Follow this link to view juan’s work. critique juan’s work by justifying correct solutions and by explaining any errors he made. for any errors made, provide and explain a correct response. be sure to explain each key aspect of the graph.
Answers
Answer:
Step-by-step explanation:
Let the exponential function given in the picture is,
f(x) = a(b)ˣ
Here, a = Initial value
b = Base value
x = Exponent
Since, the graph passes through the points (0, 1) and (1, 3)
For (0, 1),
1 = a(b)⁰
a = 1
For (1, 3),
3 = 1(b)¹
b = 3
Therefore, equation of the given function will be,
f(x) = (3)ˣ
Therefore, Initial value = 1
Base = 3
Asymptote (Horizontal) → y = 0
Vertical asymptote → None
Domain → (-∞, ∞) Or {x | x ∈ R}
Range → (0, ∞) Or {y | y > 0}
Therefore, answers given by Juan are incorrect.
Related Questions
a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
Answers
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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i need help with this 1 question
Answers
7 × 8 × 8 = 448
and that's it
What is the volume of the rectangular prism above?
A.
1/15
B.
1/5
C.
1/12
D.
1/20
Answers
Answer:
1/15 cubic meters
Step-by-step explanation:
Formula for volume of a rectangular prism is width times length times height.
1/4 x 1/3 x 4/5 = 1/15
1/12 EZ I think that's the answer
solve following problem
Answers
Answer:
p²=h²-b²
p² =10²-6²
p² =100-36
p²=64
p=( √8)²
p=8
Let \(x\) and \(y\) be the length and height, respectively, of the rectangle.
Let the bottom left vertex be the origin (0, 0), and position the triangle so that the bottom leg lies on the horizontal axis in the \(x,y\)-plane. The hypotenuse of the triangle then lies on the line through (0, 0) and (6, 8), with slope 8/6 = 4/3. Then for some \(x\) between 0 and 6, we have \(y = \frac43x\).
This means for some fixed distance \(x\) from the origin, the rectangle has length \(6-x\) and height \(\frac43x\). Thus the area of the rectangle can be expressed completely in terms of \(x\) as
\(A(x) = (6-x) \times \dfrac43x = 8x - \dfrac43 x^2\)
Non-calculus method:
Complete the square to get
\(8x - \dfrac43 x^2 = -\dfrac43 (-6x + x^2) = 12 - \dfrac43 (9 - 6x + x^2) = 12 - \dfrac43 (x-3)^2\)
which is maximized when the quadratic term vanishes at \(x=3\), giving a maximum volume of \(\boxed{12\,\mathrm{in}^2}\).
Calculus method:
Differentiate \(A(x)\) and find the critical points.
\(A'(x) = 8 - \dfrac83 x = 0 \implies x = 3\)
Differentiate again to check the sign of the second derivative at the critical point.
\(A''(x) = -\dfrac83 \implies A''(3) = -\dfrac83 < 0\)
which indicates a local maximum at \(x=3\). Hence the maximum area is \(A(3) = 12\), as before.
Can you help- TEST tomorrow
WILL MAKE YOU BRAINLIEST
{{{{{Need to show my work}}}}}}}
Answers
Answer:
m = 3/4x + 4
I am not sure if this is what you are working on, hopefully this helps.
Can someone help me please?
Answers
Answer:
Length of the diameter of the circle = 10 units long
Step-by-step explanation:
Given points A (0, -7) and B (8, -1):
We can determine the diameter of the circle by solving for the distance between the two given points.
We'll use the following distance formula:
\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }\)
Let \((x_{1}, y_{1})\) = (0, -7)
\((x_{2}, y_{2})\) = (8, -1)
Plug in these values into the distance formula
\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }\)
\(d = \sqrt{(8 - 0)^{2} + (-1 - (-7))^{2} }\)
\(d = \sqrt{(8)^{2} + (-1 + 7)^{2} }\)
\(d = \sqrt{(8)^{2} + (6)^{2} }\)
\(d = \sqrt{64 + 36}\)
\(d = \sqrt{100}\)
d = 10
Therefore, the distance between points A and B is 10 units long.
graph the parabola x=1/2(y-2)^2-4. find and graph the vertex, focus, directrix, and focal chord endpoints.
Answers
1. Find the graph of the parabola attached below
2. Vertex (-4, 2) Focus (-7/2, 2) Directrix (x = -9/2) Endpoints (-7/2, 1) (-7/2, 3)
How do we find the vertex, focus, directrix, and focal chord endpoints or the parabola?For the parabola, x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,
Vertex → (h, k)
In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴ vertex (-4, 2).
focus → (h, k) = (-4, 2); P = 1/2
Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.
∴ Focus is (-4 + p, 2)
(-4 + 1/2, 2) ⇒ (-7/2, 2)
directrix → x = d
Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.
∴ x = -4 - p ⇒ x = -4 - 1/2
x = 9/2
focal chord endpoints →
The focus of the parabola is (-7/2, 2).
The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.
Therefore, the endpoints of the focal chord are:
(-7/2, 3) and (-7/2, 1).
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Jean bought a $1,980 snow thrower on an installment plan. The installment agreement included a 10% down payment and 18 monthly payments of $116 each.
Answers
Jean purchased a snow thrower for $1,980 using an installment plan that required a 10% down payment of $198 and 18 monthly payments of $116. This allowed Jean to spread out the cost of the snow thrower over time, avoiding a large upfront cost.
Jean recently purchased a snow thrower for $1,980 using an installment plan. To start, Jean had to make a down payment of 10% of the total purchase price, which was $198. This down payment allowed Jean to spread the remaining cost of the snow thrower across 18 monthly payments of $116 each. After making all 18 payments, Jean will have paid the full purchase price of $1,980. This installment plan option is an excellent way for Jean to get the snow thrower he needs while avoiding a large upfront cost and spreading the payments out over a period of time. With this installment plan, Jean can pay off the purchase of the snow thrower while still having money left over each month to cover other expenses.
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A bag contains 10 red marbles .15 yellow marbles, 5 Green marbles and 20 blue marbles. Five marbles are drawn from the bag. what is the approximate probability that exactly 2 of the five are blue?
Answers
Answer:
c
Step-by-step explanation:
Find the value of x. NO LINKS AT ALL!!
Answers
Answer:
x= -7
The whole thing is just an awkward mirror but the lower triangle has an angle that is 1 degree smaller so the whole lower section is going to be bigger or smaller and the angle that mirrors the 80 degree angle is now 79 degrees which makes the other angle on that line 1 degree bigger which would be 101 so you put it in the expession to make it the equation -12x+17=101 and you solve for x which you would then get -7.
solve this equation 2(y + 2) = 3(y - 7)
Answers
Answer:
\(2(y + 2) = 3(y - 7) \\ 2y + 2 \times 2 = 3y - 3 \times 7 \\ 2y + 4 = 3y - 21 \\ y \: terms \: togther \\ 3y - 2y = 4 + 21 \\ y = 25\)
\(thank \: you\)
Enter the correct answer in the box.Replace the values of m and n to show the solutions of this equation,12 + 6x - 5 = 0
Answers
The expression given in the exercise is a quadratic equation in its standard form. To solve any quadratic equation we can use the quadratic formula:
\(\begin{gathered} ax^2+bx+c=0\Rightarrow\text{ Quadratic equation} \\ \text{ Where }a\ne0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \end{gathered}\)Then, in this case, we have:
\(\begin{gathered} x^2+6x-5=0 \\ a=1 \\ b=6 \\ c=-5 \end{gathered}\)We replace the values of a, b and c in the quadratic formula:
\(\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-6\pm\sqrt[]{(6)^2-4(1)(-5)}}{2(1)} \\ \text{ Apply the multiplication sign rule}\colon-\cdot-=+ \\ x=\frac{-6\pm\sqrt[]{6\cdot6+4(1)(5)}}{2} \\ x=\frac{-6\pm\sqrt[]{36+20}}{2} \\ x=\frac{-6\pm\sqrt[]{56}}{2} \\ x=\frac{-6\pm\sqrt[]{4\cdot14}}{2} \\ \text{ Apply the product rule for radicarls property : }\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b} \\ x=\frac{-6\pm\sqrt[]{4}\cdot\sqrt[]{14}}{2} \\ x=\frac{-6\pm2\sqrt[]{14}}{2} \\ x=\frac{-6}{2}\pm\frac{2\sqrt[]{14}}{2} \\ \text{ Simplify} \\ x=-3\pm\sqrt[]{14} \end{gathered}\)Now, since we have the plus and minus symbol in the above expression, then there are two solutions for the given equation:
• First solution
\(x_1=-3+\sqrt[]{14}\)• Second solution
\(x_2=-3-\sqrt[]{14}\)Therefore, the values of m and n of the solutions of the equation are:
\(\begin{gathered} \boldsymbol{m=-3} \\ \boldsymbol{n=\sqrt{14}} \end{gathered}\)The equation 320=x+7.50(36) represents the cost of ordering potted plants at a second store.
What does the x represent in this situation?
Answers
Answer:
I would say it's the amount of potted plants.
Step-by-step explanation:
x is the independent variable and y is the dependent variable. Y counts on x, so total cost counts on the amount of potted plants.
Mackenzie has a 30 ounce soft drink. She drinks 28 ounces. Enter the percentage of ounces Mackenzie has left of her soft drink. Round your answer to the nearest hundredth.
Answers
Answer:
100
Step-by-step explanation:
30-28=100 if u round it to thr nearest hundreth because
30 2-2=0
- 18-8=10
-28
10 rounded to tye nearest hunderth is 100
Using an old post still need help
Answers
Answer:
12x+20
Step-by-step explanation:
2(5x+2)+2(x+8)
or (simplified)
10x+4+2x+16=12x+20
Answer:
12x+20
Step-by-step explanation:
5x+2+x+8+5x+2+x+8
12x+20
Given a mean score of 1150, standard deviation of 90, and 500 participants, solve the following problem. Using this data and the z-score distribution provided in class. Be sure to give your answer in the units requested. Only place your answer in the box.
1. What is the score for someone in the 15th percentile?
2. What is the percentile rank of someone with a score of 1100?
3. How many students have scores of 1060 or greater?
4. How many students scored between 1200 and 1250?
Answers
Answer:
1. 1056.67
2. 29th percentile.
3. 79
4. 77
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean score of 1150, standard deviation of 90
This means that \(\mu = 1150, \sigma = 90\)
1. What is the score for someone in the 15th percentile?
This is X when Z has a p-value of 0.15, so X when Z = -1.037.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.037 = \frac{X - 1150}{90}\)
\(X - 1150 = -1.037*90\)
\(X = 1056.67\)
2. What is the percentile rank of someone with a score of 1100?
This is the p-value of Z when X = 1100. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1100 - 1150}{90}\)
\(Z = -0.555\)
\(Z = -0.555\) has a p-value of 0.29, so 29th percentile.
3. How many students have scores of 1060 or greater?
The proportion is 1 subtracted by the p-value of Z when X = 1060. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1060 - 1150}{90}\)
\(Z = -1\)
\(Z = -1\) has a p-value of 0.1587.
Out of 500:
0.1587*500 = 79
79 is the answer.
4. How many students scored between 1200 and 1250?
The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So
X = 1250
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1250 - 1150}{90}\)
\(Z = 1.1\)
\(Z = 1.1\) has a p-value of 0.8643.
X = 1200
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1200 - 1150}{90}\)
\(Z = 0.555\)
\(Z = 0.555\) has a p-value of 0.7106
0.8643 - 0.7106 = 0.1537
Out of 500:
0.1537*500 = 77
77 is the answer.
the line of symmetry for the quadratic equation y=ax^2+8x-3 is x=4. What is the value of “a”?
Answers
Answer:
The value of a is -1.
Step-by-step explanation:
The line of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
For a quadratic function in standard form, \(y=ax^2+bx+c\), the line of symmetry is a vertical line given by \(x=-\frac{b}{2a}\).
We know that the quadratic equation, \(y=ax^2+8x-3\), has x = 4 as line of symmetry. Therefore, the value of a is:
\(4=-\frac{8}{2a}\\\\4=-\frac{4}{a}\\\\4a=-4\\\\a=-1\)
Answer:
a=-1
Step-by-step explanation:
so that the other person could get brainliest
HELP ME PLEASEEEEEEEEEEEEE
Answers
Answer:
1/9
Step-by-step explanation:
120/1080 can be simplified to 1/9
The dot plot represents an order of varying shirt sizes.
A number line going from 8 to 26. 0 dots are above 8. 1 dot is above 10. 3 dots are above 12. 3 dots are above 14. 5 dots are above 16. 4 dots are above 18. 2 dots are above 20. 1 dot is above 22. 1 dot is above 24. 0 dots are above 26.
Which histogram represents the same data?
A graph shows shirt size labeled 2 to 3 thru 22 to 24 on the horizontal axis and number of shirts on the vertical axis. 0 shirts are size 2 to 3. 0 shirts are size 6 to 8. 4 shirts are size 10 to 12. 11 shirts are size 14 to 16. 12 shirts are size 18 to 20. 8 shirts are size 22 to 24.
A graph shows shirt size labeled 2 to 3 thru 22 to 24 on the horizontal axis and number of shirts on the vertical axis. 0 shirts are size 2 to 3. 0 shirts are size 6 to 8. 11 shirts are size 10 to 12. 11 shirts are size 14 to 16. 12 shirts are size 18 to 20. 8 shirts are size 22 to 24.
A graph shows shirt size labeled 2 to 3 thru 22 to 24 on the horizontal axis and number of shirts on the vertical axis. 0 shirts are size 2 to 3. 0 shirts are size 6 to 8. 4 shirts are size 10 to 12. 8 shirts are size 14 to 16. 6 shirts are size 18 to 20. 2 shirts are size 22 to 24.
A number line going from 1 to 13. 0 dots are above 1. 2 dots are above 2. 1 dot is above 3. 0 dots are above 4. 0 dots are above 5. 0 dots are above 6. 2 dots are above 7. 3 dots are above 8. 0 dots are above 9. 0 dots are above 10. 4 dots are above 11. 3. dots are above 12. 0 dots are above 13.
Answers
The histogram that represents the same data as those represented by the dot plot is: third graph.
What are Dot Plots?Dot plots involves the use of dots to represent each data point in a given data distribution.
The data represented by the third histogram perfectly represents the data in the dot plots because the frequency of each group represented by the bins in the histogram tallies with those we have that are represented by each dot in the dot plot.
Therefore, the histogram that represents the same data as those represented by the dot plot is: third graph.
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y=2 x − 12 has how many real roots?
Answers
Answer: One root
Reason:
The term "root" refers to the x intercept.
We plug in y = 0 and solve for x to get the x intercept
y = 2x-12
0 = 2x-12
2x = 12
x = 12/2
x = 6
The root is 6.
The single x intercept is located at (6,0).
Fill in the missing statement and reason of the proof below.
Given:
A
E
‾
≅
E
B
‾
AE
≅
EB
and
∠
D
A
B
≅
∠
C
B
A
.
∠DAB≅∠CBA.
Prove:
△
A
D
E
≅
△
B
C
E
△ADE≅△BCE.
Answers
The included angle of one triangle are congruent to the corresponding parts of the other triangle. Since the sides AD and BE are congruent, as well as the included angle DAB and CBA, then △ADE≅△BCE.
By the Side-Angle-Side (SAS) congruence theorem, if two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent. In this proof, the given statements provide that the sides AE and EB are congruent, as well as the angles DAB and CBA. This means that the two corresponding sides of the triangles △ADE and △BCE are congruent, and the included angles of the triangles are also congruent. Therefore, according to the SAS congruence theorem, the two triangles are congruent, and thus △ADE≅△BCE.
The SAS congruence theorem applies to any two triangles, regardless of the size or shape of the triangles. The congruence of the sides and angles is sufficient to prove that two triangles are congruent. This theorem can be used to prove other theorems, such as the Triangle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees. To prove this theorem, one could use the SAS congruence theorem to show that two right triangles are congruent, and then use the congruent angles to prove that the sum of the angles in a triangle is 180 degrees.
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Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of cosine. sin^4(x)
Answers
The expression in terms of cosine is (1 - cos^2(x))^2
How to rewrite the expression in terms of cosineFrom the question, we have the following parameters that can be used in our computation:
sin^4(x)
This can be expressed as
sin^4(x) = (sin^2(x))^2
As a general rule:
sin^2(x) = 1 - cos^2(x)
Using the above as a guide, we have the following equation
sin^4(x) = (1 - cos^2(x))^2
Hence, the solution is (1 - cos^2(x))^2
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find the height of right triangular prism
Answers
The side x of the triangular base prism is 0.4 centimetres.
How to find the side of a triangle prism?The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,
c²= a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
x² = 0.5² - 0.3²
x² = 0.25 - 0.09
x = √0.16
x = 0.4 cm
Therefore,
x = 0.4 centimetres.
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solve by elimination
x+y= 0
2x-y= 12
Answers
Answer:
m=2
Step-by-step explanation:
I calculated it sorry
Answer:
(x,y)= (4,-4)
Step-by-step explanation:
Thanks me later
How much will you need to invest at 3% to have earned $900 in interest in 4 years?
Answers
Answer:
You will have earned $113 in interest.
Step-by-step explanation:
After investing for 4 years at 3% interest, your initial investment of $900 will have grown to $1,013.
To find the amount you need to invest, we can use the formula for simple interest:
\(\displaystyle\sf \text{{Interest}} = \text{{Principal}} \times \text{{Rate}} \times \text{{Time}}\)
Here, the principal is the amount you need to invest, the rate is 3% (or 0.03 as a decimal), and the time is 4 years. We can rearrange the formula to solve for the principal:
\(\displaystyle\sf \text{{Principal}} = \frac{{\text{{Interest}}}}{{\text{{Rate}} \times \text{{Time}}}}\)
Plugging in the given values, we get:
\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.03 \times 4}}\)
Simplifying further:
\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.12}}\)
Calculating the division:
\(\displaystyle\sf \text{{Principal}} = 7500\)
Therefore, you will need to invest $7500 at 3% to have earned $900 in interest in 4 years.
Given R=1/4 Q^2 solve for Q
Answers
9514 1404 393
Answer:
Q = ±2√R
Step-by-step explanation:
Take the square root:
±√R = 1/2Q
Multiply by 2:
Q = ±2√R
100 Points! Geometry question. Photo attached. Find the measure. Please show as much work as possible. Thank you!
Answers
Answer:
The answer would lie within 31 degrees of MP and also as in PM.
Answer:
central m arc MP=118°
Step-by-step explanation:
here
central m arc MN=2* inscribed m arc MN=2*31=62°
again
central m arc MN+ central m arc MP=180° being linear pair
substituting value
62°+central m arc MP=180°
central m arc MP=180°-62°
central m arc MP=118°
For the point P(6,8) and Q(11,11), find the distance d(P,Q) and the coordinates of the
midpoint M of the segment PO.
What is the distance?
(Simplify your answer. Type an exact answer, using radicals as need.)
Answers
Answer:
The distance of PQ = \(\sqrt{34}\)
Step-by-step explanation:
Explanation:-
Given that the points are P(6,8) and Q(11,11)
Distance formula
PQ = \(\sqrt{x_{2}-x_{1} )^{2} +(y_{2} - y_{1})^{2} }\)
= \(\sqrt{11-6)^{2} +(11-8)^{2} }\)
= \(\sqrt{(5)^{2}+(3)^{2}} }\)
= \(\sqrt{25+9}\)
= \(\sqrt{34}\)
the number.
the original
by
1. Sushma is now 15 years older than Vijay but in 3 more years she will be 8 times as old as Vijay was 3
years ago. How old are they
Answers
Answer:
Vijay is 6 and Sushma is 21.
Step-by-step explanation:
Let's set up a system of equations for this question.
Let S be Sushma's age and V be Vijay's age.
\(S = 15 + V\)
\(S + 3 = 8(V - 3)\)
Manipulate the second equation to isolate S:
\(S + 3 = 8(V - 3)\)
\(S + 3 = 8V - 24\)
\(S = 8V - 24 - 3\)
\(S = 8V - 27\)
Plug in the second equation into the first:
\(8V - 27 = 15 + V\)
\(8V - V = 15 + 27\)
\(7V = 42\)
\(V = 6\)
\(S = 15 + V\)
\(S = 21\)
Hope this helped!
The city council voted on a new tax. 38 council members voted in favor of the tax. The council has 76 members. What percentage of the council members voted in favor of the tax
Answers
The percentage of the council members who voted in favor of the tax is 50%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the council has 76 members out of which 38 members voted in favor of the tax.
The percentage amount of members who favor the tax is:
(38/76) × 100%
= 50%
Hence, the percentage of the council members who voted in favor of the tax is 50%.
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