A consistent , independent system of equation is one that has at least one solution.It is independent because it has a single solution.
Step-by-step explanation:
The three types of systems of linear equations in two variables and three types of solutions.
An independent system has exactly one solution pair (x,y). The point of intersection presents the single solution.
An inconsistent system has no solution.such equations will produce two parallel lines with no solution.
A dependent system has infinitely many solution.Such lines are coincident.
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A consistent, independent system of equations is a system where the equations have a unique solution.
Explanation:A consistent, independent system of equations is a system where the equations have a unique solution. This means that there is exactly one set of values for the variables that satisfy all of the equations simultaneously.
For example, consider the following system of equations:
x + y = 52x - y = 1In this system, there is a unique solution: x = 2 and y = 3. Therefore, it is a consistent, independent system of equations.
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What is 724 times 41,000
16. WalkieTalkie phone company charges $18.00 for basic phone service per month and $0.15 per minute for long distance calls. Arena Calls charges $80.00 per month with no fee for long distance calls. What is the minimum number of minutes of long distance calls for which the cost of Walkie Talkie is more than the cost of Arena Calls?
Answer:
413 minutes of long distance calls
Step-by-step explanation:
$80.00 - $18.00 = $62.00
$62.00/$0.15 = 413.33
A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a face card or a spade?
Answer:
8/13.
There's 12 face cards & 26 black cards. In the 26 black cards, theres 6 face cards. Theres 32 cards overall that is either a black card or a face card. So in conclusion the answer is 8/13 because 52 (the total amt in the deck) divided by 32 = 8/13.
The probability of randomly selecting either a face card or a spade from a standard deck of 52 playing cards is approximately 0.4231.
The question involves calculating the probability of selecting either a face card or a spade from a standard deck of 52 playing cards. A standard deck consists of four suits (spades, hearts, diamonds, clubs), each with 13 cards, making a total of 52 cards. Among these, 12 are face cards (Jacks, Queens, Kings across all suits), and 13 are spades (including the spade face cards).
First, note that there are 3 face cards (Jack, Queen, King) in each suit, resulting in 12 face cards in total. However, 3 of these face cards are spades, and we must avoid double-counting them when adding the spade cards. Therefore, we have 12 face cards and 10 non-face card spades (since 3 spades are already counted among face cards), giving us a total of 22 unique cards that fulfill the conditions.
The probability of drawing either a spade or a face card from a deck of 52 cards is calculated by dividing the number of favorable outcomes (22) by the total number of outcomes (52), which is 22/52 or approximately 0.4231.
The Dowers make pumpkin pie. If each person wants three slices of pie,and each pie is Cut into 9 slices, how many pies do they need to make for 15 people?
Answer:
They need to make 5 pies for 15 people.
Step-by-step explanation:
15*3=45 slices of pie in total,
each pie is cut into 9 slices,
45/9=5 pies
In 25 hour, Matt can type 45 page.
What is Matt's rate in pages per hour?
Answer: Matt's rate is 2 pages per hour.
Step-by-step explanation:
25 hours = 45 pages
1. First, let's divide 45 by 25 to find how much it takes for one page to be done: [tex]\frac{45}{25}[/tex] = 1.8
2. This answer means it takes 1.8 hours to do one page.
3. Now, we can choose to round 1.8, which is 2.
Sonia is making a quilted wall hanging that is 38 in wide.if each quilt square is 4 3/4 inches wide, how many squares will she need to complete one row of the wall hanging?
A. 6 1/2
B.8
C.42 3/4
D.190
Answer:
b
Step-by-step explanation:
a countey fair charges $7 and $0.75 for each ride token. you have $15 write a exspression that represents the amount (in dollars) you have left after entering the fair and purchasing n tokens. how many tokens can you purchase? how much money do you have after purchasing 6 tokens
Answer:
$3.50
Step-by-step explanation:
15.00 - 7.00 = 8.00
6 x .75 = 4.50
8.00- 4.5 = 3.50
The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7 where n is the total number of rides
The amount left after purchasing 6 tokens is $ 3.50
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount be represented as = y
Now , the number of rides be = n
The cost of entry fee = $ 7
The cost for each ride = $ 0.75
The total amount available = $ 15
So , the equation will be
total amount = cost for each ride x number of rides + cost of entry fee
Substituting the values in the equation , we get
Total amount y = 0.75n + 7
y = 0.75n + 7
So , the equation is y = 0.75n + 7
Now , when purchasing 6 tokens , we get the remaining amount as
Substituting the value of n = 6 in the equation , we get
y = 0.75 x 6 + 7
y = 4.5 + 7
y = $ 11.5
So , the amount left = 15 - y
The total amount left = 15 - 11.5
The total amount left = $ 3.50
Hence , The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7 where n is the total number of rides
The amount left after purchasing 6 tokens is $ 3.50
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Please help me you guys
Answer:
g(x) = |x+3| - 5
Step-by-step explanation:
Let y = f(x)
⇒y = |x+3|
When y is replaced by Y + k, the graph of y = f(x) shifts k units down
⇒ y replaced by Y + 5 translates the graph of y = f(x) 5 units down
∴ Y = g(x) is represented by Y + 5 = |x+3|
⇒ Y = |x+3| - 5
or g(x) = |x+3| - 5
E
1. If 3x + 7x + 9 = 35, then x= ?
Answer:
Step-by-step explanation:
16
The value of x in the equation 3x + 7x + 9 = 35 is 2.6 after simplification and carrying out the necessary algebraic steps.
Explanation:The subject of your question is Mathematics, specifically algebra. Now, let's solve the equation: 3x + 7x + 9 = 35.
To start, combine like terms on the left side of the equation. That gives us 10x + 9 = 35. Next, subtract 9 from both sides to isolate the term with x. This gives us 10x = 26. Finally, divide both sides by 10 to find the value of x. So, x = 2.6.
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Pls help me ASAP it needs to be turned in today pls help
Answer:
13x-12 the last one
Step-by-step explanation:
Answer:
13x-12
Step-by-step explanation:
4(3x-5)+x+8
12x-20 +x+8
13x-12
5. The picture below shows the five houses on Maple Street and the five houses on Oak
Street.
6 Maple St.
_innnnn
Maple St.
4 Oak St.
SASA
Oak St.
. Each house number on Maple Street is six more than the house number to its left.
• Each house number on Oak Street is eight more than the house number to its left.
How much greater is the house number of the last house on Oak Street than the house
number of the last house on Maple Street
The last house on Oak Street has a house number 8 greater than the last house on Maple Street.
The correct answer is option C.
Let's denote the house numbers on Maple Street as M1, M2, M3, M4, and M5, where each house number is six more than the one to its left. Similarly, on Oak Street, denote the house numbers as O1, O2, O3, O4, and O5, where each house number is eight more than the one to its left.
For Maple Street:
M2 = M1 + 6
M3 = M2 + 6
M4 = M3 + 6
M5 = M4 + 6
For Oak Street:
O2 = O1 + 8
O3 = O2 + 8
O4 = O3 + 8
O5 = O4 + 8
Now, let's find the difference between the last house on Oak Street (O5) and the last house on Maple Street (M5):
The difference is (O4 + 8) - (M4 + 6) = (O3 + 8 + 8) - (M3 + 6 + 6) = (O2 + 8 + 8 + 8) - (M2 + 6 + 6 + 6) = (O1 + 8 + 8 + 8 + 8) - (M1 + 6 + 6 + 6 + 6).
Simplifying the expression, the constant terms cancel out, leaving:
The difference is O1 - M1 + (8 + 8 + 8 + 8) - (6 + 6 + 6 + 6) = O1 - M1 + 32 - 24 = O1 - M1 + 8.
So, the house number of the last house on Oak Street is 8 greater than the house number of the last house on Maple Street.
The question probable may be;
The picture below shows 5 houses on maple street anf the five houses on oak street.
Each house number on maple street is six more than the house number to its left. Each house number on oak street is eigth more than the house number to its left.
How much greater is the house number of the last house on oak street than the house number of the last house on maple street?
2
6
8
10
Which of the following is a velocity?
Question 2 options:
30 m/s
30 m/s going down
30m
30s
Answer:
The velocity is the speed in a given direction hence the units are the same as that of speed, m/s. Thus the answer is 30 m/s.
Step-by-step explanation:
I do not understand the second option.
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≤ −x − 4
(1, 10)
(−1, 10)
(10, 1)
(1, −10)
Answer:
Step-by-step explanation:
y ≤ x − 5
1<10-5
1<5
Pair: (10,1)
y ≤ −x − 4
-10<-1-5
-10<-6
Pair: (1,-10)
Answer:
(1, −10)Step-by-step explanation:
If we graph this system of inequalities, we could find the solution.
From the graph you can deduct that the only right answer is the last one (1,-10), because the area of solution is only for negative values of y.
Therefore, the right choice is the last one.
If you can't graph, you can try another method. If we replace the value in the system, it should satisfy it, that is, it should gives us a true result like 0<1 for example. Let's try
For x=1 and y=-10, we have
-10 ≤ 1 − 5
-10 ≤ −1 − 4
-10 ≤ -4
-10 ≤ -5
As you can see, the result is true, because -10 is less than -4 and -5, so that's the right answer.
A school is arranging a field trip to the zoo. The school spends 875.49 dollars on passes for 29 students and 4 teachers. The school also spends 279.56 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
Money spent on each student is $36.17
Step-by-step explanation:
$875.49 = 29 students & 4 teachers
33 people = $875.49
1 person = $26.53 (pass)
29 students = $279.56
1 student = $9.64 (lunch)
each student = $9.64 + $26.53
= $36.17
the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.
To find out how much money was spent on a pass and lunch for each student, we need to calculate the total amount spent on passes and lunch and then divide it by the total number of students.
Given:
- Total amount spent on passes for 29 students and 4 teachers: $875.49
- Total amount spent on lunch for just the students: $279.56
- Total number of students: 29
1. First, let's find the total amount spent on passes for just the students:
Total amount spent on passes for students and teachers = $875.49
Total amount spent on passes for 4 teachers = ?
Total amount spent on passes for students = $875.49 - (amount spent on passes for teachers)
Since each pass costs the same amount for students and teachers, we can divide the total amount spent on passes by the total number of passes (students + teachers) to find the cost per pass.
Total number of passes (students + teachers) = 29 students + 4 teachers = 33 passes
Cost per pass = Total amount spent on passes / Total number of passes
= $875.49 / 33
≈ $26.56 (rounded to two decimal places)
2. Now, let's find out how much money was spent on lunch for each student:
Total amount spent on lunch for students = $279.56
Cost per student for lunch = Total amount spent on lunch for students / Total number of students
= $279.56 / 29
≈ $9.63 (rounded to two decimal places)
So, the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.
48 in Long and 36 inches wide what is the area in square feet
Answer:
Area = 12 ft²
Step-by-step explanation:
Convert values to feet
12 inches = 1 foot
48 / 12 = 4 feet
36 / 12 = 3 feet
Area = l x w = 3 x 4 = 12 ft²
Answer: The answer is 1,728 in. squared
Step-by-step explanation:
All you do is multiply 48 by 36 because in order to get area,you multiply base and height.
4. Mitch took out a school loan for $24,000. The interest rate on the loan was 8%.
Mitch paid off the loan in just 5 years. How much did he pay altogether?
24000 0.08.5
p24000
R=0.08
T5 years
1920.5
u
9600+
I-
Mitch paid $ 33600 altogether
Solution:Given that mitch took out a school laon for $ 24000
The interest rate on the loan was 8%
Number of years = 5
To find: total amount paid altogether
We can use simple interest to calculate the total amount
Total amount paid altogether = simple interest + principal amount
The simple interest is calculated as:
[tex]\text { simple interest }=\frac{\text { principal } \times \text {rate of interest } \times \text {number of years}}{100}[/tex]
Plugging in values, we get
[tex]\text { simple interest }=\frac{24000 \times 8 \times 5}{100}=240 \times 8 \times 5=9600[/tex]
Total amount paid altogether = simple interest + principal amount
Total amount paid altogether = 9600 + 24000 = 33600
Thus Mitch paid $ 33600 altogether
The sale price of a trampoline before tax is $300 the sales tax is 4% find the sales tax in the total price of the trampoline
The trampoline will attract a sales tax of $12 which will take its total price to $312.
The trampoline costs $300 without taxes being accounted for yet.
The tax is 4%. In dollar terms this is:
= Sales tax percentage x Cost of trampoline
= 4% x 300
= $12
The total price of the trampoline will therefore be:
= Cost of trampoline + sales tax
= 300 + 12
= $312
In conclusion, the sales tax would be $12 and the total price would be $312.
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1. What is the percent change from 1000 to 80?
2. What is the percent change from 45 to 63?
3. What is the percent change from 250 to 60?
4. What is the percent change from 60 to 99?
Step-by-step explanation:
1.-92%
2.40%
3.-76%
4.65%
The percent changes for each scenario is: 1. From 1000 to 80: -92% 2. From 45 to 63: +40% 3. From 250 to 60: -76% 4. From 60 to 99: +65%.
To calculate the percent change between two values, we use the formula:
[tex]\[ \text{Percent Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\% \][/tex]
1. The percent change from 1000 to 80 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{80 - 1000}{1000} \right) \times 100\% = \left( \frac{-920}{1000} \right) \times 100\% = -92\% \][/tex]
So, the percent change is a 92% decrease.
2. The percent change from 45 to 63 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{63 - 45}{45} \right) \times 100\% = \left( \frac{18}{45} \right) \times 100\% = \frac{2}{5} \times 100\% = 40\% \][/tex]
So, the percent change is a 40% increase.
3. The percent change from 250 to 60 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{60 - 250}{250} \right) \times 100\% = \left( \frac{-190}{250} \right) \times 100\% = -76\% \][/tex]
So, the percent change is a 76% decrease.
4. The percent change from 60 to 99 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{99 - 60}{60} \right) \times 100\% = \left( \frac{39}{60} \right) \times 100\% = \frac{13}{20} \times 100\% = 65\% \][/tex]
So, the percent change is a 65% increase.
A number times 5,minus 6,is 8.
Answer:70
Step-by-step explanation:
You do the inverse operation which would be subtraction and multiplication. You add the 6 to the 8 and you get 14. Then you would multiply 14 by 5 to get 70. Hope this helps :D
Answer:
Step-by-step explanation:
A used-boat dealership buys a boat for $2900 and then sells it for $4500. What is the percent increase?
Alright, so we have the difference = 4500-2800=1700. To find the percent increase, we do 1700/2800=around 0.61 = around 61% percent. Hope I helped! ☺☼
I’ll put you as brainiest
A 25 kilogram object is placed on a compression spring, and it creates a displacement of 0.15 meters.
What is the weight of an object that creates a displacement of 0.23 m on the same spring?
Step-by-step explanation:
If [tex]mKg[/tex] of mass is placed on spring with spring constant [tex]k[/tex],
[tex]mg=kx[/tex]
where [tex]g[/tex] is universal gravitational constant
[tex]x[/tex] is the displacement in the spring.
In case 1:
[tex]25g=k(0.15)\\k=\frac{25g}{0.15}[/tex]
In case 2:
[tex]mg=k(0.23)[/tex]
Using result from case 1,
[tex]mg=\frac{25g}{0.15}\times 0.23[/tex]
[tex]m=[/tex][tex]38.33Kg[/tex]
Point P' is the translation of P (5, -5) under translation of 2 units to the left and 5 units up. What are the coordinates of P'?
(Graph up top)
(A.) (7, 0)
(B.) (7, 5)
(C.) (3, 5)
(D.) (3, 0)
Answer:
i dont know
Step-by-step explanation:
i dont know
-0.06 m = 7.2
m =
what is m equal to.
Answer: m = -120
Step-by-step explanation: In this equation, m is being multiplied by -0.06 so we will need to divide both sides of the equation in order to get m b itself.
On the left side of the equation, the -0.06's cancel and we are left with m. On the right side of the equation, we divide -7.2 by -0.06 and we get -120.
Now we have m = -120
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper/or digitally too. It will really pay off for you down the line.
Image provided.
When buying groceries at the store for this dinner, you can spend no more than $100. Some costs are fixed, like spices and piecrusts. That total comes to $65. The turkey, however, is priced per pound. The suggestion is that you plan for 1.5 pounds of turkey per guest. If the turkey costs $1.16 per pound, what is the largest size turkey you should buy and how many people can it feed?
Answer:
20 full people
Step-by-step explanation:
100-65=35
35/1.16= 30.1724
30.1724/1.5=20.1149
You can't feed a .1149 of a person so 20 people
Given the maximum budget and cost per pound, the largest turkey you can purchase is approximately 30.17 pounds. This will feed about 20 guests, considering each person consumes 1.5 pounds of turkey.
Explanation:The subject of this question is mathematics, specifically, problem-solving involving budgets and limits. Given that the maximum budget for this dinner is $100 and the fixed costs total to $65, we're left with $35 for the turkey. Each pound of turkey is priced at $1.16.
By dividing the remaining amount of money (which is $35) by the cost per pound of turkey (which is $1.16), we compute the total pounds of turkey we can afford. That is, $35 / $1.16 = approximately 30.17 pounds.
Each guest requires 1.5 pounds of turkey, so we now calculate how many guests can be fed by this amount of turkey. We do this by dividing the total pounds of turkey (30.17 pounds) by the amount required per guest (1.5 pounds), which gives us 30.17 / 1.5 = approximately 20.11. Since you can't invite a fraction of a person, the largest size turkey you can afford can feed about 20 people.
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L. - (6x - 5) = -6x +13
Answer:
No Solution.
Step-by-step explanation:
-(6x-5)=-6x+13
-6x+5=-6x+13
-6x-(-6x)+5=13
-6x+6x+5=13
0+5=13
5=13
Answer:
Exact form : x=-1/3
Decimal form : x=-0.3 (line over the 3!!!)
Step-by-step explanation: Isolate the variable by divinding each side by factors that don't contain the variable.
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Help!!! Can somebody answer this question and please explain how to do it?
Good evening ,
Answer:
15x⁷y⁵.
Step-by-step explanation:
5x³y²×3x⁴y³ = (5×3)(x³x⁴)(y²y³) = 15x⁷y⁵.
:)
Y+1=2/5(x+3) in standard form?
For this case we have that by definition, the equation of a line in the standard form is given by:
[tex]ax + by = c[/tex]
According to the statement we have the following equation of the line:
[tex]y + 1 = \frac {2} {5} (x + 3)[/tex]
We manipulate algebraically to write in the standard form. To do this we follow the steps below:
We apply distributive property on the right side of the equation:[tex]y + 1 = \frac {2} {5} x + \frac {6} {5}[/tex]
We subtract [tex]\frac {6} {5}[/tex] on both sides of the equation:
[tex]y + 1- \frac {6} {5} = \frac {2} {5} x\\y- \frac {1} {5} = \frac {2} {5} x[/tex]
We multiply by 5 on both sides of the equation:
[tex]5y-1 = 2x[/tex]
We subtract 5y on both sides of the equation:
[tex]2x-5y = -1[/tex]
Finally, the equation in its standard form is:
[tex]2x-5y = -1[/tex]
Answer:
[tex]2x-5y = -1[/tex]
This scale drawing of a rectangular wall has dimensions 4.75 inches by 2.5 inches. The length of the shorter side of the actual wall is 36 inches.
Enter the area of the actual wall.
I will mark the first one who answers me brainleist
_[blank]_ square inches
Answer:
2462.4 square inches
Step-by-step explanation:
To find the length of the longer wall use the following ratio and solve for x.
x/36= 4.75/ 2.5
x= 68.4
Area of a rectangle = l(w)
68.4(36)= 2462.4 square inches
The area of the wall is the product of its dimension.
The area of the actual wall is 2462.4 square inches
The scale is given as:
[tex]\mathbf{Scale = 4.75 : 2.5}[/tex]
The shorter side of the actual wall is 36 inches.
So, we have:
[tex]\mathbf{Long : 36= 4.75 : 2.5}[/tex]
Express as fractions:
[tex]\mathbf{\frac{Long }{36}= \frac{4.75 }{ 2.5}}[/tex]
Multiply both sides by 36
[tex]\mathbf{Long= 36 \times \frac{4.75 }{ 2.5}}[/tex]
[tex]\mathbf{Long= 68.4}[/tex]
So, we have:
[tex]\mathbf{Long= 68.4}[/tex]
[tex]\mathbf{Short= 36}[/tex]
The area is then calculated as:
[tex]\mathbf{Area = 68.4 \times 36}[/tex]
[tex]\mathbf{Area = 2462.4in^2}[/tex]
Hence, the area of the actual wall is 2462.4 square inches
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Which of these is usually true of a convenience sample?
A. It consists of the entire population.
B. It is randomly chosen.
C. It gives reliable results.
D. It excludes those who are indifferent.
Answer:
The correct answer is C = It gives reliable results
Answer:
D. it excludes those who are indifferent
Step-by-step explanation:
3. A crate with 20 bricks weighs 167 pounds. When the same crate has 32 bricks, it weighs
191 pounds. How much would the crate weigh if there were 19 bricks in the crate?
Explain.
The weight of crate when it has 19 bricks is 165 pounds
Solution:Given that, A crate with 20 bricks weighs 167 pounds.
When the same crate has 32 bricks, it weighs 191 pounds.
Now, let the weight of each brick be "m" pounds and weight of the crate be 'n" pounds.
Then, when crate has 20 bricks
Total weight = weight of bricks + weight of crate
[tex]167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }[/tex]
[tex]167=20 \times m+n[/tex]
20m + n = 167 ----- eqn (1)
Now, when crate has 32 bricks
Total weight = weight of bricks + weight of crate
[tex]191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }[/tex]
[tex]191=32 \times m+n[/tex]
32m + n = 191 ----- eqn (2)
Now, subtract (1) from (2)
32m + n = 191
20m + n = 167
(-) ----------------
12m + 0 = 24
m = 2
Then, from eqn (1)
20(2) + n = 167
40 + n = 167
n = 167 – 40 = 127
Now, when the box has 19 bricks
Total weight = 19 bricks x 2 pounds per brick + 127 pounds of crate
[tex]\text { Total weight }=19 \times 2+127=38+127=165[/tex]
Hence, the weight of crate when it has 19 bricks is 165 pounds.