The given equation is :
[tex]x^3-9x^2+5x-45[/tex]
Take out GCF from the first pair and the second pair
[tex]x^2(x-9)+5(x-9)[/tex]
Now (x-9) is common so
[tex](x-9)(x^2+5)[/tex]
Each week leslie jogs 20 minutes for every 10 minutes that she lifts weights. Is the number of minutes Leslie jogs each week proportional to the number of minutes that she lifts weights each week?
It is proportional because the ratio never changes and increases at a constant rate.
c - 1.5+6.8=0.6 what is x
Ok! I gotcha!
C-1.5+6.8=0.6
Steps:
Add/Subtract The #!
c+5.3=0.6
Subtract 5.3 On Both Sides!
c+5.3-5.3=0.6-5.3
Simplify!
c=-4.7
A rental car company charges a basic fee plus a price per mile. One customer drove 250 and paid 56.50, while another customer drove 400 and paid 79. Write an equation in slope - intercept form for the cost of renting a car. Use your equation to find how much it would cost to drive 325 miles?
Answer:
y = 0.15x+19 and
67.75
Step-by-step explanation:
Let us assume y for total cost and x no of miles.
Then x and y are related by a straight line.
Two points lying on the line are
(250,56.50) and (400,79)
Use two point formula
y-56.50/(79-56.50) = x-250/(400-250)
y-56.50 = 22.5(x-250)/150
y = 22.5x/150 -37.50+56.50
Or y = 0.15x+19
To find out cost for 325 miles:
x=325
y= 0.15(325)+19
= 48.75+19
=67.75
tell whether in the sequence is arithmetic if it is what is the common difference 20,11,2,-7
The sequence 20 , 11 , 2 , -7 is an arithmetic sequence.
The common difference is (20 - 11) = (11 - 2) = (2 - -7) = 9
The common difference is 9.
Yes, the given sequence is arithmetic. The common difference is -9.
Arithmetic sequenceAn arithmetic sequence is a list of numbers in which the difference between any two consecutive terms is always the same. This constant difference is called the common difference.
For the sequence shown:
1st Term: 20
2nd Term: 20 - 9 = 11
3rd Term: 11 - 9 = 2
4th Term: 2 - 9 = -7
In other words, the common difference in the arithmetic sequence is -9.
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3 problems based on rational and irrational numbers properties only
The discussion covers rational and irrational numbers' properties, particularly focusing on the absence of the smallest positive rational number and the non-manifold nature of rational numbers.
The properties of rational and irrational numbers are fundamental concepts in mathematics, particularly when studying the real number system. Rational numbers include integers and fractions where the numerator and the denominator are integers (e.g., 2/3), while irrational numbers are those that cannot be expressed as such a simple ratio (e.g., √2 or π). The completeness axiom of the real numbers ensures that every number on the number line has a place, whether rational or irrational. An example of how rational and irrational numbers interact is that a graph of a function defined only on rational numbers could approach but never touch an irrational number, which is illustrated in the claim that there is no smallest positive rational number, akin to how there is no smallest positive real number. This is due to the density of rational numbers—between any two rational numbers, there is another rational number.
Example Problems:
Prove by contradiction there is no smallest positive rational number.Discuss why a graph of a function restricted to rational inputs could approach but not contain an irrational number like √2.Explain why the rational numbers are not a manifold by considering an arbitrarily small neighborhood around √2.Please answer quickly thanks :)))
move te dotty thing to the midle them sumbtract 5 1/2
u are very smart
Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1.2 Australian dollars equals 1 US dollar
Answer:
The conversion factor to use here is ($1 US dollar) / (1.2 Austr. dollars), and the
final result is 22 Austr. dollars = US$18.33.
Step-by-step explanation:
The relevant conversion factor here is
1 US dollar
-----------------------
1.2 Aust. dollars
Then:
22 Aust. dollars 1 US dollar
------------------------ * ------------------------- = 18.33 US
1 1.2 Austr. dollars
How to write 5+0.1+0.03+0.006 in standard form
Answer:
5.136.
Step-by-step explanation:
We have been given a number in expanded form [tex]5+0.1+0.03+0.006[/tex]. We are asked to write our given number in standard form.
To convert our given number in standard form, we will add all the values to get digits in tenths, hundredths and thousandths place as:
5
0. 1
0.03
+ 0.006
5.136
Therefore, our given number in standard form would be 5.136.
For which of the following statements is the inverse false?
ANSWER
The correct answer is D
EXPLANATION
The conditional is
"If an angle's measure is [tex]35\degree[/tex], then it is an acute angle"
The above statement is true because both the premise and the conclusion are true.
Now let us consider the inverse of the above statement.
"If an angle's measure is not[tex]35\degree[/tex], then it is not an acute angle"
The above statement is false.
For example [tex]60\degree[/tex] is an acute angle even though its measure is not [tex]35\degree[/tex]
Which inequality matches the graph?
b is the answer because it hits positive two on the x axis and -3 on the y axis
a cookie recipe calls for a half cup of chocolate chips per 3 dozen cookies. How many cups of chocolate chips should be used for 10 dozen cookies?
To answer this question, you should set up a proportion that demonstrates the ratio of chocolate chips to cookies.
[tex]\frac{0.5}{36} =\frac{x}{120}[/tex]
36 and 120 are used because 1 dozen=12.
Cross multiply and solve for x to get the answer.
[tex]60=36y[/tex]
[tex]\frac{5}{3}=x[/tex]
The answer is [tex]\frac{5}{3}[/tex] cups.
The number of cups of chocolate chips that should be used for 10 dozen cookies is 1 2/3 cups.
Based on the information given, the expression to solve the question will be:
0.5/3 = x/10
Cross multiply
3 × x = 0.5 × 10
3x = 5.
x = 5/3
x = 1 2/3 cups
Therefore, the number of cups of chocolate chips that should be used for 10 dozen cookies will be 1 2/3 cups.
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Which shows the repeated multiplication for 9³?
a 9 • 9 • 9
b 9 • 9 • 9 • 3
c 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3
d 9 • 3
its A. because the exponent which in this case is 3, is multiplied 3 times. so 9 is multiplied 9 times
A. because 9 is being multiplied 3 times by itself
Eric is having a party. he'll have 3 tables for every 6 guests. complete the table showing the number of tables and the number of guests
The relationship between the number of tables and guests for Eric's party maintains a consistent ratio of 1 table for every 2 guests. By setting up a proportional table, we can see this ratio and calculate the number of tables needed for any given number of guests.
The question involves creating a table to show the relationship between the number of tables and the number of guests at Eric's party. Since we know that there are 3 tables for every 6 guests, we can create a proportional table that maintains this 1:2 ratio (one table for every two guests). For example, if there were 12 guests, you would need 6 tables (because 12 guests divided by the ratio of guests to tables, which is 2, equals 6 tables). Similarly, if there were 18 guests, you would need 9 tables, as 18 divided by 2 equals 9.
Proportional Table for Eric's Party:
6 guests - 3 tables12 guests - 6 tables18 guests - 9 tables24 guests - 12 tables30 guests - 15 tables... and so on.This table can be continued in the same manner as long as you keep the same ratio of 1 table for every 2 guests.
What is the product of (9)(-9)(-1)?
Answer:
The answer is 81
Step-by-step explanation:
Hope this helps
Find the value of x that will make L||M.
Answer: 60!
It’s already answered but I need some points ✊
Handsome Jack is buying a pony made of diamonds. The price of the pony is PPP dollars, and Jack also has to pay a 25\%25%25, percent diamond pony tax.
Which of the following expressions could represent how much Jack pays in total for the pony?
Choose 2 answers:
A: P+1/4
B: P + 0.25 P
C: (P + 1/4) P
D : 5/4 P
E: 0.25P
Answer:
B: P + 0.25 P
D : 5/4 P
Step-by-step explanation:
The price is P.
The tax is 25% of P, or 0.25P.
The total price is the price plus the tax,
P + 0.25P = P + 1/4P = 4/4P + 1/4P = 5/4P
A percentage is a number expressed fraction of hundred
The correct options for the expression that represent how much Jack pays in total are;
B: P + 0.25·P
D: (5/4)·P
Reason:
The given parameters are;
Material from which the pony is made = Diamond
Price of the pony = P dollars
Amount Jack has to pay as diamond pony tax = 25%
Required:
The expression that represents how much Jack pays per pony
Solution:
The amount Jack pays, A = The price of the pony + Tax
The amount paid as tax = 25% of P = 0.25·P
∴ A = P + 0.25·P
The total amount Jack pays in total for the pony, A = P + 0.25·P[tex]\therefore A = P + 0.25 \cdot P = P + \dfrac{1}{4} \cdot P = \dfrac{5}{4} \cdot P[/tex]
Therefore; The total amount paid = P + 0.25·P = (5/4)·PThe correct options are; B: P + 0.25·P, and D: (5/4)·P
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Can someone help me please???
A full circle = 360 degrees.
Mrs Wood and Mrs Patel = 360 - 64 = 296 degrees.
Mrs Wood is 24 more than Mrs Patel:
296-24 = 272 / 2 = 136
Mrs Patel = 136 degrees
Mrs Wood = 136 + 24 = 160 degrees.
Number of votes for Mrs Patel = 136/360 x 5220 = 1,972 votes.
Brainliest + points! Help please! Mathematicians
Answer and explain (No its not the lower extreme etc. Its the values and the actual numbers)
There are 5 parts of a box-and-whisker plot.
Lowest Value (Minimum)= that's the left end of the graph, and shows what the minimum value is. Here, the minimum is 46.
Lower Quartile (Q₁)= This is the left edge of the "box" in a box-and-whisker plot. Here it is 55.
Median (Q₂)= This is the line in the middle of the box, and represents the very center of minimum and maximum values. Here it is 58.
Upper Quartile (Q₃)= This is the right edge of the box in a box-and-whisker plot. Here it is 63.
Highest Value (Maximum)= This is the farthest right point on your plot. Here it is 66.
Hope this helps! If you have any questions, please feel free to ask in the comments below!
The term 'lower extremes' in mathematics typically refers to the minimum value of a data set, but in this case, the student is asking for the values that represent the lower extremes.
Explanation:In mathematics, the term 'lower extremes' usually refers to the lower limit of a data set, also known as the minimum value. However, since the question specifically asks for 'values and actual numbers', we can assume that the student is referring to the values that represent the lower extremes in the data set. For example, if the data set is {3, 5, 1, 2, 7}, the lower extremes would be the values 1 and 2.
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If the outlier is removed, which measure will not change?
range
mode
median
mean
A bakery has 72 half gallons of milk. It takes 1 2/3 cups of milk to make the cake. Note that 1 cup= 1/8 half gallon= 0.125 half gallon. How many cakes can the bakery make? A. 43 cakesB. 288 cakesC. 345 cakesD. 576 cakes
To determine the number of cakes the bakery can make, the required milk per cake in cups is converted to half gallons and then divided into the total available milk in half gallons. Upon calculation, the bakery can make approximately 345 cakes. Thus, the correct answer to the student's question is option C) 345 cakes.
To solve how many cakes the bakery can make using 72 half gallons of milk and with each cake requiring 1 2/3 cups of milk, we must first convert the cups needed for one cake into half gallons. Since 1 cup equals 0.125 half gallons, 1 2/3 cups is equivalent to 1.6667 * 0.125 half gallons. Now, let's calculate the number of cakes:
1 2/3 cups of milk for one cake = 1.6667 * 0.125 half gallons = 0.2083 half gallons per cake.Total available milk in half gallons = 72.Number of cakes = Total available milk / Milk per cake = 72 / 0.2083.After performing the division, we find that the bakery can make approximately 345 cakes. Therefore, the correct answer is C. 345 cakes.
Isabella sells 36 tickets to the school talent show each ticket cost $14 how much money does Isabella collect the tickets she sells
36*14=504
She gets $504 from selling 36 tickets at $14 each.
The incomplete work of a student to solve an equation is shown below:
Step 1: 3x + 12 = 3
Step 2: ?
Step 3: x = −9 ÷ 3
Step 4: x = −3
What is the missing Step 2?
Answer:
3x=-9
Step-by-step explanation:
3x+12=3
3x=3-12 --------------Move 12 to the right of the equals sign, it becomes -123x=-9
The missing step to solve the given equation is 3x= 3-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 3x+12=3.
Step 1: 3x+12=3
Step 2: 3x= 3-9
3x= -9
Step 3: x= -9 ÷3
x= -9/3
Step 4: x= -3
Therefore, the missing step to solve the given equation is 3x= 3-9.
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5q greater than or equal to 8q -3/2
5q ≥ 8q - 3/2
Add 3/2 to both sides.
3/2 + 5q ≥ 8q
Subtract 5q from both sides.
3/2 ≥ 3q
Multiply both sides by 2.
3 ≥ 6q
Divide both sides by 6.
0.5 ≥ q.
The value of q is less than or equal to 0.5.
Karissa begins to solve the 1/2 (x-14)+11=1/2x-(x-4)
Answer:
Step-by-step explanation:
C)0
if 5/8 yards of fabric costs 3.75 dollars what does one yard cost
The cost of one yard of fabric, based on given prices, is 6 dollars. This is calculated by taking the total cost and dividing by the total quantity, using the concept of ratio and proportion in mathematics.
