Final answer:
The distance formula calculates the straight-line distance between two points on a coordinate plane using the Pythagorean theorem, which is applied to the differences in the x and y coordinates of the points to form a right triangle.
Explanation:
Explaining the Distance Formula
The distance formula is a way to calculate the straight-line distance between two points in a coordinate plane. This formula is derived from the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In other words, a² + b² = c².
To understand the distance formula, consider two points (x1, y1) and (x2, y2) on a coordinate plane. The difference in the x values (x2 - x1) and the y values (y2 - y1) represent the lengths of the legs of a right triangle, where the straight-line distance we are trying to find is the hypotenuse. Thus, by the Pythagorean theorem, the distance (d) can be found by taking the square root of the sum of the squares of these differences. The resulting distance formula is d = √((x2 - x1)² + (y2 - y1)²).
The distance formula logically extends the Pythagorean theorem to two-dimensional space, where distances on the plane are calculated irrespective of the orientation or position of the line connecting the two points.
The equation Ax+By=10 goes through the coordinates (6,5) and (-2,-5)
What is the value of A?
What is the value of B?
The values of A and B of the given equation with the given coordinates are; A = 5 and B = -4
We are told the equation is;
Ax + By = 10
Since the equation goes through (6,5) and (-2,-5), then it means we have two simultaneous equations as;
6A + 5B = 10 ----(eq 1)
-2A - 5B = 10 ----(eq 2)
Add eq 1 to eq 2 to obtain;
4A = 20
A = 20/4
A = 5
Now, put 5 for A in eq 1 to get;
6(5) + 5B = 10
30 + 5B = 10
-5B = 30 - 10
-5B = 20
B = -20/5
B = -4
Thus, in conclusion, the values of A and B are 5 and -4 respectively.
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Values of A and B in the equation Ax+By=10, that pass through points (6,5) and (-2,-5), can be calculated by plugging these points into the equation, resulting in two simultaneous equations. On solving them, you find that A = 1 and B = -1.
Explanation:In order to determine the values of A and B in the equation Ax+By=10 that passes through the points (6,5) and (-2,-5), first we plug these points into the equation. This will result in two simultaneous equations.
For the point (6,5), the equation becomes 6A + 5B = 10. For the point (-2,-5), the equation becomes -2A - 5B = 10. Solving these two simultaneous equations, you will obtain A = 1 and B = -1.
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Kayla want to build a fence around her backyard for her dogs to play in. Her backyard is squared and has an area of 24 m²
4 * √24
with √24 you find a side, per 4 and you have the perimeter of the square
4 * √24
4* 4.9=
19.6
Suppose 48 out 120 people like baseball. Of the people who like baseball, 3 out 5 play baseball. If you ask 500 people, how many would you expect to play baseball?
8=- 1/4T
its a 1 step equation but not sure what to do
Answer: T = -32
Step-by-step explanation:
isolate T by multiplying both sides by -4 (the reciprocal of -1/4)
[tex]8 = -\frac{1}{4}T[/tex]
[tex](-4)8 = -(-4)\frac{1}{4}T[/tex]
-32 = T
A T-shirt department store cost 7.50.the total cost in dollar of a T-shirt is givien by the function C(a)=7.5a
Given cost function C(a) = 7.5a, where a is the number of T-shirts.
Let us complete table.
We need to plug a=1,2,3,4 in above function to get the costs to complete the table.
For a =1
C(1)= 7.5(1) = 7.50
For a =2
C(2)= 7.5(2) = 15.00
For a =3
C(3)= 7.5(3) = 22.50
For a = 4
C(4)= 7.5(1) = 30.00
In order to find the common difference we need to find the diffrences of costs 15-7.50 = 7.50
22.50-15.00=7.50.
Therefore, common difference is 7.5.a represents the number of T-shirts.
Domain of a is the numbers we can take for a.
So, we can take value for a as 0 or greater value.
Therefore, domain for a would be a is gerater than or equal to 0.
Domain : a≥0hiking up a mountain,you notice that the air temperature drops 10°c for every 1,000 meters increase in elevation to represent the decrease in temperature if you hike up the mountain 2,000 meters. Then evaluate the expression and explain it's meaning
Answer: A-500 meters
Step-by-step explanation:
HELP ME PLEASE!!! 2(b+3)-(7+b)=-7 ??
2(b + 3) - (7 + b) = -7
2b + 6 - 7 - b = -7
b = -6 + 7 - 7
b = -6
To solve this first distribute the 2, and then distribute the negative sign.
2(b+3)-(7+b)=-7
2b+6-7-b=-7
Combine like terms.
2b+(-b)=b
6+(-7)=-1
b-1=-7
Add 1 on both sides of the equation.
b-1+1=-7+1
b=-6
Admission to the circus cost x dollars for an adult and y for a child find the total cost of 6 adults and 4 children
Abby has
2
4
5
245
lb of potting soil. She needs
2
1
2
212
times that amount for her plants.
How much potting soil does she need?
Abby needs 2940 total and has 245, therefore she needs 2695 lbs
you would do 245x212= 51,940
OR
212x212= 44,944
Hope that helps its one oth those but i want to say its the first one 245x212=51,940
Can someone help me on this pls
Identify the property that is being applied at each step to simplify the expression
We are given
First expression:
[tex]4^{-5} \cdot (4 \cdot 9)^{5} \cdot 9^{-3}=4^{-5} \cdot (4^{5} \cdot 9^{5}) \cdot 9^{-3}[/tex]
We used property
power rule-II:
Product to power distribute to each base
[tex](a \cdot b)^m=a^m \cdot b^m[/tex]
Second expression:
[tex]=(4^{-5} \cdot 4^{5}) \cdot ( 9^{5}) \cdot 9^{-3})[/tex]
we used property
associative property of multiplication:
[tex]a \cdot b \cdot c \cdot d =(a \cdot b) \cdot (c \cdot d)[/tex]
Third expression:
[tex]=4^0 \cdot 9^2[/tex]
we used property
Product Rule:
Same base add exponents
[tex]a^m \cdot a^n =a^{m+n}[/tex]
Fourth expression:
[tex]=1 \cdot 9^2[/tex]
we used property
Zero Exponent :
Anything to the zero power (except 0) is one
[tex]a^0=1[/tex]
Fifth expression:
[tex]= 9^2[/tex]
we used property
Multiplicative identity:
[tex]1 \cdot a=a[/tex]
Sixth expression:
[tex]= 81[/tex]
We used simplification
A store sells 2 1/4 pounds of tomatoes in a package for $4.45. The expression 4.45p represents the cost of the tomatoes for a number of packages. What does the variable p represent?
Answer:
The variable p represent the number of packages.
Step-by-step explanation:
As 4.45 is the cost of tomatoes, and 4.45p represents the cost of the tomatoes for a number of packages, we can say that p represent the number of packages.
Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked the poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1 1/3 inches. What is the scale factor as a fraction (and how would I do this!?)
[tex]\frac{3 (ft)}{2(in)} by \frac{2(ft)}{\frac{4}{3}(in)}[/tex]
= [tex]\frac{3 (ft)}{2(in)} by \frac{2(3)(ft)}{4(in)}[/tex]
= [tex]\frac{3 (ft)}{2(in)} by \frac{3(ft)}{2(in)}[/tex]
Scale factor is: [tex]\frac{3(ft)}{2(in)}[/tex]
Answer:
9/16 is the scale factor.Step-by-step explanation:
Every transformation has an original figure and a transformed figure.
In order to find the scale factor fo the transformation, we need to divide the transformed dimensions by the original ones.
So, in this case, the poster originally had 3 feet by 2 feet. Then, the reproduced artwork has 2 inches by 1 1/3 inches. Before we divide, we need to transform feet to inches.
We know that 1 feet equals 12 inches, that means
[tex]3ft \frac{12in}{1ft} =36in[/tex]
[tex]2ft\frac{12in}{1ft}=24in[/tex]
Then, we do the divisions
[tex]\frac{36in}{2in}=18\\\frac{24in}{1\frac{1}{3}in }=\frac{24in}{\frac{4}{3}in }=\frac{96}{3}=32[/tex]
Therefore, the scale factor is [tex]\frac{18}{32}=\frac{9}{16}[/tex]
Maryland’s snowfall total for December was 1.43 inches and for January it was 12.67 inches. What was the total snowfall for December and January together?
