They are integers that follow one right after another. For example the set {1,2,3,4,5} represents consecutive numbers. Another example would be {9,10,11,12,13}
In general, if x is some integer, then x+1 is the next integer right after x, and x+2 is right after x+1 and so on. The list is {x, x+1, x+2, x+3, ...} representing any general set of consecutive numbers.
"The product of a six and a number increased by four is equal to
the product of twelve and the same number decreased by twenty."
Answer:
[tex] 6x + 4 = 12x - 20 [/tex]
[tex] x = 4 [/tex]
Step-by-step explanation:
Let "x" be the number.
Product of 6 and x (6*x), increased by 4 = [tex] 6x + 4 [/tex]
Product of 12 and x, (12*x), decreased by 20 = [tex] 12x - 20 [/tex].
Set both expressions equal to each other and solve for x as shown below:
[tex] 6x + 4 = 12x - 20 [/tex] (equation)
Subtract 12 from both sides
[tex] 6x + 4 - 12x = 12x - 20 - 12x [/tex]
[tex] -6x + 4 = -20 [/tex]
Subtract 4 from both sides
[tex] -6x + 4 - 4 = -20 - 4 [/tex]
[tex] -6x = -24 [/tex]
Divide both sides by -6
[tex] \frac{-6x}{-6} = \frac{-24}{-6} [/tex]
[tex] x = 4 [/tex]
what is the decimal 36.14 in expanded form
Answer:
Standard Form:
36.14
Expanded forms can be written like a sentence or stacked for readability as they are here.
Expanded Notation Form:
30
+
6
+
0.1
+
0.04
Expanded Factors Form:
3 ×
10
+
6 ×
1
+
1 ×
0.1
+
4 ×
0.01
Expanded Exponential Form:
3 × 101
+
6 × 100
+
1 × 10-1
+
4 × 10-2
Word Form:
thirty-six and fourteen hundredths
Step-by-step explanation:
Answer: The correct answer is: 30 + 6 + 0.1 + 0.04.
Step-by-step explanation:
We write numbers in expanded form using place value.
Regina charges c dollars per hour to babysit. If she increases her rate by 15%, which expression represents her new rate, in dollars per hour?
PLZZ HELPPPPPPPPPPPPPPPPPP
A- c + 0.15
B- c + 15
C- c + 0.15c
D- c +15c
Answer: Correct answer is C
The temperature, HH, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H=f(t)H=f(t), where tt is in minutes since the coffee was put on the counter. (a) Is f′(t)f′(t) positive or negative? negative (Be sure that you are able to give a reason for your answer.) (b) What are the units of f′(20)f′(20)? help (units) Suppose that |f′(20)|=1.5|f′(20)|=1.5 and f(20)=56f(20)=56. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case. At minutes after the coffee was put on the counter, its temperature is and will ? by about in the next 45 seconds.
Answer:
A) f'(t) is negative
B) degc/min
c ) At 20 minutes after the coffee was put on the counter its temperature is 56degc and will decrease by about 1.125 in the next 45 seconds
Step-by-step explanation:
A ) f'(t) is Negative because as the cup of coffee is placed on the counter there is loss of heat from the cup of coffee to the surrounding as t increases hence f'(t) is negative
B ) The units of f'(20) = degc/min
C) At ║f'(20)║ = 1.5 and f'(20) = 56
║f'(20)║ = 1.5 represents the rate of change of temp every 20 minutes = 1.5
therefore after 45 seconds = 3/4 mins. change in temp = (3/4 * 1.5) = 1.125
At 20 minutes after the coffee was put on the counter its temperature is 56degc and will decrease by about 1.125 in the next 45 seconds
Please help!!!
Question - the graphs below have the same shape. What is the equation of the blue graph.
O a. G(x) = (x-4) ^2
O b. G(x) = (x+4)^2
O c. G(x) = x^2 - 4
O d. G(x) = x^4 + 4
Answer:
hello
g ( 4 ) = 0
( x - 4)² = 0 ⇔ x = 4
Step-by-step explanation:
When Alvin woke up in the morning, it was
–
9°F. By the afternoon, the temperature had risen to
–
2°F.
What was the change in temperature from the morning to the afternoon?
Answer:
The answer to this question is: 7
The change in temperature from the morning to the afternoon is 7°F.
Given that, Alvin woke up in the morning, it was –9°F. By the afternoon, the temperature had risen to –2°F.
We need to find what was the change in temperature from the morning to the afternoon.
What is the change in temperature?Temperature change is a process whereby the degree of hotness of a body (or medium) changes.
You subtract the final temperature from the starting temperature to find the difference.
Now, change in teperature=-2-(-9)
=-2+9=7
Therefore, the change in temperature from the morning to the afternoon is 7°F.
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Convert y
3x2 + 6x – 5 to vertex form.
Answer:
y = 3(x + 1)^2 - 8Step-by-step explanation:
Given
y = 3x^2 + 6x – 5Converting to vertex form
y = a(x – h)^2 + ky = 3x^2 + 6x + 3 - 8y = 3(x + 1)^2 - 8The nth term of a sequence is 25 - 3n
Work out the first three terms of the sequence
Work out the first negative term of the sequence
Answer:
see explanation
Step-by-step explanation:
To find the first 3 terms substitute n = 1, 2, 3 into the formula
(a)= 25 - (3 × 1) = 25 - 3 = 22 = 25 - (3 × 2) = 25 - 6 = 19= 25 - (3 × 3) = 25 - 9 = 16
The first three terms are 22, 19, 16
Note the difference between consecutive terms is - 3
19 - 22 = 16 - 19 = - 3
Continuing this pattern
(b)16 - 3 = 13 13 - 3 = 10 10 - 3 = 7 7 - 3 = 4 4 - 3 = 1 1 - 3 = - 2
The first negative term is - 2
If you have 250 toothpicks, and want to make them into a pyramid (shown in photo), how many levels will it make?
I know there are 12 rows shown in the photo, but I'm not sure of the equation you need in order to actually find that there are 12 levels. Could anyone tell me? Thanks! :)
Answer:
12 full levels
Step-by-step explanation:
There are multiple ways to do this, what I prefer is recursion
Let's define a equation which helps us determine the number of toothpicks of a pyramid with x levels f(x)
f(1)=3
f(2)=9
f(3)=18
f(4) =30
Etc Etc...
Eventually we can see that for every level x×3 toothpicks are added to f(x-1), so
f(x) = 3*x + f(x-1), so this becomes a geometric sequence 3*(1+2+3...+x)
Now we want to find out how many levels 250 toothpicks can make
250=3*(1+2+3+4..+x)
250/3 = 1+2+3...
I assume you want full levels so I will round down the answer, the closest you can get to 250/3 is (1+2+3...12)
So 12 full levels and a bit of extra toothpicks left
There are 12 full levels it will make.
What is a triangular pyramid?Take a traingle. This is a base. Now take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.
here a equation which helps us determine the number of toothpicks of a pyramid with x levels f(x)
f(1)=3
f(2)=9
f(3)=18
f(4) =30
we can see that for every level x×3 toothpicks are added to f(x-1), so
f(x) = 3x + f(x-1), so geometric sequence 3*(1+2+3...+x)
Now we want to find out how many levels 250 toothpicks can make;
250=3*(1+2+3+4..+x)
250/3 = 1+2+3...
Thus, the closest we can get to 250/3 is (1+2+3...12)
Hence, 12 full levels and a bit of extra toothpicks left
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I need serious help on this!
Answer:
B. 3.88
Step-by-step explanation:
Point Q is 3.86 and point R is 3.92
3.88 is the only answer that is between the numbers.
iii Write down the length and width of the block.
Answer length
=
width x
Length x + 5
Height 5
X = 25
Which equation represents a line that is parallel to the line y=3-2x?
1) 4X+ 2Y=5
2)2x+4y=1
3)y=3-4X
4)y=4X-2
Answer:
(1)
Step-by-step explanation:
Slope of the given line is -2
1) 4x + 2y = 5, 2y = -4x + 5, y = -2x + 5/2, slope is -2
Parallel line, same slope so the answer is (1)
Which of these expressions is not equivalent to the others?
9 n + 11
9n+3 +2
(4 n+ 5 ) + (3 + 8 – 6)
(4 n+ 3) + 5 n+ 8 - 6
Answer:
9n + 11
Step-by-step explanation:
Solve the following;
(4 n+ 5 ) + (3 + 8 – 6)
(4 n+ 3) + 5 n+ 8 - 6
Solve;
~~~~~~~~~~~~~~~~~~~~
(4n + 3) + 5n + 8 - 6
4n + 3 +5n + 2
9n + 5
~~~~~~~~~~~~~~~~~~~~
(4n + 5n) + (3 + 8 - 6)
9n + 5
~~~~~~~~~~~~~~~~~~~~
Hence, out of these expression 9n + 11 is not equivalent to the others
~Learn with Lenvy~
Hey there!
Solve all equations
=> 9n + 11
= 9n +11
=> 9n +3 +2
=9n + 5
=> (4n +5) + (3+8-6)
= 4n + 5 + 3 + 8 - 6
= 4n + 16 -6
= 4n + 10
=> 4n+3+5n+8−6
=4n+3+5n+8+−6
Combine Like Terms:
=4n+3+5n+8+−6
=(4n+5n)+(3+8+−6)
=9n+5
Therefore, expressions that is equivalent to the others are 9n + 11 and (4 n+ 5 ) + (3 + 8 – 6)
john and his friend took 4 hour bic ycle trip. in all, they traveled 150 km. what was their average rate of speed?
PLS ANSWER I NEED IT
Answer:
37.5 kmph
Step-by-step explanation:
150km ÷ 4hr = 37.5kmph
Answer:
37.5 km/hr
Step-by-step explanation:
The trip took 4 hours to travel 150 km.
To find the average rate you have to divide 150 km by the time it took for them to travel that distance (4 hours) to find how far they travelled in one hour.
EQUATION: 150 km ÷ 4 hrs = 37.5 km
An election poll of 1,000 people indicates that 48 percent of voters favor Candidate Smith and 50 percent of voters favor Candidate Jones, with a 3 percent margin of error. What can one conclude from this poll
The election poll indicates a close race between Candidate Smith and Candidate Jones, with a margin of error of 3 percent.
Given that,
Election poll of 1,000 people conducted
48 percent of voters favor Candidate Smith
50 percent of voters favor Candidate Jones
Margin of error is 3 percent
Based on the election poll,
We can conclude that there is a close race between Candidate Smith and Candidate Jones.
With Candidate Smith at 48 percent and Candidate Jones at 50 percent, it suggests a tight competition.
However, it's important to consider the margin of error of 3 percent.
This means that the actual support for each candidate could vary within this range.
Therefore, while this poll provides valuable insights, it is not definitive and other factors should also be considered.
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Purchases made at small "corner stores" were studied by the authors of a certain paper. Corner stores were defined as stores that are less than 200 square feet in size, have only one cash register, and primarily sell food. After observing a large number of corner store purchases in Philadelphia, the authors reported that the average number of grams of fat in a corner store purchase was 21.8. Suppose that the variable
x = number of grams of fat in a corner store purchase
has a distribution that is approximately normal with a mean of 21.8 grams and a standard deviation of 7 grams.
a) What is the probability that a randomly selected corner store purchase has more than 29 grams of fat?
b) What is the probability that a randomly selected corner store purchase has between 15 and 25 grams of fat?
c) If two corner store purchases are randomly selected, what it the probability that both of these purchases will have more than 25 grams of fat?
Answer: x = number of grams of fat in a corner store purchase
has a distribution that is approximately normal with a mean of 21.8 grams
Step-by-step explanation:
Simplify. Assume all variables are positive values
Answer:
10√(w⁵v⁷)
Step-by-step explanation:
√(20wv³) × √(5w⁴v⁴) = √(100w⁵v⁷)
reduce...
10√(w⁵v⁷)
I hope this helps, please rate!!
Answer:
[tex]10w^{2}v^{3} \sqrt{wv}[/tex]
Step-by-step explanation:
[tex]\sqrt{20wv^{3} } \sqrt{5w^{4}v^{4} } =\sqrt{(5)(4)wv(v^{2}) } \sqrt{5(w^{2})(w^{2})(v^{2})(v^{2} ) }[/tex]
[tex]=(2v\sqrt{5wv} )(w^{2}v^{2} \sqrt{5} )=2w^{2}v^{3} (5)\sqrt{wv}[/tex]
[tex]=10w^{2}v^{3} \sqrt{wv}[/tex]
Hope this helps
f(x)=x + 3 and g(x)=x2−x. Find and simplify the expression.
