Use the intercepts of the following quadratic curve to find its graph.y = -1/2x^2 -3/2x+2
Answers
The correct graph is fourth option
Explanation:\(\begin{gathered} \text{The quadratic function:} \\ \text{y = }\frac{-1}{2}x^2\text{ - }\frac{3}{2}x\text{ + 2} \end{gathered}\)Using the intercepts: we have x-intercept and y-intercept
To get x intercept, we will equate the function to zero. That is y = 0
\(\begin{gathered} 0\text{ = }\frac{-1}{2}x^2\text{ - }\frac{3}{2}x\text{ + 2} \\ mu\text{ltiply through by 2:} \\ 0=-x^2\text{ - 3x + 4} \\ x^2\text{ + 3x - 4 = 0} \\ x^2\text{ - x + 4x - 4 = 0} \\ x(x\text{- 1) +4(x - 1) = 0} \\ (x\text{ + 4)(x - 1) = 0} \\ x+4\text{ = 0 or x - 1 = 0} \\ x\text{ = -4 or x = 1} \end{gathered}\)x intercepts are x = -4 and x = 1
This means the line will cross the x axis at two points: x = -4 and x = 1
To get y-intercept, we will equate x to zero:
\(\begin{gathered} \text{y = }\frac{-1}{2}(0)^2\text{ - }\frac{3}{2}(0)\text{ + 2} \\ y\text{ = 0 - 0 + 2} \\ y\text{ = 2} \end{gathered}\)y-intercept = 2
This means the line will cross the y axis at y = 2
The correct graph is fourth option
Related Questions
Find the surface area of the composite figure.
20 in.
11 in.
5 in.
I
I
19 in
12 in.
12 in.
SA
=
11 in.
5 in.
20 in.
[?] in.2
Answers
The surface area of the composite figure is 2005 in².
To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.
Let's break down the figure into its different parts and calculate the surface area step by step:
Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:
Surface Area of Rectangular Prism = 2lw + 2lh + 2wh
Plugging in the values, we have:
Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²
Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:
Surface Area of Rectangular Prism = 2lw + 2lh + 2wh
Plugging in the values, we have:
Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²
Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:
Surface Area of Rectangle = lw
Plugging in the values, we have:
Surface Area of Rectangle = (11)(5) = 55 in²
Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:
Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle
Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²
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The ordered pair (__, - 5) is a solution of the equation x = 3.
Answers
Answer:
(3, -5)
explanation:
the equation only shows x
the ordered pair is made up of (x,y)
make mathematical expression and simplify. The sum of 4 and 5 is subtracted form one-third of the difference of 40 and 4.
Answers
Answer:
X= -3
Step-by-step explanation:
(4+5)-1/3(40-4)=X
X=9- 1/3(36)
X=9-12
Un viajero ha recorrido la tercera parte de su trayecto y sabe que si cubre 65 km más completa la mitad del recorrido. Determine la distancia recorrida.
Answers
The travelled distance of the traveller is equal to 195 kilometers.
How to find the travelled distance by a traveller
According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:
x = d / 3
x + 65 = d / 2
Where:
d - Travelled distance, in kilometers.x - Initial travelled distance, in kilometers.Now we proceed to determine the travelled distance:
d / 3 + 65 = d / 2
d / 2 - d / 3 = 65
3 · d - d = 390
2 · d = 390
d = 195
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how would someone use the cross product property on an equation with 3 different values instead of two? I provided an example image
Answers
Using the cross product for the proff of Pythagoras theorem, the correct step is
By the cross product property, AB² = BC multiplied by BD
What is cross product propertyThe cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).
For the similar triangles, the ratio is as follows
BD / BA = BA / BC
BA² = BD * BC
and AB = BA, hence
BA² = BD * BC
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HELP!
Find x. Round to the nearest tenth.
64
8
Answers
Answer:
x= 3.5 (nearest tenth)
Step-by-step explanation:
Please see the attached picture for the full solution.
Please help!!!!
\((\pi \sqrt 81 \frac{\sqrt[3]{8}}{2} ) / 3\pi = ???\)
Answers
Step-by-step explanation:
\((9\pi \frac{2}{2} )\div 3\pi \\ \)
\( \frac{9\pi}{3\pi} \\ \)
\(3\pi\)
3π is the answer
Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over
Answers
If a = 2 and b = 4, then 27 - b^2 ÷ a + (11 - 5) is equal to _____.
Answers
Answer:25
Step-by-step explanation:
27-4^2/2+(11-5)= 25
Answer:
25
Step-by-step explanation:
Please take a look at the picture then write an explanation to go with the answer.
Thank you :)
Answers
Answer:
5/8 inch
Step-by-step explanation:
Subtract
1 - 3/8 = 5/8 inch
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Help me answer this please
Answers
The area of the sector in terms of π is 35.6π inches squared.
The area of the sector is approximately 111.6 inches square
How to find the area of a sector?The area of sector of a circle is the amount of space enclosed within the boundary of the sector.
Therefore,
area of a sector = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
∅ = 200 degrees
r = 8 inches
area of the sector = 200 / 360 × 8²π
area of the sector = 200 / 360 × 64π
area of the sector =12800π/ 360
area of a sector = 35.6π inches squared
Let's find the area of the sector with π = 3.14
area of a sector = 35.6 × 3.14 = 111.6 inches square
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simplify: -10+3r+2r²-r
Answers
Answer:
2r^2+2r-10
Step-by-step explanation:
collect the like terms
the like terms are
3r and r
-10+2r+2r^2
reorder the terms
2r^2 +2r-10
What is the answer to 8-5+10 divided by 5*6 + 2
Answers
8-5+10 divided by 5*6 + 2 = 17
Answer:
17
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
8 - 5 + 10 ÷ 5 × 6 + 2
Step 2: Evaluate
Division: 8 - 5 + 2 × 6 + 2Multiplication: 8 - 5 + 12 + 2Subtraction: 3 + 12 + 2Addition: 15 + 2Add: 17Solve the formula A = one-halfbh for h
Answers
Answer:
\(\frac{2A}{b} = h\)
Step-by-step explanation:
We start with the equation \(A = \frac{1}{2} bh\). First, we multiply both sides by \(2\).
\(2A = bh\)
Next, we divide both sides by \(b\) to get our answer:
\(\frac{2A}{b} = h\)
A hybrid car can go 141 miles on 3 gallons how much miles can it go on 4 gallons
Answers
141 divided by 3 is 47 so 47 times 4 is 188
find the exact value of x. 45 degree and 10 side
Answers
Answer:
The exact value of the other leg is 10.
Step-by-step explanation:
Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.
Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:
c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.
Substituting known values, we get:
(10√2)^2 = 10^2 + b^2
200 = 100 + b^2
b^2 = 100
b = 10
Therefore, the exact value of the other leg is 10.
Plz help
f(x)=2x+1 Find f(3)
Answers
Step-by-step explanation:
f(3)=2(3)+1
6+1
7
answer is 7
Answer:
f(3)=15
Step-by-step explanation:
just put 3 instead of x
HELP PLZ I WILL GIVE WHAT EVER
Answers
Answer: 112
Explanation: I find the area of the base but if there is a specfic formula on doing this what is it? But if not that should be your answer.
Answer:
75.62
Step-by-step explanation:
An airplane is flying at a constant speed of 500 mph at a bearing of 45° north of west. A 40 mph wind is blowing due south. What are the plane's actual speed and direction? Draw a diagram and show your work to justify your answer. Round the speed to the nearest tenth and the direction to the nearest degree. (5 points)
Answers
Answer:I’m pretty sure I got this one right too
Step-by-step explanation:
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
What are the x and y-components of a vector?"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."
We can assume, east as the positive x- axis and north as the positive y-axis, respectively.
Similarly, west as the negative x- and south as the negative y-axis, respectively.
Therefore, the x- and y-components of the speeds.
Now, for the airplane:
x-component: - 500 × cos(45°) mph = - 353.55 mph
y-component: 500 × sin(45°) mph = 353.55 mph
For the wind:
y-component: -40 mph
Therefore, sum of the x-components = -353.55 mph
Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph
Now, the actual speed =
\(\sqrt{(-353.55)^{2} + (313.55)^{2}}\) mph
= \(\sqrt{223313.6}\) mph
= 472.56 mph
Now, the direction of the airplane is:
tan(Ф) = \(\frac{313.55}{- 353.55}\)
⇒ Ф = tan⁻¹( \(\frac{313.55}{- 353.55}\))
⇒ Ф = - 41.57°
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
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Which expression corresponds to this graph?
Answers
Answer:
C
Step-by-step explanation:
The expression is x>55 and 55 isn't included
Answer:
c
Step-by-step explanation:
I need help. q – 12 = 1
Answers
Answer:
q=13
Step-by-step explanation:
Given q - 12 = 1
we need to find q
to do so we need to isolate the variable using inverse operations
so to get rid of the 12 we add 12 but whatever we do to one side we do to the other
so we add 12 to each side
-12+12 cancels our
1+12=13
we're left with
q=13
Help!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The answer to the given questions are b = 54, c = 24, m = 75, y = 33, p =87.
What happens to a number or a variable when it is being moved from one side of the equation to the other side ?It changes it's sign.
We have to form equation for the given questions with a variable and find the value of the variable.
In the first question
There were 45 apples in the barn her dad picked some more apples and put them into it and now the total no. of apples in the barn is 99.
Assuming here dad picked b no. of apples the the equation will be of the form
45 + b = 99
b = 99 - 45
b = 54.
∴ Her dad put 54 apples in the barn.
In the second question
Gran sold 13 clothes in the sell and after that she had 11 clothes left and c is the total no. of clothes
∴ c = 13 + 11
c = 24
So Gran knitted 24 clothes for her school fundraiser.
In the third question
leah's friend gave her 12 dollars for her birthday and after her grandparents gave her some money (m) she had a total of
87 dollars.
∴ 12 + m = 87
m = 87 - 12
m = 75
So her grandparents gave her 75 dollars of money.
In the fourth question
Lorenzo had 96 passing yards before the football game and after that he had 129 yards for the season and y be the no. of passing yards during the football game.
∴ 96 + y = 129
y = 129 - 96
y = 33.
So he made 33 passing yards during the game.
In the fifth question
An artist took 105 art pieces and after he sold some of them which is p he is left with 18 pieces
∴ 105 - p = 18
p = 105 - 18
p = 87
So he sold 87 pieces of art in the fair.
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The diagonal of a square is 60 in, as shown
in the diagram. What is the length of a side
to the nearest tenth of an inch?
Answers
Answer:
The length of side is 42.4 inches.
Step-by-step explanation:
Given that:
Diagonal of square = 60 inches
As all sides of a square are equal, thus
Side of square = x
The diagonal will be the hypotenuse of a right angled triangle.
Using Pythagorean theorem;
\(x^2+x^2=(60)^2\\2x^2=3600\\x^2=\frac{3600}{2}\\x^2=1800\)
Taking square root on both sides
\(\sqrt{x^2}=\sqrt{1800}\\x=42.4\)
Hence,
The length of side is 42.4 inches.
Which statement correctly describes the function on a given interval?
A. The function is decreasing and nonlinear between x= -7 and x= -3
B. The function is increasing and nonlinear between x= -3 and x= -1
C. The function is decreasing and linear between x= -1 and x= 1
D. The function is increasing and linear between x= 1 and x= 3
Answers
Answer:B !!!
Step-by-step explanation:
Option D is correct, the function is increasing and linear between x= 1 and x= 3.
What is a function?A relation is a function if it has only One y-value for each x-value.
By observing the graph we say that the function is increasing and linear between x= 1 and x= 3
For a function y = f(x), if the value of y increases on increasing the value of x, then the function is an increasing function.
Linear functions are those whose graph is a straight line
Hence, option D is correct, the function is increasing and linear between x= 1 and x= 3.
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I need help with this please
Answers
The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.
What is a line plot?In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:
Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)
Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)
Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8
Total sugar consumed = 22/8 + 1/4
Total sugar consumed = (22 + 2)/8
Total sugar consumed = 24/8
Total sugar consumed = 3 units of sugar.
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Find the line's slope and a point on the line.
y-3=3(x+4)
Answers
Answer:
y=3x−9
Step-by-step explanation:
Median of 3,6,9,7,4,6,7,0,7
Answers
The median, mean, range and mode will be 6, 5.4, 9 and 7.
What is median?
The median is the middle number in the data set when the data set is written from least to greatest.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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Can someone please help me with This question? I don’t understand it. Please and thank you I would really appreciate it!! :)
Answers
(A∩B)∪(A∩C) using roster method is as follows:
(A∩B)∪(A∩C) = {a, e, f}
What are sets?Sets are an organized collection of objects that can be represented in set-builder form or roster form.
Therefore,
The universal sets is as follows:
U = {a, b, c, d, e, f, g, h}
The subsets are as follows:
A = {c, e, f}
B = {a, e, f}
C = {a, b, d, g, h}
Therefore, let's find (A∩B)∪(A∩C) using roster method.
The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
Hence,
(A∩B) = {e, f}
(A∩C) = {a}
Finally,
(A∩B)∪(A∩C) = {a, e, f}
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Calculate the slope over the interval 1≤ x<3.
Answers
The slope over the interval 1 ≤ x < 3 is m = 3 / 2 .
Given :
the slope over the interval 1 ≤ x < 3
From the graph :
take two points which lies on the interval
( 1 , 0 ) and ( 3 , 3 )
slope :
Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line .
slope m = y2 - y1 / x2 - x1
= 3 - 0 / 3 - 1
= 3 / 3 - 1
= 3 / 2
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The line models the cost of renting a kayak. Write an equation in slope-intercept form for the line, where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
Answers
In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.
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