The value of y is 28
y = 28
While in Europe, if you drive 117 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro=1.26dollars.
Answer:
Total Cost of Week = 81.20 Euros
Total Cost of Week (in dollars) = $102.31
Step-by-step explanation:
117 km per day
You drive 7 days
So,
Total miles driven = 117 * 7 = 819 km
Mileage is 42 miles per gallon. So how many gallons would it require to drive 819 km?
819/42 = 19.5 gallons
We know 1 gallons = 3.78 liters
So,
19.5 gallons would be:
19.5 * 3.78 = 73.82 liters
1.10 Euro PER LITER, so the total cost:
Total Cost of Week = 73.82 * 1.10 = 81.20 Euros
In dollars (1 euro = 1.26 dollars):
Total Cost of Week (in dollars) = 81.20 * 1.26 = $102.31
The cost on gas is approximately 7.2 euros
Data given;
Distance = 117kmrate of consumption = 42.0 mi/galcost of gas = 1.10 eurosConversion of distance from km to milesIf 1mi = 1.609km
And we cover 117km daily, let's convert this into miles
[tex]1mi=1.62km\\ x mi = 117km\\ x = 117/1.62\\ x = 72.2mi[/tex]
This shows that we cover a distance of 72.2 miles daily.
But the car consumes 1 gallon in 42 miles, let's calculate the gas required to cover 72.2 miles
[tex]42mi = 1g\\ 72.2mi =x\\ x = 72.2/42\\ x = 1.719[/tex]
The total gas consumed daily is approximately 1.72 gallons.
Cost of gas dailyThe cost of gas daily can be calculated from the data given but we have to convert the volume from gallon to liter
Gallon - Liter1L = 0.26 gallon
xL = 1.72 gallons
cross multiply this and solve for x
[tex]x = \frac{1*1.72}{0.26}\\ x = 6.6[/tex]
This shows that we consume 6.6L daily.
But we were given that the cost of 1 liter of gas is equal to 1.10 euros
1L = 1.10 euros
6.6L = x euros
[tex]x = \frac{1.1*6.6}{1}\\ x = 7.26[/tex]
The cost of gas daily is 7.26 euros or approximately 7.2 euros.
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The coordinates of three corners of a square are (1, 7), (5, 3), and (9, 7). What are the coordinates of the fourth corner of the square?
A . 5,7
B . 5,11
C . 9,1
D . 13,3
Answer:
A 5,7
Step-by-step explanation:
4x-5,4(x-5),4(x+5) drag the phrases into each box to match each expression five sang the sum of four and number five more than the product of a four and a number five less than the product of a four and a number
Answer:
The answers are- 4x-5: 5 less than the product of 4 and a number.
4(x-5): The product of 4 and the difference of a number and 5.
4(x+5): The product of 4 and the sum of a number and 5.
Step-by-step explanation:
I took the test on k12 and when I reviewed it, it said were the correct answers:)
Hope this helped!!
Hope you have a wonderful day!!:)
what is 750x+150<1000
Answer:
[tex]x<\frac{17}{15}[/tex]
Step-by-step explanation:
We begin with the inequality: [tex]750x+150<1000[/tex]
We need to solve for x. This means that we need to subtract 150 from each side and then divide each side by 750. Then we need to simplify.
[tex]750x+150<1000\\\\750x<850\\\\x<\frac{850}{750} \\\\x<\frac{85}{75} \\\\x<\frac{17}{15}[/tex]
x<17/15
Step-by-step explanation:
the NACI cafeteria wants to sell two 25 cm diameter medium size pizzas for the same price as one large pizza. what should the diameter be of the large pizza so that it contains the same amount of pizza as the two medium-size pizzas?
Answer:
35.34 centimeters
Step-by-step explanation:
The amount of pizza is same as the area. The pizza is in a shape of a circle. The area of a circle is:
[tex]A=\pi r^2[/tex]
Where
r is the radius (half of diameter)
Area of one medium size pizza is (diameter 25 means radius is 25/2 = 12.5):
[tex]A=\pi r^2\\A=\pi (12.5)^2\\A=490.87[/tex]
So, area of two of these medium size pizzas is:
490.87 * 2 = 981.74
This should be the area of the large pizza. We can find the radius of that by substituting into formula. Shown below:
[tex]A=\pi r^2\\981.75=\pi r^2\\r=\sqrt{\frac{981.74}{\pi}} \\r=17.67[/tex]
Hence, the diameter would be around:
17.67 * 2 = 35.34 centimeters
Solve the equation
2z-5= 11
A)z=3
B)z=8
C)z=9
D)z=11
PLEASE HELP
B. 2 * 8 - 5 = 11
2 * 8 = 16
16 - 5 = 11
z = 8
2. Juanita is trying to find the roots for the quadratic function f(x) = x2 + 64. She argues that there is no solution. Is Juanita correct? Justify your answer.
Answer:
Yes, Juanita is correct.
Step-by-step explanation:
Given:
The function given is:
[tex]f(x)=x^2+64[/tex]
The roots of a function means the values of 'x' for which the function intersects or touches the x-axis. Therefore, the roots are nothing but the x-intercepts of the function.
In order to find the roots of the above function, we should equate it to 0.
So, [tex]f(x)=0[/tex]
[tex]x^2+64=0\\\\x^2=-64[/tex]
We know that, square of any number is always a positive quantity. But here, the square of 'x' is -64 which is a negative number. This is not possible.
So, there is no real solution to the given function. In other words, we can say that the function doesn't intersect the x-axis.
Therefore, Juanita is correct in her argument.
Ratio as a fraction 12:36
Step-by-step explanation:
[tex]12:36=\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}[/tex]
Answer: 1/3
Step-by-step explanation: The ratio 12:36 can be written as the fraction 12/36. So, we simply put the 12 as the numerator of our fraction and put the 36 as the denominator of our fraction.
12/36 can be simplified by dividing the numerator and the denominator by the greatest common factor of 12 and 36 which is 12 and we get the fraction 1/3.
The fraction 1/3 still represents the ratio 1/3 even though we have written it in the form of a/b or fraction form.
chang earns $11.70 per hour plus time and a half. he worked his regular 40 hours plus 6 hours on the weekend . what is his total pay for the week?
Answer: 173.3
Step-by-step explanation:
40 hours at rate of 11.7
40*11.7=68
6 hours paid time and a half 11.7+11.7/2=17.55
6*17.55=105.3
Total pay per week:
68+105.3=173.3
I can not figure this question out! Plz help!! A drill team is raising money by holding a car wash. The team earns $6.00 for each car washed. The team's expenses include $50.00 for advertising plus $0.50 in materials for each car washed. Let f(x) represent the team's total earnings for washing x cars and g(x) represents the team's total expenses for washing x cars. Describe how you can use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars. Then write a rule for p(x).
Answer:
Step-by-step explanation:
Total earnings = f(x) = 6x
Total expenses =g(x) = 0.5x + 50
Profit p(x) = f(x) - g(x)
= 6x - ( 0.5x + 50)
= 6x - 0.5x - 50 = 5.5x - 50
Select the correct answer. If f(x) = |x| - 4, which translation is applied fo f(x) to get g(x)?
Answer:
It is a vertical translation of f(x) four units downward.
Step-by-step explanation:
We are given the original equation f(x) = |x| and the transformed function is g(x) = |x| - 4.
It is clear that the transformed function that g(x) = f(x) - 4.
So, the y-value in g(x) is reduced by 4 units from the y-value of f(x) i.e. the transformation is by 4 units down of function f(x).
Therefore, it is a vertical translation of f(x) four units downward. (Answer)
HELPPPPPPPPPP!!!!!!!! 15 points!
daniel bought hamburgers and fries for his classmates. the hamburgers costed 1.49 each and a bag of fries cost 1.19. ben spent a total of 50.93. the number of hamburgers was five less than twice the amount of fries, how many hamburgers and fries did he buy
Number of hamburgers bought is 23 and number of bags of fries bought is 14
Solution:Let "h" be the number of hamburgers bought
Let "f" be the number of bags of fries bought
Cost of one hamburger = $ 1.49
Cost of one bag of fries = $ 1.19
Given that Ben spent a total of 50.93
Thus we can frame a equation as:
number of hamburgers bought x Cost of one hamburger + number of bags of fries bought x Cost of one bag of fries = $ 50.93
[tex]h \times 1.49 + f \times 1.19 = 50.93[/tex]
1.49h + 1.19f = 50.93 ------ eqn 1
Also given that the number of hamburgers was five less than twice the amount of fries
number of hamburgers bought = 2(number of fries) - 5
h = 2f - 5 ---------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "h" and "f"
Substitute eqn 2 in eqn 1
1.49(2f - 5) + 1.19f = 50.93
2.98f - 7.45 + 1.19f = 50.93
4.17f = 50.93 + 7.45
4.17f = 58.38
[tex]f = \frac{58.38}{4.17}[/tex]
f = 14Substitute f = 14 in eqn 2
h = 2(14) - 5
h = 28 - 5 = 23
h = 23Summarizing the results:
number of hamburgers bought = h = 23
number of bags of fries bought = f = 14
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 3y + 4z = 1
Which of the following is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
Answer:
(y+z=6)*-3
Step-by-step explanation:
using this would make the top equation or (y+z=6) turn negative and would be this [-3y-3z=-18) using the distributive property. Since the bottom equation has a positive 3y. The -3y from the top equation and 3y from the bottom ones cancel out leaving you with z=-17 when combining like terms.
Answer:
c is the answer since you are trying to make the ys number (-/+) of the value the other y contains
(3) so you will multiply the first equation by -3 to be able to eliminate y
Write the equation of a line that passes through the two points (3, 5) and (3,8).
Answer:
here the coordinates given are incorrect but I have solved it anyway see the attachment for further information
Answer:
x = 3
Step-by-step explanation:
Two points are given. The x-coordinates are one and the same. This means that x does not change, and thus the line is a VERTICAL line: x = 3.
Use the graph below to determine a1 and d for the sequence. graphed sequence showing point 1, 17, point 2, 14, point 3, 11, point 4, 8, point 5, 5, and point 6, 2 a1 = 1; d = 3 a1 = 1; d = −3 a1 = 17; d = 3 a1 = 17; d = −3
Answer:
So the Correct option is
[tex]a_{1}=17;\ d=-3[/tex]
Step-by-step explanation:
Given:
Let
A(1, 17),
B(2, 14),
C(3, 11),
D(4, 8),
E(5, 5), and
F(6, 2) be the Points For The Sequence
Solution:
For the First Term
A( 1, 17 )
[tex]a_{1}=17[/tex]
For the second Term
B(2, 14),
[tex]a_{2}=14[/tex]
For the third Term
C(3, 11),
[tex]a_{3}=11[/tex]
For the fourth Term
D(4, 8),
[tex]a_{4}=8[/tex]
For the fifthTerm
E(5, 5)
[tex]a_{5}=5[/tex]
For the sixth Term
F( 6, 2 )
[tex]a_{6}=2[/tex]
Now Common Difference 'd' is given as
[tex]d=a_{2}-a_{1}=14-17=-3\\\therefore d=-3[/tex]
So the Correct option is
[tex]a_{1}=17;\ d=-3[/tex]
Answer:
a1 = 17; d = −3
Step-by-step explanation:
9. Ms. Ortiz sells tomatoes wholesale. The function p(x)=–80x2 + 320x – 10, graphed below,
indicates how much profit she makes on a load of tomatoes if she sells them for 4- x dollars
per kilogram
What should Ms.Ortiz charge per kilogram of tomatoes to make the maximum profit, and what is the maximum profit she can make on a loaf of tomatoes
A. $230 at $3 per kilogram
B. $310 at $2 per kilogram
C. $320 at $2 per kilogram
D. $320 at $3 per kilogram
Answer:
The correct answer is B. $310 at $2 per kilogram
Step-by-step explanation:
1. Let's find out the maximum profit Ms. Ortiz can make with a loaf of tomatoes:
function p(x)=–80x² + 320x – 10
For x = 1, price per kilogram of tomatoes would be: 4 - x = 3
–80x² + 320x – 10, replacing with x = 1
-80 * 1² + 320 * 1 - 10 = -80 + 320 - 10 = 230
For x = 2 price per kilogram of tomatoes would be: 4 - x = 2
–80x² + 320x – 10, replacing with x = 2
-80 * 2² + 320 * 2 - 10 = -320 + 640 - 10 = 310
For x = 3, price per kilogram of tomatoes would be: 4 - x = 1
–80x² + 320x – 10, replacing with x = 3
-80 * 3² + 320 * 3 - 10 = -720 + 960 - 10 = 230
The correct answer is B. $310 at $2 per kilogram
Answer:The correct answer is B.) $310 at $2 per kilogram
Hope this helps :D
7x + 2y = 17
(3x +2y = 3)
Step-by-step explanation:
Multiply second equation by -1
-1 × (3x + 2y) = 3
-3x -3y = -3 now add this to the first equation
7x +2y = 17
(-3x-2y)= -3
7x +2y -3x -2y = 17 -3 (2y will eliminate -2y)
4x = 14
x = 7/2 now by using this information we found we can calculate the value for y
if 3x + 2y = 3 (replace x by 7/2)
3 ×(7/2)+2y = 3 ➡ 21/3 + 2y = 3 ➡ 2y = 3 - 21/3 ➡ 2ty = 15/2 ➡ y = 15/4
(-7,5) reflected over y axis
Answer:
add
Step-by-step explanation:
23456
Answer:
( 7, 5 )
Step-by-step explanation:
when reflected over the y axis they numbers are in quadrant 1 which means both numbers are positive.
Which ordered pair is a solution of the equation?
A- Only (4,-1)
B- Only (5,2)
C- Both (4,-1) and (5,2)
D- Neither
Write a two column proof
Answer:
Step-by-step explanation:
Given:
TU ≅ WU
∠T ≅ ∠W
To Prove:
[tex]\overline{TS} \cong \overline{WV}[/tex]
Proof:
In Δ TUS and Δ WUV
STATEMENT REASON
1. TU ≅ WU 1. Given
2. ∠T ≅ ∠W 2. Given
3.∠TUS ≅ ∠WUV 3. Vertically Opposite Angles are equal
4. ΔTUS ≅ ΔWUV 4. Angle-Side-Angle congruence test.
5. ∴ TS ≅ WV 5. Corresponding parts of congruent triangles.
[tex]\overline{TS} \cong \overline{WV}[/tex].......Proved
solve the inequality 2x<2 pleaseeeeeeeeeeeeee
Answer:
x < 1
Step-by-step explanation:
Divide both sides of the inequality by 2:
(2x)/2 < (2)/2
x < 1 . . . . . . . . . . simplify
The solution is x < 1.
12x²+28x - 5 = (6x - 1)(_).
what’s the factored form ?
(6x-1)(__)
Answer:
(6x-1) (2x+5)
Step-by-step explanation:
12x²+28x - 5
=12x² +30x -2x -5
= 6x(2x+5) -1(2x+5)
=(6x-1) (2x+5)
7. Let P = (-2,4).
a. Line r is horizontal and passes through P. Write an equation for r.
b. Line s is vertical and passes through P. Write an equation for s.
Answer:
see explanation
Step-by-step explanation:
(a)
A horizontal line parallel to the x- axis has equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (- 2, 4) with y- coordinate 4, thus
y = 4 ← equation of horizontal line
(b)
A vertical line parallel to the y- axis has equation
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 2, 4) with x- coordinate - 2, thus
x = - 2 ← equation of vertical line
A trail mix is made by adding pecans that sell for 2.50 per pound to chocolate candies that sell for 1.00 per pound. How much of each should be used to get 60 pounds of trail mix tat sell for 1.70 per pound?
Answer:
Should be used 28 pounds of pecans and 32 pounds of chocolate candies
Let
x -----> pounds of pecans used
y ----> pounds of chocolate candies used
we know that
-----> equation A
-----> -----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
Using a graphing tool
The solution is the point (28,32)
see the attached figure
therefore
Should be used 28 pounds of pecans and 32 pounds of chocolate candies
Wallpaper was applied ti one rectangular wall of a large room. The dimensions are shown below.
If the total cost of the wallpaper was $771.12, what was tye cost, in dollars, of the wallpaper per square foot?
Answer:
1.3889
Step-by-step explanation:
42*25.5=1,071
1,071/771.12=1.3889
In a school of 450 people 110 are in the choir 240 are in a band and 60 are in both
What is the probability
The question doesn't require any specific probabilities, but I'm adding my own calculations to make it easier for you to solve your own problem
Answer:
Questions added and answered below
Step-by-step explanation:
Venn Diagram
When we have different sets, some of them belong only to one set, some belong to more than one, some don't belong to any of them. This situation can be graphically represented by the Venn Diagrams.
Let's analyze the data presented in the problem and fill up the numbers into our Venn Diagram. First, we must use the most relevant data: there are 60 people in both the choir and the band. This number must be in the common space between both sets in the diagram (center zone, purple).
We know there are 110 people in the choir, 60 of which were already placed in the intersection zone, so we must place 110-60=50 people into the blue zone, belonging to C but not to B.
We are also told that 240 people are in a band, 60 of which were already placed in the intersection zone, so we must place 240-60=180 people into the red zone, belonging to B but not to C.
Finally, we add the elements in all three zones to get all the people who are in the choir or in the band, and we get 50+60+180=290. Since we have 450 people in the school, there are 450-290=160 people who are not in the choir nor in the band.
The question doesn't ask for a particular probability, so I'm filling up that gap with some interesting probability calculations like
a) What is the probability of selecting at random one person who is in the band but not in the choir?
The answer is calculated as
[tex]\displaystyle P(A)=\frac{180}{450}=0.4[/tex]
b) What is the probability of randomly selecting one person who belongs only to one group?
We look for people who are in only one of the sets, they are 50+180=230 people, so the probability is
[tex]\displaystyle P(B)=\frac{230}{450}=0.51[/tex]
b) What is the probability of selecting at random one person who doesn't belong to the choir?
We must add the number of people outside of the set C, that is 180+160=340
[tex]\displaystyle P(C)=\frac{340}{450}=0.76[/tex]
What is the product of (-12/14)×(-11/15)?
Answer:
22/35
Step-by-step explanation:
-12/14=-6/7
-6/7*-11/15=66/105=22/35
Jack is two weeks into his diet and now weighs 197 pounds. If he lost 3 pounds the first week and 6 pounds the second week, what was his starting weight?
Answer:
206
Step-by-step explanation:
197 + 3 + 6 = 206
To find Jack's starting weight before he started his diet, we need to add the pounds he lost in the first and the second week back to his current weight.
Jack's current weight is 197 pounds.
In the first week, he lost 3 pounds.
In the second week, he lost 6 pounds.
So the total weight lost over the two weeks is 3 pounds + 6 pounds = 9 pounds.
Now we just add these 9 pounds back to Jack's current weight to find his starting weight before the diet.
197 pounds (current weight) + 9 pounds (total weight lost) = 206 pounds.
Thus, Jack's starting weight was 206 pounds.
3.75x = 3
how to do this, please help.
Answer:
Here, invert the multiple of x and draw the other side, and multiply in the following equation to obtain the value of x.
Step-by-step explanation:
[tex]3.75x = 3 \\ x = \frac{3}{3.75} \\ x = \frac{300}{375} \\ \\ x = \frac{4}{5} \\ \\ x = 0.8[/tex]
The solution of expression is,
⇒ x = 0.8
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 3.75x = 3
Now, We can solve the expression as;
⇒ 3.75x = 3
Divide by 3.75;
⇒ 3.75x / 3.75 = 3 / 3.75
⇒ x = 0.8
Thus, The solution of expression is,
⇒ x = 0.8
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3n-5=19
Plz give me a step by step explanation cause i already have the answer
Answer:
n=8
Step-by-step explanation:
3n-5=19
3n=19+5
3n=24
n=24/3
n=8