Step-by-step explanation:
it is a rectangle.
the area is a rectangle is
length × width
in our case
length × width = 55 ft²
length = 3×width + 4
we use that in the first equation :
(3×width + 4)×width = 55
3×width² + 4×width - 55 = 0
the general solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
so,
width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =
= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =
= (-4 ± 26))/6
width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft
width2 = (-4 - 26)/6 = -30/6 = -5
negative numbers for the size of a physical object don't make sense, so
11/3 = 3 2/3 ft is our solution.
length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft
so,
the length = 15 ft
the width = 3 2/3 ft (or 11/3 ft)
WILL GIVE 20 POINTS.
Match each picture to its name.
Answer:
1. PQ
2. PQ + qr= pr
3. the arrow going both ways with p q
4. point p
5. the arrowing going one way with p q
Step-by-step explanation:
I took the test
Una hoja de papel rectangular tiene un área de 84 pulgadas,el ancho del papel es 5 pulgadas menos que el largo¿cual es el ancho,en pulgadas de la hoja de papel ?
Answer: I think the width is 7.
Step by step explanation:
So let's say the length is 12. This means I need to subtract 5 from it, since the width is 5 inches less than the length. Now that we know this, that means the width is 7, which is the area.
I hope this helps.
What is the measure of m?
Please help I dont understand!!!!!
Answer: This is a linear pair of angles because they are two adjacent angles that have a common side and whose other sides point in opposite directions.
Please help and provide an explanation for why the answer is f(x) = 3/2x + 7
What is the equation of the line that passes through Point (-4, 1) and has a Slope of 3/2.
Answer:
see below
Step-by-step explanation:
the point-slope equation is
y-1 = 3/2 (x+4)
Answer:
[tex]y=\frac{3}{2}x+7[/tex]
Step-by-step explanation:
To write the equation of a line, two information are needed.
Slope (also known as gradient)A pair of coordinates (or a point) on the lineThe slope can be calculated using the gradient formula as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.
In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).
y= mx +c
Given that slope= [tex]\frac{3}{2}[/tex], m= [tex]\frac{3}{2}[/tex].
Substitute the value of m:
[tex]y=\frac{3}{2}x+c[/tex]
Next, find the value of c by substituting a pair of coordinates.
When x= -4, y= 1,
[tex]1=\frac{3}{2} (-4)+c[/tex]
1= -6 +c
Add 6 to both sides:
c= 1 +6
c= 7
Substituting the value of c:
[tex]\bf{y=\frac{3}{2}x +7 }[/tex]
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HELP PLEASE!
f(x)= ³ √x+8. Find the inverse of f(x).
Answer: (D)
the answer would be D
Step-by-step explanation:
what is the slope of the line?
Answer:
slope = - 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
Answer:
-1, equation is y=-x+2
Step-by-step explanation:
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward? A. K = (-2,0), L' = (1,0), M = (1,-3), N = (-2,-3) B. K = (-2,-2), L' = (1,-2), M = (1,-5), N = (-2,-5) C. K = (-0,0), L' = (3,0), M = (3,-1), N = (0,-1) D. K = (-2,2), L' = (1,2), M = (1,-1), N = (-2,-1)
K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)
Firstly, we needt to identify the coordinates of the vertices of the quadilateral
Afterwards, we then perform the translation
The translation simply means we add 2 to the x-value and add 4 to the y-value
So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)
Let us identify the vertices;
K'
K (-4,-2)
L (-1,-2)
M (-1,-5)
N (-4,-5)
After translation, we have;
K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)
Challenge An arts academy requires there to be 4 teachers for every 92 students and 3 tutors for every 24 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?
Answer:2
Step-by-step explanation:25 students per a teacher and 33 students per a tutor.if the academy has 77student they need 2 tutors
Tracy is cutting out a rectangular board to construct a bookshelf.
The board is to have a perimeter of 38 inches, and its length is to be 5 inches shorter than double the width.
Let x be the width of the board.
State the expression for the length of the board in terms of x.
Answer:
28 inch
Step-by-step explanation:
half of 38 would be 19, and take away 5 from both 19. Equally each width ( top and bottom ) 14 inch and each lenght ( Left and right ) 5 inch. so x representing width would be 14 + 14= 28 inch.
14
5 5
14
I WILL GIVE BRAINLIEST!!!
Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.
+ Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?
+ Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?
+ What measures would you use in each case?
The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
What are symmetrical and asymmetrical data?A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean.
The standard deviation indicates; how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency, then the standard deviation should be used as the spread.
If the data is symmetrical, then the mean is the measure of central tendency; and the standard deviation is the best spread to use.
