Given:
The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.
To find:
The combined variation equation and find y when x = 6 and z= 3.
Solution:
The variable y varies directly as x and inversely as z.
[tex]y\propto \dfrac{x}{z}[/tex]
[tex]y=k\dfrac{x}{z}[/tex] ...(i)
Where, k is the constant of proportionality.
Putting x=4, y=2 and z=14, we get
[tex]2=k\dfrac{4}{14}[/tex]
[tex]2=k\dfrac{2}{7}[/tex]
[tex]2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}[/tex]
[tex]7=k[/tex]
Putting k=7 in (i), we get
[tex]y=7\dfrac{x}{z}[/tex]
Putting x=6 and z=3, we get
[tex]y=7\times \dfrac{6}{3}[/tex]
[tex]y=7\times 2[/tex]
[tex]y=14[/tex]
Therefore, the required equation is [tex]y=7\dfrac{x}{z}[/tex] and the value of y is 14 when x = 6 and z= 3.
PLEASE HELP!!!!!
Solve the equation. Then check your solution.
Select the equations that show a proportional relationship between x and y.
y = 3x - 3
y = 3x
Answer:
The answer is the 2nd one.
need help what is the equation of the purple line
Answer:
y=-2/5x +8
Step-by-step explanation:
use y=mx+b look at where the line intercepts with the y-axis and that is at 8 so that is your b. Then find two points and count how many down or up it is to get from the higher up point (i usually use the one that intercepts at the y-axis) to same line as the other point, in this case thats down two. Then count how many to the right it is and in this case it is 5. so since it went down thats -2 over 5 so then you just fill that into the y=mx+b and you should get y=-2/5x+8
Hope this helped!
ps. if this was right can you make it brainliest? thanks!
comenzando desdes el principio, una persona camina 6km al este durante el primer dia y km al este el dia siguente. ¿ cual es el desplazamiento neto de la persona desde el punto de partida en dos dias
A) 6km, oeste
B) 3km, este
C) 10km,este
D) 5km,oeste
E) 9k., este
ayuda porca cual de esta es
Answer:
Yanga ka jhcgjvvhjjio ddd....
how many groups of 1/4 are in 7?
Answer:
All you have to do is add 2/4 7 times. So 1/4 times 7 which would equal 7/4=1 3/4
Step-by-step explanation:
Division is one of the four fundamental arithmetic operations. The groups of 1/4 in 7 are 28.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The number of one-fourths in 7, can be found by dividing 7 by 1/4. Therefore, the groups of 1/4 in 7 are,
Number of one-fourth = 7/(1/4)
= (7×4)/1
= 28
Hence, the groups of 1/4 in 7 are 28.
Learn more about Division here:
https://brainly.com/question/369266
#SPJ2
Select the statement(s) that accurately describes the nature of an angle in standard position. (Select all that apply.) A)Two or more positive angles can not share the same terminal side. B)An obtuse angle is any angle whose terminal side is not in quadrant 1. C)An acute angle can have its terminal side in quadrant 4. D)Its vertex is at the origin. E)The terminal side of a negative-measured angle is generated in the clock-wise direction from the x-axis.
Answer:
Step-by-step explanation:
D) Its vertex is at the origin
E) The terminal side of a negative-measured angle is generated in the clock-wise direction from the x-axis.
The amount of rotation between the two rays forming the angle is known as the measure of the angle
The correct options are;
The options that gives the statements that accurately describes the nature of an angle in the standard position are;
D) Its vertex is at the origin.
E) The terminal side of a negative measured angle is generated in the clock-wise direction from the x-axis
Reason:
An angle is in the standard position where the location of the angle is at the origin, the positive direction is the counterclockwise, while the negative direction is the clockwise direction
The x-axis oriented ray is known as the initial side, while the other ray forming the angle is known as the terminal side
Therefore, the correct options are;
D. Its vertex is at the origin.
E. The terminal side of a negative measured angle is generated in the clock-wise direction from the x-axis
Learn more here:
https://brainly.com/question/15342488
Find two values of "b" so that x^2 + b x + 6 can be factored into binomial factors.
Given:
The expression is
[tex]x^2+bx+6[/tex]
To find:
The values of b so that the given expression can be factored into binomials factors.
Solution:
An expression is [tex]ax^2+bx+c[/tex] factorable if b is the sum of possible factors of ac.
We have,
[tex]x^2+bx+6[/tex]
Here, [tex]a=1,b=b,c=6[/tex].
[tex]ac=(1)(6)[/tex]
[tex]ac=6[/tex]
Some, factor forms of 6 are (1×6) and (2×3).
[tex]1+6=7[/tex]
[tex]2+3=5[/tex]
For b=7,
[tex]x^2+7x+6=x^2+x+6x+6[/tex]
[tex]x^2+7x+6=x(x+1)+6(x+1)[/tex]
[tex]x^2+7x+6=(x+1)(x+6)[/tex]
For b=5,
[tex]x^2+5x+6=x^2+2x+3x+6[/tex]
[tex]x^2+5x+6=x(x+2)+3(x+2)[/tex]
[tex]x^2+5x+6=(x+2)(x+3)[/tex]
Therefore, the two possible values of b are 7 and 5.
Can you help me simplify this expression 16d + 20c + 5d -7 - 8c - 7d + 3?
Answer:
12c + 14d - 4
Step-by-step explanation:
16d + 20c + 5d -7 - 8c - 7d + 3
Simplify the expression
__________________________
To solve, we need to first take in mind the fact that there are different like terms within this expression. Like terms are numbers or values that end in different symbols, such as variables or exponents. Since we are filled with variables such as c and d. We can do as followed :
Combine the "d" like terms :
16d + 5d - 7d
21d - 7d
14d
Combine the "c" like terms :
20c - 8c
12c
Combine the constants :
-7 + 3
-4
Now add all of the values together to get the final expression.
12c + 14d - 4
Answer:
14d + 12c + 3
Step-by-step explanation:
1) Add the same variables; if you see d, or c variable add or subtract them like this:
16d + 5d - 7d = 14d
20c - 8c = 12c
3 is left alone b/c there’s no any other number to add/subtract for 3.
also I know whether to add or subtract b/c the addition or subtraction sign would be before the number: ex; - 2, - 3x, + 5d, + 5
2) your equation should look like this....
14d + 12c + 3
Line segment BD divides trapezoid ABCE into a rectangle and a right
triangle as shown. What is the perimeter of the trapezoid?
===========================================================
Explanation:
Since ABDE is a rectangle, the opposite sides AE and BD are the same length. This makes BD = 24. Similarly, ED = 20 since AB = 20.
Focus on triangle BCD. Let x be the length of segment CD. We can use the pythagorean theorem to find x
a^2 + b^2 = c^2
(BD)^2 + (CD)^2 = (BC)^2
24^2 + x^2 = 25^2
576 + x^2 = 625
x^2 = 625 - 576
x^2 = 49
x = sqrt(49)
x = 7
Segment CD is 7 units long.
Since ED = 20, this means,
EC = ED + DC
EC = 20 + 7
EC = 27
The perimeter of this trapezoid is
P = sum of all exterior sides
P = AB+BC+CE+EA
P = 20+25+27+24
P = 96 units
Note that we didn't add in side BD as part of the perimeter because it is not an exterior side. Think of sides AB, BC, CE, and AE as outer walls of the house while BD is an interior wall. The perimeter is only worried about the outer walls.
96
Explanation:
Since ABDE is a rectangle, the opposite sides AE and BD are the same length. This makes BD = 24. Similarly, ED = 20 since AB = 20.
Focus on triangle BCD. Let x be the length of segment CD. We can use the pythagorean theorem to find x
576 + x^2 = 625
x^2 = 625 - 576
x^2 = 49
x = sqrt(49)
x = 7
Segment CD is 7 units long.
Since ED = 20, this means,
EC = ED + DC
EC = 20 + 7
EC = 27
The perimeter of this trapezoid is
P = sum of all exterior sides
P = AB+BC+CE+EA
P = 20+25+27+24
P = 96 units
Pens and Pencils
Mrs. Charles ordered 150 pencils and 225 pens for the academy store. The pens cost 15 cents more than the pencils. Mrs. Charles’ total order was $135. Mrs. Charles was quite surprised by this amount as she thought the total would be $120.
If the cost of one pencil and one pen is 69 cents, who do you think is right, the supplier or Mrs. Charles? Support your answer with
mathematical evidence.
What is the cost of each pencil? Each pen? Support your answer with mathematical evidence.
Find the slope between the two points (-3,3) (1,-5)
Answer: M= -2
Step-by-step explanation: Have a brilliant day mate- Lily ^-^
Help me plz will give BRIANLY
solve the equation multiple choice
Answer:
x= {-29}
Step-by-step explanation:
.....................................
Part A: find the measure of x and y
Part B: choose the correct degree measure for arc JKL
Answer:
x = 7
y = 4
Arc JKL = 262°
Step-by-step explanation:
Find the diagram attached
Using the theorem;
Sum of opposite angle of the quadrilateral is 180°
7x+131 = 180
7x = 180-131
7x = 49°
x = 49/7
x = 7
Similarly;
11x+y+99 = 180°
11(7)+y+99 = 180°
77+99+y = 180
176+y = 180
y = 180-176
y = 4
arc JKL is the obtuse angle at the centre
Arc JKL = 360-(angle at the centre)
Angle at the centre is twice angle at the circumference.
Angle at the centre = 2(7x)
Angle at the centre = 2(49)
Angle at the centre = 98°
Arc JKL = 360-98
Arc JKL = 262°
A local diner uses 4 2/3 pounds of meat to make five hamburgers. How much meat is used to make one hamburger?
Answer:14/15 pounds of meat
Step-by-step explanation:
SO, 4 2/3=14/35 HAMBURGERS ARE MADE BY USING 14/3 POUNDS OF MEAT1 HAMBURGER IS MADE BY USING 14/3×1/5 OR,14/15 POUNDS OF MEAT.BASICALLY THE ANSWER IS:14/15 pounds of meat is used to make one hamburger.(PLEASE ANSWER ASAP FOR BRAINILEST! EXPLAIN YOUR REASONING PLEASE) I bought 1 pound of grapes for $3.75. I bought 4 pounds of strawberries for $15.63. Which is least expensive per pound? Explain your reasoning.
Answer:
Step-by-step explanation:
All you have to do is divide 15.63 by 4. That way you will find out how much it costs for 1 pound of strawberries.
15.63 divided by 4 = 3.9075 ( I would round it but you don't have to.
Now look at the first 3 number for both prices
Grapes: $3.75
Strawberries: $3.90
Now you see which is less expensive ( grapes ). Now finish with a statement!
Hopefully that helps any more questions lmk!
5 divided by 1/3(just answer not like I need help though I’ll give Brainly it’s like easy money)
Answer:
15 is your answer
Step-by-step explanation:
Answer:
15 is the answer
Step-by-step explanation:
ans 15
thanx
SOLVE THIS
I WILL GIVE BRAINLIEST
hope it becomes helpful to you ☺️☺️
good luck
If 3 varies inversely as x and y=2 when x=25, find x when y=40
Answer:
you get X= 1.25!!!!! :) have a great day
Step-by-step explanation:
Use the substitution method to solve the following pairs of simultaneous
equations.
a. x = 8-3y, 2x + 5y = 13,
Answer: x= , y=
Answer:
Step-by-step explanation:
2x+5y = 13
2(8-3y)+5y =13
16-6y+5y = 13
y=3
x =8-3y = -1
David Smith and his 2 children are going to a zoo.The admission price is:
Adult: £60
Child: £45
David has a family discount card.
Family Discount Card gives
1/4
off adult price
40% off child price
Work out the total price David pays after using his discount card
Answer:
£101
Step-by-step explanation:
60 divided by 4 = 15
15 x 3 = 45
£45 = adult price
10% of £45 = £4.50
40% of £45 = £18
£45 - £18 = £27
£27 = 1 child ticket
£27 x 2 = £56
£56 = two child tickets
£56 + £45 = £101
May someone please help me out? Please show full steps ♡´･ᴗ･`♡
Answer:
Step-by-step explanation:
METHOD 1
in centre it is split by 4, each angle is equal.
in a square angles add up to 360°
360/4=90°
∴∠DOC=90°
if you have to do more work or have toexplain more, or you dont get that way there is another method:
METHOD 2
since ABCD is a square it alladds up to 360°
so ∠A=B=C=D=90°
in triangle DOC anles add up to 180°
each diagonal cuts angleA,B,C and D in half
so in triangle DOC, ∠ODC=∠CDO=45
∠DOC=180-∠DOC-∠CDO (or 180-(∠DOC+∠CDO)
∠DOC=180-45-45
∠DOC=90
In Coach Bryant’s math class, he had his students create a net of a cube. An example of the net is below.
Net of a cube. The measurements for each side 2.5 in.
What is the total surface area of the cube?
37.5 in2
6.25 in2
31.25 in2
60 in2
Answer:7.5 in2
Step-by-step explanation:A=6a2=6·2.52=37.5in²
How do you write 20% as a fraction?
Answer:
20% = 20/100 or 2/10 or 1/5
Step-by-step explanation:
Answer:
20% as a fraction can be 20/100 1/5 2/10
Step-by-step explanation:
help the pictures underneath
Answer:
Step-by-step explanation:
I believe the correct answer is A, but im not sure. Hope it helps! <3
Answer:
a
Step-by-step explanation:
it takes a long time for a river to carve a path through rock. for example it took the grand canyon 5-6 million years to form by way of river erosion
I NEED HELP WITH THIS FAST
Answer:
Option D my dude
Step-by-step explanation:
it make sense
help me pleaseee asappp solving systems of equations
Answer:
6.50
Step-by-step explanation:
-8/5 X= 56
solve
xjgzjfxgkhkufxhxkhxgykxhlxhlx
Answer:
x = -35
Step-by-step explanation:
-8/5x = 56
Start by multiplying both sides by 5 to get rid of the fraction. That will leave you with:
-8x = 280
You can then divide both sides by -8 and then you'll get x = -35
Answer:
x=-35
Step-by-step explanation:
-8/5x is gonna be -1.6x and you divide 56 by -1.6x and get x=-35
The difference between a number and its square is 20. Find the
numbers.
Answer:
-4 or 5
Step-by-step explanation:
let number be x
x²-x=20
Rearrange
x²-x-20=0
(x+4)(x-5)=0
Separate
x+4=0, x-5=0
x=-4 or 5
Find the exact area of the shaded region