Explanation:This problem revolves around the concept of unit rates in mathematics, especially ratio and proportion. If 5/8 yards of fabric costs 3.75 dollars, then to find the cost of one yard, known as the unit rate, we need to divide the total cost by the total quantity. Therefore, the cost of one yard would be 3.75/(5/8), which equals 6 dollars. Hence, one yard of fabric costs 6 dollars.
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A Light Blue Paint Is Made By Mixing 2 Parts Of Blue Paint To 7 Parts Of White Paint. Using A Proportion Determine How Many Pints Of Blue Paint (n) Should Be Mixed With 28 Pints Of White Paint To Make This Light Blue Color
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Algebra 2...can someone tell me how to do this???
Use the 2 dots on the line located at (0,1) and (-3,0).
The slope is the change in Y over the change in X:
Change in Y = 0-1 = -1
Change in X = -3 - 0 = -3
Slope = -1 / -3 = 1/3
They intercept in this case is Y1 which = 1.
The equation is y = 1/3x + 1
GEOMETRY PEOPLE HELP ME PLEASEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!
I WILL GIVE BRAINLIEST!!!!!!!!!!!!
2. Marissa labeled the corners of both the picture and the mat as shown. Complete the table
3. Marissa thinks that there could be a pattern between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image.
(a) Determine the perimeter and area of the picture and the perimeter and area of the mat.
(b) Create a table that shows the perimeter and area of the picture and the perimeter and area of the mat for scale factors of 2, 3, and 4.
Table
________________________________
Scale factor 3.
(-1-3,2+3) --> A(-4,5)
(1+3,2+3) --> B(4,5)
(1+3,-2-3) --> C(4,-5)
(-1-3,-2-3) --> D(-4,-5)
(-2-3,3+3) --> E(-5,6)
(2+3,3+3) --> F(5,6)
(2+3,-3-3) --> G(5,-6)
(-2-3,-3-3) --> H(-5,-6)
___________________________________
Scale factor 4
(-1-4,2+4) --> A(-5,6)
(1+4,2+4) --> B(5,6)
(1+4,-2-4) --> C(5,-6)
(-1-4,-2-4) --> D(-5,-6)
(-2-4,3+4) --> E(-6,7)
(2+4,3+4) --> F(6,7)
(2+4,-3-4) --> G(6,-7)
(-2-4,-3-4) --> H(-6,-7)
______________________________________________________
Second Image.
Scale Factor 2
Length = 6
Width = 8
Perimeter = 2(6+8)= 2(14) = 28
Area = 6 times 8 = 48.
Scale Factor 3
Length = 8
Width = 10
Perimeter = 2(8+10)= 2(18) = 36
Area = 8 times 10 = 80.
Scale Factor 4
Length = 10
Width = 12
Perimeter = 2(10+12)= 2(22) = 44
Area = 10 times 12 = 120.
_____________________________________________
Scale Factor 2
Length = 8
Width = 10
Perimeter = 2(8+10)= 2(18) = 36
Area = 8 times 10 = 80.
Scale Factor 3
Length = 10
Width = 12
Perimeter = 2(10+12)= 2(22) = 44
Area = 10 times 12 = 120.
Scale Factor 4
Length = 12
Width = 14
Perimeter = 2(12+14)= 2(26) = 52
Area = 12 times 14 = 168.
Why are you guys adding? Aren't you supposed to multiply the cordinates by the scale factor?!?!?!?!
Alexa is making a recipe that requires 1 cup of water and 4 cups of flour which of the following combination shows the same ratio of water to flour
Name the operation you would do first, -4 + (3) (-8) + 6(-4)
You would do 3*-8 and 6*-4
-4+(-24)+(-24)
-4-24-24
-28-24
-52
Hello there!
[tex]-4 + (3) (-8) + 6(-4)[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
You had to used order of operations.
P-Parenthesis
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
First you had to multiply and divide from left to right.
[tex](3)(-8)=-24[/tex]
[tex]-4-24+6(-4)[/tex]
Then you can multiply and divide from left to right again.
[tex]6(-4)=-24[/tex]
[tex]-4-24-24[/tex]
You can also add and subtract from left to right.
[tex]-4-24-24=-52[/tex]
[tex]=-52[/tex]
Answer⇒⇒⇒⇒=-52
Hope this helps!
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