 HCF?
Using a linear function, it is found that the monthly cost for 19 HCF is of $41.43.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the parameters of the function are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the value of y when the function crosses the y-axis(x = 0).As stated in the problem, the slope is of 1.45, hence:
y = 1.45x + b.
The monthly cost for 22 HCF is $45.78, hence when x = 22, y = 45.78, meaning that the intercept b can be found as follows:
45.78 = 1.45(22) + b
b = 45.78 - 1.45 x 22
b = 13.88.
Then the function is:
y = 1.45x + 13.88.
And the cost for 19 HCF is given by:
y = 1.45(19) + 13.88 = $41.43.
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Which angles are adjacent to <2? Select all that apply.
What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3
The initial expression is:
[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:
[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]So is option C)
I need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.
we have that
Let
x ------> the distance in miles from a point on the ground (the red line)
In the right triangle of the figure
sin(6.5)=7,000/x
solve for x
x=7,000/sin(6.5)
using a calculator
x=61,835.70 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
61,835.7 ft=61,835.7/5,280=11.71 miles
therefore
the answer is 11.71 miles15% of $764.69rounded to the nearest cent.
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
Given the exponential decay function below:Determine the intervals of increase and decrease.
Given the equation of exponential decay function:
[tex]y=(\frac{1}{3})^x-3[/tex]The given function always decreases overall the domain
so, the answer will be the intervals of decrease is:
[tex](-\infty,\infty)[/tex]Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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Complete the remander of the
table for the given function rule:
y = 3x-8
X= -4,-2,0,2,4
Y=-20,?,?,?
Step-by-step explanation:
what is the problem ?
all you need to do is put every different value of x into the spot of x and calculate the result.
x = -4
y = 3×-4 - 8 = -12 - 8 = -20
x = -2
y = 3×-2 - 8 = -6 - 8 = -14
x = 0
y = 3×0 - 8 = 0 - 8 = -8
x = 2
y = 3×2 - 8 = 6 - 8 = -2
x = 4
y = 3×4 - 8 = 12 - 8 = 4
Sort the sequences according to whether they are arithmetic, geometric, or neither. (98.3, 94.1, 89.9, 85.7,) (1, 0, -1, 0) (1.75, 3.5, 7, 14) (-12, -10.8, -9.6, -8.4) (-1, 1, -1, 1)
hello
to know what type of sequence they are, we need to test either for common difference of common ratio
first sequence
(98.3, 94.1, 89.9)
first term = 98.3
in this case there's a common difference here
we can find that by subtracting the second term from the first term or the third term from the second term
[tex]\text{common difference (d) = 94.1-98.3=-4.2}[/tex]first sequence is an arithmetic progression
second sequence
(1, 0, -1, 0)
first term = 1
common difference or common ratio does not exist here
third sequence
(1.75, 3.5, 7, 14)
first term = 1.75
in this case, there's no common difference but rather common ratio
common ratio (r) can be found by dividing the second term by the first term or the third term by the second term
[tex]\begin{gathered} \text{common ratio(r) = }\frac{3.5}{1.75}=2 \\ \frac{14}{7}=2 \end{gathered}[/tex]the common ratio here is 2 and this is a geometric progression
fourth sequence
(-12, -10.8, -9.8, -8.4)
first term = -12
in this sequence, there's no common difference or common ratio
fifth sequence
(-1, 1, -1, 1)
the fifth sequence is neither a geometric or artimethic progression because there no common difference or ratio
turn 5 7/10 into a decimal and a percent
It is a mixed number:
[tex]5\frac{7}{10}[/tex]THe whole part, 5, is going to stay 5.
Now, let's work with the fractional part.
7/10 into a decimal would require for division.
7 divided by 10 is 0.7
Thus,
IN Decimal, it will be "5.7"
To find percentage from decimal, we multiply by 100 and tag along a % sign.
So,
[tex]5.7\cdot100=570[/tex]The number, in percentage, is 570%
I dont know how to complete this please help.
A' ∩ C U B in roster form is {3, 7, 8, 9}
What is A' ∩ C U B?To write a set in a roster form, the elements in the set are written in a row within curly brackets.
The following are set symbols and their meaning:
• U = union = it means all the elements in two or more sets.
• ∩ = intersection = it means elements that are common to two or more sets.
• ' = complement = it means elements that are not in the set but in the universal set.
A' = {3, 6, 7, 8, 9}
C U B = {2, 3, 4, 5, 7, 8, 9}
A' ∩ C U B = {3, 7, 8, 9}
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How long will it take for an investment of 2900 dollars to grow to 6800 dollars, if the nominal rate of interest is 4.2 percent compounded quarterly? FV = PV(1 + r/n)^ntAnswer = ____years. (Be sure to give 4 decimal places of accuracy.)
ANSWER :
The answer is 20.3971 years
EXPLANATION :
The compounding interest formula is :
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]where :
FV = future value ($6800)
PV = present value ($2900)
r = rate of interest (4.2% or 0.042)
n = number of compounding in a year (4 : compounded quarterly)
t = time in years
Using the formula above :
[tex]6800=2900(1+\frac{0.042}{4})^{4t}[/tex]Solve for t :
[tex]\begin{gathered} \frac{6800}{2900}=(1.0105)^{4t} \\ \text{ take ln of both sides :} \\ \ln(\frac{6800}{2900})=\ln(1.0105)^{4t} \\ \operatorname{\ln}(\frac{6800}{2900})=4t\operatorname{\ln}(1.0105) \\ 4t=\frac{\ln(\frac{6800}{2900})}{\ln(1.0105)} \\ t=\frac{\ln(\frac{6800}{2900})}{4\ln(1.0105)} \\ t=20.3971 \end{gathered}[/tex]What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2
Let's make y the subject of the equation.
[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The correct option is A
There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
Drag the measurements to the containers to show equal length
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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which ordered pair is a solution of 6X + 7 < 21
Substitute 2 for x and 1 for in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]\begin{gathered} 6\cdot2+7\cdot1<21 \\ 12+7<21 \\ 19<21 \end{gathered}[/tex]The inequality is trus so point (2,1) satisfy the inequality.
Substitute 4 for x and 1 for y in the inequality to verify that ordered pair satisfy the inequality or not.
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