II. Solve the problems involving variations. Show your complete solution. (3 points each) 1. If y varies directly as the square of x, and y = 32 when x = 2, find y when x = 5. 2. The force of attraction (F) between two opposite electrical charges varies inversely as the square of the distance (d) between them. If F = 18 when d = 10, find F when d = 15. 3. If y varies jointly as x and z, find y if x = 3, k = 6 and z = 9
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
y varies directly as x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 32 when x = 2
32 = k × 2² = 4k ( divide both sides by 4 )
8 = k
y = 8x² ← equation of variation
When x = 5 , then
y = 8 × 5² = 8 × 25 = 200
(2)
Given F varies inversely as d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of variation
To find k use the condition F = 18 when d = 10
18 = [tex]\frac{k}{10^2}[/tex] = [tex]\frac{k}{100}[/tex] ( multiply both sides by 100 )
1800 = k
F = [tex]\frac{1800}{d^2}[/tex] ← equation of variation
When d = 15 , then
F = [tex]\frac{1800}{15^2}[/tex] = [tex]\frac{1800}{225}[/tex] = 8
(3)
y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
when x = 3, y = 6, z = 9 ,then
y = 6 × 3 × 9 = 162
Related Questions
X-Y=5, 6X-6Y =?
I think it's 30, but i don't know , I tried to think of a way and I thought about taking the 6 as a common and multiplying it to X-Y, Like :6(X-Y), and since X-Y =5 it'll be 30?
Answers
Answer:
Yes, it is 30
Step-by-step explanation:
And yes, you thought it through correctly. 6(X-Y) = 6*5
6(X-Y) = 30
Answer:
[tex]\displaystyle 6x - 6y = 30[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTerms/Coefficient
FactoringStep-by-step explanation:
Step 1: Define
Identify.
x - y = 5
Step 2: Solve
Factor: [tex]\displaystyle 6x - 6y = 6(x - y)[/tex]Substitute in expression: [tex]\displaystyle 6x - 6y = 6(5)[/tex][Order of Operations] Evaluate: [tex]\displaystyle 6x - 6y = 30[/tex]If AB∥ED and m∠ABC = m∠DEF. Prove CB|| EF.
Answers
Explanation:
( ) . . . . stuff that is given
∠ABE ≅∠DEG . . . . corresponding angles at a transversal
∠ABC +∠CBE = ∠ABE . . . . angle addition postulate
∠CBE = ∠ABE -∠ABC . . . . subtraction property of equality
∠DEF +∠FEG = ∠DEG . . . . angle addition postulate
∠FEG = ∠DEG -∠DEF . . . . subtraction property of equality
∠FEG = ∠ABE -∠ABC . . . . substitution property of equality
∠CBE = ∠FEG . . . . substitution property of equality
CB║EF . . . . converse of corresponding angles theorem
Five swimmers are entered into the competition. Four of the swimmers have had their turns. Their scores are 9.8s, 9.75s, 9.79s, and 9.81s. What score must the last swimmer get in order to win the competition?
Answers
Answer:
We must order these decimals from least to greatest. Then we must determine how the least compares with the winning score.
9.80 -> 3
9.75 -> 1
9.79 -> 2
9.81 -> 4
The least decimal is 9.75. Now we must determine how 9.75 compare with the winning score.
The last swimmer must get a score less than 9.75 s in order to win.
Step-by-step explanation:
Hopes this helps
Answer:
less than or equal to 9.74.
Which set of ordered pairs represents a function?
a
O {(7,4), (3,8), (-4, –4), (0,4)}
O {(-8,0), (-5,6), (-8, 1), (-6,5)}
{(-5, 1), (3, -7), (2, -4), (2,7)}
O {(4,2), (4, -9), (-9, -6), (7,1)}
Answers
(7,4), (3,8), etc
please Help NEED NOW
thank you so much
Answers
One research study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.8% now. Suppose a survey in a large high school reveals that, in a random sample of 1046 students, report using illegal drugs. Use a 0.05 significance level to test the principal's claim that illegal drug use in her school is below the current national average.
Answers
Using the z-distribution, it is found that since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
At the null hypothesis, it is tested if drug use in her school is not below the national average, that is:
[tex]H_0: p \geq 0.098[/tex]
At the alternative hypothesis, it is tested if it is below, that is:
[tex]H_1: p < 0.098[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.93 out of 1046 reported using illegal drugs, hence the parameters are:
[tex]n = 1046, \overline{p} = \frac{93}{1046} = 0.0889, p = 0.098[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.0889 - 0.098}{\sqrt{\frac{0.098(0.902)}{1046}}}[/tex]
[tex]z = -0.99[/tex]
The critical value for a left-tailed test, as we are testing if the proportion is less than a value, is [tex]z^{\ast} = -1.645[/tex]
Since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
To learn more about the use of the z-distribution to test an hypothesis, you can take a look at https://brainly.com/question/25584945
What is the solution to the following system 3x+3y+6z=9
Answers
Answer:
x=1 y=1 z=1
Step-by-step explanation:
3+3+3=9
and
3x+3y+3z=9
Simplify the expression 2i(4.5 – 20i) + 3i. Write your answer in the form a + bi.
Answers
Answer:
40 + 12i
Step-by-step explanation:
note that i² = - 1
2i(4.5 - 20i) + 3i ← distribute parenthesis by 2i
= 9i - 40i² + 3i
= 9i - 40(- 1) + 3i
= 9i + 40 + 3i
= 40 + 12i
Derek and Jeannine buy a car for a total price, including tax, of $19,795. The price of the car was $18,500. What is the tax rate.
Answers
Answer:1.07
Step-by-step explanation:
Which statement is true about the equation 4.5z = 4.5z − 4.25 + 6.25? It has no solution. It has one solution. It has two solutions. It has infinitely many solutions.
Answers
Answer:
it has infinitely many solutions
Step-by-step explanation:
hope it help bro
Answer:
d
Step-by-step explanation:
Consider the line y=-5/4x + 5
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
Answer:5
Step-by-step explanation:
Is -9 a real or imaginary number?
Answers
Answer:
-9 is a real number.
Hope you could get an idea from here.
Doubt clarification - use comment section.
i need to find the zeros by factoring but im stuck plss help me i think the zeros may be 0, 1, -4, and 4 but i dont know how to get them??
Answers
In this case. Factor by grouping, then you will have several parenthesis multiplied by each other. Set each to zero
Find the value of x
Answers
Answer:
x = 8Step-by-step explanation:
is an isosceles triangle, so 12 = x + 4
12 = x + 4
x = 12- 4
x = 8
----------------
check
12 = 8 + 4
12 = 12
the answer is good
You know the following information about triangle ABC and triangle DEF:
AB-DE and
What additional information is needed to prove that the triangles are congruent by SAS?
AB=DE
AC=DF
BC=EF
Answers
Answer:
(b) AC = DF
Step-by-step explanation:
In order to use SAS, you need to show congruence of the sides on either side of the angle. One of those sides is given as congruent: AB = DE. (This given rules out choice A, which is identical.)
The remaining needed side will have points A and D as one of the points defining the side. This rules out choice D.
The relation between other angles is irrelevant to SAS, so choice C is ruled out.
Choice B: AC = DF will supply the information necessary to show congruence by SAS.
Pick the corrrect one form the dropdown
Answers
Answer:
hard
Step-by-step explanation:
you're correct
convert NPR 180000 into
1. USD
Answers
Answer:
Solution here,
1 US dollar=NRS 120.74
Therefore Rs 180000= 180000/120.74
=$1490.99
Need some help if u don’t mind :)
A)94
C)82
C)76
Answers
Answer:
82
Step By Step Explanation:
I would have choose 86 but there is no 86 since 82 is closer I choose it.
A full angle equals 180 so 180-94=86.
Hopes This Helps
what is the greatest common factor of 32 and 56
Answers
What is an expression equivalent to 25x^2+28x+16
Answers
Multiply: (3x)(x4 + 5)
Answers
Answer:
12x² + 15x
Step-by-step explanation:
(3x × 4x) + ( 3x × 15)
Answer:
(3x) (X 4+5)
3x×(x×4+5)
3x×(4x+5)
12x^2+15x answer
Given this graph of the function f(x) a) b) c) d) please a need help
Answers
Answer:
a) 2
b) -2
c) -2
d) 1/2
Step-by-step explanation:
1) f(-4) means that x=-4 and you must locate the y value on the graph
2) f(2) means that x=2 and you must locate the y value on the graph
3) f(x)=4 means that y=4 and you must locate the x value on the graph
4) f(x)=-1 means that y=-1 and you must locate the x value on the graph
factor completely.
-3x^2+9x+30
Answers
Answer:
− 3 ( x − 5 ) ( x + 2 ) hope this helps
Step-by-step explanation:
Answer:
− 3 ( x − 5 ) ( x + 2
Step-by-step explanation:
Based on the information in the table, how much will Henry earn if he worked 7 hours?
A
$48
+
B
$72
С
$9
D
$63
Answers
Answer:
D.
Step-by-step explanation:
Solve the equation. Please
Answers
Answer:
y=3
Step-by-step explanation:
1/4 = 3/12
The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it - IM JUST KIDDING I ACTUALLY NEED HELP THO
Answers
Therefore, we can create an equation to find the measure of angle 1, given the two other angles.
76+59+x=180. x=the measure of angle 1 (unknown).
135+x=180. [76+59=135]
135-135+x=180-135 [Isolate x by subtracting 135 from both sides]
x=45.
Therefore, the angle measure of angle 1 = 45°
-)) The green marble is closer to the target than the white marble. The purple marble is
closer to the target than the green marble, and the white marble is closer to the target than
the blue marble. The purple marble is not farther from the target than the white marble.
Which marble is farthest from the target?
the purple marble
the blue marble
the green marble
the white marble
Answers
12. The area of the flower garden is 9.7 square meters
greater than the herb garden. What is the area of the
flower garden?
Answers
Answer:
F = H + 9.7 m^2
Step-by-step explanation:
Let F be the area of the Flower garden and H the area of the Herb garden.
F = H + 9.7 m^2
There is no area or information given on the Herb garden, so this is the best we can say.
URGENT WILL MARK BRAINLIEST 1. Suppose Q is the midpoint of PR. Use the information to find the
missing value.
PQ = 32 + 10 and QR = 2 + 14
Find PR.
A. 32
B. 16
C. 4
D. 2
Answers
Answer:
A.32
Step-by-step explanation:
a student answered 86% of the questions on a test correctly. he received a grade of 98%. how many questions were on the test?
Answers
Let the number of questions on the test equal X which would be 100%
They answered 86 which equaled 98
Set up a ratio:
X/86 = 100/98
Cross multiply:
98X = 8600
Divide both sides by 98:
X = 87.75
Round to 87 questions