Answer:
The equation of the line that passes through the points (0, 3) and (5, -3) is [tex]y = -\frac{6}{5}\cdot x +3[/tex].
Step-by-step explanation:
From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:
[tex]y = m\cdot x + b[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If we know that [tex](x_{1},y_{1}) = (0,3)[/tex] and [tex](x_{2},y_{2})=(5,-3)[/tex], the following system of linear equations is constructed:
[tex]b = 3[/tex] (Eq. 2)
[tex]5\cdot m + b = -3[/tex] (Eq. 3)
The solution of the system is: [tex]b = 3[/tex], [tex]m = -\frac{6}{5}[/tex]. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is [tex]y = -\frac{6}{5}\cdot x +3[/tex].
A gardener is planting a garden in the shape of a square. The gardener wants the side of the square garden to be between 15 and 18 feet long. The gardener wants to put a fence around the garden. How many yards of fencing will be required to enclose this square garden? Remember that 3 feet equals 1 yard. If every yard of fencing costs $1.50, how much will the gardener need to build the fence?
Answer:
$31.99Step-by-step explanation:
The idea begin this problem is to solve for the perimeter of the square garden using the expression for perimeter which is
Perimeter of square= 4L
given that the garden wants the side of the square garden to be between 15 and 18 ft long
Say we go with a length of 16ft (you can pick any number in the range just maintain the formula for the perimeter)
perimeter= 4(16)
perimeter= 64ft
now we have to convert ft to yard
1 yard=3ft
x yard=64ft
cross multiply we have
x=64/3
x=21.33 yards
given that a yard cost $1.5, therefore 21.33 yards will cost
=21.33*1.5
=$31.99
A student walks 2 km in 30 minutes. What is the student’s average speed in km/m?
Answer:
4km per hour
Step-by-step explanation:
are the trianlges congruent. am I right?
Answer:
The triangles are congruent.
Step-by-step explanation:
Don't let those little lines mess up. Both triangles have the same shape and size. They are congruent.
a. 7
b. 3.5
c. 5
d. 10
Answer:
I think with all the savings o will rather go with, a will I make some research
4x - 5 - 2x = x - 5
No Solution
X=0
X=4
X=5
Answer:
x = 0
Step-by-step explanation:
Step 1: Write equation
4x - 5 - 2x = x - 5
Step 2: Solve for x
Combine like terms: 2x - 5 = x - 5Subtract x on both sides: x - 5 = -5Add 5 to both sides: x = 0Step 3: Check
Plug in x to verify it's a solution.
4(0) - 5 - 2(0) = 0 - 5
0 - 5 - 0 = -5
-5 = -5
Which ones are equivalent?
40/1000 and 40%
6/5 and 120%
50/33 and 117%
1/8 and 12.5%
1/3 and 30%
Answer:
1/8= 0.125
To have a percentage, multiply by 100
0.125 x 100 = 12.5%
Hope this helps ! : )
The Pythagorean Theorem is
a2 + b2 = c2
a + b = c
c² + a²=b²
Answer:
a² + b² = c²
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We use the Pythagorean Theorem to help us solve for missing right triangle side lengths. It is wise to remember this formula.
Henry has a total of 26 quarters and dollars in his pocket. They're worth $17. How many of each type of coin
does Henry have?
A. 16 quarters and 10 dollars
B. 10 quarters and 16 dollars
C. 14 quarters and 12 dollars
D. 12 quarters and 14 dollars
Answer:d
Step-by-step explanation:
What is 3x+4=10 solve for x
Answer:
x=2
Step-by-step explanation:
3x+4=10
3x=6
x=2
Answer:
x=2
Step-by-step explanation:
3x+4=10
3x=6 by subtracting the 4
x=2 by dividing the 3
Simplify 3(2a - y) - 4(2y - a).
Answer:
10a - 11y
Step-by-step explanation:
3(2a - y) - 4(2y - a)
open the parenthesis
6a - 3y - 8y + 4a
combine like terms
6a + 4a - 3y - 8y
10a - 11y
A dad has three sons. He shares an amount of $30,000 among his three sons. One son deposited his amount in a bank that provides him interest at the rate of 7%. The second son deposited his sum in a mutual fund that gave him returns at a rate of 8%. The third son invested his in another bank that provided him an interest rate of 6%. The second sons share is 1000 more than that of the third son. The total interest that they got was $2110. Calculate each person's share if the first sons share is equal the second son and the third son put together.
