A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.
Which equation can be used to determine the amount of cherry juice in each mixture?
5q + 3(8 – q) = 36
5q + 3(8 – q) = 8
q + (8 – q) = 8
q + 5 = 5q
Answer:
I think 5q+3(8-q) =36 is the answer for this question
Based on the amount the restaurant manager spends on the juice mixture, the amount of cherry juice can be found as 5q + 3(8 – q) = 8.
What is the amount of cherry juice used?Assuming the cherry juice is q and the lime juice is r, the following formulas would be true:
q + r = 8
5q + 3r = 36
The first equation can be rewritten as:
q + r = 8
r = 8 - q
Using substitution into the second formula we get:
5q + 3r = 36
5q + 3(8 - q) = 36
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A block is being dragged along a horizontal surface by a constant horizontal force of size 45 N. It covers 8 m in the first 2 s and 8.5 m in the next 1 s. Find the mass of the block.
Answer: 15kg
Can anyone please explain this sum with proper working?
Answer:
Solution: To determine mass of the block we can use second Newton' law \vec F=m\vec a
F
=m
a
. The force and acceleration according the problem is directed along a horizontal surface, and we can omit the vector sign in Newton's law. The force we know F=45NF=45N, thus we should deduce the acceleration. The problem does not specify the initial speed at which time began to count, so for the first time interval, we may write the kinematics equation in the form
(1) S_1=v_1\cdot t_1+a\frac {t_1^2}{2}S
1
=v
1
⋅t
1
+a
2
t
1
2
, where S_1=8m, t_1=2s S
1
=8m,t
1
=2s , other quantities we don't know. The similar equation we can write for next time interval
(2) S_2=v_2\cdot t_2+ a\frac{t_2^2}{2}S
2
=v
2
⋅t
2
+a
2
t
2
2
. where S_2=8.5m, t_2=1s S
2
=8.5m,t
2
=1s
Note that during the first time interval, the speed of the block increased in accordance with the law of equidistant motion and it became the initial speed of the second interval, i.e.
(3) v_2=v_1+a\cdot t_1v
2
=v
1
+a⋅t
1
Substitute (3) to (2) we get
(4) S_2=(v_1+a\cdot t_1)\cdot t_2+ a\frac{t_2^2}{2}=v_1\cdot t_2+a\cdot t_1\cdot t_2+a\frac{t_2^2}{2}S
2
=(v
1
+a⋅t
1
)⋅t
2
+a
2
t
2
2
=v
1
⋅t
2
+a⋅t
1
⋅t
2
+a
2
t
2
2
From equation (1) and (4) we can exclude unknown quantity v_1v
1
, then remain only one unknown aa. For determine aa we dived (1) by t_1t
1
, (4) by t_2t
2
to find the average speed at time intervals and subtract (1) from (4).
(5) \frac {S_2}{t_2}-\frac {S_1}{t_1}=v_1+a\cdot t_1 +a\frac {t_2}{2}-(v_1+a\frac{t_1}{2})=a\frac{t_1+t_2}{2}-
t
2
S
2
−
t
1
S
1
=v
1
+a⋅t
1
+a
2
t
2
−(v
1
+a
2
t
1
)=a
2
t
1
+t
2
− For acceleration we get
(6) a=2\cdot ( {\frac{S_2}{t_2}-\frac{S_1}{t_1})/(t_1+t_2)}=2\cdot \frac{(8.5m/s-4m/s)}{3s}=3ms^{-2}a=2⋅(
t
2
S
2
−
t
1
S
1
)/(t
1
+t
2
)=2⋅
3s
(8.5m/s−4m/s)
=3ms
−2
For mass from second Newton's law we get
(7) m=\frac{F}{a}=\frac{45N}{3ms^{-2}}=15kgm=
a
F
=
3ms
−2
45N
=15kg
Answer: The mass of the block is 15 kg
FOR BRAINLIEST ANSWER THIS ASAP
Write an equation for the line. Write it in the form: Ax + By = C 14 ) Through——————— (4, - 2) and (5, 1)
Answer:
-3x + y = -14
Step-by-step explanation:
m = 3/1 = 3
1 = 15 + b
b = -14
Y = 3x - 14
-3x + y = -14
Determine whether ABC are functions:
A. (2,5) (3,7) (-1,4) (0, 6)
B.(-3, 1) (4, 2) (5,-2) (-3,-1)
C. (3,4) (-4, 6) (-1,0) (0,1)
A.
B.
C.
Answer:
A. Function
B. Not a function
C. function
if a line crosses the negative y-axis and the negative x-axis, then its slope is
Answer:
that description would produce a negative slope..
see image
Step-by-step explanation:
If a=(2x-5) and b=(2x+5),show that ab+25 -------- =x square 4
Step-by-step explanation:
Answer with explanation is in the attachment
Hope my answer is helpful to you
state the dimensions of the matrix. identify the indicated element
Answer:
D; 2 * 3; -4
Step-by-step explanation:
The dimension of the matrix refers to the number of elements in a row multiplied by the number of elements is a column
In a row, we have 2 elements, in a column , we have 3 elements
So the matrix is of 2 * 3 dimension
a21, refers to the element in the matrix that is in the row 2 column 1 and that is -4
1. What is the sum of 3/4 and 4/5?
En un triángulo ABC, se traza la mediana BM, si AM = 5x - 4 y MC = 3x + 6. Calcula AC.
A) 5 B) 7 C) 14 D) 21 E) 42
Answer:
A) 5
Step-by-step explanation:
Determine whether the equation represents direct, inverse, joint, or combined variation.
y = 4x^3z^3
May someone explain to me how to do this?
Answer:
All you gotta do is go to "desmos" and type in all of the 4 solutions. A, B, C, and D. and see which answer matches the graph
Step-by-step explanation:
Work out 8^1/3 divide by 5^-2
Answer:
66.6666666667
Step-by-step explanation:
answer is 66.6666666667
The solution of the division of 5⁻² by 8^(1/3) will be 50.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given numbers will be solved as:-
Division = ( 8 ^ (1/3) / 5⁻²
Division = 2 x5²
Division = 50
Therefore, the solution of the division of 5⁻² by 8^(1/3) will be 50.
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HELP ASAP ILL GIVE BRAINLIST
Imagine that your best friend missed the lesson on how to solve a system of equations using the substitution method. You want to help him or her catch up in their math class, so you decide to write an e-mail describing what they missed. Write an email to your friend including:
An explanation of what a system of equations is
A general description of how to use the substitution method
An example of a system of equations
Your solution steps and explanations including the substitution method
Your final answer for the system
I'm just going to start writing the email XD (btw, bold = non-email parts/me talking)
Hey (Friend name),
You kinda missed math the other day, and being the nice friend I am, I decided to catch you up on what we learned.
We learned how to solve a system of equations using the substitution method.
A system of equations is a set of two or more equations with common variables. We use those two equations to solve for the variables.
One example might be:
3x+y=3
4x+3y=10
Solving each of these two equations by themselves would be impossible, so this is where the substitution method comes in.
Solving by substitution means that you first solve one equation for a variable, and then you substitute the value of that variable into the other equation. You might understand better if you see how I use this method to solve the previous system.
Step 1: Solve for y.
3x+y=3
Subtract 3x from each side.
y=3-3x
Step 2: Use the substitution method (plug in the y value).
4x+3y=10
4x+3(3-3x)=10
See how we plugged in the right side of the equation that is equal to y? Now only the x variable is left and we can easily solve it!
Step 3: Simplify to get x.
4x+9-9x=10
-5x=1
x=-1/5
Step 4: Use the substitution method AGAIN (for the y).
Now we plug in the x value into the equation for y.
y=3-3x
y=3-3(-1/5)
y=3-(-3/5)
y=18/5
The final answer is x=-1/5, y=18/5.
As you can see, using the substitution method to solve two impossible equations is how we can get the values of the variables they share! It's simple, quick, and easy!
Sincerely,
(your name)
I hope this helped! :D
Explain this to me I don't understand
Answer:
26.124
Step-by-step explanation:
SOH CAH TOA
tan 43 = about 0.933
than times it by 28 and get
26.124
Find x.
a. 30.9
b. 34.4
c. 17.1
d. 15.4
Answer:
x = 17.1
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 42 = x/23
23 cos 42 = x
17.09233 =x
Rounding to 1 decimal place
x =17.1
Please help!!!
What is the measure of
Does the graph have even symmetry, odd symmetry, or neither ?
Answer:
Odd symetry I think
Step-by-step explanation:
Sorry I'm new can you be my friend too please?
Hope this helps!:)
Have a nice day.
Keep scrolling for more....
Have a great day
You can do anything you put your mind to
^_^
:)
This is it
If triangle LMQ is similar to triangle LNP, calculate the length of segment LP.
Answer:
LP = 15
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{LM}{LN}[/tex] = [tex]\frac{LQ}{LP}[/tex] , substitute values
[tex]\frac{4}{10}[/tex] = [tex]\frac{LQ}{LQ+QP}[/tex]
[tex]\frac{2}{5}[/tex] = [tex]\frac{LQ}{LQ+9 }[/tex] ( cross- multiply )
5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )
3LQ = 18 ( divide both sides by 3 )
LQ = 6
Then
LP = LQ + QP = 6 + 9 = 15
Solve for ppp. 16-3p=\dfrac23p+516−3p= 3 2 p+516, minus, 3, p, equals, start fraction, 2, divided by, 3, end fraction, p, plus, 5 p=p=p, equals
Given:
The given equation is:
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
To find:
The value of p.
Solution:
We have,
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
Multiply both sides by 3.
[tex]3(16-3p)=3\left(\dfrac{2}{3}p+5\right)[/tex]
[tex]48-9p=2p+15[/tex]
Isolating the variable terms, we get
[tex]48-15=2p+9p[/tex]
[tex]33=11p[/tex]
Divide both sides by 11, we get
[tex]\dfrac{33}{11}=p[/tex]
[tex]3=p[/tex]
Therefore, the required solution is [tex]p=3[/tex].
Answer:
p=3
Step-by-step explanation:
i got it right on khan
tanA × cosecA = secA
Step-by-step explanation:
L.H.S
tanA * cosecA
=sinA/cosA * 1/sinA
now cancel sinA and sinA
then,
1/cosA
= secA
= RHS
hence proved
can someone help me with the question?
Can someone help me with this math homework please!
Answer:
Below
Step-by-step explanation:
From the graph the first local minimum is -16.18
The local maximum is 3.75
The second local minimum is -3.
Answer:
Over the interval (-3,0), the local minimum is -16.18Over the interval [0,3], the local maximum is -3.75Over the interval [0,3], the minimum is -3----------------------
Hope it helps..
Have a great day!!
Given that $x < 5$, rewrite $5x - |x - 5|$ without using absolute value signs. WILL GIVE BRAINLIEST
Answer:
6x-5 if x<5
Step-by-step explanation:
If x<5, then x-5<0.
If x-5 is negative, then |x-5)=-(x-5) or -x+5.
5x - |x - 5|
5x-(-x+5) provided x<5
5x+x-5 by distributive property
6x-5 combined liked terms
Will Mark brainlest help please please pease
Answer:
6
Step-by-step explanation:
very easy.
this simply means what is the value of x, so that the result of the function is 7.
remember, the domain is the interval of valid values for x.
and the range is the interval of valid values of y (or functional results).
so,
7 = (3x - 4)/2
14 = 3x - 4
18 = 3x
x = 6
so, for x = 6 the function delivers 7 as result.
use the figure on the Pythagorean theorem to write an equation relating H, D and x
Answer:
h² + x² = d²
Step-by-step explanation:
h and x are legs. d is the hypotenuse.
h² + x² = d²
Suppose the group of 15 people consists of 7 men and 8 women. How many 6 person teams contain at most 3 men?
Answer:
3850 of those 6 person teams contain at most 3 men.
Step-by-step explanation:
The order in which the people are selected is not important, which means that the combinations formula is used to solve this question.
It drove 30.08 kilometers in an hour.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
0 men:
6 women from a set of 8. So
[tex]C_{8,6} = \frac{8!}{2!6!} = 28[/tex]
1 men:
5 women from a set of 8
1 men from a set of 7. So
[tex]C_{8,5}C_{7,1} = \frac{8!}{3!5!} \times \frac{7!}{1!6!} = 392[/tex]
2 men:
4 women from a set of 8
2 men from a set of 7. So
[tex]C_{8,4}C_{7,2} = \frac{8!}{4!4!} \times \frac{7!}{2!5!} = 1470[/tex]
3 men:
3 women from a set of 8
3 men from a set of 7. So
[tex]C_{8,3}C_{7,3} = \frac{8!}{5!3!} \times \frac{7!}{3!4!} = 1960[/tex]
How many 6 person teams contain at most 3 men?
28 + 392 + 1470 + 1960 = 3850
3850 of those 6 person teams contain at most 3 men.
please me in the math
Find the H.C.F
[tex] {x}^{2} - 4 \\ {x}^{3} + 8 \\ {x}^{2} + 5x + 6[/tex]
it so simple
Step-by-step explanation:
Solution
First equation x ² - 4
= (x+2) (x-2)
Second equation = x ³ +8 + = x³+2^3
= (x-2) (x² + x₁2 +2²) = (x-2) (x² + 2x+4)
3 Third equation = x ² + 5x + 6
= x² + 6x= x +6 = x(x+6)-1(x+6)
(x-1) (x+6)
H.C. F= x-2
what's is 11 divided by 620
Answer:
0.017741
Step-by-step explanation:
7. La somme de deux multiples de 3 consécutifs est de 129. Quels sont ces deux nombres?
Answer:
Les deux nombres doivent avoir une différence de 3. Algébriquement, ce serait x + (x + 3) = 129. 2x est alors égal à 126. X est égal à 63 et x + 3 est à 66. Ces nombres sont des multiples consécutifs de 3 dont la somme est de 129.
Step-by-step explanation:
The two numbers must have a difference of 3. Algebraically, it would be x + (x + 3) = 129. 2x then is equal to 126. X equals 63 and x + 3 is 66. These numbers are consecutive multiples of 3 whose sum is 129.
Find the measure of the missing angle using the triangle angle sum theorm.
Answer:
65°
Step-by-step explanation:
The sum of angles in a triangle =180
53°+62°+?°=180°
115°+?°=180°
?°=180°-115°
Rate the answer If you love everything I did n explanation
Answer:
65 degrees
Step-by-step explanation:
Angles in a triangle add up to 180, so 180 - 53 - 62 = 65.
