The sack of food Costs $300 for dogs and $250 for cats.
The unknown quantities. the cost of a bag of dog food as "x" and the cost of a bag of cat food as "y".
Based on the given information, we can establish the following equations:
2x + 6y = 2100 (equation 1)
5x + 2y = 2000 (equation 2)
Now, we can solve the system of equations using methods such as substitution or elimination.
One way to solve it is to multiply equation 2 by 3 and equation 1 by 5 to match the coefficients of "y" and then subtract the equations:
15x + 6y = 6000 (equation 3)
-10x - 30y = -10500 (equation 4)
By adding equations 3 and 4, we get:
15x + 6y - 10x - 30y = 6000 - 10500
5x - 24y = -4500 (equation 5)
Now, we can solve equation 5 to obtain the value of "x":
5x = 24y - 4500
x = (24y - 4500) / 5
Next, we can substitute this expression for "x" into one of the original equations to solve for "y". Let's use equation 1:
2((24y - 4500) / 5) + 6y = 2100
Now, we can simplify and solve for "y":
(48y - 9000) / 5 + 6y = 2100
48y - 9000 + 30y = 10500
78y = 19500
y = 250
Therefore, the cost of a bag of cat food is $250.
Substituting this value back into equation 1, we can solve for "x":
2x + 6(250) = 2100
2x + 1500 = 2100
2x = 600
x = 300
Hence, the cost of a bag of dog food is $300.
Therefore, the sack of food costs $300 for dogs and $250 for cats.
To know more about Costs .
https://brainly.com/question/29803968
#SPJ8
The product of a real number and another real number that is 6 less than the first equals 6. What are the numbers?
Answer:
\(3+\sqrt{15} \\3-\sqrt{15}\\\)
Step-by-step explanation:
if ax=6 and a = x-6...
x(x-6) = 6
Completing the square is a process such that \((x^2+2bx)=(x+b)^2-b^2\)
HELP PLEASE I DONT GET THIS
so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.
we have a line passing through (-6,0) and (0,8), side one
we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two
we have a line passing through (0,-4) and (6,4), side three
now, side four is simply the line connecting one and three.
the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?
well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.
\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)
\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)
\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)
\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)
now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to (-3 , 4). Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.
now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality
\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)
Match the property with the statement.
Transitive property of
equality
Division property of
equality
Angle congruence postulate
Subtraction property of
equality
Symmetric property of
equality
Reflexive property of
equality
1. If 7 = x then x = 7
2. p=p
3. If a = 7, a = q. q =s and s = t, then t
= 7
4. if 3x = 9 then x = 3
5.
6. 4x + 2=6 then 4x = 4
The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.
what is angle ?Two straight lines or rays intersect at a common endpoint to form an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner." Two rays (half-lines) combined into an angle have a single endpoint. The latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms. Two lines converge at a common point to form an angle.
given
The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .
The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.
The equality's subtraction property states that if 3x = 9 then x = 3.
The premise of angle congruence is Since x = 7 if 7 = x
To know more about angle visit :-
https://brainly.com/question/28451077
#SPJ1
i have no idea how to do this
A scale drawing for an apartment is shown below. In the drawing, 3cm represents 4cm. Assuming the bedroom is rectangular, find the area of the real room
The calculated value of the area of the real room is 10.67 cm²
Finding the area of the real roomFrom the question, we have the following parameters that can be used in our computation:
In the drawing, 3cm represents 4cm
This means that
Scale factor = 4/3
Also, we have the dimension of the scale drawing to be
Dimension = 3cm by 2 cm
So, the area of the bedroom in the scale is
Area = 3cm * 2cm
For the actual room, we have
Area = 3cm * 2cm * (4/3)²
Evaluate the exponent
Area = 3cm * 2cm * (16/9)
Evaluate the products
Area = 10.67 cm²
This means that the real area is 10.67 cm²
Read more about scale factor at
https://brainly.com/question/29229124
#SPJ1
3/4 is 60% of what number?
3/4 is 60% of 45.
\( \frac{60}{1} \)
\( \frac{3 \times 60}{4 \times 1 } = \frac{180}{4} \)
\( \frac{180}{4} = 45 \\ \frac{4}{4} = 1\)
\( \frac{45}{1} = 45\)
Answer:
10/8 or 1.25
Step-by-step explanation:
We can write this into an equation to help us understand what we need.
3/4=0.60x
We can make these both into fractions to make it easier.
3/4=6/10x
Divide both sides by 6/10, or multiply both sides by 10/6.
3/4×10/6=30/24=10/8=1.25
10/8=x
The graph of a function f is given. Use the graph to estimate the following.
Local maximum: (-6, 8)
Local maximum: (6, 3)
Local minimum: (0, -2)
Local minimum: (9, 2)
Increasing from: n ∈ (-∞, -6) ∪ (0, 6) ∪ (9, ∞)
Decreasing from: n ∈ (-6, 0) ∪ (6, 9)
What is local maximum and minimum?The maximum and minimum of a function, sometimes referred to as the extremum in mathematical analysis, are its biggest and lowest values, respectively, either on the whole domain or within a specified range. A maximum within a constrained domain, particularly a point on a function whose value exceeds the values of every other point in its vicinity. A point on a graph (or its related function) with a value that is lower than all other points close to it.
A real-world problem scenario can be solved by using the local maximum and minimum to get the best equational solution. It is possible to calculate the input values for which these expressions have a maximum or minimum output by using the local maximum and minimum.
Local maximum: (-6, 8)
Local maximum: (6, 3)
Local minimum: (0, -2)
Local minimum: (9, 2)
Increasing from: n ∈ (-∞, -6) ∪ (0, 6) ∪ (9, ∞)
Decreasing from: n ∈ (-6, 0) ∪ (6, 9)
To know more about local maximum refer to:
https://brainly.com/question/29273762
#SPJ1
emiko makes shibori scarves and sells them for $48 each on a website for handmade goods. the expression 48s represents the total price of buying s scarves
The expression 48s represents the number of scarves (s) and its per unit (48).
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given that, Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods.
Here, the expression 48s represents the total price of buying s scarves
We need to tell what 48s mean,
So,
48s here is the total cost for buying s scarves,
That mean, if we buy s scarves we will have to pay $48s
Similarly, if we will buy 4 scarves, we will pay = 48 × 4 = $192
For 10 scarves, we will pay = 48 × 10 = $480
Therefore, we can say $48 is the unit price of the scarf.
Hence, the expression 48s represents the number of scarves (s) and its per unit (48).
Learn more about expressions, click;
https://brainly.com/question/14083225
#SPJ1
The question was incomplete, so I answered for the question :-
Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves what do the parts of the expression 48s represents.
Answer:
Step-by-step explanation:
number of scarves
Price of scarves
Describe the transformations necessary to transform the graph of f(x) into that of g(x).
Answer:
Shift 3 units to the right.
Reflect over the x-axis
What is the solution to the division problem below you can use long division or synthetic division 2x^3-2x^2-10x-6/ x-3
Answer: 2x^2+4x+2
Step-by-step explanation:
Please help I need an equation for this graph
Two antibiotics are available as treatment for a common ear infection in children. • Antibiotic A is known to effectively cure the infection 60 percent of the time. • Antibiotic B is known to effectively cure the infection 90 percent of the time. The antibiotics work independently of one another. Both antibiotics can be safely administered to children. A health insurance company intends to recommend one of the following two plans of treatment for children with this ear infection. • Plan I: Treat with antibiotic A first. If it is not effective, then treat with antibiotic B. • Plan II: Treat with antibiotic B first. If it is not effective, then treat with antibiotic A. (a) If a doctor treats a child with an ear infection using plan I, what is the probability that the child will be cured? (b) If a doctor treats a child with an ear infection using plan II, what is the probability that the child will be cured?
Step-by-step explanation:
the probability of A working is 60% or 0.6, so the probability it does not work is 40% or 0.4.
the probability of B working is 90% or 0.9, so the probability it does not work is 10% or 0.1.
plan 1
it is the probabilty that either A works, or (if it is not working) B works.
0.6 + 0.4×0.9 = 0.6 + 0.36 = 0.96
plan 2
either B works, or (if it is not working) A works
0.9 + 0.1×0.6 = 0.9 + 0.06 = 0.96
both plans have the same success probability.
HELP ME!!!!
ZEARN!!!!!!!!!
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
A quadratic function f is defined by f (x) = (2+6) (x – 8).
1. Without graphing, identify the x-intercepts of the graph of f. Explain how you know.
2. Expand (x + 6) (2 - 8) and use the expanded form to identify the y-intercept of the graph of f. Show your work and explain how you know.
Answer:
1. The x-intercepts can be determined by taking the opposite of the constants, in this case the x-ints are -6 and +8.
2. (x+6)(x-8) = x^2+-2x-48, the y-intercept is -48
A product costs $70 today, how much will the product cost in t days if the price is reduced by $5 a day
Answer:
P ($)=70-5(t)
Where p = price at t days
t = number of days
Step-by-step explanation:
The product price initially = $70
Now, every day , it reduces $5
The rate=$5 per day reduction
The price in the days will be determined by the formula below
P ($)=70-5(t)
Where p = price at t days
t = number of days
So let's assume it's on the second day
The price after the second day
P($) = 70-5(2)
P($) = 70-10
P($)= $60
The price after two days will be reduced to $60
For the point P(13,5)and Q(18,8) find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
what's 0/0, with full steps
Answer:
undefined
Step-by-step explanation:
division by zero is undefined
Division Property of zero
For any nonzero real number a
The quotient of "a" and 0 is undefined. That is a/0 is undefined
An isosceles triangle has an angle that measures 136°. What measures are possible for the other two angles? Choose all that apply.
Answer:
The other two angles are 22° , 22°
Step-by-step explanation:
To find the other angles, we can use angle sum property of triangle.
The given angle 136° cannot be base angles. Let the base angles be x.
x + x + 136 = 180°
2x + 136 = 180°
Subtract 136 from both sides,
2x = 180 - 136
2x = 44°
Divide both sides by 2,
x = 44 ÷ 2
\(\sf \boxed{x = 22^\circ}\)
Answer:42
Step-by-step explanation:
just addC. Imagine you Deposit K10, 000 every six months for the next five years at an interest rate of 10% per annum. You would want to know what this value will be at the end of the period.
Required:
i. Using simple interest (5 Marks)
ii. Using compounded interest (5 Marks)
iii. If the deposits were made at the beginning of every six months (5 Marks)
iv. If the deposits were made at the end of every six months (5 Marks)
Step-by-step explanation:
\(Determine the contents of the accumulator after the completion of each of the following instruction group
MVI A, 4CH
ANI 85H
\)
How do I know if the function is a linear function?
Answer:
This is not a linear function.
Step-by-step explanation:
It is a quadratic function. If you were to make a table of the x and y values of the function it would look like this:
x y
0 -4
1 -1
2 8
Just by looking at these three values, we can see that they do not increase at a consistent rate. It increases by 3 from 0 to 1, but increase by 9 from 1 to 2. You can tell if a function is linear by seeing if it increases at a constant rate. (In this case it does not)
Which of the following is not a congruence theorem or postulate? A. SSS B. SAS C. SSA D. AAS
Answer:
SSA the only other right one missing is ASA
Please help it’s URGENT!
The least common denominator needed to solve the equation is given as follows:
D. x(x - 3).
How to obtain the least common denominator?The equation in this problem is given as follows:
1/x + 2/(x - 3) = 5.
The denominators of each expression are given as follows:
x.x - 3.x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:
D. x(x - 3).
More can be learned about least common denominator at https://brainly.com/question/19249494
#SPJ1
The LCM and GCF of 4,32,12
Answer: LCM =96
GCF=4
Step-by-step explanation:
I need h e l p
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box.
Answer:
17.8
Step-by-step explanation:
You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).
The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.
In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.
Learn more on functions:https://brainly.com/question/11624077
#SPJ1
Can somebody who’s really gonna help me please really do it answer ASAP
Answer:
easygtrderdcgfc
Step-by-step explanation:
drtd
efwhiuhfrie
efijewioafjiewur89308932
1321321
Answer:
What exactly does “ASAP” mean? Ok yes, it means as soon as possible, but in terms of actual time, it means nothing. Th
Why are inequalities like the last two problems graphed on a number line while the ones in the
Set portion of this assignment are graphed on a coordinate plane? What difference is there
between the inequalities in the last two problems and the ones found in problems 13-16?
It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.
Why some inequalities are graphed on a number line?The type of diagram that we need to use depends on the number of variables that we have.
A single variable ----> number linetwo variahbles ----> a coordinate plane.3 variables ---> a volume.That is the main reason, for example:
x > 2
Is graphed on a number line.
y > 3x + 4
is graphed on a coordinate plane.
learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
7.385 rounded to the nearest tenth
Answer:
10 lol..................
Answer:
It should be 7.4
Step-by-step explanation:
what is the length of leg s of the triangle below?
Answer:
the answer would be 10
Step-by-step explanation:
For the given annual rate of change, find the corresponding growth or decay factor. +50%