Answer:
First son receives $15000
Second son receives $8000
Third son receives $7000.
Step-by-step explanation:
Let first son receive $x and deposit it at 7%
Second son receive $y and deposit in 8%
Third son receive $z and deposit in 6%
Now, let's set up equation using the given information.
The second son share is 1000 more than the third son.
So, we can set up equation as
y= 1000+z
First son share is equal the second son and the third son put together.
So, x=y+z
And we can set up equation for total 30000 as
x+y+z=30000
Plug in y as 1000+z and x as y+z
We get third equation as
y+z+1000+z+z=30000
Plug in again y as 1000+z
It gives,
1000+z+z+1000+z+z=30000
Combine like terms,
2000+4z=30000
Subtract both sides 2000
4z=28000
Divide both sides by 4
z=7000
Now, plug in z as 7000 into y=1000+z to get y =8000
Now, x =y+z plug in the y and z values
x= 8000+7000=15000
Let's check with interest,
15000(7%)+8000(8%)+7000(6%)=2110
1050+640+420= 2110
2110=2110.
Yes! The calculations are correct!
The cost of 6 1/4 kg of apples is $400. How much do the apples cost per kg?
Answer: = Rs 64R
Step-by-step explanation:
The cost of 6 (1/4) kg = (25/4) of apples is Rs 400 Cost of apple per kg is = (25/4) /400 = (4/25) × 400
SPEED QUESTION!!!
the first person that answers this and gives step by step explanation gets 50 points plus brainliest answer!
GOOD LUCK!!!
Answer:
x>13 (C)
Step-by-step explanation:
1) simplify -> 2x+7>33
2) subtract 7 from both sides -> 2x+7-7>33-7 = 2x>26
3) divide both sides by 2 -> 2x/2>26/2
x>13
Solve this Proportion. If necessary round to the nearest hundredth:
5/a = 30/54
what is 0.075 and 3.56 as a fraction
Answer:
Step-by-step explanation:
1: 3/40
2:89/25
Under very specific instructions, a jeweler made one ring for the queen and one ring for the princess. The gem on the queen's ring weighed 9/10 of a carat and the stone on the princess's ring weighed 7/10 of a carat. How much heavier was the stone on the queen's ring than the stone on the princess's?
Answer: 1/5
Step-by-step explanation:
From the question, we are informed that the gem on the queen's ring weighed 9/10 of a carat and the stone on the princess's ring weighed 7/10 of a carat.
To calculate how heavier the stone on the queen's ring was than the stone on the princess will be:
= 9/10 - 7/10
= 2/10
= 1/5
amy runs 2 miles south, the turns around and runs 3 miles north. what is her displacement? a. 5 miles , b. 2 miles, c. 1 mile, d. 3 miles . i need hep now .
Option C, 1 mile is the correct answer
The displacement is 1 mile.
Given that, Amy runs 2 miles south, then turns around and runs 3 miles north.
What is displacement?Displacement is the change in the position of any point or object. It has a direction and magnitude, so it is a vector quantity. It is shown with an arrow that points from the starting position to the final position.
Now, Amy runs 2 miles south from the fixed point he runs in the north direction for 3 miles.
So, the displacement=1 mile
Therefore, the displacement is 1 mile.
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Ed training for a race. He ran 12.56 miles on one day, 12.98 miles the second day, and 13.04 miles on the third day.what is his combined distance for the first three days
Ed's combined distance for the first three days is 38.58 miles.
Given that, Ed ran 12.56 miles on one day, 12.98 miles the second day, and 13.04 miles on the third day.
What are decimal numbers?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.
The total distance can be determined as follows:
Total distance = 12.56+12.98+13.04
= 38.58 miles
Hence, Ed's combined distance for the first three days is 38.58 miles.
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april and bill went to the grocery store to buy chocolate bars. April bought 4 small chocolate bars and 6 large chocolate bars and 3 large chocolate bars. if april paid $16.50 and bill paid $11.25 what is the price of a single large chocolate bar
The cost of a large single chocolate is $0.25.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that April and bill went to the grocery store to buy chocolate bars. April bought 4 small chocolate bars and 6 large chocolate bars and 3 large chocolate bars. April paid $16.50 and bill paid $11.25.
We can write -
4x + 6y = 16.50 ... Eq{ 1 }
3x = 11.25 ... Eq{ 2 }
On solving the equation, we get -
{x} = 11.25/3
{x} = 3.75
Now, we can write -
4x + 6y = 16.50
4 x 3.75 + 6y = 16.50
6y = 16.5 - 15
6y = 1.5
y = 1.5/6
{y} = 0.25
Therefore, the cost of a large single chocolate is $0.25.
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A recipe calls for 3/4 cup of mayonnaise, 2/3 cups of sour cream, 1/2 cup of buttermilk, and 2 cups of spinach. What are the total cups of this recipe? Make sure your answer is in a mixed number fraction form.
Answer:
Step-by-step explanation:
If you were to multiply 3X25, you would have a product of 75.
Explain 2 ways you could rewrite 25 and using the distributive property still obtain a product of 75.
Include one example using addition and the other example using subtraction. For example, if I were to rewrite the integer 72, I could choose (70 + 2) or (80 – 8).
An example with addition is 3x(20+5) as 20 plus 5 is still 25, and an example with subtraction is 3x(30-5), as 30 minus 5 is 25.
Why is graphite soft
Answer:
because it has a weak inter molecular forces between its layers
Answer:
Its compound
Step-by-step explanation:
What number is 2/3 of 15
Step-by-step explanation:
2/3 of 15
2*5(3*5=15)
10
Can somebody give me a answer and explanation to 19× −(1)∙ (−15) please.
Answer:
I dont know the answer but maybe this page can help, it even gives you the explanation or the steps.
Explanation:
symbolab.com
Write the equation of a line the line that passes through (3, 9) and is parallel to the line y = 5x - 15.
Answer:
Y=5X-6
Step-by-step explanation:
Y=mx+b
m=5
when x=3 and y=9 b= -6
Adan works as an information technician and fitness trainer. As a technician, he earns $22 per hour. Last week he worked x hours as a technician and his friend paid him $50 for a day of fitness training. Write an expression to represent the total amount Adan earned last week.
Answer: t = 22x + 50
Step-by-step explanation:
t = total amount earned
x = hours worked
We know his friend payed $50, so that is our initial value. We don’t need hours for that one.
For his job as trainer, he earns $22 per hour but we don’t know how many hours he earned, so that is x. That is how I got the 22x.
Hope this helps! And of course, feel free to use any variables of your choice. :)
A car rental service charges a one-time fee of $19.99 in addition to $0.29 per mile drive. If the final total for renting the car is $73.93, select which equation best represents the situation. Let m represent the number of miles driven.
*Answer Choices*
19.99m + 0.29m = 73.93
19.99m + 0.29m = 73.93
(19.99 + 0.29)m = 73.93m
19.99 + 0.29m = 73.93
Answer:
Your answer is: D) 19.99+0.29m=73.93
We are trying to find the miles driven so therefore 0.29$ is per mile. So we have to see how many 0.29$ along with 19.99$ can fully add up to 73.93$
Step-by-step explanation:
Hope this helped : )
(02.01)
Solve 4(x + 1) = 4x + 4. (1 point)
Select one:
a. No solution
b. 0
c. All real numbers
d. 1
Answer:
the answer is Any Real Number
because 4(x + 1) = 4x + 4 for all value of x
Step-by-step explanation:
How many kg in 12980 g ?
Help?
Answer:
12.98
Step-by-step explanation:
Jenna’s science teacher changed the number of assignments for the semester to 85. This is shown as the blue line on the graph.
How many more weeks will it take Jenna to complete all the assignments if she completes assignments at the same rate?
more weeks
Answer: it would be 3 more weeks
Answer:
3
Step-by-step explanation: