The equation of the parabola with the vertex at (2,7) and passing through (-1,3) is y = -(4/9)(x - 2)^2 + 7, found by substituting the given points into the vertex form of a parabola's equation.
Explanation:To find the equation of a parabola given its vertex and a point it passes through, we use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Given the vertex at (2,7) and a point (-1,3) through which the parabola passes, we substitute these values into the vertex form to find the value of 'a'.
Substituting the vertex, we have:
y = a(x - 2)^2 + 7
Then, substituting the point (-1,3) into the equation, we get:
3 = a(-1 - 2)^2 + 7
Solving for 'a', we get:
3 = a(3)^2 + 7 \n3 = 9a + 7 \n-4 = 9a \na = -4/9
Therefore, the equation of the parabola is:
y = -(4/9)(x - 2)^2 + 7
The equation of the parabola with the vertex at (2,7) and passing through (-1,3) is y = -(4/9)(x - 2)2 + 7, found by substituting the given points into the vertex form of a parabola's equation.
To find the equation of a parabola given its vertex and a point it passes through, we use the vertex form of a parabola's equation, which is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
Given the vertex at (2,7) and a point (-1,3) through which the parabola passes, we substitute these values into the vertex form to find the value of 'a'.
Substituting the vertex, we have:
y = a(x - 2)2 + 7Then, substituting the point (-1,3) into the equation, we get:
3 = a(-1 - 2)2 + 7
Solving for 'a', we get:
3 = a(3)2 + 7n3 = 9a + 7n-4 = 9ana = -4/9
Therefore, the equation of the parabolais: y=-(4/9)(x-2)2+7
The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.
The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.
Explanation:To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.
This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.
The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.
In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.
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PLS HELP ME ASAP WITH 1 AND 2, THANK YOU!! SM!!
(Brainliest will be given hopefully!)
(Random answers gets moderated.)
Find the probability of drawing a heart or a black card from a standard deck of cards
The probability of drawing a heart or a black card from a standard deck of cards is 3/4.
Explanation:In a standard deck of cards, there are 52 cards in total. However, since we are interested in finding the probability of drawing a heart or a black card, we need to determine how many cards satisfy this condition.
There are 13 hearts in a deck, so the probability of drawing a heart is 13/52 or 1/4. Additionally, there are 26 black cards (13 spades and 13 clubs) in a deck, so the probability of drawing a black card is 26/52 or 1/2.
To find the probability of drawing a heart or a black card, we can add the probabilities together: 1/4 + 1/2 = 3/4.
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your mom is looking at he amount of sugar in two different drinks the apple juice has 216 grams sugar for every 8 serving the sprite 234 grams of sugar for every 9 serving which drink has more sugar
What are the minimum, first quartile, median, third quartile, and maximum of the data set?
12, 6, 8, 3, 10, 15, 18, 7
find the point slope equation for (-2,-20) and (9,79)
The point-slope equation for the points (-2,-20) and (9,79) is y + 20 = 9(x + 2).
Explanation:To find the point-slope equation, we can use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Firstly, we calculate the slope using the formula: m = (y2 - y1)/(x2 - x1). Given the points (-2, -20) and (9, 79), the slope is (79 - (-20))/(9 - (-2)). Simplifying the expression, we get m = 99/11 = 9.
Next, we substitute one of the points and the calculated slope into the point-slope formula. Let's choose (-2, -20). So the equation becomes: y - (-20) = 9(x - (-2)). Simplifying further, we have: y + 20 = 9(x + 2).
This is the point-slope equation for the given points: y + 20 = 9(x + 2).
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Find the value of n such that x2-10x+n is a perfect square trinomial.
A. -5
B. 50
C. 100
D. 25
Answer:
the answer is 25!!
Step-by-step explanation:
I hope this is helpful to sum of y'all!!
Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x
Answer:
2nd option
Step-by-step explanation:
What is the minimum value of the graph of y=sin x assumes
Answer:
the answer is
negative one
- 1
Step-by-step explanation:
how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936
A. 1/100
B. 1/10
C. 10
D. 100
E. 1,000
Which points in the scatter plot are outliers?
Point A
Point F
Point H
Point K
Point M
Answer:
the points are k and f
Step-by-step explanation:
David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the movie will be a comedy or a movie that he has not seen?
[tex] |\Omega|=18\\
|A|=7+4=11\\\\
P(A)=\dfrac{11}{18}\approx61\% [/tex]
Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22
Answer:
[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
Step-by-step explanation:
According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].
Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].
Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.
[tex]p(2)=4(2)^2-3(2)+22[/tex]
We simplify to obtain,
[tex]p(2)=4(4)-3(2)+22[/tex]
[tex]p(2)=16-6+22[/tex]
[tex]p(2)=10+22[/tex]
[tex]p(2)=32[/tex]
Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.
Explanation:For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.
To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.
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Which of the following is equal to 7÷9/5
A: 9×7/5 B: 7×9/5 C: 9×5/7
D: 7×5/9
Final answer:
To find the value of 7÷9/5, we multiply 7 by the reciprocal of 9/5, which is 5/9, resulting in the expression 7×5/9. The correct answer is D: 7×5/9.
Explanation:
To solve the expression 7÷9/5, we must interpret the division as multiplication by the reciprocal. In other words, dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 7 divided by 9/5 is equal to 7 multiplied by the reciprocal of 9/5, which is 5/9.
So, the calculation will be 7×5/9. Here's the math:
Identify the reciprocal of 9/5, which is 5/9.
Multiply 7 by the reciprocal of 9/5: 7 × 5/9.
Calculate the product: 7 × 5 = 35, and 35 ÷ 9 does not simplify further in this context.
The correct answer from the options provided is D: 7×5/9. The other options, A: 9×7/5, B: 7×9/5, and C: 9×5/7 do not represent the correct transformation from division to multiplication by the reciprocal.
How many Liters of a liquid can be held in a barrel
A student ate 3/20 of all candies and another 1.2 lb. Another student ate 3/5 of the candies and the remaining 0.3 lb. Altogether, what weight of candies did they eat?
JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. If JA = 10, AL = 23, and CK = 9, what is the perimeter of ∆JKL
A.84
B.66
C.42
D.38
Answer: the perimeter of JKL is 84
ik this is rlly late but to help anyone else who gets this question:
This is an equilateral triangle, so the adjacent length is gonna be the same value as its corresponding length that was listed
JA = 10
JB = JA, JB is also 10
JA + JB (10+10) = 20
AL = 23
LC = AL, LC is also 23
AL + LC (23+23) = 46
CK = 9
KB = CK, KB is also 9
CK + KB (9+9) = 18
add all those up:
20 + 46 + 18 = 84
is it always true that trapezoids height is the distance between the 2 bases?
Select all that are undefined. sec (45°) csc (0°) sec (90°)
Final answer:
The sec(45°) and sec(90°) are defined, but csc(0°) is undefined.
Explanation:
To determine which of the given trigonometric functions are undefined, we need to understand the domains of these functions. In trigonometry, the secant and cosecant functions are undefined for angles where the cosine and sine functions are equal to zero, respectively.
For sec(45°), the cosine of 45° is equal to √2/2, which is not zero. Therefore, sec(45°) is defined.For csc(0°), the sine of 0° is equal to 0, which results in division by zero. Hence, csc(0°) is undefined.For sec(90°), the cosine of 90° is equal to 0, which again leads to division by zero. Thus, sec(90°) is undefined.Using sin^2x+ cos^2 x=1 and other trig properties, simplify the following: (cos^2Ø*tan^2Ø)/(1-cos^2 Ø.
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP!! WILL GET BRAINIEST IF YOU SHOW WORK
1. Simplify the radical
2. Simplify the radical
3. Simplify the radical
4. Simplify the radical
The simplification of the radical is c/3
What are radicals in math?Radicals in math refer to expressions containing square roots or higher-order roots.
Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.
Simplifying the surd;
√3c²)/√27
= √3 × √c²)/√9 × √3
= √3c/3√3
= c/3
Therefore the simplification of √3c²)/√27 is c/3.
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A swimming pool has four faucets. the first can fill the entire pool with water in two days, the second - in three days, the third - in four days, and the last one can fill the pool in 6 hours. how long will it take to fill the pool using all 4 faucets together (be exact)?
Maria needs to mail 3 letters. Each letter costs $0.41 to mail. How much change will she get back if she gives the clerk $2.00?
Maria has to mail 3 letters, each costing $0.41, totaling to $1.23. She gives the clerk $2.00, so the change she will get back is $2.00 - $1.23 = $0.77.
Explanation:This problem is about simple arithmetic and money management. Maria has to mail 3 letters, each costing $0.41. This means that the total expense that Maria has to pay is $0.41 * 3, which equals $1.23. Maria gives the clerk $2.00, so to find out the change, subtract the total cost of the letters ($1.23) from the amount she gave to the clerk ($2.00). So, the change Maria will get back is $2.00 - $1.23 = $0.77.
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A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
Answer: The table should look like this
4 9 13
15 8 23
19 17 36
Step-by-step explanation:Happy to help
Based on the complete table, 19 people own a car, 13 people own a truck while 8 people neither own a car nor a truck.
How to complete the table
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
own a car Dont own a car Total
Own a trcuk 4 9 13
Dont own a trcuk 15 8 23
Total 19 17 36
Those that own car 15 + 4 =19
those that own truck 9 + 4 = 13
Those that own car and truck 4 (Given)
Those that owns none = 36-15-9 - 4 = 8
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The graph shows a probability distribution.
What is P(1.5≤X≤4.5)?
Enter your answer, as a decimal
P(1.5≤X≤4.5) =
evaluate a = log(0.1) and b = ln(e^3)
A. 0
B. 4
C. 2
D. -2
The sum of two numbers is 25, and the difference of their squares is 75. what are the two numbers?
If nine people are in a room and every person shakes hands exactly once with each of the other people, how many handshakes will occur
A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?
A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.
Mean cost spent is calculated by:
Total Cost/Number of Meals
(16.25+17.96+3.58+4.61+5.23)/5
47.63/5
$9.53
Mean Cost represents the average amount per meal the family has spent.
Median cost is the cost that in the middle of the five costs which is $5.23.
The mean cost is significantly different from the median cost because it is higher.
Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.