Find the vertex of the parabola.
x² + y - 6x + 10 = 0
the product of 9 and sum of a number x and 12
Answer:
9(x + 19)
Step-by-step explanation:
Product is a multiplication key word where you'll usually always put parenthesis when multiplying, and where the keyword sum comes you'd add x and 12 for your equation :)
Determine if the following relations represent y as a function of x.
================================================
Explanation:
If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.
Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.
The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.
A function assigns the values. The only function that represents y as a function of x is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.
A.) x = y⁴
It represents x in terms of y, therefore, No.
B.) 6x² + y = 4
It represents constant in terms of x and y, therefore, No.
C.) 6x + y² = -1
It represents constant in terms of x and y, therefore, No.
D.) [tex]y = \sqrt{1-x^2}[/tex]
The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.
E.) -2xy = 1
It represents constant in terms of x and y, therefore, No.
Hence, the only function that represents y as a function of x is D.\
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Can anybody help with these two problems for me please this for algebra finding slope
Answer:
Step-by-step explanation:
1. the slope is -7/2
2. the slope is 2/3
y = mx + b
m is the slope
Slope is the number before the x so
1. -7/2
2. 2/3
What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change
Answer:4mph
5mph
Slower
Step-by-step explanation:
The average rate of change for the runner is 0.667 miles per hour².
How to calculate the average rate of change?To calculate the average rate of change, we follow the following formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.
How to solve the given question?In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.
So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.
Thus, we can calculate the average rate of change a, using the formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².
Therefore, the average rate of change for the runner is 0.667 miles per hour².
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To shop a package, a company charges a one-time fee plus a fee based on the weight of the package. The table below shows the total shipping costs for four packages of different weights.
Answer:
C = $5 + $1.5(w)
Step-by-step explanation:
Given the following information :
Total shipping cost :
One time fee + fee based on package weight
Given the table :
Weight in pounds - - - - Total shipping cost($)
___4__________________11
___8__________________17
___12_________________23
___16_________________29
We can deduce from the table
For a package that weighs (w) 4 pounds
Total shipping cost = $11
Let one time fee = f
Fee based on weight = r
f + 4(r) = 11 - - - - - (1)
For a package that weighs (w) 8 pounds
Total shipping cost = $17
One time fee = f
Fee based on weight = r
f + 8r = 17 - - - - - (2)
From (1)
f = 11 - 4r - - - (3)
Substitute f = 11 - 4r in (2)
11 - 4r + 8r = 17
-4r + 8r = 17 - 11
4r = 6
r = 6/4
r = 1.5
Put r = 1.5 in (3)
f = 11 - 4(1.5)
f = 11 - 6
f = 5
Hence one time fee = $5
Charge based on weight = $1.5
Hence, Total shipping cost 'C' for a package weighing 'w' will be :
C = $5 + $1.5(w)
what number increase by 25 become s 150
Answer:
125
Step-by-step explanation:
n+25 = 150.
150-25= 125.
n must equal 125.
answer is 125.
Think about your previous math courses. Identify one tope that you learned about which
you excelled
The answer for this question I don’t think could be answered by anyone but yourself. To help you figure this out, just simply think about all of the math courses you’ve had previous to your current course and think about which course you did best in.
How does the area of the scale drawing where 1 centimeter represents 10 miles compare to the area of a the drawing where 1 centimeter represents 30 miles? Area if 1 cm= 10 mi: square miles Area if 1 cm = 30 mi: square miles The area would be times as great.
Answer:
100 square miles900 square miles9 times as greatStep-by-step explanation:
It seems rather obvious that ...
(1 cm)^2 ⇒ (10 mi)^2 = 100 mi^2 . . . on the first drawing
(1 cm)^2 ⇒ (30 mi)^2 = 900 mi^2 . . . on the second drawing
The area on the second drawing is 900/100 = 9 times as great.
_____
These are the areas represented by 1 square cm on the scale drawing. If the drawing is larger, then the represented area is correspondingly larger. The ratio of represented areas is still 9 times for drawings of the same size.
Find the slope, x and y intercepts and sketch the graph for the linear equation.
y = 2x + 1
Answer:
In bold below.
Step-by-step explanation:
The slope = coefficient of x = 2.
The y-intercept is when x = 0 and x-intercept is when y = 0.
y = 2(0) + 1 = 1 so the y -intercept is (0, 1).
