Answer:
x = 1
Step-by-step explanation:
2 x [tex]x[/tex] = 10
10 > -10
9 x [tex]x[/tex] = 9
9 < 18
What are the solutions of this quadratic equation?
x² - 6x+2=0
OA.
O B.
OC.
2-3 ± √7
CD. 2-3 ± √11
-6 ± √7
x=3+√7
4x 2x - 2 = 2x
What does “X” equal?
Answer: x=0.5
Step-by-step explanation:
4x+2x - 2 = 2x
6x-2=2x
6x=2x+2
4x=2
x=0.5
Convert the following metric units of length.
100 kilometers to meters
a 100,000 m
b 10,000 m
c 108,076 m
d 109,076 m
The conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
In this question we need to convert the metric units of length.
We need to convert 100 kilometers to meters.
We know that, 1 kilometer = 1000 meters
Let 100 kilometers = p meters
So, we get an expression,
p × 1 = 100 × 1000
From this expression we get,
p = 100,000 meters
This means, 100 kilometers = 100,000 meters
Therefore, the conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
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Chef Smith will be serving a breakfast banquet for 300 guests. Each guest will be served a two-egg
omelet. How many dozen eggs should Chef Smith order?
Answer: 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
300(2) bcuz 300 guests and each person gets 2
600(12) bcuz 300(2) is 600 and a dozen is 12
=50
Suppose a charity received a donation of $23.3 million. If this represents 58% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Step-by-step explanation:
23.3 million = 58%
1% = 58%/58 = 23.3 mil. / 58
100% = 1%×100 = 100×23.3 mil./58 =
= 2,330,000,000/58 = 40,172,413.79... ≈
≈ $40 millions
What are the possible values of x for the following functions? F(x)= x-3 / 2x+6
Answer:
(in English)
x can be anything EXCEPT -3
(in Math)
Interval Notation:
(negativeinfinitysymbol,-3)U(-3,infinitysymbol)
Set Builder Notation:
{x | x < -3 or x > -3}
Step-by-step explanation:
Since this function is a rational function (like a fraction) we have to watch out for what is going on in the denominator. The denominator cannot be zero.
So, 2x + 6 cannot be zero. Let's figure out what makes 2x+6 actually equal to 0.
2x + 6 = 0
Subtract 6.
2x = -6
Divide by 2.
x = -3
Remember this is what x canNOT be.
This question is a domain question. What is x allowed to be? x may be anything except -3.
A bowl filled with lollipops is 3/4 full. 2/3 of these lollipops are green. What fraction of the full bowl are the green lollipops?
Answer:
1/12
Step-by-step explanation:
All you need to do is subtract 3/4 by 2/3, the difference of those two numbers is 1/12.
The ratio of saving to spending is 9:4 how does she spend and how mush does she save
She will spend £250 and save £400.
Ratio is an expression that indicates how many times one quantity is more than the other.
Here, we are given that Miss penny inherits £650.
Her saving to spending ratio is 9 : 4
Thus, the proportion of money she saves is 9/ (4+9) = 9/13
therefore, the amount of money saved will be-
9/13 of 650
= 9/13 * 650
= 9 * 50
= 450
Thus, Miss Penny saves £400.
The remaining amount left with her = 650 - 400 = 250.
Thus, she spends the remaining £250.
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Miss penny inherits £650. She decides to save some of the money and spend the rest. The ratio of saving to spending money is 9:4. How much does she save and how much does she spend?
Prove that for all integers a, b, n, if n = a + b, then a ≤ n/2 or b ≤ n/2 using proof by contradiction.
From the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that all integers a, b, and n, if n = a + b, then a ≤ n/2 or b ≤ n/2. Let the value of a = 3 and b = 3 now the value of n will be:-
n = a + b
n = 3 + 3 = 6
a = 3, n = 6 then a ≤ n/2.
b = 3, n = 6 then b ≤ n/2.
Therefore, the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
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Chika's uncle makes perfect brownies. Chika noted how much sugar he uses based on how many batches
he makes:
Answer:
7.5 batches
Step-by-step explanation:
if he uses 0.6kg of sugar per 2 batches, it's 0.3kg per batch.
2.25kg would let us make
2.25kg / 0.3kg = 2.25 / 0.3 = 7.5 batches
a solid is 5.0cm tall, 3.0cm wide and 2.0cm thick. it has a mass of 387g. What is the density?
Answer: 12.9
Step-by-step explanation:
5 x 3 x 2= 30
5 x 3= 15
15 x 2= 30
D= M/V -> Try to remember the DMV
387 / 30= 12.9
30 x 10= 300
30 x 2= 60
30 x 1= 30
30 x .9= 27
10 + 2 + .9= 12.9
300 + 60 + 27= 387
A taxi ride for the airport to your hotel costs a flat fee of $10 the moment you sit in the back seat plus $0.75 each mile plus a tip of $5 to the driver at the end of the ride. Your hotel is 24 miles from the airport and you have $30 in your pocket. Do you have enough money to make it to your hotel in the taxi, including the tip? Declare what your variable represents, write the equation or inequality that models the situation, solve for the variable showing your steps, and answer the question.
Greetings from Brasil...
We have 2 fixed fees:
→ $10 when you sit on the bench
→ $5 tip
So, fixed fees = $10 + $5 = $15
The rate that varies would be the distance traveled. The fee will be $0.75 per mile moved. In this case we can write that:
C = 0.75M + fees
C = 0.75M + 15let
C = cost
M = mile(s)
for 24 miles, M = 24, then
C = 0.75M + 15
C = 0.75 · 24 + 15
C = 18 + 15
C = $33
With $30 it will not be possible to make this trip, as the total cost would be $33
One solution or alternative would be to reduce the tip amount. Instead of $5, pay only $2 of tip.
We can rewrite the cost expression involving a variable for the tip:
C = 0.75M + T + 10
let T = tip
For the exercise example.... The distance (M) its 24 miles and the value of C has to be what I have in my pocket: 30.... then M=24 and C=30
C = 0.75M + T + 10
30 = 0.75 · 24 + T + 10
30 = 18 + T + 10
30 - 18 - 10 = T
T = 2
Is it possible to do this ride if you pay only $2 tip
The equation
3x-15
= 4x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x.
Answer:
15
Step-by-step explanation:
[tex]3x-15=4x \\ \\ x-15=0 \\ \\ x=15[/tex]
A small pizza has an area of
730
730730 square centimeters.
Write an inequality that describes
p
pp, the area of a pizza that is larger than a small pizza.
The inequality that describes p, the area of a pizza that is larger than a small pizza 730(seven hundred thirty) < p
What is inequality?
Inequality refers to the miracle of unstable and/ or unjust distribution of coffers and openings among members of a given society. The term inequality may mean different effects on different people and in different surroundings. The major exemplifications of social inequality include income gap, gender inequality, health care, and social class. In health care, some individuals admit better and further professional care compared to others.
From the information given, we have that;
Area of the small pizza = 730(seven hundred thirty) square centimeters
p = area of the larger pizza
In writing inequality, we have to use the signs
< less than
> greater than
Since p has a greater area, we have
730(seven hundred thirty) < p
Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730(seven hundred thirty) < p
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Find AB→+BC→+CD→+DE→+EF→
Answer:
34 I plus the word like in number it self
Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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2.21x10^3= convert the expression to decimal form
2210
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Expanding the term,
2.21 x 1000 = 2210
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The cost of a school banquet is $95 plus $15 for each person attending. Write an equation
that represents the relationship between the total cost and number of people attending.
Answer:
95 + (15 x n) n = number of people attending
Step-by-step explanation:
the Price will vary based on how many people attend the wedding, so if the variable n represents the number of people attending you only need to times that by 15$ and then add the original 95$
Copy and complete the table of values for
y = -2x² + 4x + 9.
What numbers replace A and B?
Answer:
Below in bold.
Step-by-step explanation:
A = value of y when x = -1:
A = -2(-1)^2 + 4(-1) + 9
= -2*1 - 4 + 9
= -2 - 4 + 9
= 3.
B = value of y when x = 2:
B = -2(2)^2 + 4(2) + 9
= -2*4 + 8 + 9
= - 8 + 8 + 9
= 9.
sam had a yard sale. the next day he made a deposit with no cash back. he deposited 28 twenties, 18 tens, 32 fives, 20 ones, 18 quarters and checks for $22, $18.18 and $67.04. what was the amount of his deposit?
The total amount of money Sam deposited is $1,031.72.
Given that, Sam deposited 28 twenties, 18 tens, 32 fives, 20 ones, 18 quarters and checks for $22, $18.18 and $67.04.
We need to find out what was the amount Sam deposited.
What is the sale?Add the rate to the purchase price to determine the discount. Subtract the discount from the original price to arrive at the sale price.
The discounted price at which products or services are being sold is known as a sale price.
Now, total money = 28×20+18×10+32×5+20×1+18×0.25+22+18.18+67.04
=560+180+160+20+4.5+22+18.18+67.04
=1,031.72
Therefore, the total amount of money Sam deposited is $1,031.72.
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How many points are represented in the graph below? Enter a number or 'oo' if there are an infinite number
of points.
There are how many
points on the graph?
Answer:
Infinite
Step-by-step explanation:
The graph is continuous, so it passes through infinitely many points.
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
Answer:
each takes 3 together 3x3=9
f is the function (x)-2x+5.
(a) Find (3)
(6) Express the inverse function f' in the form f'(x)-
g is the function g(x)-²-25.
(c) Find g(-3).
(d) (1) Find gfx)
r'(x)-
Give your answer as simply as possible.
(ii) Solve g(x)-0.
gf(x) -
(1)
8
e
(5)
The given functions can be solved using composition functions.
What is a composition function?Function composition is a mathematical procedure where two functions, f and g, are taken and a function, h = g f, is produced such that h(x) = g(f(x)). The function g is applied in this operation on the outcome of applying the function f to x.
function (x)-2x+5.
(a) f(3) = 2(3) + 5
= 11
(b) f'(x)
y = 2x + 5
y - 5 = 2x
x = y - 5 / 2
f'(x) = x - 5 / 2
g is the function g(x)-²-25.
(c) g(x)-²-25
g(-3) = (-3)² - 25
g(-3) = -16
(d) g(f(x)) = g(2x + 5)² - 25
= 4x² + 25 + 20x - 25
⇒ 4x² + 20x
r'(x) = 2x + 5
(ii) g(x) - 0
⇒ g(x)
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find the distance between the two points in simplest radical form. (1,-7) and (7,0)
Step-by-step explanation:
Answer:
The distance between the two given points is equal to √85.
Step-by-step explanation:
Let's recall what the distance formula is:
\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\math
d= (x 1 −x2 ) 2 +(y 1 −y 2) 2
We are defined our two points as:
(x₁, y₁) → (1, -7)
(x₂, y₂) → (7, 0)
We can rewrite this into our different "variables":
x₁ = 1
y₁ = -7
x₂ = 7
y₂ = 0
Now given our distance formula and our variables, we can find the distance between the two points:
\begin{gathered}\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}\end{gathered}
d= (1−7) 2+(7−0) 2= (−6) 2+(7) 2 = 36+49=\math 85
∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.
Hope this helps!
Use this information to find the value of b
c = 25
s = 9
b = 4c - s2
Answer:
Step-by-step explanation:
b=4c-s2
4(25)-9(2)
100-18=82
b=82
Which expression is equivalent to the given expression?
2n−6
A −2(n−3)
B 6−2n
C −4n
D 2(n−3)
Let f(x)=12x+7. Use algebra to find the inverse function f^-1(x).
Step-by-step explanation:
Replace x with y and y with x.
Then, try to isolate the y.
x=12y+7
x-7=12y
(x-7)/12=y
f^-1(x)=(x-7)/12
Kelsey made cupcakes to sell as a fundraiser for her trip to Washington DC.
She purchased one cupcake pan for $12. She calculated that the ingredients
cost her $0.25 per cupcake. She plans to sell the cupcakes for $0.75 each.
a. Write an equation that could be used to find the number of cupcakes
(x) she will need to sell to break even.
b. Solve the equation from part a. Explain how you know
is correct.
c. If she sold 184 cupcakes, what was her profit?
your answer
Answer:
a. 12= 0.50x
b. x=24 because if 0.5 times x is 12 then 12 *2 is x
c. 80$
Step-by-step explanation:
Its above.
given f(x) = 4x+1
evaluate f(2)
f(2) = ?
evaluate f(-3)
f(-3)= ?
The value of the functions are:
f(2) = 9
f(2) = -11
Use the concept of fucntion defined as:
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
The given function is,
f(x) = 4x+1
Put x = 2 in the given fucntion,
f(2) = 4(2) + 1
f(2) = 9
Put x = -3 in the given fucntion,
f(2) = 4(-3) + 1
f(2) = -11
Hence, The functions,
f(2) = 9
f(2) = -11
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12y + 48 - 4y= 8(y - 6)