Assume that y varies inversely with x. If y=12 when x=5, find y when x=3
When y varies inversely with x, they follow the rule y = k/x. If y=12 when x=5, the constant 'k' is found to be 60. Using this constant, when x=3, y is found to be 20.
Explanation:In mathematics, when we say that y varies inversely with x, it means that as x increases, y decreases proportionally, and vice-versa. Y and x follow the rule y = k/x, where k is a constant number.
Given that y = 12 when x = 5, we can find the constant by multiplying x and y together, so: k = x * y = 12 * 5 = 60.
Now that we have our constant, we can find y when x = 3 by rearranging the formula to y = k / x which gives us: y = 60 / 3 = 20. So, when x is 3, y is 20.
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Three times the greater of two consecutive odd integers is five less than four times the smaller. find the two numbers.
Which of the following equations has only one solution?
x2 + 4x + 4 = 0
x2 + x = 0
x2 - 1 = 0
We can show that triangle abc is congruent to triangle a prime b prime c prime by translation of
Final answer:
To show congruence by translation, we need to show that corresponding sides and angles of the triangles are equal.
Explanation:
To show that triangle ABC is congruent to triangle A' B' C' by translation, we need to show that they have the same shape and size.
Translation is a transformation that moves every point of a figure the same distance in the same direction. Therefore, to show congruence by translation, we need to show that the corresponding sides and angles of the two triangles are equal.
For example, if we have AB || A'B' and AB = A'B', BC || B'C' and BC = B'C', and AC || A'C' and AC = A'C', then we can conclude that triangle ABC is congruent to triangle A' B' C' by translation.
If it rained on 3 days out of 20 days,on what percent of the days did it rain
On an up hill hike Ted climbs at 3 mph. Going back down, he runs at 5 mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer: He hiked 10 miles.
Step-by-step explanation:
3mi/hr x 1 2/3 hr = 5 miles. 5 mi/hr x 1 hr = 5 miles.
Noa drove from the Dead Sea up to Jerusalem, and her altitude increased at a constant rate of 740 meters per hour. When she arrived in Jerusalem after 1.5 hours of driving, her altitude was 710 meters above sea level.
Let A(t) denote Noa's altitude relative to sea level A (measured in meters) as a function of time t (measured in hours).
She stared at -400 meters below sea level and the equation is A(t)=740t-400
Functions and valuesFunctions are written in terms of variables
From the given question;
Let a₀ is the initial height or the height she started at
Required
Initial height
After 1.5 hours, she was 710 meters above sea level
Substitute the given time into the function
A(1.5)=740(1.5)+a₀=710
740(1.5)+a₀=710
1110+a₀=710
a₀=-400
This shows that she stared at -400 meters below sea level and the equation is A(t)=740t-400
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If the diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a
The diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a scalene trapezoid
What is a trapezoid?
The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
For a scalene trapezoid ,
The four sides are of unequal length
The angles of the scalene trapezoid are not equal
The shortest distance between two parallel sides is known as the altitude
The sides of the scalene trapezoid does not bisect each other
Hence , the diagonal is a scalene trapezoid
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What is the equation of the blue graph?
since the blue graph is 2 lines to the left of the red graph, that would mean it moved -2
so the equation needs to include -2
the correct answer is C
which figure has both line of symmetry and rotational symmetry
Answer:
A line of symmetry is when you can put a line through a shape and you can fold it and it is identical on both sides, and rotational is when you can rotate it and at some point it is in the same spot as it was before, so yes, you are right. the octogon.
Step-by-step explanation:
Solve the quadratic equation -x^2=4
How many terms are in the polynomial abcd + e - h 2? two three five six
Answer:
The number of terms in the polynomial are:
Three.
Step-by-step explanation:
We are given a polynomial expression in terms of variable a,b,c,d , e and h as:
[tex]abcd+e-h^2[/tex]
We know that in any algebraic expression the number of terms are the number of unlike expressions that are separated by a minus or plus i.e. addition sign.
Hence here by looking at our polynomial expression we see that there are three terms in the expression :
1) [tex]abcd[/tex]
2) [tex]e[/tex]
3) [tex]h^2[/tex]
Find the zeros of the function. F(x)= cube root of x
if H(x)=4x-8 and j(x) = -x solve h{j(3)}
A job is shared by 4 workers, w, x, y, and z. worker w does 1/4 of the total hours. worker x does 1/3 of the total hours. worker y does 1/6 of the total hours. what fraction represents the remaining hours allocated to person z?
Subtract 11a2+42a-6 from 14a2-24a+7
The values of subtraction of 11a²+42a-6 from 14a²-24a+7 is
3a² - 66a + 1.
What is Expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
We have to Subtract 11a²+42a-6 from 14a²-24a+7.
So, the subtraction is as follows
= 14a²-24a+7 - ( 11a²+42a-6)
= 14a²-24a+7 - 11a² - 42a + 6
= 14a²- 11a² -24a - 42a + 7- 6
= 3a² - 66a + 1
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Simplify (−34.67)0. I'm not really understanding how to do this so please someone help me.
(02.06 LC)
The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠1 and ∠2?
A. ∠1 and ∠2 are complementary because they are a pair of corresponding angles.
B. ∠1 and ∠2 are congruent because they are pair of corresponding angles
C.∠1 and ∠2 are complementary because they are a pair of alternate interior angles.
D.∠1 and ∠2 are congruent because they are pair of alternate interior angles.
If the measure of angle is 38 what is the measure of its complement
Darren drank 2 liters of water.How much millilliters of water did he drank
Write each whole number using words.
a) 325
b) 9,542,006
Order of operations? How to do?
Thanks
parenthesis first (8+5) = 13
35/5 = 7
13x7 +6
13x 7 = 91 +6 = 97
the volume of a square pyramid with height 2.4cm is 3.2cm. what is the width of the base of the pyramid?
how are the rules of signs for multiplication and division related
In a programming team of 20 persons, 1/4 are women and 3/4 are men. to obtain a team with 40% women, how many women should be hired?
To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. Currently, there are 5 women in the team (1/4 of 20). By setting up an equation and solving for x, we find that 5 women should be hired.
Explanation:To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. We know that currently 1/4 of the team are women, which means there are 5 women in the team (20 * 1/4 = 5). To find out how many women should be hired, we subtract the number of women in the team from the target number of women in the team:
Number of women to be hired = Target number of women - Current number of women
Number of women to be hired = 0.4 * (20 + x) - 5
Where x is the number of women to be hired. Now we can solve for x:
0.4 * (20 + x) - 5 = x
Distribute and simplify:
8 + 0.4x - 5 = x
Combine like terms:
0.4x - x = 5 - 8
0.6x = 3
Divide both sides by 0.6:
x = 3 / 0.6
x = 5
So, 5 women should be hired to obtain a team with 40% women.
The following table shows the data collected from 4 random samples of 50 students from a small middle school regarding the type of television shows they prefer to watch:
Television Show Preferences
Sample News Music Movies Cartoons Total
1 2 12 6 30 50
2 3 10 5 32 50
3 5 13 7 25 50
4 6 19 8 17 50
Based on the results in the table, which type of television show is preferred by the majority of students in the samples?
News
Music
Movies
Cartoons
Television show preferred by the majority of students in the samples is Cartoon
What is majority ?Majority is More than half or just the larger part.
What is addition?The addition of two whole numbers results in the total amount or sum of those values combined
Total number of students= 50+50+50+50 =200 students
Total number of student who prefer news =2+3+5+6=16 students
Total number of student who prefer music = 12+10+13+19 = 54 students
Total number of student who prefer movies = 6+5+7+8 = 26 students
Total number of student who prefer cartoon = 30+32+25+17 = 104 students
Hence, television show preferred by the majority of student in the samples is Cartoon
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five friends go out to lunch and they decide to split the bill evenly the bill comes out to 57.25 how much does each person owe?
True or false X=4 for both 1. 3x+10-(5+3)=14 2. 3x+10(3x-2)=60
Rewrite each of the following linear equation in equivalent y=mx+b
what's the slope and the y-intercept
HELP ME PLZZ
1. In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
If PX = 20, find PQ
Since C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40