Which numbers are a distance of 2 units from 8 on a number line?
Select each correct answer.
8Answer
6 and 10
Step by step explanation
a distance of 2 units from 8 on a number line
we need to find out the numbers that are 2 units from 8 on the number line
To find out the numbers we need to subtract and add 2 from 8
[tex]8+2=10[/tex]
[tex]8-2=6[/tex]
10 is 2 units from 8 on the right side
6 is 2 units from 8 on the left side
So, 6 and 10 are 2 units away from 8 on the number line.
27 is 3 times as many as what number?
A. 9 B. 81 C. 7 D. 24
two segments are ______ coplanar
A.) always
B.) sometimes
C.) never
Two segments are always coplanar. The correct option is A.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
An adjacent line to another line in the same plane. Any two intersecting lines must be coplanar, that is, they must be on the same plane. Two line segments are always in the same plane.
Straight lines that are parallel and do not intersect at any point are called parallel lines. In the same three-dimensional space, parallel planes are any planes that never cross.
Therefore, the segments are always coplanar. The correct option is A.
To know more about line segments follow
https://brainly.com/question/17256689
#SPJ2
What is the rate of change of the perimeter of the square at the instant the area is 49 m2?
Find the solution(s) to x2 – 14x + 49 = 0
Answer:
x=7
Step-by-step explanation:
[tex]x^2 - 14x + 49 = 0[/tex]
Factor the left hand side of the equation
product is 49 and sum is -14
-7 times -7 is 49
-7 plus -7 is -14
so two factors are -7 and -7
[tex]x^2 - 14x + 49 = 0[/tex]
[tex](x-7)(x-7)= 0[/tex]
Now we apply zero factor property
SEt each factor =0 and solve for x
x-7 =0 , x=7
The correct solution for the equation [tex]x^{2}- 14x+49 = 0[/tex] is [tex]x = 7[/tex].
Given equation,
[tex]x^{2}- 14x+49 = 0[/tex]
The equation is a quadratic equation. A polynomial equation of second degree is known as quadratic equation.
The standard form of a quadratic equation is:
[tex]ax^{2} + bx + c = 0[/tex]
Find the solution of given equation for x, Use the standard formula:
x = (-b ± √(b² - 4ac)) / (2a)
From the question,
a = 1, b =-4 , c = 49.
Put the value of a, b ,c in the formula to find x.
x = (-(-14) ± √((-14)² - 4(1)(49))) / 2(1)
= (14 ± √(196 - 196)) / 2
= (14 ± √(0)) / 2
= [tex]\dfrac{14}{2}[/tex]
= 7
The value of the discriminant [tex]\sqrt{b^{2} - 4ac }[/tex] is 0. this indicates that their will be only one value of x.
The equation [tex]x^{2}- 14x+49 = 0[/tex] has a single solution which is x =7.
Learn more about Quadratic equation here:
https://brainly.com/question/2925460
#SPJ6
Branliest offered
Decide which of the two points on the graph of the line
X=0
A. 0,7
B. -4,0
NEED HELP PLEASE ANSWER ASAP. Two points have the same Y-coordinates but different X-coordinates. Make a prediction about the slope of a line drawn through the points. Justify your prediction.
The slope of a line drawn through the points are zero.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points have the same Y-coordinates but different X-coordinates.
Now,
Since, Two points have the same Y-coordinates but different X-coordinates.
Hence, Take two points as;
(x, y) = (3, 4) , (5, 4)
Thus, The slope of line passing through the points (3, 4) and (5, 4) is,
⇒ m = (4 - 4) / (5 - 3)
⇒ m = 0
Thus, The slope of a line drawn through the points are zero.
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ2
PLEASE ANSWER!
1. Choose the best definition for the following term: exponent
The number listed first when combining a variable and a number
The number or value being raised to a power
A letter that holds the place of some unknown value in mathematics
Shorthand that tells how many times the base is used as a factor, or how many times the base is multiplied by itself
2. Choose the best definition for the following term: variable
A letter that holds the place for some unknown value in mathematics
A process where you must look for terms that have identical variable parts and then combine their coefficients
A process where if two things are equal, one can be put in the place of the other and nothing will change
Terms that have identical variable parts
A convex lens has a diameter of 30 mm and a depth of 5 mm at the center. How far from the vertex is the focus?
A theater sells children's tickets for half the adult ticket price. if 5 adult tickets and 8 children's tickets cost a total of $27, what is the cost of an adult ticket?
To find the cost of an adult ticket, we can set up an equation using the given information and then solve for the variable.
Explanation:To solve this problem, let's start by defining some variables. Let the cost of an adult ticket be x dollars. Since children's tickets are sold for half the price of adult tickets, the cost of a children's ticket is (1/2)x dollars.
Given that 5 adult tickets and 8 children's tickets cost a total of $27, we can set up the following equation to represent the total cost:
5x + 8(1/2)x = 27
To solve for x, we can simplify the equation:
5x + 4x = 27
9x = 27
Dividing both sides by 9, we find that x = 3.
Therefore, the cost of an adult ticket is $3.
The number of bacteria in a culture is increasing according to the law of exponential growth. after 2 hours, there are 50 bacteria, and after 4 hours, there are 200 bacteria. how many bacteria will there be after 7 hours?
An investment is currently worth 2.125×104 dollars . Ten years ago, the investment was worth 1.25×103 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago? A 0.17 B 1.7 C 17 D 170
Answer: C. 17
Step-by-step explanation:
Given : An investment is currently worth [tex]2.125\times10^4[/tex] dollars . Ten years ago, the investment was worth [tex]1.25\times10^3[/tex] dollars.
Then, the number of times the value of the investment today is greater than the value of the investment ten years ago is given by :-
[tex]\dfrac{\text{Current investment}}{\text{\text{Yen years ago investment}}}\\\\=\dfrac{2.125\times10^4}{1.25\times10^3}\\\\=\dfrac{2.125}{1.25}\times10^{4-3}\ \ [\because a^m\times a^n=a^{m+n}]\\\\=1.7\times10=17[/tex]
Hence, the value of the investment today is 17 times greater than the value of the investment ten years ago .
Worth a brainliest if the answer is correct.
If the rule (x,y) → (x+3, y-3) is applied to the original triangle, give the coordinates of and draw the image. Show your work for calculating the coordinates of the resulting image.
2/3b + 5 = 20 - b
Solve for b
The solution value of b in the equation 2/3b + 5 = 20 - b is: b = 9.
Here, we have,
given that,
the equation is:
2/3b + 5 = 20 - b
so with these equations, you collect 'like terms.'
like terms are basically grouping things that are the same together,
so for example a+a-b+2b would be 2a+b.
with this equation you want to do the same.
2/3b + 5 = 20 - b
first, make all the numbers integers (whole numbers).
we want to make 2/3b a whole number,
so we multiply the whole equation by 3 to keep everything in proportion with each other,
thus ending up with
2b + 15 = 60 - 3b
now we collect 'like terms.'
add 3b to both sides gives
5b + 15 = 60
subtract 15 from both sides
5b = 45
divide by 5 to leave the value of b
b = 9
To learn more on equation click:
brainly.com/question/24169758
#SPJ6
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal
To meet their goal of saving $8,000 for their wedding, Mike and Kate need to adjust their plan. Increasing the amount they save each month by $80 (Option B) will allow them to reach their goal.
Explanation:To determine which option will allow Mike and Kate to meet their goal of saving $8,000 for their wedding, we need to analyze the information given. They saved $4,000 in the first year, which means they saved $4,000 in 12 months. To reach their goal, they need to save an additional $4,000 in 8 months.
Option A: If they stay with saving the same amount they've been saving each month, they will save the same amount each month for the remaining 8 months. Therefore, they will not reach their goal of $8,000.
Option B: If they increase the amount they save each month by $80, they will be saving $80 more each month for the remaining 8 months. This will result in them saving an additional $640 ($80 x 8 months) and reaching their goal of $8,000.
Therefore, the correct answer is Option B - Only option B will allow them to meet their goal.
Learn more about Saving Money here:https://brainly.com/question/31411395
#SPJ2
If vx = 7.60 units and vy = -6.60 units, determine the magnitude of v⃗ .
Answer:
|v| = 10.06 units
Step-by-step explanation:
It is given that,
The x component of the vector is, [tex]v_x=7.6\ units[/tex]
The y component of the vector is, [tex]v_y=-6.6\ units[/tex]
We need to find the magnitude of vector v. The magnitude of any vector is calculated as :
[tex]|v|=\sqrt{v_x^2+v_y^2}[/tex]
[tex]|v|=\sqrt{(7.6)^2+(-6.6)^2}[/tex]
|v| = 10.06 units
So, the magnitude of vector v is 10.06 units. Hence, this is the required solution.
Faith mixes 14 liters of 12% acid solution with a 30% acid solution, which results in an 18% acid solution. let x represent the number of liters of 30% acid solution used, and let y represent the number of liters of mixture. which system of equations can be used to find the number of liters of 30% acid solution in the mixture?
Graph the function. Upload a handwritten copy of your graph as your final answer.
y={ x for x<0
-x^2 for x≥0
A sea turtle swims at a speed of 27 kilometers per hour. A girl swims 14 decimeters per second.
1 m = 10 dm
1000 m = 1 km
How much faster does the sea turtle swim than the girl in meters per minute?
Answer in meter per minute
~~~~~~~~~~The answer is 366 m/min~~~~~~~~~~~~~~~~~~ First, convert the turtles speed to meters per minute. 27 km/h * 1000 m/km = 27000 m/h / 60 min/h = 450 m/min Now convert the girls speed to meters per minute. 14 dm/s / 10 dm/m * 60 s/min = 84 m/min Now subtract the girl's speed from the turtle's speed. 450 m/min = 84 m/min = 366 m/min
Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?
Rick, Maya, and Tom worked a total of 1086 minutes.
To calculate this:
1. Convert Rick's hours to minutes: 5 hours and ½ hour = [tex]\( 5 \times 60 + 30 = 330 \) minutes.[/tex]
2. Convert Maya's hours to minutes: 6 hours and 1/10 hour = [tex]c\( 6 \times 60 + 6 = 366 \) minutes.[/tex]
3. Convert Tom's hours to minutes: 6 hours and 30 minutes = [tex]\( 6 \times 60 + 30 = 390 \) minutes.[/tex]
Now, add up all the minutes worked:
[tex]\[ 330 + 366 + 390 = 1086 \] minutes.[/tex]
Therefore, Rick, Maya, and Tom worked a total of 1086 minutes.
- Rick worked for 5 hours and ½ hour, which is 330 minutes.
- Maya worked for 6 hours and 1/10 hour, which is 366 minutes.
- Tom worked for 6 hours and 30 minutes, which is 390 minutes.
Adding these minutes together gives a total of 1086 minutes.
complete question
Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?
To solve X/0.4 = 10, you would: Add 0.4 Subtract 0.4 Multiply 0.4 Divide by 0.4
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
X/0.4= 10
We need to find the value of x .
For this, we will multiply by 0.4 on both sides, we get that
X= 0.4 × 10
X = 4
Hence, third option is correct.
Does this table represent a function? Why or why not? x:2, 4, 6, 8, 10 y:1, 3, 3, 4, 6 A.No, because two of the y-value are the same. B.Yes, because all of the x-value corresponds to one or more y-values C.Yes, because every x-value corresponds to exactly one y-value. D.No, because one x-value corresponds to two different y-values
Answer:
C.Yes, because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
A function is a relation in which each element of the domain (x) is mapped to one element of the range (y). This means that no x can be mapped to more than one y; basically it means that no x can repeat.
In this table, no x repeats; each x is mapped to only 1 y. This means that it is a function.
Answer:
The correct option is C) Yes, because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
Consider the provided table:
x y
2 1
4 3
6 3
8 4
10 6
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Or we can say that, a function is a set of ordered pairs in which x element has only one y-element associated with it.
Now observe the table for each x element we have only one y element.
Therefore, the table represent a function.
The correct option is C) Yes, because every x-value corresponds to exactly one y-value.
1. Write numbers from standard form to Scientific notation for the following: The diameter of human DNA is about 0.000000002
2. Idaho is shaped like a triangle with a base of approximately 320 miles and a height of approximately 520 miles. Calculate the area of Idaho and write the answer in scientific notation.
Find the net force f acting on the particle.
express your answer in terms of m and
a.
If the mass is represented as m and acceleration as the net force f acting on the particle will be f =ma.
What is force?Force is defined as the product of mass and change in velocity.The objects interactions with one another are what cause push and pull. Force may also be expressed using words like stretch and squeeze.
The force is in mathematical form is,
Force = mass × acceleration
If m is the mass in kilogram and a is the acceleration in m/s² is,
F = m × a
F = (1 kg) × (1 m/s²)
F = 1 kg.m/s²
As we know, 1 kg.m/s² = 1 N
F = 1 N
The measures mentioned above are taken into account by the Newton unit (N). As a result, one newton is defined as the force needed to accelerate 1 kilogram of mass 1 meter per second squared in a certain direction. 1N = 1kg (m/s²) is the way to express force.
Thus, if the mass is represented as m, acceleration as the net force f acting on the particle will be f =ma.
Learn more about the force here,
https://brainly.com/question/13191643
#SPJ2
The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.6, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.4.
a. What is the mean (±0.1) of the average number of moths x¯¯¯ (x bar) in 30 traps?
I got 18 by multiplying 30 times 0.6, I'm not confident 100% in this
b. And the standard deviation? (±0.001)
I got 0.073 by doing 0.4/ sqrt of 30...not confident
c. Use the central limit theorem to find the probability (±0.01) that the average number of moths in 30 traps is greater than 0.7:
I got 1.37 by doing 0.7-0.6 / 0.073 (0.4/sqrt of 30)
are these answers correct?
The student's calculations for mean and standard deviation are correct, although the standard deviation was slightly misunderstood. The calculation for the z-score was correct, but the student failed to convert this z-score into a probability.
Explanation:The question discusses certain calculations about the distribution of gypsy moths in traps placed by a state agriculture department. Your calculation for (a), the
mean
number of moths in 30 traps, is correct. We multiply the mean number of moths in one trap (0.6) by the number of traps (30) to obtain 18. However, for (b), the
standard deviation
of the distribution is incorrectly calculated. In fact, as we apply the formula for standard deviation of sample means σ/√n, where σ is the population standard deviation (0.4) and n is the sample size (30), it comes out to be 0.073 (rounded to ±0.001). Lastly, for (c), using the given values in the
central limit theorem
, the z-score calculator gives us a value of 1.37, but remember, this is a z-score, not a probability. To convert the z-score to a probability, you need to consult a standard normal distribution table or use a calculator with a built-in z-score to probability converter.
Learn more about Statistics here:https://brainly.com/question/31538429
#SPJ3
Please help me thank you.
1st question - answer is #2
line P & Q = x=3, Y=5
triangle question, x = 17
If y varies directly as x, and the constant of variation is -3, which equation represents this relationship?
Final answer:
The equation representing a direct variation where y varies directly as x with a constant of variation of -3 is y = -3x. It is a linear equation without a y-intercept.
Explanation:
If y varies directly as x, and the constant of variation is -3, the equation that represents this relationship can be written as y = kx, where k is the constant of variation. Since the constant of variation is given as -3, the equation becomes y = -3x. This is a linear equation similar to the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the constant of variation is -3, the slope of the line is -3 and the y-intercept is 0 because there is no addition or subtraction of a constant in the equation.
David learned 15 definitions in 90 minutes. How much time will he take to learn 10 definitions?
A florist is making blue and white flower arrangements. For the arrangements, he places a red ribbon on every 3rd arrangement and a blue ribbon on every 5th arrangement. Which arrangement will be the first to have a red ribbon and a blue ribbon?
*PLEASE HELP* Compute the amount of interest earned in the following simple interest problem. Explain how you got it please
A deposit of $5,500 at 6% for 3 years
The amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We have to find the amount of interest earned
The deposited amount or principal amount us 5500
Rate of interest is 6% and time is 3 years
The formula for simple interest is I=PRT
I = interest, P = principal, R = rate, T = time in years.
Let us convert 6% to decimal form
Divide 6 by 100
6%=0.06
I = 5500(0.06)(3)
I = $990
Hence, the amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ3