you and four friends go to johnny rockets. you all split the bill equally. each person share was $6.50. how much was the original bill. let a represent the amount of the original bill
The amount of the original bill at johnny rockets was $32.50.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Let a represent the total bill.
You and four friends split the bill equally. each person share was $6.50. Hence:
a / 5 = 6.50
a = 32.5
The amount of the original bill at johnny rockets was $32.50.
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How is the quotient 80000 divided by 2000 different from the quotient 80000divided by 200 or 80000 divides by 20
The difference in quotients arises because dividing by smaller numbers results in larger quotients. For example, 80,000 divided by 2,000 equals 40, while dividing by 200 equals 400, and by 20 equals 4,000.
To understand this, let's calculate each quotient step-by-step:
80,000 divided by 2,000:The differences in results are due to the different divisors. As you divide by smaller numbers, the quotient increases because each division breaks the total into more parts.
Division and multiplication are closely related; dividing by a number is the same as multiplying by its reciprocal.
Summary
The fundamental concept here is that dividing by a larger number results in a smaller quotient, whereas dividing by a smaller number results in a larger quotient. This difference is evident when comparing the quotients of 80,000 divided by 2,000 (40), 200 (400), and 20 (4,000).
What polynomial has roots of −6, 1, and 4?
The answer is c.
If you have a root (a), it can also be written as (x-a).
(x+6),(x-1),(x-4)
Multiply all of them together to get the equation
(x+6)(x-1)(x-4)=
(x2-x+6x-6)(x-4)=
(x2+5x-6)(x-4)=
(x3+5x2-6x-4x2-20x+24)=
x3+x2-26x+24
To find a polynomial with given roots −6, 1, and 4, we create factors (x + 6), (x - 1), and (x - 4). Multiplying these factors, we get the polynomial x3 - 5x2 - 21x + 24.
Finding the Polynomial with Given Roots
To find a polynomial with roots of −6, 1, and 4, we need to create factors that each set to zero at these roots. A polynomial is a product of its factors, and a root is a solution to the equation where the polynomial is equal to zero. The factors corresponding to the roots −6, 1, and 4 are (x + 6), (x - 1), and (x - 4) respectively. Multiplying these factors gives us the polynomial:
(x + 6)(x - 1)(x - 4) = x3 - (1 + 4)x2 + (4 - 1 - 24)x + (6 x 1 x 4)
Let's expand and simplify:
x3 - 5x2 - 21x + 24
Therefore, the polynomial with roots of
−6, 1, and 4 is x3 - 5x2 - 21x + 24.
23 decreased by the product of 44 and an unknown number is 199. What is the value of the unknown number.?
A local college recently reported that enrollment increased to 108% percent of last year. If enrollment last year was at 17,113, about how many students enrolled this year? Round to the nearest whole number. please help!!
Any of these will help???? Please help me
Find the distance, to the nearest tenth, from T(6,-5) to V(-2,6).
A.) 1.7 units
B.) 3.0 units
C.) 8.3 units
D.) 13.6 units
Place -1.25,0.1,2.9,-2.6 on a number line
Please Help Fast!!
Only answer if you are positive you know the answer, and explain why you choose that answer.
Solve for X.
X^3=1/27, or it could be worded as, X to the third power = 1 over 27
Describe the similarities and differences between a rhombus, square , and rectangle.
To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32°. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35°. Estimate the height of the mountain.
To estimate the height of a mountain using angles of elevation from two points, set up a system of trigonometric equations based on right triangles and solve for the height using algebra.
To estimate the height of a mountain given two angles of elevation at different points, we use trigonometric concepts. At the first point, the angle of elevation is 32°, and at a point 1000 feet closer, the angle is 35°. To solve this, we can set up two right triangles that share the same height (the mountain) but have different base lengths. Denote the height of the mountain as h, the distance from the first observation point to the base of the mountain as d, and use the trigonometric tangent function:
Tan(32°) = h / d
Tan(35°) = h / (d - 1000)
This creates a system of two equations with two variables. We solve for h by manipulating the equations to isolate h and substituting into one of the equations. We can use trigonometric tables or a calculator to find the values for Tan(32°) and Tan(35°), and then solve for the distance d, which subsequently allows us to find the height h by simple algebraic rearrangement.
