Answer:
[tex]y=28.5x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
Let
x------> the number of gallons
y------> the number of miles
the relationship between the number of miles and the gallons of gas represent a linear direct variation
The constant of proportionality k is equal to the slope m
[tex]m=\frac{465.3}{16.5}= 28.2\frac{miles}{gallon}[/tex]
therefore
the equation of the linear equation
[tex]y=28.5x[/tex]
Elevators have safety limits for how much weight they can lift. The elevator at the Terrace Hotel can hold up to 2,100 pounds. write an equation or inequality that represents the allowable weight on the elevator at the Terrace Hotel. Graph the solution to the equation or inequality you wrote on the number line. Explain your answer.
If SinA = 2/3, find the value of 2 secA/1+ tan2A
a varies directly as b and inversely as the square of c. If a = 197 when b = 5 and c = 5, find a if b = 3 and c = 3
Final answer:
The value of 'a' is found to be approximately 328.33 when b = 3 and c = 3, using the constant of proportionality obtained from the given values a = 197 when b = 5 and c = 5.
Explanation:
When a quantity varies directly as another quantity and inversely as the square of a third quantity, we can express this relationship with the following equation:
a = k x (b / c2)
where k is the constant of proportionality. Given that a = 197 when b = 5 and c = 5, we can solve for k:
197 = k x (5 / 52)
197 = k x (5 / 25)
197 = k / 5
k = 197 x 5
k = 985
Now we can use this value for k to find a when b = 3 and c = 3:
a = 985 x (3 / 32)
a = 985 x (3 / 9)
a = 985 x (1/3)
a = 328.333...
Hence, the value of a, when b = 3 and c = 3, is approximately 328.33.
Which equation can be used to solve for x in the following diagram?
The equation that represents the value of [x] is -
x + 4x - 85 = 90.
What is right angle? What is equation modelling? What is a mathematical equation and expression?In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or π/2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is a geometrical image as shown.
We can write the equation as -
x + 4x - 85 = 90
Therefore, the equation that represents the value of [x] is -
x + 4x - 85 = 90.
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Given the function
h
(
x
)
=
x
2
−
7
x
+
7
h(x)=x
2
−7x+7, determine the average rate of change of the function over the interval
2
≤
x
≤
9
2≤x≤9.
The average rate of change of the function h(x) = x² - 7x +7 over the interval 2 ≤ x ≤ 9 is 4.
Explanation:The average rate of change for a function is determined by the difference in y values divided by the difference in x values over a specified interval. In this case, the function is h(x) = x² - 7x + 7, and the interval is 2 ≤ x ≤ 9. First, we calculate h(2) and h(9) for the y values.
h(2) = (2)² - 7(2) + 7 = 4 - 14 + 7 = -3
h(9) = (9)² - 7(9) + 7 = 81 - 63 + 7 = 25
Then, apply the formula for average rate of change which is (h(9) - h(2)) / (9 - 2).
(25 - (-3)) / (9 - 2) = 28 / 7 = 4
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Which relationship describes angles 1 and 2?
Select each correct answer.
complementary angles
adjacent angles
supplementary angles
vertical angles
Caitlin had used more thank 2 pounds of clay to make a jar? Would the amount remaining have been more or less than your answer to Exercise 1?
Answer:
more than my Ans
Zach is filling his dogs bowl with water. Is it reasonable to say that Zach will need about 4 gallons of water?
A passenger train and a freight train leave San Jose at 3 p.m., traveling in the same direction. The passenger train is going three times as fast as the freight train. At 6 p.m. they are 240 miles apart. How fast is each travelling?
There is a 3 hour difference in travel time.
So if x is the speed of the freight train and distance is 240 miles...
3(3x)-3x=240
9x-3x=240
6x=240
x=240/6
x= 40mph for the freight train..
passenger train is 3 times faster than the freight..
3×40=120mph
A company sells cereal in two different -sized boxes.The smaller box has the dimensions of 12-inch,2-inch and 7 3/4 i.The height of the smaller box is 80% of the height of the lager box,while the other two dimensions are the same for both boxes.What is the difference in the volumes of the two boxes?
Answer: The answer is 232.5
Step-by-step explanation:First you to set up the proportion. If 80% equals to 12. You Would do 80 over hundred becuase percent is out of hundred (80/100) then you would do 12 over x or any other variable. FROM there on you would to the butter fly method. Cross multiply . ( 80 times variable, 12 times 100) now to isolate the variable you have to do inverse operation. So now do 1200 divided by 80 . And 80 divided by 80. Now you know.
X=15.
But were no done yet lol. Now do length times width times height to get the volume. 15 times 2 times 31/4 (7 3/4) . now we're done. Your welcome
The sun of 2 and 3 is less than y.
An arrow shot into the air is 160t -16^2 feet above the ground t is seconds after it is released. During what period of time is the arrow above 384 feet?
Please help,I don’t get this and my friends also need your help
Wilma bought a skateboard for 20% off. The normal price was 120.90. How much did Wilma pay for the skateboard, not including tax?
1) $96.72
2) $97.82
3) $98.92
4) $99.02
The owner purchases 5 buckets, 10 brushes, 48 towels, and 1 case of air fresheners for the car wash. The total cost of the purchases is $144.08. Each bucket costs $2.89, each brush costs $7.91, and each towel costs $0.36.
PART B: What is the total cost, in dollars, of the case of air fresheners? Explain/justify your answer.
{(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)} Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function. Select all ordered pairs that could be used to show that this claim is incorrect.