(f+g)(4)
Answer:
11
Step-by-step explanation:
Of the vegetables Aron planted, 5/12 were carrots, 3/12 were cucumbers, and the rest were tomatoes. What fraction of the vegetables was tomatoes?
A. 1/6
B. 1/8
C. 1/3
D. 5/12
12-ton pickup truck is 17 3/4 feet long. If it is parked in a garage that is 28 1/2 feet in length, how much longer is the garage than the truck?
Answer:
10 3/4 feet longer
Step-by-step explanation:
17 3/4= 17.75
28 1/2= 28.50
28.50 - 17.75 = 10.75
10.75 = 10 3/4
Lines M and N are parallel. Find the measure of ∠b.
Answer:
65 degrees
Step-by-step explanation:
Alternate interior angle therom
what is 1.0 x 10.0 in a fraction
Answer:
10.0 but if you want it in fraction it is 0.100
Step-by-step explanation:
Step 1:
[tex]1.0 \times 10.0[/tex]
Step 2:
[tex] = \dfrac{10}{10} \times \dfrac{100}{10} [/tex]
To make them in fraction we have to remove decimals
Step 3:
[tex] = \dfrac{1000}{100} [/tex]
Step 4:
[tex] = \dfrac{10}{1}✓[/tex]
Solve 4(x - 5) = 28.
A. X= 27
O B. X = 7
O C. x = 6
O
D. X = 12
Answer:
d
Step-by-step explanation:
use calculator
Answer:
x=12
Step-by-step explanation:
because 12-5=7 and do the other math and the answer is there
Five times the sum of twice a number, x, and two is ten.
Find the number.
x=?
Answer:
0
Step-by-step explanation:
5(2x + 2) = 10
10x + 10 = 10
10x = 0
x = 0
Answer:
x = 0
Step-by-step explanation:
First, let's translate this statement into an equation.
5 times the sum of twice a number, x, and two means "5(2x + 2)"is ten means "= 105(2x + 2) = 10Solving
Step 1: Simplify both sides.
[tex](5)(2x)+(5)(2)=10[/tex] [tex]10x+10=10[/tex]Step 2: Subtract 10 from both sides.
[tex]10x+10-10=10-10[/tex] [tex]10x=0[/tex]Step 3: Divide both sides by 10.
[tex]10x/10=0/10[/tex] [tex]x=0[/tex]Have a lovely rest of your day/night, and good luck with your assignments! ♡
hey id really appreciate if someone can help me here
Answer:
C (lower left corner)
Step-by-step explanation:
Lower extreme: 67
Upper extreme: 75
Median: 70
Upper quartile: 73
Lower quatile: 69
Have a great day!!
Please mark brainliest and rate!!
-7 = z/-6
[tex] - 7 = \frac{z}{ - 6} [/tex]
What is the answer?
is this correct or no?
Answer:
Uh, is what correct or no
Step-by-step explanation:
Victor says that point A is closer to 0 than point B on a number line.
What are the possible locations of A and B?
A= -5, B= -2
A= -3, B= 6
A= 7, B= -5
A= 8, B= 4
Answer:
b has more closer to 0 on number line
Step-by-step explanation:
-2 is closer than-5=B wins
-3 is closer to 0 than 6=A wins
-5 is closer to 0 than 7 is=B wins
And 4 is closer to 0 than 8 so= B wins
Hope it helps have a great day:)
please help (will give brainiest)
Answer:
Step-by-step explanatwe
1/3 would be a||b but if were talking plus mult then try (01ab 9)
Daniel,Cheryl and Li Ying earned $550 from their part time jobs. Li Ying earned $28.Daniel earned 4 times as much as the total amount of Cheryll and Li Ying's earnings. How much did Cheryl earn?
The amount Cheryl earned from the per time job is $82.
The three of them earned $550 from their part time jobs.
Li Ying earned $28.
Daniel earned 4 times as much as the total amount of Cheryl and Li Ying's earnings.
let
x = amount Cheryl earned
y = amount Daniel earned
Therefore,
y = 4(x + 28)y = 4x + 112
y - 4x = 112
The three of them earned $550. Therefore,
x + y + 28 = 550x + y = 522
Let's combine the equation.
System of equationy - 4x = 112
x + y = 522
5x = 410
x = 410 / 5
x = 82
Therefore, Cheryl earned $82.
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