The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.
Equation of the Axis of Symmetry of a Parabola:
The equation for the axis of symmetry of a parabola can be expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.
The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.
Calculating the Axis of Symmetry of a Parabola:
Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.
It is expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Or x = -2 after you substitute in the values for a and b.
Finding the Vertex of a Parabola:
To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.
When we continue with the previous example, we know that x = -2.
We substitute that value for x in the original quadratic function.
[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]
Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.
How To Find Axis of Symmetry?
Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.
[tex]x=\frac{-b}{2a}[/tex]
Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,
[tex]y = ax^{2}+bx+c[/tex].
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Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.
11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15
The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).
What is the simplified form of the expression?It follows from the task content that the simplified form of the given expression is to be determined.
Since the given expression is; -1 ⅔ - 9 ⅖.
First, the mixed numbers as in the task content must be converted to fractions so that we have;
- 1 ⅔ = -5/3 and
9 ⅖ = 47/5
Therefore, the required evaluation is; -5/3 - 47/5
= -25/15 - 141/15
= (-25 - 141) / 15
= -166/15
Therefore, the required simplified form of the expression is; negative 166 over 15.
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Solve for X please help
Answer:
17
Step-by-step explanation:
4x-10=58(alternate interior angles)
4x=68
x=17
Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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What are some ways we have learned to solve percent increase or percent decrease problems? How are these ways related to one another?
The different ways of solving percent increase or percent decrease problems has been described below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.
Another method is by multiplier method
Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then 1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease
For the first method
Suppose the number is n and it is increased by p%
Required result is
[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]
For the second method
Suppose the number is n and it is increased by p%
Here n is taken as 1 and p% is converted to decimal
then 1 and p% in decimal form is added
we get (1 + 0._p)
Now the result is obtained is multiplied by n
Required result is
n(1 + 0._p)
[tex]n(1 + \frac{p}{100})[/tex]
In this way the two methods are related
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find the median of the following: 14.8, 16.2, 4.8, 12.1, and 6.9. if needed, round your answer to the nearest tenth.
The mean will be the middle number or 12.1.
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.According to our question-
The median is the middle number in the data set when the data set is written from least to greatest.
least to greatest 4.8, 6.9, 12.1, 14.8, 16.2
Hence, The mean will be the middle number or 12.1.
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PLEASE HELP ME!!!!!!!!!!!!!!
The equivalents of the functions are f(x)+g(x) = -2x²-x+6, g(x) - f(x) = -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6
How to match the function operation with its equivalent value?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Given: f(x) = 3x + 2, g(x) = -2x²-2x+4 and h(x) = 3x²-4x
To solve this problem, just substitute the value of the function and perform the necessary operations on them.
f(x)+g(x) = (3x+2) + (-2x²-2x+4)
= 3x+2-2x²-2x+4
= -2x²-x+6
g(x) - f(x) = (-2x²-2x+4) - (3x+2)
= -2x²-2x+4-3x-2
= -2x²-5x+2
f(x).g(x) = (3x+2)(-2x²-2x+4)
= -6x³-6x²+12x -4x²-4x+8
= -6x³-10x²+8x+8
h(x) - f(x) = (3x²-4x) - (3x + 2)
= 3x²-4x-3x-2
= 3x²-7x-2
f( x) . h(x) = (3x + 2)(3x²-4x)
= 9x³-12x²+6x²-8x
= 9x³-6x²-8x
f(x)+g(x)+h(x) = (3x + 2) + (-2x²-2x+4) + (3x²-4x)
= 3x+2-2x²-2x+4+3x²-4x
= x²-3x+6
Therefore, the equivalents are f(x)+g(x) = -2x²-x+6, g(x) - f(x) = -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6. You should match them accordingly
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Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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= y = 3x - 4? help me pls
Answer:
Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating
Determine the next three terms in the following sequence:
2, 3, 5, 8, ____, ____, ____,...
a.
13, 19, 26
b.
12, 17, 23
c.
12, 16, 20
d.
