The ordered pair (7,2) is viable and Option B is the correct answer.
What is Relationship ?Relationship between variables defines the way one variable is dependent upon the other variable.
It is given that x is the number of visitors and y is the number of winners,
It has to be seen and chosen that which ordered pair makes sense
The ordered pair is viable if the no. of visitor is positive and more than the number of winners.
Therefore ordered pair (7,2) is viable and Option B is the correct answer.
To know more about Relationship
https://brainly.com/question/14389660
#SPJ1
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)
The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
The given coordinate are (8, -1) and (2, -5).
What is the slope of an equation?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
The standard form of an equation is Ax + By = C.
The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].
Multiply each term by 3 of the equation.
[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]
⇒3y + 3 = 2x - 16
Subtract 2x from both sides of a equation.
That is, -2x + 3y + 3 = - 16
Subtract 3 from both sides of a equation.
That is, -2x + 3y = - 19
Multiply each term by - 1 from both sides of an equation.
That is, 2x - 3y = 19
Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
To learn more about the slope visit:
https://brainly.com/question/3605446.
#SPJ1
Given parallelogram ABCD and AB || CD, if mAB = -5 then mCD must be:
A)-5
B)
- 1
——
5
C) 5
D) 1
—
5
The slope of CD, which is parallel to AB must be: A. -5.
What is the Slope of Parallel Segments?If two line segments are parallel to each other, their slope value (m) would be equal to each other.
Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.
Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.
Learn more about the slope of parallel segments on:
https://brainly.com/question/3823510
#SPJ1
Hey can I have help with this question. An explanation would be great as I find things difficult to understand :)
Answer:
[tex](0, -\frac{15}{2} )[/tex]
Step-by-step explanation:
When a straight line crosses the y-axis, the point that touches it is called the y-intercept. We can find the y-intercept by plugging in zero as the value for 'x', as any x value on the y-axis is zero. So plugging in x = 0 into the equation '3x - 2y = 15', we get -2y = 15, so y = -15/2. The point would be [tex](0, -\frac{15}{2} )[/tex], as x = 0 when y = -15/2.
Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0
I can’t figure this out!!!
Answer:
[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]
Step-by-step explanation:
Completing the square :
x² + 14x - 8y + 65 = 0
x² + 14x + 49 - 49 - 8y + 65 = 0
(x + 7)² - 8y + 16
(x + 7)² = 8y - 16
⇒ x = -7, y = 2 (Vertex)
Finding a :
⇒ x² = 4ay
⇒ (-7)² = 4(2)a
⇒ a = 49/8
Finding the focus :
⇒ (0, a)
⇒ (0, 49/8) (Focus)
For any positive numbers a, b, and d, with b 1,
A.
logb a logb d
B.
logb a + logb d
C.
d logb a
done
D.
logb a - logb d
Answer:
D
Step-by-step explanation:
using the rule of logarithms
log x - log y ⇔ log ( [tex]\frac{x}{y}[/tex] )
then
[tex]log_{b}[/tex] ( [tex]\frac{a}{d}[/tex] ) = [tex]log_{b}[/tex] a - [tex]log_{b}[/tex] d
A sum of money is divided among three girls, Rheanna, Kerisha and Anne, in the ratio 2:3:7, respectively. If Anne gets $15
more than Kerisha, what is the value of the total sum that was shared?
Using proportions, it is found that the value of the total sum that was shared was of $45.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:
[tex]A = \frac{7}{2 + 3 + 7}N = \frac{7N}{12}[/tex][tex]K = \frac{3}{2 + 3 + 7}N = \frac{3N}{12}[/tex]The difference is of $15, hence:
[tex]A - K = 15[/tex]
[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]
[tex]\frac{4N}{12} = 15[/tex]
[tex]\frac{N}{3} = 15[/tex]
N = 15 x 3 = 45
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Change the decimal to a fraction. (Use the “/“ in your fraction.) 0.45454545….
