Given:
The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:
[tex]x=1000-100p[/tex]
To find:
The selling price if the company wants the weekly revenue to be $1,600.
Solution:
We know that the revenue is the product of quantity and price.
[tex]R=xp[/tex]
[tex]R=(1000-100p)p[/tex]
[tex]R=1000p-100p^2[/tex]
We need to find the value of p when the value of R is $1600.
[tex]1600=1000p-100p^2[/tex]
[tex]1600-1000p+100p^2=0[/tex]
[tex]100(16-10p+p^2)=0[/tex]
Divide both sides by 100.
[tex]p^2-10p+16=0[/tex]
Splitting the middle term, we get
[tex]p^2-8p-2p+16=0[/tex]
[tex]p(p-8)-2(p-8)=0[/tex]
[tex](p-8)(p-2)=0[/tex]
Using zero product property, we get
[tex]p-8=0[/tex] or [tex]p-2=0[/tex]
[tex]p=8[/tex] or [tex]p=2[/tex]
Therefore, the smaller value of p is $2 and the larger value of p is $8.
a suit is on sale for 15% off. the sale price is $442. what is the regular price?
Answer:
520
Step-by-step explanation:
100% - 15% = 85%
85% of the original price is 442 dollars
100% = x
solve for x:
x * 0.85 = 442
x= 520 dollars
regular price is 520 dollars.
A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a frozen yogurt?
hint.. correct answer is 4096
somebody help me please
Answer:
x=-4
Step-by-step explanation:
:Distribute 2 to 9.7 and -4.8x
3.4+19.4-9.6x=61.2
:combine 3.4 and 19.4
22.8-9.6x=61.2
: subtract 22.8 from both sides
-9.6x=61.2-22.8
:divide both sides by -9.6
-9.6x/-9.6=38.4/-9.6
x=-4
Which is equivalent (Algebra ll)
Answer:
D : [tex]x^{2} +81=x^{2} +20x+100[/tex]
Step-by-step explanation:
We start with the original equation:
[tex]\sqrt{x^{2} +81} =x+10[/tex]
Squaring both sides to remove the square root we get:
[tex]x^{2} +81=(x+10)^{2}[/tex]
Expanding the right side:
[tex]x^{2} +81=(x+10)(x+10)[/tex]
Multiplying the right side out and combining like terms we get:
[tex]x^{2} +81=x^{2} +20x+100[/tex]
Find m when 2.4^m-2=√16^3m×2
Answer:
JNGTHGNH
Step-by-step explanation:
GHGNJHGYJNR56T5465465
1. make r the subject of the relation. 2. Find the value of r when s=117, m = 2 and n=-3. m=r-s ÷2nr
Answer:
Hence, the required answers are (i) r= -s/(2nm-1) and r=g.
Step-by-step explanation:
solution: m= r-s/2nr
i) m= r-s/2nr 2) m(2nr) = r-s (i) s=117 ,m=2, n=-3
2) 2xnxmxr= r-s 2) r= -s/(2nm-1)
3) move the "r" on the right to the 2) r= -117/(2x(-3)x2)-16
-2nrm-r= -s
- r(r-2nm-1)= -s 2) r= (-117/-13)=)r=g
- r= -s/(2nm-1)
Hence, the required answers are (i) r= -s/(2nm-1) and r=g.
Y =
x
+
Start Over
y
OF
9
8
6
5
4
-10 -9
-8
-6
-4
1
1
4
9
-
8
9
OT
--
-6
-9
-9
Answer:
therefore According to the diagram y= start over
The transformation of the parent graph of y = √x to y = (1/2)√x is a vertical compression by a factor of 1/2.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
As per the shown graph, for any value of x, the output of the function y = (1/2)√x is half of the output of the function y = √x. This means that the y-values of the transformed graph are compressed vertically by a factor of 1/2 compared to the parent graph, while the x-values remain unchanged.
Visually, the graph of y = (1/2)√x will be flatter and closer to the x-axis than the graph of y = √x, with the same x-intercepts (0,0) and (1,1).
Thus, the y-values of the transformed graph are compressed vertically by a factor of 1/2 compared to the parent graph.
To learn more about the transformations click here :
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Last month, a factory produced 880 television sets. This month, the same factory produced 1,210 television sets. The increase in production from last month to this month is
Answer:
330 television set
Step-by-step explanation:
Last month production = 880 television sets
This month production = 1,210 television sets
The increase in production from last month to this month = This month production - Last month production
= 1,210 - 880
= 330
The increase in production from last month to this month = 330 television set
As per linear equation, the increase in production of television of the factory is 330.
What is a linear equation?A linear equation is an equation where the variable has the highest power of 1.
Given, a factory produced 880 television sets last month.
This month, the same factory produced 1,210 television sets.
Therefore, the increase in production of television of the factory is
[tex]= (1210-880)\\= 330[/tex]
Learn more about a linear equation here: https://brainly.com/question/11203335
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kareem finished his math assignment in 1/2 hours. he finished his history assignment in 1/8 hours. how much more time did kareem spend on his math assignment
Answer:
[tex] \frac{3}{8} \: hours[/tex]
Step-by-step explanation:
Additional time =
[tex] \frac{1}{2} - \frac{1}{8} \\ = \frac{4}{8} - \frac{1}{8} \\ = \frac{3}{8} [/tex]
Answer:
3/8 hours is the time to Finnish
Find the area of the rhombus
Answer:
60 u²
Step-by-step explanation:
Finding second diagonal :-
d' = √{ 17² - 8²} d' = √{ 289 - 64 } d' = √{ 225 } d' = 15 uUsing formula :-
A = 1/2 * d * d' A = 1/2 * 15 * 8 A = 15 * 4 u²A = 60 u²PLS HELP TIMED QUESTION (I'll mark brainiest)
Please show work if possible.
Hello,
[tex]sin(45^o)=\dfrac{\sqrt{2} }{2} \\\\sin(45^o)=\dfrac{a}{c} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{a}{6} \\\\a=6*\dfrac{\sqrt{2} }{2}=3\sqrt{2}\\[/tex]
Answer A
(05.05 HC)The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. What is the area, in square units, of this polygon? 27 units2 33 units2 36 units2 51 units2
Answer:
Area = 36 squ. unit
Step-by-step explanation:
According to the Question,
Given That, The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. (Please find diagram in attachment)by using these points a quadrilateral is formed with two opposite sides 7 and 5 and with height 6 (Refer in the diagram).
Therefore, the area of this polygon isArea = 1/2 * (sum of opposite side) * height
Area = 1/2 * (7+5) * 6
Area = 3*12
Area = 36 squ. unit
Answer:
36
Step-by-step explanation:
Does anyone know the answer?
Answer:
A
Step-by-step explanation:
A and B are the only answer choices that give you imaginary number outputs
But because the function in the answer choices is a negation of the original function they give different outputs, thus a different range
Therefore A is the correct answer
BRAINLIEST PLEASEEEEEEEE
Answer:
it is the first answer... has the same domain as the function
Step-by-step explanation:
Helpppp someone please
Given:
The graph of system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].
[tex]y\leq 10[/tex].
The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].
Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]
[tex]y=1(x)+1[/tex]
[tex]y=x+1[/tex]
The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].
[tex]y> x+1[/tex]
So, the required system of inequalities is:
[tex]y> x+1[/tex]
[tex]y\leq 10[/tex]
[tex]x\geq 0[/tex]
Therefore, the correct option is B.
If you sell 25 items at $150 a piece and your commission rate is 40%, how
much commission do you earn?
Answer: 1500 dollars.
Step-by-step explanation:
25 * 150 = 3750 (dollars) - total sale amount;
3750 : 100% * 40% = 1500 (dollars) - commission.
Question 2 Multiple Choice Worth 1 points)
(01.06 MC)
If D is the midpoint of AB and AB = 15, what is AD?
Answer:
If D is the midpoint of the segment AB, then we have to find the measure of segment AD. Therefore, AD = 7.5 units will be the answer.
What is the exact value of tan (9 pi)/12
Answer:
tan(9pi/12) = 0.041146549
Step-by-step explanation:
QUESTION 4
f(x)=4x-10/x-2
4.1 Determine the x- and y-intercepts of
4.2 +9. Write f (x) in the form: f(x) = x - 2 4.3 Draw the graph of y, clearly show the intercepts with the axes and the asymptotes.
4.4 Give the equations of the asymptotes of f(x) + 3.
Answer:
4.2+9.Write f (x)in the form:f(x)=x-2 4.3Draw
Is the product of two prime numbers a prime number or a composite
number?
Step-by-step explanation:
No, the product of two (or more) prime numbers cannot result in another prime number. By definition, a prime number is a number that is divisible by 1 or itself - the act of multiplying two or more primes together will always yield a number divisible by 1, itself and the prime numbers multiplied together to achieve it.
Answer:
a composite one
Step-by-step explanation:
Why?
It is easy-peasy.
First, it is impossible to have a prime number. Because primes are only divisible by 1 and themselves.
For example, 3 is a prime. 7 is a prime. Multiply them and get 21.
I hope it helped:)
Help mee A scout troop are hiking in a forest. Starting from their base, they walk 4.2km south followed by 7.1km west. They want to walk the shortest distance back to their base. On what bearing should the scouts walk?
Answer:
They should walk on a bearing of 59.4 degrees
Step-by-step explanation:
Given
[tex]South = 4.2km[/tex]
[tex]West = 7.1km[/tex]
Required
The bearing back to the base
The given question is illustrated with the attached image.
To do this, we simply calculate the measure of angle a using:
[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan(a) = \frac{7.1}{4,2}[/tex]
[tex]\tan(a) = 1.6905[/tex]
Take arctan of both sides
[tex]a = \tan^{-1}(1.6905)[/tex]
[tex]a = 59.4^o[/tex]
The bearing that the scout should work is N59.4W for the shortest distance
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let A represent the angle that the scouts walk
tan∠A = 4.2/7.1
A = 30.6°
The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance
Find out more on Trigonometric ratio at: https://brainly.com/question/4326804
16x7[(99-64)•2] PLEASE HELP!!!
Answer:
7840
Step-by-step explanation:
start with the (). 99-64 is 35. then 35 times 2 is 70. 16 times 7 (whats on the outside) is 112 and 112 times 70 is 7840
find the point(s) in which f(x)=e^5-2x and y=6 intercept
Answer:
(1.6, 6)
Step-by-step explanation:
[tex] ln({e}^{5 - 2x} = 6)[/tex]
[tex]5 - 2x = ln(6) [/tex]
[tex]2x = 5 - ln(6) [/tex]
[tex]x = \frac{5 - ln(6) }{2} [/tex]
y = 6
According to the rational root theorem which of the following are possible roots for the function below x^4-29x^2+100
Hello,
The rational roots may be all divisors of 100
+1,-1,+2,-2,+4,-4,+5,-5,+10,-10,+20,-20,+25,-25,+50,-50,+100,-100
f(x)=x^4-29x^2+100
f(5)=5^4-29*5^2+100=0 : 5 is a root
f(-5)=(-5)^4-29*(-5)²+100=0 : -5 is a root
f(2)=2^4-29*2²+100=0 : 2 is a root
f(-2)=(-2^)^4-26*(-2)²+100= 0 : -2 is the last root.
The figure below shows the design of a truss to support the weight of a roof. In this truss design, ∠A⩭∠D and ĀF⩭DF.
Answer:
[tex]m\angle A= 30^{\circ}[/tex]
Step-by-step explanation:
In the question, we're given [tex]\angle A\cong \angle D[/tex]. Therefore, the measure of these two angles must be equal.
To find the value of [tex]x[/tex], set these two angles equal to each other:
[tex]4x-26=x+16[/tex]
Add 26 and subtract [tex]x[/tex] from both sides:
[tex]3x=42[/tex]
Divide both sides by 3:
[tex]x=\frac{42}{3}=14[/tex]
Since [tex]\angle A[/tex] was labelled as [tex]4x-26[/tex], substitute [tex]x=14[/tex] to find its measure:
[tex]\angle A=4(14)-26,\\\angle A=56-26,\\\angle A=\boxed{30^{\circ}}[/tex]
You can also substitute [tex]x=14[/tex] into the label of angle D as angle A is congruent to angle D for easier calculations ([tex]14+16=\boxed{30^{\circ}}[/tex]).
what is the answer of this questoin 2c-3b+6+7b-2b+11?
Answer:
[tex]2c+2b+17[/tex]
Step-by-step explanation:
-----------------------
Given:
[tex]2c-3b+6+7b-2b+11[/tex]
---------->>>>
Collect like terms.
[tex]2c+(-3b+7b-2b)+(6+11)[/tex]
---------->>>>
Simplify
[tex]2c+2b+17[/tex]
------------------------
Hope this is helpful.
Answer:
2c-2b+17 if using algebra
Step-by-step explanation:
firstly group like terms 2c+(-3b)+7b-2b+6+11
2c-2b+17
Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.
Answer:
there are 2 apples in the basket
there are 10 banana in the basket
Step-by-step explanation:
According to the Question,
We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.let x for apple And y for banana So, x+y=12---Equation 1
And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.Thus, 5x+7y=80 ----Equation 2
Now, (Equation 1) × 5 Subtract with (Equation 2) We get,
2y = 20 ⇒ y=10 (there are 10 banana in basket)
Put value of y=10 in Equation 2 we get5x+70=80 ⇔ x=2(there are 2 apples in basket)
Pick the correct graph and equation pleasee!
Given:
Amount of flour in a bin = 30 cups
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
To find:
The correct equation and graph for the given situation.
Solution:
Let F be the amount of flour in the bin and c be the number of signature cakes.
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
Flour required for each signature cake = [tex]1.5[/tex] cups
Flour required for c signature cakes = [tex]1.5c[/tex] cups
Amount of flour in a bin is 30 cups and it is reduced by 1.5c cups. So, the amount of flour in the bin is:
[tex]F=30-1.5c[/tex]
At [tex]c=0[/tex], we get
[tex]F=30-1.5(0)[/tex]
[tex]F=30[/tex]
At [tex]F=0[/tex], we get
[tex]0=30-1.5c[/tex]
[tex]1.5c=30[/tex]
[tex]c=\dfrac{30}{1.5}[/tex]
[tex]c=20[/tex]
Therefore, the required equation is [tex]F=30-1.5c[/tex] and the 4th graph is correct.
Can someone help with 3 and 9
Answer:
9= 512m/1000m
SIMPLIFY IT
Step-by-step explanation:
what is the inverse function f f(x)=radical x +7
Step-by-step explanation:
by switching the places of x and y ans solving for y
−3x−6+(−1)
need answer pls
Step-by-step explanation:
−3x−6+(−1)
-3x-7
Hope it helps youAnswer:
−3 −7
Step-by-step explanation:
-3x-6-1
-3x-7