The price of less expensive equipment is $1575.
Step-by-step explanation:
Let,
Price of one equipment = x
Price of other equipment = y
According to given statement;
x+y=4000 Eqn 1
x = y+850 Eqn 2
Putting Eqn 2 in Eqn 1
[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]
Putting y=1575 in Eqn 2;
[tex]x=1575+850\\x=2425[/tex]
The price of less expensive equipment is $1575.
Keywords: linear equation, substitution method
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Final answer:
The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.
Explanation:
To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:
x + (x + $850) = $4000
To solve for x, we combine like terms and get:
2x + $850 = $4000
Subtracting $850 from both sides gives us:
2x = $3150
Dividing both sides by 2, we find the value of x:
x = $1575
Therefore, the price of the less expensive piece of equipment is $1575.
what method can you use to calculate 40÷7 fast?
Answer:
Usally the fastest method to calculating a problem is to do it in your head. With enough practice your brain will be faster then most tools, ganing efficiency with practice.
Answer:
Step-by-step explanation:
In your head:
5 * 7 = 35 so its 5 point something with remainder 5.
7*7 = 49 so its 5.7 approximately.
what is 3.1 ÷ 17.36
Answer:0.17857
Step-by-step explanation:
Step 1 :
434
Simplify ———
25
Equation at the end of step 1 :
31 434
—— ÷ ———
10 25
Step 2 :
31
Simplify ——
10
Equation at the end of step 2 :
31 434
—— ÷ ———
10 25
Step 3 :
31 434
Divide —— by ———
10 25
3.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
31 434 31 25
—— ÷ ——— = —— • ———
10 25 10 434
Final result :
5
—— = 0.17857
28
Answer:
5 = 0.17857
28
Step-by-step explanation:
Change the decimals into fractions.
31 ÷ 434
10 25
*They were simplified from their natural fractions.
To divide fractions, write the division as multiplication by the reciprocal of the divisor.
31 × 25
10 434
Simplify by the greatest common factor.
775 ÷ 155 = 5
4340 ÷ 155 28
Duke went to the convenience store to buy a frozen pizza and some
toothpaste, and while he was in the checkout line, he also threw a ballpoint
pen and a banana into his shopping basket. Which two products were
impulse purchases?
A. The frozen pizza and the banana
O
O
B. The ballpoint pen and the toothpaste
C. The ballpoint pen and the banana
O
O
D. The frozen pizza and the toothpaste
Answer:
ballpoint pen and banana
Step-by-step explanation:
find c in the pic below
Answer:
A
Step-by-step explanation:
To find the angle inside the triangle (to the right side of 90 degree angle), we first have to find the adjacent angle (below it).
Angle 122 and that adjacent angle is same (parallel lines cut by transversal -- they are corresponding angles).
So that angle is 122.
The inside triangle angle (what we want) is adjacent to 122, so we can write:
Angle + 122 = 180 [straight angle/straight line is 180 degrees]
Solving for that angle, we have:
Angle = 180 - 122 = 58
Now, looking at the triangle, Side C is "opposite" of 58° and side "20" is the side that is "hypotenuse" [side opposite of 90 degree angle is hypotenuse).
Which trig ratio relates "opposite" and "hypotenuse"??
Yes, it is SIN. Thus we can write:
[tex]Sin(58)=\frac{Opposite}{Hypotenuse}=\frac{C}{20}[/tex]
We can now solve for C:
[tex]Sin(58)=\frac{C}{20}\\C=20*Sin(58)\\C=16.96[/tex]
Correct answer is A
michael mixes 60 ounces of red paint with 15 ounces of blue paint to get a shade of purple.what is the ratio of red paint to blue paint expressed in lowest terms?
Answer: 4:1
Step-by-step explanation:
Red paint = 60 ounces
Blue paint = 15 ounces
Ratio = 60/15 = 4/1 = 4:1 to the lowest term.
If it takes Trixie 8 minutes to run a mile, then 8m represents her total time where m is the number of miles she has run. List the ordered pairs (number of miles, total time) for 0, 1, 2, and 3 miles.