2x + 1 = 0
x = -0.5 so the x-intercept is (-0.5, 0)
We've seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operations, and give examples to support your answers.
Answer:
A
Step-by-step explanation:a
label the midpoint between 6.54 and 6.55
6.545, since it is the midpoint of 6.54 and 6.55.
Hopefully it helps!
Please mark brainliest :)
The mid - point between the numbers is 6.545.
We have two decimal numbers → 6.54 and 6.55
We have to determine their mid - point.
You have two numbers - 'x' and 'y'. Find the mid - point between these two numbers.The midpoint (n) between these two numbers will be -
[tex]$n=\frac{x+y}{2}[/tex]
According to the question, we have -
Number 1 → 6.54
Number 2 → 6.55
Assume the mid - point be n. Therefore -
n = [tex]\frac{6.54+6.55}{2}[/tex] = 6.545
Hence, the mid - point between the numbers is 6.545.
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³√1,000,000 how do I solve this expression?
Answer:
100
Step-by-step explanation:
try to write it exponentially
³√10⁶
(10⁶)^⅓
(10)^6/3
(10)^2
10x10 = 100
write the value of the unknown number in the verbal description
5 times the sum of 2 and a number is 80
a. 1
b. 28
c. 4
d. 16
Answer:
B.28
Step-by-step explanation:
Find the measure of angle
Answer:
angle AEF is 60 degrees
Step-by-step explanation:
120 - 90 = 30
90 - 30 = 60
Determine whether the equation defines y as a function of x.
x+y=9 and x^2+y^2=1 and x=y^2
Answer:
Function: [tex]x+y=9[/tex]
Not Function: [tex]x^2+y^2=1[/tex] and [tex]x=y^2[/tex]
Step-by-step explanation:
Given
[tex]x+y=9[/tex]
[tex]x^2+y^2=1[/tex]
[tex]x=y^2[/tex]
Required
Determine if [tex]y[/tex] is a function of [tex]x[/tex]
Solving x+y=9
[tex]x+y=9[/tex]
Make y the subject of formula
[tex]y = 9 - x[/tex]
Hence; y is a function of x
Solving [tex]x^2+y^2=1[/tex]
[tex]x^2+y^2=1[/tex]
Subtract x² from both sides
[tex]y^2=1 - x^2[/tex]
Square root of both sides
[tex]y =\± \sqrt{1 - x^2}[/tex]
This implies that
[tex]y =\sqrt{1 - x^2}[/tex] or [tex]y =-\sqrt{1 - x^2}[/tex]
Because [tex]y[/tex] can be any of those two expressions, it is not a function.
Solving [tex]x=y^2[/tex]
[tex]x=y^2[/tex]
Reorder
[tex]y^2 = x[/tex]
Take square roots
[tex]y = \±\sqrt{x}[/tex]
This implies that
[tex]y = \sqrt{x}[/tex] or [tex]y = -\sqrt{x}[/tex]
Because [tex]y[/tex] can be any of those two expressions, it is not a function.
0.456(456 repeating) as a fraction
Answer:
Try 57/125
Step-by-step explanation:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Answer:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Hope this helps! （づ￣3￣）づ╭❤～
David bought a baseball card for $40. the value of the card increased by 25%. what is the new value of the card?
Answer:
65 i think
Step-by-step explanation:
Answer:
65 Im preety sure
Step-by-step explanation:
a windshield wiper blade is 17 in Long. Calculate the area come by the blade as it rotates through an angle of 138 degrees.
Answer: 348 in²
Step-by-step explanation:
Area of a circle is πr². Area of a sector is the same formula but only for the section so you need to determine what fraction of the circle it is. You do this by dividing by 360° if degrees are provided or by 2π if radians are given.
[tex]A=\pi r^2 \bigg(\dfrac{\theta}{360^o}\bigg)[/tex]
Given: r = 17
Ф = 138°
[tex]A=\pi(17)^2\bigg(\dfrac{138^o}{360^o}\bigg)\\\\\\.\quad =289\pi \bigg(\dfrac{23}{60}\bigg)\\\\\\.\quad =\dfrac{6647\pi}{60}\pi\\\\\\.\quad =347.9\ in^2[/tex]
Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet below. What is Kendra’s net cash flow? a. $295 b. $285 c. $275 d. $255
The spreadsheet is missing, so i have attached it.
