Answer:
[tex]y = \frac{1}{2}x^{2} - 3x + 11.5[/tex]
Step-by-step explanation:
Vertex Form of a quadratic equation;
[tex]y = a( x - h )^{2} + k[/tex]
Vertex of the parabolas (h, k)
The vertex of the parabola is either the minimum or maximum of the parabola. The axis of symmetry goes through the x-coordinate of the vertex, hence h = -3. The minimum of the parabola is the y-coordinate of the vertex, so k= 7. Now substitute it into the formula;
[tex]y = a ( x + 3 ) ^{2} + 7[/tex]
Now substitute in the given point; ( -1, 9) and solve for a;
[tex]9 = a( (-1 ) + 3)^2 + 7\\9 = a (2)^{2} + 7\\9 = 4a + 7\\-7 -7\\2 = 4a\\\frac{1}{2} = a\\[/tex]
Hence the equation in vertex form is;
[tex]y = \frac{1}{2}(x - 3)^{2} + 7[/tex]
In standard form it is;
[tex]y = \frac{1}{2}x^{2} - 3x + 11.5[/tex]
The difference between the length and the width of a rectangle is 5 centimeters. What id the length (the longer side) of the rectangle, if its perimeter is equal to 106 centimeters
Answer:
29
Step-by-step explanation:
106=2(x+x+5)
53=2x+5
48=2x
24=x
24+5=29
Kent is making a scale model of his favorite train. The actual train is 12 feet long and 4 feet wide. Kent wants his model to be 6 inches in length. Which would be the width of his model if he uses the same ratio?
Answer:
2 feet
Step-by-step explanation:
Answer:
2 feet
Step-by-step explanation:
...
Identify the slope and y-intercept. If the equation is in standard form, you may need to switch it to slope-intercept form. Sketch the graph of each line.
x - 5y = 20
Identify the values of the variables. Give your answers in simplest radical form. 100 points
Answer:
3/-2 is = to 30 degrees so..
Step-by-step explanation: w=34
V=21
A laundry basket has 24 t-shirts in it. Four are navy, twelve are red and the remaining are white. What is the probability of not selecting a red shirt? *
Answer:
50%
Step-by-step explanation:
Identify the population of shirts that are *NOT red.* In this case 12 are red. This means that 12 shirts are *not red.* 12/24 = .5 or 50% probability.
1. A wise old man once said, "500 reduced by 4 times my age is
296." What is his age?
Answer:
51
Step-by-step explanation:
51×4=204
500-204=296
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression
30 points and Brainly if answer is right
what is 4.193 to the nearest ten
The answer is 4.2
The 9 is above 5 so it raises the one
Distance between (-9,-6) and (-6,-8)
Answer:
The distance is....
5
Step-by-step explanation:
15 3/5 - 3 2/7 = ?
A. 12 31/35
B. 12 11/35
C. 11 21/35
D. 11 1/35
Answer:
its A
Step-by-step explanation:
hope this helps
A: x/8=3/4
B: 2/5=x/40
Answer:
A.)x=6
B.)x=16
did u mean to solve it or do something else if this is not the way u mean i can do another way if u like
PLZ HELP HELP PLZ PLZ ASAP ASAP
Answer: 8
Step-by-step explanation: Divide 224 by 28
2.
M
28°
mZM =
N
L
mZNE
Answer:
28°
Step-by-step explanation:
..... ....... ..... ...
Select the image of the figure after a rotation of 270⁰ about the origen
Answer:
10
Step-by-step explanation:
I think I don’t evenknow !
13yd of circumference
Answer:
look it up mf
Step-by-step explanation:
1,958.55 divided by 15?????
Find the area under the curve y = 1/x^2 between the ordinates x=1 and x=5
Answer:
The area is -6/5 units
Step-by-step explanation:
We start by integrating the curve equation
1/x^2 = x^-2
So the integration will be;
x^-2+1/-2 + 1 = -1/x + k
So we have the area as;
-1/5 -1 = (-1 - 5)/5 = -6/5
-
HELP I NEED HELP ASAP
Answer:
Option C is the correct answer
Step-by-step explanation:
C. Multiply both sides of the equation by 20
what's $90.94 with 50% off..?
Answer:
Write 50% as a decimal number:
STEP 2: Multiply by 90.94:
Step-by-step explanation: answer is 49.47
Answer:
45.47$
Step-by-step explanation:
50% means to cut things off by half
(trigonometry!!) Write the ratios for sin A and cos A. If needed reduce the fractions.
Answer:
Step-by-step explanation:
sin A = [tex]\frac{35}{37}[/tex]
cos A = [tex]\frac{12}{37}[/tex]
z-x/3=y solve for z
it's on a quiz hurryyy
Answer:
z = 3y + x
Step-by-step explanation:
z - x / 3 = y
multiply both sizes by 3
z - x = 3y
add x
z = 3y + x
how do i use the substitution method for these equations
y=3x+4
y=5x+12
Answer:
hello there mate
Step-by-step explanation:
2x+3y=4 y+3x=6
find x and y
Answer:
x=-3/2y+2
y= y=−3x+6
Step-by-step explanation:
solve for x.
2x+3y=4
Add -3y to both sides.
2x+3y+−3y=4+−3y
2x=−3y+4
Divide both sides by 2.
2x/2= -3+4/2
x= -3/2 y+2
solve for y.
y+3x=6
Add -3x to both sides.
3x+y+−3x=6+−3x
y=−3x+6
The sum of 2 numbers is 49. The second number is 15 less than the first number. The first number is
represented about x and the second number is represented about y. Write the equation that goes with
this description.
Answer:
x + y = 49
y = x - 15
Step-by-step explanation:
The sum of 2 numbers is 49 means that x+y = 49. (The two numbers are x and y, and the sum of them are 49.)
The second number is 15 less than the first number, means that y = x - 15 (The second number is y, and it is 15 less than x, which is the first number.)
Therefore the equations will be
x + y = 49
y = x - 15
Answer:
Step-by-step explanation:
The sum of 2 numbers is 49
x + y = 49
The second number is 15 less than the first number.
y = x - 15
Rey paid $91 for a watch that was on sale for 30% off. Grace and Curtis were debating how much the original price was. Grace said it would be $118.30 but Curtis said the original price should be $130, which person do you agree with? Why?
Answer:
The original cost is $130
Step-by-step explanation:
Step one:
given data
We are told that Rey paid $91 for a watch that was on sale for 30%
let the original cost be x
so that 30% off x= $91 --------not the word OFF not OF
Required
the original cost x
Step two
hence
x- 30/100*x= 91
x-0.3x=91
0.7x= 91
divide both sides by 0.7
x= 91/0.7
x=$130
A pair of pants that Jessica wants are usually $39. If the store is having a 33% off sale, how much will the pants cost
Answer: $12.87
Step-by-step explanation:
You need to set up your equation. We are trying to find x.
Step 1: [tex]\frac{x}{39} = \frac{33}{100}[/tex]
Step 2: Multiply across: 39 x 33 divided by 100.
39 x 33 = 1287
1287 divided by 100 = $12.87
Answer: $12.87
When you divide 2149 by n, the remainder is 4. When you divide 1578 by n the remainder is 5. What is the least possible natural number n?
and other question
When you divide 12,650 by n , the remainder is 2. When you divide 5,800 by n the remainder is 3. What is the least possible natural number n?
Bonus If you want brainly answer these 2 other questions
n is a natural number. Find the greatest possible value of the GCD of
(2n+25) and (n+15)
Also answer
(2n+25) and (n+15)
Answer:
First Q: The smallest value for which n works is 11.
Second Q: Smallest here is 17.
Third Q: I don't know this one, sorry!
Fourth Q: n is -10.
Step-by-step explanation:
For the first two questions, find the smallest common factor between the two numbers (subtract the remainder).
Q1:
First, subtract the remainders from the numbers (2149 - 4 = 2145; 1578 - 5 = 1573)
Then, list the factors
2145: 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145
1573: 1, 11, 13, 121, 143, 1573
These two numbers share 11 and 13 in common. 11 is the smaller of these, so it is the smallest value n can work.
Q2:
Repeat the steps from Q1.
12650 - 2 = 12648; 5800 - 3 = 5797
12648: 1, 2, 3, 4, 6, 8, 12, 17, 24, 31, 34, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 372, 408, 527, 744, 1054, 1581, 2108, 3162, 4216, 6324, 12648
5797: 1, 11, 13, 17, 31, 187, 341, 527, 5797
These two share 17, 31, and 527 in common. 17 is the smallest of these, so it is the smallest value n can work.
Q4 (I don't know how to do Q3 yet):
2n + 25 = n + 15
Subtract n from both sides
n + 25 = 15
n = 15 - 25
Subtract 25 from 15 to get -10
n = -10
Again, I don't know how to do Question 3 yet. Sorry for the inconvenience! Anyhow I hope the rest of this was helpful!
The least possible natural number n is 11.
Given that, when you divide 2149 by n, the remainder is 4. When you divide 1578 by n the remainder is 5.
What is GCD?The greatest common divisor (GCD) refers to the greatest positive integer that is a common divisor for a given set of positive integers.
Question 1:
First, subtract the remainders from the numbers (2149 - 4 = 2145; 1578 - 5 = 1573)
Then, list the factors
2145: 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145
1573: 1, 11, 13, 121, 143, 1573
11 and 13 are common factors. 11 is the smaller of these, so the smallest n value is 11.
Question 2:
First, subtract the remainders from the numbers
That is, 12650 - 2 = 12648; 5800 - 3 = 5797
List the factors:
12648: 1, 2, 3, 4, 6, 8, 12, 17, 24, 31, 34, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 372, 408, 527, 744, 1054, 1581, 2108, 3162, 4216, 6324, 12648
5797: 1, 11, 13, 17, 31, 187, 341, 527, 5797
17, 31, and 527 are common factors. 17 is the smaller of these, so the smallest n value is 17.
Therefore, the least possible natural number n is 11.
To learn more about the GCD visit:
https://brainly.com/question/27227228.
#SPJ2
(-10,-7) (-8,1) find the distance between two points
Answer: [tex]\sqrt{68}[/tex] units.
Step-by-step explanation:
The distance between points (a, b) and (c, d) is given by :_
[tex]D=\sqrt{(d-b)^2+(c-a)^2}[/tex]
Given points : (-10,-7) (-8,1)
Distance between points (-10,-7) and (-8,1) = [tex]\sqrt{(1-(-7))^2+(-8-(-10))^2}[/tex]
[tex]=\sqrt{(1+7)^2+(-8+10)^2}\\\\=\sqrt{8^2+2^2}\\\\=\sqrt{64+4}\\\\=\sqrt{68}[/tex]
Hence, distance between given points = [tex]\sqrt{68}[/tex] units.
What is the x-intercept?
Answer:
(5,0)
Step-by-step explanation:
PLEASE HELP
ANSWER SERIOUSLY
Answer:
raise a product to a power.
you first simplify the parenthesis in the numerator by raising 2 by the power of three and multiplying the exponents.
i suck at explaining, but after the first step the expression looks like:
[tex](\frac{8r^{6}t^{3} }{4t^{2} })^{2}[/tex]
Step-by-step explanation: