Answer:
Sample: Kevin should have used an open circle on 1, not a closed circle. The closed circle means that 1 is included in the solution set, but the inequality is x > 1, so 1 is not part of the solution.
Mistake done by Kelvin is he used closed circle at 1 where inequality x > 1 which excludes 1.
What is open and closed circles?
" Closed circle represents that the value is included in the given range while that of open circle represents given number is not included."
According to the question,
Graph of inequality x > 1 represents all values greater 1 excluding 1.
Number line represents -3 to 5.
A closed circle at 1 means 1 is included.
As per the condition of inequality x > 1 , 1 is excluded while in closed circle 1 is included both are contradictory conditions.
Hence, mistake done by Kelvin is he used closed circle at 1 where inequality x > 1 which excludes 1.
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Roberto uses 150 roses, 120 lilies, and 45 hydrangeas to make bouquets. Each bouquet has the same number of roses, the same number of lilies, and the same number of hydrangeas. i What is the maximum possible number of bouquets he can make? ii How many roses, lilies, and hydrangeas are in each bouquet?
Answer: (i) Maximum possible number of bouquets he can make = 15
(ii) There are 10 roses, 8 lilies and 3 hydrangeas in each bouquet.
Step-by-step explanation:
Given: Roberto uses 150 roses, 120 lilies, and 45 hydrangeas to make bouquets.
(i) Maximum possible number of bouquets he can make = HCF(150, 120 , 45)
Since , 150 = 2 x 3 x 5 x 5 , 120= 2 x 2 x 2 x 3 x 5 , 45 = 3 x 3 x 5
HCF(150, 120 , 45) = 3 x 5 = 15
Now, Maximum possible number of bouquets he can make = 15
(ii) Number of roses in each bouquet = [tex]\dfrac{150}{15}=10[/tex]
Number of lilies in each bouquet = [tex]\dfrac{120}{15}=8[/tex]
Number of hydrangeas in each bouquet =[tex]\dfrac{45}{15}=3[/tex]
Hence, there are 10 roses, 8 lilies and 3 hydrangeas in each bouquet.
Enter the equation of the line in slope-intercept form. Enter the answer in fraction form.
The line perpendicular to y =
6
5
x + 2 that passes through (6, −2).
The equation of the line that passes through (6, −2) is y = .
Which is equivalent to -9.4c + 6 + c – 5.9?
A. -8.4c – 0.1
B. -8.4c + 0.1
C. 10.4c + 0.1
D. -10.4c + 0.1
Answer:
B
Step-by-step explanation:
reorganize to combine like terms
-9.4c+c or c-9.4c (they are the same) = -8.4c
6-5.9=0.1
-8.4c+0.1
Answer:
c
Step-by-step explanation:
brcause i have did it
Eli wanted to order candy online. Company A 2 1/2 pounds of chocolate for $32.50. How much is Company A charging per pound of chocolate?
Answer: Company A is charging $13 per pound of chocolate
Step-by-step explanation:
32.5/2.5=13= 1 pound
Check:
13*2.5=$32.5
Three pounds of bananas weigh $1.89. How much is it for 5 lbs of bananas
Answer:
The correct answer is $3.15
Step-by-step explanation:
To find the answer you do $1.89 divided by 3 to find the unit rate,which is 63 cents. Then you do 5 times 63 cents to equal $3.15.
HAVE A GOOD DAY!
A clothing store used the sign shown below to advertise a discount on shirts,
DISCOUNT
Buy Two Shirts
Get 50% Off Third Shirt
Celia wants to buy three shirts, which were originally priced $56 each. The store will
discount the price of the third shirt and then apply a 7% tax to the total cost of all
three shirts. Including the tax, what will be the mean cost of each shirt? (Round your
answer to the nearest cent).
Including the tax, the mean cost of each shirt is $
Answer:
$49.93Step-by-step explanation:
Original cost = $56
Cost of 3 shirts:
3*$56 = $168Cost of 3 shirts with discount:
168 - 1/2*56 = 168 - 28 = $140Add tax:
$140*1.07 = $149.8Mean cost of each shirt:
$149.8/3 = $49.93Mrs. Garcia borrowed some money at the rate of 4% per annum for the first year, at the rate of 6% pe r annum for the next 2 years, and at the rate of 7.5% per annum for the period beyond 3 years. If he pays a total interest of ₱ 15 750 at the end of 5 years, how much money did he borrow?
Answer: ₱40,909.1
Step-by-step explanation:
Given data:
Rate for first year = 4%
Rate for next two years = 6%
Rate for the next 3 years = 7.5%
Interest paid back after 5years = ₱ 15,750
Solution:
How much did she borrow.
= let the sum borrowed be P
= P * 4 / 100
= 4P/100
= 1P/25.
For the next two years
= P* 6 * 2/100
= 12P/100
= 3P/25
For the next 3years
= P* 7.5*3/100
= 22.5P/100
= 9P/40.
1P/25 + 3P/25 + 9P/40 = 15750
77P/200 = 15750
P = 15750 * 200 / 77
P = 315,0000/77
P = ₱40,909.1
The amount borrowed is ₱40,909.1
(2x + 7y) (4x – 8y)
Answer:
= 8x^2 + 12xy − 56y^2
Step by step:
(2x+7y)(4x−8y)
=(2x+7y)(4x+−8y)
=(2x)(4x)+(2x)(−8y)+(7y)(4x)+(7y)(−8y)
=8x^2−16xy+28xy−56y^2
=8x^2+12xy−56y^2
If the weight of a package is multiplied by 5/6 the result is 10 lbs. Find the weight of the package.
Answer:
Step-by-step explanation:
1
. Start by making a "let statement."
Let
x
represent the weight of the package.
2
. Create an algebraic expression.
5
7
x
=
40.5
i
pounds
3
. Isolate for
x
by dividing both sides by
5
7
.
5
7
x
÷
5
7
=
40.5
i
pounds
÷
5
7
4
. Recall that in order to divide a fraction by another fraction, take the reciprocal of the divisor and change the division sign to a multiplication sign.
5
7
x
⋅
7
5
=
40.5
i
pounds
⋅
7
5
5
. Solve for
x
.
5
⋅
7
7
⋅
5
x
=
40.5
⋅
7
5
i
pounds
x
=
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
56.7
i
pounds
a
a
∣
∣
−−−−−−−−−−−−−−−
find the surface area of this cylinder using pie.
Diana is going camping with her family. Their campsite is 7/8 miles away. They walk at a steady speed of 2 1/2 mi/h. How many minutes will it take them to get to the campsite
Answer:
21 minutes
Step-by-step explanation:
Using the formula to calculate the time expressed as;
Speed = Distance/Time
Given:
Distance = 7/8 miles
Speed = 2 1/2 mi/hr
Required
Time in minutes
Substitute the given values into the formula;
Recall that:
S = D/T
T = D/S
Time = 7/8 ÷ 2 1/2
Time = 7/8 ÷ 5/2
Time = 7/8 * 2/5
Time = 7/4 * 1/5
Time = 7/20 hour
Since 1 hour = 60 minutes
7/20 hour = (7/20 * 60)minutes
7/20 hour = 7 * 3
7/20 hour = 21 minutes
Therefore it will take them 21 minutes to get to the campsite
A line contains two distinct points, C and D. Select each correct statement,
Points C and D determine one unique line,
There are infinitely many points between points C and D.
The distance from C to D is equal to the distance from D to C.
O Any line segment that contains point C must also contain point D.
Answer:
We have a line that passes through points C and D.
a) Points C and D determine one unique line
This is true, there is only one line that passes through a given pair of points, then we can call this line as "Line CD".
b) There are infinitely many points between points C and D.
This is also true, if we define the points with real numbers in R^2, we will have a dense set, which means that between C and D we can find infinite points.
c) The distance from C to D is equal to the distance from D to C.
Also true, the distance between two points C = (cx, cy) and D = (dx, dy) is defined as:
D = √( (cx - dx)^2 + (cy - dy)^2)
And because we have squares, this will be exactly the same as:
D = √( (dx - cx)^2 + (dy - cy)^2)
Then the distance from C to D, is exactly the same as the distanco from D to C.
d) Any line segment that contains point C must also contain point D.
This is false, we can define infinite segments where the endpoint is C, and does not pass through point D (some examples are given in the image below) So this is the only false option.
which of the following if rational( )
a)
[tex]\pi[/tex]
b)log2 c)1.23123... d)none
Shane and Gemma share 35 sweetss in the ratio 1 : 4 Gemma eats 10 of her sweets and then gives Shane 1/2 of the sweets she has left. H ow many sweets does Shane have now?
Answer:
14 sweets
Step-by-step explanation:
5x+35
x=7
7*4=28
(28-10)/2=7
7+7=14
Write and solve an equation to find the number:
The perimeter of a rectangle patio is 64 feet. The length is 10 feet longer than the width.
What is the width of the patio (no units needed)
Answer:
11=w
Step-by-step explanation:
l = 10+ w
w = w
64= 2(10+w) + 2(w)
64= 20+2w +2w
64=20+4w
44=4w
11=w
Cookies are sold in the lunchroom for 1.50. Ana wants to buy cookies for a group of her friends. If she has 20 dollars,which inequality can be solved to show the number of cookies she can buy?
[tex]4−16÷4+4²[/tex]
Answer:
16
Step-by-step explanation:
[tex]4−16÷4+4² \\ \\ = 4 - \frac{16}{4} + 16 \\ \\ = 4 - 4 + 16 \\ \\ = 16[/tex]
is this proportional?
