Answers
Answer:
[tex]f(x)=2(2)^{0.5x}-3[/tex]
Step-by-step explanation:
Parent function:
[tex]g(x)=2^x[/tex]
Properties of the given parent function:
y-intercept at (0, 1)horizontal asymptote at y = 0As x → -∞, y → 0As x → ∞, y → ∞Given form of function f(x):
[tex]f(x)=a(b)^{kx}+c[/tex]
If the parent function is [tex]g(x)=2^x[/tex] then b = 2:
[tex]\implies f(x)=a(2)^{kx}+c[/tex]
From inspection of the graphed function f(x):
y-intercept at (0, -1)horizontal asymptote at y = -3Therefore, the y-intercept has shifted 2 units down, yet the asymptote has shifted 3 units down. This implies that there has been a vertical shift of 3 units down and a vertical stretch.
The vertical shift is denoted by the variable "c" so c = -3:
[tex]\implies f(x)=a(2)^{kx}-3[/tex]
The vertical stretch is denoted by the variable "a". To find value of a, substitute the point of the y-intercept into the equation:
[tex]\begin{aligned}f(0) & = -1\\\implies a(2)^{k \times 0}-3 & =-1\\a-3 & = -1\\a-3+3 & = -1+3\\a & = 2\end{aligned}[/tex]
Therefore, as a = 2:
[tex]\implies f(x)=2(2)^{kx}-3[/tex]
From inspection of the given graph, the curve passes through point (4, 5). Substitute this point into the equation to find the value of k:
[tex]\begin{aligned}f(4) & = 5\\\implies 2(2)^{4k}-3 & =5\\2(2)^{4k}& =8\\(2)^{4k}& =4\\(2)^{4k}& =2^2\\4k & = 2\\k & = 0.5\end{aligned}[/tex]
Therefore, the equation of the function f(x) is:
[tex]\implies f(x)=2(2)^{0.5x}-3[/tex]
Related Questions
25) lan bikes 18 mph for 15 miles. Which is true? a. lan rode exactly 1 hour b. lan rode more than 1 hour C. lan rode less than 1 hour
Answers
Answer:
C. Ian rode less than 1 hour
Step-by-step explanation:
It never hurts to think about what the problem statement is telling you. Ian rode at a speed that would take him 18 miles in 1 hour.
InterpretationClearly, Ian would pass the 15-mile mark in a 1-hour ride before an hour had elapsed. If he only rode 15 miles, he rode less than 1 hour.
The actual time Ian rode is given by the relation between speed, time, and distance.
time = distance/speed
time = (15 mi)/(18 mi/h) = (15/18) h = 5/6 h
Ian's riding time was 5/6 of an hour, which is less than 1 hour.
A (not necessarily convex) 11-sided polygon can have at most how many reflex interior angles?
Answers
The value for each interior angle in the polygon will be 147.27°.
How to calculate the interior angles?The total angles in the 11 sided polygon will be:
= (n - 2) × 180
= (11 - 2) × 180
= 9 × 180°
= 1620°
Each angle will be:
= 1620°/11
= 147.27°
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On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4).
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.
x =
y =
Answers
The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 is; (-2.6, 5.2)
How to find coordinate points?
The coordinate of the points are given as:
A(-4, 8)
B(2, -4)
Ratio of partition is given as; 3:10
Now, the point at the given ratio is calculated from the formula;
C = [(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]
Thus;
C = [(3*2 + 10*-4)/(3 + 10)], [(3*-4 + 10*8)/(3 + 2)]
C = (-34/13, 68/13)
C = (-2.6, 5.2)
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Answer:
-2.6, 5.2
Step-by-step explanation:
It’s is already stated on the picture.
Answers
Answer:
radius = 5
Step-by-step explanation:
Since the line is a tangent, that means the PT and OP are perpendicular (they make a right angle) Sooo, the triangle is a right triangle. Use Pythagorean Theorem to calculate or Pythagorean Triples for a shortcut (5, 12, 13)
r^2 + 12^2 = 13^2
r^2 + 144 = 169
Subtract 144
r^2 = 25
Squareroot both sides.
sqrt(r^2) = sqrt25
r = 5
The radius is 5.
I need help plsssssssss
Answers
For the given system of equation, the value of x = 4 and the value of y = -1
Solving simultaneous equationsFrom the question, we are to solve the given system of equations
-7x + 4y = -32 -------- (1)
9x - 2y = 38 -------- (2)
From equation (2)
9x - 2y = 38
2y = 9x - 38
y = 4.5x - 19 -------- (3)
Substitute this into equation (1)
-7x + 4y = -32
-7x + 4(4.5x -19) = -32
-7x + 18x - 76 = -32
-7x + 18x = -32 + 76
11x = 44
x = 44/11
x = 4
Substitute the value of x into equation (3)
y = 4.5x - 19
y = 4.5(4) - 19
y = 18 - 19
y = -1
Hence, the value of x = 4 and the value of y = -1
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Which answer choice gives the correct surface area for a triangular prism
with bases that are 4 cm² and sides that are 4 cm²?
Answers
Answer:
The answer is 20
Step-by-step explanation:
Their are two bases and three sides in a triangular prism so the total surface area is 20
(Look at picture, not this) 4. Use the following equation to perform the operations below: y = (²+5 ÷ (2+3)(2-2))-21/2₂2 4. Use the following equation to perform the operations below : y = ( ² + 5 ÷ ( 2 + 3 ) ( 2-2 ) ) - 21 / 2₂2
Thank you!
Answers
The solutions when y = 0 are x = -4.796 and x = 4.796
The graph of the functionThe function is given as:
[tex]y = (\frac{x + 5}{x + 1} \div \frac{(x + 3)(x - 2)}{(x -4)(x + 1)})- \frac{1}{x - 2}[/tex]
See attachment for the graph of the function
The vertical asymptoteWhen the function is simplified, we have:
(x +3)(x -2) at the denominator of one of the terms
Set this factor to 0
(x +3)(x -2) = 0
Expand
x + 3 = 0 and x -2 = 0
Solve for x
x = -3 and x = 2
Hence, the vertical asymptotes are x = -3 and x = 2
The feature at x = -1The feature at x = -1 is a hole and, not a vertical asymptote.
This is so because the absolute value of -1 is less than the absolute values of the vertical asymptotes at x = -3 and x = 2
The solution when y = 0From the attached graph, we have:
x = -4.796 and x = 4.796 when y = 0
Hence, the solutions when y = 0 are x = -4.796 and x = 4.796
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3. how would you use concrete objects to represent and solve the following problem: what is 30% of $60?
Answers
Answer:
adding
Step-by-step explanation:
determine the graph of the polar equation 9/1-3sin theta
Answers
Answer: can you show us the graph?
Step-by-step explanation:
Which of the following ordered pairs is a possible solution to the equation y = -2/3x - 4
Answers
The ordered pair that is the possible solution for the equation is (-6,0) (0,-4).
What is the Slope-intercept form of a linear equation?
The slope-intercept form of a linear equation takes the form y= mx + b.
Here:
Slope = mb = y-interceptThe function f(x) = y = [tex]\mathbf{-\dfrac{2}{3}x-4}[/tex]
[tex]\mathbf{y = -\dfrac{2}{3}x-4}[/tex]
The slope (m) = -2/3
The x-intercept is the value of x for which y = 0
x-intercept = (-6,0)The y-intercept is the value of y for which x = 0
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Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively.
(a) Express the position vector of p and q.
i. In terms of p and q.
ii. In terms of i, j and k
(b) Hence state the coordinates of R.
Answers
(a) i. See comment...
(a) ii. We have
[tex]\vec p = 6\,\vec\imath - 3\,\vec\jmath + 9\,\vec k[/tex]
and
[tex]\vec q = 3\,\vec\imath - 6\,\vec\jmath - 3\,\vec k[/tex]
(b) We can parameterize the line segment from P to Q by the vector function
[tex]\vec r(t) = (1-t) \vec p + t \vec q = (6-3t) \, \vec\imath + (-3-3t) \,\vec\jmath + (9-6t) \,\vec k[/tex]
with [tex]0\le t\le1[/tex]. The point R is located 1/3 of the way along this line segment, i.e. at [tex]t=\frac13[/tex], so its position vector is
[tex]\vec r\left(\dfrac13\right) = 5\,\vec\imath -4\,\vec\jmath + 7\,\vec k[/tex]
and hence its coordinates are [tex]\boxed{(5,-4,7)}[/tex].
can you please solve 2x+29+3x - 4
Answers
Answer:
5x + 25
Step-by-step explanation:
2x+29+3x+4
Step 1: Arrange it:- 2x+3x+29-4
Step 2:- Add and Subtract the terms:- 5x + 25
HOPE IT HELPS!
Hey there!
EQUATION:
2x + 29 + 3x - 4
COMBINE the LIKE TERMS
(2x + 3x) + (29 - 4)
2x + 3x + 29 - 4
SIMPLIFY IT!
5x + 25
Therefore, your answer should be:
5x + 25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
This is a linear equations question so pls help me I’m dying of stress thank you! ^^
Answers
Answer:
the answer to this problem is D:(-2,4)(1,1)
Answer:
B
Step-by-step explanation:
y = x² → (1)
y = 3x - 2 → (2)
substitute y = x² into (2)
x² = 3x - 2 ← subtract 3x - 2 from both sides
x² - 3x + 2 = 0 ← in standard form
(x - 1)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
substitute these values into (2) for corresponding values of y
x = 1 : y = 3(1) - 2 = 3 - 2 = 1 ⇒ (1, 1 )
x = 2 : y = 3(2) - 2 = 6 - 2 = 4 ⇒ (2, 4 )
please help me im stuck here U_U
Answers
Using the inverse function concept, the table that represents the inverse of the table given is table a.
How to find the inverse of a function of pairs (x,y)?The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.
In the table given, we have points (0,0), (2,1) and (4,2), hence the inverse table has points (0,0), (1,2) and (2,4), which is table a.
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One-third of the class grew peas, one-third grew carrots, and one-third grew beans. The class consisted of 63 students of which five-sevenths were girls. The teacher chose the three groups to be as equal in their boy-girl composition as possible. How many boys and girls were assigned to each team?
Answers
The number of boys and girls assigned to each team is 6 and 15 respectively.
FractionNumber of students in class = 63 Number of students who grows peas = 1/3 × 63= 63/3
= 21 students
Number of students who grows carrots = 21Number of students who grows beans = 21Number of girls = 5/7 × 63
= 315/7
Number of girls = 45 students
Number of boys = 63 - 45 = 18 students
If the three groups have equal composition of boys and girls, then,
Number of boys and girls in each group is 6 and 15 respectively.
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Solve for m. 10m = 1
m = 0
m = 1
m = 2
m = 3
Answers
Answer:
wouldn't it be 0.1
Step-by-step explanation:
If geometry symbol represented as small triangle with three sides. abc geometry congruent symbol represented as two small horizontal parallel lines and a horizontal symbol s. geometry symbol represented as small triangle with three sides. dec, what is the value of x?
Answers
The value of x in the congruent triangles abc and dec is 1
How to determine the value x?The question implies that the triangles abc and dec are congruent triangles.
The congruent sides are:
ab = de
bc = ce = 4
ac = cd = 5
The congruent side ab = de implies that:
4x - 1 = x + 2
Collect like terms
4x - x = 2 + 1
Evaluate the like terms
3x = 3
Divide through by 3
x = 1
Hence, the value of x is 1
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Complete question
Two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is 4x - 1, side bc is 4, side ac is 5. in triangle cde, side cd is 5, side de is x + 2, side ce is 4. If Δabc ≅ Δdec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
g Minimizing the sum of the squared deviations around the line is called: predictor regression. mean squared error technique. least squares estimation. double smoothing. mean absolute deviation.
Answers
Minimizing the sum of the squared deviations around the line is called Least square estimation.
It is given that the sum of squares is around the line.
Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.
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X
-3
-2
Intro
-1
0
1
2
3
f(x)
-15
0
3
0
-3
O
15
Predict which statements are true about the intervals of
the continuous function. Check all that apply.
Of(x) > 0 over the interval (-3).
Of(x) ≤0 over the interval [0, 2].
Of(x) <0 over the interval (-1, 1).
Of(x) > 0 over the interval (-2, 0).
f(x) ≥ 0 over the interval [2, ..).
Done
Answers
Answer: B, D, E
Step-by-step explanation:
Statement 1 cannot be true because f(1)<0.
Statement 2 might be true.
Statement 3 cannot be true because if f is continuous, then for some value between -1 and 0, f(x) is positive by the Intermediate Value Theorem.
Statement 4 might be true.
Statement 5 might be true
Is this right or wrong
Answers
Answer:
∠C and ∠F are right angles
Step-by-step explanation:
To prove that two triangles are congruent using HL, one must have:
a right angle congruent,a leg congruent, and the hypotenuse (the side across from the right angle) congruent.For this problem, there are two sides of the triangle already congruent: one could be the hypotenuse (if the right angle were across from it), and the other congruent side could be a leg. So, if we can prove either that angles C & F are right angles, or that angles A & D are right angles, that would be enough to use HL congruence.
Hence, from the answer choices provided, proving that angle C and angle F are both right angles would be sufficient to prove the triangles are congruent via HL congruence.
Side note: Proving angles B and E would not be enough to use HL congruence, because the hypotenuse is always across from the right angle. So, if angle B were a right angle, it would mean that side AC was the hypotenuse (which hadn't yet been proven or stated to be congruent).
While not enough to prove triangle congruence via HL, if angle B and E were congruent at all (right angles or not), it would be enough to prove that the triangles were congruent by SAS (side-angle-side) because it would have proven that two sides and the included angle were congruent.
IN
A graph of two functions is shown below:
g(x)
f(x)
Ox=1
Which of the following is an approximate solution for f(x) = g(x)?
Ox=-1
Ox=-4
Ox=2
62.5
45
37.5
30
225
15
-15
225-
-30
Answers
Hello,
Answer: We have f(x) = g(x) when x ≈ 1
(a) x = 1, is an approximate solution for f(x) = g(x).
Here, we have,
given that,
A graph of two functions is shown
f(x) and, g(x)
now, we have,
The graph has two functions, which are f(x) and g(x) and a graph.
In the graph, we can follow their intersections.
Those would be the parts of the line that would make the functions to have the same value.
The first intersection is really close to 1,
and second is very unclear, most likely beyond -2.5.
Since the highest number is 1 and the intersection is very close to 1,
we have to go with the approximate answer.
We have f(x) = g(x) when x ≈ 1.
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when x equals 12 , x+3y=21 need help
Answers
Answer:
y=3
Step-by-step explanation:
Can someone help me out with this geometry problems? And explain how u got the answers, it’s urgent
Answers
Answer:
Step-by-step explanation:
In part b, you used a combination of geogebra tools and manual calculations to find the approximate area of the original polygon. now try using the more advanced area tools in geogebra to verify your answer in part b. which method did you choose? do your results in parts b and c match?
Answers
Absolutely, over result will match in part b and c
Geogebra tools are software which is used to study an absolute geometry with zero errors.
Since, Geogebra contains various tools, In part b we have drawn a square through polygon command. Its allows to select the number of sides, so we select 4 cause square requires 4 equal sides.
Now, we very it in c part just by drawing a 4 connected lines which have 90° adjacent angles.
Here, by comparing their geometry it seems identical
Thus, the result, in part b and c matches for each other.
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What is the slope of the graphs and the equation?
Answers
Answer:
The slope formula is used to find the slope of a line that joins two points (x₁, y₁) and (x₂, y₂). Using this formula, the slope of the line is, m = (y₂ - y₁) / (x₂ - x₁). We can use the same formula to find the slope of a line from its graph also.
50 more points
sdadadada
Answers
Switch the variable x and y with each other. Then the correct option is B.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = 3x – 10
Then the inverse function of the f(x) will be
Put y in place of f(x).
x = 3y – 10
3y = x + 10
y = (x + 10) / 3
Switch the variable x and y with each other.
Then the correct option is B.
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Dalinda spins a spinner 60 times. the table shows her data.
spinner
results
color spins
red
10
blue
30
yellow
15
green
5
dalinda will spin one more time,
based on her data, what is the probability that the pointer will land on blue?
od. 110
o e
10 a 1
o b. 1 / 3
o c. 1 /
Answers
The answer is 1/2 .
What is probability ?The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes. The chance that a given event will occur. The number of ways of achieving success. the total number of possible outcomes.In given question ,
Dalinda spins a spinner = 60 times.
blue = 30
The probability that the pointer will land on blue = 30 / 60 ⇒ 1/2
Therefore, the answer is 1/2 .
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TODAY, Kyle has 11 pounds to lose to get to his goal weight. Tuesday he was 196 lbs. TODAY, he is down 3 lbs.
What is Kyle’s weight today?
What is Kyle’s goal weight?
Answers
Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER?
Answers
Answer:
66 dollars
Step-by-step explanation:
15+6=22
15×2=30
15+22+30=66
Answer:
Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER is 66 dollars.
Step-by-step explanation:
→ Is know :
Tim's money = 15 dolars Paul's money = 15 dolars + 6 dollarsRick's money = 2 × 15 dolars→ Asked :
How much did they have ALTOGETHER ?
→ Solution :
[tex] \bf{x =Tim's \: \: money + Paul's \: \: money + Rick's \: \: money }[/tex]
[tex]\bf{x =15 + (15 + 6) + (2 \times 15) }[/tex]
[tex]\bf{x =15 + 21 + 30 }[/tex]
[tex]\bf{x =36 + 30 }[/tex]
[tex]\bf{x =66 \: \: dollars }[/tex]
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help me please!!! 50 points
Answers
I am unfortunately not too sure about this, I have not heard of a proportional equation before even after getting my degree, because an equation usually isn't proportional, only expressions are and there are usually 2 terms.
Here's my best attempt. The first equation isn't proportional since y is inversely proportional to the 7 in the denominator. The second is proportional, and the k constant is 10.
I cannot provide any further explanations.
Let me know if this was helpful!
Answer: Since y is inversely proportional to the 7 in the denominator, the first equation cannot be a proportional expression. The k constant is 10 and the second is proportional.
Step-by-step explanation: