Take into account that the general function of a parabola in vertex form is given by:
[tex]f(x)=a(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola.
By comparing the previous general function with the given function:
[tex]f(x)=(x-2)^2+2[/tex]you can notice that:
h = 2
k = 2
Hence, you can conclude that the vertex of the given function is (2,2)
X -5x+4 =015.x+6=0A rectangular painting is 3 feet shorter in length than it is tall (height).12. Write a polynomial to represent the area of the painting.13. Write a polynomial to represent the perimeter of the painting.14. The painting has the unique quality of having an area that has a value that is equal to the value of theperimeter. Find the height of the painting.15. What is the extraneous solution to the polynomial created when the area is set equal to the perimeter?
The rectangular painting is 3 feet shorter in length than in height.
Let "x" represent the painting height, then its length can be expressed as "x-3"
12.
The area of the rectangular painting can be calculated by multiplying its length by its height.
[tex]A=l\cdot h[/tex]For the painting
h=x
l=x-3
-Replace the formula with the expressions for both measurements:
[tex]A=(x-3)x[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} A=x\cdot x-3\cdot x \\ A=x^2-3x \end{gathered}[/tex]The polynomial that represents the area of the painting is:
[tex]A=x^2-3x[/tex]13.
The perimeter of a rectangle is calculated by adding all of its sides, or two times its length and two times its height. You can calculate the perimeter of the painting as follows:
[tex]P=2l+2h[/tex]We know that
h=x
l=x-3
Then the perimeter can be expressed as follows:
[tex]P=2(x-3)+2(x)[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} P=2\cdot x-2\cdot3+2x \\ P=2x-6+2x \end{gathered}[/tex]-Order the like terms together and simplify them to reach the polynomial:
[tex]\begin{gathered} P=2x+2x-6 \\ P=4x-6 \end{gathered}[/tex]14.
The painting has the unique quality of having an area that is equal to the value of the perimeter, then we can say that:
[tex]A=P[/tex]-Replace this expression with the polynomials that represent both measures:
[tex]x^2-3x=4x-6[/tex]To solve the expression for x, first, you have to zero the equation, which means that you have to pass all therm to the left side of the equation. Do so by applying the opposite operation to both sides of the equal sign.
[tex]\begin{gathered} x^2-3x-4x=4x-4x-6 \\ x^2-7x=-6 \\ x^2-7x+6=-6+6 \\ x^2-7x+6=0 \end{gathered}[/tex]We have determined the following quadratic equation:
[tex]x^2-7x+6=0[/tex]Using the quadratic formula we can calculate the possible values for x. The formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient that multiplies the quadratic term
b is the coefficient that multiplies the x term
c is the constant of the quadratic equation
For our equation the coefficients have the following values:
a=1
b=-7
c=6
Replace these values in the formula and simplify:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]Next is to calculate the addition and subtraction separately:
-Addition
[tex]\begin{gathered} x=\frac{7+5}{2} \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{7-5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]The possible values of x, i.e., the possible heights of the painting are:
x= 6ft
x=1 ft
15.
To determine the extraneous solution created when the area was set equal to the perimeter you have to calculate the corresponding length for both possible values of the height:
For the height x= 1ft, the corresponding length of the painting would be -2ft. This value, although mathematically correct, is not a possible measurement for the painting's length since these types of measures cannot be negative.
hardest question on brainly stumbles college students!
Applying the vertical angles theorem and other properties, the value of x is 20. The reason for each statement has been explained below.
What are Vertical Angles?A pair of vertical angles are formed when two straight lines intersect each other at a common point. The angles that face each other directly are vertical angles and they are congruent or equal to each other.
Given the diagram below, to find the value of x, the following are the each reason that justifies each of the statements in each step:
Statement Reasons
1. m∠DOB = m∠DOE + m∠BOE 1. Angle Addition Postulate
2. m∠DOB = 90 + x 2. Substitution
3. m∠AOC = m∠DOB 3. Vertical Angels Theorem
4. 110 = 90 + x 4. Substitution
5. x = 20 5. Algebra
To solve using algebra, step 4 is solved as explained below:
110 - 90 = 90 + x - 90
20 = x
x = 20.
Therefore, applying the above steps and reasons that includes the use of vertical angles theorem, the value of x is determined to be: x = 20.
Learn more about vertical angles on:
https://brainly.com/question/14362353
#SPJ1
Triangle A has a 18.3cm side and a 3cm base. Find the hypotenuse.
Given:
The length of the sides is a=18.3 cm,
The base of the triangle is b =3 cm.
Required:
We need to find the hypotenuse.
Explanation:
Use the Pythagorean theorem.
[tex]c^2=a^2+b^2[/tex]Substitute a =18.3 and b=3 in the equation.
[tex]c^2=18.3^2+3^2[/tex][tex]c^2=343.89[/tex]Take square root on both sides.
[tex]\sqrt{c^2}=\sqrt{343.89}[/tex][tex]c=\pm18.5442[/tex]Length is always positive.
[tex]c=18.54[/tex]Final answer:
The hypotenuse is 18.54cm.
consider the line y=2/5x. What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
- 5/2
Step-by-step explanation:
If the slope of a line is m then the slope of the perpendicular line is -1/m
The slope of y = 2/5 x is 2/5
Slope of perpendicular line = - 5/2
What is the value of the trig ratio sin A?
The sine relation is given by the length of the opposite leg to the angle over the length of the hypotenuse.
So, for the given triangle, we have:
[tex]\begin{gathered} \sin A=\frac{BC}{AC}\\ \\ \sin A=\frac{20}{29} \end{gathered}[/tex]Therefore the value of sin A is 20/29.
Curt and melanie are mixing blue and yellow paint to make seafoam green paint. Use the percent equation to find how much yellowp they should use.
To solve the exercise you can use the rule of three, like this
[tex]\begin{gathered} 1.5\text{ quarts}\rightarrow100\text{ \% }\Rightarrow\text{ Green paint} \\ x\text{ quarts}\rightarrow30\text{ \%}\Rightarrow\text{ Yellow paint} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{30\text{ \% }\ast\text{ 1.5 quarts}}{100\text{ \%}} \\ x=0.45\text{ quarts} \end{gathered}[/tex]Therefore, Curt and Melanie should use 0.45 quarts of yellow paint to make seafoam green paint.
7/11% of a quantity is equal to what fraction of a quantity
7/11% can be written as:
[tex]\begin{gathered} \frac{\frac{7}{11}}{100}=\frac{7}{11}\times\frac{1}{100} \\ \frac{\frac{7}{11}}{100}=\frac{7}{1100} \end{gathered}[/tex]So 7/11% of a quantity is equal to 7/1100 fraction of a quantity
Answer:41/10,000
7/17% = 0.41% = 0.0041
41/10,000
Step-by-step explanation:
the bakers want to sell their house for 145,500.After 2 months,the bakers decided to mark down the price of their house 8% to sell more quickly. How much are the bakers selling their house for now?
Answer:
133,860
Step-by-step explanation:
The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".
* No we have our key elements:
- Starting amount = 145,500
- Rate of change = 8%
* We will get the "8%" of the number 145,500
- Firstly, "8%" means 8/100
- So, 0.08 will be our new rate of change.
* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.
- 145,500 × 0.08 = 133,860 ; the same as
145,500 × 8/100 = 133,860
A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
To solve more questions on straight line, visit the link below-
https://brainly.com/question/27730503
#SPJ1
What is an
equation of the line that passes through the points (5, 7) and (-5, -1)?
Answer:
y - 7 = 0.8(x - 5) ory = 0.8x + 3Step-by-step explanation:
Given2 points (5, 7) and (- 5, - 1)To findEquation of the line passing through the given pointsSolutionFind the slope of the line using slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\dfrac{-1-7}{-5-5}=\dfrac{-8}{-10}=0.8[/tex]Use one of the points and the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex][tex]y-7=0.8(x-5)[/tex]This can be converted to slope-intercept form:
[tex]y = mx + b[/tex][tex]y -7=0.8(x-5)[/tex][tex]y -7=0.8x-0.8*5[/tex][tex]y -7=0.8x-4[/tex][tex]y =0.8x-4+7[/tex][tex]y=0.8x+3[/tex]Which angles are adjacent to each other? Select all that apply.
Answer:
I think it's all the options but I cant confirm.
Step-by-step explanation:
adjacent angles are angles that:
- have the same vertex
- share one side
Explain how you found the diagonal length of the package.
First find diagonal of base D =√( 10^2 + 10^2)= √200
Then find diagonal lenght L = √ (D^2 + 10^2) = √ (200 + 100) =√300
L= √300 = √3•√100 = √3• 10
L= √3•10 = 10•√3 (by conmutative property)
what is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
Complete the equation, and tell which property you used.7. (3 X 10) X 8 = X (10 X 8)8. 16 + 31 = 31 +9. 0 +__= 9110. 21 x__= 9 X 21Problem Solving(RealWorld11. The Metro Theater has 20 rows of seats with 18seats in each row. Tickets cost $5. The theater'sincome in dollars if all seats are sold is (20 X 18)X 5. Use properties to find the total income.12. The numbers of students in the foursixth-grade classes at Northside School are 26,19, 34, and 21. Use properties to find the totalnumber of students in the four classes.
7. (3 X 10) X 8 = 3 X (10 X 8)
In this case, we use the associative property of the multiplication (you can group the factors in any way).
8. 16 + 31 = 31 + 16
Commutative property.
9. 0 + 91 = 91
Identity property
10. 21 x 9 = 9 X 21
Commutative property
11. The income is (20 * 18) * 5.
We can multiply the three numbers together, using the associative property.
20 * 18 * 5 = 1800
12. In this case, we have to add each of the groups:
26 + 19 + 34 + 21 = 100
We don't need to apply any properrty in particular. We can add them in any order taking into account the commutative property.
I would like some help on how to solve this problem!(please and thank you)
Answer
GH is congruent to JH and FH is congruent to HI. ∠GHF should be congruent to ∠JHI by Vertical Angles Theorem. Since GH is congruent to JH, ∠GHF is congruent ∠JHI, and FH is congruent is congruent to HI, ΔGHF is congruent ΔJHI, by SAS. Then one can assume that FG is congruent to IJ by CPCTC.
Use a proportion to solve the problem. 34% of 83x/100=34/83;40.96x/100=34/83;2.822x/83=34/100;28.22x/83=34/100;56.44
34% in decimal is equal to 0.34, which in fraction is equivalent to 34/100.
Therefore we can solve this as
x/83 = 34/100; 28.22.
the quotient of 7 and p
To get the quotient we divide.
[tex] = 7 \div p \\ = \frac{7}{p} [/tex]
A manufacturing company currently uses 15 workers to load and unload trucks. Each worker can move an average of 15 boxes per minute. A robotics firm has built a robot that can load and unload boxes at the rate of 21 boxes per minute. How many robots will it take to do the same job as the 15 humans?
It will take 11 robots to do the same job as the 15 humans
Explanation:Given:
Workers in use = 15
Each worker can move an average of 15 boxes per minute.
A robot has been built that can move an average of 21 boxes per minute
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
What is the x-intercept of the line y=-2x+6? (3,0) -6,0) (0,3) (-3,3)
The given equation is expressed as
y = - 2x + 6
The x intercept of a line is the point at which y = 0
By applying this concept, it means that
0 = - 2x + 6
Adding 2x to both sides of the equation, it becomes
0 + 2x = - 2x + 2x + 6
2x = 6
Dividing both sides by 2, it becomes
2x/2 = 6/2
x = 3
Therefore, the correct option is (3, 0)
what is the value of x of the perimeter of the following figure is 30 miles?
The Solution:
Given:
We are required to find the value of x if the perimeter is 30 miles.
[tex]Perimeter=2(3x-8)+2(6x+5)=6x-16+12x+10=30[/tex][tex]\begin{gathered} 6x+12x-6=30 \\ \\ 18x=30+6 \\ \\ 18x=36 \end{gathered}[/tex]Divide both sides by 18.
[tex]\begin{gathered} x=\frac{36}{18}=2 \\ \\ x=2 \end{gathered}[/tex]Therefore, the correct answer is 2.
4+4x=2x+8+2x-5 help please
Simplify the expression.
[tex]\begin{gathered} 4+4x=2x+8+2x-5 \\ 4x-2x-2x=8-5-4 \\ 0=-1 \end{gathered}[/tex]Thus, the equation is solved.
Bao is mixing flour and water to make dough the graph shows how much water he uses for different amounts of flour .How many liters of water does Bao use per liter or flour?------ liters for this one your answer should be a simplified proper fraction like 3/5.How many liters of flour does Bao use per liter of water?------ liters.
To know how many liters of water Bao use per liter of flour we have to divide the liters or flour so:
[tex]\frac{1}{3}=0.33[/tex]So Bao uses 0.33 or 1/3 of water per liter or flour
and to know hoy manu liters of flour Bao use per liter of water we have to made the oposite division so:
[tex]\frac{3}{1}=3[/tex]She use 3 liters of flour per liter of water
Household Income
Under $50,000
$50,000 under $75,000
$75,000 under $150,000
$150,000 or above
Percentage
27.2
27.3
37.2
8.3
Event
ABCD
Suppose that a household with home Internet access only is selected at random. Apply the
special addition rule to find the probability that the household obtained has an income
a. under $75,000.
b. $50,000 or above.
c. between $50,000 and (under) $150,000
d. Interpret each of your answers in parts (a) - (c) in terms of percentages
e. Use the complement rule to answer part (b) in this exercise.
The probability for household with income under $75,000 is 54.5/100. the probability for household with income $50,000 or above is 72.8 /100, and the probability for household with income between $50,000 and (under) $150,000 is 64.5/100.
What is probability?
Probability describes potential. This area of mathematics examines how random events happen. The value might be between 0 and 1. Mathematicians have used probability to forecast the likelihood of certain events. In general, probability relates to how likely something is to happen. You can better understand the potential results of a random experiment by using this fundamental theory of probability, which also holds true for the probability distribution. To calculate the likelihood that an event will occur, we first need to know how many possible possibilities there are.
As given in the question,
Household with Income $50,000 are 27.2%
$50,000 - $75,000 are 27.3%
$75,000 - $150,000 are 37.2%
$150,000 or above are 8.3%
a) we have to find the probability for household with income under $75,000
So, Households having income under $75,000 are equal to:
(27.3 + 27.2)% = 54.5%
Therefore, probability = 54.5/100
b) we have to find the probability for household with income $50,000 or above,
So, household with income $50,000 or above are equal to:
(27.3 + 37.2 + 8.3)% = 72.8%
Therefore, probability = 72.8 /100
c) we have to find probability for household with income between $50,000 and (under) $150,000.
so, household with income between $50,000 and (under) $150,000 are equal to:
(27.3 + 37.2)% = 64.5%
Therefore, probability = 64.5/100
d) answer a can be interpret in percentage as 54.5%
answer b can be interpret in percentage as 72.8%
answer c can be interpret in percentage as 64.5%
To know more about probability, go to link
https://brainly.com/question/13604758
#SPJ13
For the equation 5x+36=x, Which value could be a solution
Solution;
[tex]\begin{gathered} 5x+36=x \\ 5x-x+36=x-x \\ 4x+36=0 \\ \end{gathered}[/tex][tex]\begin{gathered} 4x+36-36=0-36 \\ 4x=-36 \end{gathered}[/tex][tex]x=-\frac{36}{4}=-9[/tex]x=-9
when taking a 19 question multiple choice test ,where each question has 3 possible answers ,it would be unusual to get or more questions correct by guessing alone consider "unusual " to be more than two standard deviations away from expected.
we have that
You have 1 in 3 probability of guessing the correct answer for a single question
you have 19 opportunities to guess
so
19*(1/3)=19/3=18/3+1/3=6 1/3
therefore
would be unusual to get 7 or more questions correct by guessing alone
le Figure Score: 7/100 1/13 answered Question 2 < > A pennant is in the shape of an isosceles triangle. inches, the height is 15 inches, and the length of th the area of the pennant? inches squared
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]in this case b=9.5 and h=15. Plugging the values in the formula we have:
[tex]\begin{gathered} A=\frac{1}{2}\cdot9.5\cdot15 \\ =71.25 \end{gathered}[/tex]Therefore the area is 71.25 square
Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
Find the missing side of this righttriangle.x816x= V[?]=Enter the number that belongs in the green box.Enter
As gien by the question
There are given that the right angle triangle.
Now,
To find the value of x, use Pythagoras theorem:
So,
From the Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=16^2 \\ x^2+64=256 \\ x^2=256-64 \\ x=\sqrt[]{192} \end{gathered}[/tex]Hence, the value of x is shown below:
[tex]x=\sqrt[]{192}[/tex]Exact value of tan 2pi/3
Given:
[tex]\tan\frac{2\pi}{3}[/tex]Find-:
Exact value
Explanation -
So, the value is:
[tex]=\tan\frac{2\pi}{3}[/tex][tex]\begin{gathered} =\tan\frac{2\pi}{3} \\ \\ \pi=180\text{ then,} \\ \\ =\tan(\frac{2\times180}{3}) \\ \\ =\tan(120) \end{gathered}[/tex]So value is:
[tex]\tan(120)=-\sqrt{3}[/tex]Labron James made 255/310 baskets. What percent of the baskets did he make?
82.26%
Explanations:The ratio of baskets made by Lebron James = 255/310
To find the percentage equivalent of the ratio, multiply it by 100%
Percentage of the baskets made by Lebron James = 255/310 x 100%
Percentage of the baskets made by Lebron James = 82.26%