Equation is y = 2x² + 4x + 1.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given Data
Standard form of quadratic equation
Y = ax² +bx + c
Given points
(3,9), (30,-9). (0,1)
Equating points in formula
9= a(3)² + b(3) + c
9 = 9a + 3b +c
-9 = a(30)² + 3(30) + c
-9 = 900a + 90 + c
1 = a(0)² + b(0) + c
c = 1
Equating c in the equation
9 = 9a + 3b +1
8 = 9a + 3b
-9 = 900a + 90b +1
-10 = 900a + 90b
Multiplying both sides by 100
800 = 900a + 300b
-10 = 900a + 90b
--------------------------
790 = 210b
b = 4 (rounding off)
Putting values of b into equation
8 = 9a + 3(4)
20 = 9a
a = 2 (rounding off)
Equation is y = 2x² + 4x + 1.
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Demuestra las funciones trigonométricas de 45o a partir de un cuadrado con longitud de lado igual a 1.
The most appropriate choice for trigonometric function will be given by -
sin 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = 1
cot 45° = 1
sec 45° = [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\sqrt{2}[/tex]
What are trigonometric functions?
Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.
There are six trigonometric functions-
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]
[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]
[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]
[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
Here,
The diagram of the square has been attached with this answer
∠ABC = 90° [Side of a square is 90°}
∠BAC = [tex]\frac{90}{2}[/tex]
= [tex]45[/tex]°
Side of square = 1 unit
Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side
= [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]
= [tex]\sqrt{2}[/tex] units
From [tex]\Delta[/tex] ABC,
sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
= [tex]\frac{BC}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]
= [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]
= [tex]\frac{BC}{AB}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
= [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
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Express x2-5x + 8 in the form (x-a)² + b
where a and b are top-heavy fractions.
Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
It is given to us that the expression is -
[tex]x^{2} -5x+8[/tex] ----(1)
We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.
In order to achieve the required expression in the form of [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.
The given expression from (1) is -
[tex]x^{2} -5x+8[/tex]
This expression is in the form of [tex]ax^{2} +bx+c[/tex]
Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get
[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)
Equation (2) can also be represented as -
[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]
[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)
We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].
So, we can derive that -
[tex]a=\frac{5}{2}[/tex]
and, [tex]b=\frac{7}{4}[/tex].
Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
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jonh had 5 dish soap and shared 16 how many did he share
Answer:
16
Explanation:
It states the answer in the question. Unless you meant something else?
Hope this helps!
Have a good day :)
Answer: He shared 16.
Step-by-step explanation:
Solve question.
I will give you as many points as possible.
Answer : 3500
Reasoning 2589+2920+3500=9009
Then 9009/3 = 3003
Round 3003 to 3000 and there's your answer
I need help with qeustion 36 please
Answer:
2x + 14
Step-by-step explanation:
8 + 2(x + 3) = 2x + 14
2x + 14 = 2x + 14
0 = 0; True
All real numbers
pic below!! find the surface area of a cube with side lengths of 2 m
Answer:
24
Step-by-step explanation:
the equation is 6s^2, where s=2. This equals 24
Answer:
Step-by-step explanation: area of one square 2x2 right, then you multiply to get 4 then x6 because of the six sides to a cube then you get 24
f+15+7g terms: coefficients:
Based on the given expression; there are three terms;
f157gand one coefficient; 7
Terms and coefficientsA term refers to any value (variable or constant) or expression separated from another term by a space or an appropriate character or symbol, in an overall expression.
Coefficient refers to be a constant by which an algebraic term is multiplied.
f + 15 + 7g
There are three terms in the expression;
f157gFrom the task given above,
The coefficient of 7g is 7
Also the coefficient of f is 1.
Therefore, the terms in the expression are f, 15 and 7g.
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Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
PS
Circle A and Circle B's connection
Circle A's size is more significant than Circle B's size.
As a result, circle A's radius exceeds circle B's radius.
The connection between segments
1.
Let M be the location where Segment QT and ER intersect.
Additionally, tangents from an outside point to a circle have identical lengths.
QM = ME———— (1)
MT=MR————(2)
Including (1) and (2)
MR + ME = QM + MT
Q T=ER
2.
Tangents from an exterior point to a circle have identical lengths.
We may write the following segments are equal using this property.
