Answer:
Price before discount = $20 per keyboard
Price after discount = $18 per keyboard
Before the discount, you can buy 27 keyboards. After the discount, you can buy 30 keyboards.
===============================================
Work Shown:
k = cost of one keyboard before the price reduction
540/k = amount of keyboards purchased before the price reduction
k-2 = cost of one keyboard after the price reduction
540/(k-2) = amount of keyboards purchased after the price reduction
540/(k-2) = (540/k) + 3
--------------
If you multiply both sides by the LCM k(k-2), then you'll clear out the fractions and we can solve for k like so
540/(k-2) = (540/k) + 3
540k = 540(k-2) + 3k(k-2)
540k = 540k - 1080 + 3k^2 - 6k
0 = 540k - 1080 + 3k^2 - 6k - 540k
0 = 3k^2 - 6k - 1080
3k^2 - 6k - 1080 = 0
3(k^2 - 2k - 360) = 0
k^2 - 2k - 360 = 0
(k - 20)(k + 18) = 0
k-20 = 0 or k+18 = 0
k = 20 or k = -18
We ignore the negative result because a negative price doesn't make sense.
--------------
If k = 20, then
540/k = 540/20 = 27
Meaning that you can buy 27 keyboards before the price reduction
In other words, (27 keyboards)*(20 dollars per keyboard) = 540 dollars total.
After the price reduction, the cost per keyboard is now k-2 = 20-2 = 18
We can now buy 540/(k-2) = 540/18 = 30 keyboards, which is an increase of 30-27 = 3 extra keyboards. This helps confirm we have the correct answer.
Answer:
$20
Step-by-step explanation:
X: the price of a keyboard
Y: number of keyboards to buy (original)
The shop owner spent $540 to purchase a stock of computer keyboards, so:
XY=540
⇒X=540/Y
If the price of each keyboard had been reduced by $2, he could have bought 3 more keyboards:
(X-2)(Y+3)=540
⇒3X-2Y=6
⇒3.540/Y – 2Y=6
⇒Y=27
⇒X=20
⇒ the price of one keyboard: $20
3x<11.75 solve for x please, with step on how you got to that answer!
Answer:
See below
Step-by-step explanation:
3x < 11.75
11.75 / 3 = 3.92
x < 3.92
what is the zero of the function
Answer:
A
Step-by-step explanation:
The zero is the value of x where the line crosses the x- axis
The line crosses the x- axis at x = - 5 ← zero
Answer:
-5
Step-by-step explanation:
The zero of a function is the x-value of the location where the function intersects the x-axis.
Here I read at (-5,0), the function intersects the x-axis, so the zero of the functiion is x = -5
Help is appreciated:)
Answer:
Step-by-step explanation:
(-1, 3)
y=3
Pls I need this I will give brainly if u help me
[tex]4( \frac{1}{5} x + 7) = 2x - 2[/tex]
[tex]x = 25[/tex]
Please help me this is due very soon!(Q13)
Answer:
Step-by-step explanation:
9) (25-x^2 )(a+2) = (5-x)(5+x)(a+2)
11) 9(v-3)+u^2(3-v)
9(v-3)+u^2( -v+3)
9(v-3)-u^2( v-3)
(9-u^2)(v-3)
(3-u)(3+u)(v-3)
will mark brainliest
show workings
Answer:
a) 20 km away fro the starting point.
b) The bearing from P to R is 80°.
c) Q is 60 km North P.
d) Q is - 60 km west of P
Step-by-step explanation:
Stating Facts in the Question:
P to Q is 80 km and bearing 330°
It turned around, Q to R is 60 km and bearing 250°.
a) Picture a number line (Look at the first image)
You go 80 to the right. You turn around and go 60 to the left.
80 - 60 = 20
20 km away fro the starting point
b) Picture a number line (Look at the second image)
P to Q is bearing 330°
Q to R is 60 km is bearing 250°
P to Q is red
Q to R is blue
330° - 250° = 80°
The bearing from P to R is 80°
c) P to Q is 60 km
The plane went forward or North so the answer is 60 km.
Q is 60 km North P.
d) Q to P is 60 km
Q is not to the west of P
Q is - 60 km west of P
The given pattern continues. Write down the nth term of the sequence {a} suggested by the pattern. 7,-14,21,-28
Answer:
7_14-21-28-35-42-49 -56-63-70-77-84
[tex]12 {p}^{5} r \div ( - 10pq)[/tex]
ASAP!!!! PLS HELP
Answer:
Step-by-step explanation:
[tex]\frac{12p^{5}r}{-10pq} = \frac{-6p^{5-1}r}{5q}\\\\=\frac{-6p^{4}r}{5q}[/tex]
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
Why is this a function?
X Y
3. -1
0.
0
-3
-6. 2
(3 and 0 are both assigned to 0)
This is a function because each element in the domain has one and only distinct image in the co-domain.
given the similar triangles at the left, identify the scale factor.
PLEASE HELPPPPPPPPPPPP
what is the answer? can someone help
Answer: Choice B
Explanation: The rule you use is [tex]\sqrt{m*n} = \sqrt{m}*\sqrt{n}[/tex]
Answer:
Step-by-step explanation:
A: is not the answer. The answer is √144 which is 12
B: is correct. You can do it this way, by breaking the 9 and 16 apart.
C: I don't know exactly what the logic of 36 is, but it is not the right answer.
D: I can't explain why the choice would be division. It is multiplication of some sort. D is incorrect.
The diagram shows equilateral triangle RST with altitude SV
It is given that RV = 6 meters. What is the length of ST?
Answer:
ST is 12 meters
Step-by-step explanation:
The given triangle ΔRST = An equilateral triangle
The altitude of ΔRST = SV
The length of segment RV = 6 meters
Given that ΔRST is an equilateral triangle, the base angles of the triangles = 60°, therefore, in the formed triangles, ΔRSV, and ΔTSV, ∠RSV = ∠TSV = 90° - 60° = 30°
∴ ΔRSV, and ΔTSV are congruent, based on ASA rule of congruency
∴ Side VT in ΔTSV is congruent to side RV in triangle ΔRSV
The midpoint of side ST
VT ≅ RV
Therefore, VT = RV = 6 meters
RT = RV + VT = 6 + 6 = 12 By segment addition property
In equilateral triangle, ΔRST, all the sides are equal, therefore;
RT = RS = ST = 12 m
ST = 12 meters.
Which equation represents the formula for the general term, gn , of the geometric sequence 3 , 1 , 1/3 , 1/9 . . .?
Answer:
Explicit
gn = 3(1/3)^(n-1)
Recursive
gn =1/3gn-1
Step-by-step explanation:
3 , 1 , 1/3 , 1/9 . . .
gn = ar^(n-1)
Where,
a = first term = 3
r = common ratio = 1/3
Check:
g2 = ar^(n-1)
= 3(1/3)^(2-1)
= 3/3^(1)
= 1^1
= 1
The explicit formula is
gn = ar^(n-1)
gn = 3(1/3)^(n-1)
The recursive form for a geometric sequence is gn = rgn-1
recursive form for our sequence gn =1/3gn-1
Where,
gn = 3
can someone pls answer and explain this correctly?
Answer:
[tex]6^4[/tex]
Step-by-step explanation:
All you have to do for this is follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Substraction) Which is the order of operations.
First you do parenthesis, [tex](2^2)^2[/tex], when you have a positive exponent outside a parenthesis like this, you add them together, and in this case, you get, [tex](2^2)^2=2^4=16[/tex]
After that, you do the rest of the exponents as well as multiplication, [tex]3^4=81[/tex].
Now we plug in the 81 from our last step along with the 16 from the first step and multiply them together. [tex]3^4*(2^2)^2=81*16=1296[/tex]
Then you just simply need to find which of the answers come out to be the result we got which is 1296. Out of these 4 possible answers, [tex]6^4[/tex] ends up being equal to 1296 which means that is the correct answer.
Answer:
6^4 is equivalent to 3^4 x (2^2)^2
Step-by-step explanation:
3^4 x (2^2)^2 6^8 = 1679616
3^4 x (4)^2 6^4 = 1296
81 x 16 5^4 = 625
1296 5^8 = 390625
What is the domain of the function on the graph
Answer:
The domain is all x-values or inputs of a function. hope this helps!
Step-by-step explanation:
If f(x) = 2x²+2 and g(x) = x² - 1 ,find (f- g)(x).
A. 3x² +3
B. 3x² +1
C. x² +1
D. x² +3
Step-by-step explanation:
(F-g) (X)
= f(x) - g(x)
(2x² + 2 )-(x²-1) =
3x²+3
Kim's class voted on a location for a field trip. 3/4 of the class voted for the museum and 1/8 of the class voted for the zoo. The rest of the class voted for the nature park. What fraction of the class voted for the nature park?
Answer:
1/8
Step-by-step explanation:
3/4=6/8
6/8+1/8=7/8
1-7/8=1/8
HELP I WILL AWARD BRAINLIEST
*Prove that corresponding angle bisectors in congruent triangles are congruent.
Answer:
CPCTC
Step-by-step explanation:
BESTIE MY CAPS LOCK KEY IS LIKE STUCK SO YEAH
ANYWAY, THIS IS GOING TO SOUND REALLY AGGRESSIVE
SO CONGRUENT TRIANGLES HAVE 3 EQUAL SIDES AND 3 EQUAL ANGLES
THEY ARE EXACTLY THE SAME
SINCE WE KNOW ALL OF THIS AWESOME INFORMATION, NOW WE CAN THAT THE ANGLE BISECTORS WILL BE CONGRUENT BY CPCTC -
CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT
WE CAN USE AN EXAMPLE TO UNDERSTAND BETTER
SAY YOU HAVE 2 CONGRUENT TRIANGLES
THE ANGLES ARE 50, 60, AND 70
SAY THAT THE ANGLE BISECTORS ARE ON 60
THEY WILL BE CONGRUENT BECAUSE THEY ARE THE CORRESPONDING ANGLES OF 2 CONGRUENT TRIANGLES
BUT WHEN YOU ARE ASKED FOR A REASON, IT IS BECAUSE OF CPCTC
CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT
Enter the coordinates of the point on the unit circle at the given angle. 135° (-VII, VI Enter
The coordinates of the point on the unit circle at the given angle. 135° is (-√2 / 2, √2 / 2).
What is a unit circle?A circle on the Cartesian Plane with a radius of one unit and a center position is referred to as a unit circle (0, 0). When working with angles and trigonometric functions, the unit circle is a useful tool that makes reference much simpler. The Pythagorean Theorem can be used with the unit circle.
Given:
The unit circle at the given angle 135°,
Calculate the value of sin45 as shown below,
sin (180 - 135) = 1 / √2
sin 45 = 1 / √2
cos(180 - 135) = 1 / √2
cos45 = 1 / √2
Write the coordinates as shown below,
Coordinates = (1 / √2 × √2 / √2, 1 / √2 × √2 / √2 ) (Second quadrant is (-x, y))
Coordinates = (-√2 / 2, √2 / 2)
Thus, the coordinates are (-√2 / 2, √2 / 2).
To know more about unit circle:
https://brainly.com/question/11743473
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Jorden has already saced 35$. He wants to have 80$. He earns $6 per hour doing yard work which function will help jorden gigure out how many more hours [h] he needs to work
Answer:
Number of hours= 7.5
Step-by-step explanation:
Giving the following information:
Amount saved= $35
Hourly rate= $6
Total objective= $80
To calculate the number of hours to be saved, we need to use the following formula:
Number of hours= difference needed / hourly rate
Number of hours= (80 - 35) / 6
Number of hours= 45/6
Number of hours= 7.5
Can someone Help me?
The Answer: C I did this yesterday
Step-by-step explanation:
If an angle does not have a measure of 88°, then the angle is not an acute angle.
What is the value of x in the triangle?
Round your final answer to the
nearest hundredth
Given:
In a right angle triangle,
Hypotenuse = 25 cm
Base = x
Angle between base and hypotenuse = 18 degrees.
To find:
The value of x.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
In the given right triangle,
[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]
[tex]\cos (18^\circ) \times 25=x[/tex]
[tex]0.9510565 \times 25=x[/tex]
[tex]23.7764125=x[/tex]
Round the answer to the nearest hundredth (two decimal).
[tex]x=23.78[/tex]
Therefore, the value of x is about 23.78 cm.
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
M1=44 M2=136 M3=44 M4=136
Step-by-step explanation:
M3= 44 so M1=44 due to opposite angles being equal
then if two of the angles add to 88
360-88= 272
divide 272 by 2 as M2 and M4 are equal
272/2=136
Answer:
m∠1 = 44°
m∠2 = 136°
m∠4 = 136°
Step-by-step explanation:
m∠1 explanation:
I got it from m∠3 since they're both congruent
m∠2 explanation:
Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°
Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°
m∠4 explanation:
I got it from m∠2 since they're both congruent
PLZ HELP ANY GUESS WOULD HELP
Answer:
1st onne I believe I couldd be wrong but thats what I got
Step-by-step explanation:
Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes
Answer: [tex]7.81\ km[/tex]
Step-by-step explanation:
Given
Runner A runs towards North at speed of 10 km/h
Runner B runs towards East at speed of 12 km/h
After half hour, they covered a distance of
[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]
[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]
They are running in perpendicular direction to each other
So, the distance between them is given by
[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]
hy i am in 8th class and my yesterday my math paper anyone help me and anyone in 8th class please reply
Answer:
I'm in 9th grade but i think i can help.
Step-by-step explanation:
Un frutero ha comprado 165kg de manzanas a 2 € el kilo; se le han estropeado 15 kg y el resto los vende a 4 € el kilo. ¿ Cuánto ha ganado? ( 1,25p)
Answer:
€270
Step-by-step explanation:
If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;
Cost price = 165 * 2 = €330
If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg
If he rests he sells for € 4 per kilo, then;
Selling price = 150 * 4 = €600
Amount earned = €600 - €330
Amount earned = €270
Determine whether the triangles are congruent. Explain your reasoning .
SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)
Answer:
Step-by-step explanation:
The two triangle are congruent for the rule SAS
QP congruent to TU
angle P and angle T are both right
side PR is in common
Use technology to find the line of best fit for the following data.
(1, 0), (2, 3), (3,1), (4,4), (5,5)
When the equation of the line is in the form y=mx+b, what is the value of **b**?
Enter your answer as a decimal rounded to the nearest tenths place, like this: 42.5
Given:
The data points are:
(1, 0), (2, 3), (3,1), (4,4), (5,5)
To find:
The equation of best fit line in the form of [tex]y=mx+b[/tex] and then find the value of b.
Solution:
The general form of best fit line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope of best fit line and b is the y-intercept of the line.
Using the graphing calculator, we get the equation for the best fit line and the equation is
[tex]y=1.1x-0.7[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]b=-0.7[/tex]
Therefore, the value of b is equal to -0.7.
