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A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram represents the situation. How many markers were originally in each box?
Answers
Answer:
45
Step-by-step explanation:
90/3=x-15
30=x-15
45=x
check
45-15=30
30*3=90
Answer:
45
Step-by-step explanation:
Related Questions
Describe the relationship between GPE and kinetic energy
Answers
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. :)
I need help pls someone -
Answers
Answer:
Number above 42 : 14
Number beside 2 : 1
Number above 0: 12
Step-by-step explanation:
In Triangle ABC, AB= 6cm, AC= 8cm, and BC= 12cm.
Angle ACB= 26.4
Calculate the area of triangle ABC
Answers
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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what is tan x + cot x ?
pls help
Answers
Answer:
cosecxsecx
Step-by-step explanation:
[tex]\hookrightarrow tanx+cotx\\\\\hookrightarrow \frac{sinx}{cosx} +\frac{cosx}{sinx} \\\\\hookrightarrow \frac{sin^{2}x+cos^{2}x }{sinxcosx} \\\\\hookrightarrow \frac{1}{sinxcosx} \\\\\hookrightarrow cosecxsecx[/tex]
I need help on this one
Answers
△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.
Answers
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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Enter the polynomial function f(x) in standard form given that f has leading coefficient 2 and roots 2, sqrt{3}, and -sqrt{3}.
Answers
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]
What’s the answer asp
Answers
Answer:
the 61 curv should lead to ars so the answer is ars
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?
Answers
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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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
12,10,8
Answers
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.)
x^3−x^2−2x=0 Help me factory this problem
Answers
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]
Which graphs are correct?
Answers
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.compare the x-intercepts for the two linear functions represented in the table below. which of the following statements is true?
Answers
• Given Function A:
[tex]-4x+2y=-2[/tex]You need to remember that, by definition, the value of "y" is zero when the function intersects the x-axis.
Therefore, you need to set up that:
[tex]y=0[/tex]Substitute this value into the function and then solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} -4x+2(0)=-2 \\ -4x=-2 \\ \\ x=\frac{-2}{-4} \\ \\ x=\frac{1}{2} \end{gathered}[/tex]• Given that Function B passes through these points:
[tex](0,-1),(3,2)[/tex]You need to determine the equation of the line, in order to find the x-intercept using it.
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
By definition, the value of "x" is zero when the function intersects the y-axis. Therefore, knowing the first point given in the exercise (whose x-coordinate is zero), you can determine that, for this line:
[tex]b=-1[/tex]Substitute "b" and the coordinates of the second point into this equation:
[tex]y=mx+b[/tex]And then solve for "m":
[tex]\begin{gathered} 2=m(3)-1 \\ 2+1=3m \\ \\ \frac{3}{3}=m \\ \\ m=1 \end{gathered}[/tex]Therefore, the equation of Function B in Slope-Intercept Form is:
[tex]y=x-1[/tex]Now you can find the x-intercept by using the procedure used for Function A:
[tex]\begin{gathered} 0=x-1 \\ x=1 \end{gathered}[/tex]You know that:
[tex]\frac{1}{2}<1[/tex]Hence, the answer is: Third option.
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.
Answers
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.
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?
Answers
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
View the attacted image for question.
Answers
Answer:
The limit from the left does not equal the limit from the right.
angie just bought a new lamp for her bedside table.the old lamp was 2 1/4 feet tall and the new lamp is 4 feet how much taller is the new lamp than the old lamp?
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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
Answers
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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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
Answers
Number of people = 6
(0+ 24 + 18 + 30 + 0 + 15)/ 6 = 87/6
. = 14 + 3/6
Then answer IS
Average number of cheeseburgers= 14
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?
Answers
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
question in the screenshot
Answers
Answer: 6.4
Step-by-step explanation:
if h(x)=10-x^2, then determine the value of h(f(2))
Answers
But once you have to find F then you can calculate the value of F (2). Can you plug the value into H and calculate the results
A. In a game, each player receives the same
amount of play money. They each get
twenty-five $1's, three $5's, four $10's, two
$100's. How much money does each player
get?v
Answers
6. Serita worked 6 h and earned $31.50.
What is her hourly wage?
Answers
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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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.
Answers
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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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?
Answers
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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3n -4 =11 i need to show solving steps
Answers
+4 +4
3n=15 divide both by 3
n=5
Answer:
n=5Step-by-step explanation:
To solve this, find the value of n to one side of the equation.
N is a variable.
Variable is a quantity that can assume any of a set of values.
3n-4=11
First, you add by 4 from both sides.
[tex]\sf{3n-4+4=11+4}[/tex]
Solve.
[tex]\sf{11+4=15}[/tex]
[tex]\sf{3n=15}[/tex]
Then, you divide by 3 from both sides.
[tex]\sf{\dfrac{3n}{3}=\dfrac{15}{3} }[/tex]
Solve.
15/3=5
[tex]\Rightarrow \boxed{\sf{n=5}}[/tex]
As a result, the solution is n=5, which is our answer.
I hope this helps, let me know if you have any questions.
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
Answers
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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2y^2-5y=12. can someone help me solve the quadratic equation using the quadratic formula.
Answers
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 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?
Answers
211.25 divided by 32.50 equals 6.5
he worked for 6.5 hours