Answer: (1,8) (2,16) (3,24)
Step-by-step explanation:
Because if it takes Trixie 8 minutes per mile then the ratio would be 1:8 and that means every mile you add 8 minutes.
Two customers went to a post office to buy postcards and large envelopes. Each postcard
costs the same amount, and each large envelope costs the same amount.
The first customer paid $12 for 14 postcards and 5 large envelopes.
The second customer paid $24.80 for 10 postcards and 15 large envelopes.
•
What was the cost in dollars of each large envelope?
A $1.42 c $1.15
B $0.35 D $0.63
The right answer is Option A.
Step-by-step explanation:
Let,
x be the postcards
y be the large envelops
According to given statement;
14x+5y=12 Eqn 1
10x+15y=24.80 Eqn 2
Multiplying Eqn 1 by 3;
[tex]3(14x+5y=12)\\42x+15y=36\ \ \ Eqn \ 3[/tex]
Subtracting Eqn 2 from Eqn 3;
[tex](42x+15y)-(10x+15y)=36-24.80\\42x+15y-10x-15y=11.20\\32x=11.20\\[/tex]
Dividing both sides by 32
[tex]\frac{32x}{32}=\frac{11.20}{32}\\x=0.35[/tex]
Putting x=0.35 in Eqn 1;
[tex]14(0.35)+5y=12\\4.90+5y=12\\5y=12-4.90\\5y=7.10[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{7.10}{5}\\y=1.42[/tex]
Therefore, one large envelope costs $1.42
The right answer is Option A.
Keywords: linear equations, subtraction
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Answer: A. $1.42
Step-by-step explanation: I did it on the test and got it right!
Please answer this correctly is the answer
2:29am
3:29am
1:35am
6:29am
Answer:
2:29 AM
Step-by-step explanation:
By the time the planes reaches California, the time, in Mountain time, is 14:89 AM or 3:29 AM. From the mountains to the Pacific, the time goes back by 1 hour. 3:29 - 1 hour is 2:29 AM.
Susie wants to write equations in the form y=mx + b for the lines passing through
point R that are parallel and perpendicular to line s. First she finds the slope of lines
and line v to be and the slope of line t to be 3. Point R is located at (2, 2). Which
step could be used to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point R (2,2) in y=mx+b and then solve for b for each equation.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Substitute the slope and the coordinates of point R (2,2) in y=mx+b and then solve for b for each equation.
Of all the students who participate in the school music programs in the district, 394 students play a wind instrument. If 2/5 of the students play a wind instrument, how many students in the district participate in the school music program
Answer:
985 students in the district participate in the school music program.
Step-by-step explanation:
2/5=0.4
394/0.4=985
A freight train travels 1445 miles in 25 hours. What is the train's average rate of speed?
Final answer:
The average speed of the freight train is found by dividing the distance traveled, 1445 miles, by the time taken, 25 hours, resulting in an average speed of 57.8 mph.
Explanation:
To calculate the average speed of the freight train, we divide the total distance traveled by the time it took to cover that distance. The train travels 1445 miles in 25 hours.
The formula for average speed is:
average speed = total distance / total time
Therefore, the average speed of the train is:
average speed = 1445 miles / 25 hours = 57.8 miles per hour (mph)
Jonah plants flower in garden. He plants 2 flowers in each row and 5 rows. DrAw an array to figure out how many flowers he has planted
slope = –8, (1,4) in slope intercept form
Answer:
y= -8x-12
Step-by-step explanation:
y-4= -8(x-1)
-8x+8
+4= +4
y= -8x+12
Answer:
The correct answer on E2020 Is y=-8x(1,4)+y+8x+(1,4)
Hope this helps you!
(p.s:Please mark me as brainlyest!)
Step-by-step explanation:
I just took the test
Which is the simplified version of 7x+12+3x=-6(x-7)+9x ?
Answer:
x=30/7
Step-by-step explanation:
7x+12+3x=-6(x-7)+9x
10x+12=-6x+42+9x
10x+12=3x+42
10x-3x+12=42
7x+12=42
7x=42-12
7x=30
x=30/7
1/2 / 3 equals x / 4
Answer:
x=2/3
Step-by-step explanation:
(1/2)/3=x/4
(1/2)(1/3)=x/4
1/6=x/4
cross product,
6*x=1*4
6x=4
x=4/6=2/3
x=2/3
prove the identity with steps. sin (x-y)/cos x sin y = tan x cot y -1
Step-by-step explanation:
sin(x−y) / (cos x sin y)
Use angle sum/difference formula:
(sin x cos y − sin y cos x) / (cos x sin y)
Divide:
(sin x cos y) / (cos x sin y) − 1
Rearrange:
(sin x / cos x) (cos y / sin y) − 1
Simplify:
tan x cot y − 1
Are all right triangles similar?Are all equilateral triangles similar?
Answer:
Yes to both.
Step-by-step explanation:
Similar means the same shape but the sizes may be different.
Right angles are similar and so are equilateral triangle.
Right triangles are not necessarily similar unless they have the same hypotenuse and an acute angle. All equilateral triangles are similar because they have equal angles and sides. This discussion relates to the nature of mathematical truths, which are absolute in their systems, compared to observational truths that rely on variable sensory evidence.
Not all right triangles are similar because they can have different ratios between their sides despite having a right angle. However, if two right triangles have the same length of their hypotenuse and an acute angle correspondingly, they are indeed similar according to a mathematical corollary.
In contrast, all equilateral triangles are similar because they all have equal angles (60 degrees each) and their side lengths are also in the same ratio, which is 1:1:1, making them the same shape, although they can be different sizes.
This connects to the larger questions about mathematical truths. For instance, the statement that the three interior angles of a triangle are equivalent to two right angles is a mathematical truth that is similar to definitional truths, such as 'green is a color,' since both are based on definitions and logical deductions in their respective systems.
However, mathematical truths differ from observational truths like 'there is beer in the refrigerator' because observational truths are subject to sensory evidence which can change, whereas mathematical truths are absolute within the context of their axiomatic systems.
When considering questions that lead to insights into forms, mathematical questions are often better suited over observational ones as they transcend physical reality and provoke a more abstract level of reasoning.
1. What is 15% of 60?
15%×60=
=15×60/100
=900/100
=9
Answer:
9
Step-by-step explanation:
15/100 = 60/x
Cross Multiply...
100x = 15*60
100x = 900
x = 900/100
x = 9
A student answered three questions on a 40-percent test incorrectly. What percent did the student answer correctly
Answer:
The percentage of questions correctly answered by the student was 92.5%
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of questions incorrectly answered by the student = 3
Number of questions on the test = 40
2. What percentage did the student answer correctly?
Number of questions correctly answered by the student = Number of questions on the test - Number of questions incorrectly answered by the student
Replacing with the real values:
Number of questions correctly answered by the student = 40 - 3
Number of questions correctly answered by the student = 37
Now, let's calculate the percentage:
Percentage = Number of questions correctly answered by the student /Number of questions on the test * 100
Percentage = 37 /40 * 100
Percentage = 0.925 * 100
Percentage = 92.5%
What is the product of 4.23 and 1.2
Answer:
its 5.08
Step-by-step explanation:
Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If nor more than 62 people will attend, how many tables seating four people each will she need?
Answer:16
I think this is the answer
Algebraic Woru
An algebraic word problem can be presented in either a real-life or
require you to set up and solve an equation or inequality to arrive at the
require you to translate words into an expression, equation, or inequate
1. Kyle has three times as much money in his savings account as
Hayden. Hayden has twice as much money in his savings account
as Jeremy. Combined Kyle, Hayden, and Jeremy have a total of
$612. How much money does Kyle have in his account?
(A) $68 Khles Hot money = 3
(B) $136
(C) $204
(D) $306
(E) $408
The right answer is Option D.
Step-by-step explanation:
Let,
Kyle's money = x
Hayden's money = y
Jeremy's money = z
According to statements;
Kyle has three times as much money in his savings account as Hayden.
x = 3y Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y Eqn 2
Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
[tex]3y+y+2y=612\\6y=612[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{612}{6}\\y=102[/tex]
Putting in Eqn 1;
[tex]x=3(102)\\x=306[/tex]
Kyle has $306 in his account.
The right answer is Option D.
Keywords: Linear equations, division
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if john can buy 8 liters of soft drinks at the store for $6.40 how much does it cost to buy 12 liters
Answer:
$9.60
Step-by-step explanation:
first figure out cost for 1 liter.
6.40 / 8 = 0.80
1 liter = $0.80
12 * 0.80 = 9.60
12 liter = $9.60
Mei has 8 jars of soup. Each jar obtains 300 milliliters of sup. What is the smallest pot Mei can use to heat all the soup?
Answer:
2400 milliliters of soup
Step-by-step explanation:
8*300=2400
hello! could anyone help me on this one khan acadamy question. it is soooooooo hard for me to understand this lesson.
-1 / 4 = -0.25
1 / 3 = .3
-0.25 / .3 = -0.833333333.
Answer:
-3/4
Step-by-step explanation:
Find the square root of (3√5-3)³
Answer: 76.36753237
Step-by-step explanation:
If you have trouble, you can always use Desmos Scientific calculator and get your answer straight away.
Julie has 42 sheets of paper. She gives 17 sheets of paper to karo. How many sheets of paper does julie have now explained please help me
Answer:
25
Step-by-step explanation:
Subtract 17 from 42.
Answer:
42-17=25
Step-by-step explanation:
just subtract 17 from 42
A restaurant bill comes to $28.35 find the total coast if the tax is 6.25% and 20% tip is left on the amount before tax
Answer:
The total cost of the bill = $36.146
Step-by-step explanation:
Here, the total amount of the bill = $28.35
Now, the amount of tip = 20%
So, calculating 20% on the bill amount, we get
[tex]\frac{20}{100} \times 28.35 = 5.67[/tex]
or, the amount of 20% tip = $5.67
So, the total bill amount after 20% tip = Bill Amount + Tip
= $28.35 + $5.67 = $34.02
Now, the tax is calculated on the amount of bill $34.02.
[tex]\frac{6.25}{100} \times 34.02 = 2.126[/tex]
or, the amount of tax on the bill = $2.126
So, the total bill amount after 6.25% tax = Bill Amount + Tax
= $34.02 + $2.126 = $36.146
Hence, the total cost of the bill = $36.146.
Create a 3rd degree
polynomial and divide it by x-2. Show all steps. WILL MARK BRAINLEST!
Step-by-step explanation:
Monomial = x^2, 1 term
Binomial = x^2 + x, 2 terms
Trinomial = x^2 + x + 3, three terms
Binomial is more than 3 terms
Let's do a 3rd degree polynomial like:
[tex] {x}^{3} + 2x^{2} + 4x + 8[/tex]
Now let's put parenthesis around (x^3 + 2x^2) and (4x + 8)Let's treat both of these as seperate for now. In the first part, you can see an x^2 can be factored out of itFor example:[tex] {x}^{2} (x + 2)[/tex]
As you can see, if you do the distributive property, it equals the original.Now let's factor the second part, the 4x + 8. This can be factored by a 4.
[tex]4(x + 2)[/tex]
Your new equation is:
[tex] \frac{( {x}^{2} + 4)(x + 2)}{x - 2} [/tex]
x^2 + 4 can be factored again down to (x + 2)(x + 2)
YOUR FINAL EQUATION IS:
[tex] \frac{(x + 2)(x + 2)(x + 2)}{x - 2} [/tex]
What is y - 2 = -3(x – 7) written in standard form?
Choose 1 answer:
A-y - 2 = -3x + 21
B-y=-3x + 23
C-3x + y - 23 = 0
D-3x + y = 23
Answer:
It's D
Step-by-step explanation:
-3+y=23
To write the equation in standard form, distribute and rearrange the terms. The equation is 3x + y = 23.
Explanation:To write the equation y - 2 = -3(x - 7) in standard form, we need to expand the expression and rearrange the terms. Starting with the given equation, we can distribute the -3 to the terms inside the parentheses: y - 2 = -3x + 21. Next, we can move the -3x term to the left side of the equation by adding 3x to both sides: 3x + y - 2 = 21. Finally, we can move the constant term (-2) to the right side of the equation by adding 2 to both sides: 3x + y = 23. Therefore, the equation in standard form is 3x + y = 23 (Option D).
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