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Related Questions
Water pressure can be measured in atmospheres (atm). At 30 meters in depth the water pressure measures 4 (atm). At 50 meters in depth under water the pressure is 6 (atm). Write a linear function for pressure based on the depth in meters. Please show work.
Answers
y = 0.1x + 1 is the linear function for pressure based on the depth in meters
How create a linear function for the pressure based on the depth in meters?Given that: At 30 meters in depth the water pressure measures 4 (atm)
At 50 meters in depth under water the pressure is 6 (atm)
We will consider the two given data values as our points 1 and 2 respectively. And that is what we are going to use to create a linear function for pressure
Let the y and x represent the pressure and depth respectively
point 1 (30, 4) and point 2 (50, 6)
slope(m) = y2-y1 / x2-x1
where x1 =30, y1 = 4 and x2 = 50, y2 = 6
slope(m) = 6-4 / 50-30 = 2/20 = 1/10
Linear function are of the form y-y1 = m(x-x1). Thus:
y-4 = 1/10 (x-30)
y-4 = 1/10(x) - 3
y = 1/10(x) + 1 = 0.1x + 1
Therefore, the linear function for pressure based on the depth in meters is y = 0.1x + 1
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Select all correct answers. which values are part of the solution set based on the result of the inequality? -4x + 24 < -2x + 2 9.5 -10 11.5 15 10 -3
Answers
11.5 and 15 are the values that are part of the solution set of the inequality.
Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-4x + 24 < -2x + 2
-4x + 2x < -24 + 2
-2x < -22
22 < 2x
11 < x
Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.
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an airplane is preparing to land at an airport. it is 48,000 feet above the ground and is descending at the rate of 3,200 feet per minute. at the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. when will the two airplanes be at the same altitude and what will that altitude be?
Answers
Answer:
After 8 minutes ; altitude = 22,400 feet
Step-by-step explanation:
s1 = 2800t
s2 = -3200t + 48 000
2800t = -3200t + 48 000
28t = -32t + 480
7t = -8t + 120
7t + 8t = 120
15t = 120
15/15 t = 120/15
t = 8 minutes
s = 8 * (2800) = 22400 feet
Use Heron's Formula to find the area of AHKP if h' = 24 ft, k = 21 ft, and p = 13 ft. *
(1 Point)
192. 67 sq units
435. 90 sq units
113. 38 sq units
136. 23 sq units
Answers
The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
Define the term Heron's Formula?This formula is well-known for its straightforward computation that supports the length for three triangle sides. If the lengths of the 3 sides are a, b, and c, the semi-perimeter is; s = (a+b+c)/2.Area ; A = √s(s−a)(s−b)(s−c)The three sides of the triangle are-
h = 24 ft, k = 21 ft, and p = 13 ft.
s = ( 24 + 21 + 13 ) / 2
s = 29
s - a = 29 - 24 = 5
s - b = 29 - 21 = 8
s - c = 29 - 13 = 16
Put in the formula,
Area = √s(s−a)(s−b)(s−c)
A = √ 29 x 5 x 8 x 16
A = 136.23
Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
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Can somebody please explain what this question is asking, and how I solve it. I can not solve this, need help please.
Answers
Answer:
g(10)=-33, x=3
Step-by-step explanation:
g(x)=-4x+7. --------(1)
a) g(10)=?
since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x
g(10)=-4(10)+7
g(10)=-40+7
g(10)= -33
b.)find x if g(x)=-5. ---------(ii)
g(x)=-4x+7. we will place (I) in (ii)
g(x)=-5
-4x+7=-5
-4x=-5-7
-4x=-12
cancel the minus(-) sign in both sides
4x=12
x=12/4
x=3
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Find the measure of the exterior angle.
Answers
The measure of the exterior angle as shown in the triangle is 140°.
What is exterior angle?
Exterior angle is the angle between a side of a polygon and an extended adjacent side.
Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
From the diagram below, applying the theorem above,
k = 64+76k = 140°Hence, the exterior angle is 140°.
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what's the distance between points A and B
Answers
Answer:
AB = 10 units============
GivenEndpoints A(-8, -4) and B(2, - 4)Find the length of ABSince both points have same y-coordinate, the distance between the points is the difference of x-coordinates:
AB = 2 - (-8) = 2 + 8 = 10 units
A line has a slope of -7 and includes the points (-2, -10) and (-3, h). What is the value of h?
Answers
Answer:
-3
Step-by-step explanation:
You can use to find the slope of a line going through and .
I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.
(6,h)
minus
(7,-10)
------------
-1 h-(-10)
This also said to be equal to -7:
Multiply -1 on both sides:
Subtract 10 on both sides:
[texh=-3[/tex]
So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.
Let's test it:
(6,-3)
minus
(7,-10)
----------
-1 7
So the slope is 7/-1=-7. This is the intended goal.
The check is good.
Change the standard form equation y=x^2-4x+9 to vertex form by completing the square.
Answers
Add 4 to the equation, maintaining balance as follows:
y=x^2-4x+4+9-4
Simplify the first 3 terms(x^2-4x+4) of the equation to
(x-2)^2 by completing the square and the last 2 terms(9-4) to 5
Your final simplified equation in vertex form by completing the square is y=(x-2)^2+5
Consider the infinite geometric sequence 4480, -3360, 2520, -1890…
a. Find the common ratio, r.
b. Find the 20th term.
c. Find the exact sum of the infinite sequence.
Answers
The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
a.
common ratio r = a2/a1
= -3360/4480
= -0.75.
r = a3/a2
= 2520/-3360
= -0.75
b.
[tex]a_{n}[/tex] = a*r^(n-1)
here a = 4480 and r = -0.75.
= 4480(-0.75)^(20-1)
= 4480(-0.75)^19
= 4480*(-0.00422)
[tex]a_{20}[/tex] = -18.9056.
c.
[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))
= 4480*((1--0.75^4)/(1--0.75))
= 4480*((1-0.31640625)/(1--0.75))
= 4480*(0.68359375/1.75)
= 4480*0.390625
= 1750
Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
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a fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. what is the length of the shortest lad-der that will reach from the ground over the fence to the wallof the building? g
Answers
The length of the shortest ladder is 16.64 ft.
In triangle ABC, using Pythagoras theorem
[tex]AC^{2} = AB^{2} + BC^{2}[/tex] OR
[tex]L^{2} = h^{2} + (x+4)^{2}[/tex] .....(1)
We also have similar triangles if we consider:
△ABC and △DEC
Which gives us the proportional relationship:
AB:DE = BC:EC
or h/8 = (4+x) / x
h = 8( 4+x) /x
Substituting this last expression for h into Eq [1] we get:
[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]
Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:
[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]
At a critical point the derivative is zero and so we have the equation:
= [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]
From here we can find the value x :
x + 4 = 0 1 - [tex]\frac{256}{x^{3} }[/tex] = 0
x = -4 x = [tex]\sqrt[3]{256}[/tex]
We require x > 0 so we neglect the -ve solution and only take +ve solution
therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.
[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]
L² = 277.14
L = 16.64 ft
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Which equations are true? Select all that apply.
Answers
Answer:
The equation that is true is equation two
My science class is pretty small. There are just 18 students in the class. My
teacher, Ms. Microbe, has an unusual system for pairing us up for labs. She
has given each of us a number from 1 through 18, and on lab days, she pulls
our numbers out of a bag to determine who is paired with whom. When we
did our last lab, I happened to notice that the sum of each person's number
with his/her lab, partner's number was a perfect square!
How were the partners assigned?
Answers
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9).
Square numbers:A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.
For example:
Square of 2 = 4
Square of 3 = 9
Square of 4 = 16
Here we have
A science class is pretty small
There are just 18 students in the class.
