Given:
Two small pizzas, a liter of soda, and a salad costs $14.
One small pizza, a liter of soda, and three salads costs $15.
Three small pizzas, a liter of soda, and two salads costs $22.
To find:
The cost of each item.
Solution:
Let x be the cost of a small pizza.
y be the cost of a liter of soda
z be the cost of a salad.
According to the question, two small pizzas, a liter of soda, and a salad costs $14.
[tex]2x+y+z=14[/tex] ...(i)
One small pizza, a liter of soda, and three salads costs $15.
[tex]x+y+3z=15[/tex] ...(ii)
Three small pizzas, a liter of soda, and two salads costs $22.
[tex]3x+y+2z=22[/tex] ...(iii)
From (i), we get
[tex]z=14-2x-y[/tex] ...(iv)
Putting [tex]z=14-2x-y[/tex] in (ii), we get
[tex]x+y+3(14-2x-y)=15[/tex]
[tex]x+y+42-6x-3y=15[/tex]
[tex]-5x-2y=15-42[/tex]
[tex]-(5x+2y)=-27[/tex]
[tex]5x+2y=27[/tex] ...(v)
Putting [tex]z=14-2x-y[/tex] in (iii), we get
[tex]3x+y+2(14-2x-y)=22[/tex]
[tex]3x+y+28-4x-2y=22[/tex]
[tex]-x-y=22-28[/tex]
[tex]-(x+y)=-6[/tex]
[tex]x+y=6[/tex]
Multiply both sides by 2.
[tex]2x+2y=12[/tex] ..(vi)
Subtracting (vi) from (v), we get
[tex]5x+2y-2x-2y=27-12[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
Putting x=5 in (vi), we get
[tex]2(5)+2y=12[/tex]
[tex]10+2y=12[/tex]
[tex]2y=12-10[/tex]
[tex]2y=2[/tex]
[tex]y=1[/tex]
Putting x=5 and y=1 in (iv), we get
[tex]z=14-2(5)-(1)[/tex]
[tex]z=14-10-1[/tex]
[tex]z=3[/tex]
So, [tex]x=5,y=1,z=3[/tex].
Therefore, the cost of a pizza is $5, cost of a liter of soda is $1 and cost of salad is $3.
The point (-3, 8) is translated using the rule (x + 5, y - 7). The new point is (____).
O (2, 1)
O (8,1)
O (-2, 15)
0 (-8, 1)
Answer:
(2, 1)
Step-by-step explanation:
You add 5 to the x coordinate, which is -3 and you get 2. Then add -7 to the y coordinate, which is 8 and get 1
Answer:
(2, 1)
Step-by-step explanation:
(x + 5, y - 7), (-3, 8)
(- 3 + 5, 8 - 7) = (2 + 1)
Thus, The new point is (2 + 1).
-TheUnknownScientist
4x + 2y = 32
5x - 2y = 31
Answer:
Step-by-step explanation:
-8x-y=16;3x-y=5 | | x-y=11;2x+y=4 | | -8x-8=-40y;50y-10=10x | | 0=-11y+8x+33;-1+4/9x+1/3y=0 | | 0=-16+4x+4y;0=28-7y+7x | | 3x-y=9;-3x+y=-9 | | -4x+y=8;4x-y=8 | | x=2y-8;-2x+3y=14 | | y=2x;y=2x-3 | | x-3y=2;7x+y=36 | | 2x+5y=16;2x+3y=8 | | 2c+5p=16;2c+3p=8 | | x/5;7/4 | | -(x-2)=3(y+1);2x+3=4y-1 | | 4x-12y=17;2x+6y=1 | | 1A+4C=85;3A+2C=105 | | 2x-11y=7;3x-9y=7 | | 40-2x;X=3 | | x+y=220;2x+4y=520 | | 3p+2b=29;5p+3b=47.50 | | 4x+2y=23.50;2x+4y=18.50 | | t=2r+3;5r-4t=6 | | x+y=5157.50;y-x=917.50 | | x+y=177;x=97 | | x+y=55;x+10=181 | | x+y=10;x-y=4 | | 1/5x+1/3y=14/15;1/5x+4y=78/5 | | 8x+16y=3520;-8x-8y=2560 | | 1/25x-1/100y=7/5;1/4x+4/25y=66/5 | | -2x+5y=5;-4x+10y=0 | | 1/2x+1/3y=-5/3;1/2x+4y=2 |
| 3x+2y=-3;x=21-8y | | 5x-y=27;x+y=9 | | 36x-4y=16;y=9x+4 | | -15x-10y=1;15y=1+10x | | 3x+7y=9;x=2-2y | | 2x+y=8;y=2x | | x-2y=10;x | | x+y=2;x-y=2 | | 7x-y=27;9x-4y=3 | | x+y=480;x-y=400 | | 3x+2y=78.39;2x+3y=74.61 | | 11x+15y=6912;-11x-11y=-6336 | | 1.6x+1.6y=160;x-y=10 | | y=-1/2x-5;6x-2y=24 | | x+y=4;y-x=4 | | 5x=22-y;7x=35+2y | | 3x=12+2y;-6/5x+y=-9/5 | | 3x+2y=0;12x+2=6y | | 2x-5y=-9;5x+2y=50 | | x+y=4;x+y=-2 | | 7x-y=41;x+5y=47 | | 2x-y=7;9y=2x-31 | | x+y=11;6x-y=10 | | 0.1x+0.5y=-0.8;0.8x-0.6y=7.4 | | 1/3x+1/2y=1/6;1/3x+2y=5/3 | | 16x-10y=4;8x=5y+2 | | 15x-20y=7;10y=-3+5x | | x=5y-5;-2x+10y=10 | | 5x-27=-y;4x-y=0 | | 5x-27=-1y;4x-1y=0 | | 4x+5y=3;x=3-2y | | 6x+2y=10;12x+4y=21 | | x+y=5;3x+2y=10 | | -12x+14z=-14;-14x-14z=98 |
Find the greatest common factor of 6 and 35
Answer:
6
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Lisa has scored 24, 21, and 20 points in her three basketball games so far. How many points does she need to score in her next game so that her average
(mean) is 21 points per game?
Explanation
Check
She needs to score AT LEAST 19 points
Step-by-step explanation:
24 + 21 + 20 + 19 = 84
84 ÷ 2 = 21
which of the following graph represents the solution set for 5x+38 ≤ 4(2-5x)
Answer:
Option C
Step-by-step explanation:
Given inequality is,
5x + 38 ≤ 4(2 - 5x)
5x + 38 ≤ 8 - 20x [Distributive property]
5x + 20x + 38 ≤ 8 - 20x + 20x [By adding 20x on both the sides of the inequality]
25x + 38 ≤ 8
(25x + 38) - 38 ≤ 8 - 38 [By subtracting 38 on both the sides of the inequality]
25x ≤ -30
[tex]\frac{25x}{25}\leq -\frac{30}{25}[/tex] [Dividing by 25 on both the sides of the inequality]
x ≤ 1.2
Therefore, Option (C) will be the correct graph.
what is the midpoint of the segment shown below ?
helpppppppp meeeeeeee
Answer:A
Step-by-step explanation:
There is a proportional relationship between time in hours and time in days.
A. What is the constant of proportionality?
B. what equation describes this relationship?
Of the proportional relationship between time in hours and time in days, we have that:
a) The constant of proportionality is 24.
b) The equation is [tex]h = 24d[/tex].
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:[tex]y = kx[/tex]
In which k is the constant of proportionality.Item a:
A day has 24 hours, hence the constant of proportionality is 24.
Item b:
Considering the time in hours as the output and the time in days as the input, the equation is:
[tex]h = 24d[/tex]
You can learn more about proportional relationships at https://brainly.com/question/25815502
in a cookie recipe 1 and 2/3 cups milk makes 16 cookies. How many cups of needed to make 24 cookies
Answer:
2 1/2 or 5/2 cups of milk
Step-by-step explanation:
if 16 cookies are made from 1 2/3 cups of milk which equals 5/3 cups of milk that means that you need 5/2 or 2 1/2 cups of milk to make 24 cookies because you need to multiply 5/3 by 16 and then multiply 5/48 by 24 which is 5/2 or 2 1/2 cups of milk
A wizard-in-training has 300 grams of 20% liquid-gold solution. He wishes to drain some and replace it with an 80% solution, so that he gets 300 grams of 35% solution. How many grams should the wizard drain and replace with 80% solution?
Answer:
it would take 4 grams. I hope this helps
Answer:
75 grams! hope this helps :3
A card is randomly selected out of a standard 52 deck of cards. What is the probability of selecting a queen or a
heart?
Leave your answer as a fraction in lowest terms
The radius of a ball is 7 inches. What is the approximate surface area of the ball? Round to the nearest tenth and use
3.14 fors
Recall the formula SA-4.
O 87.9 square inches
O 175.8 square inches
O 196 square inches
O 615.4 square inches
Answer:
615.832in^2
Step-by-step explanation:
Step one:
given
The radius of a ball is 7 inches.
Required:
the surface area of the ball
Step two:
the formula for the surface area is
SA= 4πr^2
substitute
[tex]SA=4*3.142*7^2\\\\SA= 4*3.142*49\\\\SA=615.832 in^2\\\\[/tex]
rename the fraction 2/5 using tenths and hundredths
Answer:
20/50
Step-by-step explanation:
i think
Write an integer for: A bank deposit of $175
Answer:
175
Step-by-step explanation:
A deposit is adding money to the bank, so the integer will be positive.
That makes our integer: 175
"Individuals, cultures, societies, and the world change through times of conflict and cooperation."
The statement above exemplifies the era of global expansion and encounter. What other word also reflects this theme?
Technology
Trade
Monopoly
Hegemony
Rosalita is making chocolate chip cookies. She needs 20 ounces of
chocolate chips. She has
2 1/4 pounds of chocolate chips. There are 16 ounces in 1 pound. How
many ounces of chocolate chips will Rosalita have left after she makes her
cookies?
A box of 6 glue sticks costs $8.95. How much will it cost to buy 5 glue sticks?
Can anyone solve this? If so tell me and make sure u know what ur doing please
Answer:
-2
Step-by-step explanation:
To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be using the points (-3, 2) and (-1, -2).
[tex]\frac{rise}{run}[/tex] = [tex]\frac{-2-2}{-1-(-3)}[/tex]
= [tex]\frac{-2-2}{-1+3}[/tex]
= [tex]\frac{-4}{2}[/tex]
= -2
The difference between teenage female and male depression rates estimated from two samples is 0.08. The estimated standard error of the sampling distribution is 0.04. what is the 95% confidence interval? Use the critical value z - 1.96.
Round all calculations to two decimal places. Put lower bound in the first box and upper bound in the second box.
Answer: (0.0016, 0.1584)
Step-by-step explanation:
Given that:
Mean (m) = 0.08
Standard Error = 0.04
Zcritical at 95% = 1.96
Using the relation :
Mean ± Zcritical * (standard error)
0.08 ± 1.96 * (0.04)
Lower boundary = 0.08 - (1.96 * 0.04)
Lower boundary = 0.08 - 0.0784 = 0.0016
Upper boundary = 0.08 + (1.96 * 0.04)
Upper boundary = 0.08 + 0.0784 = 0.1584
Confidence interval is Hence,
(0.0016, 0.1584)
The 95% confidence interval is given by (0.0016 , 0.1584) and this can be evaluated by using the mean and standard error relation.
Given :
The difference between teenage female and male depression rates estimated from the two samples is 0.08.The estimated standard error of the sampling distribution is 0.04.The critical value z = 1.96.95% confidence level.To determine the 95% confidence interval using the following relation:
[tex]\rm \mu \pm z_{critical}\times standard \;error[/tex]
[tex]0.08\pm 1.96\times 0.04[/tex]
So, the lower and upper boundary is (0.0016 , 0.1584).
Therefore, the 95% confidence interval is given by (0.0016 , 0.1584).
For more information, refer to the link given below:
https://brainly.com/question/16555520
Identify a diameter of circle E.
Answer: B) HI
Step-by-step explanation:
the polygons in each pair are similar. find the missing side length
Answer:
Can you add a picture?
Express (x+9)^2(x+9)
2
as a trinomial in standard form.
Given:
[tex](x+9)^2[/tex]
To find:
The given expression as a trinomial in standard form.
Solution:
We have,
[tex](x+9)^2[/tex]
Using the formula, [tex](a+b)^2=a^2+2ab+b^2[/tex], we get
[tex](x+9)^2=x^2+2(x)(9)+(9)^2[/tex]
[tex](x+9)^2=x^2+18x+81[/tex]
Standard form a trinomial is [tex]ax^2+bx+c[/tex].
[tex]x^2+18x+81[/tex] is in the standard form.
Therefore, the required expression is [tex]x^2+18x+81[/tex].
A cell phone is plugged in to be charged. The table shows the percent of battery power at some times
after it was plugged in.
Time
Percent charged
6:00 pm
2%
6:15 pm
10%
6:35 pm
21%
7:05 pm
38%
At what time will the battery be 100% charged? Use the data to find out and explain or show your
reasoning
Answer:7:45
Step-by-step explanation:
Muffins are sold in packages of 18. Select the expressions that can represent the total number of muffins in p packages of muffins.
A. 18 + p
B. 18 × p
C. 18 – p
D. 18 ÷ p
E. 18p
If 3/4 = x/8 then x is equal to what
Answer:
x is 6
Step-by-step explanation:
3/4 * x/8
3*8=24 then,
divide by 4 which gives you 6.
Also if you simplify 6/8, it will give you 3/4.
Answer:
6 =x
Step-by-step explanation:
g If the p-value for your test statistic in a test of hypothesis (for example, a t-test, one-tail) is 0.07 and the significance level alpha is set at 0.05, you conclude that: Both hypotheses H0 and H1 can be accepted The null hypothesis H0 cannot be rejected The null hypothesis H0 can be rejected The research hypothesis H1 can be accepted
Complete Question
If the p-value for your test statistic in a test of hypothesis (for example, a t-test, one-tail) is 0.07 and the significance level alpha is set at 0.05, you conclude that:
A
Both hypotheses H0 and H1 can be accepted
B
The null hypothesis H0 cannot be rejected
C
The null hypothesis H0 can be rejected
D
The research hypothesis H1 can be accepted
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The p-value is [tex]p-value = 0.07[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally given that it is a one tail test then the possible value of
The null hypothesis is [tex]H_o : \mu = x[/tex]
Here [tex]\mu[/tex] is the mean and x is the value
the possible values of the alternative hypothesis is [tex]\mu > x \ \ or \ \ \mu < x[/tex]
Now from the value given we see that the [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
Determine a constant in 9x + 4y -13.
A) -13
B) 9x
C) 4y
Help me please i beed this now
Answer:
well 5% of 600 is 30. so if you make 600 phone calls and an average of 5% of those calls are people signing up, then that would be 30.
EC - The ratio of three numbers is 2:7:1.
The sum of the numbers is 30. What are the
three numbers?
Answer: 6, 21, 3
Step-by-step explanation:
2:7:1
Also, 2x 7x and 1x or just x
2x+7x+x = 30
10x = 30
x=3
So the three numbers: 2(3):7(3):1(3) OR 6:21:3
Some plz help it’s for all of them
Answer:
a is 0,4
Step-by-step explanation:
Answer:
A) 4,0
G) 1,4
Q) 0,-4
N) -4,-3