UP=U Q
ZC=ZR
VC=VS
NR=NS
KC=K T
What are Tangents?
A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:
As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):
Utilizing the differentiation principles, determine the gradient function's derivative.
To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate
Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).
Circle's Tangent
A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.
Geometric Tangent
Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.
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Please answer all 8 questions and show work, thank you.
1. A square classroom has 10 square yards more than 5 times the area of the hallway outside it. The classroom and hallway have a combined area that’s 50 square yards less than 10 times the area of the hallway. Find the length of each side of the classroom.
2. The area of a magenta circle is 100 square meters more than four times the area of a yellow circle. If the magenta circle has an area of 1,500 square meters, what is the radius of the yellow circle?
3. A cubed-shaped box has a volume of 343 cu. ft. What is the surface area of the box?
4. Ace and Charles are salesmen. If Ace had made another $20 in sales, he would have sold three times as much as Charles. Combined, they sold $80 less than 7 times Charles’s sales. How much money did Ace sell?
5. Maria, Dawn, and Hina painted a fence for a total of $480. Since they spent different amounts of time painting, they divided this total in the ratio 3:5:8 (Dawn, Maria, Hina.) How much more did Maria earn than Dawn?
6. 10 years ago, Charlotte was 40 years old, while Mark was 14 years old. When will Charlotte be 8 years more than twice Mark’s age?
7. Rewrite the volume of a cone’s formula to solve for the radius, then solve for the radius when the volume is 300in cubed and the height is 4in.
8. The area of a pink square is 20 square yards more than one-third the area of a purple square. If the pink square has an area of 300 square yards, what is the length of each side of the purple square?
Thank you so much to anyone who helps.
can I get help with this one? Jaylen's equation is y=8.3x, I need help with the missing values only not the writing.
Based on Jaylen's equation and the distance, as well as the time, the missing values are:
Distance Time minutes
2.89 24.0
3 24.9
4.34 36.0
6 49.8
How to find the missing values?The missing values can be found by Jaylen's equation where y is the Time in minutes and x is the distance.
With a time of 24 minutes, the distance is:
24 = 8.3x
x = 24/8.3
= 2.89
With a distance of 3, time would be:
= 8.3x
= 8.3 (3)
= 24.9 minutes
With a time of 36 minutes:
= 36 / 8.3
= 4.34
With a distance of 6, the time is:
= 6 x 8.3
= 49.8 minutes
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Please help, have no clue what I’m doing. Math is not my specialty
Find the three solutions to the equation y = 3x - 5 for the following values of x.
Enter your answers as an ordered pair in the form (x, y).
Enter the solution when = 0.
Enter the solution when a = -1.
Enter the solution when a = 2.
(Picture below)
Answer:
1_y=3(0)-5
y=0-5
y=-5
(0,-5)
2_y=3(-1)-5
y=-3-5
y=-8
(-1,-8)
3_y=3(2)-5
y=6-5
y=1
(2,1)
Step-by-step explanation:
Isaiah measured a house and made a scale drawing. In real life, the hall closet is 5 feet long. It is 10 inches long in the drawing. What is the drawing's scale factor?
Simplify your answer and write it as a fraction.
Answer: The answer is a scale factor of 6
Step-by-step explanation:
5 feet is 60 inches, and on the drawing the closet is 10 inches while the real closet is 5 feet, so just divide 60 by whatever gets you 10.
There are thirty three students in the chess club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the chess club.
There are 14 girls and 19 boys in the chess club.
Step-by-step explanation:Let x be girls and y be boys in the chess club. First, we need to write the system.
We know there are 33 students in total.
x + y = 33
We also know there are five more boys than girls in the club.
x + 5 = y
Here is our system of equations and the solving process:x + y = 33
x + 5 = y
First, we will solve for y with substitution:
x + y = 33
x + (x + 5) = 33
2x = 28
x = 14
Now, we will plug in this x-value:
x + y = 33
(14) + y = 33
y = 19
There are 14 girls and 19 boys in the chess club.
1. What value of x makes this equation true?
X/2-2= X/4+4
A. 4
B. 8
C. 16
D. 24
Please help me anyone :'( it would mean a lot!
The x value of 24 makes the equation to be true
How to determine the value of x in the equation?The equation is given as
x/2 - 2 = x/4 + 4
Add 2 to all sides of the equation
So, we have
x/2 = x/4 + 6
Subtract x/4 from all sides of the equation
So, we have
x/2 - x/4 = 6
Multiply through by 4
So, we have
2x - x = 24
So, we have
x = 24
Hence, the value of x in the equation is 24
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Sebastian used his knowledge of exponents to simplify the following expression. Did he simplify correctly? If not, what mistake did
Sebastian make?
87.8-4.40
87+(-4).40
83.40
8³.0
0
Sebastian has solved the expression wrongly and the correct answer will be 536.
We are given the expression:
(87 × 8) - (4 × 40)
We need to simplify the expression.
For this, we need to follow the rule of PEMDAS.
So, we get that:
696 - 160
= 536
Sebastian has simplified it wrong as he has not followed the rule of PEMDAS and first subtracted 4 from 8.
Therefore, we get that, Sebastian has solved the expression wrongly and the correct answer will be 536.
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Under her cell phone plan, Salma pays a flat cost of $55 per month and $5 per
gigabyte. She wants to keep her bill under $75 per month. Use the drop-down menu
below to write an inequality representing g, the number of gigabytes she can use
while staying within her budget.
Answer: 5
Step-by-step explanation:
9. Michael needs 6 ½ feet of metal flashing to complete a household project. He has two small pieces measuring 3 1/8 feet and 1 ₴ feet. How many feet of metal flashing does Michc need to purchase?
The length of metal flashing needed to be purchase is [tex]1\frac{5}{8}[/tex] feet's.
How to find the length of feet he needs to purchase?He needs 6 ½ feet of metal flashing to complete a household project.
He has two small pieces measuring 3 1/8 feet and 1 3 / 4 feet.
Therefore, the length of metals for him to purchase can be calculated as follows;
The length he has = 3 1 / 8 + 1 3 / 4
The length he has = 25 /8 + 7 / 4
The length he has = 25 + 14/ 8
The length he has = 39 / 8 feet
Therefore
length required to purchase = [tex]6\frac{1}{2} - \frac{39}{8}[/tex]
length required to purchase = [tex]\frac{13}{2}-\frac{39}{8}[/tex]
length required to purchase = [tex]\frac{52-39}{8}[/tex]
length required to purchase = [tex]\frac{13}{8}[/tex] feet
Therefore,
length of metal flashing required to be purchase = [tex]\frac{13}{8}[/tex] feet = [tex]1\frac{5}{8}[/tex] feet
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I don't understand this can you help me?
The missing digits are 0, 4, and 5 in descending order
The complete division operation is
8 2 0 R 5
6 |4, 9 2 5
- 4 8
1 2
- 1 2
0 5
Division operationFrom the question, we are to determine the missing digits in the division operation
From the diagram,
The first two digits of the divided were divided by the divisor, this resulted into a quotient of 8 and a remainder of 1.
The divisor is 6
Let the value of the first two digits be x
Thus,
x / 6 = 8 1/6
x/6 = 49 / 6
By comparison,
The first two digits is 49
Therefore,
The dividend of the division operation is 4,925
Now, we can complete the division operation
8 2 0 R 5
6 |4, 9 2 5
- 4 8
1 2
- 1 2
0 5
Hence, the missing numbers are 0, 4, and 5
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2.5, 10, 17, 26...
a Arithmetic, geometric, or neither?
c. Explicit:
b. Recursive:
if tan x = -4/3 and x is in quadrant 2, then cos2x is
Step-by-step explanation:
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}cos(2x)=
1+tan
2
(x)
1−tan
2
(x)
Since the value of tan(x) is known, substitute the value in the identity,
\begin{gathered}\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\\end{gathered}
cos(2x)=
1+(−
3
4
)
2
1−(−
3
4
)
2
cos(2x)=
1+(
9
16
)
1−(
9
16
)
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
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Convert 180 pounds to kilograms
Answer:
"What is 180 lbs to kg?" is the same as "What is 180 pounds to kilograms?" or "What is 180 pounds to kg?" or "What is 180 lbs to kilograms?" Here we will show you how to convert 180 lbs to kg.
There are 0.45359237 kilograms per pound and there are 2.204622622 pounds per kilogram. Therefore, you can get the answer to "180 lbs to kg?" two different ways. You can either divide 180 by 2.204622622 or multiply 180 by 0.45359237. Therefore, the answer is
Step-by-step explanation:
81.6466
Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.
all of the measurement pairs that could be the dimensions of Rectangle B.
When Rectangle A measures 9 inches by 3 inches and rectangle B is a scaled copy of Rectangle A, the possible dimensions will be:
3 inches by 1 inches6 inches by 2 inchesHow to express the value?From the information, Rectangle A measures 9 inches by 3 inches. Therefore, the ratio will be:
=Length / Width
= 9 / 3
= 3:1
Therefore, a scaled copy will have an equivalent ratio of 3:1.
This can be 3 inches by 1 inches and 6 inches by 2 inches. Their ratio is:
= 6/2 = 3:1.
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suppose 39% of recent college graduates plan on pursuing a graduate degree. twenty one recent college graduates are randomly selected. a. what is the probability that no more than five of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) b. what is the probability that exactly eight of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) c. what is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree?
0.6054 is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.this is binomial with parameter n=21 and p=0.39
a)
probability = P(X<=5)= ∑x=0x (nCx)px(1−p)(n-x) = 0.1124
b)
probability = P(X=8)= (nCx)px(1−p)(n-x) = 0.1763
c)
probability = P(8<=X<=13)= ∑x=x1x2 (nCx)px(1−p)(n-x) = 0.6054
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12. The sales tax rate in a certain state is 6%.
Find the total price paid for a pair of pants
that costs $44.
Answer:
$46.64
Step-by-step explanation:
convert 6% to .06
multiply that by 44
you get 2.64.
add that to 44 to get a final ansewr of 46.64 dollers
solve 11kx+13kx=6 for x
The solution of the equation 11kx+13kx= 6 is x = 1/(4k)
The given equation is 11kx+13kx = 6
To solve this equation first we have to take x as common and rearrange the equation, so we can group the like terms together
x(11k+13k) = 6
Add the like terms in the equation
x(24k) = 6
Move 24k to the right hand side of the equation
x = 6/(24k)
Here we have to simplify the value of x, for that we have to divide 6 by 24k in the equation
x = 1/(4k)
Hence, the solution of the equation 11kx+13kx= 6 is x = 1/(4k)
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please help wth my mathsssssssss
Answer:
A = 1
B = 5
Step-by-step explanation:
I really need this done in the next 10 minutes I will give 25 points please help asap
Answer:
Step-by-step explanation:
The graph starts at 70 and decreases by 5 temp after 15 mins
70
65 o
60 o
55 o
50
45
40
35
30
25
20
15
10
5 i i i
0 5 10 15 20 25 30 35 40 45 50
time
given f(x)=3x-4 find f(4)
Answer:
f(4) = 8
Step-by-step explanation:
Hello!
You can find f(4) by substituting 4 for x in 3x - 4.
Evaluate f(4)f(x) = 3x - 4; x = 4f(4) = 3(4) - 4f(4) = 12 - 4f(4) = 8The value of f(4) is 8.
Answer:
Step-by-step explanation:
h(x)=-2x-3 h(6)
how I answer this using Commutative and Associative Properties of Addition can help you evaluate the expression.
The value of the fraction given as - 1 3/4 - (-8 1/3) - (- 4 1/4) will be 10 5/6.
How to calculate the fraction?It should be noted that a fraction is simply used to represent the numbers that aren't whole.
Based on the information given, the fraction is illustrated as:
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
Note that (-) × (-) = +
Therefore,
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
= - 1 3/4 + 8 1/3 + 4 1/4
The LCM of the denominator is 12
= - 1 9/12 + 8 4/12 + 4 3/12
= 12 7/12 - 1 9/12
= 10 10/12
= 10 5/6
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The weight of meteorite A is 3 times the weight of meteorite B. If the sum of their weights is 92 tons, find the weight of each.
The weights of meteorite A and meteorite B are 69 tons and 23 tons respectively.
It is given in the question that the weight of meteorite A is 3 times the weight of meteorite B.
Also, the sum of their weights is 92 tons.
We have to find the weights of meteorite A and meteorite B.
According to the data given in the question,
Let the weight of meteorite B be x and,
The weight of meteorite A be 3x
Hence, we can write an algebraic equation,
3x + x = 92 tons
4x = 92 tons
x = 92/4 tons
x = 23 tons
Hence, 3x = 3*23 = 69 tons.
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