Answer:
t(ties) = $8,50 and s(shirts) = $19,50
Linda's purchase total price $36,50
Step-by-step explanation:
In mathematics, a system of linear equations is a set of two or more linear equations with more than one unknown that make up a mathematical problem that consists of finding the values of the unknowns that satisfy those operations. the unknowns are usually represented with letters of the alphabet
For this example, we can represent as a system of linear equations as follows:
For Ted
[tex]4s+2t=95[/tex] where s are shirts, t are ties, and 95 the total price of both products in $.
For Stephen
[tex]3s+3t=84[/tex] where s are shirts, t are ties, and 84 the total price of both products in $.
Each shirt and each tie were buying in the same clothing store which means that it has the same price and we can and we can relate both equations with a system of equations as follows:
[tex]\left \{ {{4s+2t=95} \atop {3s+3t=84}} \right.[/tex]
Using the reduction method, which is to clear in one of the equations with any unknown.
In this case the system has two unknowns, the selected one must be replaced by its equivalent value in the other equation.
Let's clear s in the second equation
[tex]3s+3t=84\\3s=84-3t\\s=\frac{84-3t}{3} \\s=28-t[/tex]
Substituting the value of [tex]s=28-t[/tex] in the first equation
[tex]4s+2t=95[/tex] with [tex]s=28-t[/tex]
[tex]4(28-t)+2t=95\\112-4t+2t=95\\-2t=95-112\\t=\frac{-17}{-2}=8.50[/tex]
We got that the price of a tie is t = $8,50
Substituting the value of t in the first equation in order to obtain the value of s
[tex]3s+3t=84\\3s+3(8.50)=84\\3s+25.50=84\\s=\frac{84-25.50}{3} = 19.50[/tex]
We got that the price of a shirt is s = $19,50
Checking if the result satisfies the equations
With t = 8.50 and s = 19.50
[tex]\left \{ {{4s+2t=95} \atop {3s+3t=2}} \right.\\\left \{ {{4(19.50)+2(8.50)=95} \atop {3(19.50)+3(8.50)=84}} \right.\\\left \{ {{78+17=95} \atop {58.50+25.50=84}} \right.[/tex]
Linda bought 1 shirt and 2 ties at the same store. What's the total price in dollars and cents of Linda's purchase?
If a shirt value is s = $19,50 and a tie value is t = $8,50
Then s + 2t = ?
$19,50 + 2($8,50) = $36,50
The system of equations can be used to find s, the cost of each shirt in dollars and t the cost of each tie in dollars is
4s + 2t = 95
4s + 2t = 953s + 3t = 84
Given:
Cost of shirt = s
Cost of tie = t
4s + 2t = 95 (1)
4s + 2t = 95 (1)3s + 3t = 84 (2)
Multiply (1) by 3 and (2) by 2
12s + 6t = 285 (3)
6s + 6t = 168 (4)
subtract (4) from (3)
12s - 6s = 285 - 168
6s = 117
s = 117/6
s = 19.5
substitute s = 19.5 into (1)
4s + 2t = 95 (1)
4(19.5) + 2t = 95
78 + 2t = 95
2t = 95 - 78
2t = 17
t = 17/2
t = 8.5
Therefore, the cost of each shirt is $19.5 and the cost of each tie is $8.5
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4 The pet store has 6 fish tanks.
Each tank has 7 goldfish and 5
Tetras. What is the total
number of fish (f) in the tanks?
x
= f
_= f
f
72 fish total. 12 fish in each tank.
_________________________
(g+t)n=f
g=Goldfish
t=Tetras
n=Number of fish tanks
*If I got it wrong, let me know*
Final answer:
The total number of fish in the tanks is 72.
Explanation:
To find the total number of fish in the tanks, we need to multiply the number of tanks by the sum of the goldfish and Tetras in each tank. Based on the information given, there are 6 tanks, and each tank has 7 goldfish and 5 Tetras.
So, the total number of fish (f) in the tanks can be calculated as:
f = (7 goldfish + 5 Tetras) * 6 tanks
f = (7 + 5) * 6
f = 12 * 6
f = 72
Therefore, the total number of fish in the tanks is 72.
Tina sells lampshades for $7 each and paper lanterns for $4 each at a one-day craft fair. She sells k lampshades and (k + 4) paper lanterns. The expression 7k + 4(k + 4) represents Tina’s total sales.
Select all the equivalent expressions for Tina’s total sales at the fair.
A 8k+16 B 11k+4
» 11k+16 D 7k+4k+4
» 7k+4k+16. How is it equivalent?
4xk = 4K 4x4= 16 +4K + 7k = 16+ 11k ( I would double check me
help me pls asap i really need this
Answer:
26 degrees.
Step-by-step explanation:
180 - 154 = 26
Find the range of the data set represented by this box plot.
40
80
76
56
Answer:
56
Step-by-step explanation:
through estimation, you can see that the lowest value is 84 and the highest value is 140. in order to calculate the range, subtract the highest value from the lowest value. 140-84=56. The range is 56.
Answer:
56
Step-by-step explanation:
What is the degree of x^4-3x+2
A.5
B.3
C.4
D.2
Answer:
C
Step-by-step explanation:
The degree of a polynomial is determined by the value of the largest exponent of a term in the expression.
The largest exponent is 4 from the term [tex]x^{4}[/tex]
Hence the degree of the polynomial is 4 → C
Answer:
C (4)
Step-by-step explanation:
Tania took selfies with her 8 cousins. Each cousin is in exactly 2 or 3 pictures. There are 5 cousins in each picture. How many selfies did Tania take?
Answer:
4
Step-by-step explanation:
How many selfies did Tania take? (my first answer would be too many, but that's probably not the answer you're looking for :-) )
We know that each cousin appear 2 or 3 times overall.
If she would have taken each cousin exactly 2 times, that would be 16 cousins/photos
If she would have taken each cousin exactly 3 times, that would be 24 cousins/photos
We know there's exactly 5 cousins per photo...
so we have to find a multiple of 5 cousins/photos that is between 16 and 24.
The only possibility is 20 cousins/photos. 20 / 5 = 4 photos.
Final answer:
Tania took 4 selfies with her cousins. Each cousin appeared in exactly 2 selfies, with some appearing a third time to account for 16 total cousin appearances divided by 5 cousins per selfie.
Explanation:
The problem presented is a combinatorial puzzle involving selfies and cousins. Since each cousin is in either 2 or 3 pictures, we can try to minimize the number of pictures by assuming each cousin is in exactly 2 pictures first. If there are 8 cousins and 5 cousins per picture, then by multiplying 8 by 2 (every cousin appears exactly 2 times), we get 16 cousin appearances in total.
Since each selfie has 5 cousins, we divide the total cousin appearances by the number of cousins per picture: 16 / 5, which results in 3.2. However, since it's not possible to have a fraction of a picture, we need at least 4 selfies to cover all appearances. Yet, this leaves us 4 extra appearances (because 4 pictures would mean 20 cousin appearances in total).
These 4 extra appearances account for the fact that some cousins appear 3 times instead of just 2. Therefore, Tania must have taken 4 selfies with her cousins to cover the 16 cousin appearances with some cousins appearing an additional third time.
The RANGE of the function shown is
A) [4, 1]
B) [4, ∞)
C) [1, ∞)
D) [0, ∞)
Check the picture below.
recall that range is the interval over the y-axis for the graph of the function.
The range of the function shown is [4, ∝]
What is the range of the function?The collection of all a function's outputs constitutes its range. Example: Let's have a look at the function f: AB, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The elements of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all images of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.Here are the general formulas for calculating the range of various function types. The set of all real numbers is R in this instance.R is the range of a linear function.A quadratic function's range has the following values: y ≥ k if a > 0 and y ≤ k if a0A square root function's domain is y0.An exponential function has a range of y>0.R is the range of the logarithmic function.Solve the rational function y = f(x) for x and set the denominator to 0 to determine its range.To learn more about range of the function, refer to
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Express 16=2x as a logarithmic equation
Convert the exponential equation to a logarithmic equation using the logarithm base
(
4
)
(
4
)
of the right side
(
16
)
(
16
)
equals the exponent
(
2
)
(
2
)
.
log
4
(
16
)
=
2
How to do number 12
Answer:
To find the circumference of a circle you have to multiply Pi (3.14) with the diameter of the circle.
You need to find circumference of the circle first
mary has a total of 26 coins made up of quarters and nickles.the total value of mary's coins is $4.30 how many quarters does mary have
A.26 quarters
B.15 Quarters
C.11 Quarters
D.5 Quarters
help me out here asap
Answer:
d
Step-by-step explanation:
she has 16 quarters
1$=4 quarters
so 4$= 16 quarters
plus one more from the thirty cense
she could have 17 which is strange it’s not an option so go with B ig
is -77 a rational or irrational number?
