Answer:
Terry had £780 initially and Faye had £1300
Step-by-step explanation:
System of Equations
We'll call the following variables:
x = Terry's balance in his bank account
y = Faye's balance in her bank account
The initial relation between them is:
[tex]\frac{x}{y}=\frac{3}{5}[/tex]
Cross-multiplying:
5x = 3y [1]
If Terry put £220 in his account he had x+220 and if Faye withdrew £300 from her account, she had y-300. Both quantities are equal, thus
x + 220 = y - 300
Subtracting 220:
x = y - 520 [2]
Substituting in [1]
5(y - 520) = 3y
Multiplying:
5y - 2600 = 3y
Adding 2600 and subtracting 3y:
2y = 2600
Dividing by 2:
y = 1300
From [2]:
x = 1300 - 520
x = 780
Terry had £780 initially and Faye had £1300
If a football field is 100 yards long and 54 yard wide and what is the area in perimeter of that football filed
Answer:
5400
Step-by-step explanation:
you would measure the length and width. Multiply the length by the width to get the area, and add twice the length to twice the width to get the perimeter
a) Write the sequence of natural numbers which are multiplied by 3 ?
b) Write the sequence of natural numbers which are multiplied by 3 and added to 1 ?
c) Check whether the sequence obtained above is an arithmetic sequence or not?
Answer:
a) 3, 6, 9, 12, 15,...,[tex]3\cdot n[/tex], b) 4, 7, 10, 13, 16,...,[tex]3\cdot n +1[/tex], c) Both sequences are arithmetic.
Step-by-step explanation:
a) The sequence of natural numbers which are multiplied by 3 are represented by the function [tex]f(n) = 3\cdot n[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...
b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function [tex]f(n) = 3\cdot n + 1[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...
c) Both sequences since differences between consecutive elements is constant. Let prove this statement:
(i) [tex]f(n) = 3\cdot n[/tex]
[tex]\Delta f = f(n+1) -f(n)[/tex]
[tex]\Delta f = 3\cdot (n+1) -3\cdot n[/tex]
[tex]\Delta f = 3[/tex]
(ii) [tex]f(n) = 3\cdot n +1[/tex]
[tex]\Delta f = f(n+1)-f(n)[/tex]
[tex]\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)[/tex]
[tex]\Delta f = 3[/tex]
Both sequences are arithmetic.
Find the slope of the line that passes through the pair of points (4, 4) and (10, –1)
Answer:
-5/6
Step-by-step explanation:
Using the slope formula we can easily find the slope
m=(y2-y1)/(x2-x1)
m=(-1-4)/(10-4)
m=-5/6
Determine the domain on which the following function is decreasing.
(Please include an explanation)
13. Suppose a real estate agent receives 5%
commission on the fi rst $200 000 of a
house’s selling price, and 6% on the
remaining amount.
a) What does commission mean?
b) If a house sells for $345 000, how
much commission does the real estate
agent make on the sale of the house?
Answer:
Commision may be defined as a percentage cut which an employee, broker, vendor, retailer or other persons within a sale chain receive from an employer or production firm for selling a good or offering a successful service based on agreed terms by both parties. ;
$18700
Step-by-step explanation:
Given :
Commision pattern :
5% on first $200,000
6% on remaining amount
Amount of commission on $345000
0.05 * 200000 = 10,000
0.06 * (345000 - 200000) = 8700
Total commission :
10,000 + 8700 = 18,700
Are these fractions equivalent or nonequivalent?
2s/3t 4s/6t
Answer:
Equivalent
Step-by-step explanation:
2/3 times 2=4/6
4/6 divided by 2=2/3
(hope this helps :P)
Can someone please help me out?
9514 1404 393
Answer:
62°
Step-by-step explanation:
The measure of the external angle where the secants meet is half the difference of the arcs they subtend.
∠A = (DE - BC)/2
2×∠A = DE -BC
DE = BC + 2×∠A
DE = 38° +2(12°)
arc DE = 62°
A stamp collector has 1,200 stamps, and 65% of them were produced after the year 2000. How many stamps were produced after the year 2000?
Answer:
780
Step-by-step explanation:
65% of 1,200 is 780 :)
Answer:
780
Step-by-step explanation:
65% x 1,200 = 780
Can someone please help me
Answer:
y=4/5x-1 is the answer (A)
Step-by-step explanation:
Answer: Step-by-step explanation:
the first one would be your answer (y= 4/5x -1)
because the y intercept is -1 and the rise if 4 and run is 5 and that would be your slope.
please help me please will give brainliest to anyone
A container in the shape of a rectangular prism has a base with an area of 19 1/2 square inches. If the container is filled with water to a height of 4 1/2 inches, how much water is in the container?