13, 17, 23
Answer:
b. 12, 17, 23
Step-by-step explanation:
Look at the differences between the numbers.
Number Difference
2
3 1
5 2
8 3 The difference increase by 1 at each step. The next 3 increase would be:
4
5
6
The next three numbers are:
12 4
17 5
23 6
Answer:
b.
12, 17, 23
Step-by-step explanation:
A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.
The speed of the wind is 50 mile per hour .
In the question ,
it is given that
the speed of the plane is [tex]=[/tex] 200 miles per hour .
let the speed of the wind is = "w"
So ,the speed of the plane with wind is [tex]=[/tex] 200 + w
and the speed of the plane against wind is [tex]=[/tex] 200 - w
we know that , distance [tex]=[/tex] speed × time
the plane flew "500 miles" with wind ,
which means ,
500 [tex]=[/tex] (200 + w) × t .....(1)
and the plane flew 300 miles against the wind ,
which means ,
300 [tex]=[/tex] (200 - w) × t ......(2)
adding both the equations ,
we get
800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)
800 = t × 400
t = 2
Substituting , t = 2 in 500 [tex]=[/tex] (200 + w) × t
we get
500 = (200 + w) × 2
500/2 = 200 + w
250 = 200 + w
w = 250 - 200
w = 50
Therefore , The speed of the wind is 50 mile per hour .
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Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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Can someone help me with this aleks question
For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
As given in the question,
Two triangles ΔTRS and ΔQRP,
It is given that :
Line segment SR ≅ Line segment PR
Line segment SP bisects Line segment TQ
⇒ line segment TR ≅ line segment RQ
∠TRS ≅ ∠PRQ ( by vertically opposite angle )
By Side angle side theorem we have ,
ΔTRS ≅ ΔPRQ
Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.
The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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Add/Subtract Rational Numbers :
Add ; -1/2 + 2/3 (Simplify)
Evaluate ; -1/8 - (-5/6) (Simplify)
Write an equation perpendicular to y =− 3x + 2 and passes through the point (0, 8).
Answer:
y = [tex]\frac{1}{3}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 2 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
the line crosses the y- axis at (0, 8 ) ⇒ c = 8
y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
Can someone help I don’t understand??
Answer:
What you need to do is match with one is a regular, irregular, and or not a polygon.
Each shape has a label like A is a triangle and so on
Put the Label of the shape where it belongs inside the chart
Answer:
If all the sides and interior angles of the polygons are equal, they are known as regular polygons.
C and E are regular polygons.
Irregular polygons are those types of polygons that do not have equal sides and equal angles.
A, B and F are irregular polygons.
3D shapes are irregular polygons.
D is an irregular polygon.
Step-by-step explanation:
the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the fda takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams, with a standard deviation of 6.3. which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams?
From the information, observe that the food and drug Administration is a US government agency that regulates food and drugs for customer safety.
One thing the FDA regulates is the allowable insect parts in various foods.
When wheat is ground into the flour, insects that were in the wheat are ground up as well.
The mean number of insect parts allowed in 100 grams of wheat flour is 75
The FDA takes a random sample of 35 bags of floor for evaluation and finds that their average of 80 insect parts per 100 grams with a standard deviation of 6.3
In this situation use t test for population mean because the population standard deviation is not known.
Hence, the correct option is (2).
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7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?
The number of donuts that can be purchased for $10 is 20.
The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.
Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.
The price is directly proportional to the number of donuts purchased.
p ∝ n
We will remove the proportionality sign.
p = k*n
7.5 = k*15
k = 1/2
The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.
p = (1/2)n
10 = (1/2)n
n = 10*2
n = 20
Hence, the number of donuts that can be purchased for $10 is 20.
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Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13
Answer:
-3.5
Step-by-step explanation:
-4x-1+1≤ 13+1
-4x/-4 ≤ 14/-4
x≤ -3.5
Verify experimentally that the diagonals of a square are equal to each other.
The diagonals of a square are equal to each other
Let ABCD be a square.
