The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
What is the perimeter of a rectangle?The perimeter of a rectangle is P = 2(L + W) where
L = length of the rectangle and W = width of the rectangleGiven that P = 16 m,
P = 2(L + W)
16 = 2(L + W)
16/2 = L + W
L + W = 8
So, W = 8 - L
What is the area of the rectangle?
The area of the rectangle, A = LW where
L = length of the rectangle and W = width of the rectangleSince W = 8 - L, substituting W into the equation for A, we have
A = LW
A = L(8 - L)
A = 8L - L²
So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
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Check
The tiles on the left contain functions written using function r
g(f) = 2f
f(h) = h - 7
h(g) = -4+g
The input values for each of the given functions are as outlined below.
How to identify input values of functions?Input values are also defined as domain which is the set of input values for which the function is defined. Thus, let us look at each of the given functions;
1) g(f) = 2f. The input value here is f
2) f(h) = h - 7. The input value here is h.
3) h(g) = -4 + g. The input value here is g
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Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
| x - 57 | = 3
Step-by-step explanation:
Since the house is on the 57th block, Jamaal must stop walking on the 54th block or the 60th block.
Examine the system of equations.
y=2x-3
y=-3
Which statement about the system of linear equations
is true?
O The lines have different slopes.
O There is no solution to the system.
O The lines have the same slope, but different y-
intercepts.
O The solution is (-3, -9).
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.
What is the System of equations?Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.
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Please help! Both questions are in the photo. Thank you so much!
The probability that a 4 shows up is 0.20 and the proportion of 3's rolled is 0.467
The probability that a 4 shows upFrom the list of numbers, we have:
Sides = 5 i.e. numbers 1 to 5n(4) = 1 i.e. sides labelled 4The probability that a 4 shows up is then calculated as:
P = n(4)/Sides
This gives
P = 1/5
Evaluate
P = 0.2
The proportion of 3's rolledIn the list of numbers, we have:
Total = 15Number of 3's = 7The proportion of 3's rolled is then calculated as:
P = Number of 3's/Total
This gives
P = 7/15
Evaluate
P = 0.467
Hence, the proportion of 3's rolled is 0.467
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Really confused about this one anyone mind to help 100 points
Answer:
9(x - 5)
Step-by-step explanation:
Just write the equation according to the sentence. It's THAT SIMPLE.
Answer:
d
Step-by-step explanation:
If 343* = 494-x, what is the value of x?
5/8
8/5
2
8
Answer: [tex]\frac{8}{5}[/tex]
Step-by-step explanation:
343 is equal to 7 to the power of 3.
49 is equal to 7 to the power of 2.
You can then make the equation:
[tex](7^{3})^x = (7^2)^{4-x}[/tex]
The powers law means if something is to the power of something, it is multiplied.
So, we can remove the 7 and make the equation:
3x = 2(4-x)
3x = 8 - 2x
5x = 8
x = [tex]\frac{8}{5}[/tex]
You can verify this by plugging it in,
[tex]343^{8/5} = 11388.6066[/tex]
[tex]49^{4-(8/5)} = 11388.6066[/tex]
Chris wants to create a rectangular rose garden in a yard. he has 40 meters of fencing to go around the garden and he has to use it all. pick two ways he could construct the garden
Answer:
4x10 8x5
Step-by-step explanation:
the map is drawn to the scale of 1:4000 and the distance in between two places on the map is 4 cm what is the actual distance between those two places
Answer:
4 × 4000 = 16000cm or 160 meters
Find the inequality represented by the graph:
The equation of linear system in the form of inequality will be x + y ≥ 2 or y ≥ 2 – x.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The graph is given below.
The graph is a linear equation.
Then the equation of linear system in the form of inequality will be
The two point are given as (0, 2) and (1, 1). Then the equation of linear system will be
y – 2 ≥ [(2 – 1) / (0 – 1)] (x – 0)
y – 2 ≥ – x
x + y ≥ 2
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S is a subset within a universal set, u. if s = {x, y, 4, 9, ?}, which could describe u?
The set that best describes the universal set U is; U = {keys on a keyboard }
How to determine mathematical sets?We are told that S is a subset within a universal set U.
