1. Solve the given equation for y.
x - 5y = 15
-5y = -x + 15
y = (-x + 15)/-5
y = (x/5) - 3
y = (1/5)(x) - 3
The slope is 1/5. See it?
The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.
The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?
We have the slope of the new equation and one point is given.
Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.
y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)
y - 5 = -5(x - (-2))
y - 5 = -5(x + 2)
We now solve for y and that's it.
y - 5 = -5x - 10
y = -5x - 10 + 5
The equation we want is y = -5x - 5.
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if you have 2 dollars 5 pennies and three quarters how much money do you have
What is the equation of the line with an x-intercept of -2 and a y-intercept of 1?
A.y = -1/2x + 1
B.y = 1/2x + 1
C.y = 2x + 1
Describe a real-world scenario and which it would be important to apply trigonometric ratios or special right triangles.
Answer:
In forensic science trigonometry can be used to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere, or in which angle was a bullet shot etc.
Electrical engineers also use trigonometry. Modern power companies use alternating current to send electricity over long-distance wires. In an alternating current, the electrical charge regularly reverses direction to deliver power safely and reliably to homes and businesses.
Electrical engineers use trigonometry to model this flow and the change of direction, with the sine function used to model voltage. Every time you flip on a light switch or turn on the television, you’re benefiting from one of trigonometry's many uses.
The elevation of Niagara Falls which is located between Lake Erie and Lake Ontario, is 326 feet. How far is this above sea level?
Write the equation of the line that passes through the points (1,4) and (5,8) in standard form.
Question 8 options:
x + 4y = 1
5x + 8y = 4
-2x + y = 5
-x + y = 3
If f(x)=3x^2-2x+4 and g(x)=5x^2+6x-8 find (f+g)(x)
You and 2 friends have a job washing cars. you split the money you make so that you each get the same amount. on the first day, you earn $75. the second day, you earn $84. the third day, you earn $105. how much money will you each get for those 3 days?
Final answer:
Each friend would receive $88 from the total earnings of $264 over three days, after splitting the amount equally.
Explanation:
The question asks how much money each person would get from a total earning of $75 on the first day, $84 on the second day, and $105 on the third day after splitting it equally among three friends. To find this out, first, we need to calculate the total earnings by adding the amounts from all three days, and then we divide the total by three, since there are three friends.
The total earnings over the three days are $75 + $84 + $105 = $264. To find out how much each person gets, we divide this amount by 3:
$264 ÷ 3 = $88
So, each friend would get $88 for their work over those three days.
calculate the distance between the points A (-4,2) and B (15,6)
Distance between the points A (-4, 2) and B (15, 6) is 19.41.
Here,
The points are A (-4, 2) and B (15, 6).
We have to find the distance between the points A (-4, 2) and B (15, 6).
What is Distance between two points?
Distance between two points A (x₁, y₁) and B (x₂, y₂) is given by:
[tex]D_{AB} = \sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]
Now,
Distance between the points A (-4, 2) and B (15, 6) is;
[tex]D_{AB} = \sqrt{(15-(-4))^2+(6-2)^2}[/tex]
[tex]= \sqrt{19^2+4^2}[/tex]
[tex]= \sqrt{361+16}[/tex]
[tex]= \sqrt{377}[/tex]
[tex]= 19.41[/tex]
Hence, Distance between the points A (-4, 2) and B (15, 6) is 19.41.
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What are the steps for using a compass and straightedge to construct an equilateral triangle?
Drag the steps and drop them in order from start to finish.
Construct a point at one of the two intersection points of circle E and circle F and label this point G
.Construct EG¯¯¯¯¯ and FG¯¯¯¯¯ .
Construct EF¯¯¯¯¯
.Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF .
This question is based on the following paragraph
The selling price, s, of an item is s = c + mc, where c is the cost of the item and m is the percent markup based on cost. What is the formula solved for m?
Answer:
[tex]m=\frac{s-c}{c}[/tex]
Step-by-step explanation:
The given expression is
[tex]s=c+mc[/tex]
Now, to find the expression for [tex]m[/tex], we just have to isolate it. First, we have to move the term [tex]c[/tex] to the other side of the equation, and then to move the coefficient [tex]c[/tex], which is gonna pass to the other side dividing.
[tex]s=c+mc\\s-c=mc\\\frac{s-c}{c}=m\\m=\frac{s-c}{c}[/tex]
Therefore, the percent markup is defined as the difference between the selling price and cost, divided by that cost.
what is 2.31 divided by 3?
Find the Missing part of the unit rate: 40 students over 5 groups = ? Students over group
The missing part of the unit rate in the given situation is 8 students per group. This is obtained from dividing the total number of students (40) by the total number of groups (5).
Explanation:To find the missing part of the unit rate, we'll need to divide the total number of students (40) by the total number of groups (5). This is because a unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
So in this case, the unit rate would be 40 ÷ 5 = 8. Therefore, the missing part of the unit rate is 8 students per group.
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A bank contains 35 coins, all nickels and quarters. The total value of coins is $8.15. How many of each coin does the bank contain?
n + q = 35
n = 35-q
0.05n + 0.25q = 8.15
0.05(35-q) +0.25q = 8.15
1.75 -0.05q + 0.25q =8.15
1.75 + 0.20q = 8.15
0.20q = 6.40
q = 6.40 / 0.20 = 32
32 quarters and 3 nickels
2.5% TAX, $679 SEMIMONTHLY: FIND THE LOCAL TAX DEDUCTED.
Answer:
$16.98
hope this helps you! good luck ;)
You want to convert a measurement of 800 milliliters to centiliters using back-to-back conversion factors.
The conversion factors you will need are:
1 milliliter = 1/1000 liter
1 centiliters = 1/100 liters
The image shows you the template of the equation.
What is the order of the conversions you must perform?
At the beginning of a basketball season, the Panthers won 40 games out of 60 games. At this rate, how many games will they win in a normal 110-game season? Round answer to the nearest game.
The Panthers are expected to win approximately 73 games out of 110 based on their current win rate.
To find out how many games the Panthers will win in a normal 110-game season based on their current winning rate from the beginning of the season, we use a simple proportion. Initially, they won 40 games out of 60, which gives us a winning ratio.
The ratio can be written as:
40 wins / 60 games = number of wins / 110 games
To find the number of wins, we cross-multiply and solve for the unknown:
(40 wins / 60 games) * 110 games = number of wins
After the calculation:
40 * 110 / 60 ≈ 73.33
As we need to round to the nearest game, it gives us approximately 73 games out of 110.
Factor this Polynomial completely. X^2-12x-36
this cannot be factored.
there are no 2 numbers that when added will equal - 12 and when multiplied together would equal -36
Terry had $43 in a checking account. If Terry writes a check for $62, what is the new account balance? a. $105 c. -$19 b. $19 d. -$9
What equation models the data in the table if d = number of days and c = cost?
Days Cost
2 44
3 66
5 110
6 132
c = 22d
d = 22c
c = d + 22
c = d + 22d
The equation that models the data in the table is:
[tex]c=22d[/tex]
Step-by-step explanation:The table that represent the days and cost is given by:
Days Cost
2 44
3 66
5 110
6 132
We see that the cost is a constant multiple of the number of days.
i.e. the equation is given by:
c=22d
i.e. the relationship is linear.
( Since, when d=2
we have: c=22×2=44
when d=3 we have:
c=22×3=66
and so on )
What is the procedure for multiplying a two digit number by a one digit number?
Find the side of a square whose diagonal is of the given measure.
Given = 8 miles
To find the side of a square with a given diagonal length, apply the Pythagorean theorem. With a diagonal of 8 miles, the side length is calculated to be 4√2 miles.
Explanation:To find the side of a square whose diagonal is given, we can use the Pythagorean theorem. In a square, the diagonal creates two right-angled triangles, each with the square's sides as the legs.
Let the side of the square be s, and the given diagonal is 8 miles. According to the Pythagorean theorem, the diagonal (d) is calculated as d = √(s² + s²). Simplifying, this becomes d = √(2 * s²) or s = d / √2. Substituting the value of the diagonal, we get s = 8 / √2. To get rid of the radical in the denominator, we can multiply both the numerator and denominator by √2, giving us s = (8√2) / 2, which simplifies to s = 4√2 miles. Therefore, the side of the square is 4√2 miles.
I really need help. I just can't quite get it. It involves Triangle Medians and Triangle Centroid
translate the phrase into a variable expression. use the letter b to name the variable. is necessary, use the asterisk ( * ) for multiplication and the slash ( / ) for division
.......the total number of slices of bread used for the sandwiches and the 7 still left in the loaf....
The translation of a phrase into a variable expression is given by:
b+7
Step-by-step explanation:The letter ' b ' is used to name the variable.
The total number of slices of bread used for the sandwiches and the 7 still left in the loaf.
Let b be the total number of slices that were used for the sandwiches.
and also 7 are still left in the loaf
The total number of slices of bread= Number of slices used fro sandwich+Left over
Hence, the expression is:
b+7
(WILL MARK AS BRAINLIEST) Consider the graph of quadrilateral WXYZ.
Which statements about quadrilateral WXYZ are true? Check all that apply.
The slope of ZW is .
The slope of YX is .
The length of ZY is .
The length of WX is 5.
Quadrilateral WXYZ is a square.
Answer:
The slope of ZW is [tex]\frac{2}{5}[/tex]
The lenght of ZY is [tex]\sqrt{29}[/tex]
Quadrilateral WXYZ is a square
Step-by-step explanation:
Statements
case A) The slope of ZW is [tex]\frac{2}{5}[/tex]
The statement is True
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Z(-3,1),W(2,3)[/tex]
substitute
[tex]m=\frac{3-1}{2+3}[/tex]
[tex]m=\frac{2}{5}[/tex]
case B) The slope of YX is [tex]-\frac{5}{2}[/tex]
The statement is False
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
substitute
[tex]m=\frac{-2+4}{4+1}[/tex]
[tex]m=\frac{2}{5}[/tex]
case C) The lenght of ZY is [tex]\sqrt{29}[/tex]
The statement is True
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
substitute
[tex]d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case D) The lenght of WX is [tex]5[/tex]
The statement is False
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]W(2,3),X(4,-2)[/tex]
substitute
[tex]d=\sqrt{(-2-3)^{2}+(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case E) Quadrilateral WXYZ is a square
The statement is True
Because sides ZW and YX are parallel sides (has the same slope)
Slope ZY
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
[tex]m=\frac{-4-1}{-1+3}[/tex]
[tex]m=-\frac{5}{2}[/tex]
so
ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)
[tex]-\frac{5}{2}*\frac{2}{5}=-1[/tex]
Slope WX
we have
[tex]W(2,3),X(4,-2)[/tex]
[tex]m=\frac{-2-3}{4-2}[/tex]
[tex]m=-\frac{5}{2}[/tex]
ZY and WX are parallel sides (has the same slope)
distance ZW
we have
[tex]Z(-3,1),W(2,3)[/tex]
[tex]d=\sqrt{(3-1)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
distance YX
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
[tex]d=\sqrt{(-2+4)^{2}+(4+1)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
The four sides are congruent
case F) [tex]YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}[/tex]
The statement is False
[tex]YZ=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]
[tex]YZ=\sqrt{13}[/tex] ----> is not correct
the value of YZ is [tex]\sqrt{29}[/tex]
Peggy needs to pay car insurance 2 times every year. She has divided the payment by 6 and saves that amount each month. Which account below is the best account in which to save this money? a. 401-K retirement fund with matching deposits from Peggy’s employer. b. A checking account, or a savings account for other expenses (predictable), and emergencies. c. A savings account for college tuition. d. Coin jar.
Answer:
b. A checking account, or a savings account for other expenses (predictable), and emergencies.
Step-by-step explanation:
Peggy needs to pay car insurance 2 times every year.
She has divided the payment by 6 and saves that amount each month.
So, the best account in which she can save this money is - A checking account, or a savings account.
Other options are irrelevant as a 401-K retirement fund is some other type of account. It is not used for daily or monthly expenses.
Options C and D are also not correct.
What is the answer to X2+16x+60=0
Determine the value of r so that the line through (5, 2) and (7, r) has a slope of m= -1/2
Final answer:
The value of r that makes the line through (5, 2) and (7, r) have a slope of -1/2 is 1.
Explanation:
To determine the value of r so that the line through the points (5, 2) and (7, r) has a slope of m= -1/2, we use the slope formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is (5, 2) and (x2, y2) is (7, r).
Slope calculation:
-1/2 = (r - 2) / (7 - 5)
-1/2 = (r - 2) / 2
Multiplying both sides by 2 to isolate the variable r:
-1 = r - 2
r = 2 - 1
r = 1
Therefore, the value of r that makes the slope -1/2 is 1.
Find the value of b if it is known that the graph of y=−3x+b goes through point: M(−2, 4)
A delivery truck travels 21 blocks north, 12 blocks east and 26 blocks south. what is its final displacement from the origin? assume the blocks are equal length.
The truck's displacements in the North-South and East-West directions are calculated separately. The final displacement is 5 blocks South and 12 blocks East.
Explanation:To solve this problem, we need to consider the truck's displacement in the North-South direction and the East-West direction separately.
Starting with the North-South direction, the truck moves 21 blocks North and then 26 blocks South. Thus, its total displacement in the North-South direction is 21 - 26 = -5 blocks. The negative sign indicates that the truck is 5 blocks South from its starting point.
Considering the East-West direction, the truck moves 12 blocks East. Therefore, its total displacement in the East-West direction is +12 blocks.
Overall, the displacement of the truck from the origin is 5 blocks South and 12 blocks East.
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