Answer:
[tex]\dfrac{a+b+c}{a} =7[/tex]
Step-by-step explanation:
Given :-
[tex]\dfrac{a+b}{3} =\dfrac{b+c}{6} =\dfrac{c+a}{5}[/tex]And we need to prove that ,
[tex]\dfrac{a+b+c}{a} =7[/tex]So let us assume that ,
[tex]\dfrac{a+b}{3} =\dfrac{b+c}{6} =\dfrac{c+a}{5}=k[/tex]
Where k is a constant . Now equate each of the three terms separately to k . Therefore we have ,
[tex]\dfrac{a+b}{3}=k[/tex][tex]\implies a + b = 3k \quad \dots (i) [/tex]
Similarly we can say that ,
[tex]\implies c + b = 6k \quad \dots (ii)[/tex]
[tex]\implies a + c = 5k\quad \dots (iii) [/tex]
Subtracting (i) and (ii) :-
[tex]\implies a - c = -3k \quad \dots (iv) [/tex]Adding (iv) and (iii) :-
[tex]\implies 2c = 4k [/tex]
[tex]\implies \boxed{c = 4k }[/tex]
Put this is (ii) :-
[tex]\implies b +4k = 6k [/tex]
[tex]\implies \boxed{b= 2k }[/tex]
Similarly we will get ,
[tex]\implies \boxed{a = k }[/tex]
Proving the given equation :-
[tex]\implies \dfrac{a+b+c}{a} \\\\\implies \dfrac{k+2k+4k}{k} \\\\\implies \dfrac{7k}{k}=\boxed{\red{ 7}}[/tex]
Hence proved !
Jessica and two friends spent $36.93 on dinner. They left a $6.00 tip. How much money did each person spend if they split the bill and tip equally?
Answer:
14.31
Step-by-step explanation:
Anya rolls an octahedron labelled A A A B C C C C what is the probability the octahedron will land on each letter
Answer:
the probability the octahedron will land on A is 3/8
the probability the octahedron will land on B is 1/8
the probability the octahedron will land on C is 4/8 or 1/2
Step by Step explanation:
All u have to do to figure this out is to first count the total amount of letters and in this case there are 8. To find the probability of a specific letter, you have to count how many of that letter there is in the total of 8. For example the letter A's probability is 3/8 since there are 3 A's and 8 letters in total.
hope this helps!!
. The product of two integers is -84. One of them is 4, find the other integer.
Answer:
Answer :-Product of two integers = - 84
One integer = 4
Other integer = x
[tex]4 \times x = - 84 \\ 4x = - 84 \\ x = \frac{ - 84}{4} \\ x = - 21[/tex]
⎆ The value of the other integer is - 21
Annie earns $320 for 8 hours of work. At that rate, how long would she have to
work to earn $1,120?
Answer:
28 hrs
Step-by-step explanation:
in 8 hrs she earns $320,
so in 1 hr she earns $320/8=$40
no. of hrs she takes to earn $1120 is,
=1120/40= 28 hrs
Annie would need to work 28 hours to earn $1,120 at the same rate.
To determine how long Annie would have to work to earn $1,120 at the same rate, we can set up a proportion based on the given information.
Let's define:
x = the number of hours Annie needs to work to earn $1,120.
According to the information given, Annie earns $320 for 8 hours of work. This can be expressed as the rate: $320/8 hours.
We can set up the proportion as follows:
320/8 = 1120/x
To solve this proportion, we can cross-multiply and then solve for x:
320x = 8 * 1120
320x = 8960
Dividing both sides of the equation by 320:
x = 8960/320
x = 28
Therefore, Annie would need to work 28 hours to earn $1,120 at the same rate.
To know more about earn here
https://brainly.com/question/30157678
#SPJ2
AREA OF CIRCLES HELP PLS
Answer:
a=π9² is the formula with the radius plugged in
radius is half
Answer:
243in^2
Step-by-step explanation:
18/2=9
3 x 9 x 9=243
What is the midpoint of (6,3) and (-3,-7)
Answer:
(Xm, Ym) = [ x1+x2/2, y1 + y2/2]
Given (6,3) (-3,-7)
x1 y1 x2 y2
Step-by-step explanation:
(Xm,Ym) =[ 6-3/2, 3-7/4]
= [ 3/2, -1]
A type of fish for your aquarium costs $9 each. You can spend at most $63.
Write an inequality to model the problem.
