Answer:
Step-by-step explanation:
5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)
3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)
Let's use the elimination method. Multiply the first equation by -3:
-15r - 6b = -42
3r + 6b = 18
-----------------
12r = 24
Divide by 12:
r = 2
Answer:
The price per pound of the oranges is $ 2.
The price per pound of the bananas is $ 2.
Step-by-step explanation:
A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.
In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):
x: price per pounds of the orange y: price per pounds of the bananaThe price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)
The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)
Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:
[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]
One of the ways to solve a system of equations is through the substitution method. This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".
In this case, x is isolated from the first equation, obtaining:
5*x+2*y=14
5*x=14-2*y
[tex]x=\frac{14-2*y}{5}[/tex]
[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)
Replacing this equation (C) in the other equation you get:
[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]
Isolating the value of "y" you get:
[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]
[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]
[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]
[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]
[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]
[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]
y=2
Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.
Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:
[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]
[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]
[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]
x=2
Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.
PLEASE ANSWER NOW
Stephen, Paul & Bridget share some money in the ratio 3 : 4 : 2. In total, Stephen and Bridget receive £50. How much does Paul get?
Answer:
The money receive by Paul is [tex]\pounds 40[/tex].
Step-by-step explanation:
Given as :
The ratio of share of money among three people as
Stephen : Paul : Bridget = 3 : 4 : 2
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
Let The money receive by Stephen = 3 x
Let The money receive by Paul = 4 x
Let The money receive by Bridget = 2 x
Now, According to question
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
I.e 3 x + 2 x = [tex]\pounds 50[/tex]
i.e 5 x = [tex]\pounds 50[/tex]
∴ x = [tex]\frac{\pounds 50}{5}[/tex]
x = [tex]\pounds 10[/tex]
So, The money receive by Stephen = 3 × [tex]\pounds 10[/tex] = [tex]\pounds 30[/tex]
Let The money receive by Paul = 4 × [tex]\pounds 10[/tex] = [tex]\pounds 40[/tex]
Let The money receive by Bridget = 2 × [tex]\pounds 10[/tex] = [tex]\pounds 20[/tex]
Hence The money receive by Paul is [tex]\pounds 40[/tex]. Answer
The difference of c and 13 is less than -19.
Answer:
If you want the inequality, c - 13 < -19
If you want the inequality simplified, c < -6
y = 3x - 1
12x – 4y = 12
Answer:
8 and 23
Step-by-step explanation:
let the 1st equation be i and 2nd be ii
now putting the value of x in eqn ii, we get
12x -4×(3x-1) = 12
12x-12x+4=12
x=12-4
x=8
again,
y=3×8-1
y=23
answer this for me please and quick!!
Answer:
24.3
Step-by-step explanation:
a first plus twice a second number is one. twice the first number plus the second totals fourteen.
Answer:
First Number = 9
Second Number = -4
Step-by-step explanation:
Let the first number be "x" and the 2nd number be "y"
First number PLUS twice 2nd is 1, so we can write:
x + 2 y = 1
Twice First number PLUS the 2nd number is 14, so we can write:
2x + y = 14
We can write:
y = 14 - 2x
We put this into 1st equation and solve for x:
x + 2y = 1
x + 2(14 - 2x) = 1
x + 28 - 4x = 1
-3x = -27
x = 9
And now y:
y = 14 - 2(x)
y = 14 -2(9)
y = 14 - 18
y = -4
First Number = 9
Second Number = -4
Each gift bag has to contain atleast 15 candies and/or chocolate was total worth must not exceed 30 dollars. Each candy costs 1 dollar while each chocolate costs 3 dollars.
a. Write a system of inequalities that shows the various ways candies and chocolates can be combined in the bag.
b. Graph.
c. Write 3 possible combinations of candies & chocolates that can be placed in the bag.
Answer:
the answer is b
kathy has a garden that is 15 feet wide and 20 feet long.she will plant 1 bulb per square foot.each bang contains 9 bulbs.how many bag does kathy need
Answer:
2 tomato plants will left with Clara.
Step-by-step explanation:
Length of the garden = l = 7 feet
Width of the garden = w = 4 feet
Area of the garden = l × w
Area occupied by single tomato plant =
Number of tomato plants in the garden :
tomato plants
Number of tomato Clara has is 30
Number plants leftover with Clara = 30 - 28 = 2
2 tomato plants will left with Clara.
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Step-by-step explanation:
Answer:
34 bags
Step-by-step explanation:
Area =L*W
20*15 = 300 square feet
She needs to plant 300 bulbs
300/9 = 33.33333(33(1/3) bags
Since she need to purchase bags containing 9 bulbs each, she needs to buy 34 bags (It ill be 6 left since 34 bags =306 bulbs)
If she buys 33 bags it will be only 297 (3 short)
Nancy is taking inventory in the pharmacy to make sure there is enough eye medication in the pharmacy. She counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in stock. Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes. Calculate how many boxes of each Nancy needs to order.
Answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.
Step-by-step explanation:
Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.
So, there is a need to order (15 - 10) = 5 boxes of travoprost.
Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.
So, there is a need to order (12 - 3) = 9 boxes of latanoprost.
Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)
Final answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.
Explanation:
Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:
15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.
For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:
12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.
Supposed charity received a donation of $23.9 million. If this represents 54% of the charity donated funds what is the total amount of its donated funds? round your answer to the nearest million dollars.
Total amount of funds is $44.26 million.
Step-by-step explanation:
Given,
Donation received = $23.9 million
As it represents 54% of charity.
Let,
Total amount = x
Therefore,
54% of x = 23.9 million
[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]
Dividing both sides by 0.54
[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]
Total amount of funds is $44.26 million.
Keywords: percentage, division
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In the world balloons the ratio of wolves to consonant is
Answer:
The ratio of consonants to is 4:3. 4 consonants and 3 wolves.
Higher Order Thinking
Mrs. Dryson
divided her collection of 52 glass bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson make? How many bears
are in each group?
Answer:
There are 26 glass bears in each group and there are 2 equal groups.
Step-by-step explanation:
i hope that help but your problem was kind of werid at first but i foud the answer i hope you enjoy!!!...
A carpenter charges $30 per hour for up to eight hours each day and increases this rate by 50% for additional hours. The carpenter will not work more than ten hours per day. If this daily cost function is modeled by y = f(x) and graphed, which statement is not correct?
A) f(0) = 0, f(8) = 240, and f(10) = 330.
B) The domain is [0, 10] and the range is [0, 330].
C) The graph is increasing on the interval (8, 10) with a slope of 45.
D) If a $20 trip charge is added, the new x-intercept will be (20, 0).
Answer:
D. If 20$ a trip charge is added, the new x-intercept will be (20,0)
This statement is false. The original graph started at (0,0), the x-intercept. Adding a 20$ trip charge moves the graph up 20 so there would not be an x-intercept.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Help!!
Kerry has a bag containing white and yellow marbles. Kerry randomly selects one marble from the bag, records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
- A white marble was selected 41 times
- A yellow marble was selected 24 times.
Based on these results what is the probability that the next marble Kerry selects will be white?
A. 41%
B. 50%
C. 59%
D. 63%
The probability that the next marble Kerry selects will be white is; D: 63%
Probability of Selection
The results of Kerry randomly selecting one marble from the bag out of 65 selections are;
White marble = 41Yellow Marble = 24Now, these numbers of marbles represents the amount of times the respective colors are gotten for every 65 selections. Thus;
P(next marble that Kerry selects will be white) = 41/65 * 100
P(next marble that Kerry selects will be white) ≈ 63%
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Consider this function. f(x) = 2x - 2 Which graph represents the inverse of function f?
Answer:
W
Step-by-step explanation:
If its the graphs I got then yeah
The Graph that represents the inverse of function f is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We have been given a function of x as; f(x) = 2x - 2
If function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
y = 2x - 2
x = 2y - 2
x + 2 = 2y
y = (x + 2)/2
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f' function here.
To Graph the inverse, Simply use a graphing calculator and the correct graph is attached below.
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F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]
So
[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]
Hence,
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Keywords: functions, Function composition
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what is the probability that a randomly-selected driver fatality who was female was less than 16 years old the probability that a randomly-selected driver fatality who was female was less than 16 years old is approximately _____.
Answer:
0.19%
Step-by-step explanation:
To know what is the probability that a female who is less than 16 in involved in a driver fatality, we have to compare the cases of fatalities for females who are less than 16 years old, with the total cases of fatalities, commited by all kind of persons. Then, to know the proportion of the population of driver fatalities represented by female who are less than 16, we divide the amount of cases that happend under the characteristics mentioned (females <16) and the total amount of fatalities: [tex]\frac{100}{Total_{fatalities}} =\frac{100}{141+100+4970+2331+11009+....} =\frac{100}{52693}=0.0019=0.19\%[/tex], which is the probability that a randomly-selected driver fatality were commited by a females who is less than 16.
Sadie finished her math test in sixteen minutes less than three times the amount of times it took her friend Laura to finish.if their combined times was 1 hour and 8 minutes,how long did it take Sadie?
Answer:
Sadie took 47 minutes to finish her test.
Step-by-step explanation:
Let Laura's time be x minutes.
Then we have:
x + 3x - 16 = 68
4x = 84
x = 21 minutes.
So Sadie took 3(21) - 16 = 63-16
= 47 minutes.
the ratio of potatoes to turnips is 1:1 if there are are 473 potatoes how many turnips are there
Answer:
473 turnips
Step-by-step explanation:
well if its 1 to 1 that means how ever meany you have of one you will have the same exact amount of the other food
473x1 = 473x1
Final answer:
To find the number of turnips, set up a proportion using the given ratio and cross multiply to solve for the number of turnips.
Explanation:
To find the number of turnips, we can set up a proportion using the given ratio:
Number of potatoes / Number of turnips = Ratio of potatoes to turnips.
Since the ratio of potatoes to turnips is 1:1, the proportion will be:
473 / Number of turnips = 1 / 1.
To solve for the number of turnips, cross multiply:
473 * 1 = Number of turnips * 1.
Number of turnips = 473.
Therefore, there are 473 turnips in this scenario.
Which graph shows the solution set to this inequality? 4x < 12
Answer:
x=1,2
Step-by-step explanation:
we show that 4x is <12
if x=1,,,4x=4*1=4
if x=2,,,4x=4*2=8
if x=3,,,4x= 4*3=12
so 1 &2 is right ans
Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solution. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous
Answer:
1; solution is not extraneous
Step-by-step explanation:
the value 3=3 is true, meaning its not extraneous and also I got it correct on the test
The value of x is 1, and the solution is not extraneous.
Given that,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
We have to determine,
The value of x and identify if it is an extraneous solution.
According to the question,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
To find the value of the x following all the steps given below.
Squaring both the sides to solve the equation,
[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, The solution is not extraneous.
Hence, The value of x is 1, and the solution is not extraneous.
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-3x+12y=24 What is the Y intercept
Answer:
(0,2)
Step-by-step explanation:
y-intercept: when x = 0
-3(0) + 12y = 24
12y = 24
y = 2
The owner of a new restaurant is ordering tables and chairs. he wants to have only tables for two and tables for 4. the total number of people can be seated in rest is 120, then write an equation to represent the situation. What do the variables represent?
Answer:
4 M + 2 N = 120
Step-by-step explanation:
If we name "M" the number of tables for four people, and "N" the number of tables for two people, then the total number of people to be seated using M tables (of four people) would be the product "4 * M".
Similarly, the total number of people to be seated if the owner has N number of two person tables, would be: "2 * N".
Therefore, if the owner has M four people tables and N two person tables, the total number of people seated at the restaurant would be the addition:
4 * M + 2 * N. Since he wants this number to be 120, we complete the equation making this expression equal to 120:
4 * M + 2 * N = 120
The equation that represents this situation is 2x + 4y = 120, where x represents the number of tables for two and y represents the number of tables for four. Thus, this mathematical equation reflects the owner's seating arrangement plans for his restaurant.
Explanation:Let's use x to represent the number of tables for two and y to represent the number of tables for four. Since each table for two can seat 2 people and each table for four can seat 4 people, the total number of people that can be seated is 2x + 4y. The owner of the restaurant wants to seat a total of 120 people, so the equation that represents this situation is 2x + 4y = 120.
In this equation, x and y are the variables. The x value represents the number of tables for two and the y value represents the number of tables for four.
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What is CD?
6 units
12 units
18 units
24 units
Answer: 18 units
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
6 times 2 = 12
12+6=18
Help me find the value of the missing variable
Answer:
Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6
Moves to one side. 12=x
x=12
Step-by-step explanation:
x=12
Step-by-step explanation:
You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.
Haley wrote the expression 24m – 6n. Kensi wrote an expression equivalent to Haley’s. Which expression could Kensi have written? 2(6m – 4n) 4(6m – 6n) 6(4m – n) 12(2m – 2n)
Answer:
C) 6(4m-n)
Step-by-step explanation:
Because 6(4m-n)=24m-6n.
Choose a system of equations with the same solution as the following system:
6x + 2y = −6
3x − 4y = −18
---------------------
A: 8x + 4y = −4
17x + 2y = −28
B: 12x + 4y = 12
21x + 2y = −36
C: 6x + 8y = −36
15x + 6y = −60
D: 6x + y = 15
15x − y = −9
Answer
______________
The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
Now,
Solve the given system of equation as;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
By equation (i);
6x + 2y = - 6
2(3x + y) = - 6
3x + y = - 3 ..(iii)
Subtract equation (ii) from (iii), we get;
3x - 4y - (3x + y) = - 18 - (-3)
3x - 4y - 3x - y = - 18 + 3
- 5y = - 15
y = 3
And, By equation (i), we get;
6x + 2y = - 6
6x + 2 × 3 = - 6
6x + 6 = - 6
6x = - 6 - 6
6x = - 12
x = - 2
Thus, The solution of given system of equation are;
x = - 2 and y = 3
Now,
Substitute the value of x and y in all the given options and find the same solution of given system of equation as;
A: 8x + 4y = −4
17x + 2y = −28
Substitute the value of x = - 2 and y = 3;
8x + 4y = −4
8 × - 2 + 4 × 3 = - 4
- 16 + 12 = - 4
- 4 = - 4
17x + 2y = −28
17 × - 2 + 2 × 3 = - 28
- 34 + 6 = - 28
- 28 = - 28
Thus, This system of equation has same solution.
Therefore, The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
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Which graph best represents the function f(x) = (x - 1)(x + 3)(x – 3)?
Answer:
The graph you posted was Incorrect! An easy way you can check is like this:
Insert the function "f(x) = (x - 1)(x + 3)(x – 3)" into desmos, you get this which should perfectly match the function shown.
The graph that represents the function is attached to the answer.
What is a Graph?The graph is a mathematical representation of the relation between two objects.
It helps in determining the function that fits best for the data obtained.
A function is a mathematical statement that defines a relationship between a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.
The function is f(x) = (x-1)(x+3)(x-3)
The graph for the function will be determined by plotting,
The graph is plotted and attached with the answer.
The parent function is a cubic function, which is also plotted along with the function graph.
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12. What is the equation of a line perpendicular to the x-axis that passes through the point (-2,-4)? What is the slope of
this line?
what answer?
Answer: the vertical line with the equation "x=-2"
Step-by-step explanation:
if you are perpendicular to the x axis, you will be looking for vertical lines that pass through (-2,-4)
the vertical line with the equation "x=-2" will pass though the point because (-2,-4) has an x coordinate of -2
10. A square picture has a 1-inch frame around it. If the
area of the frame alone is 80 in.2, what is the area of the
picture?
Answer:
361 sq, inches.
Step-by-step explanation:
Let us assume that the dimensions of the square picture are P in × P in.
So, the area of the picture alone is, A = P²
Now, if the photo has a frame of 1 inch wide, then the dimensions of the photo with frame are (P + 2) in × (P + 2) in.
So, the area of the photo with frame is A' = (P + 2)(P + 2) = (P + 2)²
Now, the area of the frame alone is 80 sq. inches.
Hence, A' - A = 80
⇒ (P + 2)² - P² = 80
⇒ 4P + 4 = 80
⇒ 4P = 76
⇒ P = 19 inches.
So, the area of the picture is = 19² = 361 sq. inches. (Answer)
361 sq, inches.
Step-by-step explanation:
Can someone actually answer this question please QUICK
A+b=c>4
b=7
a= 2
what is c?
Answer:
9
Step-by-step explanation:
The value of c is found by adding a (2) and b (7) together, which equals 9.
Explanation:The question a + b = c is asking for the value of c when a is 2 and b is 7. To find c, we simply add the values of a and b together. In mathematics, this is known as solving for the unknown variable.
In this case:
a + b = c
2 + 7 = c
c = 9
Therefore, the value of c when a is 2 and b is 7 is 9.
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