Bill is buying several bottles of pop for a party. They each cost the same amount.
If Bill can buy 4 bottles for $7.16, how many bottles could he buy for $10.74?
Answer:
6
Step-by-step explanation:
First, divide 7.16 by 4 to find the price of one bottle, which is 1.79. Then, divide 10.74 by 1.79 to get 6.
Use Order of Operations
mot to solve.
14+7 x 54 ÷6-7
What is the product of additive inverse of -1/3 and multiplicative inverse of 5/3
Answer: 1/3 and 3/5
Step-by-step explanation:
a. What is m TVZ? Show your work.
3x
120°
T
R
v (2x+15)
(2x + 5)°
Answer:
95°
Step-by-step explanation:
You want the measure of angle TVZ, when adjacent angle (2x+5)° and its supplement (2x+15)° are given. The larger of these is a vertical angle with respect to TVZ.
Linear pairThe angles marked (2x+15)° and (2x+5)° are a linear pair, hence supplementary.
((2x+15)° +(2x+5)° = 180°
4x +20 = 180 . . . . simplify
x +5 = 45 . . . . . . . divide by 4
x = 40 . . . . . subtract 5
Angle TVZ is a vertical angle with respect to the one marked (2x+15)°, so has the same measure:
∠TVZ = (2(40)+15)°
∠TVZ = 95°
__
Alternate solution
The two angles RVW (2x+15)° and ZVW (2x+5)° obviously differ by 10°. They are a linear pair, so their sum is 180°. Finding these angles is then a "sum and difference" problem. The larger of the solutions is the one we want, as (2x+15)° is a vertical angle to TVZ. We know the larger of the solutions to the sum and difference problem will be (180° +10°)/2 = 95°, the measure of TVZ.
More about sum and difference problems:
When a+b = s, and a-b = d, the larger value (a) can be found by adding these equations: (a+b) +(a-b) = s+d, or 2a = s+d, or a = (s+d)/2. This is the expression we used above to find the larger of the two angles. (You notice it is not necessary to solve for x.)
The product of 4 and the sum of a number and is equal to the difference of twice the number and . Find the number.
The number is -4
[tex]x \times[/tex]4+4= 2[tex]x[/tex]-4
[tex]$$x \times 4+4=2 x-4$$[/tex]
Subtract 4 from both sides[tex]$x \times 4+4-4=2 x-4-4$[/tex]
Simplify
[tex]$$x \times 4=2 x-8$$[/tex]
Subtract [tex]$2 x$[/tex] from both sides [tex]$x \times 4-2 x=2 x-8-2 x$[/tex]
Simplify
[tex]$$2 x=-8$$[/tex]
Divide both sides by 2
[tex]\frac{2 x}{2}=\frac{-8}{2}$$[/tex]
Simplify
[tex]$$x=-4$$[/tex]
A strategy for teaching division is by repeated subtraction. It involves repeatedly subtracting the same integer from a big number until the result is zero. It is a fantastic approach to teach kids about division. A technique called repeated subtraction, commonly referred to as division, removes an equal amount of items from a group.
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
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The difference between 4 and the sum of a number and is equal to twice that number. The number is -4.
Given that,
The difference between 4 and the sum of a number and is equal to twice that number.
Repeated subtraction is a method for teaching division. Until the result is zero, the same integer must be repeatedly subtracted from a large number. Repeated subtraction, sometimes known as division, is a method that takes an equal number of elements out of a group.
Division's opposite is multiplication. If 3 groups of 4 total up to 12, then 4 are in each group when 12 is divided into 3 equal groups. The fundamental goal of division is to produce equal groups or to determine how many individuals are in each group following a fair distribution.
x×4+4=2x-4
Subtracting 4 on both sides
4x+4-4=2x-4-4
4x=2x-8
Now, substracting 2x from both sides
4x-2x=2x-8-2x
2x=-8
x=-4
Therefore, The number is -4.
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Write as a
14/11
as a decimal.
0 0.36
0.36
0.036
O 0.36
Answer:
Step-by-step explanation:
divide 14 by 11
which is 0.36
3. Mai realizes that each day her checking account is below zero, she is charged a
late fee of $5.75 per day. She realizes that she will not be paid until 10 days from
now. What will the balance of the account equal on the 10th day? Show your work.
the balance in the account at the 10th day will be equal to - $ 57.5.
Late fee for 1 day = $ 5.75
Number of days = 10
We will calculate the late fees for 10 days by using the operation of multiplication.
So, late fee will be:
Late fees = 10 × $ 5.75
Late fees = $ 57.5
Balance in the account at the 10th day = 0 - Late fees
Balance in the account at the 10th day = 0 - $ 57.5
Balance in the account at the 10th day = - $ 57.5
Therefore, the balance in the account at the 10th day will be equal to - $ 57.5.
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If 2 < a < 5 and 1 < b < 2 find all possible expressions a+b,ab,a-b,and a/b
The range of values for the expressions are given by these following compound inequalities:
3 < a + b < 7.2 < ab < 10.0 < a - b < 4.1 < a/b < 5.What is a compound inequality?A compound inequality is a combination of multiple inequalities, at least two, involving operations such as and and or, explained below.
The and operation between multiple sets is composed by the elements that belong to all the sets.The or operation between multiple sets is composed by the elements that belong to at least one of the sets.Hence one example of a compound inequality is:
a ≤ x ≤ b.
Which is read as follows:
x is greater or equal than a and less or equal than b.
What is the range of the addition?The smallest possible value is when both a and b are at their lower bounds, hence:
a + b = 2 + 1 = 3.
The greatest possible value is when both a and b are at their upper bounds, hence:
5 + 2 = 7.
Then the range is:
3 < a + b < 7.
Since the ranges of a and b are open intervals, the ranges of the operations will also be composed by open intervals.
What is the range of the multiplication?The smallest possible value is when both a and b are at their lower bounds, hence:
a x b = 2 x 1 = 2.
The greatest possible value is when both a and b are at their upper bounds, hence:
a x b = 5 x 2 = 10
Then the range is:
2 < ab < 10.
What is the range of the subtraction?The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:
2 - 2 = 0
The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:
5 - 1 = 4.
Hence the range is:
0 < a - b < 4.
What is the range of the division?The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:
2/2 = 1.
The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:
5/1 = 5.
Hence the range is:
1 < a/b < 5.
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Bre'Aujanaye operates a flower shop in Paris. All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and
special events. Why type of organization does Bre'Aujanaye have?
The type of market in which all employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events is Oligopoly.
What is Oligopoly?An oligopoly is a market characterized by a small number of firms who realize they are interdependent in their pricing and output policies. The number of firms is small enough to give each firm some market power.
Given situation:
All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events.
As, A market structure known as an oligopoly occurs when a few large sellers or manufacturers control a sizable portion of a market or an entire sector.
Oligopolies are frequently the outcome of corporate collaboration as a way to increase profits.
Some examples of oligopolies include the car industry, petrol retail, pharmaceutical industry, coffee shop retail, and airlines.
So, as discussed in the given case employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events to make some profit.
Hence, The type of market is Oligopoly.
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Determine the total number of roots of each polynomial function.
g(x) = (x - 5)2 + 2x3
Cory graphed y = 100 - 50x x to represent the percentage of battery life
remaining on his phone after x hours.
What is a reasonable domain for this situation?
Percentage of battery life remaining
A. 0≤x≤ 100
Remaining Battery Life
100
Time (hours)
hr
The reasonable domain of the given situation is 0≤ x ≤2 that is 0 to 2 hours.
We see that x is represented as the number of phone hours used, therefore it has to be a number larger or equal to zero, but not a negative number. So, on one end we have that the number of phone hours used (x) must be larger or equal to zero. On the other hand, when the battery goes to zero, there are no more phone hours to use. We can find what is that other limit by making the battery percent (y variable) equal to zero, and solve the equation for x, thus giving us the upper limit of usable phone hours:
=> y = 0 = 100 - 50x
=> 100 = 50x
=> x = 100/50
=> x = 2
Therefore, the phone can be used for a maximum of 2 hours and the situation may be written as 0≤ x ≤2.
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need the domain and range!
Answer: Domain: [-1, 1]
Range: [-2, 3]
Step-by-step explanation:
Domain: The x-values go from -1 to 1 with x=-1 and x=1 included.
Range: The range starts at the vertex of the function which is y=-2 and goes up to y=3 where the graph is cut off by 2 points on y=3.
A 500 kg car heads through a loop with a 20 m radius. At the top of the loop, the car is moving at 14 m/s. If air resistance is negligible, what would the car's velocity be at the bottom of the loop?
The speed of the car at the bottom of the loop is approximately 31.3 m/s
How can the velocity at the bottom of the loop be calculated?The given parameters are;
Mass of the car = 500 kg
Radius of the loop = 20 meters
Velocity of the car at the top of the loop = 14 m/s
The kinetic energy at the top of the loop is therefore;
K E. = 0.5×500×14² = 49,000
The potential energy gained = 500×9.81×40 = 196200
Total energy = 49,000 + 196,200 = 245,200
The velocity at the bottom is therefore;
0.5×500×v² = 245,200
v² = 245,200 ÷ (0.5×500) = 980.8
v = √(980.8) ≈ 31.3
The velocity at the bottom of the loop is therefore;
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Which of the following best represents the
rate of change of this function?
