Amy has $ 27, Bob has $ 80 and Ravi has $ 20 amounts in their wallets.
Finding unknown quantity using Linear Equation:
A mathematical statement used to find an unknown quantity in a given problem is known as a Linear Equation. Here to represent the unknown quantity we will use variables like x, y, and so on.
Here we have,
Amy, Ravi, and Bob have a total of $127 in their wallets.
Since we don't know the amount of each person we represent them with different variables
Let 'a' be Amy's amount
'b' be Bob's amount
'r' be Ravi's amount
Then the total amount a + b + r = 127 -----(1)
Given that,
Bob has 4 times what Ravi has
=> b = 4r ----(2)
Ravi has $7 less than Amy
=> r = a - 7 ----(3)
From (2) and (3)
b = 4(a - 7)
b = 4a - 28 ----(4)
Now substitute (3) and (4)
=> a + 4a - 28 + a - 7 = 127
=> 6a - 35 = 127
=> 6a = 162
=> a = 27
From (3)
r = a - 7 = 27 - 7 = 20
From (2)
b = 4r = 4(20) = 80
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I need help on this one
△ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. The five properties SSS, SAS, AAS, ASA, and RHS can be used to demonstrate the congruency of any two triangles.So, to prove that △ABC ≅ △CDA as follows:
BA = DC (given)∠BAC = ∠DCA (given)AC = AC (Common line)So, △ABC ≅ △CDA under SAS condition.
Therefore, △ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.
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Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
A table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
In this question, we have been given some table that shows functions.
A 2-column table consists of six rows. The first column is labeled x (input values). The second column is labeled f(x) (output values)
We need to find a function which is increasing only over the interval (–2, 1), and nowhere else.
We can observe that for a second table, the first column x with entries negative 3, negative 2, negative 1, 0, 1, 2 and the second column with entries negative 2, negative 4, negative 1, 1, 4, 3 function f(x) is increasing only over the interval (–2, 1), and nowhere else.
Therefore, a table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
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what is the total area of the shaded sections of trapezoid?
The shaded sections of the trapezoid are triangles.
We know how to find the area of triangles
A = 1/2 bh
Lets start with the left triangle
The bases is 1.1 inches and the height is 3.8 inches
A left triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
The right triangle has the same dimensions
A right triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
Add the two triangles together
2.09+2.09 = 4.18 in^2
The area of the shaded region is 4.18 in^2
What’s the answer asp
Answer:
the 61 curv should lead to ars so the answer is ars
2y^2-5y=12. can someone help me solve the quadratic equation using the quadratic formula.
Answer:
y = 4 y = -3/2 = -1.5Step-by-step explanation:
According to quadratic formula:
y = - b ± √ b²- 4ac / 2a
y = - (-5) ± √ -5²- 4(2x-12) / 2(2)
y = 5 ± √ 25 - 4(-24) / 4
y = 5 ± √ 25 - (-96) / 4
y = 5 ± √ 121 / 4
y = 5 ± √ (11)² / 4
y = 5 ± 11 / 4
Now either,
y = 5 + 11 / 4
y = 4
Or,
y = 5 - 11 / 4
y = -3/2 = -1.5
A bicycle travels at a speed of 2,808 inches
per minute. The radius of each tire on the
bicycle is 3 feet. Approximately how many
revolutions does one of these tires make in 2 minutes?
(Use the approximation 22/7 for n.)
A. 12
B 25
C. 32
D. 46
In one revolution, cycle travels 18.84 feet.
What is unitary method?A problem can be resolved using the unitary method by first calculating the worth of a single unit, and then multiplying that amount to find the required value. A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel. With the unitary method, you first determine the value of a single unit before determining the value of the necessary quantity of units.
Radius = 3 feet
If r is the radius of the wheel (including the tire), then the circumference of the wheel = 2πr
= 2 x 22/7 x 3 feet
= 18.84 feet
In one revolution, cycle travels 18.84 feet.
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x^3−x^2−2x=0 Help me factory this problem
Answer: x=0 x=2 x=-1
Step-by-step explanation:
[tex]x^3-x^2-2x=0\\\\x(x^2-x-2)=0\\\\x(x^2-2x+x-2)=0\\\\x((x-2)+(x-2))=0\\\\x(x-2)(x+1)=0\\\\x=0\\\\x-2=0\\\\x-2+2=0+2\\\\x=2\\\\x+1=0\\\\x+1-1=0-1\\\\x=-1[/tex]
Answer:
Factored form: x(x-2)(x+1)=0
Solutions: x=0, x=2, x=-1
Step-by-step explanation:
[tex]x^{3} -x^{2} -2x=0\\[/tex]
[tex]x(x^{2} -x-2)=0\\\left \{ {{x=0} \atop {x^{2}-x-2 =0}} \right. \\\left \{ {{x=0} \atop (x-2)(x+1)=0}} \right. \\x=0,x=2,x=-1[/tex]
I need help pls someone -
Answer:
Number above 42 : 14
Number beside 2 : 1
Number above 0: 12
Step-by-step explanation:
if h(x)=10-x^2, then determine the value of h(f(2))
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
12,10,8
We can see here, from the first term to the second term, we minus 2. From the second term to the third term, we minus 2.
So, we're constantly reducing by an amount, therefore making this sequence an arithmetic sequence.
The common difference, said above, is -2 (since if the terms are getting smaller the common difference is a negative number.)
Three monkey's walk into a motel on the Curious George Hotel and ask for a room. The desk clerk says a room costs 30 bananas, so each monkey pays 10 bananas towards the cost.Later, the clerk realizes he made a mistake, that the room should have been 25 bananas. He calls the bellboy over and asks him to refund the other 5 bananas to the 3 monkeys. The bellboy, not wanting to make a mess dividing the 5 bananas three ways, decides to lie about the price, refunding each monkey I banana, keeping the other 2 bananas for himself. Ultimately cach monkey paid 9 bananas towards the room and the bellboy got 2 bananas, for a total of 29 bananas. But the original charge was 30 bananas.Where did the extra 1 banana go?
Step 1
Given;
[tex]\begin{gathered} Cost\text{ for a room= \$30} \\ Each\text{ monkey pays 30 bananas} \\ Clerk\text{ ask bell boy to refund 5 bananas} \\ Bell\text{ boy refunds 3 bananas} \\ Bell\text{ boy keeps 2 bananas} \end{gathered}[/tex]Required; To determine where 1 banana went if 29 bananas are accounted for.
Step 2
Here is the break down; the balance should be like this;
[tex]\begin{gathered} 25\text{ bananas-room} \\ 3\text{ banans\lparen3}\times1\text{ banana\rparen- back to monkeys} \\ 2\text{ bananas- Bell boy} \\ Total-30\text{ bananas} \end{gathered}[/tex]Hence, there is no extra 1 banana, The monkeys spent 27 bananas of which the bellboy took 2 bananas and 25 bananas went to the room, and 3 bananas where returned to them. A total of 30 bananas
Which graphs are correct?
Question 11
The slope is 7/2 (so the line is increasing), and the y-intercept is 3.
Answer is A.Question 12
The slope is -8/3 (so the line is decreasing), and the y-intercept is -5.
Answer is D.7y+2=11y-3please help me answer
Equation
[tex]\begin{gathered} 7y+2=11y-3 \\ 11y-7y=2+3 \\ 4y=5 \\ y=\frac{5}{4} \\ \end{gathered}[/tex]Steps
1. Group the variables and constants on each side of the equality
2. Operate the variables and operate the constants.
3. Divide both parts by 4 to clear y
The answer would be y = 5/4
1. Calculate the average number of cheeseburgers eaten in a year by the followingpeople: Heidi ate 0. Tom ate 24. Diamond ate 18, Jesse ate 30, Maureen ate 0,and Makayla at 15
Number of people = 6
(0+ 24 + 18 + 30 + 0 + 15)/ 6 = 87/6
. = 14 + 3/6
Then answer IS
Average number of cheeseburgers= 14
A plumber charges $75 make a house call. He also charges $32.50 per hour for labor. If the bill from the plumber is $286.25, how many hours did he work at your house?
which expression is equivalent to 3/4-2/5
15/20-8/20
8/9-6/9
3/20-2/20
3/9-2/9
The expression that can be considered as been equivalent to 3/4-2/5 is 15/20-8/20.
How can the equivalent expression be gotten?The equivalent expression be gotten by finding the values of the given answer one after the other, from the given option, we can see that the value of the difference in the given expression is 0.35, then the value option A is also 0.35 which implies that the option A as well as the given expression have the same value.
It should be noted that the option A can as well be simplified as still get the vale of the given option.
Therefore, option A is correct.
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Santiago is going to invest in an account paying an interest rate of 3.3% compounded annually. How much would Santiago need to invest, to the nearest ten dollars, for the value of the account to reach $81,000 in 16 years?
Santiago needs to invest 50467.3 dollars for the value of the account to reach $81,000 in 16 years at a rate of 3.3%.
What are simple and compound interests?Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.
Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
Given Santiago is going to invest in an account paying an interest rate of 3.3% compounded annually for the value of the account to reach $81,000 in 16 years.
We know the formula of compound interest which is A = P(1 + r/100)ⁿ,
where A = Amount, P = Principle, n = Time in years and r = rate percentage.
∴ 81000 = P( 1 + 3.3/100)¹⁶.
81000 = P( 1 + 0.03)¹⁶.
81000 = P( 1.03)¹⁶.
81000 = P×1.605.
P = 81000/1.605
P = 50467.3 dollars.
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Please help me
:) thank you
Answer:
11 degrees
Step-by-step explanation:
Answer: 28 degrees
Step-by-step explanation: Set the two equations equal to each other, and solve. X equals 4 and then you plug that into 7x. 7x4 is 28.
Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. What was her change? Write one other combination of coins Susan could use with her $10 bill to get only bills.
The change left when Susan buys lotion for $2.33 and gives the bill is $8.
How to calculate the value?Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. The total amount will be:
= $10 + (3 × 0.1) + (3 × 0.01)
= $10.33
The change left will be:
= Total amount - Cost of lotion
= $10.33 = $2.33
= $8
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In Triangle ABC, AB= 6cm, AC= 8cm, and BC= 12cm.
Angle ACB= 26.4
Calculate the area of triangle ABC
The area of the triangle is 18 cm.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In Triangle ABC,
AB= 6cm
AC= 8cm
BC= 12cm.
Angle ACB= 26.4
The area of a triangle is given as:
Area = 1/2 x base x height
From the figure below,
Base = BC = 12
D is the midpoint of BC.
BC = BD + DC
DC = 12/2 = 6
Height = Tan 26.4
Tan 26.4 = AD / DC = AD / 6
0.50 = AD / 6
AD = 0.50 x 6
AD = 3
Now,
Area of the triangle ABC:
= 1/2 x base x height
= 1/2 x 12 x 3
= 18 cm
Thus,
The area of the triangle is 18 cm.
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View the attacted image for question.
Answer:
The limit from the left does not equal the limit from the right.
Enter the polynomial function f(x) in standard form given that f has leading coefficient 2 and roots 2, sqrt{3}, and -sqrt{3}.
Given that a polynomial function [tex]f(x)[/tex] has,
leading coefficient= 2roots = 2 , √3 , -√3And we need to find [tex]f(x)[/tex]
as we know that if a polynomial has zeroes as [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the cubic polynomial is given by,
[tex]\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ [/tex]
where ,
k is the leading coefficient.Now substitute the given zeroes, as ;
[tex]\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}][/tex]
[tex]\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ [/tex]
[tex]\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}[/tex]
and we are done!
Answer:
[tex]f(x)=2x^3-4x^2-6x+12[/tex]
Step-by-step explanation:
Given characteristics of the polynomial:
leading coefficient = 2roots = 2, √3, and -√3.As the polynomial has 3 roots, it is a cubic polynomial.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}[/tex]
Substitute the given leading coefficient and roots into the formula:
[tex]f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})[/tex]
Expand to standard form:
[tex]\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)[/tex]
[tex]\implies f(x)=(2x-4)(x^2-3)[/tex]
[tex]\implies f(x)=2x^3-6x-4x^2+12[/tex]
[tex]\implies f(x)=2x^3-4x^2-6x+12[/tex]
Describe the relationship between GPE and kinetic energy
Step-by-step explanation:
when an object gains height, Kinetic energy in the object is converted to gpe. gpe = mgh
when an object loses height and falls down, the object is accelerated by gravity (free fall) therefore, gains velocity which means the gpe is converted to kinetic energy.
kinetic energy = 1/2 × m × v²
this is applicable only when the mass is constant.
hope it helps. :)
Dave earned $637 last week. He worked 35 hours and earned the same amount rach hour. How much was he paid per hour?
HELP If r = -6, s = -2, v = 10, and w = 3; then
vs(r - s) ÷ 2 + rw =
Responses
A -98
B 58
C -22
D 22
E -62
If r = -6, s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22
The expression is
vs(r-s) ÷ 2 + rw
The values are
r = -6
s = -2
v = 10
w = 3
Substitute the values in the given expression
= 10×-2 (-6-(-2)) ÷ 2 + -6×3
First we have to do the arithmetic operation in brackets
= 10 × -2 (-4) ÷ 2 + -6×3
Next we have to do the multiplications
= 80 ÷ 2 -18
Do the division
= 40-18
= 22
Hence, if r = -6, s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22
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Does anyone know how to do this? I keep getting stuck on it. Look at this graph. What is the equation of the line in slope-intercept form?
Answer: 4/1
Step-by-step explanation: You go on the y-axis up to 6 then you count up until you get to 10 then you go over 1 so the equation would be 4/1
The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99, where n is the number of different colors in the design. Write a simplified expression that represents the cost of 15 sweatshirts.
Answer:
3.5n + 29.99 × 15
Step-by-step explanation:
Since it is an expression there are no equals, and since we do not know how many colors there are in the design we leave the variable.
A) Justin bought 27 pounds of sugar for $11. How many pounds of sugar did he get per dollat? Pounds per dollars mearest hundredth. B) A color printer prints 20 pages in 7 minutes. How many minutes does it take per page? Minutes per page nearest hundredth.
A)
[tex]\begin{gathered} \frac{27\text{ pounds }}{11\text{ dollars}}=\text{ } \\ 2.45\text{ pounds per dollar } \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{20\text{ pages}}{7\text{ minutes}}= \\ 2.86\text{ pages per minutes} \\ \\ Then: \\ If\text{ 2.86 pages are printed in 1 minute, how many minutes does it take for 1 page?} \\ \frac{1\text{ page \lparen1 minute\rparen}}{2.86\text{ pages}}=\text{ } \\ 0.35\text{ minutes takes to print 1 page. } \end{gathered}[/tex]
6. Serita worked 6 h and earned $31.50.
What is her hourly wage?
In linear equation, $5.26 is her hourly wage .
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Ax+By=C is the typical form for linear equations involving two variables. A standard form linear equation is, for instance, 2x+3y=5. It is rather simple to locate both intercepts when an equation is stated in this way (x and y).Serita worked 6 h and earned $31.50.
1 hour of wage of serita = $31.50/6
= $5.26
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a box contains 6 red, 8 green, 10 blue, 12 yellow and 15 white balls. what is the minimum number of balls we have to choose randomly from the box to ensure that we get 9 balls of same color?
The minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
Given that a box contains 6 red, 8 green, 10 blue, 12 yellow, and 15 white balls.
As the question says that the minimum number of balls chosen must ensure that we get 9 balls of the same color, so we must consider the balls of those colors which are more than 9 in number.
Here, 10 blue, 12 yellow, and 15 white balls are considered as they are more than 9.
By applying the Pigeon principle,
we can get.,
9 blue + 9 yellow + 9 white – 3 + 1 = 25
As we are picking randomly so we can get all the red and green balls before the above 25 balls.
Therefore we add the balls 6 red + 8 green + 25 = 39
Hence, the minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
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