Answer: Water in the container = 87.75 cu.inches.
Step-by-step explanation:
Formula: Volume of rectangular prism = Base area x height
Base area = [tex]19\dfrac12[/tex] sq. inches Height = [tex]4\dfrac12[/tex] inches
So,
Volume of container = [tex]19\dfrac12\times4\dfrac12\text{ cu.inches}[/tex]
[tex]=\dfrac{39}{2}\times\dfrac{9}{2}\text{ cu.inches}[/tex]
[tex]=\dfrac{351}{4}\text{ cu.inches}[/tex]
[tex]=87.75\text{ cu. inches}[/tex]
Hence, Water in the container = 87.75 cu.inches.
Four stores are having a sale on video games. Circuit Shop is selling 6 games for $24.72. Electronic Center is selling 5 games for $20.50. Game Shop has 8 games for $32.00, and Cyber Central has 4 games for $17. Which store has the best deal?
A - Cyber Central
B - Electronic Center
C - GameShop
D - Circuit Shop
Answer: Its gameshop its being sold for only 4 dollars each
Step-by-step explanation:
you divide each sum of money by the amount of games and that tells you X the price per game
find the value of c to the nearest tenth
11(2+3) =
I need help on this question
Answer:
55 is the answer I think so
Answer: 55
Step-by-step explanation:
Step One: Add: 2 + 3 = 5
Step Two: Multiple: 11 * the result of step No. 1 = 11 * 5 = 55
Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. Leave your answers in terms of pi for answers that contain pi.
Answer:
125πkm
Step-by-step explanation:
The figure shown is a cylinder :
Volume of a cylinder is obtained using tbe relation :
V = πr²h
Where ; r = Radius ; h = height
r = 5km ; height = 5km
Hence,
V = π * 5² * 5
V = 25 * 5 * π
V = 125πkm
How many solutions exist for the given equation?
} (x + 12) = 4x – 1
zero
one
two
infinitely many
Answer:
The given equation has one solution.
Step-by-step explanation:
Given equation is:
(x+12) = 4x-1
We will solve the equation to check how many solutions it has.
x+12 = 4x-1
Adding 1 on both sides
x+12+1 = 4x-1+1
x+13 = 4x
Subtracting x from both sides
x-x+13=4x-x
13 = 3x
x = 13/3
Hence,
The given equation has one solution.
if y=2x+2 and 4x+3y=26m, then find the value of x^2+y^2
Answer:
x² + y² is equal to = (4 / 81)(845m² + 78m + 18)
Step-by-step explanation:
We first need to get the values of x and y, which can be done using a system of equations, substituting one of the two functions into the other:
Given:
y = 2x + 2
3x + 3y = 26m
Then:
3x + 3(2x + 2) = 26m
3x + 6x + 6 = 26m
9x + 6 = 26m
9x = 26m - 6
x = (26m - 6) / 9
Now we can solve for y:
y = 2x + 2
y = 2(26m - 6) / 9 + 2
y = 2(26m - 6) / 9 + 18 / 9
y = (52m - 12 + 18) / 9
y = (52m + 6) / 9
Now we can sum up their squares:
x² + y²
= ((26m - 6) / 9)² + ((52m + 6) / 9)²
= (676m² - 312m + 36) / 81 + (2704m² + 624m + 36) / 81
= (3380m² + 312m + 72) / 81
= (4 / 81)(845m² + 78m + 18)
Molly is 11 years old. Kristen is 1 years older than Molly and Jane is 1 years older than
Kristen. How old is Jane?
A bottle contains 2/6 liters of soda. Ann has 12 of these bottles.
How much soda does she have in all? write in simplest form
Answer:
4 liters
Step-by-step explanation:
simplify 2/6 = 1/3
Multiply 1/3 times the 12 bottles
1/3 * 12
12/3
Simplify
4
Answer:
4 liters of soda.
Step-by-step explanation:
2/6⋅12=24/6
24/6=4
Therefore, your answer is 4 liters.
I WILL GIVE BRAINLIEST PLZZ HELP!!!!!!!!!
