Answer:
(4,0)
Step-by-step explanation:
So we have the system:
-x+5y=-4
4x+4y=16
--------------
We are asked to solve this for elimination.
We aren't totally setup for elimination though.
Both equations are in the same form, the form being ax+by=c form, so we are good there.
Now the other requirement is one the columns that contain variables need to be opposites (you will add) or same (you will subtract).
I'm going to multiply the first equation by 4. The reason I'm going to do this is because the first column will contain -4x and 4x. Those are opposites. When you add opposites, you get 0 (they cancel).
So applying the multiplication of 4 to first equation gives:
-4x+20y=-16
4x+ 4y=16
----------------- Add the equations now.
0x+24y=0 Again this is called elimination, because we made it to where a variable is canceled when combining the equations.
0x+24y=0
0+ 24y=0
24y=0
Divide both sides by 24:
y=0
So using one of the equations (you only need one of them) along with the y=0, let's find x.
I'm going to go with -x+5y=-4 with y=0.
Plugging in the 0 for y gives us:
-x+5y =-4
-x+5(0)=-4
-x+ 0 =-4
-x =-4
Multiply both sides by -1:
x =4
The solution is (x,y)=(4,0).
ANSWER
The ordered pair is
(4,0)
EXPLANATION
To solve a simultaneous equation using the elimination method means making the coefficient of one of the variables the same. We then add or subtract to eliminate that variable.
The given system has equations:
[tex] - x + 5y = - 4...(1)[/tex]
[tex]4x + 4y = 16...(2)[/tex]
Divide the second equation by 4
[tex]x + y = 4...(3)[/tex]
Add equation (1) and (3) to eliminate x.
[tex] \implies \: 5y + y = - 4 + 4[/tex]
[tex] \implies \: 6y = 0[/tex]
[tex] \implies \: y = \frac{0}{6} = 0[/tex]
Put
[tex]y = 0[/tex]
into the first equation to get:
[tex] - x + 5 \times 0 = - 4[/tex]
[tex] - x = - 4[/tex]
[tex] \therefore \: x = 4[/tex]
The ordered pair is
(4,0)
What is the missing side length in this right triangle? A. 15 B. 21 C. 225 D. 441
9,12?
Answer:
A. 15.
Step-by-step explanation:
9^2 + 12^2
= 81 + 144
= 225.
Taking the square root: we get 15.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the two sides of the triangle, therefore, using the Pythagorean theorem, the third side of the triangle can be written as,
x² = 12² + 9²
x² = 144 + 81
x² = 225
x = 15
Hence, the missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
Learn more about Pythagoras' Theorem:
https://brainly.com/question/14461977
#SPJ2
Nolan buys baseball bats to sell in his store. Each bat costs him $19.99 and he is using a mark up rate of 85%. At what selling price will Nolan sell each bat?
Answer:
The selling price of each bat is $36.98
Step-by-step explanation:
* Lets explain how to solve the problem
- Nolan buys baseball bats to sell in his store
- Each bat costs him $19.99
- He is using a mark up rate of 85%
- The selling price = cost price + markup
* Lets solve the problem
∵ The cost price of each bat is $19.99
∵ The markup is 85%
- To find the markup multiply its percent by the cost price
∴ The markup = 19.99 × 85/100 = $16.9915
∵ The selling price = the cost price + the markup
∴ The selling price = 19.99 + 16.9915 = 36.9815
* The selling price of each bat is $36.98
In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).
Answer
Both graphs have the same number of x-intercepts. The graph of the function f(t) = t² has one x-intercept, which is the value of t for which f(t) = t² = 0, and that is t = 0. The graph of the function g(t) = (t - 8)² has also one x-intercept, which is the value of t for which g(t) = 0 and that is t = 8.
The function f(t) = t² is the most simple form of a parabola, so it is considered the parent function. The function g(t) = (t - 8)² is a daughter function of f(t); then, the graph of g(t) is a horizontal translation of the graph of f(t), 8 units to the right, so the number of x-intercepts (the points where the x-axis is crossed or touched by the graph) does not change, it is just their position what changes.
Explanation:
The x-intercepts are the points where the graph of the function touches or crosses the x-axis. They are found by doing the function equal to zero. In this case f(t) = 0 and g(t) = 0.
You can solve easily f(t) = t², as, just by simple inspection, the soluton is t = 0.
Then, when you realize that the function g(t) = (t - 8)² is a horizontal translation (8 units to the right) of the parent function f(t), you can conclude quickly that the number of x-intercepts of both graphs is the same. Thus, uisng the transformation of the parent function, 8 units to the right, you conclude that both the graph of f(t) and the graph of g(t) have the same number of x-intercepts: one.
f rests at (0/0) and grows upwards, so there is only a single x-intercept. g is f moved 3 to the left, so it also only has one intercept but at (-3,0).
What is the seventh term of the geometric sequence where a1=128 and a3=8
[tex]\bf \begin{array}{lll} term&value\\ \cline{1-2} a_1&128\\ a_2&128r\\ a_3&128rr\\ &128r^2 \end{array}~\hspace{5em}\stackrel{a_3}{128r^2}=\stackrel{a_3}{8}\implies r^2=\cfrac{8}{128}\implies r^2=\cfrac{1}{16} \\\\\\ r=\sqrt{\cfrac{1}{16}}\implies r=\cfrac{\sqrt{1}}{\sqrt{16}}\implies r=\cfrac{1}{4}\qquad \leftarrow \textit{common ratio} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=7\\ a_1=128\\ r=\frac{1}{4} \end{cases}\implies a_7=128\left( \frac{1}{4} \right)^{7-1} \\\\\\ a_7=128\left( \frac{1}{4} \right)^6\implies a_7=128\cdot \cfrac{1}{4096}\implies a_7=\cfrac{128}{4096}\implies a_7=\cfrac{1}{32}[/tex]

Transversal  cuts parallel lines  and  at points X and Y as shown in the diagram. If m∠CXP = 106.02°, what is m∠SYD?
A.
73.98°
B.
90°
C.
106.02°
D.
180°
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
rewrite the fraction using the least common denominator
4/9 7/15
Answer:
20/45 & 21/45
Step-by-step explanation:
Find a common denominator. What you do to the denominator, you do to the numerator. In this case, the smallest denominator is 45.
(4/9)(5/5) = 20/45
(7/15)(3/3) = 21/45
The two fractions you have is:
20/45 for 4/9
21/45 for 7/15
~
Answer:
20/45 for 4/9 and 21/45 for 7/15
Step-by-step explanation:
The least common denominator of 4/9 is 20/45.
The least common denominator of 7/15 is 21/45.
riangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
Answer:
5 units
Step-by-step explanation:
According to the given statement Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.
To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs
The square of the required distance = 4^2+3^2 = 16+9 =25
By taking root of 25 we get:
√25 = 5
Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′ is 5 units. ..
Ms. Lund placed a 7 foot ladder against a wall with the base of the ladder 4 feet away from the wall . she decided that a different , 10 foot ladder needed to be used . for if Ms. Lund wants the longer ladder to rest against the wall at the same angle as the shorter ladder , about how far away from the wall should she place its base ?
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
[tex] \frac{7}{10} = \frac{4}{x} \\ x = \frac{40}{7} [/tex]
The distance the wall should place its base will be 5.71 feet.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between the wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
The distance will be calculated as below:-
( 7 / 10 ) = ( 4 / x )
x = ( 10 x 4 ) / 7
x = 5.71 feet
Therefore, the distance the wall should place its base will be 5.71 feet.
To know more about trigonometry follow
https://brainly.com/question/28122732
#SPJ5
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.
Answer:
Step-by-step explanation:
Let 'c' be the number of child bikes c=20
and 'a' be the number of adult bikes. a=6
According to the problem
The restriction of building time for a week is 4c+6a≤120 hours.........(1)
and the restriction of testing time for a week is 4c+4a≤100 hours..........(2)
Lets check whether company can build c=20 and a=6 bikes in a week by putting these values in (1) and (2).
4c+6a≤120 hours.........(1)
4(20)+6(6)≤120
80+36≤120
116≤120 (true)
4c+4a≤100 hours..........(2)
4(20)+4(6)≤100
80+24≤100
104≤100 (true)
Hence, the company can build 20 child bikes and 6 adult bikes in the week....
JK Rowling is autographing some of the new Harry Potter books. A store sells 56 books and she is able to autograph 5/8 of the books sold. How many books will have her autograph?
Answer:
35 books
Step-by-step explanation:
56/8 = 7
7 x 5 = 35
5/8 of 56 = 35
J.K. Rowling will autograph 35 of the 56 books sold, which is calculated by multiplying the total number of books by 5/8.
To find out how many books J.K. Rowling will autograph, we need to calculate 5/8 of the 56 books sold. Here's the step-by-step calculation:
Find out what 5/8 of the total amount is by multiplying the total number of books (56) by 5/8.
To do this, first multiply 56 by 5, which equals 280.
Then divide that number by 8, which equals 35.
Therefore, J.K. Rowling will autograph 35 books.
what is the slope of the line that passes through the points (1, −3) and (3, −5)
Answer:
Slope = -1
Step-by-step explanation:
Use the following formula:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (1 , -3)
(x₂ , y₂) = (3 , -5)
Plug in the corresponding numbers to the corresponding variables. Simplify:
m = (-5 - (-3))/(3 - 1)
m = (-5 + 3)/(3 - 1)
m = -2/2
m = -1
The slope of the line is -1.
~
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have as data the following points:
[tex](x_ {1}, y_ {1}) :( 1, -3)\\(x_ {2}, y_ {2}): (3, -5)[/tex]
Substituting the values:
[tex]m = \frac {-5 - (- 3)} {3-1}\\m = \frac {-5 + 3} {3-1}\\m = \frac {-2} {2}\\m = -1[/tex]
Thus, the slope is -1.
Answer:
The slope is -1
Refer to the figure and match the theorem that supports the statement.
1. If chords are =, then arcs are =. If BC = DE, then Arc BC = Arc DE
2. If arcs are =, then chords are =. If AX is perpendicular to BC, then BX = XC
3. Diameters perpendicular to chords bisect the chord If Arc BC = Arc DE, then BC = DE
The principles of circle geometry dictate that: if chords are equal then their corresponding arcs are equal; if arcs are equal then their chords are equal; and diameters perpendicular to chords bisect the chord. However, some of the proposed arguments in the question are not matching these principles.
Explanation:The three statements highlighted in this question are the principles of circle geometry.
1. If chords are equal, then arcs are equal: This theorem states that if two chords in a circle are equal in length, then their corresponding arcs (the part of the circumference that the chord subtends) are also equal. If BC = DE as stated, then Arc BC = Arc DE.
2. If arcs are equal, then chords are equal: This is the converse of the first theorem. If two arcs of a circle are equal, then the chords subtending these arcs are equal. However, this principle is not relevant for the condition if AX is perpendicular to BC, then BX = XC.
3. Diameters perpendicular to chords bisect the chord: This theorem states that if a diameter of a circle is perpendicular to a chord, then it bisects the chord. Therefore the statement if Arc BC = Arc DE, then BC = DE is not relevant to this theorem.
Learn more about Circle Geometry here:https://brainly.com/question/35055577
#SPJ11
If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =
Answer:
The value of k is -11
Step-by-step explanation:
If (x+2) is a factor of x3 − 6x2 + kx + 10:
Then,
f(x)=x3 − 6x2 + kx + 10
f(-2)=0
f(-2)=(-2)³-6(-2)²+k(-2)+10=0
f(-2)= -8-6(4)-2k+10=0
f(-2)= -8-24-2k+10=0
Solve the like terms:
f(-2)=-2k-22=0
f(-2)=-2k=0+22
-2k=22
k=22/-2
k=-11
Hence the value of k is -11....
the system of equations graphed below has how many solutions? y=-3/2x-3 y=-3/2x+5
Answer:
No solutions.
Step-by-step explanation:
The value of y cannot be equal to both -3/2x - 3 and -3/2x + 5.
the following table shows the distance from school as a function time
time in minutes. distance in meters
x. f(x)
0 36
3 32
6 28
9 24
12 20
find and intercept the meaning of the x intercept in this scenario
36,0 the distance away from the school
27,0 the time it takes to reach the school
36,0 the time it takes to reach the school
27,0 the distance away from the school
Answer:
27,0 the distance away from the school
Step-by-step explanation:
Apply the formula for equation of a straight line;
y=mx+c where c is the y intercept , and m is the gradient
From the graph, the slope is negative where speed decreases with increase in time
Find the gradient by applying the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking y₁=24, y₂=20, x₁=9, x₂=12
Then;
[tex]m=\frac{20-24}{12-9} =\frac{-4}{3}[/tex]
write the equation of the function as ;
y=mx+c, c=36( the y-intercept when x=0) hence the equation is;
[tex]y=mx+c\\\\y=\frac{-4}{3}x+36[/tex]
To get x-intercept, substitute value of y with 0
[tex]y=mx+c\\\\\\y=-\frac{4}{3} +36\\\\\\0=-\frac{4}{3} x+36\\\\\frac{4}{3}x =36\\\\\\4x=36*3\\\\\\x=108/4=27[/tex]
This means that the x-intercept is 27 ,and this means you will require 27 minutes to cover the whole distance to the school.
Answer:
A: 36,0 the distance away from the school
Step-by-step explanation:
At 0 it means you have spent 0 minutes going to school which means you haven't left the starting point yet.
36 is the distance left (in meters) from your current position and school. This means that the school is 36 meters away from the starting point.
for the function f(x)=3(x-1)^2+2 identify the vertex, domain, and range.
Answer:
The vertex of the function is (1 , 2)
The domain is (-∞ , ∞) OR {x : x ∈ R}
The range is [2 , ∞) OR {y : y ≥ 2}
Step-by-step explanation:
* Lets revise the standard form of the quadratic function
- The standard form of the quadratic function is
f(x) = a(x - h)² + k , where (h , k) is the vertex point
- The domain is the values of x which make the function defined
- The domain of the quadratic function is x ∈ R , where R is the set
of real numbers
- The range is the set of values that corresponding with the domain
- The range of the quadratic function is y ≥ k if the parabola upward
and y ≤ k is the parabola is down ward
* Lets solve the problem
∵ f(x) = 3(x - 1)² + 2
∵ f(x) = a(x - h)² + k
∴ a = 3 , h = 1 , k = 2
∵ The vertex of the function is (h , k)
∴ The vertex of the function is (1 , 2)
- The domain is all the real number
∵ The domain of the quadratic function is x ∈ R
∴ The domain is (-∞ , ∞) OR {x : x ∈ R}
- The leading coefficient of the function is a
∵ a = 3 ⇒ positive value
∴ The parabola is opens upward
∴ The range of the function is y ≥ k
∵ The value of k is 2
∴ The range is [2 , ∞) OR {y : y ≥ 2}
What is the distance between the points (4,3) and (1,-1) on the coordinate plane?
The set of ordered pairs in the graph below can be described as which of the following? A. a relation B. a function C. a relation and function D. neither a relation nor function
Answer:
a relation and function ⇒ answer C
Step-by-step explanation:
* Lets revise the relation and the function
- The relation is between the x-values and y-values of ordered pairs.
- The set of all values of x is called the domain, and the set of all values
of y is called the range
- The function is a special type of relation where every x has a unique y
- Every function is a relation but not every relation is a function
* Lets solve the problem
∵ The graph is a parabola
∵ The parabola is a function because every x-coordinates of the
points on the parabola has only one y-coordinate
- Ex: some ordered pairs are (-5 , -5) , (-2 , 5) , (0 , 7) , (2 , 5) , (5 , -5)
∵ Every x-coordinate has only one y-coordinate
∴ The graph represents a function
∵ Every function is a relation
∴ The set of ordered pairs in the graph below can be described as
a relation and function
If (5^0)^x = 1, what are the possible values of x?
Answer:
x can be any value
Step-by-step explanation:
(5^0)^x = 1,
5^0 =1
1^x =1
X can be any value
For this case we have the following expression:
[tex](5^{ 0})^{x} = 1[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^{n * m}[/tex]
Then, rewriting the expression:
[tex]5 ^ 0 = 1[/tex]
Thus, the variable "x" can take any value:
Answer:
The variable "x" can take any value
The graphs below have the same shape. What is the equation of the blue graph?
For this case we have that by definition of vertical translations of functions, it is fulfilled:
Assume [tex]k> 0[/tex]:
To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
In the figure it is observed that:
The original function is [tex]G (x) = x ^ 2[/tex], the function was moved 4 units down. So, the new function is:
[tex]F (x) = x ^ 2-4[/tex]
Answer:
Option B
Answer:
Option B is correct.
Step-by-step explanation:
G(x) = x^2
then f(x) = x^2-4
since the graph is shifted 4 units down because when something is subtracted from the function the graph is shifted down.
that's why f(x) = x^2-4.
Hence Option B is correct.
Find the shortest distance from A to B in the diagram below.
Answer: 14 m
Step-by-step explanation:
8 m + 6 m = 14 m
Answer:
10 cm.
Step-by-step explanation:
We have been given a cuboid. We are asked to find the shortest distance from A to B is the given diagram.
We know that shortest distance from A to B will be equal to hypotenuse of right triangle with two legs 8 meters and 6 meters.
[tex]AB^2=8^2+6^2[/tex]
[tex]AB^2=64+36[/tex]
[tex]AB^2=100[/tex]
Now, we will take square root of both sides of our given equation as:
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the shortest distance from A to B is 10 cm.
Question 12 Multiple Choice Worth 1 points)
(03.07 LC)
Choose the equation of the horizontal line that passes through the point (-8, -7).
Answer:
linear inqution
Step-by-step explanation:
relationship
ANSWER
[tex]y = - 7[/tex]
EXPLANATION
A horizontal line that passes through (a,b) has equation
[tex]y = b[/tex]
This is because a horizontal line is a constant function.
The y-values are the same for all x belonging to the real numbers.
The given line passes through (-8,-7).
In this case, we have b=-7.
Therefore the equation of the horizontal line that passes through the point (-8, -7) is
[tex]y = - 7[/tex]
X+1
-
and h(x) = 4 - X, what is the value
Oil CD
Nior
wla
olo
Answer:
8/5
Step-by-step explanation:
[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].
Start with the inside first: h(-3).
h(-3) means use the function called h and replace the x with -3. The expression that is called h is 4-x.
4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.
So the value for h(-3) is 7, or h(-3)=7.
Now this is what we thus far:
[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].
g(7) means use the function called g and replace x with 7. The expression that is called g is (x+1)/(x-2).
(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.
This is our final answer:
[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].
In a pet shop, there are 3 hamsters for every 2 guinea pigs, and there are 2 giant cloud rats for every 3 guinea pigs. If n is the total number of hamsters, guinea pigs, and giant cloud rats, and n>0, then what is the smallest possible value of n?
Answer:
n = 19.
Step-by-step explanation:
If there are x guinea pigs then there are 3/2 x and 2/3 x rats.
So n = x + 3/2 x + 2/3 x
n = 19x / 6
19x = 6n
Let x = 6 , then n = 19*6 / 6 = 19.
Now n and x must be whole numbers so x is 6 and n = 19 are the smallest possible values.
Answer:
n=19
Step-by-step explanation:
dwecefxgfg
ctgxervgrex
vgcecbexbe
crextrbtrxtev
Find the distance from the Theater to the Library. Leave your answer in simplest radical form if necessary.
12
√12
74
√74
Answer:
See explanation
Step-by-step explanation:
Some important information is missing in the question, however I will try to help.
Let us assume the theater is located at (-5,6) and the library is located at (4,1), then we can use the distance formula to find the distance from the Theater to the Library.
The distance formula is given by:
[tex]d = \sqrt{(x_2-x_1) ^{2} +(y_2-y_1) ^{2} } [/tex]
We plug in the values to get:
[tex]d = \sqrt{ {(4 - - 5)}^{2} + {(6 - 1)}^{2} } [/tex]
[tex]d = \sqrt{81 + 25} [/tex]
[tex]d = \sqrt{144} = 12[/tex]
You can plug in the points you have to get the required answer
Answer:
D, √74
Step-by-step explanation:
got it right on odyssey ware
Use the discriminant to describe the roots of each equation. Then select the best description.
x2 - 4x + 4 = 0
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 : a ≠ 0, then
The nature of it's roots can be determined by the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
For x² - 4x + 4 = 0 ← in standard form
with a = 1, b = - 4, c = 4, then
b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0
Hence roots are real and equal
This can be shown by solving the equation
x² - 4x + 4 = 0
(x - 2)² = 0
(x - 2)(x - 2) = 0, hence
x - 2 = 0 or x - 2 = 0
x = 2 or x = 2 ← roots are real and equal
(x)=3log(x+5)+2 what is the x intercept
Answer:
[tex]\large\boxed{x-intercept=-2+\sqrt[3]{0.01}}[/tex]
Step-by-step explanation:
[tex]f(x)=3\log(x+5)+2\to y=3\log(x+5)+2\\\\\text{Domain:}\ x+5>0\to x>-5\\\\\text{x-intercept is for }\ y=0:\\\\3\log(x+5)+2=0\qquad\text{subtract 2 from both sides}\\\\3\log(x+5)=-2\qquad\text{divide both sides by 3}\\\\\log(x+5)=-\dfrac{2}{3}\qquad\text{use the de}\text{finition of logarithm}\\\\(\log_ab=c\iff b^c=a),\ \log x=\log_{10}x\\\\\log(x+2)=-\dfrac{2}{3}\\\\\log_{10}(x+2)=-\dfrac{2}{3}\iff x+2=10^{-\frac{2}{3}}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n[/tex]
[tex]x+2=\left(\dfrac{1}{10}\right)^\frac{2}{3}\qquad\text{use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\\\\x+2=\sqrt[3]{0.1^2}\qquad\text{subtract 2 from both sides}\\\\x=-2+\sqrt[3]{0.01}\in D[/tex]
The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.
Part a) Total Cost
Total Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.
The total cost is ( $65,000 fixed) + (15,000 x $7.5)
=$65,000+$112,500
=$177,500
Part b) Total Revenue
Revenue from 1 tire = $25
Total tires recapped = 15000
So, Total revenue = 15000 tires x $25/tire
Total Revenue =$375,000
Part c) Total Profit
Total Profit = Revenue - Cost
Using the above values, we get:
Profit = $375,000 - $177,500
Profit = $197,500
Part d) Break-even Point
Break-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:
For break-even point
Cost of recapping x tires = Revenue from x tires
65,000 + 7.5 x = 25x
65,000 = 17.5 x
x = 3714 tires
Thus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.
If 20% of a = b, then b% of 20 is same as?
[tex]20\%\text{ of } a=b \Longleftrightarrow0.2a=b\\\\b\%\text{ of } 20 \Longleftrightarrow \dfrac{b}{100}\cdot20\\\\\dfrac{b}{100}\cdot20=\dfrac{b}{5}=\dfrac{0.2a}{5}=\boxed{\boxed{a}}[/tex]
The function f(x) = 2.54 can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the
multiplicative rate of change of the function?
Answer:
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.
Step-by-step explanation:
I think your function is off... but I can look at your ordered pairs.
(1,10)
(2,50)
(3,250),..
As the x increases by 1 the y is being multiply by a factor of 5 each time.
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.