Taking into account the definition of a system of linear equations, the cost of each shirt is 12 and the cost of each pair of slacks is 18.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be found and they must give the solution proposed in both equations.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"S" is the cost of each shirt."PS" the cost of each pair of slacksYou buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96.
So, the system of equations to be solved is
[tex]\left \{ {{3S + 2PS=72} \atop {2S + 4PS=96}} \right.[/tex]
To solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Isolating the variable S from the first equation, you obtain:
3S= 72 - 2PS
S= (72 - 2PS)÷3
S= 72÷3 - 2PS÷3
S=24- 2/3PS
Replacing this expression in the second equation:
2(24 - 2/3PS) + 4PS= 96
Solving:
2×24 - 2×2/3PS+ 4PS= 96
48 - 4/3PS + 4PS= 96
48 + 8/3PS= 96
8/3PS= 96 - 48
8/3PS= 48
PS= 48÷ 8/3
PS= 18
Replacing this value in the expression S=24- 2/3PS, you obtain:
S= 24 -2/3×18
S= 24 - 12
S= 12
Finally, the cost of each shirt is 12 and the cost of each pair of slacks is 18.
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30. Which of the following choices shows the slope-intercept form of the equation below?
31. Which of the following choices shows the standard form of the equation below?
The equation of the lines in slope intercept form and standard form is y = -2x + 10 and 2y+3x = 10
Equation of a line in slope intercept formThe equation of a line in point slope form is y = mx + b.
Given the equation below:
y-7 =-5/2(x+4)
2(y-7) = -5(x+4)
2y-14 = -4x - 20
2y = -4x-20+40
2y = -4x + 20
y = -2x + 10
For the equation;
y = -3/2 x + 5
Multiply through by 2
2y = -3x + 2(5)
2y = -3x + 10
2y+3x = 10
Hence the equation of the lines in slope intercept form and standard form is y = -2x + 10 and 2y+3x = 10
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Which equation matches
Answer:
The first one
Step-by-step explanation:
Please help with problem 27
Answer:
Step-by-step explanation:
I have a tip for you have you ever used the website Desmos graphing calculatr if you havnt i can help you a lot thats how i passed that class
The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. how many times smaller is the bacterial cell than the amoeba cell? write the final answer in scientific notation with the correct number of significant digits. 1.4 x 101 7 x 101 143 x 101 7 x 103
The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
What are scientific notations?
Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.
Calculation of the amount by which a bacterial cell is smaller than the amoeba cell
Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)
The length of a bacterial cell in scientific notations is 5 × 10^(- 6)
To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.
= 3.5 × 10^(- 4) / 5 × 10^(- 6)
= 0.7 × 10^(2)
= 7 × 10^(1)
Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
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3
Point 0 is on live segment NP.
If OP= 3 and NO=15, what is
length of NP.
According to the length, the length of the NP become 18.
According to the statement
We have to find that the length of the NP.
So, For this purpose, we know that the
The length of this line segment is the distance between its endpoints A and B.
From the given information:
Point O is on live segment NP.
If OP= 3 and NO=15,
Then
Let draw a diagram and after seeing it in image we know that the:
NO=15 and OP= 3
And
Np is the sum of the op and no.
Then
NP = OP + NO
NP = 3+ 15
NP = 18.
Then the length of the NP become 18.
So, According to the length, the length of the NP become 18.
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What's 960 divided by 40?
Answer:
24
Step-by-step explanation:
960/40 =
To make it simpler you could divide 10 by both digits to simplify them (as in fractions).
960/10 = 96
40/10=4
Now your have 96/4
Again this can be simplified by dividing both by 2
96/2 = 48
4/2 = 4
48/2
48 is definitely a multiple of 2, so dividing this your answer is 24
The expression 960 divided by 40 is 24.
We have,
Expression:
960 divided by 40
This can be written as,
960 ÷ 40
40 ) 960 (24
80
160
160
0
The quotient is 24 and the remainder is 0.
Thus,
The expression 960 divided by 40 is 24.
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admission to a certain university is determined by an entrance exam. the scores of this test are normally distributed with a mean of 400 and a standard deviation of 60. only students who score in the top 30% will be offered admission. april scores 425 on the test. choose the most accurate statement.
Only students who score in the top 30% will be offered admission - this statement is accurate.
What is the mean and standard deviation of the entrance exam?In insights, the standard deviation is a proportion of how much variety or scattering of a bunch of values. A low standard deviation shows that the qualities will generally be near the mean of the set, while an elevated expectation deviation demonstrates that the qualities are fanned out over a more extensive territory. The standard deviation can generally be determined considerably more effectively with a number cruncher, and this might be satisfactory in certain tests. On my adding machine, you go into the standard deviation mode. Consequently, the main distinction among change and standard deviation is the units. For instance, in the event that we took the hours of 50 individuals running a 100-meter race, we would catch their time like a flash. Standard deviation assumes a vital part in the realm of money. In finance standard deviation is a factual estimation, when it's applied to the yearly pace of return of a venture.
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if a deli offers 10 fillings, 9 types of bread, and 6 condiments, and each sandwich consists of a filling, a type of bread, and a condiment, how many different sandwiches can the sandwich shop create?
540 and 5760 sandwiches can the sandwich shop create
10 fillings, 9 bread, 6 condiments
= 10 possibilities × 9 possibilities × 6 possibilities
=540
10 fillings, 9 bread, 6 condiments
= 10 possibilities × 9 possibilities × 64 possibilities
=5760
sandwich can have any no.of condiments,
let say A,B,C are condiment then possibilities are
A,B,C,AB,BC,AC,ABC , no condiment
i.e, [tex]2^{6}[/tex] = 64 possibilities.
What do you mean by possibilities?A likelihood that something will or won't occur or exist: the condition or reality of being possible There is a chance of rain today. A potential event or object that might exist It's possible that life exists on other worlds. More about potential from Merriam-Webster.
An example of a probability that you will attend a party is if there is a 50/50 chance that you might do so. The green dress is an example of a potential option you may select from when given the choice between wearing a red dress or a green dress.
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the sum of her test scores 88+80=168 also she took 2 tests. her average would be?
the answer should be written in the form of coordinates.
Asap pls
Answer: her average is 84
Step-by-step explanation:
88+80=168/2 =84
the square quilt block shown is used in a larger quilt. the four small squares in the block are congruent, and the four small vertical rectangles in the block that are not squares are also congruent. the total area of the shaded regions is what fraction of the total area of the block? express your answer as a common fraction.
The total area of the shaded regions in fraction of the total area of the block is 3/8 as the common fraction.
What is common fraction?A common fraction, sometimes known as a common fraction, is a fraction with an integer numerator and denominator. A common fraction may be used to identify a portion of a larger whole or set.
What is the formula for calculating a common fraction?Multiply each component of a fraction by both the denominator of another fraction to find the common denominator. To calculate the common denominator of 1/3 + 2/5, multiply the 1 through 3 by 5 and the 2 and 5 by 3. You should obtain a total of 5/15 + 6/15. The fractions can then be calculated.
According to the given data:Let's divide each square across four equal sections, for a total of 16 sections..
Using symmetry, one of the four portions in the top left square is shaded, and the same is true for the bottom right square.
Furthermore, two of the four squares inside this top right and bottom left corners are darkened.
Consequently,
the shaded area is:
{1 + 1 + 2 + 2}/ 16
6 /16 = 3 / 8
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round each decimal to the nearest whole number 10.76
Answer:
11
Step-by-step explanation:
Answer: 11
Step-by-step explanation: Hope this helps:)
An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural. what is the ratio of blue paint tubes to all the tubes of paint used?
The ratio of blue paint to all tubes of paint = 3:10
Number of tubes of red paint = 6 tubes
Number of tubes of yellow paint = 2 tubes
Number of tubes of white paint = 13 tubes
Number of tubes of blue paint = 9 tubes
Total no. of paint tubes = 6 red tubes + 2 yellow tubes+ 13 white tubes + 9 blue tubes = 30 tubes of paint
We use the following formula to find the required ratio:
The ratio of blue paint tubes to all tubes of paint = Number of blue paint tubes: Number of all tubes = 9:30 or 3:10
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|60| ___ |-60| = < >
Answer:
It is equal
Step-by-step explanation:
60 and -60 cancel each other out so the answer is equal.
Answer: |60|=|-60|
Step-by-step explanation:
|-60| would turn into 60 and |60| would remain 60 so they are equals
Given y = x^2 - 4, what is the value of y when x = -5?
Answer:
21
Step-by-step explanation:
y = [tex]x^{2}[/tex] -4 Substitute in -5 for x
y = [tex](5)^{2}[/tex] - 4
y = 25 - 4
y = 21
Answer:
y = 21
Step-by-step explanation:
Plug in -5 into the equation
(-5)² - 4
25 - 4 = 21
can i please have help
Answer:
Side 3 = 5cm
Step-by-step explanation:
135/9=15
15/3=5
Which is the solution set of the inequality 15y - 9 < 36?
A. y > 9/5
B. y < 9/5
C. y > 3
D. y < 3
Answer:
D
Step-by-step explanation:
y < 3
20 points How do you write four x cubed and also two x squared with numbers? asap please
Answer:
this should be the answer 4x^3 & 2x^2
Solve for X
I need help please
Answer:
x = 24.5
Step-by-step explanation:
First find angle G: 90 degrees
Then do 90 degrees minus 41: 49 degrees
Find 49 = 2x - 8
Do 49 + 8: 57
57/2 = x
X = 24.5
I can figure out the steps -X=35
Answer:
-35
Step-by-step explanation:
−X=35
Multiply both sides by −1.
X=−35
I hoped this helped! Contact me for more information if you need anything else!
293 + 8 will mark brainiest
Answer:
301
Step-by-step explanation:
bro :(
Answer:
301
Step-by-step explanation:
What is the difference of 18 ‒ (‒8)?
Answer: 26
Step-by-step explanation:
Answer:
26 is the answer because we have to subtract when the signs of the number are diffrent and add when it is same . so +18 - (-8) = 26
auto pistons at wenming chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: day mean bold x overbar (mm) range r (mm) 1 156.9 4.4 2 155.2 4.4 3 155.6 4.1 4 155.5 5.2 5 154.6 4.3 part 2 a) what is the value of x double overbar ? x double overbar equalsenter your response here mm (round your response to two decimal places).
The value of the x double bar (mean) of the given data is 155.16mm.
What is mean?
The mean (average) of a records set is observed with the aid of using including all numbers withinside the records set after which dividing with the aid of using the quantity of values withinside the set. The median is the center price while a records set is ordered from least to greatest. The mode is the quantity that takes place most customarily in a records set. Created with the aid of using Sal Khan
X bar = sum of all means / numbers of means
X bar = (156.9 + 153.2+153.6+155.5+156.6) / 5
X bar = 775.8 / 5
X Bar = 155.16mm
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There are 900 boys and 300 girls at eqinisweni secondary school. martha claims that 25% of the learners are girls. verify her claim by means of calculations
Martha's claim that the 25% of the learners are girls, is correct.
In this question,
There are 900 boys and 300 girls at Eqinisweni secondary school.
Martha claims that 25% of the learners are girls.
We need to verify her claim by means of calculations.
Based on the given conditions, we formulate:
300 / (900 + 300)
We simplify above expression.
= 300 / 1200
= 1/4 ..................(Cross out the common factor)
Now multiply a number 25 to both the numerator and the denominator:
= (1 × 25)/(4 × 25)
= 25/200
Now we rewrite a fraction with denominator equals 100 to a percentage: 25%
This means, Martha's claim that the 25% of the learners are girls, is correct.
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write a two-column proof to verity each conjecture. If -3r+1/2= 4 the r=-7/6
If -3r + 1/2 = 4, then it is true that r=-7/6
How to write a two-column proof to verity each conjecture?The equation is given as:
-3r + 1/2 = 4
And the solution is given as
r=-7/6
The two-column proof is as follows:
-3r + 1/2 = 4 ---- Given-3r = 4 - 1/2 ----- Subtract property of equation-3r = 3 1/2 ----- Subtract property of equation-3r = 7/2 ----- Convert to improper fractionr = -7/6 ----- Division property of equationHence, if -3r + 1/2 = 4, then it is true that r=-7/6
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elijah says that 9.56556555 is a rational number.Donna disagrees and says the number is irrational. Decide who is correct and what might likely cause one of them to make the error.
Answer:
It is a rational number because it is a repeating number.
Step-by-step explanation:
One might think it isn't rational because it isn't just one number repeating. But because it has a consistent number, it is rational.
I need help please….
Answer:
Graph A shapes are not congruent.
Graph B Shapes are congruent.
Step-by-step explanation:
For Graph A, Shape EFGH is 1 unit longer than shape ABCD.
For Graph B, the are the same, but rotated 90 degrees.
Rewrite the equation 4 = -6x + 3y + 3x in slope intercept form. (y = mx + b)
a.) y = 4/3 x +1
b.) y = x + 4/3
c.) y = -x + 4/3
d.) y = - 4/3 x + 1
Answer:
the answer will be
b.)
4 = -6x+3y+3x
4 = -3x+3y
3y = 3x+4
y. = x+4/3
The area of the top face of a cube is 9 square centimeters. use 9 of these cubes to make a rectangular prism. What is the volume of the rectagular prism
The volume of the rectangular prism is 243 cm³
given that
The top face of the cube has an area of 9 cm²
since All the faces of the cube are squares
therefore The top face is a square
∵ Area of any square = L² , where L is the length of the side of
the square
∵ Area of the top face is 9 cm²
∴ L² = 9 ⇒ take √ for both sides
∴ L = 3 cm
∵ The volume of any cube = L³
∵ L = 3 cm
∴ The volume of the cube = (3)³ = 27 cm³
- We will use 9 cubes to make a rectangle prism
∴ The volume of the rectangle prism is equal to the volume of
the 9 cubes
∴ The volume of the prism = 9 × volume of a cube
∵ The volume of the cube is 27 cm³
∴ The volume of the prism = 9 × 27 = 243 cm³
* The volume of the rectangular prism is 243 cm³
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A football team must move the ball forward at least 10 yards from its starting point to make a first down if the team has 2 losses of 2 yards each and a gain of 12 yards does the tean make a first touchdown justify your answer
No ,the team will not make the first down.
The definition of a yard is an outdoor area of a house or other building. An example of a yard is the lawn in front of your house; a front yard. An example of a yard is the area around a train repair center where trains are stored; a rail yard.
the first of a series of usually four downs in which a football team must net a 10-yard gain to retain possession of the ball.
If the team with the ball can pick up one yard or more on the third-down play, then they will be given a first down, which means they get to start all over with a new set of four downs. A team can continue moving the football down the field as long as they continue to pick up first downs.
we have been given that -
the ball forward at least 10 yards from its starting point to make a first down if the team has 2 losses of 2 yards each and a gain of 12 yards
Here are the integers that are represented by the scenario.
-2 + -2 = -4
-4 + 12 =8 yard gain.
There are 2 yards less of the first down.
Hence, the team will not make the first down.
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cosec4A-1/cot4a=1+2tan2a
Answer:
See image for answer.