Answer:
(Some textbooks describe direct variation by saying " y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x . ") This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.
Solve these simultaneous equations:
2x + 4y = 38
7x - 4y =7
Answer:
Step-by-step explanation:
Answer:
x=5, y=7
Step-by-step explanation:
2x+4y= 38
+7x-4y= 7
9x= 45
9x/9= 45/9
x=5
2x+4y=38
2(5)+4y= 38
10+4y= 38
-10 -10
4y= 28
4y/4= 28/4
y=7
If the value of y varies inversely with x , which function represents the relationship between x and y if y = 48 when x = 3?
A. Y= 144/x
B. Y= 16/x
C. Y= x/16
D. Y= x/144
Answer:
A. Y = 144/x
Step-by-step explanation:
Inversely means y = 1/x
If y = 48, when x = 3
so 144/3 = 48
Therefore the answer is A
If the value of y varies inversely with x then the function Y= 144/x represents the relationship between x and y if y = 48 when x = 3
What is a function?A relation is a function if it has only One y-value for each x-value.
If y varies inversely with x, it means that y is inversely proportional to x, or y=k/x, where k is a constant of proportionality.
To find k, we can use the given values of y and x:
y = k/x
48 = k/3
k = 144
Now that we know k, we can write the function that represents the relationship between x and y:
y = 144/x
Therefore, if the value of y varies inversely with x then the function Y= 144/x represents the relationship between x and y if y = 48 when x = 3
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If h:k = 2:5, x:y=3:4 and 2h+x:k+2y = 1:2, find the ratio h-x: k-y.
Given:
[tex]h:k=2:5,x:y=3:4,2h+x:k+2y=1:2[/tex]
To find:
[tex]h-x:k-y[/tex]
Solution:
We have, [tex]h:k=2:5[/tex] and [tex]x:y=3:4[/tex].
Let the values of h and k are 2a and 5a respectively.
Let the values of x and y are 3b and 4b respectively.
We have,
[tex]2h+x:k+2y=1:2[/tex]
It can be written as
[tex]\dfrac{2h+x}{k+2y}=\dfrac{1}{2}[/tex]
[tex]\dfrac{2(2a)+(3b)}{5a+2(4b)}=\dfrac{1}{2}[/tex]
[tex]\dfrac{4a+3b}{5a+8b}=\dfrac{1}{2}[/tex]
[tex]2(4a+3b)=1(5a+8b)[/tex]
On further simplification, we get
[tex]8a+6b=5a+8b[/tex]
[tex]8a-5a=8b-6b[/tex]
[tex]3a=2b[/tex]
[tex]a=\dfrac{2b}{3}[/tex]
Now,
[tex]h-x:k-y=\dfrac{h-x}{k-y}[/tex]
[tex]h-x:k-y=\dfrac{2-3b}{5a-4b}[/tex]
[tex]h-x:k-y=\dfrac{2\times \dfrac{2b}{3}-3b}{5\times \dfrac{2b}{3}-4b}[/tex]
[tex]h-x:k-y=\dfrac{\dfrac{4b}{3}-3b}{\dfrac{10b}{3}-4b}[/tex]
On further simplification, we get
[tex]h-x:k-y=\dfrac{\dfrac{4b-9b}{3}}{\dfrac{10b-12b}{3}}[/tex]
[tex]h-x:k-y=\dfrac{-5b}{-2b}[/tex]
[tex]h-x:k-y=\dfrac{5}{2}[/tex]
[tex]h-x:k-y=5:2[/tex]
Therefore, the ratio [tex]h-x:k-y[/tex] is [tex]5:2[/tex].
A child has a box of colored building blocks. He will choose one block without looking. The odds against choosing a blue block are 13/4. What is the probability of choosing a blue block?
Answer:
The answer is "0.2352".
Step-by-step explanation:
Given:
The chance of selecting a odds blue block [tex]= \frac{13}{4}[/tex]
[tex]=\frac{\text{Amount of unfavourable blue block evets} \ (13)}{\text{Amount of unfavourable blue block evets} \ (4)}[/tex]
total number of events are 13+4= 17
Calculating the probability of choosing the blue block
[tex]=\frac{\text{Amount of unfavourable blue block evets} }{\text{Amount of unfavourable blue block evets} } \\\\ = \frac{4}{17} \\\\ =0.2352[/tex]
John has $55 . He buys 6 books. Each book costs the same amount. He now has $10 . Drag expressions to complete the tape diagram shown to model this situation.
Answer:
well each book would cost $7.50
Step-by-step explanation:
Part A: Xavier needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items. Choose the correctly written inequality to represent the number of cans, c, that Xavier must still collect (before solving)
A 64 + c ≥ 120
B 64 + c < 120
C c - 120 ≤ 64
Answer:
A
Step-by-step explanation:
He needs to collect at least 120 so if c is what he must still collect
64 +c must be greater than or equal to 120
Please help! Will give brainlist
Answer:
vertical
Step-by-step explanation:
bdvdhdvdhdvdhdhdvdhbdbdd
Answer:
adjacent
Step-by-step explanation:
Which shape shows the cross-section of the square pyramid when it is cut by a plane parallel to the base?
Answer:
Triangle
Step-by-step explanation:
A pyramid is a strong-solid shape that is comprised of triangles, square shapes, squares, and different polygons. Pyramids are arranged depending on the state of their base. For instance, the outline given is a square-based pyramid in light of the state of its base(which is a square). Different sorts incorporate the three-sided based pyramid, three-sided based pyramid, and other polygon-based pyramids.
In the event that this square pyramid is cut with a plane that is corresponding to the base of the pyramid, the state of its cross-area will be a triangle since the shapes that are corresponding to the base are altogether triangles. So slicing the plane corresponding to the base is like removing one side of the triangle making up the pyramid.
Cody hits a baseball. The highest distance it travels is represented by the ______ of the parabola.
A. Maximum
B. Minimum
C. x-intercept
D. y-intercept
Answer:
A
Step-by-step explanation:
Not B and Not C
How do you solve an inequality, then verify the solution by subsituting 3 different numbers?
Answer and Step-by-step explanation:
To solve an inequality, you must solve for the variable. Let's look at an example:
4x + 2 > 10
We solve for x by subtracting 2 from both sides, then dividing 4 on both sides.
(Solve as if you were solving a regular equation)
4x > 8
x > 2
We get x > 2 as our inequality.
To plug in 3 values, simply plug in any number that is greater than 2. That would be the solution to the inequality.
If when solving the inequality and you have to divide by a negative, the sign will change. Ex:
-5x > 25
x < -5
To show that the sign should switch, let's solve it this way.
-5x > 25
0 > 25 + 5x Add the 5x to both sides.
-25 > 5x Subtract the 25 from both sides
-5 > x Divide by 5 from both sides.
As we can see, the inequalities turn out to be the same, which is why you flip the sign when you divide.
#teamtrees #PAW (Plant And Water)
PLS USE the information given! DONT GUESS!
Write the equation of the circle.
A: (x+3)2+(y−6)2= 2
B: (x−3)2+(y+6)2= 2
C: (x+3)2+(y−6)2= 4
D: (x−3)2+(y+6)2= 4
Answer:
C. (x + 3)² + (y - 6)² = 4Step-by-step explanation:
Get the center and radius from the graph.
Center is: (-3, 6)Radius is: 2Use the circle formula:
(x - h)² + (y - k)² = r²We have:
h = -3, k = 6, r = 2Substitute and get the equation:
(x - (-3))² + (y - 6)² = 2² ⇒(x + 3)² + (y - 6)² = 4Correct choice is C
help help
Prove the following:
[tex] \sf\frac{ \tan( \theta) }{1 - \cot( \theta) } + \frac{ \cot( \theta) }{ 1 - \tan( \theta) } = \sec( \theta) \cdot \: \csc( \theta) + 1[/tex]
[tex]\text{note: explanation is obvious}[/tex]
Answer:
the pictures are attachedplease see the explanation in the attached pictureAnswer:
note:[tex]\theta =y[/tex]
Your answer is in the attachment.
we have
siny(cosy-siny)
taking - common from this
-siny(-cosy+siny)
-sin y(siny-cosy)
i need help with this..
Answer:
a = 9
Step-by-step explanation:
sin45 = a/9√2
a = 9√2(sin45)
a = 9
A bag contains 24 discs.
8 are red and 16 are blue.
One disc is taken out at random and replaced by two of the other colour.
Another disc is then taken out at random and replaced by two of the other colour.
Another disk is taken out at random
Work out the probability that all three discs are taken out red
Answer:
Step-by-step explanation:
8/24 are Red
Pick and return 2
So it will be 7/25
Again pick and return 2
Then it is 6/26
Now multiply the results
8/24 × 7/25 × 6/26 = 7/ 325
The probability that all three discs are taken out of red will be 7/ 325.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a bag contains 24 discs. 8 are red and 16 are blue. One disc is taken out at random and replaced by two of the other colour. Another disc is then taken out at random and replaced by two of the other colour.
The probability will be calculated as,
Red = 8/24
Pick and return 2 it will be 7/25
Again pick and return 2 then it is 6/26
Now the overall probability will be,
P = 8/24 × 7/25 × 6/26 = 7/ 325
Therefore, the probability that all three discs are taken out of red will be 7/ 325.
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solve each system by substitution y=2x-1. 3x+8y=11
Answer:
x=1, y=1
Step-by-step explanation:
Sub y=2x-1 into 3x+8y=11
3x+8(2x-1)=11
3x+16x-8=11
19x=11+8
19x=19
x=1
Sub x=1 into y=2x-1
y=2(1)-1
y=2-1
y=1
EMERGENCY HELP PLS: The distance from P to the airplane is ? m.
Answer:
distance from P to the plane = 8957.6 m
Step-by-step explanation:
sin23 = 3500 / distance from P to the plane
distance from P to the plane = 8957.6 m
Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets.
Answer:
3 student tickets and 5 adult tickets
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
how do you find the circumference of a circle
Answer:
circumference = pi (3.14 or 22/7, whatever your teacher wants or whatever the problem asks) x the diameter
Step-by-step explanation:
Answer:
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).
Step-by-step explanation:
I hope the images help!!
5. Write an equivalent expression to 1/4 (24x + 7 – 12x).
Answer:
Step-by-step explanation:
The easiest and most proper way to approach this task is to combine like terms inside parentheses: (24x + 7 – 12x) => (12x + 7).
Then (1/4)(24x + 7 – 12x) = (1/4)(12x + 7). This is an acceptable answer. There is the option of carrying out the multiplication, which results in
3x + 7/4, which is another acceptable answer.
Please answer the following:
Answer:
Conner's work is correct
Step-by-step explanation:
In exponent multiplication, if base are same, add the exponents.
[tex]a^{m}*a^{n} =a^{m+n}[/tex]
For example,
5² * 5³
5² = 5 * 5
5³ = 5* 5 * 5
5² * 5³ = 5 * 5 * 5 * 5 * 5 = 5⁵ = 5⁽²⁺³⁾
Answe
Conner is correct .Step-by-step explanation:
Because as he used the laws of indices to answer the questionHeeeelp me Asp need this
Answer:
False; True; True
Step-by-step explanation:
If the radius is 4, the area of the circle is
pi*r*r = pi * 4 * 4 = 16pi; The second statement is true.
The entire circle's "angle" is 2pi, so the sector takes (2pi/3) / 2pi of it all, equal to 1/3 of the entire circle - hence the area of the sector is
16pi * 1/3 = 16pi/3; the first statement is false
The length of the entire circle is 2 * pi * r = 2 * pi * 4 = 8pi
The sector is 1/3 of that, so 8pi/3; the third statement is true.
Plz help
Rewrite the fraction in the sentence below as a percentage.
In a certain class,
23/25
of the students got problem 10 wrong on Friday's math test.
*ANSWER ASAP* Earth has a diameter of approximately 7926 miles. Determine the volume of Earth.
Answer:
Rounding to the nearest whole number, 49 moons can fit in the earth.
Rounding to the tenth place, 50 moons can fit in the earth.
Step-by-step explanation:
To find how approximately how many moons could fit inside the earth, you would need yo find the volumes the earth and the moon.
V = 4/3 π r^3
Earth:
d = 2r
d = 7926 miles
7926 = 2r
3963 miles = r
V = 4/3 π (3963)^3
V = 4/3 π (62240377347)
V = 82987169796π cubic miles
Moon:
d = 2r
d = 2159 miles
2159 = 2r
1079.5 miles = r
V = 4/3 π (1079.5)^3
V = 4/3 π (1257963209.88)
V = 1677284279.83π cubic miles
Now you divide the volume of earth by the volume of moon to find how many moons can fit in earth
82987169796π ÷ 1677284279.83π =
approx 49
Help plz :)
Determine the measure of each unknown angle using the diagram.
Express the ratio as a fraction in simplest form.
18:24
1/2
2/3
3/4
6/7
Identify the slope and y-intercept of the following equation:
3x - 2y = -10
Answer:
m=3/2,y-int=5
Step-by-step explanation:
y=mx+b is the slope equation. since -10 is at the end of the equation and it does not have a variable next to it yk it is the y-intercept. if you want you draw this on a graph and you can see that you go up 3 and over 2
what is the distance between -a and a
Answer:
2a
Step-by-step explanation:
-a + a = 0, 0 + a = a. Therefore -a + 2a = a
a ball has a circumference of 9.42 cm. what is the diameter
In the school election James ran against Ben for
secretary. James received 75% of the votes. If 240
students voted, how many votes did James
receive?
