Given:
The value of y is directly proportional to the value of x.
y = 45 when x = 180.
To find:
The value of y when x = 80.
Solution:
Since the value of y is directly proportional to the value of x, therefore
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
where, k is constant of proportionality.
Putting y=45 and x=180, we get
[tex](45)=k(180)[/tex]
[tex]\dfrac{45}{180}=k[/tex]
[tex]k=\dfrac{1}{4}[/tex]
Substituting [tex]k=\dfrac{1}{4}[/tex] in (i), we get
[tex]y=\dfrac{1}{4}x[/tex]
Put x=80 in this equation.
[tex]y=\dfrac{1}{4}(80)[/tex]
[tex]y=20[/tex]
Therefore, the value of y is 20 when x=80.
What is the median?
5, 10, 8, 9, 9, 9
TYPE ONLY THE NUMERIC ANSWER
Answer:
9
Step-by-step explanation:
5, 8, 9, 9, 9, 10
(9+9)/2=9
Answer:
3n
5,10,8,9,9,9
= 5 , 1 , 0
5-1=4 - 1 3
What is the solution of the equation 6x - 4 = 2(3x - 2). Explain your steps.
Answer: x= 4/3 but in decimal form =1.333
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4-(2*(3*x-2))=0
4 - 2 • (3x - 2) = 0
Pull out like factors :
8 - 6x = -2 • (3x - 4)
Solve : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
Answer:
x= undefined
Step-by-step explanation:
In order to make u understand , if u multiply 2(3x-2) it becomes 6x-4 which is the exact same as the left hand side . Therefore u cant find x from here in this manner .
For this however we can try the method bellow .
Lets say f(x)=y=6x-4=2(3x-2)
we can get the followig points for inserting domains and finind the domains . we can make graph for each . (We will not do them however)
As we have seen that both of those parts of the equation are one and the same so they will produce the exact same Line or curve .
Therefore every signle points on them r the same exact points and there fore they are the same exact line .
So the value of x is undefined and can be anything between every points on that line (Which can be infinit amounts of points) .
Is 1/4 equivalent to 1/8
Answer:
No.
Step-by-step explanation:
1/4 is equivalent to 2/8, but not with 1/8.
Answer:
No.
Step-by-step explanation:
To find equivalent fractions, multiply the numerator and denominator by the same number.
Start with 1/4.
Multiply the numerator and denominator by 2.
You get 2/8.
2/8 is an equivalent fraction to 1/4.
2/8 and 1/8 are not equivalent.
Answer: No.
Select all of the expressions which correctly show how to convert 18 inches into yards
The length of a rectangle is 5 more than twice the width. If the perimeter of th
rectangle is 34, what is the length?
The length of a rectangle is 5 more than twice the width. If the perimeter of the rectangle is 34 cm find the length?
Explanation -:In this question we are provided with the perimeter of the rectangle = 34 cm and it is given that the length of the rectangle is 5 more than the twice it's breadth and asked to find out the length of the rectangle.
[tex] \small \orange{ \underline{\rm \blue{length \: of \: a \: rectangle \: is \: 5 \: more \: than \: twice \: the \: width.}}}[/tex]
Let us assume breadth as x then length = 2x +5
We know,
[tex] \star \: \large\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]
Substituting the values we get
34 = 2(2x +5 + x)
→ 34 = 2(3x + 5)
→ 34 = 6x + 10
→ 34 - 10 = 6x
→ 24 = 6x
→ [tex]\dfrac{24}{6}[/tex] = x
x = 4
Length = 2x + 5 = 2 × 4 + 5 = 8 + 5 = 13 cm
Breadth = x = 4cm
Length = 13 cm.
multi step equation 3x+3-x+12=x+5
Answer:
x= -10
if u need explanation pls let me know
Susan walked 1 2/3 miles in 1 1/4 hours how many miles Susan walked in 1 hour
Answer: 3/4 of a mile
Step-by-step explanation:
The radius of a circle is 5 miles. What is the length of a 135° arc?
Answer:
75
Step-by-step explanation:
an arc is half a circle
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Answer:
x = 33°
explanation:
The interior angles sum up to 180°
solve:
x + 20° + 4x - 5° = 180°
x + 4x + 20° - 5° = 180°
5x + 15° = 180°
5x = 180° - 15°
5x = 165°
x = 33°
Answer:
x = 33
Step-by-step explanation:
Sum of consecutive interior angles = 180°
⇒ (x + 20) + (4x - 5) = 180
⇒ 5x + 15 = 180
⇒ 5x = 165
⇒ x = 33
8 increased by twice Goran's age
Use the variable g to represent Goran's age.
Answer:
8+2g
Step-by-step explanation:
A side of the triangle below has been extended to form an exterior angle of 161°. Find the value of x.
Answer:
111
Step-by-step explanation:
180-161=19
19+50=69
180-69=111
Answer:
x=111°..............
5. The measure of the second angle of a triangle is 20 more than the measure of the first, and the measure of the third angle is 10 less than three times the first. What is the measure of each of the three angles of a triangle?
So first we have to find equation form angles.
Let :-first angle of triangle be xPart one :-Statement :- The measure of the second angle of a triangle is 20 more than the measure of the first.
Equation :-
second angle = 20 + x
{ Remember people get's confused when to multiply and when to add. when ever there "more than" then we will add and when there is ,"times" we will multiply}
Part 2 :-Statement :-
the third angle is 10 less than three times the first
Now just see first less means we have to subtract 10 from 3 times the first means 3 × first angle.
Equation :-
third angle = 3x - 10
Part 3 :-Now let's represent :-
First angle be ∠1Second angle be ∠2third angle be ∠3We know sum of angles of triangle is equal to 180°
So :-
∠ 1 + ∠ 2 + ∠ 3 = 180°x + 3x - 10 + 20 + x = 180°4x - 10 + 20 + x = 180°5x - 10 + 20 = 180°5x + 10 = 180°5x = 180° - 10°5x = 170x = 170/5x = 34°Measure of angles :-
∠1 = x∠ 1 = 34°∠2 = 20 + x∠2 = 20 + 34°∠2 = 54°∠3 = 3x - 10∠3 = 3 × 34 - 10∠3 = 102 - 10∠3 = 92°[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-We have given in the question that, The measure of second angle is 20 more than the measure of first angle The measure of third angle is 10 less than three times the first. To Find :- We have to find the measure of all the three angles of triangle. Let's Begin :-Let the first angle be x
According to the question,
Second angle = x + 20[ 2nd angle is 20 more than the first angle ]
Third angle = 3x - 10[ 3rd angle is 10 less than thrice times the first angle ]
By using Angle sum property
It states that the sum of the angles of triangles are equal to 180°That is,
[tex]\sf{ x + ( x + 20) + ( 3x - 10) = 180{\degree}}[/tex]
[tex]\sf{ x + x + 20 + 3x - 10 = 180{\degree}}[/tex]
[tex]\sf{ 5x + 10 = 180{\degree}}[/tex]
[tex]\sf{ 5x = 180 - 10}[/tex]
[tex]\sf{ 5x = 170}[/tex]
[tex]\sf{ x = }{\sf{\dfrac{ 170}{5}}}[/tex]
[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 170}{5}}}}[/tex]
[tex]\bold{ x = 34{\degree}}[/tex]
Thus,
The first angle is 34°The second angle [tex]\sf{ = 34 + 20}[/tex][tex]\bold{ = 54{\degree}}[/tex]The third angle [tex]\sf{ = 3(34 ) - 10}[/tex][tex]\sf{ = 102 - 10}[/tex][tex]\bold{ = 92 {\degree}}[/tex]Hence, The three angles of the given triangle are 34° , 54° and 92°
[tex]\bold{\huge{\underline{ Verification }}}[/tex]
Here, we have
The first angle = 34°The second angle = 54°The third angle = 92°By using Angle sum property :-
[tex]\sf{ 34 + 54 + 92 = 180{\degree}}[/tex]
[tex]\sf{ 88 + 92 = 180{\degree}}[/tex]
[tex]\sf{ 180 = 180{\degree}}[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Hence, Verified
I need help
a)104
b)128
c)120
d)74
e)87
Answer:
m∠JTS = 104° ⇒ (A)
Step-by-step explanation:
The measure of an exterior angle of a triangle at one of its vertices equals the sum of the measures of the opposite interior angles.
Let us use this fact to solve the question
In ΔTSR
∵ T ∈ ray RJ
∴ ∠JTS is an exterior angle of ΔTSR
→ By using the fact above
∴ ∠TSR and ∠TRS are the opposite interior angles to ∠JTS
∴ m∠JTS = m∠TSR + m∠TRS
∵ m∠JTS = 27x - 4
∵ m∠ TSR = 30°
∵ m∠TRS = 18x + 2
→ Substitute their values in the equation above
∴ 27x - 4 = 30 + 18x + 2
→ Add the like terms in the right side
∴ 27x - 4 = 18x + 32
→ Add 4 to both sides
∴ 27x = 18x + 36
→ Subtract 18x from both sides
∴ 9x = 36
→ Divide both sides by 9
∴ x = 4
→ To find m∠JTS substitute x by 4 in its measure
∴ m∠JTS = 27(4) - 4 = 108 - 4
∴ m∠JTS = 104°
Please help! 15 Points!
Answer:
Option C and D
Step-by-step explanation:
2π/3 refers 120°which falls in the second quadrant. In second quadrant sin value is positive and tan & cos value is negative.
tan 120 = - tan 60 = -√3
Find the equation of a line that passes through the point (-3,-1) and has a gradient of -2. Leave your answer in the form y = m x + c
Answer:
Step-by-step explanation:
y-y1 = m (x-x1), where (x1,y1) is the point the line passes through and m is the slope
y-(-1) = 2 (x-3)
y+1 = 2x - 6
calculate the rate of change from the graph below
Answer:
The rate of change is 0.75 gallons per minute
Step-by-step explanation:
The rate of change of the linear relation is represented by the slope of the line which represents this relation
The rule of the slope of a line is
m = Δy/Δx, where
Δy is the vertical changeΔx is the horizontal changeFrom the given graph
∵ The line passes through points (0, 0) and (4, 3)
∴ Δx = 4 - 0 = 4
∴ Δy = 3 - 0 = 3
→ Use the rule of the slope above to find the slope of the line
∴ m = [tex]\frac{3}{4}[/tex] = 0.75
∵ The x-axis represents the time in minutes
∵ The y-axis represents the amount in gallons
∵ m represents the rate of change
∴ The rate of change = 0.75 gallons per minute
15. Find the value of x.
(68 - x)
3x
Answer:
17=x
Step-by-step explanation:
In this case, we need to use Vertical Angles Theorem to solve this problem. Basically, because of the position of the angles, they are congruent.
68-x = 3x
Add x to both sides
68=4x
Divide by 4
17=x
Hope this helps!
Answer:
The value of 'x' is: 17°
Step-by-step explanation:
From what is being shown, there are two angles that are given:
(68 - x)°
3x°
Since they are congruent angles, meaning they are equal to each other, they will be put into a(n) equation such like shown below:
(68 - x)° = 3x°
(Then remove the parenthesis)
68° - x° = 3x°
+ x°=+3x°
------------------
68° = 4x°
------------------
(Divide both sides by 4)
[tex]\frac{68}{4} = \frac{4x}{4}[/tex]
------------------
17° = x
------------------
Your value of 'x' is 17.
What is the solution of (4 x minus 16) Superscript one-half Baseline = 36? x = 5 x = 13 x = 20 x = 328.
The solution of the given equation [tex](4x-16)^{1/2} = 36[/tex] is 328.
The given equation is:
[tex](4x-16)^{1/2} = 36[/tex]
What is solution of an equation?The solution of an equation is to find out the numeric value of the variable such that Left-hand side and Right-hand side becomes equal.
Squaring both sides of the given equation.
[tex][(4x-16)^{1/2} ]^2= (36)^2[/tex]
[tex]4x-16 = 36^{2}[/tex]
[tex]4x -16 =1296[/tex]
[tex]4x =1296+16[/tex]
[tex]4x = 1312[/tex]
x= 328
Therefore, The solution of the given equation [tex](4x-16)^{1/2} = 36[/tex] is 328.
To get more about equations visit:
https://brainly.com/question/9423572
4 (3r+4) = -8 (2r+5)
Answer:
-2
Step-by-step explanation:
Open the brackets on both sides
12r + 16 = -16r - 40
collect like terms
12r + 16r = -40 - 16
28r = -56
r = -56/28
r = -2
Find the area of the figure. Use 3.14for.
18 m
22m
The area of the figure is about ____ m2
Area of triangle = 1/2 x base x height
Area of the triangle = 1/2 x 22 x 18 = 198 square m.
Area of semi circle = 1/2 x PI x r^2
Area of semi circle = 1/2 x 3.14 x 11^2 = 189.97 square m.
Total area = 198 + 189.97 = 387.97 square m.
Round up to 388 square m.
k(t) = 13t-2k(t)=13t−2k, left parenthesis, t, right parenthesis, equals, 13, t, minus, 2
k(3)=k(3)=k, left parenthesis, 3, right parenthesis, equals
Answer:
Step-by-step explanation:
right parenthesis, equals, 13, t, minus, 2 so think about it when you divide
k(t) = 13t-2k(t)=13t−2k then your answer would maybe be k=134
Answer:
The answer is 39 -2k
Step-by-step explanation:
which algebraic expression represents the number of cups of dog food per week needed to feed 3 dogs if each dog eats x CUPS per day
A 7+3x
B 7(3x)
C 7x
D 21÷x
You start driving north for 6 miles, turn right, and drive east for another 19 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answer:
Okay, here's the method I'm going to use.
If you drive north 6 miles, and then drive east 19 miles, you are technically making a triangle.
19 miles
l_______________
6 milesl
l
You are just missing the last side of the triangle: the straight line stretching from across your starting point to the ending point. You can find this by using the Pythagorean theorem.
a^2 + b^2 = c^2
6^2 + 19^2 = c^2
36 + 361 = c
397 = c
[tex]\sqrt{397}[/tex] = 19.924859
Rounded to the nearest tenth, your answer is
19.9 miles
9. Rusty can ride his bicycle 21 miles in 3 hours. Find the unit rate of the
situation. *
O A. 7 hours per mile
O B.6.7 miles per hour
O C.63 miles per hour
D. 7 miles per hour
Rate = distance / time
Rate = 21 miles / 3 hours
Rate = 7 miles / hour
The answer is choice A. Hope this helps.
What is the distance between (-2,1) and (-1,2) on a coordinate plane
Answer:
√2 or 1.414
Step-by-step explanation:
the distance between two points
HELP WILL GIVE CROWN
Answer:
When dividing with same base and different exponents, you need to subtract the exponents.
[tex]7^8/7^4\\= 7^8^-^4\\= 7^4[/tex]
Answer: C
Step-by-step explanation: 7^8= 5764801. And 7^4 = 2401. 5764801/2401 = 7^4
Answer please ????
Answer:
[tex]\mathsf{\cos T=\dfrac{28}{53}}[/tex]
Step-by-step explanation:
[tex]\mathsf{\cos(\theta)=\dfrac{adjacent\ side}{hypotenuse}}[/tex]
[tex]\implies \mathsf{\cos T=\dfrac{28}{53}}[/tex]
pls give me the correct answer and solution
due date : 1:30pm
Answer:
where's the question?
Step-by-step explanation:
carry on laern
How do I find the slope point equation of this when I only have (4,-2) and no slope?
Answer:
B
Step-by-step explanation:
AM LACKING TIME
What operation would you use for your exponents when raising a power to a power
a
Division
b
Addition
c
Subtraction
d
Multiplication
Answer:
d multiplication