The decimal: 0.4545...
Can be written in fraction form as 45/99.
How to write the number as a fraction?
Here we have the number:
N = 0.4545...
Notice that the repeating digits are two, 4 and 5.
Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:
100*0.4545... = 45.4545...
Now if we subtract the original number, we get:
45.4545... - 0.4545... = 45
This means that:
(100 - 1)*0.4545... = 99*0.4545... = 45
Then we can multiply and divide our number by 99, so we get:
[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]
So the fraction is 45/99
If you want to learn more about fractions:
https://brainly.com/question/11562149
#SPJ1
The domain of the function
Step-by-step explanation:
[-5, 4] because it is an empty circle, meaning less than
cotpheta•sin2pheta=
1+cos2pheta
1+cospheta
1+sin2pheta
Answer:
Step-by-step explanation:
Did you mean.
[tex] = \cot( \theta) . \sin(2 \theta) [/tex]
[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]
[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]
[tex] = 2 \cos {}^{2} ( \theta) [/tex]
[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]
[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]
No option Solution.
Zippy company manufactured 10,000 units in december with a total product cost of $22,900 they had zero finished goods inventory at the start of december. in december zippy sold 7,796 units at a unit price of $5.54. period expenses were $4,723. what is the amount of zippy's gross profit (otherwise know as gross margin).? round any intermediate calculations to four decimal places
The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
Gross profitSales revenue $43,189.84
(7,796 units × $5.54)
Less Cost of goods sold $17,852.84
[($22,900/10,000)×7,796]
Gross profit $25,337
( $43,189.84-$17,852.84)
Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
Learn more about gross profit here:https://brainly.com/question/942181
#SPJ1
The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)
Answer:
339
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Given information:
a = 240 (initial population of bacteria)x = time (in hours)y = population of bacteriaTherefore: [tex]y=240b^x[/tex]
To find an expression for the population after 1 hour, substitute x = 1 into the found equation:
[tex]\implies y=240b^1[/tex]
[tex]\implies y=240b[/tex]
We are told that the population after 9 hours is double the population after 1 hour. Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:
[tex]\implies 2(240b)=240b^9[/tex]
[tex]\implies 480b=240b^9[/tex]
[tex]\implies 480=240b^8[/tex]
[tex]\implies 2=b^8[/tex]
[tex]\implies b=\sqrt[8]{2}[/tex]
[tex]\implies b=2^{\frac{1}{8}}[/tex]
Therefore, the final exponential equation modelling the given scenario is:
[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]
[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]
To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:
[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]
[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]
[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]
Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.
How do the graph of f(x) and f^(-1)(x) relate?
A.They are rotations of each other.
B.They are reflections of each other.
C.They are the exact same graph.
D.They are translations of each other.
The correct option regarding the inverse function is given by:
B.They are reflections of each other.
What is the relation between the graphs of the original function and it's inverse?The inverse function is the reflection of the original function over the line y = x, that is, they are reflections of each other, hence option B is correct.
More can be learned about inverse functions at https://brainly.com/question/8824268
#SPJ1
What are the y-intercept and the asymptote of g(x) = 4x – 6?
(0, –5); y = –6
(0, –2); y = –4
(0, 4); y = 6
(0, 6); y = 4
The y-intercept of the line is (0 -6). The given function has no vertical and horizontal asymptotes
y-intercept and asymptotes of an equationA linear equation is an equation that has a leading degree of 1. Given the equation
g(x) = 4x - 6
The y-intercept occurs at a point where x = 0
g(0) = 4(0) - 6
g(0) = -6
Hence the y-intercept of the line is (0 -6)
The given function has no vertical and horizontal asymptotes
Learn more on intercept here: https://brainly.com/question/18831322
#SPJ1
3.5 decimals to mixed numbers
find sizes of unknown angles
Answer:
a=75
b=70
c=110
d=105
e=110
f=105
Step-by-step explanation:
Please help!!!!
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 135 feet. The smallest path bordering the patch of grass measures 60 feet. The smallest angle formed by the paths measures 26°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest degree. Show all your work.
The measure of the largest angle of the triangular patch of grass is 81 degrees
Application of sine ruleIn order to determine the measure of the largest angle, we will use the expression below;
[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]
Cross multiply
135sin26 = 60sinx
sinx = 135sin26/60
sinx = 59.18/60
sinx = 0.986
x = 80.5 degrees
Hence the measure of the largest angle of the triangular patch of grass is 81 degrees
Learn more sine rule here; https://brainly.com/question/27174058
#SPJ1
In the triangle above, what is the measure of
A.
M
B.
M
C.
M
D
, cannot be determined
which of the following is a rational number
a.√5
b.π
c.1/2
d.√(77)
Select the correct answer.
Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons.
The correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.
What is an expression?Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.
Here we have two pieces of information
Gas station A:-
3 gallons for $9.15
1 gallons for $9.15 / 3 = $ 3.05
Gas station B:-
P = 3.08g
It means that station B is selling the gasoline at a higher price.
Therefore the correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
Which point is on the graph of f(x) = 3.4^x
O A. (1, 12)
OB. (0, 12)
O C. (12, 1)
O D. (0,0)
The point on the graph f(x) = 3.4ˣ is (0, 1)
None of the given options is correct.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.
Let's try each option:
A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.
B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.
C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.
D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.
Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.
To learn more about the function;
brainly.com/question/28303908
#SPJ7
Identify the method that will be used to solve for x for each equation.
4x = 20
x 119
5x + 6x = 22
5(x - 2) = 30
The solution of the equation 4x = 20, x – 11 = 9, 5x + 6x = 22, and 5(x – 2) = 30 will be 5, 20, 2, and 8.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x = 20
x = 5
x – 11 = 9
x = 20
5x + 6x = 22
11x = 22
x = 2
5(x – 2) = 30
x – 2 = 6
x = 8
The complete question is attached below.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
17. Find the height of a rectangular room that
measures 4.7 m long and 3.2 m wide, if
the space within it is 33.84 m³.
Answer:
the height: h=2,25
Step-by-step explanation:
volume of rectangular box = wide*long*the height
----> the height = volume of rectangular box / ( wide*long) = 2,25
give me 5 stars and hearts^^
what is the answr to -5(b + 1) = 8
[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]
PLEASE GIVE BRAINLIEST
\\\///\\\///\\\///\\\///\\\///\\\///\\///\\\///\\\///\\\///\\\///\\\//\\//\\//\\//\\\///\\//\\\///\\\///\\\///\
[tex]\Rsh[/tex] Hey! [tex]\Lsh[/tex][tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]
>>> First, let's multiply -5 by b and 1. Then we obtain
[tex]\pmb{-5b-5=8}[/tex].
>>> Now we add 5 to both sides.
[tex]\pmb{-5b=13}[/tex]
>>> And then, divide both sides by -5.
[tex]\pmb{b=-\dfrac{13}{5}}[/tex]
>>> That is the value of b.
><><><><><<><><><><><><><><><><><><><><><><><><><><><><><><><><>
Hope the answer - and explanation - assisted you!
Happy studies! :)
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ1
Answer: B
Step-by-step explanation:
For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/
A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.
#A
New side
X+8Area
(x+8)²x²+16x+64 cm²#2
Now it has turned rectangle
Sides
x+12 and x-7
Area
(x+12)(x-7)Answer:
A) (x + 8)² cm² = (x² + 16x + 64) cm²
B) (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²
Step-by-step explanation:
Formula
Area of a square = s² (where s is the side length)
Given side length of square field:
x cm⇒ Area of field = x² cm²
Part A
If the side length of the square field is increased by 8 cm then:
⇒ new side length = (x + 8) cm
Substitute the new side length into the formula for the area of a square:
⇒ Area of field = (x + 8)² cm²
Expand and simplify:
⇒ Area = (x + 8)²
⇒ Area = (x + 8)(x + 8)
⇒ Area = x(x + 8) + 8(x + 8)
⇒ Area = x² + 8x + 8x + 64
⇒ Area = (x² + 16x + 64) cm²
Part B
If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:
⇒ new side length a = (x + 12) cm
⇒ new side length b = (x - 7) cm
Substitute the side lengths into the formula for area of a square:
⇒ Area of a square = s × s
⇒ Area of a square = a × b
⇒ Area of the field = (x + 12)(x + 7) cm²
Expand and simplify:
⇒ Area = (x + 12)(x + 7)
⇒ Area = x(x + 7) + 12(x + 7)
⇒ Area = x² + 7x + 12x + 84
⇒ Area = (x² + 19x + 84) cm²
2(2x – 1) + 7 < 13 or –2x + 5≤-10
Answer:
2, 7.5
Step-by-step explanation:
2(2x - 1) + 7 < 13
4x - 2 + 7 < 1
4x + 5 < 13
4x < 8
x < 2
-2x + 5 ≤ -10
-2x ≤ -10 - 5
-2x ≤ -15
x ≤ -15 / -2
x ≤ 7.5
PLEASE HELP!!! I will give brainliest pleasee help. each question has to be solved, there are no options for answers.
The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.
What is Intersecting Secant Theorem?
When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.
a(a+b)=c(c+d)
1.)
6(x+6) = 5(5+x+3)
6x + 36 = 25 + 5x + 15
x = 4
2.)
4(2x+4)=5(5+x)
8x + 16 = 25 + 5x
3x = 9
x = 3
3.)
8x(6x+8x) = 7(9+7)
8x(14x) = 112
112x² = 112
x = 1
4.)
(x+3)² = 16(x-3)
x² + 9 + 6x = 16x - 48
x² - 10x - 57 = 0
x = 14.0554
Learn more about Secant:
https://brainly.com/question/10128640
#SPJ1
Do you know how fast last year's winner was traveling? san francisco laser boat.
The average speed of the Australian team's laser boat in the San Francisco final was 68.81 km/h.
What is the laser boat?
The laser boat is a type of boat that uses the wind to move on the water. This type of boat is used in the SailGP Championship.
In the phase of San Francisco, the United States the winner was the team of Australia that had an average speed of 68.81 km/h and a maximum of more than 90 km/h.
Learn more about laser boat in: https://brainly.com/question/362440
#SPJ1
Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.
A system of equations. x plus 5 y equals 21. x plus y equals 9.
The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.
Answer:
x= 6 , y = 3
Step-by-step explanation:
x + 5y = 21
i am using trail and error method and i got the answer easily
the logic behind this is simple
the first equation is x + 5y = 21 so we can say that y will be 5 x 1 , 5 x 2 , 5 x 3 , 5 x 4
first i did 5 x 4 = 20
x + 5 x 4 = 21
x= 1 but the equation x + y = 1 + 4 = 5 which is not equal to 9
second i tried with 5 x 3 =15
and the equation will be
x + 5 x 3 = 21
6 + 15 = 21
this time the second equation became true
x + y = 9
6 + 3 = 9
the no of pounds of salsa = 6
no of pounds of tomato = 3
Which inequality represents all the solutions of
9(4x-8) < 4(6x + 9)?
Answer:
x < 9
Step-by-step explanation:
Our original inequality:
[tex]9(4x-8) < 4(6x+9)[/tex]
Firstly, let's expand the brackets on both sides:
[tex]36x - 72 < 24x + 36[/tex]
Now, we add the 72 over to isolate the [tex]x[/tex]:
[tex]36x < 24x + 108[/tex]
Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:
[tex]12x < 108[/tex]
Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:
[tex]x < 9[/tex]
This means our final answer is [tex]x < 9[/tex].