We need to prove that the diagonals are equal to each other
AC=BD and AC and BD bisect each other at right angles
(i) Considering the ΔABC and ΔBAD,
AB=AB ( common line)
BC=AD ( opppsite sides of a square)
∠ABC=∠BAD ( = 90° )
ΔABC≅ΔBAD( By SideAngleSide property)
AC=BD ( by CPCT).
(ii) Now in triangles ΔOAD and ΔOCB,
AD=CB ( opposite sides of a square)
∠OAD=∠OCB ( transversal AC )
∠ODA=∠OBC ( transversal BD )
ΔOAD≅ΔOCB (ASA property)
OA=OC ---------(i)
Similarly OB=OD ----------(ii)
From (i) and (ii) we can conclude that AC and BD bisect each other.
Now in a ΔOBA and ΔODA,
OB=OD ( from (ii) )
BA=DA
OA=OA ( common line )
ΔAOB=ΔAOD----(iii) ( by CPCT
∠AOB+∠AOD=180° (linear pair)
2∠AOB=180°
∠AOB=∠AOD=90°
Therefore, it is proved that AC and BD bisect each other at right angles.
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer: $2738.02
Step-by-step explanation:
1) (3000x0.97) = 2910 } Year 1
2) (2910x0.97) = 2822.7 } Year 2
3) (2822.7x0.97) = 2738.019 } Year 3
A pot of soup, currently 74°C above room temperature, is left out to cool. If that temperature
difference decreases by 5% per minute, then what will the difference be in 14 minutes?
If necessary, round your answer to the nearest tenth.
°C
Answer:36.1
Step-by-step explanation:
ixl
L, M and N are points on a circle, centre O.
QMT is the tangent at M
(1) find LNOM
(2) find LNMQ
Please help me guys it urgent it would really make my day.
The size if the angle NOM is 54.
What is angle?
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
What is tangent of circle?
A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.
Given,
M and N are points on a circle.
QMT is the tangent
O is the center.
angle NOM = 2 angle NLM
NOM = 2(27)
= 54.
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Please help
The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?
6 feet
2.7 feet
8 feet
3 feet
The value of their horizontal change is 2.7 feet
How to determine the value of their horizontal change?The equation of the function is given as
y = -8/3x + 40
From the question, the distance travelled by the rider is given as
Distance = 8 feet downward
This means that
Horizontal change = slope
A linear equation is represented as
y = mx + c
Where
Slope = m
By comparing y = mx + c and y = -8/3x + 40, we have
Slope = m = 8/3
This gives
Horizontal change = 8/3
Evaluate
Horizontal change = 2.7
Hence, the horizontal change is 2.7 feet
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PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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students and courses have ....... relationship: a. one to one b. one to many c. many to many d. none. mcq answer
The students and courses have one to many relationship.
A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.
In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.
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How do i solve this equation? 4x - 2y > 12
As per the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
As given in the question,
Given equation in inequality form is :
4x - 2y > 12
Simplify the given equation in intercept form we get,
2y < 4x -12
⇒ y < 2x -6
If we write this inequality in equation form we have,
y = 2x -6
slope of the line is 2
x -intercept is x = 3
y - intercept is y = -6
And in inequality form x > 3 and y < -6.
Therefore, for the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
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Given: AD
Prove: DE
A
D
BC and ZBCD ZADC
CE
C
Intro
B
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
reflexive property
Statements
✓1. AD BC
✓ 2. ZDEA and CEB are
vertical angles
3. ZBCD
ZADC
vertical angles theorem
Reasons
1. given
2. def. of vertical angles
3. given
Triangle ADC and ΔBDC are congruent. then DE ≅ CE
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Given,
AD ≅ BC
∠BCD ≅ ∠ADC
In triangle ADC and ΔBDC
AD ≅ BC ( GIVEN )
∠BCD ≅ ∠ADC ( GIVEN )
DC = DC ( Common line)
so triangle ADC and ΔBDC are congruent.
then DE ≅ CE
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