How are postulates and theorems related?
Answer:
A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven
Step-by-step explanation:
Answer:
Theorems and postulates are statements of geometrical truth.
Explanation:
We create theorems based on postulates.
Postulates are the mathematical statements we assume to be true without any proof while theorems are mathematical statements we can or must prove as true.
--------------------
Hope this helps!
Have a great day and God bless! :)
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.
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]
what is the sum of 5x and 9x
Answer:
14x
Step-by-step explanation:
We just add the bases because they have the same variable terms, (they are like terms)
9 + 5 = 14
14x
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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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
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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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
PLEASE HELP WILL MARK WHAT IS 25-29
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
I’m not really sure what to do
I WILL GIVE BRAINLIEST!!!
Please help me.
Translate all word problems into equations.
You only need to give equation+answer for number 7 and 9.
7. Between noon and midnight, the temperature
dropped 20°F. If the temperature was -8°F at
midnight, what was the temperature at noon?
8. If a strawberry pie is divided into 6 equal slices, each
slice has 240 calories. How many calories are in the
whole pie?
9. A chest was resting on the ocean floor 1000 ft below
the surface. It was lifted to the deck of a ship 8 ft
above the surface. How far was the chest lifted?
10. When all the kids who tried out for Little League
were divided into teams of 20 players, there were
exactly 8 teams. How many kids tried out?
Number 7:
-8=x-20
-8+20=x
12=x
A food manufacturer donates money to schools based on the number of
its product labels the school collects. The students at one school collected
2,100 product labels in three months. The number of labels collected in the
first two months was three times the number of labels collected in the thirc
month. How many product labels were collected in the third month?
The total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.
Let the number of labels collected in the first two months be 3 x.
We are given that the number of labels collected in the first two months was three times the number of labels collected in the third month.
So, the number of labels collected in the third month = 3 x / 3 = x
Now, we are also given that:
The total number of labels collected by the students at the school = 2100.
So, we get the equation as:
3 x + x = 2100
4 x = 2100
x = 2100 / 4
x = 525 labels.
Therefore, we get that, the total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.
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Find the product of √6 x √12
pls help for brianlest
The product of √6 and √12 is option b 6√2.
Given,
Two square roots : √6 and √12
We have to find the product of these square roots:
That is,
√6 × √12
Multiplying square roots:
Multiply the two numbers as usual without considering the square root.After multiplying consider the square root of the product.It will be the product of the square roots.So here,
Multiply the numbers,
√6 × √12 = 6 × 12 = 72
Now consider the square root of 72
√72 = √36 × √2 = 6√2
That is, the product of the square roots √6 and √12 is 6√2
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Find the surface area of the figure.
6 in.
6 in.
6 in.
SA = [?]in.²
Hint: Area of Triangle = b•h
(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
4x1+6-9x3-6; answer 7
Add Brackets Or Parentheses to solve
Answer:
-23
Step-by-step explanation:
Remember Bedmas/Pedmas
P/B = Bractets or parentheses ( )
E = Exponents 3⁵
D = Division ÷
M = Multiply ×
A = Addition
S = Subtract
(4x1)+6-9x3-6
4+6-(9×3)-6
(4+6)-27-6
(10-27)-6
-17-6
-23
THERE ARE 2 DECKS OF PLAYING CARDS
Answer:
100 cards?
Step-by-step explanation:
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:
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
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 I’m struggling!!
Answer:
5
2
8
4
6
1
3
7
Step-by-step explanation:
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:
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
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
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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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
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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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 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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