Answer:
[tex]y= x^{2} -12x+32[/tex]
Explanation:
[tex]y=x^{2} -8x-4x+32\\y= x^{2} -12x+32[/tex]
Ryan works for a delivery service. The function f(n) is used to calculate
his daily pay, in dollars, on a day when he makes deliveries.
f(n)=6n+85
Use the function to fill in the blanks the table shown. Make sure you
have an answer for Blank A, Blank B, and Blank C
Answer:
0=85
4=109
10=145
the answers are Blank A=85,Blank B=109 and Blank C= 10
Robyn wants to place a television set 8ft from her lounge chair. Can the other two distances shown be 5ft and 9ft? Identify the answer with the correct explanation.
Answer:
Yes, the sum of any two lengths is greater than the third length
Step-by-step explanation:
Yes, the sum of any two lengths is greater than the third length. Then the correct option is B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Any two parts of a triangle can be added together to have a length larger than the third side.
Robyn needs to put a TV 8ft from her parlor seat.
Applying the Triangle Inequality Theorem
1) 9 + 5 > 8 which is ok
2) 8 + 5 > 9 which is ok
3) 8 + 9 > 5 which is ok
Yes, the sum of any two lengths is greater than the third length. Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
The complete question is attached below.
A rectangular painting has a diagonal measure of 17 inches and an area of 120 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.
Answer:
Length = 8 inches
Width = 15 inches
Step-by-step explanation:
A rectangular painting has a diagonal measure of 17 inches and an area of 120 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.
Let:
a = length of painting
b = width of painting
Area of painting = 120 = ab
Pythagorean Theorem says
a² + b² = Diagonal²
a² + b²= 17²
[120 =ab means b= 120/a]
a² + (120/a)² = 17²
Multiply through by a²
a⁴ + 14400 = 289
z² + 14400 = 289z [for now, substitute z for a²]
z² - 289z + 14400 = 0
z² - 64z - 225z + 14400 = 0
z(z - 64) -225(z - 64) = 0
(z - 64)(z - 225) = 0
z - 64 = 0
z = 64
z - 225 = 0
z = 225
Note that:
z for a²
Hence:
a² = 64
a = √64
a = 8 inches
The same applies for b
b² = 225
b = √225
b = 15 inches
(03.01 LC)
The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle? (1 point)
Question 1 options:
1) The square root of 5
2) The square root of 7
3) 5
4) 7
Question 2 (1 point)
Saved
(03.01 LC)
What is the length of the hypotenuse of a right triangle if each of the two legs is 7 units? (1 point)
Question 2 options:
1) Square root of 14
2) 7
3) The square root of 98
4) 49
Answer:
√7 units, √98 units
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2. So 9+b^2=16. So b^2=7. So b=√7
a^2+b^2=c^2. SO 49+49=c^2. So 98=c^2. So c=√98.
Answer:
√7 units, √98 units
Step-by-step explanation:
r minus the sum of 4 and p equals
Answer:
r - (4 + p)
Step-by-step explanation:
{that's how you write it if that's what you are asking}
Can anybody help plzz?? 65 points
Answer:
[tex]\frac{dy}{dx} =\frac{-8}{x^2} +2[/tex]
[tex]\frac{d^2y}{dx^2} =\frac{16}{x^3}[/tex]
Stationary Points: See below.
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesCalculus
Derivative Notation dy/dx
Derivative of a Constant equals 0.
Stationary Points are where the derivative is equal to 0.
1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undefBasic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]f(x)=\frac{8}{x} +2x[/tex]
Step 2: Find 1st Derivative (dy/dx)
Quotient Rule [Basic Power]: [tex]f'(x)=\frac{0(x)-1(8)}{x^2} +2x[/tex]Simplify: [tex]f'(x)=\frac{-8}{x^2} +2x[/tex]Basic Power Rule: [tex]f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}[/tex]Simplify: [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Step 3: 1st Derivative Test
Set 1st Derivative equal to 0: [tex]0=\frac{-8}{x^2} +2[/tex]Subtract 2 on both sides: [tex]-2=\frac{-8}{x^2}[/tex]Multiply x² on both sides: [tex]-2x^2=-8[/tex]Divide -2 on both sides: [tex]x^2=4[/tex]Square root both sides: [tex]x= \pm 2[/tex]Our Critical Points (stationary points for rel max/min) are -2 and 2.
Step 4: Find 2nd Derivative (d²y/dx²)
Define: [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Quotient Rule [Basic Power]: [tex]f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2[/tex]Simplify: [tex]f''(x)=\frac{16}{x^3} +2[/tex]Basic Power Rule: [tex]f''(x)=\frac{16}{x^3}[/tex]Step 5: 2nd Derivative Test
Set 2nd Derivative equal to 0: [tex]0=\frac{16}{x^3}[/tex]Solve for x: [tex]x = 0[/tex]Our Possible Point of Inflection (stationary points for concavity) is 0.
Step 6: Find coordinates
Plug in the C.N and P.P.I into f(x) to find coordinate points.
x = -2
Substitute: [tex]f(-2)=\frac{8}{-2} +2(-2)[/tex]Divide/Multiply: [tex]f(-2)=-4-4[/tex]Subtract: [tex]f(-2)=-8[/tex]x = 2
Substitute: [tex]f(2)=\frac{8}{2} +2(2)[/tex]Divide/Multiply: [tex]f(2)=4 +4[/tex]Add: [tex]f(2)=8[/tex]x = 0
Substitute: [tex]f(0)=\frac{8}{0} +2(0)[/tex]Evaluate: [tex]f(0)=\text{unde} \text{fined}[/tex]Step 7: Identify Behavior
See Attachment.
Point (-2, -8) is a relative max because f'(x) changes signs from + to -.
Point (2, 8) is a relative min because f'(x) changes signs from - to +.
When x = 0, there is a concavity change because f"(x) changes signs from - to +.
$20 s= X s= $21
Solve the compound inequality. Round each answer to the hundredths place.
Answer: x =420 s = 21
Step-by-step explanation:
Simultaneous equations
y=x+2
y=x^2
Answer:
(- 1, 1 ) and (2, 4 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = x² → (2)
Substitute y = x² into (1)
x² = x + 2 ( subtract x + 2 from both sides )
x² - x - 2 = 0 ← in standard form
(x - 2)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )
x = - 1 → y = - 1 + 2 = 1 ⇒ (- 1, 1 )
Find the mean, median, mode and range in each problem.
1)
Nine conical flasks have sodium chloride solution of different quantities. The
amount of solution (ml) in each flask is given below.
2, 10, 16, 2, 20, 18, 22, 14,9
Mean:
Median
Mode :
Range:
Answer:
mean - 12.5
median - 14
mode - 2
range - 20
Step-by-step explanation:
mean = total of the numbers divided by how many numbers there are.
median = average is the middle number in a set of data , when the data has been written in ascending size order. If there is an even number of items of data, there will be two numbers in the middle.
mode = the value that appears most frequently in a data set.
range = the difference between the highest and lowest values in a set of numbers.
What is the ratio of blue paint to red paint in the mixture?
Answer: I think the answer is 5:2 Hope This Helps
It's 5:3
Hoped I helped!
Have a wonderful day-
Bye!
Wesley subscribes to a telecommunication company’s movie package.The plan includes a basic monthly charge of $40 and an additional charge of $1.50 for every movie ordered. 2a) Write an equation for the total charge for a month, C, in terms of the number of movies, m, Wesley orders per month. This is a required question 2b) If Wesley ordered 4 movies one month, what was his total charge for the month?
Answer:
46
Step-by-step explanation:
So, the plan
monthly =40 + 1.50x
and he orders 4 movies in a month your problem to solve now looks like this
1 month = 40+1.50x4
Then, 1 month= 40 + 6
1 month= 46
pls help me with question 8
9514 1404 393
Answer:
weight = 5, 6.5, 7.2, 9, 16
cost = $2.50, $3.25, $3.60, $4.50, $8.00
Step-by-step explanation:
The first column tells you the cost is ...
$2.50/(5 lb) = 0.50 $/lb
That is, each bottom number is half the top number, or each top number is double the bottom number.
The table is ...
weight = 5, 6.5, 7.2, 9, 16
cost = $2.50, $3.25, $3.60, $4.50, $8.00
6. Triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form
Triangle
ABC: Which transformation can be used to map each point (.y) on Triangle ABC
to its corresponding point on Triangle A B C?
A
G.y) - (y + 3, x)
B
6. y) - (x+3)
(x, y) - (y+3.x)
D. (.y)-( y. x+3)
C
Given:
Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.
To find:
The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.
Solution:
If a figure rotated 90 degrees counterclockwise, then
[tex](x,y)\to (-y,x)[/tex]
[tex]P(x,y)\to P_1(-y,x)[/tex]
If a figure translated 3 units up, then
[tex](x,y)\to (x,y+3)[/tex]
[tex]P_1(-y,x)\to P'(-y,x+3)[/tex]
If triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is
[tex](x,y)\to (-y,x+3)[/tex]
Therefore, the required rule of transformation is [tex](x,y)\to (-y,x+3)[/tex].
Note: Option are not in proper form.
All the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
Case 1: If the point is in first quadrant:Subcase: Clockwise rotation:
Then (x,y) → (x, -y)
Subcase: Counterclockwise rotation:
Then (x,y) → (-x, y)
Case 2: If the point is in second quadrant:Subcase: Clockwise rotation:
Then (x,y) → (-x, y)
Subcase: Counterclockwise rotation:
Then (x,y) → (x, -y)
Case 3: If the point is in third quadrant:Subcase: Clockwise rotation:
Then (x,y) → (x, -y)
Subcase: Counterclockwise rotation:
Then (x,y) → (-x, y)
Case 4: If the point is in fourth quadrant:Subcase: Clockwise rotation:
Then (x,y) → (-x, y)
Subcase: Counterclockwise rotation:
Then (x,y) → (x, -y)
Case 5: For points on axesYou can take that point in any of the two surrounding quadrants. Example, if the point is on positive x axis, then it can taken as of first quadrant or fourth quadrant.
Case 6: On originNo effect as we assumed rotation is being with respect to origin.
Since no quadrant is specified, we assume triangle is fully in first quadrant. That means all points (x,y) will turn (-x,y) after counter clockwise rotation.
Now translation of 3 units up means all y coordinates will be increased by 3, thus, all (x,y) points of triangle first become (-x,y) then (-x, y+3).
Thus, all the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.
Learn more about rotation and translation here:
https://brainly.com/question/2418278
I have no idea :( Please help
Answer:
59; 44 & 68; 22.5; 44Step-by-step explanation:
10.
x + 57 = 116x = 116 - 57 x = 5911.
y = 180 - 112 = 68x= 180 - 2*68 = 4412.
4x + 10 = 180 - 2*404x + 10 = 1004x = 90x = 90/4x = 22.513.
SG = HT/2SG = 88/2 = 44Evaluate the expression for 1/2(2x+8)+6x and explain your process
Answer:
7x+4
Step-by-step explanation:
1/2(2x+8)
=x+4
x+4+6x
=7x+4
PLS GIVE BRAINLIEST
Answer:
7x+4
Step-by-step explanation:
1/2(2x+8)+6x
divide by 2 or multiply 1/2 it equals the same anyway
x+4+6x
add like terms
7x+4
THIS IS TIMED!
Thanks:)
The area, A, of a square is equivalent to the square of its side lengths. A = (6)(6) square units A = s2 square units A = (x)(x) square units A = (x+x) square units A = 2(6) square units
Answer:
(6)(6) square units
(x+x) square units
Step-by-step explanation:
Answer:
A=s^2 and A=(x)(x)
Step-by-step explanation:
Need help now! fist gets brainlest
Answer:
x=88
Step-by-step explanation:
180-48-44=88
88+48+44=180
Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
With more than 33 species, more species of bats live in Texas than anywhere else in the United States. If Texas contains fewer than 3% of the species of bats in the world, how many species of bats are there worldwide?
ckgcujcfyfxgxhfccvcchf
5/6+4(3/4g-6) in standard form
Answer:
3g- 139/6
Step-by-step explanation:
The sum of two numbers is 37. Their difference is 7. What are the numbers?
Answer:
22 and 15
Step-by-step explanation:
22+15=37
22-15=7
e. Find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) Ć(1, -3).
Answer:
Length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21
Step-by-step explanation:
We need to find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) C(1, -3).
