For a line to be parallel to another line, the slope will be the same
1st equation:
\(\begin{gathered} 2x\text{ - 5y - 8 = 0} \\ \text{making y the subject of formula:} \\ 2x\text{ - 8 = 5y} \\ y\text{ = }\frac{2x\text{ - 8}}{5} \\ y\text{ = }\frac{2x}{5}\text{ - }\frac{8}{5} \end{gathered}\)\(\begin{gathered} \text{equation of line:} \\ y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}\)\(\begin{gathered} \text{comparing the given equation and equation of line:} \\ y\text{ = y} \\ m\text{ = 2/5} \\ b\text{ = -8/5} \end{gathered}\)Since the slope of the first line = 2/5, the slope of the second line will also be 2/5
We would insert the slope and the given point into equation of line to get y-intercept of the second line:
\(\begin{gathered} \text{given point: (-7, 6) = (x, y)} \\ y\text{ = mx + b} \\ 6\text{ = }\frac{2}{5}(-7)\text{ + b} \\ 6\text{ = }\frac{-14}{5}\text{ + b} \\ 6\text{ + }\frac{14}{5}\text{ = b} \\ \frac{6(5)\text{ + 14}}{5}\text{ = b} \\ b\text{ = }\frac{44}{5} \end{gathered}\)The equation for the line that passes through (-7, 6) and parallel to line 2x - 5y - 8 = 0:
\(\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{2}{5}x\text{ + }\frac{44}{5} \end{gathered}\)Some friends decided to equally split the cost of gas on their trip. The expression 3g/4 represents how much money each person had to pay in dollars for g gallons of gas. What does the expression 3g in the numerator represent?
A the cost per person
B the number of people splitting the cost of the gas
C the total cost of the gas before it was split among the friends
D the cost per gallon of gas
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Answer: The total cost of the gas before it was split among the friends.
Explanation: If they split it equally, they divide. 3g is divided by 4 so you know that there are 4 friends/people.
Since they are splitting the [total] amount of gas for 4 people, 3g must be the total cost of the gas.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer:
c
Step-by-step explanation:
i took the quiz
People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
250
7
2
+6
2
(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
100
7
2
+
150
6
2
(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
250
7
2
+6
2
(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
100
7
2
+
150
6
2
The mean and standard deviation (in ) of the sampling distribution of the difference in sample means \(\sigma_1\) - \(\sigma_2\) = (7)² ÷100+ 6² /150.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Level A:
S.D. = 7
Level B: Mean = 20
S.D. = 6
So, \(\nu_1\) = 22
\(\nu_2\) = 20
Then, \(\nu_1\) - \(\nu_2\) = 22-20=2
and, \(\sigma_1\) - \(\sigma_2\)
= (7)² ÷100+ 6² /150
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Help me please someone for brainliest
Answer:
I think the answer is 1.5
Step-by-step explanation:
Using Pythagoras theorem
(6r)²= 9²+r²
36r²-r²=81
35r²=81
r²=81/35
r²=2.3
r=√2/3
r=1.5
-5/8x-7/24x+1/3x=-56
Answer:
x =
Step-by-step explanation:
First, add like terms. You can take out the x if it's too confusing and add it again.
-5/8 - 7/24 + 1/3 (multiply get a common denominator--in this case it's 24)
-15/24 - 7/24 + 8/24
-14/24 (then, simplify!)
-7/12
(add back the x → -7/12x)
-7/12x = -56 (multiply by reciprocal)
(-12/7) (-7/12x) = (-56) (-12/7)
x = 96
What's the measure of an arc with a central angle of 120°?
Answer:
the answer is 240 degrees
Which graph represents the equation 3x+y=-1?
Answer:
The answer is c
Step-by-step explanation:
I put this into my graphing calculator to solve it. To do this by hand though you need to choose two numbers and enter then for x and that should give you the numbers the you need to plot on your graph.
Hope that help :)
How do I Estimate how many cups of Fruit Trail Mix the recipe can make
Please help I don’t understand
which pair of numbers does not have a least common multiple less than 100
use the map for exercises 13 to 15
Answer:
yes he is correct for 13
peyton hikes. 6 1/80
no it would not be a greater distance because if you do 9/10 times 3 and turn the answer into a decimal the red trail is a greater distance.
Step-by-step explanation:
yes he is correct for 13
peyton hikes. 6 1/80
no it would not be a greater distance because if you do 9/10 times 3 and turn the answer into a decimal the red trail is a greater distance.
A truck with 30-in.-diameter wheels is traveling at 50 mi/h.
Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes:
_________rad/min
How many revolutions per minute do the wheels make?
___________rpm
Answer:
A. the angular speed is 3771.4 rad/min
b. 5921 rpms
Step-by-step explanation: I just got this same question right on a test.
11 Evaluate d-fif d = 7 and f = -15.
PLS help me with my math
i dont know either your on your own
Step-by-step explanation:
i just dont know
Express 18 hours to 2 days in its lowest term
Answer:
1 : 3
Step-by-step explanation:
We know that 1 days is 24 hours
2 days = 2*24 = 48 hours
16 hours : 48 hours
Divide each by 16
16/16 : 48/16
1 : 3
Answer:
\(3 : 8\)
Step-by-step explanation:
\(18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8\)
Find the radius of a circle that has an area of 121 pi f2
Answer: r=11
Step-by-step explanation:
A=πr^2
A=121π
121π=πr^2
r^2=121
r=11
Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
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You started your dream business. Month 1, you make $1,200 and in 5 months you will have $5,800. Write and solve a linear equation to find out how much money you will make in 9 months.
Answer:
below
Step-by-step explanation:
Let's call the number of months since you started the business "x" and the amount of money you make "y". We know two points on this line: (1, $1,200) and (5, $5,800).
From this information, we can write the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Using the first point, we can solve for b:
$1,200 = m * 1 + b
$1,200 = m + b
b = $1,200 - m
Using the second point, we can solve for m:
$5,800 = m * 5 + $1,200 - m
$5,800 = 6m + $1,200
$4,600 = 5m
m = $920
So the equation of the line is: y = $920x + $1,200
Finally, to find out how much money you will make in 9 months, we can plug in x = 9:
y = $920 * 9 + $1,200
y = $8,280
Therefore, in 9 months, you will make $8,280.
Answer:
Step-by-step explanation:
Lets write a linear equation from two known points
Point 1 = (x1, y1) = (1,1200)
Point 2= (x2,y2)= (5,5800)
The general expression for a linear equation is:
Y-y1 = m (X-x1)
Where:
\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{5800-1200}{5-1}\)
\(m=\frac{4600}{4}\)
m= 1150
Therefore, if terms are replaced in the general expression, the linear equation is given by:
Y-1200 = 1150 (X-1)
Y=1150X-1150+1200
Y=1150X+50
Where:
Y= The amount of money you make for the given month
X= Month No.
I need some help with this
Answer:
The area of the circle is pi r^2,
and they substitute 3 for pi
and the radius is 6,
so we have 6^2 = 36 times 3
equals
108
brainliest please?
Answer:
108cm^2
Step-by-step explanation:
pi = 3
r = 6
A = pi(r)^2
A = (3)(6)^2
Use order of operations
A = 3 * 36
A = 108cm^2
send helpp pleaseeeeee
Answer:
1. VR and TS
2. TS and RS
3. TV and RS
Step-by-step explanation:
Pedro goes to the store and buys a binder, a folder, and a highlighter. The folder's
cost is half the cost of the binder, and the highlighter's cost is $1 more than the
binder. The total cost of the three supplies, with no tax, is $6. Write an equation to
represent the situation. Show your work.
The equation that represents this situation is 4.75 = 2.5x - 1.25x.
What is a linear equation in one variable?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax + b = 0, where a and b are two integers and x is a variable. 2x + 3 = 8, for example, is a linear equation with a single variable.
Let the cost of the binder be represented with x.
The cost of the folder is x = 0.5x
The cost of the highlighter = x - $1.25
The total cost of the items = cost of binder + highlighter + folder
4.75 = x + 0.5x + x - 1.25
Add similar x terms together, and we get
4.75 = 2.5x - 1.25x
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A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x^2−6x+9 yd^2.
Area of the flagpole plot: x^2−6x+9
Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.)
The length of the base of the flagpole is
Answer:
\(x-3\)
Step-by-step explanation:
The area of the flagpole base is \(x^2-6x+9\ \text{yd}\)
where the factor of the equation is the length of the base.
In order to find the length we need to factorize the equation
\(x^2-6x+9\)
\(=x^2-3x-3x+9\)
\(=x(x-3)-3(x-3)\)
\(=(x-3)(x-3)\)
The length of the base of the flagpole is \((x-3)\ \text{yd}\).
The area of a square base is the product of the side lengths.
The length of the base is x - 3
The area is given as:
\(\mathbf{Area =x^2 - 6x + 9}\)
Expand
\(\mathbf{Area =x^2 - 3x - 3x + 9}\)
Factorize
\(\mathbf{Area =x( x- 3) - 3(x - 3)}\)
Factor out x - 3
\(\mathbf{Area =( x- 3) (x - 3)}\)
Express as squares
\(\mathbf{Area =( x- 3)^2}\)
Rewrite the area as:
\(\mathbf{Length^2 =( x- 3)^2}\)
Take square roots of both sides
\(\mathbf{Length =x- 3}\)
Hence, the length of the base is x - 3
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a father is four times as old as the sun in 10 years time the father will be twice as old as the son .if the father is 20years and son is 5 years currently, how old will the father be 29 years from now?
29 years from now, the father will be 49 years old.
Let's start by setting up the given information:
Currently, the father is 20 years old, and the son is 5 years old.
In 10 years, the father will be twice as old as the son.
The father is currently four times as old as the son.
Determine the age of the father and son in 10 years:
In 10 years, the father's age will be 20 + 10 = 30 years.
In 10 years, the son's age will be 5 + 10 = 15 years.
Write equations based on the given information:
The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.
The father's current age is four times the son's current age: 20 = 4 × 5.
Solve the equations:
From the second equation, we find that the son's current age is 5 years.
Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).
Simplifying further, we have: 30 = 2 × 15, which is true.
Determine the current age of the son in 29 years:
The son's current age is 5 years.
Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.
Determine the current age of the father in 29 years:
The father's current age is 20 years.
Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.
Therefore, 29 years from now, the father will be 49 years old.
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Two people are planning their wedding. For the reception, they found the the cost C for 50 guests, g is $2150 whereas the cost for 75 guests is $3025. Calculate the slope to find the cost per guest?
The slope which shows the cost per guest is $35 per guest
The given cost for 50 guests is $2150.
The cost for 75 guests is $3025.
It can also be represented as:
(Guest, Cost) =(50, $2150) & (75, $3025)
The slope can now be calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (50, $2150) & (75, $3025)
Substituting the given values in the equation as follows:
Slope = (3025 - 2150)/(75 - 50)
Slope = 35
Hence, the slope is $35 per guest.
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Please help thank u!!
Answer:
3500 mL = 3 1/2 L
Step-by-step explanation:
1 L = 1000 mL
3 1/2 L = (3 1/2)(1000 mL) = 3500 mL
3500 mL = 3 1/2 L
_____
Additional comment
The SI prefix "m" is an abbreviation for "milli-", meaning 1/1000. That is, 1 mL = 1/1000 L, or 1 L = 1000 mL.
Two adjacent
angles on a straight are in the ratio of 5:4 find the measure of both angles
Answer:
hope this is what u want
if I m correct mark me brainlist plz
Find the surface area and volume of the prism.
Answer:
840 square cm
Step-by-step explanation:
28 * (5+12+13)
28 * 30
840 square cm
If cos a= 0.93. Sin 0 =0.26, and tan ß = 0.84, find a + B + 0.
Answer:
77°
Step-by-step explanation:
From the question given above, the following data were obtained:
Cos α = 0.93
Sine θ = 0.26
Tan β = 0.84
α + β + θ =?
Next, we shall determine the value of α. This can be obtained as follow:
Cos α = 0.93
Take the inverse of Cos
α = Cos¯¹ 0.93
α = 22°
Next, we shall determine the value of θ. This can be obtained as follow:
Sine θ = 0.26
Take the inverse of Sine
θ = Sine¯¹ 0.26
θ = 15°
Next, we shall determine the value of β. This can be obtained as follow:
Tan β = 0.84
Take the inverse of Tan.
β = Tan¯¹ 0.84
β = 40°
Finally, we shall determine the value of α + β + θ . This can be obtained as follow:
α = 22°
θ = 15°
β = 40°
α + β + θ = 22 + 40 + 15
α + β + θ = 77°
A triangle has vertices x(2,1), y(5,4), z(5,1). What is the base and height of the triangle
Answer:
The base is XZ and the height is ZY.
The measure of base is: 3 Units
The measure of Height is: 3 Units
Step-by-step explanation:
The explaination is given in the pictures...
6. Consider the polynomial p(x) = x^2 + kr^2 +x+6. Find a value of k so that x+1 is a factor of P. Find all the zeros of P.
If x + 1 is a factor of p(x) = x³ + k x² + x + 6, then by the remainder theorem, we have
p (-1) = (-1)³ + k (-1)² + (-1) + 6 = 0 → k = -4
So we have
p(x) = x³ - 4x² + x + 6
Dividing p(x) by x + 1 (using whatever method you prefer) gives
p(x) / (x + 1) = x² - 5x + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
x² - 5x + 6 = (x - 3) (x - 2)
so that, in addition to x = -1, the other two zeros of p(x) are x = 3 and x = 2
Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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a statistics student is trying to decide whether she should take a gamble and play bingo. the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8. if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
Select all that apply: 0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80
The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.
Standard deviation
In statistics, standard deviation refers the square root of variance by determining each data point's deviation relative to the mean.
Given,
Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.
And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80
Here the standard deviation of the sample distribution is calculated as,
=> σₓ = √1.80 = 1.34
Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.
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