Answer:
D half a barrel an hour
Step-by-step explanation:
hope it helps
At 5:30 p.m., the temperature was recorded as 4 °F. At 10:00 p.m., the temperature had dropped 2 °. Which number line below best shows the
temperature at
10:00 p.m.?
Answer:
the answer is A
Step-by-step explanation:
Which method can you use to prove that the triangles are congruent
Answer:
ΔASA ≅ ΔASA
Step-by-step explanation:
Which statement best explains the relationship
between lines FG and HJ?
O They are perpendicular because their slopes are
equal.
O They are perpendicular because their slopes are
O They are not perpendicular because their slopes are
O They are not perpendicular because their slopes are
negative reciprocals.
equal.
not negative reciprocals.
Answer:
they are perpendicular because they have slopes that are negative reciprocals
Step-by-step explanation:
th
The statement that best explains the relationship between lines FG and HJ is "They are not perpendicular because their slopes are not negative reciprocals."
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
To find the slope of a line passing through two given points, we use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For line FG, the two points are F(-4, 1) and G(0, -2):
slope of FG = (-2 - 1) / (0 - (-4)) = (-2 - 1) / 4 = -3/4
For line HJ, the two points are H(-4, -2) and J(0, 4):
slope of HJ = (4 - (-2)) / (0 - (-4)) = 6/4 = 3/2
The slopes of lines FG and HJ are not equal. However, we can see that they are not negative reciprocals of each other:
slope of FG = -3/4
slope of HJ = 3/2
Therefore, lines FG and HJ are not perpendicular because their slopes are not negative reciprocals of each other.
To learn more about the slope;
brainly.com/question/3605446
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From the equation y−3=−2(x+1), identify the slope and a point on the line.
Answer:
slope = - 2, point on line = (- 1, 3 )
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = - 2(x + 1) ← is in point- slope form
with slope m = - 2 and (a, b ) = (- 1, 3 )
The slope of equation y−3=−2(x+1) is -2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
y−3=−2(x+1)
Using Slope- Intercept form
y= mx + b
So, the slope for the equation is -2.
Hence, the slope is -2.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
Solve the equation for X and show your work.
3x= 15
Answer:
5
Step-by-step explanation:
15/3=5
I need help graphing -8x-y=8
Answer:
y = -8x - 8
Step-by-step explanation:
Add -8x on both sides to get -y = 8x + 8 and flip the y sign on the left to get your slope function which is y = - 8x - 8.
To graph the function, you would need to put (0, -8) as your y-intercept, and each unit will go down 8 units when you add 1.
Answer:
y=8x+8
Step-by-step explanation:
Just rewrite the problem so it's in y=mx+b format then it's easy to graph
Remember the y intercept is 8 because when x=0 y=8 and the slope is 8 so go up 8 and right 1
6(x-4)-x=6x+4 one solution, no solution or infinite solution
Answer:
no solution
Step-by-step explanation:
Given
6(x - 4) = 6x + 4 ← distribute left side
6x - 24 = 6x + 4 ( add 24 to both sides )
6x = 6x + 28 ( subtract 6x from both sides )
0 = 28 ← not possible
This indicates the equation has no solution
- Ms. Ali needs to have her car repaired but does not want to spend more than $225
for the repairs. The mechanic says that the part needed for the repair will cost $78,
and that labor will cost an additional $35 per hour. Which inequality below
represents the greatest number of hours the mechanic can work without exceeding
Ms. Ali's budget? Use the steps below to solve. Then, HIGHLIGHT YOUR ANSWER.
a. 225 - 35x < 78
b. 35x + 78 > 225
c. 35 + 78x ≤ 225
d. 35x + 78 ≤ 225
Answer:
D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
It has to be less than or equal to 225, and you know you only need one part, so it has to be 35x +78 _< 225
Explain how please I’m not sure
Answer:
164 degrees
Step-by-step explanation:
The measure of the individual internal angle in a polygon is;
(n-2)180/n
n = 22
So we have;
(22-2)180/22
= (20 * 180)/22
= 163.64 degrees
To the nearest whole number, this is 164
Giving brainliest!
If Chris divides one fifth of a pound of marbles equally between 9 bags, how much goes into each bag?
A) 14 pounds
B) 1/45 of a pound
C) 9/45 of a pound
D) 45 pounds
Answer:
B) [tex]\displaystyle \frac{1}{45}\:of\:a\:pound[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{9} \times \frac{1}{5} = \frac{1}{45}[/tex]
I am joyous to assist you at any time.
Answer:
its B
Step-by-step explanation:
simple just b