Answer:
f(x) = log x – 1 ⇒ x-intercept = (10 , 0)
f(x) = -(log x – 2) ⇒ x-intercept = (100 , 0)
f(x) = log(-x – 2) ⇒ x-intercept = (-3 , 0)
f(x) = -log -(x – 1) ⇒ x-intercept = (0 , 0)
Step-by-step explanation:
* lets talk about the log
- If log a = b, that means the base of the log is 10
- To solve it we will change it to exponential function
∴ [tex]10^{b}=a[/tex]
* Now do that in each one of the problem
* ∵ f(x) = log x - 1
- To find the x-intercept put y = 0
∴ log x - 1 = 0 ⇒ add 1 to both sides
∴ log x = 1 ⇒ change it to exponential function
∴ [tex]10^{1}=x[/tex]
∴ x = 10
* The x-intercept = (10 , 0)
* ∵ f(x) = -(log x - 2)
- To find the x-intercept put y = 0
∴ -(log x - 2) = 0 ⇒ Multiply both sides by -1
∴ log x - 2 = 0 ⇒ add 2 to the both sides
∴ log x = 2 ⇒ change it to exponential function
∴ [tex]10^{2}=(x)[/tex]
∴ x = 100
* The x-intercept = (100 , 0)
* ∵ f(x) = log (-x - 2)
- To find the x-intercept put y = 0
∴ log (-x - 2) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=(-x-2)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -x - 2 = 1 ⇒ add 2 to the both sides
∴ -x = 3 ⇒ multiply both sides by -1
∴ x = -3
* The x-intercept = (-3 , 0)
* ∵ f(x) = -log -(x - 1)
- To find the x-intercept put y = 0
∴ -log -(x - 1) = 0 ⇒ multiply both sides by -1
∴ log -(x - 1) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=-(x-1)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -(x - 1) = 1 ⇒ multiply both sides by -1
∴ x - 1 = -1 ⇒ add 1 to both sides
∴ x = 0
* The x-intercept = (0 , 0)
Answer:
Please mark as Brainliest :)
Step-by-step explanation:
Fred bags groceries at Bilo. On average, he fills 21 bags for every three customers. The graph below, represent the total bags Fred filled based on the number of customers. What does the average rate of change represent?
Question 1 options:
For every customer, Fred fills 7 bags of groceries.
For every bag, there are 7 customers.
The customers who do not buy any groceries.
None of the above
Answer: For every customer, Fred fills 7 bags of groceries.
Answer:
The correct answer is : 'For every customer, Fred fills 7 bags of groceries'.
Step-by-step explanation:
Number bags filled by Fred for every 3 customers = 21 bags
Number bags filled by Fred for 1 customer = [tex]\frac{21 bag}{3}=7 bag[/tex]
So, 7 bags were filled for every customer.
The rate of change will be represented by 7 bags for each customer.
From the given option the correct statement is ;
For every customer, Fred fills 7 bags of groceries.
Choose the graph that matches the following system of equations:
4x + 2y = −2
x − 3y = 24
A) a line includes points 0 comma 8 and 3 comma 7. A line includes points negative 1 comma 0 and negative 6 comma 10
B) a line includes points 0 comma 8 and 3 comma 7. A line includes points negative 1 comma 3 and negative 2 comma 7
C) a line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6
B) a line includes points 0 comma negative 1 and 1 comma negative 5. A line includes points negative 1 comma negative 9 and 2 comma negative 6
Answer:
Option C.
Step-by-step explanation:
we have
[tex]4x + 2y = -2[/tex] -----> equation A
[tex]x-3y=24[/tex] -----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
using a graphing tool
see the attached figure
The intersection point is (3,-7) -----> is a common point both lines
The point (1,-3) belong to the line A
The point (6,-6) belong to the line B
therefore
a line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6
how can you calculate the area of the circle if you know the circle's circumference?
Answer with step-by-step explanation:
We know that the formula for area of a circle is given by:
Area of a circle = [tex] \pi r ^ 2 [/tex]
So to find the area of circle, we basically need to know the radius of the circle.
If we know the circumference of the circle, we can calculate the area of the circle too.
Formula for the circumference of the circle is given by:
[tex]2\pi r[/tex]
So if we know the circle's circumference, we can find the value of radius and then find the area of circle with it.
Answer:
We can calculate area of circle if we know the circumference
Step-by-step explanation:
Points to remember
`1). Circumference of circle = 2πr
2). Area of circle = πr²
Where 'r' is the radius of circle
Find area of circle
From the above two equations we have to calculate area and circumference of a circle with radius.
