1. A merchant sets the selling price of an article 40% above what it cost him. Then, seeing it did not sell, he decided to reduce the figure by 15%. The final selling price was $8.65. What did the article originally cost?
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Work Shown:
x = original cost (in dollars)
1.40x = increasing the cost by 40%
0.85*1.40x = decreasing the previous cost (1.40x) by 15%
Notice how a decrease of 15% means you pay the remaining 85% of the price, which is where the 0.85 comes from.
The expression 0.85*1.40x simplifies to 1.19x after multiplying the 0.85 and 1.40
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The expression 1.19x is the final cost after the increase of 40% and the decrease of 15%
Set this equal to 8.65 and solve for x
1.19x = 8.65
x = 8.65/1.19
x = 7.2689075630252 which is approximate
x = 7.27 dollars
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Let's check the answer
x = 7.27
1.40x = 1.40*7.27 = 10.178 = 10.18
After an increase of 40%, the cost is now $10.18
Now decrease it by 15%
discount = 15% of 10.18 = 0.15*10.18 = 1.527 = 1.53
The customer saves $1.53 and the final price is 10.18-1.53 = 8.65
So everything works out as we expect. The answer is confirmed.
Solve the right triangle. Round decimal answers to the nearest tenth.
Answer:
c=√a²+b²
Step-by-step explanation:
You can use this equation to solve it.
NEED HELP FAST ILL MAKE BRAINLIEST
Jenna's English teacher tells her that there are 5 vowels in the alphabet. Based on this information, Jenna states that given any word in the English language, the probability of randomly choosing a vowel from among the word's letters is 5/26.
Explain the flaw in Jenna's reasoning.
Provide a word where the probability of randomly choosing a vowel from the word's letters is 1/2.
Answer:
Number of alphabets in English = 26 Number of vowels = 5 (a, e, i, o ,u) So, the probability of choosing a vowel = 5/ 26.
PLEASE HELP Given the function [tex]f(x)=\sqrt{3x+3+2}[/tex]
Answer:
98.97
Step-by-step explanation:
I used my notes on page 34
Jeremiah buys 3 lbs of cheese at $3.50
a pound. He also buys 5 lbs of sliced
turkey. If he spends $46.75 in total for
the cheese and turkey, what is the
price per pound of sliced turkey?
Answer: $7.25 per pound
Step-by-step explanation:
3x3.5 + 5x = 46.75
5x+10.5 = 46.75
5x = 36.25
x = 7.25
Answer:
the price per pound for the turkey would be 7.25
Step-by-step explanation:
first you would do 3x3.50 to find the total cost for the cheese
now you subtract that from 46.75
once you have that answer you divide by 5 :)
Which inequality is equivalent to the given inequality?
-4(x+7) < 3(x - 2)
What is the value of the expression?
8 1/2-2+4 3/4
PLEASE HELP !! two angles in a triangle have measurements of 20 degrees and 50 degrees. what is the measure of the third angle? the options are 70 degrees, 30 degrees, 110 degrees, and 120 degrees
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Answer:
110°
Step-by-step explanation:
The sum of angles in a triangle is 180°. The measure of the third angle is ...
180° -20° -50° = 110° . . . third angle
Answer:
The measurement of third angles of triangle is 110°.
Step-by-step explanation:
Given :-
Two angles in a triangle have measurements of 20° and 50 °.
To Find :-
Measurement of third angles of triangle
Solution :-
We know that the sum of all angles of triangle is 180°.
Measurement of third angles = x20° + 50° + x = 180°
combine like terms
70° + x = 180°
subtract both side from 70°.
70° - 70° + x = 180° - 70°
x = 110 °
Hence, measurement of third angie of triangle is 110°.
Find the area of the given quadrilateral.
Pls :)
I think your teacher may have made a typo. Refer to the diagram below. If we ignore segment ZA for now, we can see a rectangle forms with angle W = angle Y = 90. Also, we can see that WX = 6 is the horizontal base and WZ = 8 is the vertical height.
However, the side opposite WZ (which is XY) should also be 8 cm tall, and not 6 cm. If XY was 6 cm, then point Y would move to where point A is located (and the quadrilateral would be WXAZ instead of WXYZ). This new quadrilateral would not have a 90 degree angle at point Y's new location.
In other words, if we want angle Y to be 90 degrees, then side XY must be 8 units long. I have a feeling this is where the typo is, but your teacher might have been intending to say something else.
Two Points P and Q, 25 meters apart, are on the same Straight line, the same side and the same ground Level as the foot of the tower. If the angle depression of P and Q from the top of the tower are 33 and 40° respectively, find to the nearest metre, the; 1.distance from Q to the foot of tower. 2.height of the tower.
Answer:
b
Step-by-step explanation:
. has endpoints B(5, 9) and C(–4, –3). Find the coordinates of the midpoint of . (0.5, 1.5) (1, 3) (0.5, 3) (1, 6)
Answer:
(0.5,3)
Step-by-step explanation:
Hi there!
We are given a line that has the endpoints of (5,9) and (-4,-3); we need to find the midpoint of the line.
The midpoint formula is given as ([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2}}{2}[/tex]), where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex], and [tex]y_{2}[/tex] are values of coordinate points
to avoid any confusion, we can label the values of the coordinates and then substitute them into the formula to find the midpoint
[tex]x_{1}[/tex]=5
[tex]y_{1}[/tex]=9
[tex]x_{2}[/tex]=-4
[tex]y_{2}[/tex]=-3
now substitute into the formula
so to find the value x in the midpoint, we'll use this part of the formula: [tex]\frac{x_{1}+x_{2} }{2}[/tex]
substitute 5 and -4 into the formula
[tex]\frac{5+-4}{2}[/tex]
do the addition on the numerator
[tex]\frac{1}{2}[/tex] or 0.5
now let's find the value of y in the midpoint. we'll use this part of the formula: [tex]\frac{y_{1}+y_{2}}{2}[/tex]
substitute 9 and -3 into the formula
[tex]\frac{9+-3}{2}[/tex]
do the addition on the numerator
[tex]\frac{6}{2}[/tex] or 3
Therefore the midpoint is (0.5,3)
Hope this helps! :)
You move down 2 units and up 8 units. You end at (0, 4). Where did you start?
Given:
You move down 2 units and up 8 units.
You end at (0, 4).
To find:
The starting point.
Solution:
Let the starting point be [tex](x,y)[/tex].
You move down 2 units and up 8 units. So, the rule of translation is:
[tex](x,y-2+8)=(x,y+6)[/tex]
You end at (0, 4).
[tex](x,y+6)=(0,4)[/tex]
On comparing both sides, we get
[tex]x=0[/tex]
[tex]y+6=0[/tex]
[tex]y=4-6[/tex]
[tex]y=-2[/tex]
Therefore, the starting point is (0,-2).
A tourist bought a Nepali cap with 20% discount and 13% value added tax when returning to his country the VAT amount Rs. 83.20 returned back to home at the airport. What was the marked price of the cap? Find it
Answer:
Marked price = Rs 800
Step-by-step explanation:
Let the marked price of the cap be Rs.“x”.
Discount = 20%
VAT = 13%
VAT amount = Rs. 83.20
We know,
Discount = Marked price – Selling Price
⇒ Selling price = Marked price – discount
The price after giving a discount or Selling price:
[tex]= x - 20 \% \ of \ x \\\\= x - \frac{20}{100} \times x\\\\=\frac{100x - 20x }{100}\\\\=\frac{80x}{100}\\\\=\frac{8x }{10}\\\\=\frac{4x}{5}[/tex]
VAT amount = VAT% of Selling Price
[tex]83.20 = 13 \% \ of \ \frac{4x}{5}\\\\83.20 = \frac{13}{100} \times \frac{4x}{5}\\\\13 \times 4x = 83.20 \times 100 \times 5\\\\4x = \frac{8320 \times 5}{13}\\\\4x = 3200\\\\x = 800[/tex]
Thus, the marked price of the cap is Rs. 800.
Use complete sentences to explain how the coordinate plane is a useful tool for geometric proofs.
Answer:
Step-by-step explanation:
The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the Cartesian Plane to make an argument. ... The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .
Answer:
The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the Cartesian Plane to make an argument . Coordinate geometry proofs employ the use of formulas such as Slope Formulas, the Midpoint Formula and the Distance Formula, as well as postulates, theorems and definition s. The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas . The facilitate verification is a proof of a geometric hypothesis which utilizes " summed up" indicates on the Cartesian Plane make a contention. The strategy for the most part includes doling out factors to the directions of at least one focuses, and afterward utilizing these factors in the midpoint or separation equations. For instance, the accompanying is an arrange evidence of the Triangle Midsegment Theorem, which expresses that the fragment interfacing the midpoints of two sides of a triangle is parallel to the third side and precisely a large portion of the length.
Which of the following is a property of all rhombi? O A. They have 4 right angles. B. The diagonals are congruent. O C. All 4 sides are congruent. D. They contain 4 right angles.
Step-by-step explanation:
the diagonals are congruent
what is the answer to 2x + 9(x – 1) = 8(2x + 2) – 5
Answer:
-4 =x
Step-by-step explanation:
2x + 9(x – 1) = 8(2x + 2) – 5
Distribute
2x +9x -9 = 16x+16 -5
Combine like terms
11x-9 = 16x +11
Subtract 11x from each side
11x-9-11x = 16x-11x+11
-9 = 5x+11
Subtract 11 from each side
-9-11 = 5x+11-11
-20 = 5x
Divide by 5
-20/5 = 5x/5
-4 =x
how did you find x? pls answer
Answer:
x = 8 degree
Step-by-step explanation:
8x - 4 = 60 degree (being alternate interior angle)
8x = 60 + 4
8x = 64
x = 64/8
x = 8 degree
Answer:
[tex] both \: are \: alternate \: interior \: angle \\ \\ = > both \: are \: equal \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > (8x - 4) = 60 \: \: \: \: \: \: \\ \\ = > 8x \: = \: 60 + 4 \\ \\ = > 8x = 64 \\ \\ = > x = 64 \div 8 \\ \\ = > x = 8 \: \\ \\ hope \: it \: is \: helpful \: to \: you[/tex]
An empty container has a capacity of 60000 liters to 1 s.f. Tony pours in 5400 liters of water to 2 s.f. He says he filled more than 10 % of container is he correct ? Show working
Answer:
Tony poured is 9% of the total
Step-by-step explanation:
Given data
The capacity of the container= 60000 liters
Amount of water that tony pours= 5400 liters
Let us compute the percentage to know if it is up to 10%
= 5400/60000*100
=0.09*100
=9%
Hence the amount of water Tony poured is 9% of the total
Answer:
He is wrong
Step-by-step explanation:
60 000 LB=55000
60 000 UB=65000
5400 LB= 5350
5400 UB=5450
65000x0.10=6500
55000x0.10=5500
he is wrong
Lauren uses a calculator to find Three-fourths divided by StartFraction 3 plus 9 over 36 EndFraction and gets a result of Nine-fourths. Which statement best describes her work?
Answer:
11/20
Step-by-step explanation:
Total health care costs in the United States in 2016 was $1.7 trillion. he US population was 290.9 million. What was the average amount spent per person on health care?
Answer:
$5,843.9
Step-by-step explanation:
2016
Total health care cost in US = $1.7 trillion
= $1,700,000,000,000
Population in US = 290.9 million.
= 290,900,000
Average amount spent per person on health care = Total health care cost in US / Population in US
= 1,700,000,000,000 / 290,900,000
= $5843.9326228944
Approximately,
$5,843.9
To the nearest whole number
= $5,844
Simplify
5^3/5^7
Leaving your answer in index form
Answer:
5^-4
Step-by-step explanation:
5^3/5^7=5^(3-7)=5^-4
Please help needed!!! Help me!!!
a = 85°
Step-by-step explanation:
Method 1
5x = 2x + 57° (An exterior angle of a triangle is equal to the sum of its two interior opposite angles)
3x = 57°
x = 57/3 = 19°
a = 180 - 57 - 2x
a = 180 - 57 -2(19)
a = 85°
Method 2
2x + a + 57° = 180°
2x + a = 123° ==> 1
5x + a = 180°
x = (180° - a)/5 ==> 2
By substitution
2((180° - a)/5) + a = 123°
(360° - 2a)/5 + a = 123°
(360° - 2a)/5 = 123° - a
360° - 2a = 5(123° - a)
360° - 2a = 615° - 5a
-2a + 5a = 615° - 360°
3a = 255°
a = 85°
Kevin needs 2/3 cups of sugar to make his favourite brownie recipe. How many cups of sugar does he need to make six batches of brownies for a bake sale? 
NO LINKS ALLOWED OR YOU’LL BE REPORTED!
Apply the distributive property to factor out the greatest common factor.
6+30=6+30=6, plus, 30, equals
Answer:
so 6+30=36
we can use the distributive property
36-6=30
36-30=6
Hope This Helps!!!
how much should your mom set aside and invest in a fund earning 3% compounded quarterly is she needs 85,000.00 in 20 months
Answer:
PV= $73,201.14
Step-by-step explanation:
Giving the following information:
Future value (FV)= $85,000
Number of periods (n)= 20 months
Interest rate (i)= 0.03/4= 0.0075
To calculate the lump-sum required to reach the objective, we need to use the following formula:
PV= FV / (1 + i)^n
PV= 85,000 / (1.0075^20)
PV= $73,201.14
5. There is a circular field of area of approximately
500 m2. How can you find its area accurately by
using a measuring tape?
Step-by-step explanation:
It is known that area of a circular is calculated as follows.
[tex]Area = \pi \times r^{2}[/tex]
So, when a circular field of area of approximately 500 [tex]m^{2}[/tex] is there then diameter of the field is calculated using the measuring tape from one side of the circular tape to the other. Now, to calculate the radius it is required to divide the diameter by 2.
Hence, put these values into the above formula to find out the area. In this way we can find out the area of given circular field accurately by using a measuring tape.
What are the solutions of the equation −2x−6=−2^x−6 ?
Select each correct answer.
x=−1
x = 0
x = 1
x = 2
x = 3
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Answer:
x = 1, x = 2
Step-by-step explanation:
A graphing calculator shows the graphs cross at x=1 and x=2.
__
There is no algebraic method of solving an equation like this. Trial and error is another method that works.
On a coordinate plane, a curved line with a minimum value of (0, 1) and a maximum value of (negative 1.3, 2.2), crosses the x-axis at (negative 2.2, 0) and crosses the y-axis at (0, 1).
Which statement correctly identifies a local minimum of the graphed function?
Over the interval [–3, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 2.2.
Over the interval [–1, 0.5], the local minimum is 1.
Over the interval [0.5, 2], the local minimum is 4.
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
cuz i did the test
which phase best describes the translation from tge graph y=2(x-15)^2 to the graph of y=2(x-11)^2+3?
Answer:
Graph translates 4 units to the left then 3 units up.
Step-by-step explanation:
The constant in the bracket changes for - 15 to -11 . A change of + 4.
This shifts the whole graph horizontally 4 units to the left.
The + 3 moves the whole graph 3 units upwards.
What is a dept of 24 dollars?