Now, from the subset S = (x, y, 4, 9, ?), we will need to find among the given sets the one that describes the best set.
From the subset, we see that the Universal set will be keys on a key board due to the fact that the keys on a keyboard will have alphabets, numbers and punctuation marks mentioned in the set.
Therefore U = {keys on a keyboard } will be the correct answer.
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Sienna is solving the quadratic equation by completing the square.
3x2 + 9x – 4 = 0
3x2 + 9x = 4
A(x2 + 3x) = 4
Answer:
See below
Step-by-step explanation:
3 (x^2 + 3x) = 4
3 ( x + 3/2)^2 = 4 + 27/4
Find the nth term of the sequence -2,6,14,22...
Answer:
[tex]\boxed{a_{n} = 2(4n - 5)}[/tex]
Step-by-step explanation:
Given :
⇒ a = -2
⇒ d = 14 - 6 = 8
Formula for nth term :
[tex]\boxed {a_{n} = a + (n-1)d}[/tex]
Solving :
⇒ aₙ = -2 + (n - 1)(8)
⇒ aₙ = -2 + 8n - 8
⇒ aₙ = 8n - 10
⇒ aₙ = 2(4n - 5)
A sector of a circle of radius 14cm containing
an angle 60° is folded to forma cone
Calculate the radius of the base of the circle
}
answer is 2 ⅓
Explanation
Length of arc = circumference of the base of the
cone
is β/360 x 2πR=2πr
make r the subject of formula
r =βR/360
r=60 x 14/360
r=2⅓cm
please mark as brainliest if i am right
Which points can be connected to draw a line of symmetry through this diamond?
Drag and drop an answer to the box to complete the statement. please answer asap!
The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
What is a line of symmetry?It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.
We have given a figure in the picture.
The figure is a quadrilateral(a kite)
As we know, lines of symmetry make exactly two halves with similar shapes and sizes.
IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.
Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
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Answer:
point C
Here is a step-by-step explanation of the statement:
1. Draw a point B and a point C on a piece of paper or a computer screen.
2. Draw a straight line that goes through both point B and point C.
3. Fold the paper along the line you just drew, so that the line is the fold line.
4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.
5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.
6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.
On the first journey, a cyclist travelled 1 1/2 km in x minutes.
On the second journey, the same cyclist travelled for y hours at the same average speed as on his first journey. Express, in terms of x and
total distance travelled in km for both journeys.
The equation D = 1.5x/y represents the total distance traveled in km in terms of x.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
On the first journey, a cyclist traveled 1 1/2 km in x minutes.
As we know,
Speed = distance/time
Distance = 1 1/2 = 3/2 km = 1.5 km
time = x
Speed = 1.5/x
On the second journey, the same cyclist traveled for y hours at the same average speed as on his first journey.
Distance = speed×time
Distannce(D) = (1.5/x)(y)
D = 1.5x/y
Thus, the equation D = 1.5x/y represents the total distance traveled in km in terms of x.
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Add the equations. Two-Variable Systems: Elimination (question is linked with the screenshot below)
Answer:
2y = 24Given -
5x - y = (-1)
-5x + 3y = 25
To find - Summation of this
5x - y = (-1)
+ (-5x) + 3y = 25
adding both the equation we get,
5x +(-5x) - y + 3y = (-1) + 25
0 + 2y = 24
2y = 24.
Answer:
2y = 24
Step-by-step explanation:
5x – y = -1
+ - 5x + 3y = 25
2y = 24
Hence, A. 2y = 24 is the right answer.
Find the value of x to the nearest tenth.
Answer: 44
What is [tex]S\frac{O}{H} C\frac{A}{H}T\frac{O}{A}[/tex] ?
[tex]S\frac{O}{H} C\frac{A}{H}T\frac{O}{A}[/tex] is an abbreviation for how to making finding the angle measurements of right triangles easier!
[tex]S\frac{O}{H}[/tex] is also known as sine. Using the opposite side length of the triangle [O] and the hypothenuse [H], can help you find the missing angle measurement of a triangle.
C is cosine and T is tangentA is adjacent side lengthAs stated before, this abbreviation is typically used to help find missing angles, but in this question, you already have your angle measurements. You are missing a side length.
Using the angle 54° as a reference point, the side length 32 is adjacent to it, so you have [A]. With A, you can use either Cosine or Tangent.
The missing side is opposite the 54° angle, so you have [O]. The only ratio with O and A belongs to Tangent, so we will use this ratio to solve for the missing side.
Write this equation down and use your calculator to solve for x:
*make sure your calculator is in degrees*
tan (54°) = [tex]\frac{x}{32}[/tex]
32 × tan (54°) = x
44.04 ≈ 44 =x
Abigail works as a salesperson at an electronics store and sells phone: accessories. Abigail earns a $12 commission for every phone she sells commission for every accessory she sells. On a given day, Abigail mad $258 in commission and sold 6 more accessories than phones. Write a equations that could be used to determine the number of phones sold a number of accessories sold Define the variables that you use to write thigail works as a salesperson at an electronics store and sells phones and phone cessories. Abigail earns a $12 commission for every phone she sells and a $3 mmission for every accessory she sells. On a given day, Abigail made a total of 258 in commission and sold 6 more accessories than phones. Write a system of quations that could be used to determine the number of phones sold and the umber of accessories sol Define the variables that you use to write the system.
The system of equations are:
$12p + $3a = $258
a - p = 6
Where:
a = phone accessories p = phoneWhat are the system of equations?Two linear equations would be derived from the question. The linear equations would be a function of the phones and accessories sold. These equations are known as simultaneous equations and they would have to be solved together in order to determine the required values.
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2. Given that 5-6 ÷ 5p = 125º, find the value of 1/2p
Answer: -50
Step-by-step explanation:
5 - 6 / 5p = 125 degrees
1/2p = ?
First, subtract 5 from both sides, that way, the 5 on the left side will cancel out.
-6/5p = 125-5 degrees
-6/5p = 120 degrees
now, multiply 5p on both sides.
-6 = 120 * 5p degrees
-6 = 600p degrees
divide 600 on both sides
-6/600 = p degrees
-0.01 = p degrees
p = -0.01
1/2p = 1 / -0.02 = -50
Hope I helped!
(15-10)-(14+12+ (8+5)
Answer:
-34
Step-by-step explanation:
Remove all brackets by multiplying the existing math signs then take it from there
(15-10)-(14+12+ (8+5)
5 - (14 + 12 + (8 + 5)
5 - (14 + 12 + 13)
5 - 39
-34
Are the equations 5x=3-x and 5x=-x+3 equivalent?
Answer:
yes
Step-by-step explanation:
The commutative property of addition applies to let you swap the order of the summands.
__
Here is how the commutative property can be applied.
5x = 3 -x . . . . . given
5x = (3) +(-x) . . . . shown as a sum
5x = (-x) +(3) . . . . order swapped using commutative property of addition
5x = -x +3 . . . . . . equivalent equation
What is the area of triangle ABC?
Answer:
3 square units
Step-by-step explanation:
Use BC as the base = 2
Use y -axis to C (or B) as the height = 3
Area of triangle = 1/2 * base * height = 1/2 * 2 * 3 = 3 units^2
Please help me with this question
Answer:
7
Step-by-step explanation:
OK, so we're looking for the index in the fourth column and the fourth row
which is gonna be 7 if you count correctly
Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.
The graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete:
The complete question is:
Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?
Please refer to the attached picture.
The given line:
y = 4x - 2
The slope of the line m = 4
The slope of the line which is perpendicular to the above line:
M = -1/4 = -0.25
The graph second has a slope of -0.25
[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]
y - 2 = -0.25x - 1
y = -0.25x + 1
Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
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Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
a) y=6x
The above function is a linear function
b) y=3/x
or
xy = 3
The above function shows an inverse variation.
c) y=1/3x
or
y = (1/3)x
The above function is a linear function
d) y= -.07x
The above function is a linear function
e) y= 2/x+4
or
y = (2+4x)/x
xy = 2 + 4x
The above function shows an inverse variation.
f) xy=-3
The above function shows an inverse variation.
Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
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y=5+3x for x
Show work
Answer:
[tex]x = \frac{y - 5}{3}[/tex]
Step-by-step explanation:
Hello!
To solve for x, we have to first isolate the variable.
Solve for x[tex]y = 5 + 3x[/tex][tex]y - 5 = 3x[/tex][tex]y - 5 = 3(x)[/tex][tex]\frac{y - 5}{3} = x[/tex]The value of x is [tex]\frac{y - 5}{3}[/tex].
I read 1/3 of a book in an hour.
How much more of the book will I read in 2 1/5 hours
Answer:
Step-by-step explanation:
To find the number of pages of the book in the given hour:
To find the number of pages in 2 1/5 hours, multiply the number of pages read in 1 hour by 2 1/5 hours.
[tex]\sf \text{ Number of pages read in 2 $\dfrac{1}{5}$ hours = $\dfrac{1}{3}*2\dfrac{1}{5}$ }[/tex]
[tex]\sf = \dfrac{1}{3}*\dfrac{11}{5}\\\\=\dfrac{11}{15}[/tex]
[tex]\sf \text{Number of pages read more in 2 $\dfrac{1}{5}$ hours = $\dfrac{11}{15}-\dfrac{1}{3}$}[/tex]
[tex]\sf =\dfrac{11}{15}-\dfrac{1*5}{3*5}\\\\=\dfrac{11}{15}-\dfrac{5}{15}\\\\=\dfrac{6}{15}[/tex]
Answer:
see below
Step-by-step explanation:
Here is another way
1/3 book / hr * 2 1/5 hr =
1/3 * 11/5 = 11/15 read in 2 1/5 hr
1/3is the same as 5 /15
11/15 - 5 /15 = 6/15 = 2/5 more read in 2 1/5 hr that 1/3 hr
Compare the ratios using the models.
7 to 16
6:8
Which statements are true? Check all that apply.
The model for the ratio 7 to 16 should show 7 cells
shaded.
The model for the ratio 6:8 should show 8 cells
shaded.
The ratio 7 to 16 is greater than 6:8.
The ratio 6:8 is greater than the ratio 7 to 16.
The correct options are Option A: the ratio 7 to 16 should show 7 cells shaded and Option D: 6:8 is also greater than 7:16.
The ratio is the representation of the fraction where the fraction is represented by : symbol.
In the ratio a:b, it simplifies that a number of parts are shades among b number of cells.
Here given two ratios are 7:16 and 6:8.
The ratio 7:16 simplifies that 7 cells are shaded from 16 number of cells.
similarly, 6:8 simplifies that 7 cells are shaded from 8 number of cells.
As 6:8 and 7:16 can be written as in the fraction form which are 6/8 and 7/16.
Then multiply 2 in both denominator and numerator of 6:8 will be
6/8= 12/16
Now comparing between 12/16 and 7/16
12/16 > 7/16 as the denominator is same and the numerator is greater in 12/16.
Then 6:8 is also greater than 7:16.
So by checking all the options
Option A is correct: from above i is clear that the ratio 7 to 16 should show 7 cells shaded.
Option D is correct: 6:8 is also greater than 7:16.
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Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Answer:
Mikaela's team scored 5.3 points, in whole number form 5.
Step-by-step explanation:
If Viktoria's team's score was 7, 2 more than twice is (7*2) +2.
(7*2)+2=16
16 is three times Mikaela's team's score. Reduced by three means just to divide.
16/3=5.3
Mikaela's team scored 5 points.
Hope this helps!
If not, I am sorry.
Answer:
8
Step-by-step explanation:
Make it into an equation.
2x+2=(3x7)-3
2x+2=21-3
2x+5=21
2x=16
x=8
8
Solve -5<4x+3<_<7
Not really sure how to solve, line under greater than sign
The solution to the complex inequality as in the task content is; -2 < x <= 1.
What is the solution of the inequality?The inequality in discuss is; -5<4x+3 <= 7.
Hence, solving the inequalities separately; we have;
-5 < 4x +3
-8 < 4x
-2 < x
Also; 4x+3 <= 7
4x <= 4
x <= 1.
Ultimately, the solution to the inequalities is;
-2 < x <= 1.
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