Mixed multiplication problems.PLEASE SHOW THE WORK THANKS
evaluate 16/6 - 2/9
4 2/3
1 5/9
2 2/3
2 4/9
which division expression is equivalent to 4 1/3 ÷ -5/6
[tex]4\dfrac{1}{3}\div\left(-\dfrac{5}{6}\right)\qquad(*)\\\\\text{Convert the mixed number to the improper fraction:}\\\\4\dfrac{1}{3}=\dfrac{4\cdot3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\(*)=\dfrac{13}{3}\div\left(-\dfrac{5}{6}\right)\\\\\text{By dividing by a fraction, we multiply by its reciprocal.}\\\\=\dfrac{13}{3}\cdot\left(-\dfrac{6}{5}\right)\qquad\text{simplify}\\\\=\dfrac{13}{3\!\!\!\!\diagup_1}\cdot\left(-\dfrac{6\!\!\!\!\diagup^2}{5}\right)=-\dfrac{13\cdot2}{1\cdot5}=-\dfrac{26}{5}=-\dfrac{25+1}{5}=-5\dfrac{1}{5}[/tex]
Answer:
the answer is 13/3 ÷ ( - 5/6 ) my luv :)
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Step-by-step explanation:
Am I doing this right?
16,14=4
15,35=5
24,32=4
27,63=9
20,80=20
18,38=2
14,49=7
66,99=33
9,35=1
6,24,42=6
30,50,70=10
32,48,96=12
10w,5w=5
16xy,24xy=8
21ab,35a=7
10jk,15k=5
3mn,9mn,12mn=3
6xy,9x,3y=3
A photocopy clerk copies 80 pages in 4 min. How much time will he take to copy 200 pages?
math question down below
Solve. (–12.7) ∙ 3.8 ∙ (–7.2) = x ∙ (3.8) ∙ (–12.7) A. –12.7 B. –7.2 C. 1 D. 3.8
The function f (x) varies directly with x and f (x) =90 when x=30
what is f (x) when x=6
2
5
15
18
f(x)=-2x^4+13x^3-25x^2+8x+12
How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
Answer:
How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
⇒ 1 triangle(s)
How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?
⇒ 0 triangle(s)
Answer:
The first one is 1. The second one is 0.
Step-by-step explanation:
I just did it and got it right.
The twenty-six coins are all dollars and quarters, and they add up to seventeen dollars in value. How many dollars and how many quarters are there?
d +q = 26
d=26-q
1d +0.25q = 17
1(26-q) +0.25q = 17
26 -q +0.25q = 17
26-0.75q = 17
-0.75q = -9
q = -9 / -0.75 = 12
12 quarters and 14 dollars
check 12 * 0.25 = 3
3+14 = 17
The distance between R and T on the coordinate grid is ___ units. (Input whole numbers only.)
Image of a coordinate grid with point R R located at negative 30, 10 and point T located at 15, 10.
the distance between the R and the T is
4 units
A tape costs $4 less than the CD. Okasha bought 1 CD in five tapes. If the total cost was $70 what was the price of the CD ?
8(3m+5)=2m-4 and plz show how you got it
Use the simple interest formula to find the ending balance.
$1500 at 7% for 1.5 years. 13 points
The cost of a barrel of oil has recently increased by 20% and is now selling for $72.00. How much was the barrel of oil before the increase?
Answer:
[tex]\$60[/tex]
Step-by-step explanation:
Let
x------> the cost of the barrel of oil before the increase
we know that
[tex]100\%+20\%=120\%[/tex]
[tex]120\%=\frac{120}{100} =1.2[/tex]
so
[tex]1.2x=72[/tex]
Solve for x
[tex]x=72/1.2=\$60[/tex]
A builder uses squares to lay out various projects. Write two equations. The first equation should express the area of the square (a) as a function of the length (l) of a side. The second should express the volume of a cube (v) as a function of the length (s) of a side.
Answer:
The area of the square:
a = l²
The volume of a cube:
v = s³
Jacob put 2/18 tablespoons of oil into the bowl. Then he put 1 2/8 tablespoons of milk into the bowl. How much liquid did Jacob put into the bowl?
One foot is equivalent to 30.48 centimeters . Write this value as a mixed number in simplest form. PLEASE HELP!!!