Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:
C(n) = 1200 + 45n.
Now, we have to solve for n when C(n) = 4800, hence:
1200 + 45n = 4800
45n = 3600
n = 3600/45
n = 80.
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What should be done to both sides to solve the equation?
Solve x-2=10
Answer:
add 2 to each side of the equation
Step-by-step explanation:
x-2=10
To solve for x, we need to add 2 to each side of the equation
x-2+2 = 10+2
x = 12
Which of the following rational functions is graphed below?
-10
A. F(x)=
(x-1)(x+1)
X+1
B. F(x)=xx-1)
10
C. F(X) = XX+1)
x-1
x(x+1)
D. F(x) = (x+1)(x − 1)
X
Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now, In the graph,
we can see that we have a vertical asymptote at x = -1.
Hence, This means that the denominator of the rational equation becomes zero when x = -1.
So the equation must be:
⇒ y = 1 / (x + 1)
Here, The denominator is x + 1, and as expected, it becomes zero when, x = -1.
Then, we conclude that the correct option is C.
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I’m not sure how to do this if someone could help it would be much appreciated
Answer:
(b) y = 18/x; y = 9/4
Step-by-step explanation:
Different kinds of variation are generally described by the equation ...
y = k·( ) . . . . . . . where k is the constant of proportionality
__
kinds of variationWhat goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.
direct: xinverse: 1/xas the square: x²as the square root: √xas the inverse of the square: 1/x²jointly as: xzThe value of k can be found by solving the variation equation with given values of the variables.
__
inverse variationThe variables x and y are said to vary inversely, so the appropriate equation is ...
y = k(1/x) = k/x
Using the given values, we can find k:
9 = k/2
9·2 = k = 18
So, the equation is ...
y = k/18
__
for x=8Using the above equation, the value of y for x=8 is ...
y = 18/8 = 9/4
Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.
Draw a line representing the “rise” and a line representing the “run” of the line. State the slope of the line in simplest form.
The slope of the line in its simplest form is 3.
The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].
We need to find the slope of the line in its simplest form.
What is the slope?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 is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.
Select any two points on the line like A and B.
From the below figure it is clear that
Rise = Change in y = -2-(-5) = 3
Run = Change in x = 9-0 = 9
Now, [tex]\frac{9}{3} =3[/tex]
Therefore, the slope of the line in simplest form is 3.
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13 t-shirts cost total of $156. What is the unit cost per t-shirt?
Step-by-step explanation:
please mark me as brainlest
Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is defined by rolling a sum greater than 8Which of the following shows the sample space of event A?
Answer:{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
Step-by-step explanation:
Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.
What is a random sample?Random sampling is the method of selecting the subset from the set to make a statical inference.
Utilizing two six-sided number solid shapes, each named with the numbers 1 through 6.
The number of the total events will be given as,
Total events = 6²
Total events = 6 x 6
Total events = 36
The total sample is given below.
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.
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determine whether the given graph is a function or not.
Answer:
Function
Step-by-step explanation:
Yes, the graph is a function. For each x value, there is a unique y value that corresponds with it.
A graph can also be tested as a function by using the popular "vertical-line test".
Sam and Joe are working to solve 6 divided 1/4 Sam thinks the answer is 24. Joe thinks the answer is . Explain who is correct. Use a model to help explain your thinking.
Answer:
Sam is correct
Step-by-step explanation:
6 divided by 1/4.
This is asking how many times can 1/4 go into 6? This might be a calculation needed if Sam brought 6 pies to the party of 24 people. How should Sam cut the pies so that each person gets an equal share, and there is none left over. This is a serious issue because Sam only knows how to cut pies into quarters. He always gets confused when having to split a pie into 5, 6, 7, 8 or even 9 equal pieces. Sam decided that if he cuts the pies into quarters, that he'll have exactly 24 pieces of pie, all equal in size, and exactly enough to feed everyone.
Sam says 24 is wrong. I don't see the figure that Sam has in mind, but it apparently is not 24.
When a pie is cut into quarters, it will serve 4 people. If one has 6 pies, and everyone takes only one slice, then there would be 4 x 6 or 24 pieces of pie, exactly what is needed: one for each person.
A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters
The area of the swimming pool on the scale drawing will be 300 sq. centimeters.
What is the scale ratio?A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.
For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,
40 meters = 40/2 centimeters = 20 centimeters
The width of 30 meters one scale drawing will be equal to,
30 meters = 30/2 centimeters = 15 centimeters
Now, the area of the swimming pool on the scale drawing will be,
Area= 20 centimeters × 15 centimeters = 300 sq. centimeters
Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.
The complete question is:
A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?
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hii can someone help me find the area of this square
Answer:6.76 cm2
Step-by-step explanation:
You have multiply 2.6 by 2.6 and then you have to square the cm so it will be 6.76 cm2
Answer: A. 6.76 [tex]cm^2[/tex]
Step-by-step explanation:
Area is just length times width.
The length is 2.6 cm and the width is 2.6 cm, so just multiply the two.
2.6 x 2.6 = 6.76 [tex]cm^2[/tex]
Make sure you don't forget the squared in questions that ask for area.
The coordinates of triangle LMN are shown. L(-1,4) M(-1, -3) V N (4, -1) What is the length of LM? Enter the answer in the box. unit(s) The coordinates of triangle LMN are shown . L ( -1,4 ) M ( -1 , -3 ) V N ( 4 , -1 ) What is the length of LM ? Enter the answer in the box . unit ( s )
Answer:
7
Explanation:
Use the distance formula to find the answer
Answer:
7 units
Step-by-step explanation:
since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.
LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7
or
LM = | - 3 - 4 | = | - 7 | = 7
Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left? (Round your answer to the nearest tenth)
===================================================
Explanation:
She has already ran 8 miles, so she has 26-8 = 18 miles left to go.
She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.
I used the equation distance = rate*time, and solved for time to get time = distance/rate.
--------------------
Another approach:
Here's how you can use algebra.
x = time she has left in hours
7.5x = distance covered in those x hours
7.5x+8 = total distance
7.5x+8 = 26
7.5x = 26-8
7.5x = 18
x = 18/(7.5)
x = 2.4
If point C is between points A and B, then ___ + CB = AB.
A. BC
B. CA
C. ABC
D. AB
Answer:
[tex]\fbox {B. CA}[/tex]
Step-by-step explanation:
Picture the line segment :
⇒ A ---------------- C ------------------ B
Then :
⇒ CA + CB = AB
Lines l1 and l2 are parallel and l3 is a transversal.
Which statement is true?
A
m∠2+m∠4=180°
B
m∠2+m∠3=180°
C
m∠1=m∠4
D
m∠1=90°
Answer:
C. m∠1 = m∠4
Step-by-step explanation:
A. m∠2 + m∠4 = 180°
∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.
Hence, it's a false statement.
B. m∠2 + m∠3 = 180°
∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.
It's a false statement.
C. m∠1 = m∠4
∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.
Therefore, it's a true statement.
D. m∠1 = 90°
As clearly visible in the diagram;
It's a false statement.
The polynomial p(x)=1-2x^2-3x^3+4x has what order?
Please Help!! [ tough geometry question :( ]
Answer: [tex]133^{\circ}[/tex]
Step-by-step explanation:
Opposite angles of a cyclic quadrilateral are supplementary, so:
[tex]4x+5+x+15=180\\\\5x+20=180\\\\5x=160\\\\x=32[/tex]
This means that [tex]m\angle A=4(32)+5=\boxed{133^{\circ}}[/tex]
A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14. A hiker in Africa discovers a skull that contains 72 % of its original amount of C 14 .
If the 72% of its original amount of C-14. Then the number of years will be 3285.
The complete question is attached below.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.
Then the function is given below.
[tex]\rm N= N_0 \ e^{-kt}[/tex]
Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.
[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]
We have N = 0.72N₀, the time will be
[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]
Take log on both side, then we have
ln 0.72 = -0.001 × t × ln e
-0.33 = -0.001 × t
t = 3285 years
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Question 7 of 25
If f(x)=6x²,-4 and g(x)=2x+2, find (f- g)(x).
OA. 2x-5x2-2
OB. 6x²-2x-6
OC. 4x²-6
O D. 6x²2-2x-2
Answer:
x2
Step-by-step explanation:
x2
8.6 + 5.6x - 1.5 = 40.7
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]8.6 + 5.6x - 1.5 = 40.7\\5.6x = 33.6\\x=6[/tex]
Answer:
x = 6Step-by-step explanation:
solve for x
8.6 + 5.6x - 1.5 = 40.7
5.6x = 40.7 - 8.6 + 1.5
5.6x = 33.6
x = 33.6 : 5.6
x = 6
-----------------------------
check
8.6 + 5.6 * 6 - 1.5 = 40.7
40.7 = 40.7
the answer is good
Which of the following is the graph of the piecewise function h of x is defined as negative x squared plus 2 for x is less than or equal to negative 2, or one half times x for negative 2 is less than x is less than 2, or x squared minus 2 for x greater than or equal to 2.?
The attached graph represents the piecewise function h(x)
Complete questionWhich of the following is the graph of the piecewise function
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
How to determine the graph of the function?The function is given as:
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
The above means that the piecewise function has 3 domains
2 of which are quadratic functionsThe last one is a linear functionNext, we plot the graph using a graphing tool
See attachment for the graph of the piecewise function h(x)
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If a is a negative number, then a
always, always
and b is a negative number, then product ab is ?
Answer:
if a and b are both negative numbers, the product is a positive number
Consider the ordered pairs (1, 4), (–1, 2), and (0, 3). Which of the four equations below could have been used to generate these three ordered pairs? A. y = x + 3 B. y = –x – 6 C. y = – x + 3 D. y = – x – 3
The equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3
How to determine the equation?The ordered pairs are given as:
(1, 4), (–1, 2), and (0, 3)
From the above ordered pairs, we can see that the difference between the x and y values is 3.
This means that:
y - x = 3
Add 3 to both sides
y = x + 3
Hence, the equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3
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Which quadrilateral has exactly one pair of parallel sides?
a) rhombus
b) kite
c) trapezoid
d) parallelogram
Answer:
trapezoid
the horizontal side lengths wont touch each other if you extend them out
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
the answer pf x its 15
by adding the middle sum to 90 degreess and by dividing 6 and 90 you get 15
PLEASE HELP 15 POINTS
Answer:
B
Step-by-step explanation:
Used elimination method.
first plugged in (0,0)which remove A,D
than saw the line is not solid so chose B
Which equation represents a side that is perpendicular to side d? O y = 2x+5 Oy=-2x+5 NG 0 Y=2x-5/2 OY--12-12 = Which equation represents a side that is perpendicular to side d ? O y = 2x + 5 Oy = -2x + 5 NG 0 Y = 2x - 5 / 2 OY -- 12-12 =
The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.
What is the slope?A numerical assessment of a line's angle relative to the ground is known as the slope.
The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.
The given linear equation in the problem is;
y = 2x+5
Compare the equation with the standard equation;
[tex]\rm y = mx+ c[/tex]
where,
m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;
m = 2
The product of the slope of the two-line perpendicular to each will be -1.
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is;
y = -2x+c.
m₁=2
m₂=-2
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is y = -2x+5.
Hence, option B is correct.
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A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after t seconds is given by the following.
A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
[tex]t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\[/tex]
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
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If f(x)=x^2 then evaluate (2+3i)
Answer:
-5 + 12 i
Step-by-step explanation:
(2 + 3i)^2 = 4 + 6i + 6i + 9i^2
= 4 + 12 i + 9(-1)
= - 5 + 12 i
does this table represent a function? why or why not x:2,2,3,4,5 y:1,4,4,2,5
Answer:
No, the table does not represent a function.
Step-by-step explanation:
By definition, a function will not have 2 or more results for the same input.
The table shows two values of y for the same x: (2,1) and (2,4). The same input, 2, results in two different values, 1 and 4.
See attached image.
Name the relationship between x and y:
Answer:
They are the same angle.
Step-by-step explanation:
We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.
Option 2: Corresponding angles.
Hope this helps!
If not, I am sorry.