If we have circumference, the we can calculate radius of the circle
r = circumference/2π
If we get radius 'r' the we can calculate area
Area of circle = πr²
what percent of 5 is 7.4
148% soooo yeah that is the answer
Answer:
Step-by-step explanation:
Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the total length
One centimenter is 0.01 meters. So, you can write the measures as
[tex] 152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}[/tex]
Once this rewriting is done, getting the total length [tex]T[/tex] is quite trivial, since all measurements are in the same unit, and we can simply sum everything:
[tex]T = 152.40+205.10+310.39 = 667.89[/tex]
Hayley Baked A Cheescake. She used 5/8 pound cream cheese, 4/16 pound sugar, and 6/8 pound peaches. How much did the ingredients weigh altogether?
8 is a factor of 16, so you would multiply the numerator and denominator of 5/8 and 6/8 by 2. this would be 10/16 and 12/8. add all of the numbers together = 10+12+4 which equals 26. it’d be 26/16 or 1 and 10/16.
Answer:
1[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
equation: [tex]\frac{5}{8}[/tex]+[tex]\frac{14}{16}[/tex]+[tex]\frac{6}{8}[/tex]=x
but we cannot solve this because not all of the fractions have an equal denominator. so, we can multiply [tex]\frac{5}{8}[/tex] and [tex]\frac{6}{8}[/tex] each by two.
why?
because 8x2 is 16 and if you multiply them you get a common denominator of 16, making it way easier to add up the fractions.
so, what you do to the top you do to the bottom:
[tex]\frac{5}{8}[/tex] [tex]\frac{x2}{x2}[/tex] [tex]\frac{10}{16}[/tex] [tex]\frac{6}{8}[/tex] [tex]\frac{x2}{x2}[/tex] [tex]\frac{12}{16}[/tex]
so, [tex]\frac{10}{16}[/tex]+[tex]\frac{12}{16}[/tex]+[tex]\frac{4}{16}[/tex] equals to [tex]\frac{26}{16}[/tex].
[tex]\frac{26}{16}[/tex] = 1 [tex]\frac{10}{16}[/tex].
however 1[tex]\frac{10}{16}[/tex] can be simplified more.
divide top and bottom by 2 and get 1[tex]\frac{5}{8}[/tex]
the picture would be the work shown. messy kuz i used paint from windows with a mouse but tried to make it neat as possible.
plz give me a brainliesttttt
Attachments Are Below 15 Points
Answer: A is not true
Step-by-step explanation: This is because a rule of dilation. If you dilate an object, then the angle will stay the same. thus, statement A is false.
Subtract.
(5x^2 - 3x - 2) - (-2x^2 - +10)
Express the answer in standard form.
Enter your answer in the box
Answer:
7x^(2)-3x+8
Step-by-step explanation:
(5x^(2) - 3x - 2) - (-2x^(2) - +10)
(5x^(2))- (-2x^(2))=7x^(2)
(- 2)-(+10)=+8
7x^(2)-3x+8
Final answer:
To subtract (-2x² + 10) from (5x² - 3x - 2), change the signs of the second polynomial and combine like terms. The final result is 7x²- 3x - 12.
Explanation:
The question asks to subtract one polynomial from another, specifically to subtract (-2x²+ 10) from (5x² - 3x - 2). The subtraction of polynomials involves changing the signs of the polynomial being subtracted and then combining like terms. The process will be as follows:
First, change the signs of the second polynomial: -(-2x²) becomes +2x², and -(+10) becomes -10.
Then, combine the like terms with the first polynomial: (5x² + 2x²) becomes 7x², -3x stays the same as there are no like terms, and (-2 - 10) becomes -12.
Therefore, the answer in standard form is 7x²- 3x - 12.
Find the equation of the line below.
y=1/2x is your answer :)))
Answer:
y=1/2x is your answer :)))
Step-by-step explanation:
Two cars left the city for a suburb, 120 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 1 hour before the other car. Find the speeds of both cars.
Answer:
V1 = 60 km/h
V2 = 40 Km/h
Step-by-step explanation:
The speed of an object is defined as
Speed = distance / time
Let
V1 be the speed of the faster car
V2 be the speed of the other car
t1 the time it took for the first car to arrive
t2 the time it took for the second car to arrive
d1 the distance traveled by first car
d2 the distance traveled by second car
We know thanks to the problem that
V1 = V2 + 20 Km/h
t1 = t2 - 1 hour
d1 = d2 = 120 Km
d1 = V1 * t1
d2 = V2* t2
V1 * t1 = V2* t2
V1* t1 = (V1 -20)*(t1 +1)
The system of equations
(V1 -20)*(t1 +1) = 120
V1 * t1 = 120
120 + (120/t1) -20*t1 = 140
(120/t1) -20*t1 = 20
Which gives,
t1 = 2
This means
V1 = 60 km/h
V2 = V1 - 20 Km/h = 40 Km/h
Answer: 60 km/h, and 40 km/h
Step-by-step explanation:
(X+1)^3/2-2=25 solve
Answer:8
Step-by-step explanation:
Move all terms not containing x to the right side of the equation.Raise each side of the equation to the 2 /3 power to eliminate the fractional exponent on the left side.
Solve the equation for x .
Answer:
[tex] x = 8 [/tex]
Step-by-step explanation:
[tex] (x + 1)^\frac{3}{2} - 2 = 25 [/tex]
[tex] (x + 1)^\frac{3}{2} = 27 [/tex]
[tex] \left((x + 1)^\frac{3}{2} \right)^\frac{2}{3} = 27^\frac{2}{3} [/tex]
[tex] x + 1 = 3^2 [/tex]
[tex] x + 1 = 9 [/tex]
[tex] x = 8 [/tex]
ABC HAS A VERTICES. A(-2,10), B(4,8),C(2,4). determine the coordinates of A',B',AND C' HAS UNDERGONE THE DESCRIBED TRANSFORMATION. A DILATION WITH THE SCALE FACTOR OF3 AND A CENTER OF DILATION AT THE ORIGIN.
Answer:
A'(-6,30)
B'(12,24)
C'(6,12)
Step-by-step explanation:
By definition, dilation is a tranformation in which the the image and the pre-image have the same shapes but differente sizes.
You know that:
- The vertices of ABC are: A(-2,10), B(4,8),C(2,4).
- The scale factor is 3.
- The center of dilation is at the origin.
By definition, if the scale factor is greater than 1, then the image is an enlargement.
Therefore, you must multiply each original vertex by 3:
(x,y)→(3x,3y)
Then the coordinates A',B' and C' are:
A'→ [tex](-2(3), 10(3))=(-6,30)[/tex]
B'→ [tex](4(3), 8(3))=(12,24)[/tex]
C'→ [tex](2(3), 4(3))=(6,12)[/tex]
Hello people of AMERICA!!! :)
PLEASE HELP ME
When keeping records, expenses should be
A. added
B. subtracted
C. multiplied
D. divided
Help me accidentally checked in
Answer: b) 16
Step-by-step explanation:
[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=2\cdot \cdot 2\cdot 2\cdot 2=\boxed{16}[/tex]
Answer:
[tex]\boxed{\bold{16}}[/tex]
Step By Step Explanation:
Factor: [tex]\bold{64=4^3}[/tex]
[tex]\bold{\left(4^3\right)^{\frac{2}{3}}}[/tex]
Apply Exponent Rule [tex]\bold{\left(a^b\right)^c=a^{bc}: \ \left(4^3\right)^{\frac{2}{3}}=4^{3\cdot \frac{2}{3}}=4^2}[/tex]
[tex]\bold{4^2}[/tex]
Refine
[tex]\bold{16}[/tex]
Use the image to determine the volume of the rock.
Initial volume:
Final volume:
Volume of rock:
Answer:
Initial Volume: 20 mL
Final Volume: 32 mL
Volume of the rock: 12mL
Step-by-step explanation:
From the image we see that the initial volume of water is 20 mL, and after the rock is put into the flask, the final volume is 32 mL. From this we conclude that the volume of the rock must be 32mL-20mL = 12 mL.
Thus we have:
Initial Volume: 20 mL
Final Volume: 32 mL
Volume of the rock: 12mL.
Answer:
20
32
12
Step-by-step explanation:
Chad's family traveled [tex]\frac{5}{8}[/tex] of the distance to his grandmother’s house on Saturday. They traveled [tex]\frac{1}{3}[/tex] of the remaining distance on Sunday. What fraction of the total distance to his grandmother’s house was traveled on Sunday?
a whole or 1, is when the numerator and denominator are the same, namely 2/2, 3/3, 10000/10000 is a whole.
on Saturday they travelled 5/8 of the way, now, the whole being 8/8, so if we take 5/8 from 8/8, we're simply left with 3/8, that's the remaining distance to grandmas house.
on Sunday they travelled 1/3 of that remaining amount, how much is that? well, is simply their product,
[tex]\bf \cfrac{3}{8}\cdot \cfrac{1}{3}\implies \cfrac{3}{3}\cdot \cfrac{1}{8}\implies \cfrac{1}{8}[/tex]
Which of the following options is true about the solution to the given set of equations
y=6x + 9
y=6x + 2
Answer:
y=6x + 9
Hope this helped!
an actor will earn d dollars this year. His agent Collects a Commission of 10% of all his earnings. which expression shows how many dollars the actor will earn this year after the agent's commission is Deducted?
Answer: d - (d x .1)
Step-by-step explanation: The expression that will show how much the actor will earn is d - (d x .1). D is the actor’s earnings and d x .1 is the commission of their agent.
Final answer:
The expression that shows how many dollars the actor will earn this year after the agent's commission is deducted is d - 0.1d. The agent collects a commission of 10% of the actor's earnings, which is subtracted from the total earnings.
Explanation:
The expression that shows how many dollars the actor will earn this year after the agent's commission is deducted is:
d - 0.1d
Since the agent collects a commission of 10% of the actor's earnings, we can multiply the earnings by 0.1 to find the amount of commission. Subtracting this amount from the total earnings gives us the amount the actor will earn after the commission is deducted.
Find the area of a 6-gon with side length 10. Round to a whole number.
Answer:
Area = 260
Step-by-step explanation:
The formula for the area of a 6-gon is
Area = 3*sqrt(3) * side^2 / 2
side = 10
Area = 3 * 1.7321 * 100/2
Area = 259.8
Area = 260
Can you help me with this?
Volume is L x W x H. Since the three dimensions are all multiplied by each other it doesn't matter the order.
This means the answer would be D.
Which of the following is a point slope equation of a line that passed through the points (10,5) and (4-7)
Answer:
y - 5 = 2(x - 10)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (10, 5) and (4, -7). Substitute:
[tex]m=\dfrac{-7-5}{4-10}=\dfrac{-12}{-6}=2[/tex]
[tex]y-5=2(x-10)[/tex]
A room contains 55 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the number of rows.
Answer:
i believe its 27
Step-by-step explanation:25 times two= 50 27 times two= 54 +one more is 55. so it is 27
Answer:
11 rows.Step-by-step explanation:
Givens
The room contains 55 chairs arranged in rows.The number of rows is one more than twice the number of chairs.We know that the total number of chairs must be the product between the number of chairs per row and the total number of rows, which can be expressed as
[tex]c \times r = 55[/tex]
Where [tex]c[/tex] represents the number of chairs per row and [tex]r[/tex] representes the number of rows.
The second given statment defined a second equation
[tex]r=2c+1[/tex]
Now, we can substitute the second equation into the first one, and solve
[tex]c \times r = 55\\c (2c+1)=55\\2c^{2}+c-55=0[/tex]
Which can be factored by multiplying the expression by 2, and solve has a perfect trinomial
[tex]2(2c^{2}+c-55)=0\\2^{2}c^{2}+2c- 110=0\\(2c)^{2}+2c-110=0[/tex]
So, we need to find two number which product is 110 and is 1. If you think this through, those numbers are 11 and 10, because 11*10=110 and 11-10=1.
The factors are
[tex]\frac{(2c+11)(2c-10)}{2} =0[/tex], we have to divide by the number we multiplied before, then we simplify this number with the second factor
[tex](2c+11)(c-5)=0[/tex]
Where the positive solution is the only one that can be part of the answer because it doesn't make sense if we say -3 chairs. So,
[tex]c-5=0\\c=5[/tex]
This means there are 5 chairs per row.
Then, we use this value to find the other one.
[tex]c \times r=55\\5 \times r=55\\r=\frac{55}{5}\\ r=11[/tex]
Therefore, there are 11 rows and 5 chairs per row.
find missing number. show work. 120-35=100-?=60+?
Answer:
15 and 25
Step-by-step explanation:
First find 120-35=85
so 100-?=85 so ?=15
and 60+?=85 so ?=25
Answer: 120-35= 100 - 15 = 60 + 25
Step-by-step explanation:
You are just trying to make them all equal to 85 because the original sum of 120-35 is 85. so you are setting the rest of the equations to 85 as well.
Kaitlin spent 2/3 of an hour on homework. Her sister Judy spent 1 1/2 times that amount. Explain why Judy’s homework time is between 2/3 of an hour and 1/2 of an hour?
[tex]\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Judy spent time}}{\stackrel{\textit{Kaitlin's time}}{\cfrac{2}{3}}\cdot \cfrac{3}{2}}\implies \cfrac{2}{2}\cdot \cfrac{3}{3}\implies 1~\hfill \boxed{\cfrac{1}{2}}\rule[0.35em]{3em}{0.25pt}\stackrel{\stackrel{Judy's}{\downarrow }}{1}\rule[0.35em]{5em}{0.25pt}\stackrel{1\frac{2}{3}}{\boxed{\cfrac{2}{3}}}[/tex]
so, Judy's time is really 1 hour exactly.
and on the number line, we could place that 1 in between the first half and the two thirds of the of the next number, as you see above.
There is a mistake in the question as Judy's homework time cannot be between 2/3 and 1/2 of an hour if she spent 1 1/2 times as much time as Kaitlin who spent 2/3 of an hour. Judy's homework time would be 1 hour.
The question seems to have a typo or a logical error, as it is not possible for Judy's homework time, which is 1 1/2 times Kaitlin's time, to be between 2/3 of an hour and 1/2 of an hour. Instead, if Kaitlin spent 2/3 of an hour on homework, Judy would have spent (2/3) * (3/2) = 1 hour on homework, which is more than both 2/3 and 1/2 of an hour. It appears that Judy's actual homework time would be exactly one hour, not between the two given times.
Pick the correct description of the line y=-5/3x
This line is in slope intercept form y = mx+b
Since we can write it as y = (-5/3)x + 0
m = -5/3 is the slope
b = 0 is the y intercept
The two points (0,0) and (3,-5) are on the straight line.
Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get right
Answer: The correct answer is 85%
Step-by-step explanation:
If you divide 17 by 20 then you'll get 0.85 which is the same as 85%.
17 ÷ 20 = 0.85, OR, 85% ← Work* Hopefully this helps:) Mark me the brainliest:)!!!
Claire got 85% of the questions correct on her vocabulary quiz by answering 17 out of 20 questions correctly.
Claire got 17 out of 20 questions correct on her vocabulary quiz. To calculate the percentage of questions Claire got right, you would use the following formula:
Percentage Correct = (Number of Correct Questions \/ Total Number of Questions) x 100%
Applying Claire's numbers to this formula:
Percentage Correct = (17 \/ 20) x 100% = 0.85 x 100% = 85%
Therefore, Claire got 85% of the questions correct on her quiz. This is a high percentile, which indicates she did very well, considering that seventy percent of students answered 16 or fewer questions correctly and thirty percent of students answered 16 or more questions correctly. A higher percentile is generally considered good, as it means answering more questions correctly, which is desirable.
which answer choice is equivalent to the expression 3x-1/2?
guys oml please help me i am failing this class and i need to get all 400 points of the extra credit assignment. PLEASE )):
You can substitute a number in for x and compare the answer choices (not the most efficient way but it's how I would do it). Let's just say x = 5. Then the expression would equal 0.25819889. Substitute 5 in for x is the answer choices and see which one is the same.
A) simplified is 0.004 repeating
B) simplified is 0.25819889
C) simplified is 0.12
D) simplified is 1.341640786
We can see that B is the right answer
Captain Tellez plans to reach a cruising altitude in his passenger plane and then maintain a cruising speed of 570 miles per hour for approximately 400 miles. Which is closest to the length of time, in minutes, that his plane will maintain cruising speed?
A. 0.70
B. 1.43
C. 42
D. 86
Answer:
option (c)
42 minutes
Step-by-step explanation:
Given in the question:
cruising speed of passenger plane = 570 miles/hour
distance passenger plane travelled = 400 miles
Formula to usedistance = speed x time
time = distance / speed
time = 400 / 570
= 0.7018 hours
1 hour = 60 minutes
228000 hours = 60 x 0.7018 minutes
= 42.1052 minutes
≈ 42 minutes
Closest to the length of time, in minutes, that Captain Tellez's plane will maintain cruising speed is 42 minutes.
Write an expression the represents the sum of any number plus 3
Answer: x + 3
Step-by-step explanation: In this question you need to know that a sum is the answer when you add numbers. In this case x = any number. The expression is x + 3
Answer:
Step-by-step explanation:
Hello
Being X represented on any number, the expression will be:
X+3
Best regards
A 50-foot flagpole is at the entrance of a building that is 300 feet tall. If the length of the flagpole's shadow is 30 feet at a certain time of day, how long is the building's shadow at that time? PLEASE HELP
Answer:
hard question
Step-by-step explanation: