HELP ME PLEASE!!
Solve the simultaneous equations.
x + 2y = 13
x + 5y = 28
x =
y=
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Here, We have given two equations that is ,[tex]\sf{ x + 2y = 13\:\: and\:\: x + 5y = 28}[/tex]To Find :-We have to find the value of x and y.Concept used :-Linear equations are those equations which having highest power of degree as 1 .Linear equations can be solved by subsitute method, elimination method and cross multiplication method. Here, I have used substitution method to make calculation easier. In subsitute method, you have to subsitute the value of one variable of eq(1) in eq(2) .Let's Begin :-Here,
We have two equations, let consider these two equations as eq(1) and eq(2) that is,[tex]\sf{ x + 2y = 13 ...eq(1)}[/tex]
[tex]\sf{ x + 5y = 28 ...eq(2)}[/tex]
By solving eq(1) :-
[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ x = 13 - 2y ...eq(3)}[/tex]
Subsitute eq(3) in eq(2) :-
[tex]\sf{ (13 - 2y) + 5y = 28 }[/tex]
[tex]\sf{ 13 - 2y + 5y = 28 }[/tex]
[tex]\sf{ 13 + 3y = 28 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 15 }[/tex]
[tex]\sf{ y = }{\sf{\dfrac{ 15}{3}}}[/tex]
[tex]\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}[/tex]
[tex]\bold{ y = 5 }[/tex]
Thus, The value of y is 5
Now,Subsitute the value of y in eq(1) :-
[tex]\sf{ x + 2(5) = 13 }[/tex]
[tex]\sf{ x + 10 = 13 }[/tex]
[tex]\sf{ x = 13 - 10 }[/tex]
[tex]\bold{ x = 3 }[/tex]
Hence, The value of x and y are 5 and 3 .
[tex]\bold{\huge{\underline{ Let's \: Verify }}}[/tex]
Equation 1 :-[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ 3 + 2(5) = 13 }[/tex]
[tex]\sf{ 3 + 10 = 13 }[/tex]
[tex]\sf{ 13 = 13 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Equation 2 :-[tex]\sf{ x + 5y = 28 }[/tex]
[tex]\sf{ 3 + 5(5) = 28 }[/tex]
[tex]\sf{ 3 + 25 = 28 }[/tex]
[tex]\sf{ 28 = 28 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Let's use elimination method
Subtract eq(2) from eq(1)We get
[tex]\\ \rm\Rrightarrow 2y-5y=13-28[/tex]
[tex]\\ \rm\Rrightarrow -3y=-15[/tex]
[tex]\\ \rm\Rrightarrow y=\dfrac{-15}{-3}[/tex]
[tex]\\ \rm\Rrightarrow y=5[/tex]
Putting on eq(1)
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow x+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow x+10=13[/tex]
[tex]\\ \rm\Rrightarrow x=13-10[/tex]
[tex]\\ \rm\Rrightarrow x=3[/tex]
(x,y)=(3,5)[tex]\LARGE{\underbrace{\underline{\rm{Verification:-}}}}[/tex]
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow 3+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow 3+10=13[/tex]
[tex]\\ \rm\Rrightarrow 13=13[/tex]
And
[tex]\\ \rm\Rrightarrow x+5y=28[/tex]
[tex]\\ \rm\Rrightarrow 3+5(5)=28[/tex]
[tex]\\ \rm\Rrightarrow 3+25=28[/tex]
[tex]\\ \rm\Rrightarrow 28=28[/tex]
Hence verified!
The list of all ordered pairs in the given relation R on the set T is (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), _____, (4, 4), (5, 5), and (6, 6).
Answer:
1,1. 4,4. 5,5 and. 6,6
Step-by-step explanation:
Because they are all the same numbers :)
Design An art class is making a mural for their school which has a triangle drawn in the middle.
The length of the bottom of the triangle is X. Another side is 5 more than four times the length of the
bottom of the triangle. The last side is 11 more than the bottom of the triangle. Write and simplify
an expression for the perimeter of the triangle.
Answer:
6x+16
Step-by-step explanation:
Bottom :x
Side1:4x+5
Side2:x+11
perimeter = x+4x+5+x+11
=6x+16
Problems Involving Fundamental Counting Principle
1. Patrick wants to buy a computer system. In a computer shop, a customer can choose one of the 4 monitors, one of the 2 keyboards, one of the 4 CPU, and one of 3 printers. Determine the number of possible systems that Patrick can choose from.
2. An ice cream parlor is offering different flavors of ice cream with two kinds of containers available, cone and paper cup. The flavors of their ice cream include cheese, vanilla, mango, and chocolate. What is the total number of possible combinations if a customer can choose a container and 3 flavors of ice cream?
3. Emma has 5 blouses, 3 skirts, and 4 pairs of shoes. In how many different ways consisting of a blouse, a skirt, and a pair of shoes can Emma dress up?
4. Tess, Rina, Rose, Ronnie, Bryan, and Gab are all members of the Student Council. In how many ways can you form a committee of three students?
Problems Involving Probability of Simple Events
5. A letter is to be chosen from the letters of the word EXTRAVAGANT. What is the probability that it is a consonant?
6. An auditor of a club is to be selected from 8 Grade 7, 9 Grade 8, 12 Grade 9, and 5 Grade 10 students. What is the probability that he/she is not a Grade 8 student?
7. A spinner is divided into parts and whose colors are similar to a color wheel. What is the probability that the pointer lands on a secondary color?
8. Slips of paper are numbered 4, 5, 6, …, 34, folded into similar squares and placed in a bowl. If a paper is to be picked at random, what is the probability that the number is a prime number?
The questions are illustrations of combination and probability
Combination involves the ways of choosing or selecting an item from a group of itemsProbability involves the chance of choosing or selecting an item from a group of items1. Number of systems to choose fromThe given parameters are:
Monitors = 4
Keyboard = 2
CPU = 4
Printer = 3
The number of systems to choose from is:
n = 4 * 2 * 4 * 3 = 96
Hence, Patrick can choose from 96 systems
2. Combination of Ice creamThe given parameters are:
Containers = 2
Flavors = 4
The number of total combination to choose from is:
n = 2 * 4C3 = 8
Hence, the number of total combination is 8
3. Emma dressing upThe given parameters are:
Blouse = 5
Skirt = 3
Shoes = 4 pairc
The number of ways to dress up:
n = 5 * 3 * 4 = 60
Hence, Emma can dress up in 60 ways
4. Members of committeeThe given parameters are:
Students = 6
Members of committee = 3
The number of ways to form a committee is:
n = 6C3 = 20
Hence, there are 20 ways to form the committee
5. Probability of consonantWe have:
Letters = 11
Consonnats = 7
The probability of selecting a consonant is:
P = 7/11
P = 0.636
Hence, the probability of selecting a consonant is: 0.636
6. Probability of not selecting a grade 8 studentWe have:
Total students = 34
Students not in grade 8 = 25
The probability that a student is not in grade 8 is:
P = 25/34
P = 0.735
Hence, the probability that a student is not in grade 8 is 0.735
7. Probability of a secondary colorNot enough details to solve
8. Probability of a prime numberThere are 9 prime numbers in a total number of 31 numbers from 4 to 34.
So, the probability that a number is prime is:
P = 9/31
P = 0.290
Hence, the probability that a number is prime is 0.290
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A puppy weighs534pounds.
how many ounces does the puppy weigh?
a.23 oz
b.46 oz
c.92 oz
ds.184 oz
Answer:
none of those answers are correct unless u mean 5 and 3/4
Step-by-step explanation:
The floor of the cafeteria storage room is being tiled. The room is shaped like a parallelogram. The
parallelogram has a base of 19.5 feet and a height of 8 feet. Each package of tile will cover 4 square feet.
How many packages of tile will be needed to tile the floor?
Answer: 39
Step-by-step explanation: formula is bh. 19.5 times 8 is 156. divide by 4 because a package will cover 4 sq ft.
Answer:
39
Step-by-step explanation:
parallelogram area is base x height
A = b x h
A = 19.5 x 8 = 156 ft^2 or square feet
156 divided by 4 = 39
i know this is probably simple but ive forgotten how to do it and i cant find it in my notes help appreciated!
Answer:
? = 13.6
Step-by-step explanation:
the angle between a tangent and the diameter = 90°
Then the triangle is right with legs 2 × 6 = 12 and 6.4
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the legs , that is
? ² = 12² + 6.4² = 144 + 40.96 = 184.96 ( take square root of both sides )
? = [tex]\sqrt{184.96}[/tex] = 13.6
Why 00,13,589 is not the smallest possible 7-digit number?
Answer:
1000000 is the smallest 7-digit number
8. If the area of Figure A is 216 square yards, find
the area of Figure B.
Step-by-step explanation:
the area is
baseline × height.
remember, 2 lengths are multiplied.
since both figures are similar to each other, it means that both lengths are changed by the same scaling factor.
18 × f = 63
f = 63/18 = 7/2
this factor f applies (as mentioned) to the baseline AND to the height.
therefore, the area changes by f×f = f² = 49/4.
that means the area of the larger figure is
216 × 49/4 = 54 × 49 = 2,646 yd²
A family goes to a fundraiser for their local library. Each ticket is $12, and they give a single donation of $10
at the end of the evening. There are six members of the family, and they spend a total of $82. Which equatic
could represent this situation?
Answer:
x=12y + 10 or even just entirely solved... 82=12(6) +10
Step-by-step explanation:
Answer:
ImnotI'm not sure
this is the same im on
Step-by-step explanation:
A vacant rectangular lot is being turned into a community vegetable garden with a uniform path around it. area of the lot is represented by 4x^2 40x - 44 where x is the width of the path in meters. Find the wisdom the path surrounding the garden.
By factorizing the expression, 4x² + 40x - 44, the width of the path (x) is calculated as: 11 meters.
How to Factorize an Expression?To factorize an expression, such as 4x² + 40x - 44, we need to determine the two factors that will give us -176 when multiplied, and also give us 40 when added.
To find the width of the path, x, we need to factorize 4x² + 40x - 44, using the two factors, 4 and -44.
4x² - 44x + 4x - 44
(4x² - 44x) + (4x - 44)
4x(x - 11) + 4(x - 11)
(x - 11)(4x + 4) = 0
x = 11 or x = -4/4 = -1
The value of the width of the path, x, cannot be negative. Therefore, the width of the path would be: 11 meters.
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Kelly's monthly profit for selling candles is represented by the function P (x) = 7.5x - 200, where x represents the number of candles sold. Complete each table
Profit is selling price minus cost price, we assumed that the number of candles sold is 100, then the profit is $550
Note: The question is not complete
Cost and Selling priceGiven Data
From the expression we can see the followingcost per candle = $7.5Number of candles sold for the month = xTotal cost of candles purchased for the month = $200We have the expression
P (x) = 7.5x - 200
Assuming the number of candles sold is x = 100
P (100) = 7.5*100 - 200
P (100) = 750 - 200
P (100) = $550
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Question 3(Multiple Choice Worth 5 points)
(07.03 MC)
Given g(x)= X-5. on what interval is the function negative?
Is –6 − 65 positive or negative?
Answer:
It is negative.
Step-by-step explanation:
-6 - 65 is -71
Hope that helps!
Answer:
negative
Step-by-step explanation:
The equation -6 - 65 equals -71 because 65 is a positive number and -6 is not which means it must keep going negative because a negative plus a positive goes negative.
The human resources department at a large company regularly conducts an employee satisfaction survey. One item on the survey presents employees with the statement, “I am happy overall at work.” Based on historical data, here is the distribution of responses to this item:
Answer:
There is sufficient evidence to conclude that the distribution of responses is different now than it was historically.
Step-by-step explanation:
Since the p-value is less than the alpha significance level you reject the null hypothesis that the histrocial data matches the current.
We don't have enough evidence to conclude that the distribution of responses is different now than it was historically.
What is human resources department?Human resources are the people who make up an organization's, business sector's, industry's, or economy's workforce.
A more specific concept is human capital, which refers to the knowledge and skills that individuals possess.
The chi-square goodness-of-fit test has a p-value of 0.089 at a significance level of 0.10. We cannot reject the null hypothesis because the p-value is greater than 0.10.
As a result, we lack sufficient evidence to conclude that the distribution of responses is different now than it was previously.
"We don't have enough evidence to conclude that the distribution of responses is different now than it was historically," is the correct answer.
Thus, this can be concluded regarding the given scenario.
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Your question seems incomplete, the probable complete question is:
Transcribed image text: Inference for categorical data (chi-square tests); Unit test The human resources department at a large company regularly conducts an employee satisfaction survey. One them on the survey presents employees with the statement, "I am happy overall at work. Based on historical data, here is the distribution of responses to this item Response Strongly Agree agree Disagree Strongly disagree 70% 15% 5% 10% Historical distribution The human resources department wants to test if the most recent responses fit the historical distribution. Here is a sample of 150 of the most recent responses to the statement along with a chi-square goodness-of-fit test. Response Strongly agree Agree Disagree Strongly disagree Inference for categorical data (chi-square tests): Unit test Response Strongly Agree Disagree Strongly agree disagree Observed 104 20 12 Expected 105 22.5 7.5 15 Components 0.01 0.28 5.63 0.6 x 6.52, DF - 3 P-value=0.089 Assume that all conditions for inference were met. At the a = 0.10 significance level, what should the human resources department conclude about the distribution of responses? Choose 1 answer: There is sufficient evidence to conclude that the distribution of responses is different now than it was Inference for categorical data (chi-square tests: Unit test Assume that all conditions for inference were met At the a 0.10 significance level, what should the human resources department conclude about the distribution of responses? Choose 1 answer: There is sufficient evidence to conclude that the distribution of responses is different now than it was historically We don't have enough evidence to conclude that the distribution of responses is different now than it was historically There is sufficient evidence to conclude that the distribution of responses is the same as it was historically No conclusions can be made from this test, because O expected counts cannot include decimals. There must have been a mistake in the calculations.
Pls Help Choose the correct word to complete the statement: If BC intersects circle A only at point B, and mCBA = 90°, then CB is a
Line CB touches circle A only at one point (point B), hence CB is a tangent.
What is a circle?A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
When a line intersects a circle in exactly one point the line is said to be tangent to the circle
Hence since Line CB touches circle A only at one point (point B), hence CB is a tangent.
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help meeeeeeeeeeeeeee!!!!!!! NO LINKS OR FILLES
Answer:
i think four but im prolly wrong
Step-by-step explanation:
Is a triangle with sides 7 feet, 12 feet, and 14 feet a right, acute or obtuse triangle?
Answer:
Acute
Step-by-step explanation:
This should be an acute triangle because if this was a right angle, then the three sides should be figured out by the Pythagorean Theorem.
An obtuse angle wouldn't be right either, you need an angle to be over 90.
Mandy has a total of $2.00 in change in her purse. Complete each set of coins below to show amounts equivalent to $2.00.
4 quarters, 5dimes,
______nickels
10 pennies, ____
dimes, 3 quarters, 5 nickels
2 quarters, 12 dimes, 3 nickels,______
pennies
______quarters, 4 dimes, 6 nickels, 5 pennies
Answer:
10 nickels
9 dimes
5 quarters
Step-by-step explanation:
Answer:
10 nickels, 9 dimes, 15 pennies, 5 quarters
Step-by-step explanation:
I'm a little confused by the question, but, I'll assume that each one is separated by a space.
4 quarters + 5 dims = 1.50. So, there would be 10 nickels.
10 pennies + 3 quarters + 5 nickels = 10+75+25=110. So, 9 dimes
2 quarters + 12 dimes + 3 nickels= 50 + 120 + 15 = 15. So, 15 pennies
4 dimes + 6 nickels + 5 pennies = 40+30+5=75. So, 5 quarters
NEED ANSWER ASAP
Which graph best represents the equation 3x + y = -5? A. B. C. D.
Graph B has a slope of -3 and a y-intercept of -5, therefore, the best graph that represents the equation is: Graph B.
How to Identify the Graph of the Equation of a Line?The equation of a line can be rewritten in slope-intercept form as, y = mx + b.
The graph that represents the equation of the line, would have a slope of m and a y-intercept of b.
Given the equation:
3x + y = -5
Rewrite in slope-intercept form:
y = -3x - 5
The slope of the graph, would be m = -3, and the y-intercept would b b = -5.
Thus, graph B has a slope of -3 and a y-intercept of -5, therefore, the best graph that represents the equation is: Graph B.
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Answer:
B
Step-by-step explanation:
Took the quiz on EDGE 2022
For what values of a is the expression true? |a+5|=a+5
Answer:
a>=-5
Step-by-step explanation:
when a+5>/=0
a>/=-5 because the if the contents of the absolute value are equal to the same expression in the absolute value if the expression is non negative. So we find the values of a when the expression is nonnegative.
NEED HELP: There are approximately 3.1 miles in 5 kilometers. Thaddeus is supposed to ride his bike for 20 kilometers for a charity ride.
Part A: How many meters are in this ride?
Part B: How many miles are in this ride?
Maryam scored an 8 out of 10 on her spelling test one week. The next week, her score decreased by 25%. What was her score for the second week?
a.) 5 out of 10
b.) 6 out of 10
c.) 7 out of 10
d.) 4 out of 10
find the 19th term in each sequence. 11, 33, 99, 279
Answer:
Step-by-step explanation:
hello : note 297 no 279
297 =3×99
99 = 3 ×33
33=3×11
this the geometric sequence. ( comon : 3)
the nth term is : An = A1 × r^n when : r = 3 and A1 =11
if n = 19 A19 = 11×3^19
help please??? and thank you! <33
Answer:
90.69 Rounded to the nearest tenth is 90.7
Step-by-step explanation:
✓ Rounded to the nearest 0.1 or
the Tenths Place.
✓ Hopefully this helps you! :)
wishing you a amazing day! ･ﾟ★,｡･
-Keira <33
A trapezoid has bases that measure 9 cm and 5 cm. The height of the figure is 4 cm. What is the area of the
trapezold?
O 28 cm?
O 36 cm
45 cm?
O
90 cm?
Answer: 28 cm.
Step-by-step explanation: To find the area of trapezoids, you need to add base 1 and base 2, multiply the height, and divide it all by 2. The work is done below:
b1 + b2 x h / 2, where b1 and b2 are the bases and h is the height.
5 + 9 x 4 / 2 = ?
Step 1 (Add): 5 + 9 = 14.
Step 2 (Multiply): 14 x 4 = 56.
Step 3 (Divide): 56 / 2 = 28.
Therefore, 28 cm is your answer.
Hope this helps! :)
Given the definitions of f(x) and g(x) below, find the value of (g•x)(1).
=
f(x) = 3x2 + 2x - 3
g(x) = -x + 4
Step-by-step explanation:
f(x) = 3x2+2x-3
g(x) = -x+4
(g.f)(x) = g[3x2+2x-3]
= -(3x2+2x-3)+4
= -3x2-2x+3
(g.f)(1) = -3(1)2-2(1)+3
= -3-2+3
= -2
Select the correct answer
Choose the number sentence that ilustrates the distributive property of multiplication over
Answer:
b
Step-by-step explanation:
a x (b + c) = (a x b) + (a x c)
Answer:
B is the answer...
2(5+6)
(2×5)+(2×6)
Which statement about the ordered pairs (2, -9) and (3,6) is true for the equation 5x - y/3 = 13?
A) (3, -6) is a solution to the equation.
B) Neither ordered pair is a solution.
C) (2, -9) is a solution to the equation.
D) Both ordered pairs are solutions.
Answer:
C) (2, -9) is a solution to the equation.
Step-by-step explanation:
To find if both or one point is the solution to the equation, substitute the x and y-values of both points into the equation to find which one makes a true and correct statement (the answer).
For (2, -9):
[tex]\sf5x - \frac{y}{3} = 13\\\\5(2) - \frac{-9}{3} = 13\\\\10-(-3)=13\\\\10+3=13\\\\ \boxed{13=13}\\\\\ \textsf{This is a true statement}\\\textsf{This means that (2, -9) is a solution to 5x - y/3 = 13}[/tex]
For (3, -6);
[tex]\sf5x - \frac{y}{3} = 13\\\\5(3) - \frac{-6}{3} = 13\\\\15-(-2)=13\\\\15+2=13\\\\ \boxed{17=13}\\\\\ \textsf{This is not a true statement}\\\textsf{This means that (3, -6) is not a solutions to 5x - y/3 = 13}[/tex]
Therefore, the correct answer is C
Hope this helps!
What is the 30th term of the following arithmetic sequences
17, 21, 25, ...
Answer:
133
Step-by-step explanation:
an = a1 + f × (n-1)
an= 17+4 x (30-1)
an= 17+4 x 29
an= 17+116
an=133