The direction of fastest increase is along the line \(y = x + 1\).
Given that [tex]\(y\)[/tex] varies directly as the square root of [tex]\(x\)[/tex], we can express this relationship as:
[tex]\[ y = k \sqrt{x} \][/tex]
where [tex]\(k\)[/tex] is the constant of variation.
We are given that when [tex]\(x = 16\), \(y = 12\)[/tex]. Let's find the constant of variation:
[tex]\[ 12 = k \sqrt{16} \][/tex]
[tex]\[ 12 = 4k \][/tex]
[tex]\[ k = 3 \][/tex]
Now we can write the equation of variation:
[tex]\[ y = 3 \sqrt{x} \][/tex]
To find [tex]\(x\)[/tex] when [tex]\(y = 15\)[/tex], we can solve for [tex]\(x\):[/tex]
[tex]\[ 15 = 3 \sqrt{x} \][/tex]
[tex]\[ \sqrt{x} = \frac{15}{3} \][/tex]
[tex]\[ \sqrt{x} = 5 \][/tex]
[tex]\[ x = 5^2 \][/tex]
[tex]\[ x = 25 \][/tex]
Therefore, when [tex]\(y = 15\)[/tex], the corresponding value of [tex]\(x\)[/tex] is 25.
Which is the quadratic variation equation for the relationship y varies directly with x^2 and y=72 when x=3
y =72
x = 3
X^2 = 3^2 = 9
k = y/x = 72/9 =8
so you should have an option of:
y =8x^2
Factor this expression: ab + 4 + a + 4b
Grouping method works best on this one:
ab+a+4+4b=a(b+1)+4(b+1)
=(a+4)(b+1)
Answer:
Grouping method works best on this one:
ab+a+4+4b=a(b+1)+4(b+1)
=(a+4)(b+1)
Step-by-step explanation:
How to solve it using the system of substitution
Please help me with this!!
A card is drawn from a standard deck of 52 playing cards. find the probability that the card is an ace or a black card.
The probability that the card is an ace or a black card is 7/13
Probability is the likelihood or chance that an event will occur.
A standard card contains 52 cards. Hence the total outcome is 52.
Since there are 4 aces, the expected outcome is 4The total number of black cards is 26The total card that is ace and black is 2Get the required probability;
Prob(ace or black card) = Prob(ace) + Prob(black card) - P(ace and black card)
Prob(ace or black card) = 4/52 + 26/52 -2/52
Prob(ace or black card) = 28/52
Hence the probability that the card is an ace or a black card is 7/13
Learn more on probability here: https://brainly.com/question/14192140
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
bh+hr=25
solve for h and r
To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.
Explanation:To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:
bh + hr = 25
Factor out h from the left side of the equation:
h(b + r) = 25
Divide both sides by (b + r) to solve for h:
h = 25 / (b + r)
Now, let's solve for r. Replacing h in the original equation:
bh + hr = 25
b(25 / (b + r)) + r(25 / (b + r)) = 25
Multiply both sides by (b + r) to get rid of the denominators:
25b + 25r = 25(b + r)
Expand the equation:
25b + 25r = 25b + 25r
As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.
Learn more about Solving equations here:https://brainly.com/question/14410653
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Y -2 > -11 what is the answer to this
David bought a used car for $3,000 and later sold it for $1,000. What was the approximate percent decrease in the price of the car?
Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2
Write 3 ½% as a fraction
Answer:
7/200
Step-by-step explanation:
3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200
_____
The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.
What type of angles are 6 and 8?
The coefficients of the expression 5x^4-4x^2+3 are??
The blade of a circular saw rotates at a rate of \2500 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a 7 and one fourth7 1 4 inch diameter blade?
The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.
Explanation:To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:
Linear velocity = 2 * π * radius * angular velocity
Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:
Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.
To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):
Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.
The graph of a line goes up and to the right when
Answer: When the coefficient of X is positive!
In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance? In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance?
Answer:
The weight loss program is statistically significant.
Step-by-step explanation:
We can define a statistically significant difference or result as a result which is not attributed to chance. In other words we can say that a statistical significance shows if the difference observed between groups is real or if it has occurred simply due to chance.
Here, given is that 40 subjects lost a mean of 3.0 lb after 12 months.
So, here the weight loss program is statistically significant as the results are unlikely to occur by chance.
find an angle measure that is supplementary to this angle 126 degrees
Answer:
Step-by-step explanation:
Answer:
54°
Step-by-step explanation:
The sum of the measures of two supplementary angles is 180°.
180° - 126° = 54°
Answer: 54°
A scatter plot has been created with a line of best fit that matches the equation y = 11x + 340. Using this line of best fit, determine the output value when the input is 10. Do you think this matches a point on the scatterplot? Why or why not?
5. A piece of plywood has a length that is 5 more than twice its width. Write the expression that represents the area of the plywood.
for the function:
f(x) = -3x^4
complete the table of values using at least 5 points.
x -2 -1 0 1 2
f(x)
A friend creates an IRA (Individual retirement account) with an APR of 6.25%. She starts the IRA at the age of 25 and deposits $50 at the end of each month. How much will her IRA contain when she retires at the age of 65?
what is 63 as the product of prime factors in ascending order?
Please do not make into a fraction because I can’t use a fraction as an answer. Rewrite using a negative exponent.
1/(xy)^1
What is an equation of the line in slope-intercept form? m = 2 and the y-intercept is (0, 3)
Marla has a pet hamster. The hamster makes 3 laps around her cage every minute.
What line represents the situation?
Line a
Line b
Line c
Line d
Let
x-------> the time in minutes
y------> the number of laps
we know that
In this problem the linear equation represent a direct variation and the slope is equal to
[tex]m=3\frac{laps}{minute}[/tex]
so
the equation of the line is
[tex]y=3x[/tex]
For [tex]x=1\ minute[/tex]
the value of y is equal to
[tex]y=3*1=3\ laps[/tex]
Plot the point [tex](1,3)[/tex] in the graph
therefore
the answer is
The solution is the line b
see the attached figure to better understand the problem
How many solutions are there?
Else's math class has 11 female students and 10 male students.Write the ratio of female students to the total number of students in two different ways.
The detailed answer explains how to write the ratio of female students to the total number of students in two different ways.
The ratio of female students to the total number of students:
11 female students to 21 total students: 11/21
Alternatively, you can simplify the ratio to 1 female student to 2 total students: 1/2
Dani is working a sample booth at the national soda and beverage convention. She is paid $1.50 for each of the first ten tastings $2.50 for each of the next twenty tastings and $4.00 for each tasting beyond thirty she conducts each day. Today Dani conducted 36 tastings. How much total pay did Dani earn today?
What is 2(6+5•2)=5(4-2•5)
Answer: Not true
Step-by-step explanation: 2(16)=5(-6)
32=-30
This is not true
willie wants to save for a new racing bike. if he deposits $250 in a saving account at 4% simple annual interest, what willis balance be after 3 years?
A.15
B.30
C.265
D.280