The fence is 33 feet long when measured in yards.
Here,
In order to erect a fence around a rectangular flower garden on his property, Craig has 72 feet of material.
If the fence must be 3 feet in width, then, assuming he uses the entire 72 feet of material, we must determine the fence's length in yards.
What is the rectangle's perimeter?
The rectangle's perimeter is 2 (l + b). l being the length. b=breadth (width).
Now,
A rectangular flower bed should be x feet long.
(Length + Width)2 = the perimeter of a rectangular flowerbed.
72 = 2 (x + 3)
36 = x + 3
x = 33 feet
Hence, The fence is 33 feet long when measured in yards.
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PLEASE HELP WILL MARK WHAT IS 25-29
I’m not really sure what to do
The table below gives the annual sales (in millions) of a product. year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 222 276 318 348 366 372 366 348 318 What was the average rate of change of annual sales a) Between 2003 and 2004 millions of dollars/year b) Between 2003 and 2006 millions of dollars/year
Using it's concept, the average rate of change is given as follows for the intervals:
a) -6 millions of dollars per year.
b) -18 millions of dollars per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
In 2003, the amount is of 372 million sales.In 2004, the amount is of 366 million sales.Hence:
r = (366 - 372)/1 = -6 millions of dollars per year.
For item b, we have that:
In 2003, the amount is of 372 million sales.In 2006, the amount is of 318 million sales.Hence:
r = (318 - 372)/3 = -18 millions of dollars per year.
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For Brianna's lemonade recipe, 2 lemons are required to make 4 cups of lemonade. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Using a proportional relationship, it is found that:
1 lemon is required for 2 cups.6 cups are required for 3 lemons.The graph for this relationship is given at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, we have that the variables are:
x: number of lemons.y: number of cups.Hence the proportional relationship between these two variables is given by:
y = 2x.
Then:
1 lemon is required for 2 cups. (y = 2, then x = 1).6 cups are required for 3 lemons. (x = 3, then y = 6).The linear graph of the relationship, considering the given points, is given at the end of the answer.
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A car travels 560 miles In 8 hours(driving at a constant speed) how long did it take the car to go 200 miles
Answer:
see below
Step-by-step explanation:
RATE is 560 mi / 8hr = 70 mi/hr
Rate * time = distance
then
time = distance / Rate = 200 mi / 70 mi/hr = 2.857 hr ( or 2 hr 51 min)
An empty shipping box weighs 250 grams. The box is then filled with t-shirts. Each t-shirt weighs 132.5 grams.
The equation W=250+132.5t represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and is the number of shirts in the box.
If the company ships 100 t-shirts in a box, how much will the box weigh?
________ grams
========================================================
Explanation:
t = number of t-shirts
t = 100 shirts are in the box
Plug this into the equation and simplify to find W
W = 250+132.5t
W = 250+132.5(100)
W = 250+13250
W = 13500
The box weighs 13500 grams
This is equivalent to 13500/1000 = 13.5 kg
THERE ARE 2 DECKS OF PLAYING CARDS
Answer:
100 cards?
Step-by-step explanation:
Gabriella's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 14 senior citizen tickets and 14 child tickets for a total of $252. The school took in
$154 on the second day by selling 9 senior citizen tickets and 7 child tiekets. Find the price of a
senior citizen ticket and the price of a child ticket.
The ticket price of
A Senior citizen = $14
A Child = $4
First day of ticket sales :
Senior citizen tickets (s) = 14
Child tickets (c) = 14
Total price of both tickets = $252
14s + 14c = 252 eq. (1)
Second day of ticket sales :
Senior citizen tickets (s) = 9
Child tickets (c) = 7
Total price of both tickets = $154
9s + 7c = 154 eq. (2)
Multiplying equation 2 with 2, we get
18s + 14c = 308 eq. (3)
Now, we will subtract eq. (1) from eq. (3)
18s + 14c = 308 eq. (3)
-14s - 14c = -252 eq. (1)
____________________
4s = 56
s = 56/4
s = 14
We get the ticket price of one senior citizen which is 14 Dollars.
Now, we will put s = 14 in eq. 2,
So, 9s + 7c = 154
(9×14) + 7c = 154
7c = 154 - 126
c = 28 / 7
c = 4
Ticket price of one child is 4 Dollars.
Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.
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Help jwhsiwoeodjdjdjiejf
Help my cousin
Answer:
I. 1) 32124, 32456, 32532, 32934, 32983
2) 62279, 62312, 62345, 62387, 62398
3) 89123, 90246, 89345, 89534, 89923
4) 19087, 19216, 19312, 19432, 19910
5) 31821, 31839, 31861, 31876, 31890
II. 1) 58240, 58204, 58042, 58024
2) 10908, 10809, 10098, 10089
3) 85703, 85370, 85307, 85073
4) 98705, 98570, 98507, 98057
5) 41810, 41108, 41081, 41018
Step-by-step explanation:
20pts. Please help ASAP!
Answer:
given
Step-by-step explanation:
When doing a two-column proof, you usually begin with what you are given.
Please help me find ABCD!!
For the function f(x) = -(x + 1)² + 4, identify the vertex, domain, and range.
Answer:
Vertex: (-1, 4)
Domain: All Real Numbers
Range: y < or equal to 4
Step-by-step explanation:
Vertex: Using my calculator, i determined the vertex. The vertex is the most bottom/top point of the parabola, depending on if it opens down or up.
Domain: All the answers have all real numbers so its obvious.
Range: the parabola opens down at (-1, 4), so all the numbers on the y axis below 4 fit in with the line
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 2 and 3+ i
The polynomial function of least degree with only real coefficients is y = x³ - 8 · x² + 22 · x - 20.
What is the polynomial function of least degree with real coefficients?
The statement indicates that the polynomial has a leading coefficient of 1 and zeros of 2 and 3 + i. By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then, all the roots of the polynomial function of least degree are 2, 3 + i and 3 - i. The complete expression is shown below:
y = 1 · (x - 2) · (x - 3 - i) · (x - 3 + i)
y = (x - 2) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]
y = (x - 2) · (x² - 6 · x + 9 - i²)
y = (x - 2) · (x² - 6 · x + 10)
y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20
y = x³ - 8 · x² + 22 · x - 20
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A single hamburger costs $5.00. French fries cost $3.00. If you buy them as a combo the cost is $6.50. What is the savings, expressed in percent if you order the combo?
The the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50
What is the amount saved when combo is ordered?
The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo
total cost for individual orders=$5.00+$3.00
total cost for individual orders=$8.00
combo cost=$6.50
savings on combo=total cost for individual orders-combo cost
savings on combo=$8.00-$6.50
savings on combo=$1.50
% savings on combo=$1.50/$8.00
% savings on combo=18.75%
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a family is comparing different car seats. one car seat is designed for a child up to and including lb. another car seat is designed for a child between lb and lb. a third car seat is designed for a child between lb and lb, inclusive. model those ranges with compound inequalities. which car seats are appropriate for a -lb child?
According to the given statement the following car seats are adequate for a 32-pound child:
car seat suited for a youngster weighing between 15 and 40 pounds, andcar seat intended for children weighing 30 to 85 poundsWhat is an interval notation?Interval notation tells which part of the number line, from left to right, is included in the solution (i.e., which part of the number line is shaded). Parentheses are written next to endpoints which are NOT included in the solution while brackets are written next to included endpoints.
According to the given statement:The Inequality car seat is intended for children weighing up to 30 pounds.
let the child's weight = x
x ≤ 30
Inequality for a car seat built for a child weighing between 15 and 40 pounds;
15 < x < 40
Inequality for a car built for a youngster weighing between 30 and 85 pounds;
30 < x < 85
According to the given statement the following car seats are adequate for a 32-pound child:
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The given question is not complete.
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
i don't Know how to solve this please help
Answer:
f(0) = 0
f(-2) = 0
f(5) = 15
f(-10) = 16
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases} \begin{aligned}-2x-4 & \;\;\textsf {if }\;x < 0\\3x & \;\;\textsf {if }\;x\geq 0\\\end{aligned}\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]\textsf{$f(x)=-2x-4$ when $x$ is less than zero}.[/tex][tex]\textsf{$f(x)=3x$ when $x$ is more than or equal to zero}.[/tex]When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of the function
Substitute zero into the first function:
[tex]\implies f(0)=-2(0)-4=-4[/tex]
Place an open circle at point (0, -4).
To help graph the line, find another point on the line by inputting another value of x that is less than zero into the same function:
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
Place point (-2, 0) and draw a straight line from the open circle at (0, -4) through (-2, 0). Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of the function
Substitute zero into the second function:
[tex]\implies f(0)=3(0)=0[/tex]
Place an closed circle at point (0, 0).
Again, to help graph the line, find another point on the line by inputting another value of x that is more than zero into the same function:
[tex]\implies f(2)=3(2)=6[/tex]
Place point (2, 6) and draw a straight line from the closed circle at (0, 0) through (2, 6). Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
To find the given functions, decide which function to use based on the given value of x, then solve.
f(0) means to find the value of the function when x = 0.
Therefore, input x = 0 into the second function as x ≥ 0.
[tex]\implies f(0)=3(0)=0[/tex]
f(-2) means to find the value of the function when x = -2.
Therefore, input x = -2 into the first function as x < 0.
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
f(5) means to find the value of the function when x = 5.
Therefore, input x = 5 into the second function as x ≥ 0.
[tex]\implies f(5)=3(5)=15[/tex]
f(-10) means to find the value of the function when x = -10.
Therefore, input x = -10 into the first function as x < 0.
[tex]\implies f(-10)=-2(-10)-4=16[/tex]
Fawzia owns a small business selling used books. She knows that in the last week 45 customers paid cash, 10 customers used a debit card, and 64 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.
Answer:
0.08
Step-by-step explanation:
[tex]\frac{10}{45+10+64}[/tex] The numerator is the number of times a customer used a debit card. The denominator is the total of all the ways that customers have paid.
[tex]\frac{10}{19}[/tex] = 0.08403361344
This rounded to the nearest hundredths is
0.08
Answer:
0.08
Step-by-step explanation:
45 cash, 10 debit card, and 64 credit card.
= 45+10+64=119
There were a total of 119 customers. 10 paid with a debit card.
Probability the next customer will pay with a debit card:
10/119
=0.084033...
≈0.08
What is the distance between points F and G? number line from negative 10 to 14. point f is at negative 6. point g is at 12.
18 units is the distance between points F and G.
Assume a line with points marked on it.
Center is 0.
Left to the point 0 indicates negative numbers.
Right to the point 0 indicates positive numbers.
Given,
A number line is marked with negative 10 to positive 14.
Point F is placed at negative 6.
Point G is placed at positive 12.
We have to determine the distance between points F and G.
We can consider the number line.
From 0 to negative 10 there were 10 units.
From 0 to positive 14 there were 14 units.
Now points F and G,
From 0 to negative 6 there were 6 units.
From 0 to positive 12 there were 12 units.
We can add this together:
That is,
6 units + 12 units = 18 units.
Therefore, the distance between points F and G is 18 units.
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find the slope of the line through the given points: (-3,4) and (2,-4) leave answer as a fraction. slope=
Step-by-step explanation:
it is always the same. the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.
the direction itself does not matter, but it is important to use the same direction for the x and the y comparison.
I prefer to go from left to right, so let's go from
(-3, 4) to (2, -4).
x changes by +5 (from -3 to 2).
y changes by -8 (from 4 to -4).
the slope is
-8/+5 = -8/5
The function g(x) is a transformation of the cube root parent function,
f(x)=√x. What function is g(x)?
5-
N
-5-
g(x)
f(x)
-5
O A. g(x)=√x+2+1
B. g(x)=√x-1+2
C. g(x)=√x-2+1
O D. g(x)=√x+1+2
Using translation concepts, function g(x) is given as follows:
C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is given by:
[tex]f(x) = \sqrt[3]{x}[/tex]
The translations for g(x) are as follows:
One unit up, hence g(x) = f(x) + 1.Two units right, hence x -> x - 2.Thus the rule is:
C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]
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A cup of cereal has 12 grams of fiber, which is 40% of the amount of fiber jared’s doctor recommends he consume each day. how much fiber does jared’s doctor recommend he consume each day?
The amount of fiber asked by the doctor to be consumed is 30 grams .
Method to calculate percentages :
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .
Let the amount of fiber asked by the doctor to be consumed be x .
According to question ,
40 % of x = 12
Solving the equation ,
( 40 / 100 ) * x = 12
x = 1200 / 40
x = 30
Hence , the amount of fiber asked by the doctor to be consumed is 30 grams .
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Answer:
30
Step-by-step explanation:
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal
- - - - - - - - - - - - - - - - - - - - - - - -
Work below!
- - - - - - - - - - - - - - - - - - - - - - - -
Simply multiply the inches by 20 (the scale per inch), and you have your answer!
3.5 x 20 = 70
The height is 70 inches.
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
(Consider leaving a Brainliest if this helped!)
~pinetreee
Answer:
70
Step-by-step explanation:
If you multiply 3.5 times 20 you get 70
1. Jenny went bowling. She paid $2.75 to rent bowling shoes and she paid $4.25 for each game. If Jenny paid a total of $24, how many games did she bowl?
2. Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Gary have?
3. If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
4. Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Mark have?
5. Tony spent a total of 140 minutes studying for his Algebra test. This total was 5 more than 3 times the amount of minutes he spent studying for his Biology test. How many minutes did Tony spend studying for his Biology test?
6. If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the length of the rectangle?
Group of answer choices
7. A transportation company charges a fee of $125 plus $50 per hour to rent a limousine. If John paid $425 for a limousine, for how many hours did he rent the limousine?
8. The sum of two numbers is 37. One of the numbers is 15 more than the other number. What are the two numbers?
9. Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Pamela now?
10. Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Debra now?
(Easy way to gain points)
Please show your work :)
Using equations, the solutions for the problems are given as follows:
1. She played 5 games.
2. Gary had 7 rebounds.
3. The width of the rectangle is of 38 inches.
4. Mark had 21 rebounds.
5. Tony spent 45 minutes studying for his Biology test.
6. The length of the rectangle is of 72 inches.
7. He rented the limousine for 6 hours.
8. The two numbers are 11 and 26.
9. Pamela is 8 years old.
10. Debra is 1 year old now.
What is the solution for item 1?The situation is modeled by the following linear function:
P(n) = 2.75 + 4.25n.
We have that P(n) = 24, hence we have to solve for n.
24 = 2.75 + 4.25n.
n = (24 - 2.75)/4.25
n = 5.
She played 5 games.
What is the solution for item 2?The situation is modeled by the following system of equations:
x = 3y.x + y = 28.Hence:
3y + y = 28
4y = 28
y = 7.
Gary had 7 rebounds.
What is the solution for item 3?Considering the equations for the perimeter of the triangle, and the situation described, we have that:
l = 2w - 4.2(l + w) = 220.Hence:
2(2w - 4 + w) = 220
2(3w - 4) = 220
3w - 4 = 110
3w = 114
w = 114/3
w = 38.
The width of the rectangle is of 38 inches.
What is the solution for item 4?Solution x for item 2, hence:
x = 3y = 3 x 7 = 21.
Mark had 21 rebounds.
What is the solution for item 5?This situation is modeled by the following equation:
3x + 5 = 140
3x = 135
x = 135/3
x = 45.
Tony spent 45 minutes studying for his Biology test.
What is the solution for item 6?This is the solution for l of item 3, hence:
l = 2w - 4 = 2 x 38 - 4 = 72.
The length of the rectangle is of 72 inches.
What is the solution for item 7?The situation is modeled by the following equation:
P(x) = 125 + 50x.
We have that P(x) = 425, hence we solve for x as follows:
425 = 125 + 50x
50x = 300
x = 300/50
x = 6.
He rented the limousine for 6 hours.
What is the solution for item 8?The situation is modeled by the following system:
x + y = 37.x = 15 + y.Hence:
15 + y + y = 37
2y = 22
y = 11.
x = 15 + 11 = 26.
The two numbers are 11 and 26.
What is the solution for item 9?The situation is modeled by the following system:
y = x - 7.x + 6 = 2(y + 6).Hence:
x + 6 = 2(x - 7 + 6)
x + 6 = 2(x - 1)
x + 6 = 2x - 2
x = 8.
Pamela is 8 years old.
What is the solution for item 10?This is the solution for y of the previous item, hence:
y = x - 7 = 8 - 7 = 1.
Debra is 1 year old now.
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A package of 4 pairs of insulated socks costs $21.96. What is the unit price of the pairs of socks?
The unit price is $ per pair of socks.
Answer: $5.49
Step-by-step explanation:
Unit price = 21.96/4 = 5.49
Pls help, and answer both questions I will try to give you brainly.
Answer: J(2,2) K(1,-1) thats all I got
Step-by-step explanation:
Alexia landed her plane. The plane's elevation relative to the ground (in meters) as a function of time (in seconds) is graphed. How high was the plane after 1000 seconds?
A) 8500 meters
B) 1500 meters
C) 3500 meters
D) 5 meters
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
The given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determined by using Pythagorean theorem which is the correct option (C).
What is Pythagoras theorem?Pythagoras theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
The given triangle whose sides are 6cm, 10cm, and 12cm
Now, applying Pythagorean's theorem:
⇒ 6² + 10² = 12²
⇒ 36 +100 = 144
⇒ 136 = 144
Here, it is clearly observed that 136 < 144 therefore, the triangle is obtuse.
Therefore, the given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle
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(x + 1)3 − x (x − 2)2 − 1
Answer:
x = -0.27 or 3.77
Step-by-step explanation:
explanation in pic
Answer:
This simplifies to 7x^2 - x.
Step-by-step explanation:
(x + 1)3 − x (x − 2)2 − 1
= x^3 + 3x^2 + 3x + 1 - x(x^2 - 4x + 4) - 1
= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 -4x - 1
= 7x^2 - x
Find FH .
FH = {Blank}
Answer:
26
Step-by-step explanation:
[tex]FH=7+19=26[/tex]
Answer:
FH = 26
Step-by-step explanation:
The equation will be,
→ FH = FG + GH
Then the value of FH will be,
→ FH = 19 + 7
→ [ FH = 26 ]
Hence, the value of FH is 26.
find the difference. (6d+5)-(2-3d)
Solving the Question
[tex](6d+5)-(2-3d)[/tex]
We subtract algebraic expressions exactly as we would integers, or as we would in a 'normal' subtraction sentence. First, we must open up the brackets:
[tex]= 6d+5-2+3d[/tex]
Now, combine like terms:
[tex]= 9d+5-2\\= 9d+3[/tex]
Answer9d+3