If the data is asymmetrical, the median is the best measure of central tendency; and the inter-quarterly range is the best spread to use.
The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
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The length of each side of triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
Which list shows the angles of triangle LMN in order from least measure to greatest measure?
The angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L which is determined by the triangle inequality theorem.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
The length of each side of the given triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
According to the triangle inequality theorem, in a triangle, the largest angle is the one opposite to the longest side of the triangle.
Therefore, in triangle LMN, we have the greatest angle as angle ∠ L
And the smallest angle is ∠ N
Arrange the angles in ascending order,
angle ∠ N < angle ∠ M < angle ∠ L
Thus, the angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L.
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A painter
mixes 2%, pints
of yellow paint with
4 pints of red paint to make a certain shade of
orange paint. How many pints of yellow paint
should be mixed with 10 pints of red paint
to
make
this shade of orange?
In linear equation, 0.005 pints are pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange.
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations. As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Given,
A painter mixes 2%, pints of yellow paint with 4 pints of red paint
So to make this shade of orange ⇒
10 red pints × (2 % yellow pints/ 4 red pints) ≈ 0.005 pints
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24 yd
15 yd
35 yd
the volume
Answer: 9633.4 cubic meters
I only assumed the shape and length, height, width, etc. so this is my best guess. Please provide with a three dimensional shape of the object being calculated and specify which measurements are the length, height, width, depth, or circumfrence. I will answer it right away :)
Answer:
12600 yd^3
Step-by-step explanation:
The equation to finding the volume of 3 dimensional shapes only including cubes, and rectangles.
L * W * H = V
Which means Length multiplied by width, multiplied by height.
So in this instance:
35 * 24 = 840 * 15 = 12600.
Hope this answers your questions.
If so please make brainliest.
Also if it does feel free to ask me any other questions needed.
Question 3 (1 point)
(03.06 LC)
Determine if the sequence is arithmetic or geometric, and find the common difference or ratio
Arithmetic, Common Difference = -9
The Correct option is (b).
What is Common Difference?
The common difference of an arithmetic sequence is the difference between any of its terms and its previous term. An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same amount. The number added (or subtracted) at each stage of an arithmetic sequence is called the "common difference", because if we subtract (that is if you find the difference of) successive terms, you'll always get this common value. Most often, "d" is used to denote the common difference.
Given,
x = 1 2 3 4
f(x)= 81 72 63 54
Now, According to the question:
2nd term - 1st term = 72 - 81 = -9
3rd term - 2nd term = 63 - 72 = -9
4th term - 3rd term = 54 - 63 = -9
Hence, Arithmetic, Common Difference = -9
The Correct option is (b).
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Please need asappp Graphs of inverse functions
50 POINTS!
A line goes through the points (3, -4) and (-1, 8). Write the equation of the line in point-slope form. Show your work for full credit. (Show the steps for how you went from the two points, above, to having the equation in point-slope form. All calculations must be written down.)
can someone show how they do this instead of just only giving the answer.
Answer:
y= -3x + 5
Step-by-step explanation:
m= (y2-y1)/(x2-x1)
m= [8-(-4)]/(-1-3)
m=12/-4
= -3
y= mx + b
-4=(-3)(3) + b
-4=9+b
b=5
therefore, y= -3x+5
A gym membership costs $25 to join and $14 each month. Write and use an algebraic
expression to find the cost of the gym membership for 6 months.p
The algebraic expression to find the cost of the gym membership for 6 months is given by 25+6×14.
What is algebraic expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c. Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions.
Given, the cost of joining membership = $25
The cost of each month = $14
Cost of 6 months = 6 multiplied by 14
Cost of gym membership for 6 months = 25+6×14
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A local building code requires that all factories must be surrounded by a lawn. The width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. What must be the width of a lawn surrounding a rectangular that measures 120 m by 80 m?
PLEASE HELP
Answer:
20 m
Step-by-step explanation:
You want to know the uniform width of a lawn around a 120 m by 80 m building such that the area of the lawn is equal to the area of the building.
SetupLet x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:
(120 +2x)(80 +2x) = 2(120·80)
SolutionDividing by 4 gives a slightly simpler equation.
(60 +x)(40 +x) = 60(80)
2400 +100x +x^2 = 4800 . . . . eliminate parentheses
x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form
(x +120)(x -20) = 0 . . . . . . . factor
Values of x that make the factors zero are ...
x = -120, x = 20
Only the positive solution makes any sense in this context.
The width of the lawn must be 20 m.
__
Additional comment
The total area of the plot is ...
total area = (building area) + (lawn area)
When the lawn area is equal to the building area, then we have ...
total area = (building area) + (building area)
total area = 2·(building area)
This is the relation we used in the solution above.
tweleve is no less than the sum of a number n and 3
Robert cuts a string that is 4 feet long into pieces that are each foot long. a. Complete the model to show 4 ÷2/6
24 pieces make up the solution to this puzzle.
I assume the query is how many pieces does she receive.
I'll respond to it. Leave a note if it is incorrect.
6 pieces will be produced from 1 foot, each measuring 1/6 of a foot (12/6 = 2 inches).
4 feet will provide 24 pieces (4 * 6).
24 pieces make up the solution to this puzzle.
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Write an equation of the parabola. Justify your answer.
Check the picture below.
so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so
[tex]\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill[/tex]
How do
you
create equations and use them to solve
problems?
Answer:
define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.
Need help with this
Answer:
<XMN = 122°
Step-by-step explanation:
An angle around a point is 360°
If LMN = 145° then the rest would be 360 - 145
360 - 145 = 215
4x + 5 + 6x - 10 = 215
Simplify = 10x - 5 = 215
work out = 215 + 5 = 220 ÷ 10 = 22
x = 22
XMN = 6x - 10
6 × 22 = 132
132 - 10 = 122
XMN = 122
place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
Absolute Value Calculator: Heron's Calculator
Coterminal Angle Calculator: Graphing Functi...
Step-by-step explanation:
Answer:
1. -[tex]\sqrt{13}[/tex] = -3.605...
2. -18/5 = -3.6
3. -[tex]\sqrt{12.25}[/tex] = -3.5
4. -|3.4| = -3.4
5. |-3.6| = 3.6
what is the slope of the line ?
Answer:
Step-by-step explanation:
5/2
Answer: f(x)= 2x-3
Step-by-step explanation: The formula for slope is y=mx+b, where m is equal to the slope of the line and b is equal to the y-intercept. We can find the slope by looking at the line OR solving algebraically using the following calculations:
(y2-y1)/(x2-x1)
Pick 2 points on the line and plug in.
(x1,y1)-->(2,1) and (x2,y2)-->(3,3)
(3-1)/(3-2)=2/1=2
So, the slope of the line is 2. m=2.
To find the y-intercept, we can solve algebraically or look at the graph.
y=2x+b
Plug in a point from the graph to find b, the y-intercept.
3=2(3)+b
3=6+b
-3=b
So, the y-intercept is b.
Now, we plug our values into the slope intercept equation, y=mx+b
y=2x-3
Again, you look look at the graph and see where x=0 is to find the y intercept. To find the slope you can use rise/run and count to see that to get from one point on the graph to the next, you count up 2 (rise 2) and to the right 1 (run 1) which gives you 2/1. 2/1 is equal to 2, giving you the slope of 2.
Hope this helped :))
[tex]6x^{2} -7=9x+8x^{2}[/tex]
How do you write 2.467 x 10^10 in standard form?????? helpppp
Answer: 24670000000
Step-by-step explanation:
1) First, the scientific form can help you learn that each 10 in a power will increase the number its multiplying by 10.
Since we know that when multiplying a decimal number by 10, it would move the decimal once to the right. We can apply this to the equation by moving the decimal to the right 10 times.
2) Answer
12345678910 <= This indicates the decimal moving one place
24670000000.00
There are a total of 235 books in the library. On Monday, 113 books were checked out. On Tuesday, fifty-six books were checked back in. How many books are there in the library on Wednesday morning?
Answer:
178
Step-by-step explanation:
235-113=122
122+56=178
Answer:
178 books
Step-by-step explanation:
235 minus 113 books that werr checked out and plus 56 books that came back in total it's 178, if nobody stole anything :)
Find the equation of the line with slope −35 and y-intercept (0,−3).
Answer:
y = -35x -3
Step-by-step explanation:
We can use the formula y = mx + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y-intercept
From these, they have already given the slope of the line.
m ⇒ -35
And now we have to find the c ( y-intercept ) of the line using the given coordinate,
( 0 , -3 ) ⇒ ( x , y )
So, to find the y-intercept you have to replace x, y & m with 0, -3 & -35 respectively, and solve for c.
Let us solve it now.
y = m x + c
-3 = -35 × 0 + c
-3 = 0 + c
-3 = c
And now we can write the equation of the line like this.
y = m x + c
y = -35x -3
Answer:
Equation of line is given as y =mx + c, where m is the slope and c is the y-intercept.
Since slope is -35, equation of line is y = -35x + c.
Substitute (0,-3) into equation to find c.
-3 = -35(0) + c
c = -3
Hence, equation is y = -35x - 3.