A. (–10, –10)
B. (–9, –6)
C. (–5, 1)
D. (1, 12)
E. (4, 7)
(-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given ordered pairs are {(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)}
minus nine comma one,
minus five comma two
zero comma seven
one comma three
six comma minus ten
If Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function.
Then we can replace with (-9, -6) (-5,1 ) (1,12) to make it incorrect. Two x values should not have same value.
Hence (-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.
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Which side lengths form a right triangle?
Choose all answers that apply:
(Answers in picture)
Option (C). 2, 2, √8, forms a right triangle.
Explanation:A right triangle is a triangle that has one angle measuring 90 degrees.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Therefore, to determine if a set of side lengths forms a right triangle, we can check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
Option A: 4, 8, 12Based on the calculations above, only option C, 2, 2, √8, forms a right triangle.
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The correct answer is: C. [tex]\(2, 2, \sqrt{8}\)[/tex]
Step 1
To determine which sets of side lengths form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 2
Let's check each option:
A. [tex]\(4, 8, 12\)[/tex]
- [tex]\(4^2 + 8^2 = 16 + 64 = 80\)[/tex]
- [tex]\(12^2 = 144\)[/tex]
- [tex]\(80 \neq 144\)[/tex]
Therefore, option A does not form a right triangle.
Step 3
B.[tex]\(2, 3, \sqrt{5}\)[/tex]
- [tex]\(2^2 + 3^2 = 4 + 9 = 13\)[/tex]
- [tex]\((\sqrt{5})^2 = 5\)[/tex]
- [tex]\(13 \neq 5\)[/tex]
Therefore, option B does not form a right triangle.
Step 3
C. [tex]\(2, 2, \sqrt{8}\)[/tex]
- [tex]\(2^2 + 2^2 = 4 + 4 = 8\)[/tex]
- [tex]\((\sqrt{8})^2 = 8\)[/tex]
- [tex]\(8 = 8\)[/tex]
Therefore, option C forms a right triangle.
Sarah is making flower bouquets that she will put in 10 vases. She will put 15 roses and some lilies in each vase.
Which expressions represent the total number of flowers Sarah will put in all the vases?
Choose all answers that are correct.
a. 10 *(15+f) b. 10+15+f c. (10*15)+(10*f) d. 10*(15*f)
Hey please please please please please help have a Struggling with this all day
Can You show me how to do this?
NEED HELP ASAP need help with number 2
Lucy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lucy
$5.75
per pound, and type B coffee costs
$4.10
per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of
$819.55
. How many pounds of type A coffee were used?
Answer:
I think it is $204.88, but I'm not positive.
Step-by-step explanation:
819.55 divided by 4
Please answer This with the Right anawer
The graph of the function f(x)=3/x+5 is shown below.
What is the vertical asymptote of the function?
A. x = –5
B. x = –3
C. x = 3
D. x = 5
A is the answer
The vertical asymptote of the function f(x) = (3/x) + 5 is A. x = - 5
What are asymptotes?A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar contexts.
By observing the graph we can conclude that the asymptote or more specifically the vertical asymptote of the function f(x) = (3/x) + 5 is at x equals to - 5.
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I really need help on this!! God bless you!!
Which word best describes the numbers 10 and –10?
Opposites
Coordinate
Absolute Value
Expression
What answers factor the expression 24y + 88x
This is LCM and GCF I think
The picture below shows a container that Sue uses to freeze water: A cylinder is shown with base diameter of 4 centimeters and the height as 6 centimeters. What is the minimum number of identical containers that Sue would need to make 2,000 cm3 of ice? (Use π = 3.14.) (1 point) 12 18 27 7
Answer:
[tex]27\ containers[/tex]
Step-by-step explanation:
step 1
Find the volume of one container (cylinder) is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=6\ cm[/tex]
substitute
[tex]V=(3.14)(2^{2})(6)=75.36\ cm^{3}[/tex]
step 2
By proportion
Find the the minimum number of identical containers that Sue would need to make [tex]2,000\ cm^{3}[/tex] of ice
[tex]\frac{1}{75.36}=\frac{x}{2,000}\\ \\x=2,000/75.36\\ \\x= 26.5\ containers[/tex]
Round to the nearest whole number
[tex]26.5=27\ containers[/tex]
Answer: 27
Step-by-step explanation:
Given: The height of the cylindrical container = 6 cm
Diameter of container = 4 cm
Then the radius of the container = [tex]\frac{4}{2}=[/tex]2 cm
Now, the volume of the cylindrical container is given by :-
[tex]\text{Volume}=\pi r^2 h\\\\\Rightarrow\text{Volume}=(3.14)(2)^2(6)=75.3982236862\approx75.4\ cm^3[/tex]
Now, the minimum number of identical containers that Sue would need to make 2,000 [tex]cm^3[/tex] of ice is given by:-
[tex]\frac{2000}{75.4}=26.525198939\approx27[/tex]
Hence, the minimum number of identical containers that Sue would need to make 2,000 [tex]cm^3[/tex] of ice is 27.
The diameter of an ancient chariot wheel is 2 meters. What is the approximate distance the chariot travels if the wheel rotates 120 times? Assume the wheel does not slip.
1,506.4 meters
753.6 meters
376.8 meters
240 meters
The approximate distance the chariot travels is 753.6 meters.
What is the distance the chariot travels?
The distance the chariot travels in one journey is equivalent to the circumference of the wheel.
Circumference of a circle = πD
Distance in 120 trips = πD x 120
3.14 x 2 x 120 = 753.6 meters.
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