log₅125 = c
[tex]125 = 5^{c}[/tex]
[tex]5^{3} = 5^{c}[/tex]
3 = c
Answer:
log₅125 = c
Step-by-step explanation:
The local service center advertises that it charges a flat
fee of $50 plus $8 per mile to tow a vehicle. The function
Cx x ( ) = + 8 50 represents the cost C (in dollars) of
towing a vehicle, where x is the number of miles the
vehicle is towed. Identify the slope and y-intercep
The slope of the linear equation C(x) = 8x + 50 is 8, indicating an $8 charge per mile, and the y-intercept is 50, the flat towing fee. Similar service-based costs from other examples also follow this linear model, with their unique slopes and y-intercepts corresponding to the per-hour or per-mile charges and flat fees.
Explanation:The function C(x) = 8x + 50 represents the cost of towing a vehicle, where C is the cost in dollars, and x is the number of miles the vehicle is towed. The slope of this line is 8, which indicates that the cost increases by $8 for every mile the vehicle is towed. The y-intercept is 50, representing the flat fee charged regardless of the distance towed, which is the cost when x (the number of miles) is 0.
Relating to the other examples provided, we can see a pattern in how these equations are structured for service-based costs. For instance, in Aaron's Word Processing Service, the total cost equation is y = 32x + 31.50, where the slope is 32 representing the hourly charge, and the y-intercept is 31.50, the fixed cost. Similarly, for Ethan's household appliance repairs, the equation is y = 20x + 25, with a slope of 20 and a y-intercept of 25. All these models illustrate how fixed fees and variable rates per service hour or mile can be represented in a linear equation format.
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What is the midpoint of ?
point M
point N
point P
point Q
Answer:
the answer is point N
Step-by-step explanation:
i dont have a graph to explain
The midpoint of a line segment is calculated using the formula Midpoint = ((x1 + x2)/2 , (y1 + y2)/2), which finds the average of the x-coordinates and y-coordinates of the two points. Unfortunately, without specific points, we can't provide a concrete midpoint.
Explanation:Unfortunately, your question is slightly unclear as we need more detail to accurately determine the midpoint of the segment. Generally, if you want to find the midpoint of a segment, you need two defined points. Knowing these two points, you can calculate the midpoint using the formula: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2). This formula calculates the average of the x-coordinates and y-coordinates of the two points, which gives you the coordinates of the midpoint.
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Solve for x.
2x^2-4x=0
Hey there!!
Equation given :
2x² - 4x = 0
Taking the common terms
2x ( x - 2 ) = 0
Divide by 2x on both sides
x - 2 = 0
Adding 2 on both sides ...
x = 2
And another answer would be zero as the whole equation is zero,
Hence the answer : ( 0 , 2 )
Hope it helps@+!!
The value x for equation 2x² - 4x = 0 is 2.
Given equation:
2x² - 4x = 0
Add 4x on both side,
2x² = 4x
Divide x on both side
2x = 4
Divide 2 on both side,
x = 2.
Therefore, the value x for equation 2x² - 4x = 0 is 2.
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if(x)=x/2-3 and g(x)=4x2+x-4 find (f+g)(x)
[tex](f+g)(x)=4x^2+\frac{3}{2}x-7[/tex]
Answer:
[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=\dfrac{x}{2}-3[/tex]
[tex]g(x)=4x^2+x-4[/tex]
To find: (f+g)(x)
It is a composite function. Sum of f and g function.
[tex]h(x)=f(x)+g(x)[/tex]
[tex]h(x)=\dfrac{x}{2}-3+4x^2+x-4[/tex]
Combine the like term
[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]
Hence, The sum of f(x) and g(x) would be [tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]
The total daily cost (in dollars) of manufacturing scented candles is given by the function C(b) = 250 + 3b, where b is the number of candles manufactured. Which function represents the average manufacturing cost, A, in terms of b?
The average total cost of manufacturing scented candles is given by the formula A(b) = C(b)/b = (250 + 3b)/b, where b is the number of candles manufactured.
Explanation:The concept of average total cost is key in the calculation. Given the function for total cost of the candles, C(b) = 250 + 3b, the average cost, A, can be calculated by dividing the total cost by the number of candles, b. Therefore, the function representing the average cost, A, in terms of b is given by A(b) = C(b)/b = (250 + 3b)/b. It's important to note that this function also signifies the 'economies of scale', stating as output number increases, the average cost falls.
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How to know what to do next in a geometry two column proof?
To do a two-column proof, you must know the definitions of the terms that are being used. Also, you must know the postulates and theorems you have learned so far. You look at the given information, and using the definitions, postulates, and theorems, you reason in your mind how to go from the given to the conclusion, step by step. You write each step and the accompanying reason that allows you to conclude each step.
Which expression is the completely factored form of 27x^3+y^6
Answer:
your answers C
Step-by-step explanation:
The factored form of the expression [tex]27x^3+y^6[/tex] is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]. The correct answer of the factored expression is option A
Given the expression;
[tex]27x^3+y^6[/tex]
This can be expressed as the sum of cubes
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
The given expression can also be written as the sum of cubes as shown:
[tex]27x^3+y^6 = (3x)^3+(y^2)^3[/tex]
We can see that:
a = 3x
b = y²
Substituting the given parameters into the formula above;
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\(3x)^3+(y^2)^3=(3x+y^2)((3x)^2-3xy^2+(y^2)^2)\\(3x)^3+(y^2)^3=(3x+y^2)(9x2-3xy^2+y^4)\\[/tex]
Hence the factored form of the expression is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]
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Maria had planned to walk 10 1/8 miles on wednesday, if she walked 7 2/8 miles in the morning how far would she need to walk in tge afternoon ?
Answer:
Distance Maria had to walk in the afternoon is [tex]2\frac{7}{8}[/tex]
Step-by-step explanation:
Lets take that Maria walked [tex]x[/tex] miles in the afternoon.
Distance walked in the morning + distance walked in the afternoon = [tex]10\frac{1}{8}[/tex]
⇒[tex]7\frac{2}{8} +x=10\frac{1}{8}[/tex]
[tex]\frac{58}{8} +\frac{8x}{8} =\frac{81}{8}[/tex]
[tex]\frac{58+8x}{8} =\frac{81}{8}[/tex]
[tex]58+8x=81[/tex]
[tex]8x=81-58\\[/tex]
[tex]8x=23[/tex]
[tex]x=\frac{23}{8}[/tex]
[tex]x=2\frac{7}{8}[/tex]
THIS one u probably have to choose more than one
Replace [tex]a_{n}[/tex] with 27, solve for [tex]a_{n-1}[/tex], and see if the result is a whole number.
27 = 2a ⇒ [tex]\frac{27}{2}[/tex] = a not a whole number NO
27 = 2a + 1 ⇒ 26 = 2a ⇒ 13 = a 13 is a whole number YES
27 = 3a ⇒ 9 = a 9 is a whole number YES
27 = 3a + 6 ⇒ 21 = 3a ⇒ 7 = a 7 is a whole number YES
27 = 3a + 1 ⇒ 26 = 3a ⇒ [tex]\frac{26}{3}[/tex] = a not a whole number NO
Answer: B, C, D
Which description is correct for the polynomial 4x^2+3x-2?
The first one is correct it is a Quadratic Polynomial.
Theo's mom bought an 8 pack of juice boxes at the store for $4. Find the unit rate for the juice boxes
A segment has a midpoint or ray AB is the name of ray
T T—>T
T F—>T
F T —>T
F F—>F
answer is TT->T or a
Answer:
A)
Step-by-step explanation:
Doughnuts are sold in bags anf cartons a bag holds 4 doughnuts and a carton holds ten doughnuts. Tom buys b bags of dougnuts and c cartons of doughnuts he buys a total of t doughnuts. Erite down a formula for t in terms of b and c
The formula is
T=4B+10C
A car drives at a speed of 90km/h for 2 hours and 20 mins how far does the car travel
Final answer:
The car travels approximately 210 kilometers in 2 hours and 20 minutes by multiplying its speed of 90km/h by the time duration converted to hours (2.333 hours).
Explanation:
The student's question involves calculating the distance a car travels at a constant speed over a given period of time. In this case, the car drives at a speed of 90km/h for 2 hours and 20 mins. To find the distance, you can use the formula: distance = speed × time. First, convert 2 hours and 20 mins into hours, which is 2 hours + 20/60 hours = 2.333 hours.
Next, multiply the speed by the time to get the distance:
Distance = 90km/h × 2.333 hours = 209.97 km
So, the car travels approximately 210 kilometers in 2 hours and 20 minutes.
Which platonic solid has twelve faces that are regular pentagons
Answer:
Dodecahedron
Step-by-step explanation:
Pls help! will give brainliest(geometry)
2. Linear Pair Postulate
4. 60° + m∠ACB = 180°
5. m∠ACB = 120°
6. definition of obtuse angle
Sue is placing cookies in bags. She has 10 peanut butter cookies and 16 oatmeal cookies. She will place the same number of cookies in each bag and there will be only one type of cookie in each bag. If sue places the greatest number of cookies possible in each bag, how many bags will she need?
How to turn 72 divided by 24 into a fraction
Every time you divide something by something else, you already have a fraction. A fraction is simply a different way to visualize a division. So, the following writings express the same concept:
[tex] 72\div 24 = \dfrac{72}{24} [/tex]
There's no conceptual difference between the two expressions, so you're not actuall "turning" 72 divided by 24 "into" a fraction, you're just writing it in another way.
x^2+50=0
What are the solutions to the equation over the complex numbers?
x=
or
x=
ANSWER= +/- 5i sqrt2
sqrt=square root sign to solve you subtract 50 so x^2=-50 then get the square root on both sides and you're left with x=5isqrt 2 the i comes from the negative sign inside the square root
+/- 5i sqrt2 is the solution
Triangle XYZ is isosceles with <Z as the vertex angle.
If <X = 5x+33, <Y = 33x+42,
Find <Z
Answer: ∠Z = 117.2°
Step-by-step explanation:
∠X and ∠Y are isosceles so they are congruent (equal to each other)
5x + 33 = 33x + 42
-5x -5x
33 = 28x + 42
-42 -42
-9 = 28x
[tex]\frac{-9}{28} = \frac{28x}{28}[/tex]
[tex]-\frac{9}{28} = x[/tex]
************************************************************
∠X + ∠Y + ∠Z = 180° Triangle angle sum theorem
5x + 33 + 33x + 42 + ∠Z = 180°
38x + 75 + ∠Z = 180°
-75 -75
38x + ∠Z = 105°
38[tex](-\frac{9}{28})[/tex] + ∠Z = 105°
-12.2 + ∠Z = 105°
+12.2 +12.2
∠Z = 117.2°
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Use the imaginary number i to rewrite the expression as a complex number:
The answer to the question is 10 + 9i, B.
A group of 485 people take a canoe trip. They fill up all avalible canoes that each hold 3 people with 273 people. The rest of the group will ride in canoes
that each hold 2 people. How many canoes will the group need? Write equations with unknown to show your steps.
Answer:
They will need 197 canoes.
Step-by-step explanation:
The first step is to find the ''3-people canoes'' that they filled.
Given that 273 people filled a certain number ''a'' of canoes that each hold 3 people, we know that is we multiply the number of canoes ''a'' by the number of people that can each canoe hold, we will obtain the number of people who
will take the canoe trip in the ''3-people canoes''. We write :
[tex]3a=273[/tex] ⇒
[tex]a=\frac{273}{3}=91[/tex]
We find that [tex]a=91[/tex] canoes. This means that 91 ''3-people canoes'' were filled each one with 3 people in order to hold 273 people in total.
The second step is to find the remaining people that won't take the ''3-people canoes''. We do this by subtracting 273 people to the total 485 people.
[tex]485-273=212[/tex]
We know that 212 people will travel in the ''2-people canoes''. Using a similar reasoning and defining as ''b'' to the total number of ''2-people canoes'' we write :
[tex]2b=212\\b=\frac{212}{2}=106\\ b=106[/tex]
We find that [tex]b=106[/tex] canoes is the total number of ''2-people canoes'' that we need If we want them to be filled up with 212 people.
The total number of canoes that the group will need is the sum of ''3-people canoes'' and ''2-people canoes'' :
[tex]Total=a+b=91+106=197[/tex]
The group of 485 people will need 197 canoes.
The ratio of cats to dogs seen by a veterinarian on one day is 2 to 5. If the vet saw 40 dogs in one day how many cats did he see
Answer:
He sees 16 cats that day
Step-by-step explanation:
If the veterinarian sees 5 dogs a day then he also sees 2 cats.
If he sees 40 dogs a day then,
⇒[tex]\frac{2}{5} *40[/tex]
=[tex]16[/tex] Cats
He sees 16 cats that day.
The correct option is C.
Approximately 29 dogs were seen by the vet in one day.
To solve this problem, we first need to find the fraction of dogs among the total animals seen by the vet.
Given that the ratio of cats to dogs is 2 to 5, the total parts in this ratio is 2 + 5 = 7.
Now, to find the fraction representing dogs, we divide the number of parts representing dogs (5) by the total parts (7). This gives us 5/7.
Next, to find out how many of the 40 animals were dogs, we multiply the total number of animals seen (40) by the fraction representing dogs:
40 animals × (5/7) = (40 × 5) / 7 = 200/7 ≈ 28.57
Since we're looking for an approximation, we round this to the nearest whole number, which is 29.
So, approximately 29 of the animals seen were dogs, which corresponds to option C.
The complete question is here:
The ratio of cats to dogs seen by a vet in a day is about 2 to 5. If a vet saw 40 animals in one day, about how many were dogs?
A. 5
B. 12
C. 29
D. 40
A frost has caused a temporary spike in the price of orange juice. The price is now $10 a gallon. Before the frost, the price was $4 a gallon. How much more expensive is orange juice now? A) 0.25 times b) 1.5 times c) 2.5 times d) 5 times e) 6 times
HELP ASAP PLEASE!!!
When we measure something, we do not have specify what units we are measuring in.
A. True
B. False
Answer:
B- False
Step-by-step explanation:
that is very false bc the units mean alot
What is the remainder when the polynomial 5x2+10x−15 is divided by x + 5? Enter your answer in the box.
There are two ways you can approach this:
1) Factor [tex]\frac{5(x-1)(x+3)}{x+5}[/tex] this equals to [tex]\frac{5x^2+10x-15}{x+5}[/tex]
2) or divide which equals to 5x+35+[tex]\frac{160}{x+5}[/tex]
Write y= -4x² -16x -14 in vertex form.
A) y= -4(x-16)² -14
B) y= 4(x+4)² +2
C) y= -4(x+2)² +2
D) y= (x+2)² -14
B and D are both wrong. B has +4 outside the brackets. It is - 4
D is wrong because there is no 4 of any kind outside the brackets.
A is incorrectly represented inside the brackets as 16. That's not right
That only leaves C. <<<< Answer
Graphs
Notice that the red parabola and the green one are the same thing.
Red: y = -4x^2 - 16x - 14
Green: y = -4(x + 2)^2 + 2
Question 6
Solve the following system of equations by using the elimination method.
x + y = 4
2x + 3y = 9
(3, 1)
(-2, 1)
(3, -1)
Answer is (3,1)
x + y = 4
2x + 3y = 9
We multiply the first equation by -2 to eliminate x
-2x - 2y = -8
2x + 3y = 9
-------------------(add both equations)
0 + y = 1
So y =1
Now plug in 1 for y in first equation
x + y = 4
x + 1 = 4
Subtract 1 on both sides
x = 3
Answer is (3,1)
Find the slope between the pair of points using the slope formula. (4,−5) and (0,−13)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (4, -5) and (0, -13).
Substitute:
[tex]m=\dfrac{-13-(-5)}{0-4}=\dfrac{-13+5}{-4}=\dfrac{-8}{-4}=2[/tex]
NEED ANSWER ASAP!!!!!!
3. A local band had a concert and made $1,824 from ticket sales. If each ticket cost $16, how many tickets did the band sell? (Write and solve an equation.)
What are you trying to find?
What is the important information?
Write the equation below. What does the variable represent?
Solve and show work below.
First take not of the total sales and the cost of each ticket.
1,824 and 16
Now setup the equation
16x=1824
To solve this divide 1824 by 16 getting
X=144
x is the total tickets sold
Each ticket (t) costs $16. The band made a total of $1,824 from ticket sales, meaning that 16t=1,824, because the total amount of 16 dollar tickets sold is equal to the total made from ticket sales.
The equation is:
16t=1,824.
You are trying to find the amount of tickets sold by solving the equation.
t stands for the total amount of tickets sold.
Solving the equation:
16t=1,824
Divide both sides by 16.
t=114
114 tickets were sold. 114*16=1,824. This means that when 114 $16 tickets were sold, the band did make $1,824, which shows that 114 is the correct answer.
I hope this helps :)