Let x be a time in hours and y be an amount of remaining entries. You have that:
At start Ariel wants to write 8 entries for her blog. This means that x=0 and y=8 (0 entries were written). The point with coordinates (0,8) belongs to needed graph.After 2 hours, she has 5 entries left. This gives you that at x=2, y=5 and graph passes through the point (2,5).After 4 hours, she has 2 entries left. This gives you that at x=4, y=2 and graph passes through the point (4,2).Find the slope of the line that is passing through the points [tex] (x_1,y_1)[/tex] and [tex] (x_2,y_2)[/tex] by formula
[tex] \dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope is
[tex] \dfrac{5-2}{2-4}=-1.5.[/tex]
Answer: graph of line going through (0, 8) with a slope of -1.5
Could a reflection followed by a rotation ever be described as a single rotation?
A freight train travels 260 km in the same time a passenger train travels 320 km. If the passenger train averages 15km/hour faster than the freight train, what is the average speed of the freight?
Answer:
13
Step-by-step explanation:
If F(x)=integral of sqrt(t^3+1) dt from 0 to x, then F'(2)=?
F'(2) = 3
[tex]\int\limits^x_0 {\sqrt{t^3+1}} \, dt[/tex]
Using Fundamental Theorem of Calculus:
Since x = 2, you now have:
[tex]\int\limits^2_0 {\sqrt{t^3+1} } \, dt[/tex]
so F'(x) = [tex]\sqrt{t^3+1}[/tex]
--> F'(2) = [tex]\sqrt{2^3+1}[/tex] = [tex]\sqrt{9}[/tex] = 3
so F'(2) = 3
F'(2) is the square root of [tex](2^3+1)[/tex], which simplifies to 3.
Explanation:If F(x) is defined as the integral of [tex]\sqrt(t^3+1)[/tex] dt from 0 to x, then F'(x) represents the derivative of F with respect to x. According to the Fundamental Theorem of Calculus, the derivative of an integral function of this form is simply the value of the function inside the integral evaluated at x. Therefore, F'(2) is the square root of (2^3+1), which simplifies to sqrt(9), or 3.
In the Diagram, rectangle ABCD is split in half by like AC. What is the value of tan X?
A. 3/4
B. 4/5
C. 3/5
D. 5/4
E. 4/3
The answer is E)4/3
That is because tangent X = a/b
Since this is a rectangle, the parallel sides are equal.
In this case, a=4, B=3, and C=5.
So, tanX = 4/3
Hope this helps!
Eight scores have an average of six. Scores of 15 and x increase the average to 7. Find x
Final answer:
To find the value of x, multiply the original average of 6 by the original number of scores (8) to find the initial total. Then, use the new average of 7 to find the new total when the two scores (15 and x) are added. Solve for x to find that it equals 7.
Explanation:
The question asks to find the value of x such that when two new scores, 15 and x, are added to a set of eight scores with an average of six, the new average for all ten scores is seven.
To solve this, first calculate the total sum of the original scores by multiplying the average by the number of scores: 6 × 8 = 48. Adding the two new scores, the equation to find the new total sum is 48 + 15 + x = 7 × 10 (since there are now ten scores). Simplify this to get 63 + x = 70, therefore x equals 7.
Select the best possible first step to solving the system by first eliminating the x variable.
3x – 9y = 6
2x – 11y = 6
Multiply the first equation by –2 and multiply the second equation by 3.
Multiply the first equation by –2 and multiply the second equation by –3.
None of the above
Multiply the first equation by 2 and multiply the second equation by 3.
Select the best possible first step to solving the system by first eliminating the x variable.
3x – 9y = 6
2x – 11y = 6
Multiply the first equation by –2 and multiply the second equation by 3.
Multiply the first equation by –2 and multiply the second equation by –3.
None of the above
Multiply the first equation by 2 and multiply the second equation by 3.
Final answer:
The best step to eliminate the x variable from the given system of equations is to multiply the first equation by –2 and the second by 3, facilitating the cancellation of the x terms and allowing for straightforward calculation of y.
Explanation:
To select the best possible first step to solving the system by first eliminating the x variable from the given equations 3x – 9y = 6 and 2x – 11y = 6, we need to make the coefficients of x in both equations equal in magnitude but opposite in sign. This way, when we add the equations together, the x terms will cancel out, leaving us with an equation in terms of y only. Here are the options analyzed:
Multiply the first equation by –2 and multiply the second equation by 3, resulting in –6x + 18y = –12 and 6x - 33y = 18. Adding these together will eliminate the x variable, which is the desired outcome.
Multiplying the first equation by –2 and the second equation by –3 does not effectively eliminate x because it gives us –6x + 18y = –12 and –6x + 33y = –18, which does not help in eliminating x when added or subtracted.
Multiplying the first equation by 2 and the second equation by 3 does not suit our needs for elimination as it results in 6x – 18y = 12 and 6x – 33y = 18, where adding or subtracting does not eliminate x.
Therefore, the correct first step is to multiply the first equation by –2 and multiply the second equation by 3. This approach aligns with standard algebraic methods for solving systems of equations by elimination, providing a clear and effective strategy to simplify the problem by removing one variable, allowing for the straightforward solution of the other.
if m1 = 40 what is the measure of 4
x=3g+2
how do i make g the subject?
The equation will be if x = 3g + 2 after transformation g as subject g = x / 3 - 2 / 3.
What is equation?An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.
Given:
x = 3g + 2
Rearrange the terms as shown below
x - 2 = 3g (Here the constant term is brought to the left)
x - 2 / 3 = g (Take the term 3 to the left side as shown)
x / 3 - 2 / 3 = g
g = x / 3 - 2 / 3
Thus, the equation will be g = x / 3 - 2 / 3.
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The g subject of the equation x = 3g + 2 is g = (x - 2) / 3.
To make g the subject of the equation x = 3g + 2, you need to isolate g on one side of the equation. Here is a step-by-step guide:
Subtract 2 from both sides of the equation to get x - 2 = 3g.
Divide both sides of the equation by 3 to isolate g, resulting in g = (x - 2) / 3.
Now, g is the subject of the equation, and it can be expressed as g = (x - 2) / 3.
2m²·2m³=?
Simplify.Your answer should contain only positive exponents.
Applying the rule of exponents, 2m² × 2m³ will be simplified as: [tex]4m^5[/tex].
The Product Rule of ExponentsWhen multiplying exponents with the same base, add the exponents.
The rule is: [tex]a^m \times a^n = a^{(m+n)}[/tex].
Given:
2m² × 2m³
Apply the product rule of exponents for multiplication
(2 × 2)(m²+³)
2m² × 2m³ = [tex]4m^5[/tex]
Therefore , applying the product rule of exponents, 2m² × 2m³ will be simplified as: [tex]4m^5[/tex].
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Using the completing-the-square method, find the vertex of the function f(x) =- 3x2 + 6x − 2 and indicate whether it is a minimum or a maximum and at what point.
To find the vertex of the quadratic function using the completing-the-square method, rearrange the equation in vertex form, complete the square, and simplify. The vertex of the given function is located at (1, 1) and represents a maximum point.
Explanation:To find the vertex of the function f(x) = -3x^2 + 6x - 2 using the completing-the-square method, follow these steps:
Start by rearranging the equation in the form f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Factor out the coefficient of x^2. In this case, factor out -3: f(x) = -3(x^2 - 2x) - 2.Complete the square by adding and subtracting the square of half the coefficient of x. In this case, add and subtract (2/2)^2 = 1: f(x) = -3(x^2 - 2x + 1 - 1) - 2.Simplify: f(x) = -3((x - 1)^2 - 1) - 2.Expand and simplify: f(x) = -3(x - 1)^2 + 3 - 2.Final vertex form: f(x) = -3(x - 1)^2 + 1.The vertex of the function is at the point (1, 1). Since the coefficient of x^2 is negative, the vertex represents a maximum point. Therefore, the vertex is a maximum point located at (1, 1).
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Charlie, who is 4 feet tall, walks away from a streetlight that is 16 feet high at a rate of 4 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time. (Hint: First use similar triangles to express s as a function of the distance d from the streetlight to Charlie.) ...?
Write some multiples of 5 and 8. Use the least common multiple to simplify 120\160
Christopher is a graphic designer who creates business websites. It takes him 2.4 hours to complete one website page. He finds out about a new software program that will cut his time in half for completing one page, but it will take him 15 hours to learn the new program.
Which equation can be used to find the number of website pages, x, that Christopher needs to create so that his time spent using the new program will be the same as his current time?
Answer:
1. 2.4x=1.2x+15
2. 13
Step-by-step explanation:
What is the solution to the equation 9 –3x ≈ 7 ?
Answer?
x = 0.376
x = 0.295
x = –0.295
x = –0.376
...?
x=0.295 this is the correct answer
By decreasing each side of a rectangle by 1 unit, the area decreased from 60 square feet to 44 square feet. Find the perfect decrease in area. ...?
Answer:
Decrease in area would be 26.67%
Step-by-step explanation:
By decreasing each side of a rectangle by 1 unit area of the rectangle decreases from 60 square feet to 44 square feet.
So decrease in area = 60 - 44 = 16 square feet.
Percentage decrease in the area will be = [tex]\frac{\text{Decrease in area}}{\text{Area before decrease}}\times 100[/tex]
= [tex]\frac{16}{60}\times 100[/tex]
= [tex]\frac{160}{6}[/tex]
= 26.67%
Decrease in area would be 26.67%
The perfect decrease in area of the rectangle when each side is decreased by 1 unit, resulting in a decrease from 60 square feet to 44 square feet, is 16 square feet.
The question asks to calculate the perfect decrease in area of a rectangle when each side is decreased by 1 unit, resulting in a change in area from 60 square feet to 44 square feet. To solve for this, let's assign variables to the original dimensions of the rectangle. Let the length be L and the width be W.
The original area A1 is given by L imes W = 60. After reducing each dimension by 1, the new length and width are L - 1 and W - 1, respectively, so the new area A2 is (L - 1) imes (W - 1) = 44. The perfect decrease in area is the difference between the original and new areas, which is 60 - 44 = 16 square feet.
Brady Seitz’s charge account statement showed a previous balance of $1,247.55, a finance charge of $4.72, and new purchases of $112.50. What is the new balance? A. $1,364.77 B. $1,987.00 C. $987.66 D. None of the above.
In one community ,84% of the animals shelters microchip cats and dogs before adoption. if 21 shelters in the community microchip cats and dogs, how many animal shelters are in that community
B 6 /5 = 10
a. 44
b. 4
c. 56
d. 8
Here are the IQ scores of 10 randomly chosen fifth-grade students: 145,139,126,122,125,13,96,110,118,118. TRUE OR FALSE If the value 96 were removed from the data set, the IQR of the remaining 9 IQ scores would be lower than the IQR of all 10 scores.
False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.
The given observations are 145, 139, 126, 122, 125, 113, 96, 110, 118, 118.
What is inter quartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Interquartile range = Upper Quartile - Lower Quartile
Q2=Q3 - Q1
Ascending order of the given observation is
96, 110, 113, 118, 118, 122, 125, 126, 139, 145
Here, Q1 (median of lower quartile) =113 and
Q3 (median of upper quartile) =126
Q2= 126-113
= 13
The value 96 were removed from the data set, so
110, 113, 118, 118, 122, 125, 126, 139, 145
Q1 =(113+118)/2 =115.5
Q3 =(126+139)/2
= 132.5
Q2 =132.5-115.5
= 17
False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.
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By selling old cd's, sarah has a store credit card for $153.a new cd costs $18 .what are the possible numbers of new cd's sarah can buy
Julia is allowed to watch no more than 5 hours of tv a week. So far this week, she has watched 1.5hr. Write and solve the inequality to show how many hours of tv Julia can still watch this week. This also has to be explaned
Select all ratios equivalent to 3:10
2:4, 21:70, 18:60, 10:12
Bianca has 25¢ she has some nickles an. d pennies how many different combonation of nickles and pennies could bianca have?
I will fan you if you help!!
name all of the angles that are congruent to <B in the figure below
we know that
m∠C=m∠B ----------> by vertical angles
m∠F=m∠B ----------> by corresponding angles
m∠G=m∠B --------> by alternate exterior angles
therefore
the answer is
Angles C, F and G
The angles of a triangle are 2x, 3x, and 4x degrees. Find the value of x.
A) 20
B) 30
C) 40
D) 50
Answer:
Option A) 20 ... ... ... ✔
Step-by-step explanation:
[tex] \underline{\tt{❖ \: Given \: \: ❖}}[/tex]
interior angle of triangle 2x,3x4x[tex] \underline{\tt{❖ \: Solution \: ❖}}[/tex]
We know that interior sum of all angle is 180°
[tex]\; \;\dashrightarrow \;\pmb {2x+3x+4x=180°}[/tex]
[tex]\; \;\dashrightarrow \;\pmb {9x=180°}[/tex]
[tex]\; \;\dashrightarrow \;\pmb {x = \dfrac{180}{9} }[/tex]
[tex] \; \;\dashrightarrow\; \; {\pmb{\underline{\boxed{\red{\frak { x = 20 }}}}}} \; \green\bigstar[/tex]
How many solutions to this equation?
9x + 16 = 4x
A. 1
B. 0
C. infinitely many
12.56 rounded to the nearest tenth
12.56 rounded to the nearest tenth becomes 12.6.
Rounding some number to a specific value is making its value simpler for better readability or accessibility.
The digit in the hundredth place is 6. The next smaller place value is the tenth place.
If the digit in the next smaller place value is 5 or greater, round up:
Since the digit in the tenth place is 5, we round up.
Change the digit in the hundredth place to 0 and increase the digit in the tenth place by 1:
12.56 rounded to the nearest tenth becomes 12.6.
Therefore, 12.56 rounded to the nearest tenth is 12.6.
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what will an investment of 6000 Euro at 7% p.a compound interest amount to after 5 years if the interest is compounded:
a) annually b)quarterly c) monthly? what will an investment of 6000 Euro at 7% p.a compound interest amount to after 5 years if the interest is compounded:
a) annually b)quarterly c) monthly?
Graph x2 + 9y2 = 25. What are the domain and range?
Someone please help me !
(Picture below)
A two-digit number from 10 to 99, inclusive, is chosen at random. What is the probability that this number is divisible by 5?
The probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.
How to find the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus he probability of failure of a event is equal to the difference of the 1 to the success of the event.
A two-digit number from 10 to 99, inclusive, is chosen at random. The probability that this number is divisible by 5 has to be find out.
The number of two-digit numbers which is divisible b 5 from 10 to 99 are 18.
[tex](10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95)[/tex]
There are total number from 10 to 99 are 90. Thus, the probability that the chosen number is divisible by 5
[tex]P=\dfrac{18}{90}\\P=\dfrac{1}{5}\\P=0.2[/tex]
Hence, the probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.
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Final answer:
The probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5 is 1/5 or 20%.
Explanation:
To find the probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5, we first establish the total number of two-digit numbers, which is 99 - 10 + 1 = 90. Numbers divisible by 5 end in either 0 or 5, so we can count how many of these there are within our range. Starting from 10, the first such number, we have 10, 15, 20, ..., 95. We clearly have two of such numbers per every 10 numbers, resulting in a total of 90/10 * 2 = 18 numbers divisible by 5 between 10 and 99. Hence, the probability is the number of favorable outcomes (numbers divisible by 5), divided by the total number of possible outcomes (two-digit numbers), which gives us a probability of 18/90 = 1/5 or 20%.