14.1 inches is the total snowfall for Dec. and Jan. together.
i need help please and thanks
1. 3p: Add 6 to negative 3, and carry over the "p"
3. 6x: Subtract 1 from 7 and carry over the "x"
5. -4v: Add 6 to negative 10 and carry over the "v"
7. -4r + 9: Add 5 to -9 and carry over the "r". Then put "+9" after the variable, since the other 9 was by itself.
9. 14n: Add 5 to 9 and carry over the "n".
I hope this helps!
to make a shade of plant called Jasper Green, Mix 4 quarts of green paint with 2/3 cups of black paint. how much green paint should be mixed with 4 cups of black paint to make Jasper Green?
Answer
24 quarts of green paint should be mixed with 4 cups of black paint.
That is (96 cups)
Step by step explanation
Jasper Green mix 4 quarts of green paint with 2/3 cups of black paint.
Let's convert 4 quarts into cups.
1 quart = 4 cups
4 quarts = 16 cups
Here mix 16 cups of green paint with 2/3 cups of black paint.
Let's use the proportion
Green paint Black paint
16 2/3
x 4
16/x =2/3 divided by 4
[tex]\frac{16}{x} = \frac{2/3}{4}[/tex]
Cross multiplying, we get
16*4 = 2/3 x
64 = 2/3 x
x = 64/(2/3)
x = 64 * 3/2
x = 192/2
x = 96 cups
96 cups of green paint should be mixed with 4 cups of black paint.
We can covert 96 cups into quarts by dividing by 4
96/4 = 24 quarts
24 quarts of green paint should be mixed with 4 cups of black paint.
Thank you.
To make Jasper Green with 4 cups of black paint, you need to create a proportional relationship and solve for the amount of green paint needed, which is 96 cups.
Explanation:To solve this, we need to set up a proportional relationship between the amounts of green paint and black paint. In the first mixture, we have 4 quarts of green paint for every 2/3 cups of black paint. Converting 4 quarts to cups (since 1 quart = 4 cups), we get 16 cups of green paint.
Then we can set up the proportion: (16 cups green / 2/3 cups black) = (x cups green / 4 cups black). Cross multiplying and solving for x, we get x = 96 cups of green paint. So, to make Jasper Green with 4 cups of black paint, you need to mix in 96 cups of green paint.
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Oscar and Julie Ashton are celebrating their 15th anniversary by having a reception at a local reception hall. They have budgeted $2,000 for their reception. If the reception hall charges a $90 cleanup fee plus $31 per person, find the greatest number of people that they may invite and still stay within their budget.
To determine the greatest number of people Oscar and Julie can invite within their budget, we can set up an inequality and solve for the variable 'x'. The total cost equation is $90 + $31x ≤ $2,000. Solving this inequality, we find that the greatest number of people they can invite is 61.
Explanation:To determine the greatest number of people that Oscar and Julie may invite and still stay within their budget, we need to set up an inequality based on the given information. Let's denote the number of people they invite as 'x'. The total cost of the reception hall is $90 (cleanup fee) + $31 (per person) * x (number of people). This should be less than or equal to their budget of $2,000. So, the inequality is 90 + 31x ≤ 2000. To solve for 'x', we need to isolate the variable. Subtracting 90 from both sides, we have 31x ≤ 1910. Dividing both sides by 31, we find x ≤ 61.935. Since we can't have a fraction of a person, the greatest number of people they can invite is 61.
Three friends all have same ages that are consecutive integers. The sum of their ages is 180. What is the age of the oldest friend?
a) 61
b) 59
c) 62
d) 60
Answer:
a) 61
The friend's ages are consecutive, therefore they are each one year apart. There are 3 friends whose ages add up to 180 in total.
[tex]180 / 3 = 60[/tex]
In order to make three consecutive numbers, subtract one and add one to 60.
[tex]60 - 1 = 59\\60 + 1 = 61[/tex]
You get 59, 60, and 61.
61 is the oldest age, that's your answer.
How can i write this in standard form? (7x^3+2x-1)+(8x^2-6+2x-x^3)
7x^3 +0x^2 + 2x -1
+ -x^3 +8x^2 +2x -6
----------------------------------------
6x^3 +8x^2 +4x -7
standard form is from largest exponent to smallest exponent
The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g?
g(x)=f(x3)
g(x)=3f(x)
g(x)=13f(x)
g(x)=f(3x)
Answer: The correct option is second, i.e., [tex]g(x)=3f(x)[/tex].
Explanation:
A functions g(x) is stretch or compressed of graph of function f(x) is defined by the equation,
[tex]g(x)=kf(x)[/tex]
Where, k is a constant and it shows the compress or stretch factor.
If k>0, then it is a stretch factor and the graph of f(x) is stretched by factor of k.
If k<0, then it is a compress factor and graph of f(x) is compressed by factor k.
Since the graph of g(x) is a vertical stretch of the graph of function f(x) by a factor of 3, therefore,
[tex]g(x)=3f(x)[/tex]
So, the option second is correct.
What is the algebraic expression for the following word phrase: the quotient of y and 6
A quotient is the answer that results from a number being divided by another number. In other words, it is the answer to a division problem. So, the quotient of y and 6 means that y is being divided by 6. Algebraically, you write this as y ÷ 6, or [tex]\frac{y}{6}[/tex]
A bag contains 6 blue marbles, 10 red marbles, and 9 green marbles. If two marbles are drawn at random without replacement, what is the probability that two red marbles are drawn?
Answer:Your Answer of the probability would determindedly be 3/25.
Step-by-step explanation:
Factor 3x2 − 12x − 36 completely.
a) 3(x − 6)(x + 2)
b) (3x + 6)(x − 2)
c) 3(x + 4)(x − 3)
d) (3x − 4)(x + 3)
The answer would be A, 3(x-6)(x+2)
Not sure on this one can someone help plz
Jack has g golf balls. The balls came in 8 packages. How many golf balls were in each package?
A olympic runner set a récord for the 100m dash. The time was sixsty-two hundred seconds.How Would you write this as a number
sixty-two hundred= This would be 6200.
The height of a baseball thrown from the catcher to first base is modeled by the function h(t)=-0.08t^2+0.72t+6, where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds. The ball is in the air for 10 seconds before being caught. What’s the initial height of the ball?
A. 4.2 feet
B. 5.72 feet
C. 6 feet
D. 9 feet
answer is C. 6 feet.
10 points!
Find the domain and range.
The domain is the first x of each ordered pair. The domain is 1, -30, -12, -11
The range is the y value : -27,30,21,4
Solve for x: 3|x − 3| + 2 = 14 (5 points)
x = 0, x = 7
x = −1, x = 7
No solutions
x = −1, x = 8.3
[tex]Solution, solve\:for\:x,\:3\left|x-3\right|+2=14\quad :\quad x=-1\quad \mathrm{or}\quad \:x=7[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}, 3\left|x-3\right|+2-2=14-2[/tex]
[tex]\mathrm{Simplify}, 3\left|x-3\right|=12[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3, \frac{3\left|x-3\right|}{3}=\frac{12}{3}[/tex]
[tex]\mathrm{Simplify}, \left|x-3\right|=4[/tex]
[tex]|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a, x-3=-4\quad \quad \mathrm{or}\quad \:\quad \:x-3=4[/tex]
[tex]x-3=-4\quad :\quad x=-1[/tex]
[tex]x-3=4\quad :\quad x=7[/tex]
[tex]\mathrm{Combine\:the\:ranges}, x=-1\quad \mathrm{or}\quad \:x=7[/tex]
The correct answer is B. x=-1, x=7
Hope this helps!!!
What is the LCM between 12,7
Hello there!
You had to find the prime factorization of 12
3*2*2=12
Then you find the prime factorization of 7.
7*1=7
7*3*2*2=84
Answer⇒⇒84
The least common multiple of 12 and 7 is 84.
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
The shipping cost for an on-line company increases exponential based on the number of dollars the consumer has spent. It can be represented by the equation y = 0.003(2)x where x represents every $10 spent. Shipping charges will max out at $20. The company has decided that they need to add a base shipping charge of $5. What will this new function be?
Answer:
[tex]y = 5 + 0.003(2^{x})[/tex]
Step-by-step explanation:
If a base shipping charge of $ 5 is collected, it means that regardless of the amount of money spent, a base payment of $ 5 must be made for the shipment. Therefore the graph of the exponential function must move 5 units up on the positive y axis. Your new cutoff point with the positive y axis will be y = $ 5.003
Therefore, the new function that represents the shipping cost will be:
[tex]y = 5 + 0.003(2^{x})[/tex]
with [tex]x \leq 20[/tex]