5 - 2x >= 1 × 7
5 - 2x >= 7
-2x >= 7 - 5
-2x >= 2
x <= -1 sign changes when divided by negative number
If f ( x) = 4x
2 and g( x) = 5x , what is
g( f (2x)) ?
Answer: 40x
First, let's find f(2x)
[tex]f(2x)=4(2x)=8x[/tex]
Using this, let's find g(f(2x)):
[tex]g(f(2x))=g(8x)=5(8x)=40x[/tex]
That's the answer. Let me know if you need any clarifications, thanks!
Answer:
80x²
Step-by-step explanation:
f(x) = 4x², g(x) = 5x
f(2x) = 4(2x)² = 16x²
g(f(2x)) = 5(16x²) = 80x²
A candle burns at a constant rate of 2.5cm/h. The candle is 15cm tall when it is first lit. Let "t" represent the time is it burning in hours and let "h" represent the height of the candle in centimetres.
Answer:
The initial height of the candle is H = 15cm
The rate at which the candle burns is 2.5 cm per hour
Then after one hour, the height of the candle is:
h = 15cm - 2.5cm = 12.5cm
after two hours is:
h = 15cm - 2*2.5cm = 10cm
then, after t hours, the height of the candle is:
h = 15cm - (2.5cm/h)*t
now, the domain of h (or the range of the function) is:
h ∈ [0cm, 15cm]
when t = 0, h(0h) = 15cm
and the maximum value of t will be such that the candle is totally consumed:
h(t) = 0 = 15 - 2.5*t
t = 15/2.5 = 6
Then the domain of the function is:
t ∈ [0h, 6h]
In one U.S. city, the taxi cost is $3 plus $0.60 per mile. If you are traveling from the airport, there is an additional charge of $5.50 for tolls. How far can you travel from the airport by taxi for $26.50?
the airport by taxi for $26.50?
Answer:
30 milesStep-by-step explanation:
How far can you travel from the airport by taxi for $26.50 ?($26.5 - $3 - $5.50) : $0.6/m =
= $18 : 0.6$/m
= 30 miles
Determine the equation for a line perpendicular to y=1/3+4 and has an x-intercept of 2.
Answer:
y = -3x + 6
Step-by-step explanation:
Any line perpendicular to
y = (1/3)x + 4
has a slope of -1/(1/3) = -3
and equation
y = -3x + b .................(1)
If the line has an x intercept of 2 at (0,2), then
0 = -3(2) + b
solving
b = 6
By substituting b=6 into (1), the line required
y = -3x + 6
Answer:
y = -3x + 2
Step-by-step explanation:
y= [tex]\frac{1}{3}x +4[/tex]
Slope [tex]m_{1}=\frac{1}{3}[/tex]
slope of the perpendicular line [tex]m_{2}[/tex] = [tex]\frac{-1}{m_{1}}[/tex] = [tex]\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\[/tex]
b= 2
Slope intercept form of required line: y = mx + b
y = -3x + 2
Determine what type of model best fits the given situation:
A model rocket fired straight up from the ground, where h is the height of the rocket and t is the time in seconds.
Answer:
Ok, i will suppose the situation that:
The rocket has a constant speed S (So the acceleration of the rocket is equal in magnitude, but opposite in direction, to the gravitational acceleration)
Here we can remember that:
Velocity = distance/time.
Then if the distance is the height of the rocket, we can write this as:
H = velocity*time
h = S*t
This is a linear model that represents the height of the rocket as a function of time.
Case 2:
The rocket is fired with an initial velocity v0, but no acceleration:
In this case the only acceleration acting on the rocket is the gravitatonal acceleration pulling the rocket down, so the acceleration is:
a = -g
To get the velocity as a function of time, we should integrate:
a = -g*t + v0
To get the height as a function of time, we integrate again:
h(t) = (-g/2)*t^2 + v0*t + p0
Where p0 is the initial position of te rocket, but the rocket starts at the ground, so p0 = 0m.
The height as a function of time is:
h(t) = (-g/2)*t^2 + v0*t
This is a quadratic equation.
need help adding and subtracting functions
Answer:
Step-by-step explanation:
[x/2-2/1] × [2x^2 + x -3]
we can solve this very simply by multiplication
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Answer:
a. (True) Since ∠6 and ∠8 are vertical angles, they are congruent.
b. (False) ∠1 and ∠2 are supplementary but 65 + 125 ≠ 190.
c. True
d. True
e. True
Answer:
The answer is Freddy Kruger
Step-by-step explanation:
Elm Street, duh
choose one answer. please help i dont get it at all
Answer:
x < 6
Step-by-step explanation:
open circle < or >, closed circle ≤ or ≥
vertical stretch of the graph f(x)= x² by a factor of 5
PLEASE HELP!!
Answer:
f(x) = 5x^2
Step-by-step explanation:
A vertical stretch is in the y direction
y = Cf(x) C > 1 stretches it in the y-direction
f(x) = 5x^2
Find side AC and round your answer to the nearest hundredth, help please.
Answer:
Step-by-step explanation:
Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:
[tex]tan(70)=\frac{?}{3}[/tex] and
3tan(70) = ? so
? = 8.24
For every 2 males birds in a birdcage, there are 5 females. What is the ratio of
males to females? *
Answer:
2:5
Step-by-step explanation:
The structure of a ratio is x:y.
So all you have to do is place the former as the first digit and the latter as the second and separate them by a colon.
area perimeter for grade 4
Answer:
what is the questions.
solve for x, if a solution is extraneous identify in the final answer. thx :)
Answer:
x = 6 and x = 11.
Step-by-step explanation:
sqrt(x - 2) + 8 = x
sqrt(x - 2) = x - 8
(sqrt(x - 2))^2 = (x - 8)^2
x - 2 = x^2 - 16x + 64
x^2 - 16x + 64 = x - 2
x^2 - 17x + 66 = 0
We can use the discriminant to find whether there are solutions to the equation.
b^2 - 4ac; where a = 1, b = -17, and c = 66.
(-17)^2 - 4 * 1 * 66
= 289 - 264
= 25
Since the discriminant is positive, we know there are two valid solutions to the equation.
x^2 - 17x + 66 = 0
(x - 6)(x - 11) = 0
The solutions are when x - 6 = 0 and x - 11 = 0.
x - 6 = 0
x = 6
x - 11 = 0
x = 11
Hope this helps!
Answer:
x=11 solution
x=6 extraneous
Step-by-step explanation:
sqrt( x-2) + 8 = x
Subtract x from each side
sqrt(x-2) = x-8
Square each side
(sqrt(x-2))^2 = (x-8) ^2
x-2 = x^2 -8x-8x+64
x-2 = x^2 -16x+64
Subtract ( x-2) from each side
0 = x^2 -17x +66
Factor
0 = (x-6) ( x-11)
Using the zero product property
x=6 x=11
Checking the solutions
x=6
sqrt( 6-2) + 8 = 6
sqrt(4) +8 = 6
2 +8 = 6
False not a solution
x=11
sqrt( 11-2) + 8 = 11
sqrt(9) +8 =11
3 +8 = 11
solution
Please help with this inequalities problem attached below.
Answer:
1) A. 5 + 2.75 * S ≤ 21
2) 5
Step-by-step explanation:
Well there is an initial price of $5 and $2.75 per stop, and she can only spend less than or equal to $21 we can make the following inequality,
5 + 2.75 * S ≤ 21,
Meaning, Q.1 is A
Now #2 is 5 stops because if we plug in 5 for s we get 18.75.
Thus, the most amount of stops she can afford is 5.
Hope this helps :)
HELP ASAPPP ITS TIMED
Given that sin thata= 21/29, what is the value of cos thata, for 0°<thata<90°?
a- sqrt 20/29
b -20/29
c 20/20
d sqrt 20/29
Answer:
The value of cos theta for 0° < theta < 90° will be 20 / 29
Step-by-step explanation:
To solve this problem we can express three trig functions as ratios involving the sides of a right-angle triangle, the adjacent side, the opposite side and the hypotenuse. In this case sin θ = a / c, such that a = 21 and c = 29.
By Pythagorean Theorem,
[tex]b = \sqrt{c^2-a^2} = \sqrt{29^2-21^2} = \sqrt{841-441} = \sqrt{400} = 20[/tex]
Therefore cos θ = b / c = 20 / 29. This is the cosine ration of the adjacent side over the hypotenuse.
Your sister asks you to pick out one of her CDs to listen to. She has 6 rock, 4 country, and 4 rap CDs. If you pick one at random, what is the probability that you pick a country CD?
Hey there! I'm happy to help!
We have 6 rock, 4 country, and 4 rap CDs. If we add these all together ,we have 14 total CDs.
Since there are 4 country CDs, we have a 4/14 chance of picking one, which simplifies to 2/7 chance.
Have a wonderful day!
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
h(x) = -15.6(x - 3.8)² + 241
Step-by-step explanation:
if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.
or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)
the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.
Answer the problem below
Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
Answer:
4 z^3
Step-by-step explanation:
( 64 z^9) ^ 1/3
Rewriting 64 as 4^3
( 4^3 z^9) ^ 1/3
We know that ( ab) ^c = a^c * b^c
4^3 ^ 1/3 z^9 ^ 1/3
We know that a^ b^c = a^ ( b*c)
4^(3 * 1/3) z^ (9 * 1/3)
4 ^ ( 1) z^ ( 3)
4 z^3
Ama has a rectangular garden measuring 12m and 25m.He wants to divide it into square plots of equal sizes .What is the largest sized square he can use?
Given that StartFraction D F Over P R EndFraction = StartFraction F E Over R Q EndFraction = three-halves, what additional information is needed to prove △DEF ~ △PQR using the SSS similarity theorem?
Answer:
The additional information required to prove ΔDEF ~ ΔPQR is the value of the ratio DE/PQ which has to be equal to three-halves for ΔDEF to be similar to ΔPQR
Step-by-step explanation:
Given DF/PR = FE/RQ = 3/2
The Side Side Side, SSS, similarity theorem states that where there are two triangles that have corresponding sides that are proportional to each other, the two triangles are said to be similar
Given ΔDEF and ΔPQR, have sides DF/PR = FE/RQ, to prove that ΔDEF and ΔPQR, then the additional information required is the ratio of the third sides of the triangles which is DE/PQ.
If DE/PQ = Three-halves, the two triangles ΔDEF and ΔPQR are similar, if not, that is DE/PQ ≠ Three-halves, then the two triangles ΔDEF and ΔPQR are not similar.
Answer:
D: DE/PQ = 3/2
Step-by-step explanation:
Did it on edge 2020
what is the 6th term in the geometric sequence described by this explicit formula ?
Answer:
the answer is d. -5120
Step-by-step explanation:
[tex]a_{n} =-5(4)^{n-1}\\a_{6}=-5(4)^{6-1} \\a_{6}=-5(4)^{5} \\a_{6}=-5(1024)\\a_{6}=-5,120[/tex]
What the correct answer now fast
Answer:
y = 12.9
Step-by-step explanation:
To find the value of the side y, simply apply the law of cosines.
y^2 = (14)^2 + (9)^2 - 2(14)(9)cos(64)
y^2 = 196 + 81 - 110.47
y^2 = 166.53
y = 12.9
Therefore, your solution should be y = 12.9
Cheers.
Solve.
y=x - 7
5+2y=7
Answer:
[tex]\huge\boxed{x=8;\ y=1\to(8;\ 1)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}[/tex]
[tex]\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}[/tex]
Answer:
(8, 1).
Step-by-step explanation:
y = x - 7
5 + 2y = 7
5 + 2(y) = 7
5 + 2(x - 7) = 7
5 + 2x - 14 = 7
Subtract 5 from both sides
2x - 14 = 2
Add 14 to both sides
2x = 16
Divide both sides by 2
x = 8
Since x = 8...
y = x - 7
y = 8 - 7
y = 1.
To check our work...
5 + 2y = 7
5 + 2 * 1 = 7
5 + 2 = 7
7 = 7
Since it works out, your answer is (8, 1).
Hope this helps!
Classify the following expression by degree and term: x^3y + 5xyz A: 3rd degree trinomial B: 4th degree binomial C: 3rd degree binomial D: 5th degree binomial
Answer:
4th degree binomial
Step-by-step explanation:
x^3y + 5xyz
Add the exponents on each term
3+1 = 4 1+1+1 =3
The highest power is the degree, so it is a 4th degree
It also has 2 terms so it is a binomial
4th degree binomial
Answer:
B: 4th degree binomial
Step-by-step explanation:
I took the test flvs
An item is selling for $7,000. This item gets a discount and it is now $4,900. What percentage was the discount?
Answer:
30%Step-by-step explanation:
Discount =$7000-$4900
Discount% =
[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]
can someone help....
Answer:
-7 is no, -2 is no, 7 is no, and 10 is yes
Step-by-step explanation:
-5+9*(-7)>58
-5+-63>58
-68>58
-5+9*(-2)>58
-5+-18>58
-23>58
-5+9*(7)>58
-5+63>58
58>58
-5+9*(10)>58
-5+90>58
85>58
so the only one that is a solution is v=10, hope this helps
Answer: No, No, No, Yes
Step-by-step explanation:
Solve the equation for "v":
-5 + 9v > 58
9v > 63
v > 7
Check the options to see if they make a true statement:
-7 > 7 False
-2 > 7 False
7 > 7 False
10 > 7 TRUE!
how do i find x?
is the formula
"the sum of exterior angles=360°" false for concaved polygons?
Answer:
To find x you need to divide polygon into trianglesThe formula : "the sum of exterior angles=360°" is false for concaved polygonsStep-by-step explanation:
α = 180° - 135° = 45°
β = 180° - 120° = 60°
γ = 180° - 60° = 120°
δ = 180° - x
ε = 180° - 80° = 100°
If we divide the pentagon into five triangles then:
5•180° = α + β + γ + δ + ε + 4x
900° = 45° + 60° + 120° + x + 100° + 4x
900° = 325° + 5x
5x = 575°
x = 115°
60° + 120° + 135° + 80° + 115° = 510° ≠ 360°
Paul has four paper strips of the same length. He glues two of them together with a 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30 cm long strip with the other two strips. How long should the overlap be?
Answer:
10 cm overlap required to make a 30 cm long strip.
Step-by-step explanation:
Given:
Four paper strips of the same length.
Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.
To find:
Overlap required to make a strip which is 30 cm long = ?
Solution:
First of all, let us understand the concept of overlap.
Please refer to the attached image.
Let length of each strip be [tex]x[/tex] cm.
Given that there is 4 cm overlap resulting in new strip of length 36 cm.
The overlapping length is counted only once as clear from the figure attached.
So, Let us try to find the equation:
[tex]x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm[/tex]
i.e. each strip length is 20 cm.
Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.
The equation will be:
[tex](20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm[/tex]
Brandon mows his lawn once every 4 days. Thomas mows his lawn once every 8 days. Celena mows her lawn once every 6 days. If they are all mowing the lawn today, in how many days will they be mowing their lawns together again? A. 72 B. 24 C. 18 D. 12
Answer: B
Step-by-step explanation:
4,8 and 6 all go into 24
which of the following is the Pythagorean theorem
Answer:
[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
The Pythagorean Theorem is used to find a missing side length in a right triangle, and the formula [tex]a^2+b^2=c^2[/tex] is used to find the missing side, assuming a and b are legs, while c is the hypotenuse.
Answer:
in a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length