Point A is located at –24 and point C is located at 36 on the number line below. Which value would represent point B, halfway between point A and point C?
Answers
Answer:
Point B will be 6
Step-by-step explanation:
We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.
To find the middle between two points we have to add the two numbers and divide them by 2:
We would have:
(A+C)/2
We substitute the values of A and C:
B = (-24+36)/2
B = 12/2
B = 6.
We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.
Related Questions
Cost of a comic book: $3.95
Markup: 20%
Answers
If yes, you can simply change the percent to a decimal and then multiply it by the original price to see the price of the markup. Once you have that answer, you just add to the original cost.
Example: $3.95 x .20 = $0.79
$3.95 + $0.79 = $4.74
I hope this helps.
Take care,
Diana
what are the properties of an obtuse triangle
Answers
An obtuse triangle will have one and only one obtuse angle.
The other two angles are acute angles.
The sum of the two angles other than the obtuse angle is less than 90º.
The side opposite to the obtuse angle is the longest side of the triangle.
The points of concurrency, the Circumcenter and the Orthocenter lie outside of an obtuse triangle, while Centroid and Incenter lie inside the triangle.
Alicia is writing the program for a video game. For one part of the game, she uses the rule (x,y) -> (x - 3, y + 4) to move points on the screen.
(a) What output does the rule give when the input is (-6,0)? Show your work.
(b) What output does the rule give when the input is (3,-4)? Show your work.
Answers
A) (-6,0) = -6-3, 0+4 so it moves to (-9,4)
B) (3,-4) = 3-3, -4+4 so it moves to (0,0)
Find the polynomial equation of least degree with roots -1, 3, and (+/-)3i
Answers
The polynomial equation of least degree with the roots -1, 3, and (+/-)3i is x⁴ - 2x³ + 10x² + 2x - 27 = 0.
We have to find the polynomial equation of least degree with the given roots -1, 3, and (+/-)3i. As complex roots occur in conjugate pairs, if 3i is a root, then -3i must also be a root. Therefore, our polynomial will be of degree 4 since it has four roots in total.
The polynomial of least degree with roots x1, x2, x3, x4 can be expressed as:
(x - x1)(x - x2)(x - x3)(x - x4) = 0
Plugging in the roots given, we get:
(x + 1)(x - 3)(x - 3i)(x + 3i) = 0
To simplify this expression, let's first multiply the complex factors:
(x - 3i)(x + 3i) = x² - (3i)² = x² + 9
Now, multiply the remaining real factors with the result we just got:
(x + 1)(x - 3)(x² + 9) = 0
Expanding this, we obtain the polynomial equation:
x⁴ - 2x³ + 10x² + 2x - 27 = 0
This is the simplified equation of the polynomial with roots -1, 3, and (+/-)3i.
Ammon and nakia volunteer at an animal shelter. nakia worked 3 more hours than ammon. they each worked a whole number of hours. together they worked more than 27 hours. what is the least number of hours each worked
Answers
Final answer:
The least number of hours Ammon could have worked is 13 hours, and Nakia worked 16 hours since Nakia worked 3 hours more than Ammon, and together they worked more than 27 hours.
Explanation:
Let's denote the number of hours that Ammon worked as A and the number of hours that Nakia worked as N. According to the question, Nakia worked 3 more hours than Ammon, which can be written as N = A + 3. It's also given that together they worked more than 27 hours, so we can write this as A + N > 27. Substituting the first equation into the second, we get A + (A + 3) > 27, which simplifies to 2A + 3 > 27. By subtracting 3 from both sides, we get 2A > 24. Dividing by 2 gives us A > 12. Since A must be a whole number, the smallest whole number greater than 12 is 13.
Now that we know A is at least 13, we can find the minimum number of hours Nakia worked, which is A + 3. That gives us N = 13 + 3 = 16. Therefore, the least number of hours Ammon worked is 13 hours and Nakia worked 16 hours.
John is calculating 6% tax on an item in a store. he means to multiply the price of the item by 0.06, but he accidentally divides by 0.06. his answer is
Answers
Hope this helps!
Answer:
His answer will have a very large value.
Step-by-step explanation:
Lets take an example:
Let the item price be = $50
John is calculating 6% tax on an item. This becomes:
[tex]0.06\times50=3[/tex] dollars
But he accidentally divides by 0.06. This becomes: [tex]\frac{50}{0.06}= 833.33[/tex] dollars
We can see that the answer is completely wrong and the value is very large.
Anyone knows the answer
Answers
2y = -x - 6
x + 2y + 6 = 0
Evaluate: −9^4
A) −36
B) −6,561
C) 36
D) 6,561
Answers
Jason drives 400 miles in 10 hours. Which unit of measure is most appropriate for speed?
Answers
u just divide 400 by 10
PLEASE HELP I NEED THIS ASAP!!!
Part A: Compare the data in the table with the relation f(x) = 3x – 10. Which relation has a greater value when x = 8? (2 points)
Part B: Using the relation in Part A, what is the value of x if f(x) = 80? (5 points)
THIS IS THE TABLE!!!
Input
(x) 2 4 6 8
Output
(y) 1 2 3 4
Answers
f(8) = 3(8) - 10 = 24 - 10 = 14
g(8) when input, or x, equals 8, the output, or y, equals 4, so f(x) produces a greater value when x = 8.
Given that
∠A≅∠B, Gavin conjectured that ∠A and ∠B are complementary angles.
Which statement is a counterexample to Gavin 's conjecture?
m∠A=45° and m∠B=45°
m∠A=25° and m∠B=25°
m∠A=10°and m∠B=15°
m∠A=30°and m∠B=60°
Answers
2) Two angles are complementary angles if they sum up 90°.
So, let's examine the four statements:
A) m∠A=45° and m∠B=45°
This is not a counterexample, because it is a particular case where the two angles are congruent and they add up 90°, which is the very point of Gavin.
B) m∠A=25° and m∠B=25°
This is, indeed, a counterexample, because both angles are congruent and they do not add up 90°, driving to conclude that the conjecture of Gavin is not valid.
C) m∠A=10°and m∠B=15°
It is not a counter example because the two angles are not congruent.
D) m∠A=30°and m∠B=60°
It is not a counterexample because the two angles are not congruent.
Answer: It's B
B) m∠A=25° and m∠B=25°
If f(x) = x2 + 7, what is the equation for f–1(x)?
Answers
To find the inverse of f(x) = x² + 7, replace f(x) with y and solve for x, resulting in the inverse function f–1(x) = √(x - 7), considering the domain x ≥ 7.
Explanation:To find the inverse function of f(x) = x² + 7, we must first replace f(x) with y, giving us y = x² + 7. To find the inverse, we solve for x. We start by subtracting 7 from both sides to get y - 7 = x². Taking the square root of both sides, we get x = ±√(y - 7).
Since the square root has two values (positive and negative), we choose the one that matches the domain and range of the original function. If f(x) is defined for all nonnegative values of x, the inverse would be f–1(x) = √(x - 7). If f(x) includes negative values of x, then we would consider both, resulting in two different functions.
However, because we're dealing with f(x) that implies only one output for each input without restrictions, we consider the principal square root. Thus, the equation for the inverse function is f–1(x) = √(x - 7), considering the domain where x is greater than or equal to 7.
What is another name for this ?
Answers
What is the number in standard form?
Drag the answer into the box to match the number.
5.708×10−8
Answers
A standard form or a scientific notation is known as the value of any number that can be expressed or written as a decimal, usually within the range of 1.0 - 10.0 multiplied by the power of 10.
It is an effective technique of expressing large numbers in a simpler form.
From the information given, we are not provided with any decimal number to be converted into a standard form but we have a number in its standard form already.
i.e.
5.708 × 10⁻⁸
The standard number from above can be converted back into its decimal form, which is:
= 0.00000005708
From the above explanation, we can conclude that we've understood how to approach and solve questions related to the Standard form.
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Marcus has $5.45. He pays $1.25 for a bus ticket. He will buy some snacks before getting on the bus. Each snack will cost $0.75.
a) Write an equation that can be used to find the maximum number of snacks (x) that Marcus can buy.
b) What is the maximum number of snacks Marcus can buy?
( I've already done it but I don't think I'm right, I just want to be sure. )
Answers
0.75x = 5.45 - 1.25
0.75x = 4.20
x = 4.20 / 0.75
x = 5.6.....the maximum number of snacks he can buy is 5 <==
b To find this, we have to subtract 1.25 from both sides. Then we'll be left with 0.75x = 4.20. Divide 0.75 to dance out the x. Then do 4.20/0.75. 4.20/0.75 is 5 with a remainder left over. The highest number of snacks Marcus can buy is 5.
A scientist now has exactly 4.365 liters of water in a container. There were 5 liters of water in the container, but some of the water evaporated.How much water evaporated from the container?
Answers
5 - 4.365
0.635 liters
Hope this helps!
Answer:
amount evaporated = 0.635 liters
Step-by-step explanation:
The scientist initially had 5 liters of water in a container . After evaporation took place he had only 4.365 liters of water remaining in the container.
The amount of water that evaporated can be computed when you remove the amount of water remaining after evaporation from the initial amount before evaporation.
Mathematically,
amount evaporated = initial amount before evaporation - amount remaining after evaporation
initial amount before evaporation = 5 liters
amount remaining after evaporation = 4.365 liters
amount evaporated = 5 - 4.365
amount evaporated = 0.635 liters
How to solve negative exponents with a negative base?
Answers
Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write "not enough information". Explain your answer
Answers
Suppose f is a linear function such that f(5) = 10 and f(9) = 3. find the equation for f.
Answers
f(5)=-1.75*5+18.75=10
f(9)=-1.75*9+18.75=3
The equation for the function f would be; f(x) = -1.75x + 18.75.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Function is a type of relation, or rule, that maps one input to specific output.
Given that f is a linear function such that f(5) = 10 and f(9) = 3, then
Consider that the function of x would be;
f(x) = -1.75x + 18.75
Now plug x = 5 in the given function, if it satisfy the function
f(5) = -1.75(5) + 18.75
f (5) =10
Again plug x = 9 in the given function, if it satisfy the function
f(9) = -1.75(9) + 18.75
f(9) =3
Therefore, the equation for the function f would be; f(x) = -1.75x + 18.75.
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Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes 3x+6y−12=0
Answers
3x + 6y = 12
to find the x intercept, sub in 0 for y and solve for x
3x + 6(0) = 12
3x = 12
x = 12/3
x = 4.....so ur x intercept is (4,0)
to find the y int, sub in 0 for x and solve for y
3(0) + 6y = 12
6y = 12
y = 12/6
y = 2....so ur y intercept is (0,2)
hope this helps:D
plz give brainiest
Enter the solution to the inequality in the box.
7−3(x+5)+8x≤17
Answers
Answer:
The solution to the given inequality is (-∞,5].
Step-by-step explanation:
An inequality is a relation which makes a non-equal comparison between two numbers.
Given : 7-3(x+5)+8x≤17
=7-3(x+5)+8x ≤ 17
= 7- 3x - 15 + 8x ≤ 17
= -8 + 5x ≤ 17
Adding 8 on both sides:
= -8 +8+ 5x ≤ 17+8
= 5x ≤ 25
x ≤ 5
The solution to the inequality : (-∞,5].
Find the derivative of 4/square root of x
Answers
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{4}{\sqrt{x}}[/tex]
Step 2: Differentiate
Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 4 \frac{d}{dx} \bigg[ \frac{1}{\sqrt{x}} \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = 4 \Bigg( \frac{1}{x^\Big{\frac{3}{2}}} \Bigg)[/tex]Simplify: [tex]\displaystyle y' = \frac{4}{x^\Big{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Becca and alice are training for a race. becca runs 3 3/4 miles in 1/2 of an hour, and alice runs 5 1/4 miles in 3/4 of an hour. who runs faster and by how many miles per hour? justify your answer.200 words left
Answers
(3(3/4) miles in 1/2 hour)2
=7.5 miles in 1 hour
Alice: in 1 hour;
(5(1/4) miles in 3/4 hours)
She travels 5(1/4)/3 = 1.75 miles in 1/4 hours.
Travels 1.75x4 = 7 miles in 1 hour
As seen, Becca runs faster, 0.5 miles per hour faster.
Hope I helped :)
suppose a population of 250 crickets doubles in size every six months. How many crickets will there be after two years?
Answers
double every 6 months
in 6 months there would be 250*2 = 500 crickets
in 1 year there would be 500*2 = 1000 crickets
in 1.5 years there would be 1000 *2 = 2000 crickets
in 2 years there would be 2000 *2 = 4000 crickets
Which expressions are equivalent to 3(62)? Select each correct answer. 3(60 + 2) 3(6 + 2) 3(6 + 56) 3(60 + 20)
Answers
3(60 + 2) <=
3(6 + 56) <=
A) 3(60 + 2)
C) 3(6 + 56)
Two students are to be selected at random from a class with 10 girls and 12 boys. what is the probability that both will be girls?
Answers
Mei is writing a coordinate proof involving a right isosceles triangle. Mei places her triangle on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
~ What coordinates should she assign to this third vertex of the right isosceles triangle?
Answers
Answer: (a,a)
Step-by-step explanation:
Given: A right isosceles triangle which is placed on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
From the given figure one vertex is on origin(0,0) and second on x -axis as (a,0) .ii.e. one side of the triangle is on the x axis with length 'a' and the side parallel to the y axis should perpendicular to the x axis with length 'a'.(∵ two sides are equal in a right isosceles triangle)
So the coordinates should she assign to the third vertex of the right isosceles triangle is (a,a).[as the point lie above the point (a,0), so its x abscissa should be same]
The third vertex of a right isosceles triangle where one leg lies on the x-axis and the second leg is parallel to the y-axis would have equal x and y coordinates, assuming the second vertex is at (a,0). Therefore, the third vertex would be at (a,a), for any real numerical value of 'a'. This makes use of key concepts in coordinate geometry.
Explanation:In the context of mathematics, specifically coordinate geometry, Mei can assign the third vertex of this right isosceles triangle to any point that is equally distant from both the x and y axes. Assuming the other two vertices of the triangle are at the origin (0,0) and on the x-axis (a,0), then the coordinates of the third vertex would be (a,a).
Right isosceles triangle is a special type of triangle where two sides are equal in length and the angle between them is 90 degrees. Since the legs of the triangle are along the x and y axes, this leads to the third vertex being on the line y=x.
A coordinate proof involves using the properties and definition of the geometric figures in the coordinate plane. It involves calculations with the coordinates of the vertices of the figures. In the case of coordinate geometry, it's essential to understand the placement of points on the x-y plane.
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Chico is financing a car for $9,550 and an APR 8.9 percent for 3 years. What is his monthly payment if the monthly payment per $100 is $3.52?
A. $336.16
B. $352
C. $251.48
D. $235.24
(I divided 9550 by 100 and then multiplied that by 3.52 and got A but I don't know if that's the right way to do it)
Answers
Answer:
A. $336.16
Step-by-step explanation:
The payment per $100 can be set up as a ratio:
[tex]\frac{3.52}{100}[/tex]
Let the unknown payment be x. Now setting up the ratio over the full value:
[tex]\frac{x}{9550}[/tex]
Set them equal and solve for x:
[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]
1[tex]100x=33616[/tex]
This gives x = $336.16
Therefore, the answer is option A.
Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this case, approximately 1.25 billion years). suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40k to be 67 million years old. what is the maximum age of a fossil that we could date using 40k? (round your answer to one decimal place.)
Answers
[tex]N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{ \frac{1}{2} }}[/tex]
Given that potassium-40 has a half life of approximately 1.25 billion years.
The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:
[tex]0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\ \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\ \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\ \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\ \\ t=9.966(1.25)=12.5[/tex]
Therefore, the maximum age of a fossil that we could date using 40k is 12.5 billion years.
The maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.
Explanation:Potassium-40 (40K) has a half-life of 1.25 billion years.
The minimum detectable amount for dating using 40K is 0.1%. If a dinosaur is dated using 40K to be 67 million years old, we can calculate the maximum age of a fossil that could be dated using 40K.
To find the maximum age, we can set up a proportion using the half-life of 40K:
(67 million years) / (1.25 billion years) = (x years) / (100%)
Solving for x, we get:
x = (67 million years) * (100%) / (1.25 billion years)
Calculating this, we find that the maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.
A car travels 85 km from town a to town b, then 45 km from town b to town
c. the total trip took 1.5 h. what was the average speed of the car?
Answers
Final answer:
The average speed of the car is 86.67 km/h.
Explanation:
The average speed of a car can be calculated by dividing the total distance traveled by the total time taken. In this case, the car traveled 85 km from town A to town B and then 45 km from town B to town C, for a total distance of 85 km + 45 km = 130 km. The total trip took 1.5 hours. To find the average speed, divide the total distance by the total time: 130 km / 1.5 h = 86.67 km/h.