The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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p=2a+c, solve for c.
The given equation is expressed as
[tex]\begin{gathered} p\text{ = 2a + c} \\ To\text{ solve for c, we would subtract 2a from both sides of the equation. It becomes} \\ p\text{ - 2a = 2a - 2a + c} \\ p\text{ - 2a = c} \\ c\text{ = p - 2a} \end{gathered}[/tex]i need help on 8 I will provide I bigger picture
Explanation
Step 1
the sum of the internal angles in a triangle equals 180, then
for triangle CDE
[tex]\begin{gathered} rigth\text{ angle+blue angle+yellow angle=180} \\ \text{replace } \\ 90+10+\measuredangle\text{EDC}=180 \\ 100+\measuredangle\text{EDC}=180 \\ \text{subtract 100 }in\text{ both sides} \\ 100+\measuredangle\text{EDC-100}=180-100 \\ \measuredangle\text{EDC}=80 \end{gathered}[/tex]Step 2
as we can see, in poitn c, we have a 180 degrees angle(ACD)
so
[tex]\begin{gathered} \text{red angle+gre}enangle+yellow\text{ angle}=180 \\ \text{replace} \\ 70+\measuredangle BCE+\measuredangle EDC=180 \\ 70+\measuredangle BCE+80=180 \\ 150+\measuredangle BCE=180 \\ \text{subtract 150 in both sides} \\ 150+\measuredangle BCE-150=180-150 \\ \measuredangle BCE=30 \end{gathered}[/tex]I hope this helps you
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,6) and perpendicular to 3 x + 7y = 1.a) The equation of the line in slope-intercept form is enter your response here
The equation
[tex]3x+7y=1[/tex][tex]7y=-3x+1[/tex][tex]y=\frac{-3x}{7}+\frac{1}{7}[/tex]has slope -3/7.
The product of perpendicular lines must be -1, so the slope of the new equation must be:
[tex]m\cdot-\frac{3}{7}=-1[/tex][tex]m=\frac{-1\cdot7}{-3}=\frac{7}{3}[/tex]The line with that slope and that passes throught (1,6) is:
[tex](y-6)=m(x-1)[/tex][tex](y-6)=\frac{7}{3}(x-1)[/tex][tex]y-6=\frac{7}{3}x-\frac{7}{3}[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+6[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+\frac{18}{3}[/tex][tex]y=\frac{7}{3}x+\frac{11}{3}[/tex]The following graph shows both equations:
[tex]y=\frac{7}{3}x+\frac{11}{3}[/tex][tex]3\cdot y=(\frac{7}{3}x+\frac{11}{3})\cdot3[/tex][tex]3y=7x+11[/tex][tex]-7x+3y=11[/tex]Mr. Webster sells vacation rentals and
earns a 3.5% commission on every
vacation rental he sells. How much
commission would he earn on a vacation
rental that sold for $4,200?
Answer:
$134.50
Step-by-step explanation:
4200 x .035 = 134.50
3.5% Percent means per 100
3.5/100 when you divide by 100, you move the decimal two places to the left.
The commission amount is $147
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.
He sold $4200.
So, 3.5% of commission:
4200 x 3.5 / 100
= 147
Therefore, the commission is $147.
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n your initial post, answer the following questions: identify the many variables that a hospital needs to consider in layout design? what are the advantages of the circular pod design over the traditional linear hallway layout at arnold palmer? what suggestions about wheeled coach layout would you make to bob collins?
The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.
What is the layout of a hospital?Layout design generally seeks to arrange organizational units inside a building so that the space is used to its fullest potential and total distances are kept to a minimum.
The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. It must be able to endure the pressure and environmental conditions that they might encounter.
A facility's layout and design are crucial to a company's overall operations because they may both suit the needs of employees and maximize the efficiency of the production process. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.
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what is equivalent to 0.5×0.6
Answer: 0.3
5/10 x 6/10 = 30/100 = 3/10 = 0.3
In Exercises 45-48, solve the equation.
