The number of pie each got-
Alex -7Bob - 15Chuck - 9What is the method of elimination?To create an equation in one variable, use the elimination method and can either add or subtract this same equations. Whenever the coefficients with one variable are opposites, the equations are added to eliminate a variable; when the coefficients with one variable are equal, the equations are subtracted to eliminate a variable.For the given question;
Let the number of pie eaten by Alex be 'a'.
Let the number of pie eaten by Bob be 'b'.
Let the number of pie eaten by Chuck be 'c'.
Then, for the given condition.
If you add Alex’s and bobs pie total together, they ate 22 pies,
a + b = 22 .....eq 1.
Bobs and chucks pies sum to 24.
b + c = 24 .......eq 2
Alex and chucks pie together be 16.
a + c = 16 .......eq 3
Solving equation 1 and 3 by elimination.
Subtract eq 3 from 1.
c = b - 6 .....eq 4
Solving equation 4 and 2.
b = 15
Put in eq 4
c = 9
Put the values of b and c in eq 1.
a = 7
Thus, the number of pie shared by Alex, Bob and Chuck are 7, 15 and 9 respectively.
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Ila invested $42,000 into an account earning 4% compounded annually. She makes no other deposits and does not withdraw any money.
What is the balance of Ila's account in 5 years?
Ila invested $42,000 into an account earning 4% compounded annually. She makes no other deposits and does not withdraw any money, the balance of Ila's account in 5 years is $510,99.42.
What is compound interest?Compound interest is when you receive the interest on both your interest income and your savings.
For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest. Compound interest allowed you to earn 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.
The yearly interest rate is raised to number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from loan's entire original amount.
The formula is
A=[tex]p (1+r)^t[/tex]
A= future value?
P= present value 42000
R= interest rate 0.04
T= time 5years
A=[tex]42,000*(1+0.04)^5[/tex]
A=51,099.42
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2. There is a 13-foot ladder leaning against the side of a building. The ladder reaches up the building 12 feet.
How far is the bottom of the ladder from the bottom of the building? Picture
Question 5 only need help asap
The number of runs that Jack must score will be 90.
How to calculate the value?It should be noted that the mean score from 8 matches is 45. Therefore, the total score will be:
= 8 × 45
= 360
When the coach says that he must increase the mean to 50 in the next match, the total score will be:
= 50 × 9
= 450
Therefore, the number of points that must be scored will be:
= 450 - 360
= 90
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Write the sentence as a conditional.
4x-9 = 19
The sentence for 4x-9 = 19 is "when 9 is subtracted from 4 times a number, it equals 19."
What in mathematics is a conditional sentence?Definition. A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences. P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement. The implication of "If P then Q" is that whenever P is true, Q must also be true.
We have a conditional statement, for instance. In the event of rain, we will not play. Let's say A: It's raining and B: We're not going to play. If A is true—that is, if it is raining—and B is false—that is, if we played—then A implies that B is untrue.
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can u please help me on b guys ty
Answer:
circle is 22
Triangle is 34
Step-by-step explanation:
22 + 22 + 22 = 66
22 + 34 + 34 = 90
Take 90 - 22 = 68
Divide 68 by 2 to get 34
Directions - Multiply the binomials.
(3x³ + 2x) (x³ − 5) =
Answer:
3x^6-15x^3+2x^4-10x
Step-by-step explanation:
you know x is a number less than 4. Select all the inequalities that must be true
The inequality is (3,∞) < x < 4.
What is an inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given Data
x is a number less than 4
x<4
Numbers which are less than 4 are 3 to infinity
So,
The inequality is:
(3,∞) < x < 4
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can someone help me with work being shown?
Answer:
D. 12(2x − 3) > 60
Step-by-step explanation:
Area of rectangle = length x width
The length of the rectangle is 12 feet, and the width is (2x - 3) feet.
Area = 12 x (2x - 3)
= 12(2x - 3)
From the given question,
area of rectangle > 60 square feet
So that;
12(2x - 3) > 60
24x - 36 > 60
24x > 60 + 36
24x > 96
Divide both sides by 24, to have;
=
x > 4
Therefore,
width = (2x -3)
since x > 4, then;
width > (2x4 - 3)
> 8 -3
width > 5 feet
Thus,
length x width > 60
Lincoln went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. Lincoln purchased a total of 13 cans of soup and frozen dinners which collectively contain 4450 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
There are 9 cans of soup and the 4 frozen dinners that were purchased.
How to explain the information?Let x = the number of cans of soup purchased.
Let y = the number of frozen dinners purchased.
Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that
x + y = 13 ..... i
x = 13 - y
The equation will be illustrated as
250x + 550y = 4450 .... ii
Substituting x = 13 - y into equation ii, it becomes
250(13 - y) + 550y = 4450
3250 - 250y + 550y = 4450
- 250y + 550y = 4450 - 3250
300y = 1200
y = 1200/300
y = 4
4 frozen dinners
Substituting y = 4 into x = 13 - y, it becomes
x = 13 - 4 = 9
9 cans of soup.
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Work clothes costing $25.95, $23.95, $26.50, $39.95, and $41.25.
Ayana's favorite brownie recipe calls for
1
2
of a cup of flour for every
1
3
of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
cups of flour
Answer:
4/5 cup
Step-by-step explanation:
Answer: 1 1/2
Step-by-step explanation:
1/2 divided 1/3 = 3/2 = 1 1/2
1/2 divided 1/3
= 1/2 x 3/1
1 × 3
2 × 1
= 3/2
= 1 1/2
A plumber have an estimate for the renovation of a kitchen. Her hourly pay is $26 per hour and the plumbing parts will cost $80 flat. If her total estimate is $366, how many hours does she expect this job to take?
I need to show work too so please help!! thank you!
Answer:
11 hours
Step-by-step explanation:
let x represent the hours worked
26(x) + 80 = 366
26(x)=366-80
26(x)=286
x=11
.˙. the plumber worked 11 hours
Simple Solutions Science
Lesson #22 I need answer 2 to 10 asap!!!!!
You want to fence off a rectangular area of yard using the back side of your house as one of the sides. You have a total of 150 yards of fence. If the area of the fenced in portion comes to 2,800 square yards, what are the dimensions of the fenced-in area? Show all work for full credit.
The dimensions of the fenced-in area is given as
either length is 35 yards and width is 80 yards ,
or length is 40 yards and width is 70 yards .
In the question ,
given that the total length of the fence (perimeter) = 150 yards
let L be the length of the portion to be fenced
let B be the width of the house
Given that , one side of the portion is fenced using the back side of the house
So, the perimeter of the portion to be fenced is 2L+B
equating both the perimeter ,we get
2L+B=150
B=150-2L ....(i)
Also , given that the area of the fenced-in portion = 2800 yards
also the formula for area of fenced-in portion = L×B
hence
L*B=2800
Substituting the values of B from equation(i) , we get
L*(150-2L)=2800
150L - 2L² = 2800
2L² - 150L + 2800 = 0
simplifying further , we get
L² - 75L + 1400 = 0
L² -40L -35L +1400 = 0 .....using splitting the middle term
L(L-40) -35(L-40) = 0
(L-35)(L-40) = 0
So , L = 35 yards or L = 40 yards
Using L = 35 yards , we get B = 150-2(35) = 80 yards
and using L =40 yards , we get B = 150-2(40) = 70 yards .
Therefore , the dimensions of the fenced-in area is given as
either length is 35 yards and width is 80 yards ,
or length is 40 yards and width is 70 yards .
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Timmy has stamps. He wants to organize them on pages that hold stamps each. He has pages. Does Timmy have enough pages to organize all his stamps?
Using division we can infer that 50 pages will not be enough.
Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number.
Multiplication, subtraction , and addition make up the remaining operations. The division with remainder, also known as Euclidean division, of two natural numbers produces an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that is left over, when it is impossible to allocate any more full chunks of the size of the second number during the computation of the quotient after the division.Timmy has 810 stamps.
Now each page can hold 16 stamps and he has 50 pages.
Now we will divide 810 by 16 to calculate the number of pages required to put all the stamps.
∴ 810 ÷ 16 = 50 remainder 10.
Therefore after completing the 50 pages there are 10 stamps left.
Hence from division we can infer that 50 pages will not be enough.
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Timmy has 810 stamps. He wants to organize them on pages that hold 16 stamps each. He has 50 pages. Does Timmy have enough pages to organize all his stamps?
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7, 5, 2, 1
For the sequence above:
i.) Find the general term
ii.) Find the next three terms
iii.) Hence- find the 25th term
The sequence 7, 5, 2, 1, then the
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
The sequence is,
⇒ 7, 5, 2, 1
[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]
( i ) . The general term,
Let us assume general term = d
We can use this formula,
d = [tex]a_{n+1} -a_{n}[/tex]
where,
[tex]a_{n+1} = 5\\a_{n} = 7[/tex]
d = 7 - 5
d = 2
So,
The general term d = 2
( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]
We can use this formula,
[tex]a_{n+1} =a_{n} +d[/tex]
[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]
[tex]a_{5} = 1+2\\a_{5} = 3[/tex]
[tex]a_{6} = 3+2\\a_{6} = 5[/tex]
[tex]a_{7} = 5+2\\a_{7} = 7[/tex]
So,
The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term
We can find nth term,
We can use this formula,
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n} = 7+(n-1)2[/tex]
[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]
Then, 25th term is,
We can substitute n = 25
[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]
So,
The 25th term [tex]a_{25}[/tex] = 55
Therefore,
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
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Describe the type of correlation between the two variables on your graph. How do you know?
A graph's correlation between two variables reveals the relationship between them. The correlation is given a name based on the characteristics of the variables represented on the graphs.
What does the term correlation mean?
The data points of a person with two different factors are related in a scatterplot. The term "correlation" refers to this connection.
A correlation is the relationship between any two variables represented on any graph.
The correlation is divided into three main categories based on the sort of relationship between the variables. Those are
i) Positively correlation
ii) Negative correlation
iii) No correlation
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Find the amount in a continuously compounded account for the given conditions.
Principle: $5000
Annual Interest Rate: 6.9%
Time: 30 years
Round to the nearest cent and do not include the $ symbol.
Answer:
A= 5000 e
A= 39,624.12
Step-by-step explanation:
Answer:
no round to the nearest cant and do no
Please answer the question
The four students; Michal, Hypatia, clodoveo and Jamal's attempt to explain the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is incorrect
Simplification of expressionThis means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.
3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³
Using PEMDAS
P = parenthesisE = ExponentM = multiplicationD = divisionA = additionS = SubtractionCorrect workings:
3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³
3 - 5 × (1 × 2)² - 1 + 2(-1)³
= 3 - 5 × (2)² - 1 + 2(-1)
= 3 - 5 × (4) - 1 - 2
= 3 - 20 - 3
= - 20
Michal made the mistake of writing 2 instead of 20 Hypatia made the mistake of doing 3 - 5 first instead of opening the parenthesis according to PEMDASClodoveo's mistake was finding the cube of -1 to be 1 instead of -1Jamal's mistake was missing the 2 in 2(-1)³In conclusion, the correct simplification of the expression "3 - 5 × (4 - 3 × 2)² - 1 + 2(1 - 2)³" is -20
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A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. what is the slope in the situation?
A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. then the slope in the situation is 2
How do you find the slope of a line?
We need to find the ratio of the difference between the y-coordinates and x-coordinates of the two points, that form the line. The resulted value is the slope of the line. It shows the rise of the line along the y-axis over the run along x-axis.
since seed planted 1 inch deep then y1 = -1 and initial x1 =0
the plant grow an average of 3 inches every 2 weeks then y2 =3 and x2=2
putting in the formula
slope= y2 -y1 /x2 -x1
= 3-(-1)/2-0
= 4/2
=2
thus the slope in this situation is 2
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PLSSSS HELPPPP
ABCD is a rectangle. Trapezoid AEFB is congruent to
A
trapezoid CFED. G is the midpoint of segment EF.
E
Select all the ways we could describe the rigid transformation that takes AEFBto CFED.
Answer:
Rotate AEFB 180 degrees counterclockwise around point G
Rotate AEFB 180 degrees clockwise around point G
Translate AEFB by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.
Step-by-step explanation:
Last oneee helpppp
Factor Completely. 6x^3 + 10x^2 - 4x
Answer: 2x(3x−1)(x+2)
Step-by-step explanation:
Answer: 2x(3x-1)(x+2)
Step-by-step explanation:
6x^3 + 10x^2 - 4x=
2x(3x^2 + 5x - 2)=
2x(3x^2 + 6x - x - 2)=
2x(3x(x+2) - 1(x+2))=2x(3x-1)(x+2)
help please, geometry.
Answer:
400
Step-by-step explanation:
the volume of a pyramid with a square base is [tex]\frac{lwh}{3}[/tex] so the volume is 12*10*10 divided by 3, which is 1200/3, or 400
Which line matches the equation?
Answer:
23) D
24) A
25) C
26) B
Step-by-step explanation:
23)
4x + 4y = -8 Let's find the intercepts. The x intercept is when y = 0 and the y intercept is when x = 0
Let y = 0
4x + 4y = -8
4x = -8
x = -2
(-2,0)
4x + 4y = -8
Let x = 0
4y = -8
y = -2
(0,-2)
We are looking for the line that goes through the points (-2,0) and (0,-2) That is line D.