It’s a rational number.
Hope this helps!
Answer:
Rational
Step-by-step explanation:
Irrational numbers are numbers that are infinite and non- repeating numbers
irrational- pi, square root of 2, etc
rational- anything else.
rational- .333333..., 1/3, 2, 1, -5, .111..., .7171..., etc.
Thirty six pencils are packed in three boxes. How many pencils are packed in five boxes
Each pencil box usually contains same amount of pencils. In given context the number of pencils in five boxes is 10 pencils.
How to decide the number of containment of items?Suppose that its given that 'a' boxes contains 'b' items, then, assuming that each box contains 'x' items, then
[tex]x + x + ... + x \text{ (a times)} = b\\\\x \times a = b\\\\x = \dfrac{b}{a}[/tex]
Thus, there are 'b/a' items contained in each box.
Since there are six pencils in three boxes, let there are 'x' pencils in one box, then we have:
[tex]x + x + x = 6\\3 \times x = 6\\\\\text{Dividing both sides by 3}\\\\x = \dfrac{6}{3} = 2[/tex]
Thus, there are 2 pencils in each pencil box.
Thus, for 5 boxes, we get [tex]2 \times 5 = 10[/tex] pencils.
Thus,
In given context the number of pencils in five boxes is 10 pencils.
Learn more about division here:
https://brainly.com/question/2689177
Final answer:
By using proportional reasoning, if three boxes contain 36 pencils, then five boxes would contain 60 pencils.
Explanation:
If thirty-six pencils are packed in three boxes, then there are twelve pencils per box because 36 divided by 3 equals 12.
To find out how many pencils are packed in five boxes, we multiply twelve pencils (the number of pencils per box) by five boxes.
Therefore, 12 pencils/box × 5 boxes = 60 pencils in five boxes.
This is a simple proportional reasoning problem, often encountered in mathematical exercises in school.
Which expression best represents the area of the rectangle?
Answer:
length×width
Step-by-step explanation:
Multiplying the length of a rectangle by the width will always give you the area. If one value is missing replace it with x.
Length x width should give you the answer your needing
Find the perimeter of a square that is 3 3/4 inches on a side. 7 inches 15 inches 12 inches 30 inches
Answer:
15 inches
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of its sides. A square has 4 sides, all the same length. We can either add up the side lengths, or we can recognize that multiplication of one side's length by 4 is a useful alternative.
perimeter = 4 × (3 3/4 in)
= (4×3 +4×3/4) in
= 12 in + 3 in = 15 in
Which is the graph of f(x)=3 √x?
I would make a table and plug values(or just plug in x values) in to figure out the equation's graph: (plug in values that will make it easy for you since you have a √)
f(x) = 3(√x)
x = 0
f(0) = 3(0) = 0 ------> (0 , 0)
x = 1
f(1) = 3(√1) = 3(1) = 3 ------> (1 , 3)
x = 4
f(4) = 3(√4) = 3(2) = 6 ------> (4 , 6)
Now that you have found some points, find a graph/line that goes through these points
Which shows the correct substitution of the values a,b, and c from the equation 0=-3x^2-2x+6 into the quadratic formula ?
Answer:
a = -3
b = -2
c = 6
Step-by-step explanation:
The quadratic formula states that for an equation of the form:
[tex]ax^{2} + bx + c = 0[/tex]
The solution to that equation is:
[tex]\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]
In this case we have:
0=-3x^2-2x+6
Where:
a = -3
b = -2
c = 6
The distance between points (3,7) and (x1,y1) is the square root of (x1 - 3)2 + (y1 - 7)2
True or False?
Answer : True
Explanation : It is according to distance formula.
The answer is True -Apex
Given the equation of a circle, determine the center and the radius.〖(x+5)〗2+〖(y-1)〗2=9.
The equation of a circle is (x-h)2 +(y-k)2 = r2
Answer:
The center is (-5,1)
and
the radius is 3
Step-by-step explanation:
The given equation of the circle is
[tex](x+5)^2+(y-1)^2=9[/tex]
We can rewrite this equation in the form;
[tex](x-h)^2+(y-1)^2=r^2[/tex]
This implies that;
[tex](x--5)^2+(y-1)^2=3^2[/tex]
When we compare, we get;
(h,k)=(-5,1) which is the center and r=3 the radius.
The answer is:
The center of the circle is located on the point (-5,1) and the radius is equal to 3 units.
Why?To determine the center and the radius of a circle from its equation, we need to look for "h" and "k", being "h" the x-coordinate of the center and "k" the y-coordinate the center, then, calculate the radius.
Since we are given the ordinary equation of the circle, we can find the radius and the center directly.
The ordinary equation is:
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
Where,
h is the x-coordinate of the center
y is the y-coordinate of the center
r is the radius.
So, we are given the circle:
[tex](x+5)^{2} +(y-1)^{2} =9[/tex]
Which is also equal to:
[tex](x-(-5))^{2} +(y-(1))^{2} =9[/tex]
Where,
[tex]h=-5\\k=1[/tex]
[tex]r^{2}=9\\\sqrt{r^{2}}=\sqrt{9} \\r=3units[/tex]
Hence, the center of the circle is located on the point (-5,1) and the radius is equal to 3 units.
Have a nice day!
George took a test with a certain number of questions. Each question had the same value. He answered 10 questions incorrectly, which resulted in an accuracy score of 60%. How many questions were on the test
10 questions = 40%
X question = 100%
40x = 1000
X = 25 questions
25 questions were on the test.
What is accuracy?There are two ways to assess observational error: accuracy and precision. Precision measures how closely spaced or widely separated a set of measurements are from one another, whereas accuracy measures how near or far off a given set of measurements are from their true value.
Given
60% accurate means 40% inaccurate.
10 inaccurate answers means 40% inaccurate
10/40 x 100 = 25
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Whch experision is equialent to 5(4x+3)-2x?
A.18x+15
B.18x+3
C.7x+8
D.2x+8
Let's open up parenthesis:
20x+15-2x
Then simplify.
18x+15
...Which is A.
Hope I helped!
~Mshcmindy
Answer:
The correct answer is option A. 18x + 15
Step-by-step explanation:
It is given an expression in variable x,
5(4x + 3) - 2x
To simplify the given expression
5(4x + 3) - 2x = (5 * 4x) + (5 * 3) - 2x (open the bracket)
= 20x + 15 - 2x
= 20x - 2x + 15
= 18x + 15
Therefore the correct answer is 18x + 15
The correct option is option A. 18x + 15
Which list shows all the factors of 36? 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 8 , 9, 12, 18, 36 2, 3, 4, 6, 9, 12, 18 2, 4, 6, 8, 9, 12, 18 help fast
These are the factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 9, 12, 18, 36
1 x 36 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
2 x 18 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
3 x 12 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
4 x 9 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
6 x 6 = 36
Hope this helped!
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
I took test on edge 2021
which of the following could be the graph of the line y=3x-2
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x-2[/tex]
Plot the line
To plot the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=3(0)-2=-2[/tex]
The y-intercept is the point (0,-2)
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]0=3x-2[/tex]
[tex]x=2/3=0.667[/tex]
The x-intercept is the point (0.667,0)
Plot the intercepts and then draw the line
4 times the sum of 1 plus a number equals 24. Find the number.
Answer:
the number is 5
Step-by-step explanation:
we can divide 24 by 4 in order to find the number
24/4 = 6
now we need to determine what number plus 1 equals 6 by subtracting 6 - 1
6 - 1 = 5
the answer is 5
we can check this by plugging 5 into the equation:
4(5+1) = 24
4(6) = 24
24 = 24
A die is tossed. Find p(less than 5/even)
Answer:6/36
Step-by-step explanation:
The probability of rolling a number less than 5 and even on a die is 1/2.
Explanation:To find the probability of rolling a number less than 5 and even, we need to determine the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes.
There are three outcomes that satisfy both conditions: {2, 4, 6}. The total number of possible outcomes is six since a die has six sides.
Therefore, the probability of rolling a number less than 5 and even is 3/6, which simplifies to 1/2.
simplify the following:a)12:18:36. b)320:480. c)16mm:480
Step-by-step explanation:
[tex]a)\ 12:18:36=\dfrac{12}{6}:\dfrac{18}{6}:\dfrac{36}{6}=2:3:6\\\\b)\ 320:480=32:48=\dfrac{32}{16}:\dfrac{48}{16}=2:3\\\\c)\ 16mm:480=\dfrac{16mm}{16}:\dfrac{480}{16}=1mm:30[/tex]
To simplify the given ratios, find the greatest common divisor (GCD) and divide all terms by the GCD. The simplified ratios are 2:3:6, 2:3, and 1:30. Refer to the solution for more details.
To simplify ratios, we divide both sides by their greatest common divisor (GCD).
a) 12:18:36
Find the GCD of 12, 18, and 36. It is 6.
Divide each number by 6:
12 ÷ 6 = 218 ÷ 6 = 336 ÷ 6 = 6The simplified ratio is 2:3:6.
b) 320:480
Find the GCD of 320 and 480. It is 160.
Divide both numbers by 160:
320 ÷ 160 = 2480 ÷ 160 = 3The simplified ratio is 2:3.
c) 16mm:480
Find the GCD of 16 and 480. It is 16.
Divide both numbers by 16:
16 ÷ 16 = 1480 ÷ 16 = 30The simplified ratio is 1mm:30. However, if there is no importance to specify units, simply 1:30 would be enough.
what is the relationship between the graphs of y=2^x and y=2^-x
One is rational and one is exponential.
Answer:
Step-by-step explanation:
the relationship between the graphs of y=2^x and y=2^-x is : symmetry by y-axis
(r-8)^5
find the coefficient of the given term
r^3
98 points max
Answer:
640
Step-by-step explanation:
Expanding the binomial :
r⁵ - 40r⁴ + 640r³ - 5120r² + 20480r - 32768
The coefficient of r³ is 640
Answer:
Step-by-step explanation:
Apply binomial theorem to expand (a+b)^n where a = r, b = -8 n n = 5
the r^3 term is (5!/(2!*(5-2)!)*r^3*(-8)^(5-3)
=(5*4*3*2*1/1*2*1*2*3)*r^3*(-8)^2
=640*r^3
So the coefficient is 640.
Surface area
Math
Help
The answer for your question is d
Answer:
D)15+15+10+10+6+6
Step-by-step explanation:
the formula to find the SA of a rectangular prism is:
2(lw)+2(lh)+2(hw)
where
l=length
w=width
and
h=height
let's substitute the values,3,2,and 5 into the equation
2(5*3)+2(5*2)+2(3*2)=62
62 is the SA
from the options:
10+6=16
10+10+6+6=32
15+15+10+10+6=56
and
15+15+10+10+6+6=62
so option D is correct
I’m hella confused on all this. What’s EF
rationalized form means that the number shoudnlt be a decimal that has never ending digits.
hope this answer to your question :)
Consider the equation y = -2x + 5. Create a table of five ordered pairs that satisfy the equation. What is the y-intercept of the equation? What is the x-intercept of the equation?
a.
y-intercept (5, 0); x-intercept (-5/2,0)
b.
y-intercept (0, 5); x-intercept (0,5/2)
c.
y-intercept (5, 0); x-intercept (5/2,0)
d.
y-intercept (0, 5); x-intercept (5/2,0)
Answer with step-by-step explanation:
Ordered pairs that satisfy the given equation:
x 0 1 2 3 4
y 5 3 1 -1 -3
To find the x-intercept, we will substitute y = 0 and solve for x to get:
[tex]0 = -2x + 5[/tex]
[tex] -2x = -5[/tex]
[tex]x = 5/2[/tex]
x-intercept = (5/2, 0)
To find the y-intercept, we will substitute x = 0 and solve for x to get:
[tex]y = -2(0) + 5[/tex]
[tex]y = 5[/tex]
y-intercept = (0, 5)
Answer: option d.
Step-by-step explanation:
To create a table of five ordered pairs that satisfy the equation, you need to give values to the variable "x" and substitute these into the function to find the corresponding value of "y":
For [tex]x=-2[/tex]
[tex]y = -2(-2) + 5=9[/tex]
For [tex]x=-1[/tex]
[tex]y = -2(-1) + 5=7[/tex]
For [tex]x=0[/tex]
[tex]y = -2(0) + 5=5[/tex]
For [tex]x=1[/tex]
[tex]y = -2(1) + 5=3[/tex]
For [tex]x=2[/tex]
[tex]y = -2(2) + 5=1[/tex]
Then, you can make the table:
x -2 -1 0 1 2
y 9 7 5 3 1
To find the x-intercept, substitute [tex]y=0[/tex] into the function and solve for "x". Then:
[tex]0 = -2x + 5\\\\x=\frac{-5}{-2}\\\\x=\frac{5}2}[/tex]
This is: ([tex]\frac{5}{2}[/tex], 0)
To find the y-intercept, substitute [tex]x=0[/tex] into the function and solve for "y". Then:
[tex]y= -2(0) + 5\\\\y=5[/tex]
This is: (0,5)