45. n - 5.3
-7.4
46. |2x + 5| = 3x
47. 7c+ 10-12c=-11-2c
48. (3h + 8) + 2 = 13
49. Determine whether the relation is a function.
Explain.
(0, -6), (1, -3), (3, 2), (5, 1), (2, -3)
50. Write the sentence as an inequality.
Seven is at most the quotient of a number d
and -5.
Just do 46, 48, and 50
Will give brainliest
The equations are solved to give;
46. x = 5
48. h = 1
50. The inequality is 7 ≤ d/ -5
What is an algebraic expression?An algebraic expression is described as a mathematical expression that is composed of terms, factors, coefficients, constants and variables.
They are described as expressions made up of arithmetic operations which includes;
ParenthesesSubtractionAdditionMultiplicationDivisionBracket, etcGiven the expression;
46. |2x + 5| = 3x
Take the absolute value, we have;
2x + 5 = 3x
collect like terms
2x - 3x = - 5
-x = -5
x = 5
48. (3h + 8) + 2 = 13
expand the bracket
3h + 8 + 2 = 13
collect like terms
3h = 13 - 10
3h = 3
Make 'x' the subject of formula
h = 1
50. Seven is at most the quotient of a number d and -5.
This is expressed as;
7 ≤ d/ -5
Hence, the values are x = 5, h = 1 and 7 ≤ d/ -5
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thought provoking the postulates and theorems in this book represent euclidean geometry. in spherical geometry, all points are points on the surface of a sphere. a line is a circle on the sphere whose diameter is equal to the diameter of the sphere. explain how many right angles are formed by two perpendicular lines in spherical geometry.
Inequality involving the sum of the angles of a triangle i.e,
[tex]\alpha +\beta +y > \pi[/tex]
The area of a spherical triangle ABC with angles a, B, Y are
AABC = ([tex]\alpha[/tex] + [tex]\beta[/tex]+ Y- [tex]\pi[/tex] ) [tex]R^{2}[/tex]
The AA'B'C' = AABC (by sss) as we discuss move.
We just need to demonstrate that IACI = IAC' and C'L IBCI = 1BC '1 will proceed similarly.
since AC & ATC resulted in the same.
the middle.
We now have external proof that the surface and their mon- are real. As of (ABCA) and LA'B'C) cover. A overlapping sphere with appropriate angles for each letter of the alphabet Las offered my first figure of $ segments that are completely separate from one another, so we may write -
( AABC A ) + ( A A'B'C' )A + ( An -x ) + ( Ax-B ) + ( An-V ) = [tex]4\pi R^{2}[/tex]
2 ( A ABC A ) =[tex]4\pi R^{2}[/tex] - 2 ( [tex]\pi -\alpha[/tex] ) [tex]R^{2}[/tex]- 2 ( [tex]\pi -\beta[/tex])[tex]R^{2}[/tex]-2([tex]\pi -Y[/tex])[tex]R^{2}[/tex]
AABCA = [tex](\alpha +\beta +Y-\pi )R^{2}[/tex]
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find X and Y so that the quadrilateral is a parallelogram 5 y 55 ,11x
A few properties of a parallelogram.
1) Opposite sides are always equal.
2) Opposite angles are always equal.
3) The sum of all the angles is 360.
In part 2, we are given the angles. Therefore, we can apply the 2nd property.
11x = 55
5y = z (lets say the unknown is z).
Now, 11x = 55
x = 55/11
x = 5
Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.
55 + 55 + 5y + z = 360
110 + 5y + z = 360
5y + z = 360 -110
5y + z = 250. (i)
According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get
5y + z = 250
z + z = 250
2z = 250
z = 250/2
z = 125
From the value of z, we can find the value of y using z = 5y
125 = 5y
5y = 125
y = 125/5
y = 25
Hence, x = 5 and y = 25
What is the equation of the line that passes through the point (-3,1) and has a slope of -3?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since line has a slope of -3, equation is y = -3x + c.
Substitute (-3,1) into the equation to find c.
1 = -3(-3) + c
c = -8
Hence, equation of line is y = -3x - 8.
Please help me. Please don’t give me a answer on the internet
Answer
A) f(w) = 80w + 30
B) w represents the number of weeks and f(w) the number of flowers that bloomed
C) 2830 flowers
Step-by-step explanation
A) To find the function f, which represents the number of flowers that bloomed, as a function of w, the number of weeks, we have to evaluate f(s) with s = s(w) = 40w, as follows:
[tex]\begin{gathered} f(s)=2s+30 \\ \text{ Substituting }s=s(w), \\ f(s(w))=2s(w)+30 \\ \text{ Substituting }s(w)=40w \\ f(s(w))=2\cdot40w+30 \\ f(w)=80w+30 \end{gathered}[/tex]B) w represents the number of weeks and f(w) the number of flowers that bloomed, like before.
C) Substituting w = 35 weeks into f(w), we get:
[tex]\begin{gathered} f(w)=80(35)+30 \\ f(w)=2800+30 \\ f(w)=2830\text{ flowers} \end{gathered}[/tex]A number has 3, 4, and 8 as some of its factors. Which number could this be?
The number with 3,4 and 8 as its factors is 24
What is Lowest Common Multiples?The least common multiple(LCM) can be defined as the smallest multiple that two or more numbers have in common
The Lowest Common Multiples of 3 are:3, 6, 9, 12, 15, 18, 21, 24, 27 and 30
The Lowest Common Multiples of 4 are: 4, 8, 12, 26, 20, 24, 28, 32, ...
The Lowest Common Multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
From the Lowest Common Multiples above, 24 is the only number that is common among the multiples of 3,4 and 8
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Ingrid is buying her
grandmother a new
coffeemaker for
her birthday. If the
tax rate is 8.5%, how
much tax will she
pay on a coffee-
maker with a sales
price of $48.90?
085,
The total price of that Ingrid has to pay is $52.90.
How to find percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
Sales price = $48.90
Amount needed to be paid = 8.5% of $48.90 + $48.90
= 4.15 + $48.90
= $52.90
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Select all that appear in the DOMAIN {(-8,-12),(4,-8), (2, -10),(-10.-16) -16 -12 -10 -8 -2-4
We know the domain is the set of all x when is represented by ordered pairs: (x, y)
In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):
Domain = { -8, 4, 2, -10}
Domain = {-10, -8, 2, 4}Estimate 71.47 + 54.357 by first rounding each number to the nearest whole number.
Answer:
125
Step-by-step explanation:
71.47 rounded to the nearest whole number would be 71.
54.357 rounded to the nearest whole number would be 54.
Now, when we add 71 and 54, we get:
71+54=
125
The total would be 125
Think the length of a rectangle is 5 inches longer than its width if the perimeter of the rectangle is 42 inches find it’s area
The area of the rectangle is 104 inches²
Define Area of Rectangle
The area of a rectangle is the space occupied by the rectangle inside its perimeter.
Given that, the perimeter is 42 inches
we know, the formula of perimeter of rectangle = 2(L + W)
so, the first equation will be
2(L + W) = 42
or, 2L + 2W = 42 ----------eq(i)
Next, the length of a rectangle is 5 inches longer than its width, so
L = W + 5
or, L - 5 = W --------------eq(ii)
Now, the eq(i) is
2L + 2W = 42
Put W value from eq(ii),
2L + 2(L- 5) = 42
=> 2L + 2L - 10 = 42
=> 4L - 10 = 42
=> 4L = 52
=> L = 13
We got, L = 13 put this value in any of the equation
I'm putting the value in eq(ii) as it easy for to solve
=> 13 - 5 = W
=> W = 8
If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that
2(13) + 2(8) = 42 (correct)
13 - 5 = 8 (correct)
Now, we got length and width so now just put the values of L and W in area of rectangle formula,
Area of rectangle = Length * width
= 13 * 8
Area of rectangle = 104 inches²
Hence, The area of the rectangle is 104 inches²
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Solve the equation 5x = 85 for x.
Answer: x=17
Step-by-step explanation:
Simplifying
5x = 85
Solving
5x = 85
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '5'.
x = 17
Simplifying
x = 17
The value of x in the equation is 17 .
Given,
5x = 85
Solving
5x = 85
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '5'.
x = 17
Simplifying
x = 17
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Write the sentence as an equation.
312 equals the total of 380 and p
Answer:
P+380=312
Step-by-step explanation:
The total, meaning addtion, and equals meaning equals sign. P+380=312
help please!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Since City a is an equation, you would have to solve it for its population, which is 280000, and since City B is 1,620,000 and City C is double city B, 3,240,000/280000 would get you the population, which is:
11.57, you would round up after that, which would get you the answer:
12
4
Ryan is installing new flooring in his house. Ryan can install 144 square feet of flooring in
3 hours. How much new flooring can Ryan install in 21 hours?
OA. 1,008 square feet
OB. 252 square feet
OC. 3,024 square feet
OD. 3,049 square feet
is there a right triangle in which two side lengths are simple fractions (ratios of integers such as 2/7 or 2/3), and the other side length is an integer?
Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .
In the question ,
we have to find , whether a Right Triangle can be made by two fractions and an integer length .
yes, we can make a Right Triangle with two lengths as fractions and other length as integer .
let us prove it with the help of an example .
Consider the triplet 7 , 24 , 25 .
let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be 1 .
We know that for the Right Triangle
(side1)² + (side2)² = hypotnuse²
(7/25)² + (24/25)² = 1²
49/625 + 576/625 = 1
(49+576) / 625 =1
625/625 = 1
1 = 1
hence ,it is a Right Triangle .
Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .
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Composite Functions 60 POINTS Help please asap
Answer:
(g ∘ f)(6) = 216
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x) = 2x - 6 and g(x)=x³
We want to find the value of (g∘f)(6), where we first find the value of f(6), and then substitute that value into g(x).
SolvingSubstitute 6 as x in f(x)=2x-6.
f(6)=2(6)-6
Multiply
f(6)=12-6
Subtract
f(6)=6
Now substitute 6, which is the value of f(6) as x in g(x) = x³.
g(6)=6³ = 6 * 6 * 6 = 36 * 6 = 216
The value of g(6) is the same as the value of (g ∘ f)(6), as the 6 that we plugged into g(x) is the value of f(6).
Therefore, (g ∘ f)(6) = 216.
Please help ASAP for 20 Points! and a brainliest!
You are running a fuel economy study. You want
to find out which car can travel a greater distance
on 1 gallon of gas.
a. What is the gas mileage, in miles per gallon,
for the blue car?
b. What is the gas mileage, in miles per gallon,
for the silver car?
c. Which car could travel the greater distance
on 1 gallon of gas?
Thank you!
Answer:
a) gas mileage of blue car: 23.667 miles/gallonb) gas mileage of silver car: 34 miles/gallonc) The silver car would travel a greater distance on 1 gallon than the blue car.Step-by-step explanation:
a) gas mileage of blue car:gas mileage = miles covered/gallons used
but:
miles covered = [tex]35\frac{1}{2}[/tex]
= 35.5
gallons used = 1[tex]\frac{1}{2}[/tex]
= 1.5
gas mileage = 35.5/1.5
gas mileage = 23.667 miles/gallon (to 3 decimal places)
b) gas mileage of silver car:gas mileage = miles covered/gallons used
but:
miles covered = [tex]27\frac{1}{5}[/tex]
= 27.2
gallons used = [tex]\frac{4}{5}[/tex]
= 0.8
gas mileage = 27.2/0.8
gas mileage = 34 miles/gallon
c)
gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon
gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon
Hence the silver car would travel a greater distance on 1 gallon than the blue car.
PLS HELP ALL THIS IS DUE TOMORROW AND I HAVE NO TIME ! ( the red box is the stuff I need answers for )
Answer:
The answers are all below.
Step-by-step explanation:
7. Yes
Plug 10 in for t
10-3 ≥ 2
7 ≥ 2
8. No
Plug 1 in for w
6(1) < -2
6 < -2 (Nope)
9. Yes
Plug 5 in for p
5 + 1.6 ≤ 4
6.6 ≤ 4
10. Yes
Plug 0 in for d
[tex]\frac{1}{2}[/tex](0) > -3
0 > -3
11.
1(------------------>k
12.
n<------------------]2.5
13.
In order to try out for one of the parts in a play at the local theater, you must be at most 12 years old. Write an inequality that represents this situation.
x≤12
x<-----------------]12
14. Yes
Plug 2 in for h
3(2) - 7 < 2
Simplify
6 - 7 < 2
-1 < 2
15. No
Plug -12 in for q
-12 + 8 ≥ [tex]\frac{-12}{4}[/tex]
Simplify
-4 ≥ -3 (Nope)
16.
a. Yes
Plug 0 in for x
-2(0) < 10
and
-6 < -2(0)
Simplify
0 < 10
and
-6 < 0
b. No
Plug 4 in for x
-2(4) < 10
and
-6 < -2(4)
Simplify
-8 < 10
-6 < -8 (Nope)
c. -1
Plug -1 in for x
-2(-1) < 10
and
-6 < -2(-1)
Simplify
2 < 10
and
-6 < 2
The set of ordered pairs shown below is a relation that is
a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
Which ordered pairs could be included in the set so that
the relation remains a function of x?
O (-3,0), (-1, 1)
O (-6, 1), (-5, 1)
O (-6, 1), (-1, 1)
O (-2, 2), (-1, 1)
The ordered pairs that could be included in the set so that the relation remains a function of x is (-6, 1), (-1, 1).
What is defined as the relation of function?A function is a relation that states that there must be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the relationship between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.For the given relation that is a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
As, from the definition of the function, the domain of the function will not repeat in the set.
Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.
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Max organized a community toy drive for the holidays. he asked each family to donate a total of 3 gifts. fifteen families participated in the toy drive. write and solve an equation that represents how many gifts were donated.
Answer: g/15 = 3 ; g = 45 gifts.
Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.
g/15 will equal 3.
Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).
This will get you the answer 45.
So, you will get the answer choice A.
Multiply. Write your answer as a fraction in simplest form.
8/15(−2/3)=
Answer:
8/15(-2/3)
we simply multiply them
-8*2/15*3
as we know that+*-=-
-16/30
so simply divided by 2 because it whole decide them 16/2and30/2
-8/15
LMNP is rotated 90 degrees clockwise around the orgin.What are the coordinates of L ?A. L(0,-1)B. L(-1,0)C. L(0,1)D. L(1,0)
Consider that a rotation of 90° clockwise is given by:
T(x,y) => (y,-x)
The coordintates of the point L is L(0,1), the, after the rotation you have:
T(0,1) => (1,0)
answer:
D. L(1,0)
joanne graphed a linear funtion with a slope of -4 passing through 0,-2 nick graphed the function y=-2x - 4
Answer:
Explanation:
The slope-intercept form of the equation of a line can be written as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So if Joanne graphed a linear function with a slope(m) of -4 passing through (0, -2), let's go ahead and determine the y-intercept of the line as shown below;
[tex]\begin{gathered} -2=-4(0)+b \\ -2=b \\ b=-2 \end{gathered}[/tex]Therefore, the equation of line will be y = -4x - 2 as graphed below;
Given Nick's function as y = -2x - 4, combining both graphs, we'll have the below;
The red line is Joanne's line while the blue line is Nick's line.
We can see from the above graph of both lines that Joanne's line intersects the y-axis above Nick's line's
3 ( x -5 ) = 3x - x - 8
Answer:
3(x-5) =3x - x - 8
3x-15 = 2x - 8
3x-2x= -8+15
x=7
Step-by-step explanation:
first 3 will multiply by x and -5,which are in bracet like this
3(x-5)= 3x - x -8
after they would became 3x-15 = 2x (because 3x will be subtracted by x) -8
so it will become like this
3x-15=2x-8
after that 3x will be subtracted by 2x like this 3x-2x and -8 will be add in +15 so it would be
x=7