24)
3x -2y = -6
Let y = 0
3x = -6
x = -2
(-2,0)
Let x = 0
-2y =-6
y = 3
(0,3)
We are looking for the line that goes through the points (-2,0) and (0,3). That is line A.
25)
x + 2y = 2
Let y = 0
x = 2
(2,0)
Let x = 0
2y = 2
y = 1
(0,1)
We are looking for the line that goes through the points (2,0) and (0,1). That is line C
26)
3x - y = 3
Let y = 0
3x = 3
x= 1
(1,0)
Let x = 0
-y = 3
y= -3
(0, -3)
we are looking for the line that goes through the points (1,0) and (0, -3) which is line B
Answer: 23. D 24. A 25. C 26. B
Step-by-step explanation:
y=mx+b
The intersection of the straight line with the y-axis equals b
23.
4x+4y=-8
Divide both parts of the equation by 4:
x+y=-2
x+y-x=-2-x
y=-x-2
⇒b=-2 (D)
24.
3x-2y=-6
3x-2y+2y=-6+2y
3x=2y-6
3x+6=2y-6+6
3x+6=2y
Divide both parts of the equation by 2:
1,5x+3=y
⇒ b=3 (A)
25.
x+2y=2
x+2y-x=2-x
2y=-x+2
Divide both parts of the equation by 2:
y=-0.5x+1
⇒ b=1 (C)
26.
3x-y=3
3x-y+y=3+y
3x=y+3
3x-3=y+3-3
3x-3=y
⇒ b=-3 (B)
I just don’t know how to solve it
Answer:
1594
Step-by-step explanation:
Simplify the expression.
the expression negative five eighths times k minus 8 plus the expression 2 plus one third times k
A: 7 over 24 times k plus negative 6
B: negative 4 over 11 times k plus negative 10
C: negative 7 over 24 times k plus negative 6
D: negative 23 over 24 times k plus negative 10
Answer: C
Step-by-step explanation:
- 5/8k -8 + 2 + 1/3k
-5/8 = -15/24
1/3 = 8/24
-15/24k -8 + 2 + 8/24
-7/24k -6
When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6/216. What is the probability that the three numbers do not all match?
If your answer is a repeating decimal, type the repeated portion of the decimal only once.
For example:
for you only type in 3.6
for you only type in 0.45
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Kira's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs kira $5.85 per pound, and type b coffee costs $4.20 per pound. this month's blend used four times as many pounds of type b coffee as type a, for a total cost of $611.55. how many pounds of type a coffee were used?
39 pounds of type coffee were used.
Type a coffee costs, Kira, $5.85 per pound, and type b coffee cost $4.20 per pound.
let, A pound of type a coffee,
B pounds of type b coffee.
according to the question;
this month's blend used 3 times as many pounds of type B coffee as type A coffee.
Total pounds of coffee = x + 3x
The total cost then is:
(cost for Type A)(x) + (cost for Type B)(3x) = 717.60
=>5.65x + 4.25(3x) = 717.60
=>5.65x + 12.75x = 717.60
=>18.40x = 717.60
x = 39 pound
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Zander downloads a combination of 30
games and songs. He downloads 8
more songs than games. The equation g+(8+g)=30
can be solved to determine g
, the number of games Zander downloaded. How many games and songs did Zander download?
Zander Downloaded _ games and _ songs
Would someone help me please and thank you
Zander downloaded a total of 19 Songs and 8 Games.
In the given question, it is stated that Zander's downloads had a combination of 30 games and songs in which he downloaded 8 songs more than games. The equation representing the given situation is g + (8 + g) = 30. Here, g represents Games, and (g+8) represents songs.
Now, to find out the number of games and songs, we need to calculate the value of g by the equation.
=> g + (8 + g) = 30
=> 2g + 8 = 30
=> 2g = 22
=> g = 11
We get value of g = 11, So, downloaded games will be 11 and songs will be 19
Hence, the number of Games and Songs will be 11 and 19 respectively.
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the sum of 2 numbers is 96. the larger number is 9 less than 4 times the smaller. find boh nmbers.
The sum of 2 numbers is 96, this can be expressed as
[tex]x+y=96[/tex]The larger number is 9 less than 4 times the smaller, this can be expressed as
[tex]x=4y-9[/tex]Now, we replace the second equation in the first one
[tex]\begin{gathered} 4y-9+y=96 \\ 5y=96+9 \\ y=\frac{105}{5} \\ y=21 \end{gathered}[/tex]We use this number to find x.
[tex]x=4\cdot21-9=84-9=75[/tex]Hence, the numbers are 75 and 21.