Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (3, 5) and a = 2, hence
y = 2(x - 3)² + 5 ← in vertex form
The equation of the quadratic function in vertex form with given vertex and leading coefficient is y=2(x-3)²+5.
What is quadratic equation in vertex form?The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
Given that, the vertex is at (3,5) and has a leading coefficient of 2
Here, (h, k) = (3, 5) and a = 2
Substitute (h, k) = (3, 5) and a = 2 in f(x) = a(x - h)² + k, we get
y=2(x-3)²+5
Therefore, the equation of the quadratic function in vertex form is y=2(x-3)²+5.
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[(x-1)/3]=(x+3)/4 in R
Whats in the [ ] is the whole part
Answer:
4 is the [ ] in whole part.Step-by-step explanation:
Given equation [(x-1)/3]=(x+3)/4
Let us first get rid denominators from both sides.
On cross multiplying both sides, we get
4(x-1) = 3(x+3)
4x-4 = 3x+9
Adding 4 on both sides, we get
4x-4+4 = 3x+9+4
4x = 3x +13
Subtracting 3x on both sides, we get
4x-3x = 3x-3x +13
x = 13.
Now, we need to find the value of [ ] fraction We have [(x-1)/3] in given equation.
Plugging x= 13 in (x-1)/3, we get
13-1/3 = 12/3 = 4.
Therefore, 4 is the [ ] in whole part.Alexis counted 16 commercials while watching 30 minutes of TV. At this rate, how many commercials would play in a day?
30 minutes is half an hour.
so in 30 minutes is 16 commercials, so in 1 hour is twice as many, 32 commercials.
there are 24 hours in a day, so 32 commercials 24 times, 32 * 24.
Is 2 times the square root of 3 rational?
Answer:
Yes
Step-by-step explanation:
2 x √3 = 3.46410161514 , which is a rational number, because it is a real nomber
I’ll give brainlest!!!!! Pleaseeeeee!!!!!!
Answer:
38ft
Step-by-step explanation:
wellcut it in two a rectangle 8 by 3
triangle with the base of 7 and the hight of 4
area for a rectangle bxh so 8 times 3 = 24ft
area for a triangle is bxhx1/2 so 7x4= 28 divided by 2= 14
now add 14+24= 38ft
Given that the points (-1, 5) and (2, 1) are vertices of a rectangle with sides parallel to the axes, how much longer is the length than the width? A) 1 unit B) 2 units C) 3 units D) 4 units
Answer:
Correct choice is A
Step-by-step explanation:
Two vertices of the rectangle have coordinates A(-1, 5) and B(2, 1). If rectangle sides are parallel to the axes, then two remaining vertices have coordinates C(-1,1) and D(2,5) (see attached diagram for details).
Find the length and the width:
[tex]AC=\sqrt{(-1-(-1))^2+(5-1)^2}=4\ units,\\ \\AD=\sqrt{(2-(-1))^2+(5-5)^2}=3\ units.[/tex]
Then the length is 1 unit longer than the width.
Woody wants to earn $250 to buy a bicycle by selling lemonade it cost him$0.05 dollars to make a glass of lemonade,which he sells for$0.25. how many drinks does he have to sell to earn$250
Answer:
1,250 drinks
Step-by-step explanation:
Woody spends $0.05 to make a glass of lemonade and makes $0.25 when he sells one, so his net gain is $0.20. 250 / .20 is 1,250.
Final answer:
Woody needs to sell 1,250 glasses of lemonade to earn the $250 required to buy a bicycle. Calculated by dividing the goal ($250) by the profit per glass ($0.20), which is the difference between the selling price ($0.25) and the cost price ($0.05).
Explanation:
Woody is operating a small business of selling lemonade and seeks to achieve a certain amount of total revenues to purchase a bicycle. To solve this, one must determine the profit per glass of lemonade sold, which is the selling price minus the cost to make it. Since Woody sells a glass for $0.25 and it costs $0.05 to make, the profit per glass is $0.25 - $0.05 = $0.20.
To calculate the total number of glasses Woody needs to sell to earn $250, divide his goal by the profit per glass. Thus:
Total number of glasses = ($250 / $0.20 per glass) = 1250 glasses
Hence, Woody must sell 1,250 glasses of lemonade to earn enough money to buy the bicycle.
If f(x) =-x2 +6x -1 and g(x)=3x2-4x-1 find f-g (x)
Answer:
- 4x² + 10x
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
= - x² + 6x - 1 - (3x² - 4x - 1) ← distribute
= - x² + 6x - 1 - 3x² + 4x + 1 ( collect like terms )
= - 4x² + 10x
Final answer:
To find f-g (x), subtract g(x) from f(x) and combine like terms. The resulting function is f-g (x) = -4x² + 10x.
Explanation:
To find the difference of the functions f(x) and g(x), denoted as f-g (x), we simply subtract the function g(x) from f(x). In the given problem:
f(x) = -x² + 6x - 1
g(x) = 3x² - 4x - 1
We subtract the expressions:
f-g (x) = (-x² + 6x - 1) - (3x² - 4x - 1)
Removing the parentheses and simplifying, we get:
f-g (x) = -x² + 6x - 1 - 3x² + 4x + 1
Combine like terms:
f-g (x) = -4x² + 10x
Thus, the function f-g (x) is -4x² + 10x.
What is the sum of ¾ + ⅔ in simplistic form
We must find the common denominator.
The list of multiples of 4: 0, 4, 8, 12, 16, 20, ...
The list of multiples of 3: 0, 3, 6, 9, 12, 15, 18, ...
The common denominator is 12.
[tex]\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}[/tex]
Therefore:
[tex]\dfrac{3}{4}+\dfrac{2}{3}=\dfrac{9}{12}+\dfrac{8}{12}=\dfrac{9+8}{12}=\dfrac{17}{12}=\dfrac{12+5}{12}=1\dfrac{5}{12}[/tex]
Answer: 17/12 = 1 5/12Tools of Geometry:Question 2
Circle K has a center at (3,7) and has a radius of 1. Circle K' has a center of (7,–3) with a radius of 1. What is the transformation of circle K to circle K'?
Answer:
I think it's rotated 90 degrees clockwise
Step-by-step explanation:
The transformation of circle K to circle K' is a translation, specifically a movement of 4 units to the right and 10 units down, represented by T(4, -10).
Explanation:The transformation that maps circle K to circle K' is a translation. In a translation, every point of the object moves the same distance in the same direction. For circle K to circle K', this would be a shift 4 units to the right and 10 units down. The coordinates of the center of the circle move from (3,7) to (7,-3). We can calculate this movement by subtracting the initial coordinates from the final ones: (7-3, -3-7) = (4, -10). Therefore, the transformation would be written as T(4, -10).
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What is the relationship between the changes in the radii and the volume?
Answer:
The relationship between the volume of a cylinder and its radius. To see that as the radius changes, the volume changes in proportion. Be able to comfortably use the volume of a cylinder formula. π is a constant and height, h, is a constant in this task.
Maya earns 72 dollars for working 5 hours. How long will it take for her to earn 216 dollars at the same pay rate?
Answer:
15 hours
Step-by-step explanation:
Because you have to divide 72 by 5 to find out much money she makes per hour. You then find out that he makes $14.40 an hour and then you mutliply it bu different numbers until you get 216 and 14.40 times 15 is 216
PLEASE HELP QUICK, GIVING BRAINLIEST
A cone-shaped hat is shown:
(below)
What is the approximate height of the hat?