The teacher gave each of them numbers from 1 through 18 on lab days
Start from 1 and find by adding which number we will get a square number
Here 1 + 15 = 16
2 + 14 = 16
3 + 13 = 16
4 + 12 = 16
5 + 11 = 16
6 + 10 =16
After the above combinations, the remaining numbers are
7, 8, 9, 16, 17, 18
which can be added as given below to get square number 25
=> 18+7=25
=> 17+8=25
=> 16+9=25
Therefore,
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9)
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Hi I'm honestly really confused on this problem and have no idea what I'm meant to do. It'd be helpful if someone could explain this
Answers
As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.
What does converse of corresponding angles theorem states?
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
How can we show two lines are parallel to each other?
We can show lines are parallel by finding a pair of corresponding angles that are congruent.
Proving if two lines are parallel then third line is parallel too.
According to the given data:
It is given in the question that line x is parallel to line yTherefore, ∠5 ≅ ∠7 (i.e. corresponding angles)
∠5 = ∠7
Similarly as given line y is parallel to line z∠6 ≅ ∠8 (Corresponding angles are equal)
∴ Measure of angles is also equal ⇒ ∠6 = ∠8
∠5 = ∠8 (transitive property of equality of angles which says if
∠a = ∠b and ∠b = ∠c then ∠a = ∠c)
∠5 ≅ ∠8 (If measure of angles is same then they are congruent)
Therefore, line x || line z
(Converse of the Corresponding Angles Theorem).
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A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
Answers
They should produce 1091 units each day to yield a minimum cost.
What is the vertex formula?
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
We have,
C = 70,000 - 120x + 0.055x²
C = 0.055x² - 120x + 70,000
Hence, for this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, find and put the values of x.
minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )
= 120 ÷ 0.11
= 120 ÷ 0.11
= 1090.90 ≈ 1091 units
The minimum cost will be yield for 1091 units.
Therefore, They should produce 1091 units each day to yield a minimum cost.
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When Lily left her house in the morning, her cell phone battery was partially charged. The charge remaining in Lily's battery, as a percentage, can be modeled by the equation B=-4t+52,B=−4t+52, where t is the number of hours since Lily left her house. What is the x-intercept of the equation and what is its interpretation in the context of the problem?
Answers
The x-intercept of the equation is 13 and its interpretation in the context of the problem is the number of time in hours for which Lily left her house.
What is x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
Next, we would determine the number of time for which Lily has left her house since in the morning by substituting the value of B with zero (0) as follows:
B = -4t + 52
0 = -4t + 52
4t = 52
Time, t = 52/4
Time, t = 13 hours.
Therefore, the x-intercept of the given equation is (0, 13).
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help meeeeeeeeeeeeeeeeee please
Answers
Answer:
I believe it's 4.5 seconds
Find the variables in the figure (x and y) please and thank you!!
Answers
Read the left colum top to bottom then the right column top to bottom, hope this helps
A line with a slope of –
5 passes through the points (7,–
2) and (8,q). What is the value of q?
Answers
The line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.
How to find the value of q with the slope?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (7, –2) and (8, q) with a slope of - 5.
Hence, let's find q.
y = - 5x + b
Let's find y-intercept
-2 = -5(7) + b
b = -2 + 35
b = 33
Therefore,
y = -5x + 33
Hence, let's find q.
y = -5(8) + 33
q = -40 + 33
q = -7
Therefore, q = - 7
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To find the equation of a regression line, y = ax + b, you need these formulas:
Sy
a=rsa
b =ỹ - ax
A data set has an r-value of 0.793. If the standard deviation of the x-
coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772,
what is the slope of the line to three decimal places?
Answers
The slope of the line is 0.393.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").
Given,
A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.
We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:
m = 8ₓ/8ₐ
where m is the slope of the best-fit line.
8ₓ = Standard deviation of the x-coordinates is 5.591,
8ₐ = the standard deviation of the y-coordinates is 2.772.
Slope is:
m = 8ₐ/8ₓ
m = (0.793)(2.772)/5.591
m = 0.393
The slope of the line is 0.393.
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Which one is greater 1 1/2 or 1.456
Answers
1.456 x 100 = 145.6
So therefore 1 1/2 is greater
1 1/2 > 1.456
-8-(b-3)=13-4b i need an answer but not a fraction or decimal
Answers
Answer:b=2/3 if u don't need an answer that is not a fraction or decimal u can write 17. as a whole number.
Step-by-step explanation:
solve the system by substitution
Answers
Answer:
Step-by-step explanation:
since x=y, you can either substitute for x or for y,
lets do x
-3x - x = 4
-4x=4
x=-1
Now we can just plug in
-3(-1) - y = 4
3-y = 4
y=-1
125 in the ratio 2:3
Answers
Answer:
50:75
Step-by-step explanation:
let the ratio of 2:3 be x
now,
125=2+3x
or,5x=125
therefore,x=125/5
x=25
now,
2x=25*2
=50
3x=25*3
=75
Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
Answers
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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Make x the subject:
Q1) 9y-5x = 4
Answers
Answer:
x = 9/5 y - 4/5
Step-by-step explanation:
Make x the subject:
9y - 5x =4
Subtract 9y from each side
9y-9y - 5x =-9y+4
-5x = -9y +4
Divide each side by -5
-5x/-5 = -9y/-5 + 4/-5
x = 9/5 y - 4/5
Answer:
x = (9/5)y - (4/5)
Step-by-step explanation:
Given equation,
→ 9y - 5x = 4
Solving for the required value of x,
→ 9y - 5x = 4
→ -5x = -9y + 4
→ x = (-9y + 4)/-5
→ [ x = (9/5)y - (4/5) ]
Hence, value of x = (9/5)y - (4/5).
How do I do this can someone help me plss
Answers
Answer:
I think is 50m.
Step-by-step explanation:
A movie theater showed an old, classic movie on Saturday and Sunday. Tickets cost c dollars for children under the age of 13 and d dollars for others.
On Saturday they sold 84 children's tickets and 157 tickets for others and collected $2,640 from ticket sales. On Sunday they sold 67 children's tickets and 134 other tickets and collected $2,211 from ticket sales. This can be represented by this system of equations
84c + 157d = 2,640
67c + 134d = 2,211
A. What could the equation 17c + 23d = 429 mean in this situation?
B. The solution to the original system is the pair c = 9 and d = 12. Explain why it makes sense that this
pair of values is also a solution to the equation 17c + 23d = 429.
Answers
The equation in the given question is answered in main body.
What is equation?
In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main body:
according to question :
A) equation for Saturday sale = 84c +157d = 2640
equation for Sunday sale = 67c +134d = 2211
when subtracted we will get, 17c +23d = 429
This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.
B) According to second part solution are c= 9 , d= 12.
equation given : 17c+23d = 429
now substituting value of c and d.
⇒17(9) + 23(12)
⇒153+276
⇒429 = R.H.S
Hence equation satisfies.
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can someone do these for me pls i’m lazy
Answers
-1/3 slope
X intercept is 12
Y intercept is 4
Graph is attached
Step by step
Slope is rise over run
-4 rise over 12 run = -4/12 simplified to -1/3
X intercept
Substitute 0 for y and solve
1.5x + 4.5y = 18
1.5x + (4.5)(0) = 18
1.5x = 18
x = 18/1.5
x = 12
Substitute 0 for x and solve
1.5x + 4.5y = 18
(1.5)(0) + 4.5y = 18
4.5y = 18
y = 18/4.5
y = 4
Beverly is making peanut butter-banana bread. She always doubles the amount of nuts and peanut butter chips. The total amount of chips and nuts after doubling is 412 cups.
Write and solve an equation to find the original amount of nuts, x, in the recipe.
Answers
The original amount of nuts, x, in the recipe is 103
The equation for the original amount is 2x + 2x = 412
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.
These expressions are also known to be made up of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have that;
Beverly doubles the amount of nuts and peanut butter chips
Total number = 412
This is represented as;
2x + 2x = 412
collect like terms
4x = 412
Make 'x' the subject of formula
x = 412/ 4
x = 103
Hence, the value is 103
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