Answer:
Option A - $295
Step-by-step explanation:
From the spreadsheet, net pay = $2300 and interest earned on savings = $20
Therefore, her total income = $2300 + $20 = $2320
Now,from the spreadsheet, total expenses = 800 + 120 + 90 + 45 + 95 + 80 + 275 + 520 = $2025
Now, net cash flow = Total income - Total expenses
Net cash flow = $2320 - $2025
Net cash flow = $295
Answer:
a. 295
Step-by-step explanation:
Dimensional analysis. How many years of your life will you be sleep if you live 3.95 x 10^7 minutes and average 8 hours sleep/night.
Answer:
The total years of sleep = 25.05 years
Step-by-step explanation:
Given total time in minutes = 3.95 x 10^7
Now convert the total time in hours = (3.95 x 10^7) / 60 = 658333.333 hours
Now covert the total hours into the day. Since a day has 24 hours so divide the total hours by 24 = 658333.333 / 24 = 27430.5555 days.
A person sleeps 8 hours a day, so total hours of sleep = 8 × a number of days.
A person sleeps 8 hours a day, so total hours of sleep = 8 × 27430.5555 days.
Thus, total sleeping hours = 219444.444
Now convert it into a number of years.
Convert total hours into the day and then years.
Number of days = 219444.444 / 24 = 9143.5185 days.
Now covert the total days in to years = 9143.5185 / 365 = 25.05 years
Find an equation of the line passing through the given points. Use function notation to write the equation. (1,-1) and (2,2) f(x) = ? PLEASE HELP!
Answer:
Good luck!
Step-by-step explanation:
Roots = 1, 2
Sum of roots = 3
Product of roots = 2
Use f(x) = ax^2 - bx + c
Therefore, f(x) = x^2 - 3x + 2
3421 ounces equals how many tons
Answer:
0.1069062
Step-by-step explanation:
divide the mass value by 32000
hope this helps.
5 4th power times 5 to the 2 power
Answer:
15625
Step-by-step explanation:
Answer:
(5⁴)(5²) or 15625
Step-by-step explanation:
When looking at a problem like this you need to look for keywords such as "Power" and "times"
5 to the 4th power looks like this 5⁴
And 5 to the 2nd power looks like this 5²
Making this (5⁴)(5²)
But if you want the answer after that the answer is 15625
evaluate the 1/3 of 10.2
Answer:
3.4
Step-by-step explanation:
Find the distance from the point P to line m in the given figure. A) [tex]\sqrt{170}[/tex]B)[tex]\sqrt{85}[/tex] C) [tex]\sqrt{17}[/tex]D)[tex]\sqrt{34}[/tex]
Answer:
C. [tex]\sqrt{17}[/tex]
Step-by-step explanation:
use pythagorean
= [tex]\sqrt{1^2 + 4^2}[/tex]
= [tex]\sqrt{17}[/tex]
therefore, the answer is C. [tex]\sqrt{17}[/tex]
Answer:
C. √17
Step-by-step explanation:
point P to line m
= √(1² + 4²
= √17
Equivalent expression 31/8 - 21/2
Answer:
-6 5/8 or -6.625
Step-by-step explanation:
31/8 - 84/8 = -53/8
-53/8 = -6 5/8 or -6.625
The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?
Answer:
width=4
length=18
Step-by-step explanation:
length-6=3width
length=3width+6
also:
perimeter of the rectangle=2(length+width)
44/2=width+length
22=width+length
now put the length we found in the 1st equation, in 22=width+length
=>22=width+3width+6
22-6=4width
width=4
now do the exact same thing with one of these equations:
22=width+length
length=3width+6
I'd do it with the 1st one:
22=4+length
22-4= length
length=18
Construct the perpendicular bisector for the segment in the following figure. What process did you use? Explain.
Answer:
Perpendicular bisector for the given segment AB is shown below.
Step-by-step explanation:
Construction steps for the perpendicular bisector for the given segment AB are:
1. Open your compass more than half of the distance between end points of the given segment, i.e., A and B.
2. Place the compass on point A and mark two arc on each side of line segment AB.
3. Place the compass on point B and mark two arc on each side of line segment AB, which intersect the previous arcs.
4. Arcs meet at two points. Mark them C and D.
5. Draw the line between C and D.
The perpendicular bisector for the given segment AB is shown below.
40 points!! tysmmmm <33
Answer:
54 lol not 40 its 20
Step-by-step explanation: