Answer:
B. 110
Step-by-step explanation:
In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?
A. 90
B. 110
C. 130
D. 180
Answer:
Let x represent the amount of calories in 1 servings of juice, y represent the amount of calories in 1 servings of milk and z represent the amount of calories in 1 servings of Soda.
Joe consumption can be represented by:
x + 2y + z = 530 (1)
Darius consumption can be represented by:
2x + y = 370 (2)
Marian consumption can be represented by:
3y + z = 510 (3)
The equations can be represented in matrix form as:
[tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] ^{-1}\left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\[/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0.33&0.33&-0.33\\-0.67&0.33&0.67\\2&-1&-1\end{array}\right]\left[\begin{array}{c}530\\370\\510\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}130\\110\\180\end{array}\right][/tex]
The amount of calories in one serving of milk is 110 calories
GIVING 30 POINTS
need it RN
Which equation represents a line which is perpendicular to the line
5x + 4y = -24?
The absolute value on number line
Can you guys help me find the supplements for question 6
Answer:
d
Step-by-step explanation:
i looked it up
What is the product of -3(-6r+6)
Step-by-step explanation:
-3 times -6r= 18r
-3 times 6 =-18
18r=-18
R=-1
If the answer is wrong try just 1
Answer:
0
Step-by-step explanation:
remove r first
-3(-6+6)
-3x-6= 18 -3x6|=-18
18-18=0
or
-3(-6+6)
=-3(0)
=-3x0
=0
don't forget the r you removed which equals to one
so you got 1
-3(-6r+6)=1
wish it could help
PLEASE help. Will give brainliest.
Answer:
y=5
x=10 and
z=2
Step-by-step explanation:
since they are equivalance then,
for
triangle ABC and triangle DFE
AB=DF,BC=FE and AC= DE
So, AB=DF
8y-20= 4y
or, y=5
Then, BC= FE
2x+5=x+15
or, x=10
and
AC=DE
3z+9=10z-5
or, z= 2
hope u got ut.
The triangles are parallel thus their sides are equal to each other peer to peer.
So ;
[tex]x + 15 = 2x + 5[/tex]
Subtract sides -5
[tex]x + 15 - 5 = 2x + 5 - 5[/tex]
[tex]x + 10 = 2x[/tex]
Subtract sides -x
[tex]x - x + 10 = 2x - x[/tex]
[tex]x = 10[/tex]
_________________________________
[tex]4y = 8y - 20[/tex]
Subtract sides -8y
[tex]4y - 8y = 8y - 8y - 20[/tex]
[tex] - 4y = - 20[/tex]
Negatives simplifies
[tex]4y = 20[/tex]
Divided sides by 4
[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]
[tex]y = 5[/tex]
_________________________________
[tex]10z - 5 = 3z + 9[/tex]
Plus sides 5
[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]
[tex]10z = 3z + 14[/tex]
Subtract sides -3z
[tex]10z - 3z = 3z - 3z + 14[/tex]
[tex]7z = 14[/tex]
Divided sides by 7
[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]
[tex]z = 2[/tex]
_________________________________
And we're done....♥️♥️♥️♥️♥️
Helpppppp ASAP!!!!!!!
Answer:
x=2
Step-by-step explanation:
Hi i need help on letters:
L,A,E,R,T,C,I,S,F,G,H,D,N,and O
Im giving 14 points if u answer all of them!!;)
Answer:
Step-by-step explanation:
E = 10:15 C = 4:5 F = 1:10 D = 1:2 R = 1:3 I = 30: 80 G = 16:48 N = 20: 40
A = 2:1 T = 6:10 S= 9:12 H = 9 O = 1: 11
(wouldve explained them but im in class :)
WHAT IS THE VALUE OF B helpppp plz ?
Which situations can represent the expression n+ 2? Check all that apply.
Ramya's grade increased by two points
the difference between Escher's highest score and two
the number of chapters Wally read plus two more
O two fewer than the maximum number of absences Ellie is allowed
two added to Allison's age.
the sum of Mikel's height and two
Answer:
Yes: Ramya's grade increased by two points
No: the difference between Escher's highest score and two
Yes: the number of chapters Wally read plus two more
No: O two fewer than the maximum number of absences Ellie is allowed
Yes: two added to Allison's age.
Yes: the sum of Mikel's height and two
Step-by-step explanation:
If it says yes, it is because it was adding 2. If it says no, it was either subtracting 2 or any other form of math other than adding 2.
Answer:
A,C,E,F
Step-by-step explanation:
Just shortening it up! The person above me is correct, though. Don't forget to make them brainliest (if you want to of course)! Major Big brain moment... lol!
Answer answered by Jordan
Stay Safe <3
↖(^ω^)↗
Cody has two bags of counters, bag A and bag B.Each of the counters has either an odd number or an even number written on it. There are 10 counters in bag A and 7 of these counters have an odd number written on them. There are 12 counters in bag B and 7 of these counters have an odd number written on them. Cody is going to take at random a counter from bag A and a counter from bag B.
a) Complete the tree diagram.
Harriet also has a bag of counters. Each of her counters also has either an odd number or an even number written on it. Harriet is going to take at random a counter from her bag of counters. The probability that the number on each of Cody's two counters and the number on Harriet's counter will all be even is 3/100.
b)Find the least number of counters that Harriet has in her bag.
monke monked mon key
Find the solution of the differential equation that satisfies the given initial condition. xy' + y = y2, y(1) = −5
Answer: [tex]y=\dfrac{5}{5-6x}[/tex]
Step-by-step explanation:
The given differential equation: [tex]xy' + y = y^2[/tex]
[tex]\Rightarrow\ xy'=y^2-y[/tex]
[tex]\Rightarrow\ \frac{1}{y^2-y}y'\:=\frac{1}{x}\\\\\Rightarrow\ \dfrac{1}{y(y-1)}\dfrac{dy}{dx}=\frac{1}{x}\\\\\Rightarrow\dfrac{y-(y-1)}{y(y-1)}dy=\dfrac{1}{x}dx\\\\\Rightarrow\dfrac{1}{(y-1)}dy+\dfrac{1}{y}dy=\dfrac{1}{x}dx[/tex]
Integrate both sides , we get
[tex]\int\dfrac{1}{(y-1)}dy+\int\dfrac{1}{y}dy=\dfrac{1}{x}dx\\\\\Rightarrow\ \ln(y-1)-\ln y=\ln x+c\ \ \ \ (i)[/tex]
At x=1 , y=-5 (given)
[tex]\ln(-5-1)-\ln -5=\ln 1+c\\\\\Rightarrow\ \ln (-6)-\ln(-5)=0+c\\\\\Rightarrow\ \ln(\dfrac{-6}{-5})=c\\\\\Rightarrow\ \ln(\dfrac{6}{5})=c[/tex]
[tex][\ \ln a+\ln b=\ln ab ,\ \ \ \ \ \ln a-\ln b=\ln\dfrac{a}{b}\ ][/tex]
Put value of x in (i), we get
[tex]\ln(y-1)-\ln y=\ln x+\ln (\dfrac65)\\\\\Rigtarrow\ \ln (\dfrac{y-1}{y})=\ln(\dfrac{6}{5}x)[/tex]
[tex]\Rightarrow\ 1-\dfrac{1}{y}=\dfrac{6}{5}x\Rightarrow\ \dfrac{1}{y}=1-\dfrac{6}{5}x\\\\\Rightarrow\ \dfrac{1}{y}=\dfrac{5-6x}{5}\\\\\Rightarrow\ y=\dfrac{5}{5-6x}[/tex]
hence, the required solution: [tex]y=\dfrac{5}{5-6x}[/tex]
The solution to the differential equation
[tex]xy'+y=y^2[/tex]
given the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Given the differential equation
[tex]xy'+y=y^2[/tex]
We can rearrange it as follows:
[tex]x\frac{dy}{dx}+y=y^2\\\\x\frac{dy}{dx}=y^2-y\\\\\frac{1}{y^2-y}\frac{dy}{dx}=\frac{1}{x}\\\\\frac{1}{y^2-y}dy=\frac{1}{x}dx[/tex]
Factoring the denominators of the LHS, and decomposing into partial fractions, we get
[tex]\frac{1}{y(y-1)}dy \implies \frac{1}{(y-1)}dy+\frac{1}{y}dy[/tex]
The final rearranged equation is
[tex]\frac{1}{(y-1)}dy+\frac{1}{y}dy=\frac{1}{x}dx[/tex]
Integrating both sides;
[tex]\int\frac{1}{y-1} dy +\int\frac{1}{y}dy=\int\frac{1}{x}dx\\\\ln(y-1)-ln(y)=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+c[/tex]
(We made of a law of logarithms on the last line to simplify the equation)
The initial condition [tex]y(1)=-5\implies y=-5 \text{ when }x=1[/tex]
Substituting into the general solution we got earlier
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{-5-1}{-5})=ln(1)+c\\\\ln(\frac{-6}{-5})=ln(1)+c \\\\(\text{since }ln(1)=0)\\\\ln(\frac{-6}{-5})=c\\\\ln(\frac{6}{5})=c[/tex]
Substituting the value of [tex]c[/tex] back into the general solution
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+ln(\frac{6}{5})\\\\ln(\frac{y-1}{y})=ln(\frac{6x}{5})\\\\\frac{y-1}{y}=\frac{6x}{5}[/tex]
When [tex]y[/tex] is made the subject of the formula
[tex]y=\frac{5}{5-6x}[/tex]
Therefore, the solution that satisfies the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Learn more about solving differential equations here: https://brainly.com/question/4537000
What is the difference between –12 and –5?
Answer:
-7
Step-by-step explanation:
(-12)-(-5)
negative and negative make a positive
-12+5
= -7
Answer:
-7
Step-by-step explanation:
the other one is 27
Answer:
the scale factor is 9 and x = 58.5
Step-by-step explanation:
to get the scale factor just do DE/AB so 27/3
Please help with this problem thank you.
-8 + n = 62 What is n?
Answer:
n = 70
Step-by-step explanation:
-8 + n = 62
n = 70
K^2+k=0 what does k=
Answer:
k = K^2
Step-by-step explanation:
Subtract K^2 from both sides of the equation.
CAN SOMEONE HELP ME ASP!!
The profit function, P(x) , revenue function, R(x), and cost function, C(x), are related by the equation P(x)=R(x)-C(x) . Manuel has determined that the revenue and cost functions for a new product line at his business are given by these functions. R(x)=3x C(x)=600+2x. What is the profit function in standard form for Manuel's new product line
Answer:
P(x) = 5x - 600
Step-by-step explanation:
Given
Cost function C(x) = 600+2x
revenue function R(x) = 3x
If the profit function is related by the equation
P(x)=R(x)-C(x)
P(x)= 3x - (600-2x)
open the parenthesis
P(x) = 3x - 600 + 2x
P(x) = 3x+2x - 600
P(x) = 5x-600
Hence the profit function in standard form for Manuel's new product line is P(x) = 5x - 600
A machine is used to fill 1-liter bottles of a type of soft drink. We can assume that the output of the machine approximately follows a normal distribution with a mean of 1.0 liter and a standard deviation of .01 liter. The firm uses means of samples of 25 observations to monitor the output, answer the following questions: Determine the upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control
Answer:
1.00434
Step-by-step explanation:
Given the following :
Given a normal distribution ;
Mean (m) = 1.0 liter
Standard deviation (σ) = 0.01 liter
Sample size (n) = 25
For 97% sample means (sm) = 0.97
Z = (m - sm) / s
Zcrit = 1 - (100% - 97%)/2
Zcrit = 1 - (0.03/2)
Zcrit = 1 - 0.015 = 0.985
The z score which corresponds to 0.985 = 2.17
Upper limit : m + z*(σ/√n)
Upper limit : 1.0 + 2.17*(0.01/√25)
Upper limit : 1. 0 + 2.17*(0.01/5)
= 1.0 + 2.17*0.002
= 1.0 + 0.00434
= 1.00434
Please help!
Simplify the expression using order of operations:25 - 5 + 36/9 - 6(7)
Answer:
-18
Step-by-step explanation:
Follow these steps to get your answer!
Divide 36/9 and multiply -6(7)
25 - 5 + 4 - 42
Subtract 25-5
20 + 4 -42
Add 4 to 20.
24-42
Subtract 42 from 24.
-18
Answer:
-18
Step-by-step explanation:
start with the figure in brackets. 6(7)=42
then do division. 36/9=4
our expression now is 25-5+4-42
addition first 25+4=29
finish with subtraction. 29-5-42=-18
answer=-18
3/4of 16/27/23/14+12/18 using bodmas rule
If m<3 =54°. find each measure.
Answer/Step-by-step explanation:
Given:
m<3 = 54°
m<2 = right angle
a. m<1 + m<2 + m<3 = 180° (angles in a straight line)
m<1 + 90° + 54° = 180° (substitution)
m<1 + 144° = 180°
m<1 = 180° - 144°
m<1 = 36°
b. m<2 = 90° (right angle)
c. m<4 = m<1 (vertical angles)
m<4 = 36° (substitution)
d. m<5 = m<2 (vertical angles)
m<5 = 90°
e. m<6 = m<3 (vertical angles)
m<6 = 54°
f. m<7 + m<6 = 180° (same side interior angles)
m<7 + 54° = 180° (substitution)
m<7 = 180 - 54
m<7 = 126°
g. m<8 = m<6 (alternate interior angles are congruent)
m<8 = 54°
h. m<9 = m<7 (vertical angles)
m<9 = 126°
i. m<10 = m<8 (vertical angles)
m<10 = 54°
j. m<11 = m<4 (alternate interior angles are congruent)
m<11 = 36° (substitution)
k. m<12 + m<11 = 180° (linear pair)
m<12 + 36° = 180° (substitution)
m<12 = 180° - 36°
m<12 = 144°
l. m<13 = m<11 (vertical angles)
m<13 = 36°
m. m<14 = m<12 (vertical angles)
m<14 = 144° (substitution)
HELPPPP PLZZZ ASAPPP!!!Look at the illustration of four letters from the American Manual Alphabet. Decide whether the description of the letter is a good definition. If not,
choose a counterexample.
The letter I is formed by sticking up the smallest finger and folding all the other fingers into the palm of your hand with the thumb folded over them.
The letter J is a counterexample
The letter y is a counterexample
The letter A is a counterexample
This is a good definition
while keeping your hand still
Answer: I think it’s J, because the picture is also holding the smallest finger up (the pinky) and the rest of the fingers are folded inside the palm of the hand and the thumb is folded over them, I hope this helps!!
Step-by-step explanation:
The letter J is a counter example. Option a is correct.
Letters of alphabet to be determine.
Alphabets are the sets of letters from A to Z.
Here, the little finger is up and all the finger is folded and the thumb folded over the three finger implies its 'J'.
Thus, the letter J is a counter example.
Learn more about alphabets here:
https://brainly.com/question/20261759
#SPJ2
Unit 4: Lesson 9: Parallel and Perpendicular Lines Unit Test Parallel and Perpendicular Lines does anyone have the answers for this 13 question test ??
Answer:
I need these answers and the ones he put in in the comments are all wrong
8(3x-2)-8x=9(2x-6) find x
Answer:
x=19
Step-by-step explanation:
8(3x-2)-8x=9(2x-6) Distribute.
24x-16-8x=18x-54 Combine like terms.
16x-16=18x-54 Subtract 16x from both sides (getting rid of a variable first
-16x -16x is easier).
-16=2x-54 Add 54 to both sides.
+54 +54
38=2x Divide both sides by 2.
/2 /2
19=x
Hope this helps!! Have a great day ^^
The triangular arrangement of numbers shown is known as Pascal's triangle. Use inductive reasoning to find the 6 missing numbers.
Answer:
1 5 10 10 5 1
Step-by-step explanation:
The complete question has been attached as an image.
Looking at the triangle, we see a pattern. The first level we have 1, in the next level we have 1 1, the next evel we have 1 2 1, the next level we have 1 3 3 1 and so on. From here, we see that to get the numbers of the next level, we have to write 1 as the first number, then add 1 to the next number after it in the previous level to get the second number in the next level then add the second number of the previous level to the next number beside it to get the third number in the next level and so on until you get to the last number before 1 in the previous level, add that number to 1 to get the second to the last number in the next level and finally put 1 as the last number in the next level. Now, we have
1 4 6 4 1
1 5 10 10 5 1
And that is the required set of numbers.
a positive real number is 2 more than another. if the sum of the squares of the two numbers is 14, find the numbers
9514 1404 393
Answer:
√6 -1 ≈ 1.44949√6 +1 ≈ 3.44949Step-by-step explanation:
Let x represent the smaller number. Then the sum of squares is ...
x² +(x+2)² = 14
2x² +4x +4 = 14 . . . eliminate parentheses
2x² +4x -10 = 0 . . . put in standard form
x² +2x -5 = 0 . . . . . divide by 2 (because we can)
(x +1)² -6 = 0 . . . . . complete the square
x +1 = √6 . . . we want the positive root
x = -1 +√6
x+2 = 1 +√6
The numbers are √6±1.
What is the answer for 8
Answer:
no they share the same y value for two different x values
H-4/x =y solve for x
Answer:
x - 1
Step-by-step explanation:
the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate is the base b(t) chaging when the height h=15cm and the area A= 130cm2
Answer:
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
Step-by-step explanation:
From Geometry we understand that area of triangle is determined by the following expression:
[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (Eq. 1)
Where:
[tex]A[/tex] - Area of the triangle, measured in square centimeters.
[tex]b[/tex] - Base of the triangle, measured in centimeters.
[tex]h[/tex] - Height of the triangle, measured in centimeters.
By Differential Calculus we deduce an expression for the rate of change of the area in time:
[tex]\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}[/tex] (Eq. 2)
Where:
[tex]\frac{dA}{dt}[/tex] - Rate of change of area in time, measured in square centimeters per minute.
[tex]\frac{db}{dt}[/tex] - Rate of change of base in time, measured in centimeters per minute.
[tex]\frac{dh}{dt}[/tex] - Rate of change of height in time, measured in centimeters per minute.
Now we clear the rate of change of base in time within (Eq, 2):
[tex]\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}[/tex]
[tex]\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}[/tex] (Eq. 3)
The base of the triangle can be found clearing respective variable within (Eq. 1):
[tex]b = \frac{2\cdot A}{h}[/tex]
If we know that [tex]A = 130\,cm^{2}[/tex], [tex]h = 15\,cm[/tex], [tex]\frac{dh}{dt} = 2.5\,\frac{cm}{min}[/tex] and [tex]\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}[/tex], the rate of change of the base of the triangle in time is:
[tex]b = \frac{2\cdot (130\,cm^{2})}{15\,cm}[/tex]
[tex]b = 17.333\,cm[/tex]
[tex]\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)[/tex]
[tex]\frac{db}{dt} = -2.262\,\frac{cm}{min}[/tex]
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
A human gene carries a certain disease from the mother to the child with a probability rate of 39%. That is, there is a 39% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. Round to the nearest thousandth.
Answer:
[tex]Probability = 0.023[/tex]
Step-by-step explanation:
Given
Represent the given probability with P(Gene)
[tex]P(Gene) = 39\%[/tex]
[tex]Children = 4[/tex]
Since all 4 children get the disease, the required probability is calculated as thus:
[tex]Probability = P(Gene)^4[/tex]
[tex]Probability = 39\%^4[/tex]
Convert % to decimal
[tex]Probability = 0.39^4[/tex]
[tex]Probability = 0.02313441[/tex]
[tex]Probability = 0.023[/tex] Approximated
What is the length of a segment with endpoints at F(6, 4) and G(14, 19)? Round to the nearest whole number.
Answer:
17
Step-by-step explanation:
d = √( (x₂ - x₁)² + (y₂ - y₁)² )
= √( (14 - 6)² + (19 - 4)² )
= √( 8² + 15² )
= √( 64 + 225 )
= [tex]\sqrt{289}[/tex]
= 17