Please Help!! 25 points!!
Write the equation of the function in vertex form that has the vertex (1, 2) and the point (-3, 6). If necessary, use reduced fractions and not
decimals.
Answers
The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
What is vertex form?
A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.
Here, we have
Given
The vertex (1, 2) and the point (-3, 6).
we have to find the equation of the function in vertex form.
We know that
The vertex form of the equation is :
f(x) = a (x-h)² +k
Now, we put the value of x, h, and k and we get
6 = a(-3-1)² + 2
6 = 16a + 2
4 = 16a
a = 1/4
Now, we put the value of a in the vertex form equation and we get
f(x) = 1/4 (x-1)²+2.
Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
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Related Questions
A coordinate grid with 2 lines. The first line labeled f(x) passes through (negative 3, 3), (0, 2), and (3, 1). The second line labeled g(x) passes through the points at (negative 3, 0) and (0, 2) What is the solution to the system of linear equations? (–3, 0) (–3, 3) (0, 2) (3, 1)
Answers
Was Gud! How are you?
Anyway, the correct answer my brother/sister is: C- (0,2)
Hope you have a wonderful/blessed day ;>
a survey for kindergartners asked about their favorite color. the children were asked to check the box corresponding to blue, red, green, yellow, or orange. what is the scale of measurement for this question? group of answer choices ordinal interval nominal ratio
Answers
Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.
Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.
Ratio scales are interval scales where lengths are expressed in relation to a rational zero.
Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.
Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.
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A school hires an artist to create a mural. The artist draws a model of the mural on a coordinate grid. Each unit on the grid represents one foot. The school pays the artist $20 for each square foot of the mural. How much does the school pay the artist?.
Answers
The amount which the school will pay the artist $960 based on the area of the rectangle.
The dimensions are taken from the cartesian plane on the image:
Length: 7 - 1 = 6 feet.
Width: 10 - 2 = 8 feet.
Hence the area is given by:
Area = length x width
A is equal to 6 x 8 = 48 square feet.
The artist was paid $20 per square foot, so his total remuneration is as follows:
20 x 48 = $960.
The area of a rectangle of length l and width w is calculated by multiplying the dimensions.Area is an important concept in modern mathematics.
The area is the amount of space occupied by a two-dimensional figure, form, or planar lamina in the plane. In simple terms, the area is the amount of fabric or material with a specified thickness required to make a model of the shape or the amount of paint required to cover the surface of the shape with a single layer, i.e. one coat.
It is a two-dimensional representation of a curve's length or a solid's volume, where length is a one-dimensional concept and volume is a three-dimensional related term.
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Pip was thinking of a number. Pip doubles it and gets the answer of 50.8. What was the original number?
Answers
Answer:
25.4
Step-by-step explanation:
If double of the number 'x' is 50.8, (2x=50.8)
Then the original number must be half of that value, (x=50.8/2)
50.8/2 = 25.4
COS (1-x) X sin x O A. True B. False
Answers
Given:
\(\cos(\frac{\pi}{2}-x)=\sin x\)Required:
To find whether the given statement is true or false.
Explanation:
Let,
\(\cos(A-B)=\cos A\cos B+\sin A\sin B\)Therefore,
\(\cos(\frac{\pi}{2}-x)=\cos\frac{\pi}{2}\cos x+\sin\frac{\pi}{2}\sin x\)But
\(\begin{gathered} \cos\frac{\pi}{2}=0 \\ \\ \sin\frac{\pi}{2}=1 \end{gathered}\)So,
\(\begin{gathered} \cos(\frac{\pi}{2}-x)=0+(1)\sin x \\ \\ =\sin x \end{gathered}\)Final Answer:
The given statement is TRUE.
\(\cos(\frac{\pi}{2}-x)=\sin x\)what is 23,411 + 35,507
Answers
Answer:
58918
Step-by-step explanation:
35,507
+ 23,411
---------------
58918
A train traveled at a constant speed
for six hours and traveled a distance of
408 miles. What is the best estimate
of the number of miles the train could
travel in 2.5 hours?
Answers
Answer:
170
Step-by-step explanation:
you have to set up a proportion and cross multiply.
\( \frac{408 \: miles}{6 \: hours} = \frac{x \: miles}{2.5 \: hours} \)
that would cross multiply to
\(408 \: miles \: \times 2.5 \: hours \: = 6 \: hours \: \times x \: miles\)
which would simplify to
\(1020 = 6x\)
then, you isolate x by dividing 6 from both sides to get the final answer of
\(170 \: miles = x\)
Bridget, Jim and Krutika share some sweets in the ratio 4:3:1. Bridget gets 45 more sweets than Krutika. How many sweets are there altogether?
Answers
Answer:
120 sweets
Step-by-step explanation:
Bri:Jim:Kru
4: 3: 1
find the difference in the ratio of Bridget and Krutika
4-1=3
ratio 3 is equivalent to 45 sweets
total ratio(4+3+1)--------> ?
total no. of sweets= 8x45
3
=120sweets
The mean is ? = 137.0 and the standard deviation is ? = 5.3.
Find the probability that X is between 134.4 and 140.1.
0.4069
0.6242
0.8138
1.0311
Answers
The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.
To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:
z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906
z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.
To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:
P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.
As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.
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Describe a normally distributed phenomena using standard nomenclature.
Answers
In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).
A normally distributed phenomenon using standard nomenclature can be described as follows:
A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).
For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).
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what is the result of converting 20 ounces into pounds? remember that 1 pound = 16 ounces
Answers
Answer:
1.25 pounds
Step-by-step explanation:
20/16=1.25
^ Ounces
^Ounces in pound
^Result/pounds
Identify the pattern and type of
sequence for each(two separate answers);
2, 4, 8, 16, 32....
1, 6, 11, 16, 21, 26....
3, 12, 48, 192....
5, 10, 15, 20...
Answers
Answer:
1st one is x2
2nd is +5
3rd is not sure
4th is 5
Step-by-step explanation:
2x
+5
not sure
+5
The two-digit number B6, where B is the tens digit, is the square of a positive integer. How many distinct possible values are there for B?
Answers
There are only 2 possible solutions for B, 1 and 3, so that the number forms the two-digit numbers 16 and 36, which are the positive squares of the positive integers 4 and 6.
Now, we have been given a two-digit number, B6.
The numbers whose squares are 2 digit numbers are:
1, 4, 9, 16, 25, 36, 49, 64, 81
From this list, it is evident that there are 2 numbers that end with 6 and are perfect positive squares of a number, in this case, 4 and 6.
4x4 = 16, 6x6 = 36.
Therefore, B can take 2 values, 1 and 3. These are the only distinct possible values of positive integers for B to take.
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use multiples to determine the LCM of 45and 60
Answers
Answer:
LCM of 45 and 60: 180
Step-by-step explanation:
find the future value of $750 deposited each month at 3.25% for 15 years
Answers
Answer:
P=1538.461
Step-by-step explanation:
do it by the formula of
I=PRT, I=750 R=3.25% T=15
find the hypotenuse: c =
Answers
Use algebra to show that \( p_{k+1}(n)-p_{k+1}(n-1)=p_{k}(n) \). Note do not expand \( p_{k+1}(n), p_{k+1}(n-1) \), and \( p_{k}(n) \) have a lot of common factors.
Answers
Compare the left-hand side and the right-hand side and observe that they are equal. Use the same definition of the prime partition function to simplify the right-hand side \(p_k(n)\).
To summarize the proof:
1. Start with the left-hand side: \(p_{k+1}(n) - p_{k+1}(n-1)\).
2. Use the definition of the prime partition function to express the left-hand side as a sum over partitions of \(k+1\) into primes.
3. Rewrite the sum by shifting the index from \(i = 1\) to \(n\) to \(i = 1\) to \(n-1\) and \(i = n\) separately.
4. Note that the sum over partitions of \(k\) into primes is the same as the sum over partitions of \(k-1\) into primes, except for the contribution of partitions that contain 1.
5. Simplify the expression by recognizing that the difference between the two sums is the contribution of partitions of \(k\) into primes that contain 1.
Therefore, you have successfully proven the equation \(p_{k+1}(n) - p_{k+1}(n-1) = p_k(n)\).
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What does calculus early transcendentals cover?
Answers
Calculus Early Transcendentals is a branch of mathematics that deals with the study of rates of change and slopes of curves. It is a fundamental area of mathematics that is widely used in a variety of fields, including engineering, physics, economics, and science.
The core concept of Calculus Early Transcendentals is differentiation, which is the process of finding the derivative of a function. A derivative is essentially the rate of change of a function at a given point, and it is used to determine how the value of the function changes as its input changes.
In addition to differentiation, Calculus Early Transcendentals also covers integration, which is the process of finding the area under a curve. Integration is the inverse of differentiation and is used to find the total change in a function over a given interval.
Another important area covered in Calculus Early Transcendentals is optimization, which is the process of finding the maximum or minimum value of a function. This is a useful tool in many real-world applications, such as finding the minimum amount of time or energy required to perform a task.
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compute the determinant by cofactor expansion. at each step, choose a row or column that involves the least amount of computation.
Answers
The determinant of A is 1.
What is matrix?The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them.
The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively.
A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.
We can compute the determinant of the 2x2 matrix A =
| 1 0 |
| 1 1 |
by expanding along the first column since it involves the least amount of computation:
| 1 0 |
| 1 1 |
det(A) = 1 * |1 1| - 0 * |1 1|
= 1
So, the determinant of A is 1.
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Complete question:
Compute the determinant by cofactor expansion. At each? step, choose a row or column that involves the least amount of computation.
A multiple-choice test has 5 questions each with 5 possible answers, the probability of guessing all the questions correctly is
Answers
In a multiple-choice test that has 5 questions, each with 5 possible answers, the probability of guessing all the questions correctly can be found using the formula:p = (1/5) × (1/5) × (1/5) × (1/5) × (1/5) = 1/3125.
The probability of guessing one question correctly is 1/5 since there are five possible answers. Since there are five questions, we multiply the probability by itself five times.
Therefore, the probability of guessing all the questions correctly is 1/3125, which is approximately 0.00032. This means that the chance of guessing all the questions correctly by random chance is very low.
This indicates that one should have studied for the test rather than relying solely on guesswork.
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Earth has a diameter of 7,926 miles. What is its diameter in kilometers? (1 mile = 1.6 kilometers)
A. 49,553 km
B. 120,586 km
C. 1,392,650 km
D. 12,682 km
Answers
The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.
Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:
Diameter in kilometers = Diameter in miles × Conversion factor
Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile
Diameter in kilometers = 12,681.6 kilometers
Rounding this value to the nearest whole number, we get 12,682 kilometers.
Therefore, the correct answer is option D: 12,682 km.
Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.
Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.
Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.
In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
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find the cube of 2x+1/3x
Answers
Answer:
Step-by-step explanation:
(2x + 1/3x)³
= (7/3x)³
= 343/27 x³
shira was riding the screamer when it broke down. her seat was 53 jorizontal feet from the central support pole. What was her seat's angle of rtation. Is there more tahn one possible solutions
Answers
Answer:
The possible solutions are 58 degree, 122 degrees, 302 degrees and 238 degrees
Step-by-step explanation:
Please see the attachment
From the figure, it is evident that
cos AOB = OB/OA = 53/100 = 0.53
Thus, cos-1 (0.53) = 58 degrees
AOB = 58 degree
Also, there are can be other values depending on the quadrants
COB = 180 -58 = 122 degrees
FOB = 360 -58 = 302 degrees
EOB = 180 + 58 = 238 degrees
Calculate the slope.
Answers
Answer: 2/3
Step-by-step explanation:
Since the line is going through the origin it slope will use the formula y/x = k where k is the slope. So you can use any point on the number line to determine the slope.
use the point (3,2) using the formula y/x = k divide the y by x.
k = 2/3
Answer: 0.67
Step-by-step explanation:
Look at the points (3,2), (6,4), and (9,6)
Paul's time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for viking was 5 hours longer than her swimming time. She ran for 4 hours 50 minutes. Assuming she took no breaks in between each event, how long did it take her to complete all three parts of the race?1 hour =60 minutes
Answers
It took Paul a total of 12 hours and 40 minutes to complete all three parts of the Ironman triathlon.
Paul’s time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for biking was 5 hours longer than her swimming time, so her biking time was (1 hour + 5 hours) = 6 hours 25 minutes. She ran for 4 hours 50 minutes. The total time it took her to complete all three parts of the race is (1 hour 25 minutes) + (6 hours 25 minutes) + (4 hours 50 minutes) = 12 hours 40 minutes.
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Which transformation can NOT be used to prove that AABC is congruent to
ADEF?
Answers
Answer: delation
Step-by-step explanation:
The three sorts of unbending changes are interpretation, revolution, and reflection. Each of these changes can be utilized to demonstrate that two triangles are compatible, as long as the comparing sides and points are compatible after the change.
Be that as it may, there's one change that cannot be utilized to demonstrate coinciding between two triangles, which may be a enlargement. A expansion may be a change that changes the estimate of an protest, but does not protect separations or points. Subsequently, in case we expand one triangle, we cannot ensure that the comparing sides and points of the two triangles will be compatible.
Complete the following statement. 8 + ( ) = 6
Answers
Answer:
8+(-2)=6
Step-by-step explanation:
i finished all of these but i wanted to make sure these were correct! i will be posting others and thank you for answering :)
Answers
Answer:
Step-by-step explanation:
Where are your answers?
Anybody good at geometry I need help with this worksheet Hame: Unit 4: Solving Quadratic Equations Bell: Homework 8: Solving Quadratics Review Thiais 2 2-page documentt Date: Directons: Solve eadh equabon using the indicated method: r=6r-91 (Factoring) 2 -2r" -146 = -34 (Square Roots} 3 r-14r-53 = 9 (Completing the Square) 4.3r*+6r-62 =7 (Completing the Square) 5. -rtZr=l (Quadratic Formula) 6.5r =,-2 (Quadratic Forula)'
Answers
1)r = 18.2
2) Square root of 56 = 7.48
3)Square of -4.7 = 22.09
4) Square of 7.6 = 57.76
5) -tz = l/r
6) r = -2/5
Factoring
To include something when you are doing a calculation, or when you are trying to understand something: People are earning more, but when inflation is factored in, they are no better off.
1) r=6r-91 (Factoring)
r-6r = - 91
-5r = -91
r = 91/5
r = 18.2
Square Root
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
2) -2r" -146 = -34 (Square Roots}
- 2r’’ = -34 + 146
- 2r’’ = 112
-r’’ = 112/2
-r’’= 56
r’’ = - 56
Square root of 56 = 7.48
3) r-14r-53 = 9 (Completing the Square)
- 13r = 9+53
- 13r = 62
- r = 62/13
r = - 4.7
Square of -4.7 = 22.09
4) 3r*+6r-62 =7 (Completing the Square)
9r = 7+62
r = 69/9
r = 7.6
Square of 7.6 = 57.76
5) -rtZr=l (Quadratic Formula)
- r(tz) = l
- tz = l/r
6) 5r =-2 (Quadratic Formula)
r = -2/5
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Liam has 1 3 cup of raisins which can make 1 4 of a cookie recipe. How many cups of raisins are needed to make one whole cookie recipe?
Answers
We need 4/3 cups of raisins to make one whole cookie recipe.
What is proportion?The two ratios given are equal to one another, as demonstrated by the proportional equation. For instance, it would take five hours for a train to cover 500 kilometres when it travels at 100 km per hour.
If 1 3 cup of raisins makes 1 4 of a cookie recipe, then we need to find how many cups of raisins are needed to make one whole cookie recipe.
Let's use a proportion to solve this problem:
1 3 cup of raisins is to 1 4 of a recipe as x cups of raisins is to 1 whole recipe.
We can cross-multiply to get:
1 3 * 1 = 1 4 * x
1/3 = 1/4 * x
x = 4/3
Therefore, we need 4/3 cups of raisins to make one whole cookie recipe.
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