Answer:
9x>63$
Step-by-step explanation:
nine $ aquarium , at most > 63$
A triangle has sides with length of 11 feet 12 feet and 13 feet. Is it a right triangle
Answer:
No
Step-by-step explanation:
It will be a right triangle if it follows Pyhthagoras Theorem . Where the sum of squares of two smaller sides is equal to the square of the 3rd side. Let's check ,
→ 11²+ 12² = 13²
→ 121 + 144 = 169
→ 265 ≠ 169
Hence the ∆ is not a right angled triangleWhat is the correct algebraic representation of the transformation displayed on the graph?
A- (y,-x)
B- (-y,x)
C- (-x,y)
D- (-x,-y)
Answer:
[tex]transformation: (y,-x)[/tex]
----------------------------
hope it helps...
have a great day!!
HELP ME I BEGGGG THANK U PLEASE ITS DUE
Answer:
y=6x+24
Step-by-step explanation:
Determine the solution to the equation. 2(9x - 6) = 6(3x - 2) + 2
A. Infinite
B. One Solution
C. No Solution
A sweater regularly priced at $135 is on sale at 15% off. How much would you pay
for the sweater, including taxes of 13%?
4
How would you tell someone to plot (4,-3)?
pick the two best answers
1
go right 4
go left 4
go up 3
go down 3
What I pic
Step-by-step explanation:
go right 4
go down 3
it is the answer
A farm allows customers to cut their own Christmas trees. The farm uses the equation y = 15x + 10 to determine the total charge, Y,
based on the number of trees, x, the customer purchases. A customer was charged $460. How many trees did the customer purchase?
a- 10 trees
b- 30 trees
c- 31 trees
d- 15 trees
Answer:
Step-by-step explanation:
The answer would be b, 30 trees, the reasoning is in the photo, hope this helps!
Two sides of a parallelogram are 65 feet and 87 feet. The measure of the angle between these sides is 52°. Find the area of the parallelogram to the nearest square foot.
Answer:
Area of the parallelogram is approximately 4,456.2 square feet
Step-by-step explanation:
The lengths of the sides of the parallelogram are 65 feet and 87 feet
The measure of the angle between the sides, Y = 52°
The formula for finding the area of a parallelogram is given as follows;
Area of a parallelogram = A·B·sin(Y)
Where;
'A' and 'B' are the length of the parallel sides and 'Y' is the measure of the angle between them
Let 'A' and 'B' represent the 65 feet and the 87 feet respectively, we get;
Area of the parallelogram = 65 ft. × 87 ft. × sin(52°) ≈ 4,456.2 ft.²
Help me please!!:((((
Answer:
.01*.5ˣ
Step-by-step explanation:
we can see that x=0 y= .01
so in our equation
a*bˣ
a=.01
This is throuhg plugging in 0 for x
a*b⁰=.01
a*1=.01
a=.01
Now it's just a matter of finding b
to do this just plug in a value
we know that when x=1 y=.005
.01*b¹=.005
b= .5
So our final equation is : .01*.5ˣ
A triangle has vertices of (−3, 3), (−3, 2), and (1, −2). What are the coordinates after dilating from the origin by a scale factor of 1 2 ?
Answer:
(-1.5, 1.5), '(-1.5, 1) and (0.5, -1)
Step-by-step explanation:
Given the coordinate (x, y) If dilated by a factor k, the resulting coordinate will be (kx, ky).
Similarly given the coordinates of a triangle (−3, 3), (−3, 2), and (1, −2)
when dilated by a factor of 1/2, the new coordinates will be at;
A (-3, 3) = A'(1/2*-3, 1/2 * 3) = A'(-1.5, 1.5)
B (-3, 2) = B'(1/2*-3, 1/2 * 2) = B'(-1.5, 1)
C (1, -2) = C'(1/2*1, 1/2 * -2) = C'(0.5, -1)
What are some websites that someone does your math assignment for you help ASAP
When Cosmo wears his new shirt properly as shown below, the horizontal stripes form seven closed rings around his waist. This morning he buttoned his shirt incorrectly, as shown on the right. How many closed rings were there around Cosmo's waist this morning?
Answer:
6
Step-by-step explanation:
It is given that Cosmo bought a new shirt which have several horizontal strips printed on the shirt that forms horizontal rings when the shirt is buttoned up. When Cosmo rightly button up the shirts, the horizontal strips forms seven closed rings.
One day when Cosmo wrongly wear the shirt and wrongly buttoned up the shirt, the horizontal strips on the shirt did not matched properly.
So as seen from the figure, when Cosmo wrongly button up the shirt, the closed strips forms 6 horizontal rings around Cosmo's waist.
Three yrs hence, a men will be three time his brother age and the sum of present age is 18 find their present age
Answer:
Step-by-step explanation:
Let the age of a man = x
Age of his brother = y
Three yrs hence, a man will be three time his brother age
This is written as:
x + 3 = 3(y + 3)
x + 3 = 3y + 9 .... Equation 1
The sum of present age is 18
= x + y = 18
x = 18 - y
We substitute 18 - y for x in Equation 1
find their present age
18 - y + 3 = 3y + 9
Collect like terms
21 - 9 = 3y + y
12 = 4y
y = 12/4
y = 3 years
x = 18 - y
x = 18 - 3
x = 15 years
Ken has 7 baseballs. Each baseball weighs 0.3 pound. Ken wants to use this
model to find the total weight of the baseballs. Each hundredths block in the
model represents 1 whole.
Use the drop-down menus to explain how Ken can use the model to find the total
weight of the baseballs. Click the arrows to choose an answer from each menu.
To represent the weight of one baseball, 0.3 pounds, Ken should shade 3
Choose...
To represent the weight of all of the baseballs, he should
shade this amount Choose... times. The shaded part of the model will represent
the expression Choose... The total weight of the baseballs is 7.3
pounds
My Progress
Answer:
2.1 pounds
Step-by-step explanation:
Given that :
Number of baseballs = 7
Weight of each baseball = 0.3 pounds
1 block = 0.1 pounds
Hence, each ball will represent 0.3 / 0.1 = 3 blocks
Hence, 3 blocks = 1 ball
7 balls will be : 3 * 7 = 21 blocks
Recall:
1 block = 0.1
Hence, 0.1 * 21 = 2.1
Therefore, the weight of the 7 balls = 2.1 pounds
Please help I give out brainliest .....Kellie bought 8 towels and spent $39.60. Each towel costs the same amount.
Part A
Use the drop-down menus to create an equation that can be used to determine t, the
price, in dollars, of 1 towel.
+
8
39.60
V
Part B
What is the price, in dollars, of 1 towel?
Enter your answer in the box.
Answer:
Each Towel is 4.95 each
Step-by-step explanation:
We can use 8t = 39.60 as our equation
8t = 39.60
Divide 8 on both sides.
t = 4.95
Hope this helps! ^^
PLEASE HELP ASAP!! will mark brainlest
Answer:
B!!!!!
Step-by-step explanation:
Enter the value of 3 over 4
Answer:
1. Three fourths
2. 3/4
3. 0.75
4. 75%
Step-by-step explanation:
i dont know which one you want
Answer:
.75
Step-by-step explanation:
3 over 4 means [tex]\frac{3}{4}[/tex], and a fraction is just a division problem. 3 ÷ 4 = .75
Hi please help me!! thanks
Answer:
3.2 x 10^13
Step-by-step explanation:
(8x10^4)(4x10^8)
reorder the terms using the commutative property
(8x4)x(10^4x10^8)
multiply
32x (10^4 x 10^8)
= 32 x 10^4+8
= 32 x 10^12
now convert to scientific notation
=3.2 x 10^13
Find two numbers that round to 387.4 when rounded to the nearest tenth. Drag the numbers to the box.
Answer:
hi
Step-by-step explanation:
omhg hi
HOW TO DO THIS QUESTION PLEASE
AREA OF A CIRCLE HELP PLS
Answer:
254.34 in²
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex]
d = 18 inches, so r = d/2 = 9 inches
Area = 3.14 * 9 * 9
= 254.34 in²
What is the volume of the pyramid in the diagram?
9 cm
height = 3 cm
5 cm
S cm
OA 25 cm3
OB.
75 cm
O C.
105 cm
OD. 135 cm
E.
225 cm
Answer:
A. 25 cm^3.
Step-by-step explanation:
Volume = 1/3 * area of base * perpendicular height,
= 1/3 * 5^2 * 3
= 5^3
= 25.
The correct option is A. Volume of the pyramid is 25 cm³ which is option A.
What is the volume of the pyramid?
The volume of a pyramid is given by lbh/3. It is also given by the product of the base area and height of the pyramid and then divided by 3.
The base of the pyramid is in the form of a square as all sides are 5 cm. Find the area of the square that is the base area.
5×5=25 cm²
Now multiply 25 by the height of the pyramid which is 3 cm.
25×3=75 cm³
Divide 75 by 3 to find the volume of the pyramid.
75÷3=25 cm³
Thus, the volume of the pyramid is 25 cm³ which is option A.
Learn more about the volume of the pyramid at https://brainly.com/question/17615619
#SPJ2
A full waterbed mattress is 8 ft by 3 ft by 2 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:
2995
Step-by-step explanation:
volume is 48^3
theres 62.4 pounds per square ft