Answer: The equation of line parallel to given line passing through (8,-7) is:
Step-by-step explanation:
Given line is:
5x+4y=16
first of all, we have to convert the equation of given line in slope-intercept form
Dividing both sides by 4
Slope intercept form is:
The slope of given line is:
Let m1 be the slope of line parallel to given line
"The slopes of two parallel lines are equal"
The equation of line parallel to given line will be:
Putting the value of slope
Putting the point (8,-7) in the equation
Putting the value of b
Hence,
The equation of line parallel to given line passing through (8,-7) is:
a box with a square base and open top must have a volume of 42592 c m 3 . we wish to find the dimensions of the box that minimize the amount of material used. first, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [hint: use the volume formula to express the height of the box in terms of x .] simplify your formula as much as possible. wyzant
a formula for the surface area of the box in terms of only x , the length of one side of the square base is A = x² + 170368 cm³/x
The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.
Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are
A = 2lh + lw + 2wh
Now for a box of square base, l = w = x.
So, A = 2xh + x² + 2xh
A = x² + 4xh
Since V = x²h and V = 42592 cm³,
h = V/x² = 42592/x²
substituting h into A, we have
A = x² + 4xh
A = x² + 4x(42592 cm³/x²)
A = x² + 4 × 42592 cm³/x
A = x² + 170368 cm³/x
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ii) (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle.
Given, (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle, the width is 1 unit shorter.
What is a rectangle?A rectangle is a quadrilateral with the four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with the four equally long sides. Oblong is occasionally used to describe a rectangle that isn't square. Rectanglen is the symbol for a rectangle having the vertices ABCD. ABCD in PNG.
Rectangulus, a combination of rectus (as an adjective, right, proper), and angulus, is the source of the English word rectangle (angle).
A crossed rectangle is a quadrilateral that is formed by the intersection of two diagonals and the two opposite sides of a rectangle (therefore only two sides are parallel). Although opposite angles are equal, it is a specific example of an antiparallelogram in which the angles are not all right angles and equal. There exist so-called rectangles in other geometries, including spherical, elliptic, and hyperbolic ones, with opposite sides of equal length and equal angles that are not right angles.
Many tiling issues use rectangles, like tiling the plane with rectangles or tiling a rectangle with polygons.
By plotting given points in the coordinate plane,
We get rectangle ABCD having vertices,
A(-1,6), B (3,6), C (3,1), D (-1,1)
By distance formula,
Shorter side or width of rectangle,
AB= [tex]\sqrt{ [3-(-1)]^{2}+ (6-6)^{2}} = \sqrt{4^{2}+0 } = 4 units[/tex]
Longer side or length of rectangle,
BC= [tex]\sqrt{(3-3)^{2}+(1-6)^{2}}=\sqrt{5^{2} } = 5 units[/tex]
The difference between length and width,
BC-AB= 5-4= 1units
Hence, width of rectangle is 1 unit less than the length.
active attachment
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The volume of this cylinder is 2,000.18 cubic yards. What is the radius?
Use 3.14 and round your answer to the nearest hundredth.
Answer:56.52
Step-by-step explanation:
3.123=9.369.1/3 is is true or false
20=5x+10y help me please
Answer:x=2(-y+2)
Step-by-step explanation:easy
1/2 + 1/4= write as a fraction and as a decimal.
1/2 + 1/4 =
2/4 + 1/4 = = 3/4 = 0.75
2- x+2/x-3 - x-6/x+3
A=
B=
It can be written in the form is like ax+b/x^2-9
so we only need the A and B.
Please reply to this ASAP
Step-by-step explanation:
so, if I understand your text correctly, we need to bring
2 - (x+2)/(x-3) - (x-6)/(x+3)
into a form
(ax + b)/(x² - 9)
what we notice immediately is
(x+3)(x-3) = x² - 9
that makes sense, as we want to transform all terms into fractions with the same denominator.
and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.
so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.
2 :
multiply by (x²-9)/(x²-9)
2(x²-9)/(x²-9) = (2x²-18)/(x²-9)
(x+2)/(x-3) :
multiply by (x+3)/(x+3)
(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =
= (x²+5x+6)/(x²-9)
(x-6)/(x+3) :
multiply by (x-3)/(x-3)
(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =
= (x²-9x+18)/(x²-9)
for the whole expression we get then
(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =
= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =
= ( 0 + 4x - 42 )/(x²-9)
a = 4
b = -42
Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 10 minutes, clock B every 15 minutes, and clock C every 20 minutes.The three clocks sound together every _minutes.
Answer:
Given that,
Calvin has three alarm clocks which sound at different intervals.
Clock A goes off every 10 minutes
Clock B every 15 minutes
Clock C every 20 minutes.
To find: the three clocks sound together every _minutes
The three clock sounds together for every least common minutes of the 3 clocks (A,B,C)
To find LCM of 10,15,20.
we get,
LCM of 10,15,20 is 60
Therefore we get that,
The three clock sounds together for every 60 minutes.
Answer is:
The three clock sounds together for every 60 minutes.
63 = 3x + 15 solve for x simplify your answer as much as possible
Answer:
The answer is x=16
Step-by-step explanation:
63=3x+15
63-15=3x Put like terms together and subtract
48=3x
x=48/3 isolate the variable
x=16
Find the HCF of 200 and 240
Answer:
its 40
Step-by-step explanation:
200 and 240 have an HCF of 40.
Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF).
So, let's determine factors of 200
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200 are all factors of 200.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240 they are all factors of 240.
now, we will select the highest common factors of 200 and 240.
the highest common factors of 200 and 240 is 40.
Hence, the HCF of 200 and 240 is 40.
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At one store Roberto bought 10 packages of batteries. Each package had 24 batteries. At another store, he bought 10 packages of batteries, but each
What is the domain and range of this function?
Answer:
Domain(X-value): {-5,-4,-3,-2,-1,0,1,2,3,4,5}
Range (Y-value): {-2,-1,0,1,2}
Step-by-step explanation:
The domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
what is the slope of the line?
Answer:
3
Step-by-step explanation:
Use the slope formula
y2-y1/x2-x1
A giant tortoise can travel 0.17 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1.1 miles?
It would take the tortoise
hours.
(Type an integer or decimal rounded to one decimal place as needed.)
...
Answer:
1.07
friend me? anyone
Answer:
6.5 hours
Step-by-step explanation:
distance = rate times time
1.1 = .17t t stands for time Divide both side by .17
my calculator shows 6.47058823527 We need to round to one decimal place
time = 6.5 hours or 6 1/2 hours
PLEASE HELP!!!!!! It’s algebra
Answer:
Y=3X-4
Step-by-step explanation:
1. Find the slope using matching (x,y) values. (5,11) and (2,2) for example. (Change in Y)/(Change in X) [tex]\frac{11-2}{5-2}[/tex] = [tex]\frac{9}{3}[/tex] = 3
2. Use the point-slope form to find the equation. Pick a matching (x,y) value. (2,2) for example. and plug it in for Y₁ and X₁ in the equation Y-Y₁=M(X-X₁)
with M as the slope. Y-2=3(X-2).
3. Simplify
Y-2=3X-6
Y=3X-4
Given the function f(x) = 8x + 7, find each of the following. f(1), f(-9), f(0)
IN THE PLACE OF X YOU INSERT THE NUMBER GIVEN AS F(X<<<) AND SIMPLIFY .
[tex]f(1) = 8(1) + 7 \\ f(1) = 8+ 7 \\ f(1) = 15[/tex]
[tex]f( - 9) = 8( - 9) + 7 \\ f( - 9) = - 72 + 7 \\ f( - 9) = - 65[/tex]
[tex]f(0) = 8(0) + 7 \\ f(0) = 0 + 7 \\ f(0) = 7[/tex]
GOODLUCK !!
help me if you answer your smartest person on the world
The value that makes the inequality true for the first inequality is x < 4 and x >4 for the second inequality
Find the unknown value in the InequalityTo solve this problem, we have to solve each of the inequality and find the missing values that holds them true.
For the first inequality,
Let x represent the unknown value
[tex]8 * \frac{x}{4} < 8\\\frac{8x}{4} < 8\\x < 4[/tex]
For the second inequality;
Let x represents the unknown value.
[tex]8 * \frac{x}{4} > 8\\ x > 4[/tex]
In the first inequality, x < 4 and the second inequality, x > 4.
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1 (a). Determine if each of the following is true or false. Explain your reasoning.i. There are 12 cubic inches in a cubic foot.ii. There are 144 squares inches in a square foot. iii. If I triple the length and width of a rectangle, then the area increase by a factor of 3.iv. If I triple the length and width and height of a cube, then the volume increases by a factor of 27.
1 cubic foot is equivalent to 1728 cubic inches, this is why the statement is false.
(ii)1 square foot is equivalent to 144 square inches, so the second statement is also false.
(iii)The third statement is also false because if we triple both dimensions of a rectangle, the area will be increased by a factor of 9.
[tex]A=3w\times3l=9wl[/tex](iv)This statement is true because when we multiply 3x3x3 we actually get a factor of 27
[tex]V=3w\times3l\times3h=27\text{wlh}[/tex]It's possible to build a triangle with side lengths of 3, 3, and 9.
O A. True
O B. False
it is possible to make a triangle with the sides 3, 3 and 9
true
Sarah invests £400 at 3%
interest for 6 years
Circle the correct calculation to
work out how much she has now.
Answer: £900
Step-by-step explanation:
Select the correct answer. Consider the function f(x) = 3x and the function g, which is shown below. How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the left. C. The graph of g is the graph of f shifted 2 units to the right. D. The graph of g is the graph of f shifted 2 units down.
The graph of g will differ from the graph of f as the graph of g is the graph of f shifted 2 units to the right. Option C
This is further explained below.
What is a function?A relation between a collection of inputs and one output for each of those inputs is the definition of a function.
A function is a connection between inputs in which each input is associated with precisely one output.
To put it another way, a function is a relationship between inputs. Each function has both a domain and a codomain or range that it operates inside.
Generally, The progression towards
g(x) = f(x -h) +k
depicts a translation with k units added on top and h units added to the right.
Since you have h equal to 0 and k equal to -2, this means that the graph is moved 0 units to the right and 2 units in the opposite direction of up.
The graph of g may be found by shifting f's graph down by two units.
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
model2 is times and model on is 432
48 < 8w solve the inequality for w and simplify your answer as much as possible
Answer:
w > 6
Step-by-step explanation:
48 < 8w
48 ÷ 8 < w
w > 6
I switched the sign if you dont want that you can write 6 < w
Write an equation that represents the line.
Use exact
numbers.
Answer:
y = -1/3x -3.5
Step-by-step explanation:
line interesects y axis at -3.5, distance between dots is down 1 and forward 3
Hi I have question on solving algebraic fractions. How would I find the LCD for this?
(x/x+1)+(x-1/4)=(11/12)
I tried multiplying the denominator by the opposites (x+1 and 4) to make them the same denominator and then add them and cross multiply, however, I never got the right answer
The value of x is either 2 or -7/3.
Given expression:-
(x/x+1)+((x-1)/4)=(11/12)
We have to find the value of x.
The LCM of (x + 1) and 4 is 4(x - 1).
We can write,
[4x + (x + 1)(x - 1)]/4(x + 1) = 11/12
[tex]\frac{4x+x^2-1}{4(x+1)}=\frac{11}{12}[/tex]
We can multiply 4 to the given equation, and get,
[tex]\frac{4x+x^2-1}{(x+1)}=\frac{11}{3}[/tex]
By cross multiplying, we can write,
[tex]12(4x+x^2-1)=11(4(x+1))[/tex]
12x + [tex]3x^2[/tex] -3 = 11x + 11
[tex]3x^2[/tex] + 12x - 11x -3-11 = 0
[tex]3x^2[/tex] + x-14 = 0
Using the middle-term split theorem, we can write,
[tex]3x^2[/tex] + 7x - 6x -14 = 0
x(3x + 7) - 2(3x + 7) = 0
(3x + 7)(x - 2) = 0
x = -7/3, 2.
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Which of the following correctly sets up the synthetic division for x^3 − 4x^2 − 3 divided by x + 1?
let's recall that for a synthetic division, or even a long division as well, the dividend and divisor must be in descending order from left-to-right. Check the picture below.
(30p algebra 2) is this an observational study or an experiment? and why
The sales director is conducting a experiment study.
There are different types of studies related to researches. The researchers may conduct simply, a survey, more thoroughly, an observational study or an experiment to get more details of things of their research.
An observational study is based on observations and analysis of different comparable situations. A survey is actually a method to study about things directly through personally involving into the situations.
Experiments are mostly used in situations which asks for a solution to certain issue. An experiment is implementing new measures first and then check if it works and get on conclusions about it. Such experiments leads to new inventions.
So here, the sales director conducted an additional training program for the sales representatives to increase the sales in Midwest and Northeast regions.
Then he studied the effectiveness of this implementation by comparing the sales from trained and non-trained representatives.
Thus the sales director conducted an experiment based study here.
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A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in. If the container holds 1096 cubic feet of shipped goods, what percent is empty?
As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.
Volume of a rectangular prism
The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.
The formula for the volume of rectangle prism is
V = l x w x h
where
l represents the length
w represents the width
h represents the height
Given,
A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.
Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty
According to the given question,
Let us consider the length is 30ft, Width is 8ft and Height is 7ft.
Here the value 3ft refers the depth.
That one is also multiplied with the volume.
Therefore, the volume of the container is
=> 8 x 7 x 30
=> 1680
Therefore, the volume of the container is 1680 cubic feet.
So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,
=> 1680 - 1096
=> 584
The percent of empty space is,
=> x% of 1680 = 584
=> x% = 584/1680
=> x% = 0.3476
=> x = 34.76
Therefore, 34.76% of rectangular prism container is empty.
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1.if the m∠7 = 115° , find the measure of ∠2
Show your work
Answer: The measure of is 115°.
Step-by-step explanation:
Now, assuming those angles are supplementary, then
m<7 + m<2 + 180
Because, supplementary angles sum 180\°, due to their position on a straight angle.
We know by given that m<7 = 115 , replacing this value, we have
115 + m<2 + 180
m<2 = 180 - 115
m<2 + 65
Step-by-step explanation:
Which of the following is not a step in the help seeking process