Functions can be represented using equations and graphs Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
How to determine the key features?The domain of the function is defined as the set of the numbers we are allowed to put in the function while the range is the assumed data put in the function.
The functions are given as:
[tex]F(x)=e^{-x}\\\\\\g(x)=-\sqrt{x-4}[/tex]
Using a graphing calculator:
The domain of g(x) is [4, ∞)
The range of g(x) is [0, ∞)
The domain of f(x) is (–∞, ∞),
The range of f(x) is [0, ∞)
Both functions have positive values for their domains
By comparing the above highlights, the true statement between functions g(x) and f(x) is option 3
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Answer:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
I got it right on the test.
Find the equation of an ellipse satisfying the given conditions
If the value of a and e is 5 and 4, then the value of b is 3. Then the equation of the ellipse will be given below.
[tex]\rm \dfrac{x^2 }{25} +\dfrac{y^2}{9} = 1[/tex]
What is an ellipse?Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.
The vertices (±5,0) and foci (±4,0) are given. Then the equation of the ellipse will be
We know that the general equation of the ellipse will be
[tex]\rm \dfrac{x^2 }{a^2} +\dfrac{y^2}{b^2} = 1[/tex]
Then the value of a will be
a = 5
And the value of the eccentricity will be
e = 4/5
Then the value of the b will be
[tex]\rm b^2 = a^2 - a^2e^2\\\\b^2 = 5^2 - 5^2 \times \dfrac{4^2}{5^2}\\\\b^2 = 25 - 16\\\\b \ = 3\\[/tex]
Then the equation will be
[tex]\rm \dfrac{x^2 }{5^2} +\dfrac{y^2}{3^2} = 1\\\\\rm \dfrac{x^2 }{25} +\dfrac{y^2}{9} = 1[/tex]
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Subtract:
-6x-3 from 2x-5
Answer:
8x -2Step-by-step explanation:
Subtract:
-6x-3 from 2x-5
2x - 5 -(-6x - 3) =
2x - 5 + 6x + 3 =
8x -2
what does 5 times the quotient of 3 and a number look like
Answer:
5 times the quotient of 3 ----> 5*(x/3)
a number look like ------> 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, ....., 10000, ......, 10000000, ............
Does anyone loves math TvT
The solution to all parts are given below:
What is experiment?The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.
1. The experiment is to spin the wheel and get the number and related to that number reward will be there.
2. The outcomes will be,
{1, 2, 3, 4, 5, 6, 7, 8}
3. Sample space
{1, 2, 3, 4, 5, 6, 7, 8}
4. Event of red with even number
= 2 , 6
5. Event of red with odd number
= 3,7
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HELP ME PLEASE TELL ME THE ANSWER YALL
Answer:
I might be wrong but i thik its 1...
If im wrong ill give u 100 points
Step-by-step explanation:
Solve for x,
x = 10
x = 15
x = 8
x = 12
[tex]~~~~~~(8x-17)+(3x+2)+63 = 180\\\\\implies 11x +48=180\\\\\implies 11x = 180-48\\\\\implies 11x = 132\\\\\implies x= \dfrac{132}{11}\\\\\implies x= 12[/tex]
Answer:
x = 12.
Step-by-step explanation:
The sum of the 3 angles is 180, so:
8x - 17 + 3x + 2 + 63 = 180
11x -15 + 63 = 180
11x = 180 + 15 - 63
11x = 132
x = 132/11 = 12
A cone with a volume of 1152 pi m^3 has a radius of 12 m. Which of these statements is correct?
Answer:
The answer is b (the second option)
Step-by-step explanation:
can someone help me with this question
Answer:
Step-by-step explanation:
im pretty sure its 16 or 17,
Answer:
[tex]12+x+4=16+x[/tex]
Step-by-step explanation:
Find the length of x please
Answer:
42.29
Step-by-step explanation:
a^2+b^2=c^2
5^2+45^2=c^2
25+1764=c^2
1789 = c^2
sqrt 1789
= 42.29
What is the radius of this circle if the circumference is 18 (pie) cm? c= 18 (pie) cm 3 cm 9 cm 18 cm 36 cm
Answer:
9, if you round to 2 Decimal Places.
(C = 18π = 18 × π = 56.54 (2 DP))
r = C ÷ 2π
= 56.54 ÷ 2 × π ≈ 9
Marilyn has been notified that her health insurance premiums will increase by 18% next year. She currently pays $523.00/month for herself and her family. How much will her monthly payment be next year?__________________
Answer:
she will pay 614.14 because 523 + 18% = 6.14.14
Step-by-step explanation:
Hope this helps!!
y=3x^2+6x-9. Use the table function to see when the y value would be about 20.
Answer:
1311
Step-by-step explanation:
Write the counts for the rhythms shown below:
Answer:
1, 2 +, 3 | 1, +, + | 1 +, 2 +, +
1, 2, 3, 4 | 2, 3, 5, 6 | 1, 3, 4, 5, 6
Step-by-step explanation:
Jasper was testing H_0: \mu=36H
0
:μ=36H, start subscript, 0, end subscript, colon, mu, equals, 36 versus H_\text{a}: \mu\neq36H
a
:μ
=36H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 36 with a sample of 161616 observations. His test statistic was t=2. 4t=2. 4t, equals, 2, point, 4. Assume that the conditions for inference were met. What is the approximate P-value for Jasper's test?
Answer:
0.02<P-value<0.04
Step-by-step explanation:
solved in Khan Academy
a basket contains red, green, yellow apples. An apple is selected at random if p(red) is 2/5 P(yellow) is 1/4 what is p(green)?
A. 3/20
B. 7/20
C. 1/10
D. 13/20
The probability of getting the green apple is 7/20 option (B) 7/20 is correct.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
P(red) = 2/5
P(yellow) = 1/4
The sum of the probability of the event is 1.
P(red) + P(yellow) + P(green) = 1
2/5 + 1/4 + P(green) = 1
P(green) = 1 - (2/5 + 1/4)
P(green) = 7/20
Thus, the probability of getting the green apple is 7/20 option (B) 7/20 is correct.
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Use the method of symmetry to find the extreme value of each quadratic function and the value of x for which it occurs.
f(x)=(x-3)(x+8
a) x-intercepts are _________
b) midpoint of the x-intercepts is ___________
c) the extreme value is _______________
d) f(_) = ______________
Answer:
(a) (3, 0) and (-8, 0)
(b) (-2.5, 0)
(c) x = -2.5
(d) f(-2.5) = -30.25
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=(x-3)(x+8)[/tex]
Part (a)The x-intercepts are when [tex]f(x)=0[/tex]
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-3)(x+8)=0[/tex]
[tex]\implies (x-3)=0 \implies x=3[/tex]
[tex]\implies (x+8)=0 \implies x=-8[/tex]
Therefore, the x-intercepts are (3, 0) and (-8, 0)
Part (b)Midpoint between two points:
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad[/tex]
[tex]\textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
[tex]\implies \textsf{Midpoint of the x-intercepts}=\left(\dfrac{-8+3}{2},\dfrac{0+0}{2}\right)=\left(-2.5},0\right)[/tex]
Part (c)The extreme point of a quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]x=-\dfrac{b}{2a}[/tex]
Therefore, expand the function so that it is in standard form:
[tex]\implies f(x)=x^2+5x-24[/tex]
[tex]\implies a=1, b=5[/tex]
Therefore, the extreme value is:
[tex]\implies x=-\dfrac{5}{2}=-2.5[/tex]
Alternative method
A quadratic function has an extreme value at its vertex.
The x-value of the vertex is the midpoint of the x-intercepts.
Therefore, the extreme value is x = -2.5
Part (d)[tex]\begin{aligned}\implies f(-2.5) & =(-2.5-3)(-2.5+8)\\& = (-5.5)(5.5)\\& = -30.25\end{aligned}[/tex]
please help quick you need
Answer:
Box 2
Step-by-step explanation:
Box 1: 2x3x2=4x3=12
Box 2: 2x3x1=6x1=6
Box 3: 2x3x4=6x4=24
What is
(j^-13)(j^4)(j^6)
simplified?
PLS HELP
The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30°. Find the height of the tree.
•
A. 39.1 ft
•
B. 43.3 ft
•
C. 14.4 ft
•
D. 17.7 ft
Given
[tex] \text{Length of the tree= 25 feet} \\ \text{Angle of Elevation= 30°}[/tex]
To Find[tex] \text{Height Of The Tree}[/tex]
[tex] \text{Let The Height of the Tree be ‘x’}[/tex]
We Know:-
[tex] \tan\theta = \frac{ \text{perpendicular}}{ \text{base} }[/tex]
[tex] \tan \theta = \frac{ \text{height of the tree}}{ \text{length of the base}} \\ \\ \implies \tan30 = \frac{ \text{x}}{25} \\ \\ \implies \text{x }= 25 \times \tan30 \\ \\ \implies \text{x }= 25 \times 0.577 \\ \\ \implies \text{x} = 14.425 \\ \\ \implies \text{x} = 14.43[/tex]
[tex] \therefore \text{height of the tree(\text{x})} = \red{14.43 \: \text{feet}}[/tex]
Option C is the correct answer
Hope This Helps!!find the best price portfolio
Please help and explain will try to give the brainiest if two people answer. Really need your help
Question
The following sphere has a diameter of 18 cm.
Answer: A
Step-by-step explanation:
(-4s+9) + (4s-6) simplify
Step-by-step explanation:
[tex] = ( - 4s + 9) + (4s - 6)[/tex]
[tex] = - 4s + 9 + 4s - 6[/tex]
[tex] = - 4s + 4s +9 - 6[/tex]
Now subtract.....
[tex] = \boxed{\sf{3}}[/tex]
hence the answer is 3 ....
hope it helped !!!!
A biased coin is flipped twice.
The probability of the coin landing on tailsis 0.4. Find the probability the coin lands on tails exactly once.
Answer:
0.48.
Step-by-step explanation:
There are 2 ways that a tail lands once:-
Tail + head or
head + tail.
Prob(Tail on one throw) = 0.4
Prob(Head on one throw) = 1 - 0.4 = 0.6.
Prob(Tail first then head) = 0.4 * 0.6 = 0.24
Head then tail has the same probability (0.6*0.4).
So the requred probability = 0.24 + 0.24
= 0.48.
Use a table to find (−3+2j)(4j−7).
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression (−3+2j)(4j−7) is 8j²-26j+21.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression (−3+2j)(4j−7) can be expression is,
(−3+2j)(4j−7)
= -12j + 21 + 8j² -14j
= 8j² -26j +21
Hence, the value of the expression (−3+2j)(4j−7) is 8j²-26j+21.
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Mechanical energy is as much of potential and kinetic energy. Mechanical energy is never lost but only transformed from one form to another. As long as all the mechanical energy is as much as the potential energy then the kinetic energy is 0J. The mechanical energy of an object is found by summing its potential energy and kinetic energy.
Given the bag of marbles below, determine the probability of drawing blue, then green, then blue, then blue with replacement
Answer:
bule is in the spot of green in the sixth place of box 5
Step-by-step explanation:
Factor Completely x^4-2x^2y^2+y^4
100 Points pls help me and i will give the brainliest also pls if u can attach maybe some easier ways to solve problems like these...
[tex]\bf (x+y)^2(x-y)^2[/tex]
==============
Solving Steps:===============
[tex]\rightarrow \sf x^4-2x^2y^2+y^4[/tex]
breakdown
[tex]\rightarrow \sf x^4-x^2y^2-x^2y^2+y^4[/tex]
factor common term
[tex]\rightarrow \sf x^2(x^2-y^2)-y^2(x^2-y^2)[/tex]
collect in groups
[tex]\rightarrow \sf (x^2-y^2)(x^2-y^2)[/tex]
apply difference between two square method: x² - y² = (x+ y)(x-y)
[tex]\rightarrow \sf (x+y)(x-y) (x+y)(x-y)[/tex]
simplify
[tex]\rightarrow \sf (x+y)^2(x-y)^2[/tex]
what is the measure of x 100
Answer:
don't understand
what do u mean
Agroup of friends were working on a student film with a budget of $500, which they
spent on equipment and costumes, They spent $55 on costumes, What percent did
they spend on equipment?
Answer:
89%
Step-by-step explanation:
500-55=445
445/500=0.89
0.89x100=89
$500- $55= $445
445/500 = 89/100
89/100 × 100/1= 89%
Answer: 89%