A -1/2
B 1/2
C 2
D -2
Answer:
Step-by-step explanation:
Need more clarification! Which function?
Name a point that is collinear with points E and H.
Answer:
Point J
Step-by-step explanation:
Collinear means in a line
Point J is on the same line with E and H
What is this number sequence called?
7, 22, 11, 34, 17, 52, 26, 13 and so on.
The numbers 7, 22, 11, 34, 17, 52, 26, 13 and so on represent hailstone sequence.
What is a hailstone sequence?These patterns are referred to as hailstone sequences because the values frequently rise and fall, resembling a hailstone inside a cloud.
It should be noted that such numbers can either rise or fall.
Therefore, the numbers 7, 22, 11, 34, 17, 52, 26, 13 and so ob represent hailstone sequence.
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Find the length of FH
Determine the slope & y-intercept
5y-7x=9
What is the difference between -5 and 3 on a number line
Answer:
8
Step-by-step explanation:
-5 is 5 units left of zero.
3 is 3 units right of zero.
The difference is 8.
10=7-m
Do I minus by 10 on each side or do I add minus by 7?
Answer:
[tex] \sf \large{m=−3}[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
10=7−m
Step 1: Simplify both sides of the equation.
10=7−m
10=7+−m
10=−m+7
Step 2: Flip the equation.
−m+7=10
Step 3: Subtract 7 from both sides.
−m+7−7=10−7
−m=3
Step 4: Divide both sides by -1.
−m/−1= 3/−1
m=−3
What is the lowest form of this fraction 48/100
Answer:
12/25
Step-by-step explanation:
you have to start by reducing it by the lowest divisible numbers gradually till you get a fraction that cannot be divisible again.
start with two
48/100 = 24/50 = 12/ 25
12/25 cant be divided by any other number ahain therefore that's your final answer.
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Three angles add up to 180 degrees, angle one has a measure of 4x+8, angle two has a measure of 8x+3 and angle three has a measure of 9x+3.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Answer:
39.60°
Step-by-step explanation:
The sum of three angles is 180 degrees.
Show this as equation and solve for x:
4x + 8 + 8x + 3 + 9x + 3 = 18021x + 14 = 18021x = 166x = 166/21x = 7.90 (rounded)Angle one is:
4*7.90 + 8 = 39.60If l = √m-5 and m = 4n²-3, what is l when n = 2? What is n when l = 4?
what of disibility rules?
given g(x) is ...............
Answer:
-40
Step-by-step explanation:
It states with g(-2) that x = -2, so we can plug -2 for x.
g(x) = 3x^3 - 2x^2 + 4x
g(x) = 3(-2)^3 - 2(-2)^2 + 4(-2)
g(x) = 3(-8) - 2(4) + 4(-2)
g(x) = -24 - 8 - 8
g(x) = -40
A student showed their work when dividing fractions. Explain their errors and find the correct solution!
6 \ 3/4=6/1x3/4
=18/4
4 2/4 or 4 1/2
The correct solution of division fractions is 18/4.
What is division?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.
When describing how much of anything is left over, a fraction is used. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator
Given that,
The division fraction is 6× 3/4
So, the fraction is 6/1×3/4
Therefore, the division fraction is 4×2/4 or 18/4
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The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
A) Find an equation in the form
y=mx+b
where
x
is the number of monthly minutes used and
y
is the total monthly of the Ringular plan.
The equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
How to represent a linear equation?The customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
Using linear equation in slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence,
x = the number of monthly minutes used
y = the total monthly of the Ringular plan
Therefore, the equation in slope intercept form can be represented as follows:
(500, 132)(700, 172)
let's find the slope,
m = 172 - 132 / 700 - 500
m = 40 / 200
m = 4 / 20
m = 1 / 5
Hence,
y = 1 / 5x + b
using (500, 132) let's find the y-intercept
132 = 1 / 5 (500) + b
132 = 100 + b
b = 132 - 100
b = 32
Therefore, the equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
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5. Estimate:
$53
X 4
+what do I add
Math
What is the slope of the line passing through the points (-3, 4) and (2, - 1)?
Answer:
-1
Step-by-step explanation:
[tex]m= \frac{y2 - y1}{x2 - x1} [/tex]
put the values you will get your answer.
f(x)=8x+2, evaluate f(6)
Answer:
50
Step-by-step explanation:
The answer is 50 because f(6) basically means to substitute 6 for x.
8(6)+2
48+2
50
So the evaluation of f(6) is 50
write an equivalent expression
Answer:
[tex]3^{-9}[/tex]or [tex]\frac{1}{3^{9} }[/tex]
Step-by-step explanation:
3^3/3^12 = 3^3 * 3^(-12) = 3 ^(3-12) = 3^(-9) or 1/3^9