Answer:
B
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant.
Using the distance formula
[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] = | y - 6 |
Squaring both sides
(x + 2)² + (y - 4)² = (y - 6)² ← distributing
x² + 4x + 4 + y² - 8y + 16 = y² - 12y + 36 ( subtract y² - 12y + 36 from both sides )
x² + 4x + 4 + 4y - 20 = 0 ( subtract x² + 4x + 4 from both sides )
4y - 20 = - x² - 4x - 4 ( add 20 to both sides )
4y = - x² - 4x + 16 ( divide through by 4 )
y = - [tex]\frac{1}{4}[/tex] x² - x + 4, that is
f(x) = - [tex]\frac{1}{4}[/tex] x² - x + 4 → B
Answer:
Option B
Step-by-step explanation:
Given that a parabola has a focus at (−2, 4) and a directrix of y = 6.
We have to find the equation of the parabola in std form
We know that a parabola is a conic section in which all points are equidistant from the focus and vertex.
Let (x,y) be any point on the parabola
Distance of (x,y) from the focus =[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] ...i
Distance of (x,y) from directrix = difference in y coordinate = [tex]|y[-6|[/tex]...ii
Since i = ii, square and equate both
[tex](x+2)^2+(y-4)^2=(y-6)^2\\x^2+4x+4 -8y+16 = -12y+36\\4y=-x^2-4x+16\\y = \frac{-1}{4} d^2-x+4[/tex]
Hence option B is right.
Norma's credit card has an APR of 16%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. Her credit card record for the last 7 months is shown in the table
below.
Norma's credit card balance at the end of the 7th month is $1,487.22.
How to solveCalculate the interest for each month.
Interest = (Previous month's balance * APR) / 12
Calculate the new balance for each month.
New balance = Previous month's balance + Purchases + Interest - Payments
Here's the calculation for each month:
Month 1:
Interest: 0 (No interest on the first month)
Balance: $500 + $0 = $500
Month 2:
Interest: ($500 * 0.16) / 12 = $6.67
Balance: $500 + $200 + $6.67 - $10 = $696.67
Month 3:
Interest: ($696.67 * 0.16) / 12 = $9.29
Balance: $696.67 + $300 + $9.29 - $20 = $986.29
Month 4:
Interest: ($986.29 * 0.16) / 12 = $13.15
Balance: $986.29 + $100 + $13.15 - $20 = $1079.44
Month 5:
Interest: ($1079.44 * 0.16) / 12 = $14.39
Balance: $1079.44 + $150 + $14.39 - $10 = $1233.83
Month 6:
Interest: ($1233.83 * 0.16) / 12 = $16.45
Balance: $1233.83 + $0 + $16.45 - $15 = $1235.28
Month 7:
Interest: ($1235.28 * 0.16) / 12 = $16.47
After all the computations, taking into consideration the amount spent and paid earlier,
Norma's credit card balance at the end of the 7th month has amounted to $1,487.22.
Read more about credit card here:
https://brainly.com/question/26857829
#SPJ1
Norma's credit card has an APR of 16%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. Her credit card record for the last 7 months is shown in the table below.
Month Purchases Payments
1 $500 $0
2 $200 $10
3 $300 $20
4 $100 $20
5 $150 $10
6 $0 $15
7 $250 $15
Calculate Norma's credit card balance at the end of the 7th month.
Answer: 389.46
Step-by-step explanation:
Add all payments received.
trust
The product of 9 and x is less than or equal to -17
Answer:
9+x< -17
(make sure there's a line under the less than sign to make it work to)
Step-by-step explanation:
the product of 9 and x describes an addition problem, so it would be 9+x. after you put the less then or equal to sign and then -17.
Hope this helps
To solve the inequality 9x ≤ -17, divide both sides by 9 to find x ≤ -17/9, meaning x can be any value less than or equal to approximately -1.888.
The student's question pertains to an inequality in mathematics involving a variable x and requires an understanding of algebraic inequalities. To solve the inequality 9x ≤ -17, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 9, which gives us x ≤ -17/9. It is important to note that dividing by a positive number does not change the direction of the inequality sign.
The value of x must satisfy this inequality, so any number less than or equal to -17/9 is a solution to the inequality. That means x could be -2, -3, or any other value that is less than or equal to approximately -1.888... (since -17/9 is a decimal approximation of -1.888...).
What is the slope of (5,3) and (5,-9)
The slope is the change in Y over the change in X.
A point is written as ( X,Y), where the first number is the X and the second number is the Y.
You have:
(5,3) and (5,-9)
The change in Y is -9 - 3 = -12
The change in X is 5-5 = 0
The slope becomes -12/0
Because you have a 0 on the bottom of the fraction the slope is undefined because you cannot divide by 0.
The slope is undefined.
% of 50 shirts is 35 shirts.
Answer:
35/50
= x/100
3500=50x
x=3500/50=70
70%
Answer:
Step-by-step explanation:
% of 50 s:hirts is 35 shirts: (35×50)/100 = 17.5
model the number 5.55 on the place value chart
Answer:
Here's what I get
Step-by-step explanation:
Each digit in a number has a place value, based on its distance from the decimal point.
The value of a digit is the digit multiplied by its place value.
The place value of a digit increases by a factor of 10 as we move left on the place value chart and decreases by a factor of 10 as we move right.
Numbers to the left of the decimal point increase in the order: ones, tens, hundreds, thousands, etc.
Numbers to the right of the decimal point decrease in the order: tenths, hundredths, thousandths, etc.
So, we put the digits of 5.55 on the chart according to their place value.
Use the number 913,256.
4. Write the name of the
period that has the
digits 913.
Answer:
ummm the thousands im pretty sure
Step-by-step explanation:
I’d like for you to Show work please:)
Write an even number between 7 and 16 draw a picture and the write a sentence to explain why it is an even number
The even number I picked was 6, here is why it is an even number.
You can put each in even groups, without having one group be more or less then the other, if I picked an odd number like 7, one group would had more, and the other 2 groups would have less.
------------------------------------------------
Hope this helped, have a great day!
x + (-y)= -y + x
What’s the property
hm
Step-by-step explanation:
I'd go with associative because its re grouping
Answer:
Step-by-step explanation:
the property is : a+b= b+a comutative for +
The expression above can also be written in the form of
Answer:
a= 7
b=9
c=4
Step-by-step explanation:
Answer:
a= 7
b=9
c=4
Step-by-step explanation:
lol
The shaded rectangle shown below is a scale drawing of a rectangle whose area is 288 square feet. What is the scale factor of the drawing? (Note: Each square on the grid has a length of 1 unit.)
Answer:
2881
Step-by-step explanation:
Answer:
1 sq.unit = 9 sq.feet
Step-by-step explanation:
Length of shaded rectangle = 6 square on grid
We are given that Each square on the grid has a length of 1 unit.
So, Length of shaded rectangle = 6 units
Breadth of shaded rectangle = 4 square on grid = 4 units
Area of shaded rectangle = [tex]Length \times Breadth = 8 \times 4 = 32 units^2[/tex]
We are given that area of original square = 288 sq.feet
32 sq.unit = 288 sq.feet
1 sq.unit = [tex]\frac{288}{32} =9[/tex]
So, 1 sq.unit = 9 sq.feet
Hence Scale is 1 sq.unit = 9 sq.feet
−7⋅8 pls help asap help
Answer:What do you need help with
Find the slope and the y-intercept of the line.
y=9x-1
slope:
y-intercept:
Hey!
------------------------------------------------
Solution:
The equation is written in slope-intercept form!
~Formula
y = mx + b
~Terms
m = slope
b = y-intercept
------------------------------------------------
Answer:
[tex]\large\boxed{9~=~slope!}\\\large\boxed{1~=~y~intercept!}[/tex]
------------------------------------------------
Hope This Helped! Good Luck!
Hi, let me help you out!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
We are given an equation in slope-intercept form:
[tex]\longrightarrow\tt{y=mx+b}[/tex]
Where m is the slope, and b is the y-intercept.
Now let's find the slope of the given line.
Note: The slope is the coefficient of x.
The slope is 9, and the y-intercept (the constant term added to or subtracted from the slope) is -1.
I hope this helps you! Have an awesome day!
If you need any explanation or clarification, feel free to ask! :D
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Which of the following transformations is shown?
A. Translation 1 unit down
B. Translation 2 units down
C. Translation 3 units to the right
D. Reflection across the line y-axis
Answer:
B. Translation 2 units down
Step-by-step explanation:
Each time you start from a certain y-intercept, its prime gets translated two below each time:
n[1, 0] to n'[-1, 0]
m[4, 0] to m'[2, 0]
Now, it does not look perfectly shifted down for m' and m, but it it is definitely translated.
I am joyous to assist you anytime.
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
The answer is f(x)=5(x+8)-80f ( x ) = 5 ( x + 8 ) − 80
Find the length of segment CD with points C(2,2) and D (-1,8)
A. 8.1
B. 5.2
C. 4.3
D. 6.7
Answer:
D
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = C(2, 2) and (x₂, y₂ ) = D(- 1, 8)
CD = [tex]\sqrt{(-1-2)^2+(8-2)^2}[/tex]
= [tex]\sqrt{(-3)^2+6^2}[/tex]
= [tex]\sqrt{9+36}[/tex] = [tex]\sqrt{45}[/tex] ≈ 6.7 → D
a cone has a radius of 5 m and a height of 3 m.What is the volume of the cone?
Answer:
78.54 [tex]m^3[/tex]
Step-by-step explanation:
Use the formula for the volume of a cone of circular base with radius "R" and height "H", using the given values for the radius R (5 meters), and the cone's height (3 meters)
[tex]Volume= \pi R^2 \frac{H}{3} \\Volume = \pi 5^2 \frac{3}{3} m^3 = 78.539816.... m^3[/tex]
And we round the answer to two decimals:
Volume = 78.54 [tex]m^3[/tex]
Please help with this math question!
Answer:
74 feet in total. All it is is the perimeter
What is (f ° g)(2) and (g ° f)(2) with the set of points f: {(0,4), (1,2), (2,0), (3,2), (4,4)} and g: {(0,4), (1,3), (2,2), (3,1), (4,0)}
Answer:
[tex]\large\boxed{(f\circ g)(2)=0}\\\boxed{(g\circ f)(2)=4}[/tex]
Step-by-step explanation:
[tex]f:\{(0,4), (1,2), \underline{(2,0)}, (3,2), (4,4)\}\\\\g:\{\underline{(0,4)}, (1,3), \underline{(2,2)}, (3,1), (4,0)\}\\\\(f\circ g)(x)=f\bigg(g(x)\bigg)\\\\g(2)=2\qquad/from\ (2,2)/\\f\bigg(g(2)\bigg)=f(2)=0\qquad/from\ (2,0)/\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(2)=0\qquad/from\ (2,0)/\\g\bigg(f(2)\bigg)=g(0)=4\qquad/from\ (0,4)/[/tex]
One positive number is 3 times another number. The difference between the two numbers is 62. Find the numbers
Answer:
31
93
Step-by-step explanation:
Let the larger number = y
Let the smaller number = x
y = 3x
y - x = 62
3x - x = 62
2x = 62
2x/2 = 62/2
x = 31
y = 3x
y = 3*31
y = 93
Final answer:
To find two positive numbers where one is 3 times the other and their difference is 62, let one number be x, then solve the equation 3x - x = 62 to find the numbers 31 and 93.
Explanation:
To find the numbers:
Let one number be x, then the other number is 3x.
Form an equation: 3x - x = 62.
Solve for x: 2x = 62, x = 31.
So, the two numbers are 31 and 93.
Find the value of W and please show step by step working out
Answer:
w = 60
Step-by-step explanation:
Given
[tex]\frac{4w}{10}[/tex] + 28 = 52 ( subtract 28 from both sides )
[tex]\frac{4w}{10}[/tex] = 24
Multiply both sides by 10 to clear the fraction
4w = 240 ( divide both sides by 4 )
w = 60
-7 1/3 written as a fraction is
- 10/3
- 21/3
- 22/3
Answer:
-22/3
Step-by-step explanation:
Multiply the whole number by the denominator, and then add the numerator to get the improper fraction.
8. Minnie has 6 country CDs and 5 rock CDs.
Amanda has 5 rock CDs and 6 country CDs.
Who has more CDs? Explain.
Answer: They have the same amount (11 )
Step-by-step explanation: just because the numbers are switched, doesn’t mean anything( no difference in the numbers.
Esther works for a marketing company. She earns $12 per hour, and she gets $50 travel allowance every month. Which linear equation could be used to find her monthly pay rate?
Answer:
y = 12x + 50
Step-by-step explanation:
Given,
The fixed amount of monthly allowance = $ 50,
Also, the earning per hour = $ 12,
If she works x hours in a month,
Then her total earning in x hours = 12x,
Also, total earning for a month ( say y ) = earning for x hours + fixed allowance
⇒ y = 12x + 50
Which is the required linear equation.
Answer:
y = 12x + 50
Step-by-step explanation:
Just took post-test 15/15
Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point
(5, -4)? Select three options.
y=-2 X-2
2x +hoy = -10
L2x - 5y = -10
y+ 4 = _{(x - 5)
y- 4 = 5(x+5)
Answer
See below
Step-by-step explanation:
The given line has equation
[tex]5x - 2y = - 6[/tex]
The slope intercept form is
[tex]y = \frac{5}{2} x + 3[/tex]
The slope of this line is
[tex] m = \frac{5}{2} [/tex]
The line perpendicular to this line has slope
[tex] - \frac{2}{5} [/tex]
If this line passes through (5,-4), the point-slope form is
[tex]y + 4 = - \frac{2}{5} (x - 5)[/tex]
The slope-intercept form is
[tex]y = - \frac{2}{5} x- 2[/tex]
The standard form is
2x+5y=-10
The product of a number m and 1.7 is 6.63.
What is the value of m?
Drag and drop the correct number into the box so that the equation is true.
Answer:
3.9
Step-by-step explanation:
If m and 1.7 is 6.63, then m will be:
6.63 ÷ 1.70 = 3.9
Therefore the correct answer is 3.9
PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)
BRAINLIEST ASAP
solve for x
2x+9=35
Hey!
---------------------------
Solution:
2x + 9 = 35
2x + 9 - 9 = 35 - 9
2x = 26
2x/2 = 26/2
x = 13
---------------------------
Answer:
x = 13
---------------------------
Hope This Helped! Good Luck!
Answer:
x = 13
Step-by-step explanation:
Given
2x + 9 = 35 ( isolate 2x by subtracting 9 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13
How much does 8.20 X 10-3dm3 (1dm3 = 1L) sample of aluminum weigh in grams?
centimeters?
Answer:
8.20 grams ; 8.20 cm³
Step-by-step explanation:
At first convert it to m³ from dm³
we know,
1 dm³ =10⁻³ m³
∴ 8.20 X 10⁻³dm3 = 8.20 X 10⁻³ x 10⁻³ m³
=8.20 X 10⁻⁶ m³
m³ to gram :
1 m³ = 10⁶ grams
∴ 8.20 X 10⁻⁶ m³ = (8.20 X 10⁻⁶x10⁶) grams
= 8.20 grams
m³ to cm³ :
1m³ = 10⁶ cm³
∴8.20 X 10⁻⁶ m³ = (8.20 X 10⁻⁶ x 10⁶) cm³
=8.20 cm³
Note:
1 cm³ = 1 gram
Write an equation in slope intercept form of the line with slope of 3/5 and y intercept of -3
Answer: y= 3/5x-3
Step-by-step explanation:
Jordan will hike the trail shown at a rate of 4 mi/h. Write a linear equation to represent the distance Jordan still has to walk after x hours.What does the y-intercept of the equation
represent?
What we know:
Start of trail:
0 miles
End of trail:
25 miles
Answer:
Y=25-4x
Y means the distance Jordan still has to walk after x hours
Step-by-step explanation:
Answer:
y = 25 - 4*x
The y-intercept represents the total distance Jordan has to walk
Step-by-step explanation:
By Definition, speed = distance/time. We are interested in distance, then:
distance = speed*time
Calling x the hours of walking, and knowing that his speed is 4 mi/h, then:
distance = 4*x
The trail length is 25 miles, so if he walked 1 mile, 25 - 1 = 24 miles are left, in general:
y = 25 - 4*x
where y is the distance Jordan still has to walk.
The y-intercept is found replacing with x = 0, then:
y = 25 - 4*0
y = 25
which represents the total distance Jordan has to walk