3.51 centimeters, because height = Square root of the difference of 18 and 5.7
17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7
18.88 centimeters, because height = Square root of the sum of the squares of 18 and 5.7
4.87 centimeters, because height = Square root of the sum of 18 and 5.7
This is classic Pythagorean solving:
Side^2 + Side^2 = Hypotenuse^2
The hypotenuse is the longest side of a triangle, and it connects the leg and the base usually. In this triangle, 18 is the hypotenuse -- so since we are solving for the unknown side, the equation is:
a^2 + 5.7^2 = 18^2 -- now solve
a^2 = 18^2 - 5.7^2
a^2 = 291.51
a = sqrt(291.51)
a = 17.07 -- because height is the square root of the difference of the squares of 18 and 5.7
The answer is choice B.
The correct answer is b. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.
To find the approximate height of the cone-shaped hat, we need to use the Pythagorean theorem. The height of the cone (h) can be found using the formula:
[tex]\[ h = \sqrt{r^2 - a^2} \][/tex]
where r is the slant height of the cone and a is the radius of the base of the cone.
Given that r = 18 cm and a = 5.7 cm, we substitute these values into the formula:
[tex]\[ h = \sqrt{18^2 - 5.7^2} \][/tex]
[tex]\[ h = \sqrt{324 - 32.49} \][/tex]
[tex]\[ h = \sqrt{291.51} \][/tex]
Now, we can approximate the square root of 291.51 to find the height:
[tex]\[ h \approx 17.07 \text{ cm} \[/tex]]
Therefore, the approximate height of the hat is 17.07 centimeters. The other options are incorrect because they do not correctly apply the Pythagorean theorem:
a. 3.51 centimeters: This is the square root of the difference of 18 and 5.7, which does not use the correct formula for the height of a cone.
c. 18.88 centimeters: This is the square root of the sum of the squares of 18 and 5.7, which would be the length of the slant height, not the height of the cone.
d. 4.87 centimeters: This is the square root of the sum of 18 and 5.7, which is not a correct application of the Pythagorean theorem for finding the height of a cone."
Lines b and c are parallel.
What is the measure of 2?
m2 = 31°
m2 = 50°
m2 = 120°
m2 = 130°
The correct measure of angle 2 is [tex]\( m\angle2 = 130\°\)[/tex].
To find the measure of angle 2, we need to use the properties of parallel lines and the angles formed when a transversal intersects them. When a transversal intersects two parallel lines, corresponding angles are equal, and alternate interior angles are also equal.
In the given scenario, lines b and c are parallel, and we assume that the transversal intersects these parallel lines at points not shown in the conversation. Let's denote the angles formed by the intersection of the transversal with line b as angles 1, 2, 3, and 4, and with line c as angles 5, 6, 7, and 8, respectively.
Since lines b and c are parallel, we have the following relationships:
1. [tex]\( m\angle1 = m\angle5 \)[/tex] (corresponding angles)
2. [tex]\( m\angle2 = m\angle6 \)[/tex] (corresponding angles)
3. [tex]\( m\angle3 = m\angle7 \)[/tex] (corresponding angles)
4. [tex]\( m\angle4 = m\angle8 \)[/tex] (corresponding angles)
5. [tex]\( m\angle1 = m\angle8 \)[/tex] (alternate interior angles)
6. [tex]\( m\angle2 = m\angle7 \)[/tex] (alternate interior angles)
7. [tex]\( m\angle3 = m\angle6 \)[/tex] (alternate interior angles)
8. [tex]\( m\angle4 = m\angle5 \)[/tex] (alternate interior angles)
From the given options, we can eliminate [tex]\( m\angle2 = 31\° \)[/tex] and [tex]\( m\angle2 = 50\° \)[/tex] because these options would imply that [tex]\( m\angle6 \) and \( m\angle7 \)[/tex] are also [tex]\( 31\° \) and \( 50\° \)[/tex], respectively. This would mean that the sum of the angles in the triangle formed by the transversal and line c would be less than [tex]\( 180\° \)[/tex], which is impossible.
Next, we consider [tex]\( m\angle2 = 120\° \)[/tex]. If this were true, then [tex]\( m\angle7 \)[/tex] would also be [tex]\( 120\° \)[/tex]. However, this would imply that the sum of the angles in the triangle formed by the transversal and line c would be [tex]\( 120\° + 60\° \)[/tex] (since [tex]\( m\angle6 \) and \( m\angle8 \)[/tex] would be supplementary, adding up to [tex]\( 180\° \)[/tex]), which again is impossible because the sum of angles in any triangle is [tex]\( 180\° \).[/tex]
Finally, we consider [tex]\( m\angle2 = 130\° \)[/tex]. This option is possible because if [tex]\( m\angle2 = 130\° \)[/tex], then [tex]\( m\angle7 \)[/tex] would also be [tex]\( 130\° \)[/tex]. The remaining angle in the triangle formed by the transversal and line c (which is [tex]\( m\angle6 \) or \( m\angle8 \)[/tex]) would be [tex]\( 180\° - 130\° = 50\° \)[/tex]. This satisfies the triangle angle sum property, as [tex]\( 130\° + 50\° = 180\° \)[/tex].
Therefore, the correct measure of angle 2 is [tex]\( m\angle2 = 130\° \)[/tex].
The complete question is:
Lines b and c are parallel. What is the measure of 2?
m2 = 31°
m2 = 50°
m2 = 120°
m2 = 130°
Which of the following points lies in the solution
Answer:
B. (2, 0) - True, True, True
Step-by-step explanation:
A. (2, 3) - False
y ≤ 6x - 12 (False)
y ≤ 1/2x + 6 (False)
y ≥ -x - 4 (True)
B. (2, 0) - True, True, True
y ≤ 6x - 12 (True)
y ≤ 1/2x + 6 (True)
y ≥ -x - 4 (True)
C. (-3, 0) - False
y ≤ 6x - 12 (False)
y ≤ 1/2x + 6 (False)
y ≥ -x - 4 (True)
D. (1,1) - False
y ≤ 6x - 12 (False)
y ≤ 1/2x + 6 (False)
y ≥ -x - 4 (True)
Brainliest?
What is the answer I need help
Answer:
A
Step-by-step explanation:
Monday he ran the highest because 4.5 is greater than the other numbers given.
Answer:
Monday.
Step-by-step explanation:
We want to know on which day he ran the greatest number of miles. The largest number is the greatest number of miles. 4.5 is the largest number and that is on Monday
The graph of a proportional relationship passes through the points (4,3) and (x,9). Find x.
If x and y are proportional, then y : x = constant.
[tex]\dfrac{y}{x}=a\to y=ax[/tex]
We have (4, 3) and (x, 9). Substitute:
[tex]\dfrac{9}{x}=\dfrac{3}{4}[/tex] cross multiply
[tex]3x=(9)(4)[/tex]
[tex]3x=36[/tex] divide both sides by 3
[tex]\boxed{x=12}[/tex]
Irving can I remember the correct order of the five digits on his ID number he does remember that the ID number contains the digits 1.4,3,7,6 what is the probability that the first three digits of Irvings ID number will be odd numbers
Answer: [tex]\frac{27}{125}[/tex]
Step-by-step explanation:
Here the total numbers are 1, 4, 3, 7, 6
Since the total number of possible arrangement = [tex]5\times 5 \times5 \times 5 \times 5=5^5[/tex]
The total number of the odd numbers in the given numbers = 3
Thus the possible arrangement that the first three digits will be odd numbers = [tex]3\times 3\times 3\times 5\times 5=3^3\times 5^2[/tex]
Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement = [tex]\frac{3^3\times 5^2}{5^5} = \frac{3^2}{5^{5-2}}[/tex]
= [tex]\frac{3^3}{5^3} = \frac{27}{125}[/tex]
Find the distance of line AB if A(3, 5) and B(-3,-3).
8
6
12
10
The distance of line AB if A(3, 5) and B(-3,-3) is D.10.
[tex]\sqrt[/tex] (5--3)^2 + (3-(-3))^2 = V100 = 10.
How to calculate the AB distance?
To calculate the distance AB between points A (x1, y1) and B (x2, y2), first draw a right triangle with segment ¯AB in the hypothalamus. AC is a horizontal distance, so it's just a difference in x-coordinates: | (x2-x1) |. Similarly, BC is the vertical distance | (y2-y1) |. ..
The vertical distance of the line (Ax + By + c = 0) from point
is equal to | Ax'+ By' + c√A2 + B2 |. Where (x', y') are the coordinates of the point. Since we need the distance of the line from the origin, the coordinates will be (0,0), which is the vertical distance of the line from the origin.
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What are the prime factors of 80
Answer:
The easiest way to get this is through divide and conquer.
Therefore take 1, 2, 3, 5, 7, 9, and 11.
1 is a factor obviously.
2 is a factor since 80 is divisible by 80. We found a factor so divide the value 80 by 2 and we get 40. Is 2 a factor of 40? Yep, so divide again and we have 20. Is 2 a factor of 20. Yep. So is 10. So now we are at 5. But 5 is not a factor of 2. 5 is a factor of 5.
So we have the following 1, 2, 2, 2, 2, and 5. Thus 2 and 5 are your prime factors of 80. Note this is NOT the prime factorization of the number 80. That value is 2^4 * 5. You asked the prime factors of 80. Those are 2 and 5.
Hope this helped good luck
-Emily
What is the product of −225 and −356 ? −915 −6730 613 915
Hello from MrBillDoesMath!
Answer:
80,100 (which is NONE of the provided answers)
Discussion:
-225 * -356 =
+ (225 * 356) = as the product of two negative numbers is positive
80,100
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
The answer should be D. 9 1/5
Please help. I really need help with this so please help.
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Write an inequality for this situation.
To ensure Trisha has at least 5 times as many key chains as thumb drives in each gift bag, the inequality x ≥ 5y can be used, where x is the number of key chains and y is the number of thumb drives. Considering she needs to make at least 50 bags, the inequality x + y ≥ 50 is also relevant.
For Trisha to satisfy the condition of having at least 5 times as many key chains as thumb drives in each gift bag, the following inequality can represent her situation:
x ≥ 5y
Here, x is the number of key chains and y is the number of thumb drives. Trisha must also create at least 50 gift bags, so another inequality to consider is the total number of gift bags:
x + y ≥ 50
Since Trisha has 25 thumb drives (y) and 200 key chains (x), she is limited by the number of thumb drives. The maximum number of gift bags she can create with one thumb drive in each is 25 bags, which means she can use up to 125 key chains (5 times 25). Thus, Trisha can satisfy the requirement by using all 25 thumb drives and up to 125 key chains, ensuring there's a minimum of one thumb drive or key chain per bag.
A triangle with angle measures of 45°, 45°, and 90° is an equilateral triangle. True False
Answer: False
equilateral triangle means all the sides are the same so each one be 60 degrees
Answer:
FALSE.
Step-by-step explanation:
In an equilateral triangle, all angles are equal.
Since they add up to 180°, tke measure of each angle is
180/3 = 60°
Your triangle has two equal angles, so it is an isosceles triangle.
Brian wants to purchase a piece of fabric that is between 49 and 53 inches long. He can choose between three pieces of fabric. Choice A is 4 3/4 feet long. Choice B is 4 1/2 feet long. Choice C is 4 1/4 feet long. Which price of fabric should Brian purchase?
Answer:
the correct answer is c
Step-by-step explanation:
Answer:
Choice C.Step-by-step explanation:
We now that Brian wants the piece of fabric between 49 and 53 inches, this range is expressed like this
[tex]49<x<53[/tex]
Now, to choose the right answer, we have to transform the from feet to inches and see which one falls into this interval.
Choice A.We know that 1 ft equals 12 in. If we have [tex]4\frac{3}{4}=\frac{19}{4} ft[/tex], how much inches would be?
[tex]\frac{19}{4}ft\frac{12in}{1ft}=57in[/tex]
As you can see, the choice A is not the right answer because is more than 53.
Choice B.We do the same process. We know that, [tex]4\frac{1}{2}=\frac{9}{2}ft[/tex] how much inches would be?
[tex]\frac{9}{2}ft\frac{12in}{1ft}=54in[/tex]
Choice B is not the answer neither, because it's outside the interval.
Choice C.[tex]4\frac{1}{4}=\frac{17}{4}ft[/tex] how much inches would be?
[tex]\frac{17}{4}ft\frac{12in}{1ft}=51in[/tex]
As you can observe, choice C is in the interval. Therefore, the right answer is choice C, because 51 inches is between 49 and 53 inches.
Which is the best first step when solving the following system of equations?x+y=3 and 4x-y=7
I Need Answer ASAP
A. Multiply the first equation by 4.
B. Add the first equation to the second equation.
C. Multiply the second equation by -1
D. Subtract the second equation from the first equation.
The best first step to solve the given equation is to add the first equation to the second equation.
What is an elimination method?In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Given that are two equations, x+y=3 and 4x-y=7
To solve them we will use elimination method, because, in both equations coefficients of y are -1 and +1, if we will add them they will get cancelled, leaving x alone, that will help us find the value of x easily.
Hence, the best first step to solve the given equation is to add the first equation to the second equation.
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As an estimation we are told £3 is €4.
Convert £12.30 to euros.
Give your answer rounded to 2 DP.
Answer:
€16.40
Step-by-step explanation:
First, we need to divide £12.30 by 3 to find out how many groups of 3 there is:
12.3 ÷ 3 = 4.1
Now we can multiply this by 4 to find the euro equivalent:
4.1 * 4 = 16.4
So £12.30 is €16.40
solve for y.
enter your answer in the box.
y= __
Answer:
y = 10 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
The angles of this triangle should all add up to 180 degrees.
There are 3 angles so 180 ÷ 3 = 60. Each angle will = 60 degrees.
To find y:
5y + 10 = 60
5y = 60 - 10
5y = 50
y = 50 ÷ 5
y = 10
what is sin 45 degree?
Answer:
The answer is 1/square root 2
Step-by-step explanation:
Jaimie swims 12 the length of the swimming pool every 14 of a minute.
Enter the number of lengths of the swimming pool Jaimie swims per minute.
_[blank]_ lengths
Jaimie swims 12 the length of the swimming pool every 14 of a minute. Then in one minute, he will swim = 14/12=1.16 So, he will be able to swim 1.16 length in 1 minute.
What is the GCF of 18 and 27?
Answer: 9
Step-by-step explanation:
The factors of 18: 1, 2, 3, 6, 9, 18
The factors of 27: 1, 3, 9, 27
The GCF of 18 and 27 is 9. This means that 9 is the largest number that can evenly divide both 18 and 27 without leaving any remainder.
Step 1: Find the Factors of Each Number
To find the factors of a number, you identify all the whole numbers that divide that number without leaving a remainder. Here are the factors of 18 and 27:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
Step 2: Identify the Common Factors
Next, we look for the common factors between the two sets of factors. These are the numbers that appear in both lists:
Common factors of 18 and 27: 1, 3, 9
Step 3: Determine the Greatest Common Factor (GCF)
The GCF is the greatest or largest number among the common factors. In this case, the greatest common factor among 1, 3, and 9 is 9.
Therefore, the GCF of 18 and 27 is 9. This means that 9 is the largest number that can evenly divide both 18 and 27 without leaving any remainder.
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What is the length in feet ?
Answer:
The length is 81 feet.
Step-by-step explanation:
If you plot the equations for both length and width on a graph, making them both equal to y of course, you find that they cross each other in two places. The places they cross are (81, 11) and (70, 0). It is impossible for the answer to have the width as 0 feet, so the answer is 81 feet.
Answer:
depends on the how many fee your talking
Step-by-step explanation: