The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)
Given the functions f(x)=x+7 and f(x)=[tex]x^{2}[/tex]
To know when to exceed, need to equate both functions.
⇒[tex]x^{2} =x+7[/tex]
⇒[tex]x^{2} -x-7=0[/tex]
x=[tex]\frac{-b+\sqrt{D} }{2a}[/tex] and [tex]\frac{-b-\sqrt{D} }{2a}[/tex]
⇒x=[tex]\frac{1-\sqrt{29} }{2}[/tex],[tex]\frac{1+\sqrt{29} }{2}[/tex]
f(x)=[tex]x^{2}[/tex] decreases from -∞ to 0 and increases from 0 to ∞ it cuts the graph of x+7 two times and for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞) f(x)=[tex]x^{2}[/tex] is greater than f(x)=x+7
Therefore,The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)
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A person is 2 meters tall casts a shadow 6 meters long. At the same time, a flagpole casts a shadow 24 meters long. How tall is the
flagpole?
2m
бm
24m
Answer:
8 meters
Step-by-step explanation:
Given that:
Height of person = 2metres
Length of person's shadow = 6 meters
Height of flagpole =?
Length of flagpole shadow = 24 meters
Height of person = length of person's shadow
Height of flagpole = length of person's shadow
2 = 6
x = 24
Cross multiply
6x = 48
x = 48 / 6
x = 8 meters
if f(x)=4x−1 find f(4)
Answer:
f(x)=4x-1
substitute x=4
f(4)=4×4-1
f(4)=15
A concession stand sold Takis for $3 each and drinks for $2 each and made $370. The total Takis sold was 20 more than the drinks. How many
bags of Takis were sold?
Answer:
102 Takis sold
Step-by-step explanation:
x = # drinks sold
y = $ Takis sold
System of Equations:
x = y - 20
3x + 2y = 370
Use substitution method to solve.
A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according
to the formula r(t) = 5t + 2, express the area A burned as a function of time, t (minutes).
The area A burned as a function of time, t is
A(t)=78.5t²+62.8t+12.56
What is Radius of the circle?A circle's or sphere's radius is any of the line segments that connect the object's center to its perimeter; in more recent usage, it is also their length.
According to the given values ;
r(t)=5t+2
.°. A(t)=πr²=π*(5t+2)²
=π(25t²+20t+4)
= 78.5t²+62.8t+12.56
hence ,the area A burned as a function of time, t is
A(t)=78.5t²+62.8t+12.56
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I'll give brainliest
Answer:
C=√4^2+100^2=100.08
The answer to a division problem is the __________.
dividend
quotient
divisor
remainder
Please answer correctly !!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answer:
you would need to use 2 differant types of tools the first one to measure the air pressure whitch would be a barometer and the second tool would be a thermometer.
help me someone!!pls
Answer:
lower right
Step-by-step explanation:
The lower quartile is located at the left side of the box
The upper quartile is located at the right side of the box
The lower quartile 24 and upper quartile 42
are positioned correctly on the lower right box plot
Please i need help ASAP!!! Extra points!!
The cost of 3-D movie tickets is $12 for 1 ticket,$24 for 2 tickets, and $36 for 3 tickets. Determine whether the cost is proportional to the number of tickets by graphing on the coordinate plane.Explain your reasoning.
Answer:
yes the cost is proportional to the number of tickets
Step-by-step explanation:
for each 1 ticket added, it is $12 more
you can graph it by using the equation y=12x where x is the amount of tickets and the y-intercept is (0,0)
should be simple work!!!
Answer:
Lier, if it was simple then do. Just ban me already
Step-by-step explanation:
The FitnessGram Pacer test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter Pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal *boop*.
If you made 3 lawns and made 25.50 how much per lawn
Answer:
76.5
Step-by-step explanation:
25.50 x 3 = 76.5
Answer:
$8.50
Step-by-step explanation:
put 25.50/3 and you get 8.50
An 8-pint jug of water costs $5.76. What is the price per cup?
$
Answer:
1.38888888889
If m2 = 9x + 7 and m3 = 5x + 5, what is m1?
Answer:
B
Step-by-step explanation:
∠ 2 and ∠ 3 are a linear pair and sum to 180°
∠ 2 + ∠ 3 = 180 , that is
9x + 7 + 5x + 5 = 180
14x + 12 = 180 ( subtract 12 from both sides )
14x = 168 ( divide both sides by 14 )
x = 12
Then
∠ 3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65°
∠ 3 and ∠ 1 are vertically opposite angles and are congruent , so
∠ 1 = 65°
please please help!!!! this is my last question! thank you!!!
Answer:
B) 5
Step-by-step explanation:
Divide the volume by the formula and you get that 1000=r^3. r is 10, but every second it gains 2 cm, so divide 10 by 2 to get 5
help! I only have a certain amount of time.... easy points! The sum of 3 times a number and 4 is 13. Find the number.
Answer:
The number is 3
Step-by-step explanation:
Ok, first thing's first: we need to make the words into an actual equation.
since it just says a number I'll use x
3 times x + 4 = 13
3x +4 =13
Now that we have our equation, we can solve for x
3x + 4 = 13
-4 -4
3x = 9
I subtracted 4 on both sides to get rid of the 4 and move it to the other side of the equation, so we can try to get x by itself.
3x =9
/3 /3
x = 3
I divided both sides by 3 to get rid of the 3 that's being multiplied by x
Now we have our number : x = 3
I hope this helps :)
pls helppp
math work
bleh
Answer:
Yes
Step-by-step explanation:
The solved equation will be n<-1
-11 is less than -1 so that will be answer
In the square pyramid below, line segment AB is parallel to line segment ___.
Answer: segment CD
Step-by-step explanation:
if in a drug-study to test the effectiveness of a new drug for treating the common cold, you are randomly assigned to a group that gets the drug, this would mean that you
This means that you are in the experiment group
It is common to choose a group of people to study the effect of certain things like the one given in this question. The selection of people is done after designing the sample size for a certain population. The design varies depending on whether the analysis is qualitative or quantitative.
The people who lie in the sample size actually contribute to the experiment are said to be part of it.
Therefore, if you are part of the study that is used to test the effectiveness of a new drug for treating the common cold. It means you are part of the experiment group.
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PLEASE DOMEONE HEP ME FIND X ILL GIVE YOU BRAINLIEST
Answer:
4
Step-by-step explanation:
if one pound of ground beef costs $5 then how much would a 1/2 pound costs
It would cost 2 dollars and 50 cents
Simplify it I will give brainlessly
Answer:
1+3+2+2=8
Step-by-step explanation:
Answer:
1/3+3+4(1/2)+2/3 = ♥♥♥♥6♥♥♥♥
Step-by-step explanation:
Sam used the identity [tex](a+b)^{2}[/tex] to solve [tex]103^{2}[/tex].
the steps he used are listed below.
Step 1 :[tex](100+3)^2\\[/tex]
Step 2 : [tex](100)^2 + 3^2[/tex]
Step 3 : 10,000 +9
Step 4 : 10,009
In which step did he go wrong?
a)Step 1
b)Step 2
c)Step 3
d)Step 4
Answer:
Step 2
Step-by-step explanation:
(100 + 3)² = 100² + 2 x 100 x 3 + 3²
This is by the law of squares
(a + b)² = a² + 2ab + b²
A salesman sells an item for $125. He gets a 20% commission. How
much money did he make?
Answer:$25
Step-by-step explanation:
20% of 125 is $25 dollars so his commission would be $25
Answer:
25 dollars
Step-by-step explanation:
125/100=1.25
multiply by 20
1.25*20=
25 dollars
He does not get the money for the item because the person is a salesman
Brainliest Please
Jim's science class is making slime from cornstarch and glue. Jim is helping pass out materials. He gives each student 80 grams of cornstarch from a 2-kilogram bucket. If Jim's class has a total of 21 students, how many grams of cornstarch will he have left?
The total amount of corn starch left is 320 grams.
How to find the grams of corn starch left?He gives each student 80 grams of corn starch from a 2-kilogram bucket.
Each students collected 80 grams of corn starch.
Therefore,
1 student = 80 grams of corn starch
His class has a total of 21 students.
Therefore,
total mass of corn starch distributed = 21 × 80
total mass of corn starch distributed = 1680 grams
The corn starch from the bucket = 2 kg
1kg = 1000 g
2kg = 2000g
Hence,
The corn starch from the bucket = 2000 grams
Finally,
amount in grams of corn starch left = 2000 - 1680
amount in grams of corn starch left = 320 grams.
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Can someone help me out with this inequality problem?? Will give brainliest to best answer!!
Answer:
250x + 525y ≤ 7800
no, 15 refrigerators and 8 pianos will not fit on the truck
Step-by-step explanation:
we know that x is the refrigerators and each one is 250 lbs
this can be written as 250x
we know that y is the pianos and each one is 525 lbs
this can be written as 525y
we also know that "no more than" is the same that as less than equal to
so this can be written as ≤
we can also say that the refrigerators and pianos has to be ≤ 7800
so now we have: 250x + 525y ≤ 7800
plug in 15 to x and 8 to y
250(15) + 525(8) ≤ 7800
3750 + 4200 ≤ 7800
7950 ≤ 7800
this statement is not true so no, 15 refrigerators and 8 pianos will not fit on the truck
the adams family and the green family each used their sprinklers last summer. the water output rate for the adams family's sprinkler was per hour. the water output rate for the green family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?
The duration of the sprinkler used by each families are-
Adams family: 25 hoursGreen family: 30 hoursWhat is linear equation in two variables?Linear equations in two variables are equations with one, none, and infinitely many solutions where each of the two variables has the highest exponent order of 1.
A two-variable linear equation has the standard form ax + by + c = 0, where x and y are the variables. The solutions could also be composed in pairs, such as (x, y).Now, as per the given question;
Let the total time taken by Green family is 'x'.
Let the total time taken by Adams family is 'y'
The total time for which the sprinkler are used is 55 hours.
Thus, x + y = 55 (equation 1)
The water output rate for the Green family's sprinkler was 30 L per hour.
The water output rate for the Adams family's sprinkler was 20 L per hour.
The total output of the water is 1400 L.
Then,
30x + 20y = 1400 (equation 2)
Substitute the value of x from equation 1 in equation 2.
30(55 - y) + 20y = 1400
Dividing whole equation by 10.
3(55 - y) + 2y = 140
Solving the equation.
165 - 3y + 2y = 140
y = 165 - 140
y = 25 hours. (Time for which Adams family used the sprinklers)
Put value of y in equation 1 to find x.
x = 55 - y
x = 55 - 25
x = 30 hours. (Time for which Green family used the sprinklers)
Therefore, the time for which both of the families used the sprinklers is estimated.
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The complete question is-
The Green family and the Adams family each used their sprinklers last summer. The water output rate for the Green family's sprinkler was 30 L per hour. The water output rate for the Adams family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1400 L. How long was each sprinkler used?
Archie and three friends go on holiday together for a week. The costs of the holiday will be shared equally between the 4 friends.
These are:
£1360 for 4 return plane tickets
£850 for the accommodation
£210 for the car hire for a week
How much does Archie have to pay for his share of the costs? £605
The amount Archie has to pay for his share of the cost is £605
How to find the amount Archie have to pay for his share of the cost?The costs of the holiday will be shared equally between the 4 friends.
These are:
£1360 for 4 return plane tickets£850 for the accommodation£210 for the car hire for a weekThe 4 of them will share the total cost equally. This means Archie paid the same amount with his friends.
Therefore, the amount Archie have to pay for his share of the costs can be calculated as follows:
total cost = 1360 + 850 + 210
total cost = £2420
Amount Archie paid = 2420 / 4
Amount Archie paid = £605
Therefore, the amount Archie has to pay for his share of the cost is £605
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John has $190 in his savings account. He earns 10% in interest per year.
What will John’s saving account balance be at the end of the year?
Answer:
1,900
Step-by-step explanation:
Which point is not in plane M.
X
P
Y
N
Answer:
i think y is correct
hope this helps
PLS SOLVE I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Answer:
y = -1.50x + -3
---------------------------------------------
Step 1: Calculating Slope (m).
m = y2-y1/x2-x1
m = 3-0/-4--2
m = 3/-2
m = -1.50
Now putting value of m in equation (i)
y = -1.50x + b
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (-2,0) for calculating y-intercept:
y = mx + b
0 = -1.50(-2) + b
0 = 3 + b
-3 = b
b = -3
Now putting value of b in equation
y = -1.50x + -3