I
If it is-
Explain why, give an ordered pair that would represent the unit rate, and what it means
If it is not-
Tell me why :(
If you decide to help, Thank you you will get , 20 points for helping :D if u do not know what the answer is please dont waste my time by commenting unnecessary things :) i really have to study for a test thats tommrow and i have to finish this first!
Answer:
yes it is because they all = to 3 when I divide them so they are proportinal
Step-by-step explanation:
An airplane flies 1250 km in 1 hour 20 minutes. What is its average speed in kilometers per hour?
Answer:
tiiiuhhhghhjpjjhhjhgghhuuhh
through: (2, 5), slope = 1/2 *50 POINTS!*
Answer:
y−5=−2(x−2)
Step-by-step explanation:
Point slope form of a line is the standard
Plzz what the answer I’m stuck
Answer:
the answer to your question is 576 square feet
Step-by-step explanation:
Step 1: 96 ÷ 4 = 24
Step 2: 24×24 =576
State the slope and the y-intercept for the graph of the equation. -x+y=4
Answer:
Slope: 1
Y-intercept: (0,4)
Step-by-step explanation: I hope that helps!
Help!!!!!!!!!!!!!!!!!!!!!!!!
=======================================================
Explanation:
Look through the table to see when f(x) = g(x)
This happens when both are equal to 1, which is in the fourth row, or when x = -1.
In other words,
f(-1) = 1g(-1) = 1So f(-1) = g(-1)
We can then say the solution to f(x) = g(x) is x = -1.
Given the points P(2, –6) and R(8, 3), what is the component form of Vector P R?
⟨6, -3⟩
⟨10, -3⟩
⟨6, 9⟩
⟨10, 9⟩
Answer:
C
Step-by-step explanation:
The component form of vector PR is ⟨6, 9⟩.
How to determine the component form of vector PRTo find the component form of vector PR, we need to subtract the coordinates of point P from the coordinates of point R.
The x-component of the vector is obtained by subtracting the x-coordinate of point P from the x-coordinate of point R:
x-component = 8 - 2 = 6
The y-component of the vector is obtained by subtracting the y-coordinate of point P from the y-coordinate of point R:
y-component = 3 - (-6) = 3 + 6 = 9
Therefore, the component form of vector PR is ⟨6, 9⟩.
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Zola and her friends are going bowling. The bowling alley charges each person a $14 fee to rent shoes, plus $4.50 per game. Which equation represents the cost, y, for each friend to go bowling in terms of the number of games played, x?
Answer:
X+14=y
Step-by-step explanation:
2 1/3 + 3 2/4 =
Fractions
Step-by-step explanation:
2 1/3+3 2/4=7/3+14/4
=28/12+42/12 (common denominater)
=70/12
=5 10/12
Joey and Krysta are at the Richmond Fair and are waiting in line to ride on the Ferris Wheel. They are trying to figure how long they will need to wait before they get to the front of the line. The more people in the line ahead of them, the longer they will need to wait.
p = the number of people in line ahead of Joey and Krysta
w = the length of time Joey and Krysta will need to wait
Which variable is the independent variable?
Answer:
P, the number of people in line ahead of Joey and Krysta is the independent variable.
Step-by-step explanation:
the difference of two numbers is 72 and their quotient is 10 plz help
Answer:
The numbers would be 80 and 8
Step-by-step explanation:
Hope this helps
Answer:
We have, x - y = 72
and, x = 10y
so, 10y - y = 72
y = 8
so, x= 80
Step-by-step explanation:
PLZ HELP!!!!
Write a function rule for the area of a rectangle whose length is 6 ft more than its width. What is the area of the rectangle when its width is 7 ft? Write a function for the area A of the rectangle using the independent variable-width W.
In a lighting, green light glows after every 12 seconds, red light glows after every 30 seconds, blue light glows after every 34 seconds and yellow light glows after every 56 seconds. Find the least time in minutes after which they all glow together.
Answer:
238 minutes
Step-by-step explanation:
We are told:
In a lighting, green light glows after every 12 seconds, red light glows after every 30 seconds, blue light glows after every 34 seconds and yellow light glows after every 56 seconds.
We solve this question by using LCM Method
We find the Least Common Multiple of 12, 30, 36 and 56
= 14,280 seconds.
Hence, the least time in seconds after which they glow together is 14,280 seconds.
To find the least time in minutes after which they all glow together.
We convert from seconds to minutes
60 seconds = 1 minute
14280 seconds = x
Cross Multiply
60 × x = 14280 × 1
x = 14280/60
x = 238 minutes
The least time in minutes after which they all glow together.
238 minutes
Answer:
238 minutes
Step-by-step explanation:
LCM OF 12,30,34,56
= 14280
THEN, 14280 seconds convert to minutes
= 238 minutes
