Given:
The equation is:
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
To find:
The constant of proportionality.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
We have,
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
On cross multiplication, we get
[tex]9x=2y[/tex]
Divide both sides by 2.
[tex]\dfrac{9}{2}x=y[/tex]
Interchange the sides.
[tex]y=\dfrac{9}{2}x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=\dfrac{9}{2}[/tex]
The constant of proportionality is [tex]\dfrac{9}{2}[/tex]. Therefore, the correct option is B.
The values in the table represent a function.
A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12.
Use the drop-down menus to complete the statements.
The ordered pair given in the first row of the table can be written using function notation as
.
f(3) is
.
f(x) = –5 when x is
.
Answer:
4rfjq3yr i
Step-by-step explanation:
Answer:
✔ f(–6) = 8
✔ –2
✔4
Step-by-step explanation:
Got them right just now on Edge !!!
John had to pay a combined electric and gas bill $150. The electric portion of the bill was $90. What is the ratio of money spent on electric to that on gas?
Given:
John had to pay a combined electric and gas bill $150.
The electric portion of the bill was $90.
To find:
The ratio of money spent on electric to that on gas.
Solution:
Let x be the amount of gas bill.
The electric portion of the bill was $90 and John had to pay a combined electric and gas bill $150. So,
[tex]90+x=150[/tex]
[tex]x=150-90[/tex]
[tex]x=60[/tex]
The gas portion of the bill was $60.
The ratio of money spent on electric to that on gas is:
[tex]\text{Required Ratio}=\dfrac{\text{Electric bill}}{\text{Gas bill}}[/tex]
[tex]\text{Required Ratio}=\dfrac{90}{60}[/tex]
[tex]\text{Required Ratio}=\dfrac{3}{2}[/tex]
[tex]\text{Required Ratio}=3:2[/tex]
Therefore, the ratio of money spent on electric to that on gas is 3:2.
Oscar charges $25 for the first hour of tutoring and $15 for each additional hour of fraction of an hour counting as a whole hour. the rates that Latoya charges for x hours of tutoring are modeled with with the function shown.
Choose.. will charge (5,10,15,20) more to tutor for 5.5 hours
Answer:
Latoya will charge $10 more to tutor for 5.5 hours
Step-by-step explanation:
We shall look at the total charges of both tutors individually.
Oscar charges $25 for the first hour of tutoring and $15 for each additional hour of fraction of an hour counting as a whole hour.
This means that for the first hour, Oscar charges $25.
For every subsequent hour, regardless of whether the student was tutored for the full hour or only partial, Oscar still charges $15 for the particular hour. To clarify, here is an example.
If a student is tutored for 2 hours, the cost for Oscar's tutoring is $25 (first hour) + $15 (second hour) = $40. However, if the student is still tutored for 1.5 hours, the cost for Oscar's tutoring is still $25 (first hour) + $15 (second hour) = $40. This is because Oscar counts the partial minutes as a full hour in tutoring costs.
For 5.5 hours, the cost of Oscar's tutoring is
$25 (first hour) + $15*4 (2nd to 5th hours) + $15 (the last half an hour) = $100.
Now, we shall look at Latoya's tutoring cost.
f(x) =
30x,
[tex]0 \leqslant x \leqslant 3[/tex]
20x,
[tex]3 < x \leqslant 6[/tex]
10x,
[tex]x > 6[/tex]
The tutoring cost depends on x, the number of tutoring hours. In this case, x is 5.5. The cost for 5.5 hour depends on the formula 20x since 5.5 is more than 3 but less than 6.
Hence, the tutoring cost for Latoya is $20*5.5 = $110.
In this case, Latoya charges $110-$100=$10 more to tutor for 5.5 hours.
If equation is x + y = 3 and x - y = 7 then the value of x will be?
A) 0
B) -3
C)-2
D)2
Its on the topic Simultaneous equations
Answer:
x = 5
Step-by-step explanation:
Add the equations
x + y = 3
x - y = 7
––––––––
2x = 10
Divide both sides by2
x = 5
Note: for the equations in the question,
none of the given answers are correct.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer si
des is 6.3 centimeters, which equation can be used to find the length of the base
Answer:
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 3.1
please give answer I will mark as brainliest if you give the right answer
a) 8.68 x 10^25
b) 1.439 x 10^12
Answer:
(8.6810±0.0013)×10^26 kg
1.439 time 10^12
Step-by-step explanation:
standard for is the whole numer with thousandth's place times 10^n or the number of zeroes
What value of c is needed to complete the square?
X2 + 10x + c = -3+ c
Answer:
Step-by-step explanation:Let's solve for c.
x2+10x+c=−3+c
Step 1: Add -c to both sides.
x2+c+10x+−c=c−3+−c
x2+10x=−3
Step 2: Add -x^2 to both sides.
x2+10x+−x2=−3+−x2
10x=−x2−3
Step 3: Add -10x to both sides.
10x+−10x=−x2−3+−10x
0=−x2−10x−3
Step 4: Divide both sides by 0.
0
0
=
−x2−10x−3
0
c=
−x2−10x−3
0
Answer:
c=
−x2−10x−3/0
hope it helps :D
Mark is building a sandbox inside a play area. How much play area remains outside of the sandbox?
Answer:125
Step-by-step explanation:
A bag contains three red marbles and two blue marbles.
(1.) What is the probability of reaching in and pulling out a red marble?
(2.) Chloe reaches in the bag, pulls out a marble, puts it back in the bag, and pulls out another marble. What is the probability that both marbles are blue?
(3.) Chloe reaches in the bag, pulls out a marble, does NOT put it back in the bag, then pulls out another marble. What is the probability that both marbles are blue?
Thank you
Answer:
1. 3/5
2. 2/5
3. 1/5
Step-by-step explanation:
I'm pretty sure this is the answer :)
Which is NOT a way to state the meaning of the expression c+5?
Question and choices are in the photo please explain the answer
Answer: The correct option is B.
Step-by-step explanation:
(x+5)(2x-1)=3(x+5)
Multiply the parentheses
2x^2 - x + 10x - 5 = 3x + 15
Collect like terms
2x^2 + 9x - 5 = 3x + 15
Move the expression to the left hand side and change its sign, then equate it to 0
2x^2 + 9x - 5 - 3x -15 = 0
Collect like terms
2x^2 + 6x - 20 = 0
Divide each term of the equation by 2
x^2 + 3x - 10 = 0
Rewrite the expression in factorized form
x^2 + 5x - 2x - 10 = 0
Factor the expression
x(x + 5) - 2(x + 5) = 0
(x + 5) (x - 2) = 0
Separate into possible cases but when the product of factors equals 0, at least one factor is 0.
x + 5 = 0———equation (1)
x - 2 = 0———-equation (2)
Solve the equations
x + 5 = 0———equation (1)
Make x the subject
x = 0 - 5
x = -5
x - 2 = 0———equation (2)
Make x the subject
x = 0 + 2
x = 2
Hence, the possible values of x are -5 and 2.
A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.
Answer:
749 lbs
Step-by-step explanation:
weight of the water in the mattress = volume of the mattress x weight of water
volume of the mattress = volume of a cuboid = length x width x height
6 x 2 x 1 = 12 ft³
weight of the water in the mattress = 12 x 62.4 = 748.8 lbs
749 lbs to the nearest pound
https://imgur.com/a/n3PRcMY
Step-by-step explanation:
hakdogg happyly ever after
A hula hoop is 113 inches around. What is its diameter to the nearest inch?
HURRY PLEASE
Answer:
35.97
Step-by-step explanation:
113 divided by pie (3.14)
What's The actual length of QR (round to 3 decimal places) ?
Answer:
4.383
Step-by-step explanation:
Pythagoras
a² + b² = c²
with c being the baseline of the rectangular triangle (the line opposite to the 90 degree angle).
so, in our example here c=6.5cm, a=QR, b=4.8cm
a² = c² - b² = 6.5² - 4.8² = 19.21
a = sqrt(19.21) = 4.383
Question and choices are in the photo please explain the answer
Answer:
[tex]\text{A) }68\:\mathrm{cm}[/tex]
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.
Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.
To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a [tex]90^{\circ}[/tex], creating right triangles [tex]\triangle TOP[/tex] and [tex]\triangle SOP[/tex].
The Pythagorean Theorem states that the following is true for any right triangle:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the triangle
Thus, we have:
[tex]10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24[/tex]
Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.
What we know:
[tex]TP=SP=24[/tex][tex]TO=SO=10[/tex]Thus, the perimeter of the quadrilateral PTOS is equal to [tex]24+24+10+10=\boxed{\text{A) }68\:\mathrm{cm}}[/tex]
Answer:
the other one should get a brainliest.
I'm just answering to make it technically possible.
What is the range of the function shown below?
Answer:
y ≤ 0
Step-by-step explanation:
The correct option is option C. The range of the given function is less than or equal to zero i.e., y ≤ 0.
What are domain and range of a function?
Range is the set of all values that the given function can output, whereas domain is the input or set of values for which the function is defined.
The graph of a function is shown. We know that the range of function is the output of the input of values we give to the function. Another thing to keep in mind is that we often plot functions with the outputs on the vertical axis and the inputs on the horizontal axis.
From graph it is clear that the function is going down from axis to negative y - axis.
So , it is clear that range will be less than or equal to zero.
i.e.,
Range is :
y ≤ 0
Therefore , the correct option is option C. The range of the given function is less than or equal to zero i.e., y ≤ 0.
Learn more about range of a function here :
https://brainly.com/question/10197594
#SPJ2
Find the value of x.
Answer:
10
please mark brainiest
help guys pls i beg u cannot do the math this so hard someone help ☺️☺️☺️☺️☺️☺️☺️☺️
in a cave, a stalactite gets 4 millimeters longer each year. This year it is 72 centimeters long. How many years until it is 1 meter long?
statement of pythagoras theorm no need proof only statement plz need fast
Answer:
Pythagoras Theorem: It is a basic relation in Euclidean geometry among the sides of a right-angled triangle. Pythagoras Theorem is commonly used to find the length of an unknown side in a right-angled triangle. It describes the interrelationship between the base, perpendicular and hypotenuse of a right-angled triangle. The converse of Pythagoras Theorem is used to check whether a triangle is a right-angled triangle or not
Step-by-step explanation:
Statement of Pythagoras Theorem
The Pythagoras Theorem states that in a right-angled triangle the sum of square of the base and square of the perpendicular is equal to the square of the hypotenuse.
Pythagorean theorem
In the right angled triangle there is a relationship that governs the length of the three sides. if we knows the length of any two sides, the third side may be calculated by the use of the Pythagorean theorem. this theorem States the square on the hypotenuse of a right angle triangle is equal to the sum of the squares on the remaining two sides.
what is the word capacity mean
Answer:
the maximum amount that something can contain. hope this helps :)
Step-by-step explanation:
Frida goes shopping and buys one sweater for $35 and jeans that cost $25 per pair. She has $115. Which inequality represents the number of jeans Dalecia can buy.
Answer: i have no idea how do i get rid of this answer
Step-by-step explanation:
Show that 0-58200-48826-5 is a valid UPC number.
Answer:
Proved
Step-by-step explanation:
Given
[tex]UPC = 0-58200-48826-5[/tex]
Required
Show that it is valid
Add up the elements at odd positions
[tex]Odd = 0 + 8 + 0 + 4+8+6[/tex]
[tex]Odd = 26[/tex]
Multiply by 3
[tex]Product = 26 * 3[/tex]
[tex]Product = 78[/tex]
Add up the elements at even positions
[tex]Even = 5 + 2 + 0 + 8 + 2 + 5[/tex]
[tex]Even = 22[/tex]
Add up both results
[tex]Result = 78 +22[/tex]
[tex]Result = 100[/tex]
Take modulus of 10
[tex]Result \% 10 = 100 \% 10[/tex]
[tex]Result \% 10 = 0[/tex]
Since the result of the modulus is 0, then the number is valid
True or false, with method of elimination, think about what you can multiply one equation by so that a variable will be eliminated when the two equations are added.
Answer:
True i think
Step-by-step explanation:
Anna is cutting several lengths of twine. The length of the first piece is 4 inches. She cuts the second piece one inch longer than 3 times the length of the first piece. If Anna continues the pattern, which sequence shows the lengths of the first four pieces?
Answer:
the pattern is 4, 13, 4, 13. I dont know what the answer choices are, but the first 4 legths put together are 34 inches.
Step-by-step explanation:
look above, hope this helps...
brainliest...
Answer:
The order of the first four strings is 1: 4in 2: 13in 3: 40in 4: 121in
Jessica wants to make tarts. To make tarts, she needs ¾ of a cup of flour per batch of tarts. If Jessica has 9 cups of flour, then how many batches of tarts can Jessica make?
Answer:
108
Step-by-step explanation:
Jesicca wants to make tarts
She uses 3/4 cup of flour per batch
Jessica has 9 cups of flour hence the number of batches she will make can be calculated as follows
= 9÷ 3/4
= 9÷ 0.75
= 12
= 12×9
= 108
Hence Jessica will make 108 batches of tart
Answer for points
3(3x3)(45x6)(45x7)(56x5)(5x5)x0
Answer:
0
Step-by-step explanation:
3(3x3)(45x6)(45x7)(56x5)(5x5)x0 =0
A computer store bought a program at a cost of $40 and sold it at a selling price of $32.5. Find the percent markdown (Rounded to a whole number) .
Answer:
answer is 18.76 percent.
Step-by-step explanation:
CP= $40
SP= $32.5
Markdown percent=?
now,
markdown %= CP-Sp/CP×100%
=7.5/40×100%
=750/40
=18.75%
The amount to be reduced is: $40 - $32.5 = $7.5
The percentage decrease is: (7.5 : 40) * 100 = 18.25%
What is the product?
Answer:
[tex]21x^{7}y^{11}[/tex]
Step-by-step explanation:
Remove the parentheses and take out the constansts.
[tex](7 x 3) x^{2} x^{5} y^{3} y^{8}[/tex]
Simplify 7 x 3 to 21.
[tex]21x^{2} x^{5} y^{3} y^{8}[/tex]
Use the product rule: [tex]x^{a} x^{b} = x^{a + b}[/tex]
[tex]21x^{2 + 5}y^{3+8}[/tex]
Simplify 2+5 to 7.
[tex]21x^{7}y^{3+8}[/tex]
Simplfiy 3 + 8 to 11.
[tex]21x^{7}y^{11}[/tex]