We have three sides of triangle AB, BC and AC
The length of side can be calculated using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now finding lengths of sides AB, BC and AC
i) Length of side AB
We have A (7,4), B (-8, 6)
and [tex]x_1=7, y_1=4, x_2=-8, y_2=6[/tex]
Putting values in formula and finding length
[tex]Length \ of \ side \ AB \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AB \ =\sqrt{(-8-7)^2+(6-4)^2}\\Length \ of \ side \ AB \ =\sqrt{(-15)^2+(2)^2}\\Length \ of \ side \ AB \ =\sqrt{225+4}\\Length \ of \ side \ AB \ =\sqrt{229}\\Length \ of \ side \ AB \ =15.13[/tex]
So, Length of side AB is 15.13
ii) Length of side BC
We have B (-8, 6) and C(1, -3)
and [tex]x_1=-8, y_1=6, x_2=1, y_2=-3[/tex]
Putting values in formula and finding length
[tex]Length \ of \ side \ BC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ BC \ =\sqrt{(1-(-8))^2+(-3-6)^2}\\Length \ of \ side \ BC \ =\sqrt{(1+8)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{(9)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{81+81}\\Length \ of \ side \ BC \ =\sqrt{162}\\Length \ of \ side \ BC \ =12.72[/tex]
So, Length of side BC is 12.72
iii) Length of side AC
We have A (7,4)and C(1, -3)
and [tex]x_1=7, y_1=4, x_2=1, y_2=-3[/tex]
Putting values in formula and finding length
[tex]Length \ of \ side \ AC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AC \ =\sqrt{(1-7)^2+(-3-4)^2}\\Length \ of \ side \ AC \ =\sqrt{(-6)^2+(-7)^2}\\Length \ of \ side \ AC \ =\sqrt{36+49}\\Length \ of \ side \ AC \ =\sqrt{85}\\Length \ of \ side \ AC \ =9.21[/tex]
So, Length of side AC is 9.21
So, length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21
1. How many feet long is the space Mr. Hamilton wants to fill with pictures? Explain how you know.
Write your answer in the space below.
Answer:
✔️Length of the space Mr. Hamilton wants to fill with pictures = 4 ft long
✔️8 pictures can be fit on this wall by Mr. Hamilton
Step-by-step explanation:
The wall = 9.75 ft long
Window = 5¾ ft long = 5.75 ft
Each President's picture = 6 in. wide = 0.5 ft wide (note: 1 ft = 12 in.)
✍️Length of the space Mr. Hamilton wants to fill with pictures = 9.75 ft - 5.75 ft = 4 ft
✍️ Numbers of pictures that can fit on this wall = the space Mr. Hamilton wants to fill ÷ the width of each picture
= 4 ft ÷ 0.5 ft
= 8.
8 pictures will can be fit on the wall.
Should I do light pink nails or light blue nails???
Hurry I Need an answer
Answer:
blue!!
Step-by-step explanation:
<3
The cost of a pencil box is $2.50. The function f(x) = 2.5x gives the cost of x pencil boxes. Identify the domain, range, and graph of this function.
Answer: hey want to talk
Step-by-step explanation:
Find the slope of the line containing the pair of points.
(-10,6) and (-11,7)
Answer:
Step-by-step explanation:
(-10,6)(-11,7)
Slope is -1
Jason bought a new truck at $25,000. The truck depreciates 15% of its value continuously each year. How much is it worth after 5 years? Round the answer to nearest dollar.
Answer:
A = $11093
Step-by-step explanation:
Given the following data;
Principal = $25,000
Rate = 15% = 15/100 = 0.15
Time, t = 5
To find the future value, we would use the compound interest formula;
[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.Substituting into the equation, we have;
r = -0.15 because it's depreciating.
[tex] A = 25000(1 + \frac{-0.15}{1})^{1*5}[/tex]
[tex] A = 25000(1 - 0.15)^{5}[/tex]
[tex] A = 25000(0.85)^{5}[/tex]
[tex] A = 25000*0.4437[/tex]
A = 11092.63 ≈ $11093
Therefore, the future value, A after 5 years is $11093.
Answer:
11809
Step-by-step explanation:
pls help plz plz plz plz plz plz plz plz plz
Answer:
eat sleepless duduehei
ASAP GIVING BRAINIEST AND 20 points 1. How can technology be both positive and negative when it comes to modified crops?
2. Why do you think it is important to find ways to improve crops?
Answer:
Technology can be both negative and positive when it comes to modified crops. It can be positive because it allows us to have more crops and resist pests and disease. It can be negative because it may cause deformities or health risks.
I really hope that helps you.