okay so the coordinates are (2,16) & (-3,5) & what you have to do is use the distance formula. if you use it & solve your way through it, your answer should be 5 rounded to the nearest tenth
2(1-k), k-1, k+8 are the first three terms of a geometrical sequence. Find the value of k.
If these are terms of a geometric sequence, they have a common ratio. That is, ...
... (k -1)/(2(1 -k)) = (k +8)/(k -1)
... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.
... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses
... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)
... 3(k +5)(k -1) = 0 . . . . . . . . . factor
Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)
The value of k is -5.
_____
The three terms are 12, -6, 3. The common ratio is -1/2.
What number has the opposite value from 20.04? please show your work.
-20.04 because they are opposites
The opposite value of a number is a number that when added to the original number, results in zero. In this case, the opposite value of 20.04 is -20.04.
Explanation:The question is asking for the opposite value of 20.04. In mathematics, the opposite value, also known as the additive inverse, is a number which when added to the original number, results in zero. In other words, it's the number you would have to add to a specific number to get a sum of zero. Therefore, the opposite value of 20.04 is simply -20.04.
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The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.
Answer:
B
Step-by-step explanation:
The wording in the problem statement is ...
... "less than 3 years"
... "at least 3. but less than 6 years"
so we expect the inequality symbols to look like ...
... 0 ≤ x < 3
... 3 ≤ x < 6
These match the second piecewise function.
What number needs to be added to both sides of the equation in order to complete the square? x ^2+16x=18 Enter your answers in the boxes.
Find the number needs to be added to both sides of the equation in order to complete the square
x ^2+16x=18
In completing the square , we take the coefficient of x and divide it by 2
Then square it and add it on both sides.
The coefficient of x is 16
Half of 16 is 8
Then we square it . [tex](8)^2 = 64[/tex]
Add 64 on both sides
[tex]x ^2+16x + 64=18+64[/tex]
Now we factor x^2 + 16x+64
[tex](x+8)(x+8)=18+64[/tex]
[tex](x+8)^2=82[/tex]
so 64 is added to both sides of the equation in order to complete the square.
Which could be the graph of f(x) = |x - h| + k if h and k are both positive? Image for option 1 Image for option 2 Image for option 3 Image for option 4
In general, if you have a parent function, f(x), the graph of a daughter function f(x - h) + k is related with the graph of the parent function as per these rules:
Therefore, the graph of f(x) = |x - h| + k is a translaion of h units to the right and k units upward fo the function f(x) = |x|.
Since, the graph of f(x) = |x| has vertex (0,0), the graph of f(x) = |x - h| + k has vertex (h, k).
To visualize the images of the graph, assume some positive value for h and k. For instance, h = 3 and k = 5.
See the image attached showing the graphs for the functions f(x) = |x| (red line) and f(x - 3) + 5 = |x - 3| + 5 (blue line). As you can see, the blue line is the translation of the red line 3 units to the right and 5 units upward.
Answer:
its A
Step-by-step explanation:
i know things...
2+x=5 solve the equation show your work.
2(4x-8)=32 solve and show your work
Worth 12 points
Answer correctly plz
I’m so confused I really need help. Plz and thx
Answer:
The first answer is that x = 3. The second is that x = 6.
Step-by-step explanation:
To find either of these, we need to follow the order of operations.
2 + x = 5 ----> Subtract 2 from both sides
x = 3
2(4x - 8) = 32 ----> Distribute
8x - 16 = 32 -----> Add 16 to both sides
8x = 48 -----> Divide both sides by 8
x = 6
Will someone please answer this quick question question for me?
Answer:
x=1
Step-by-step explanation:
When the argument of the absolute value is positive, the equation has no solutions. It is equivalent to -3 = -1.
So, the only solution is found where the argument of the absolute value is negative:
-(2x -3) = 2x -1
4 = 4x . . . . . . . . add 2x+1
1 = x . . . . . . . . . . divide by 4
One week, Kerry travels 125 miles and uses 5 gallons of gasoline. The next week, she travels 175 miles and uses 7 gallons of gasoline. Which best describes the function that can be used to represent m, the number of miles traveled, and g, the number of gallons used? direct variation; m = kg direct variation; gm = k inverse variation; inverse variation;
Answer:
m = kg
Step-by-step explanation:
125 = 5k , k = 25 where k is the constant of variation.
175 = 7k, k = 25
Direct variation m = kg
Answer:
[tex]m=kg[/tex] direct variation
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
Let
m------> the number of miles traveled
g------> the number of gallons used
we have that
[tex]\frac{125}{5}\frac{miles}{gallons}=25\frac{miles}{gallons}[/tex]
[tex]\frac{175}{7}\frac{miles}{gallons}=25\frac{miles}{gallons}[/tex]
The linear direct variation that represent the situation is equal to the equation
[tex]\frac{m}{g}=k[/tex] or [tex]m=kg[/tex]
where
k is the constant of proportionality
In a direct variation the constant k is equal to the slope m of the line, and the line passes through the origin
[tex]k=25\frac{miles}{gallons}[/tex]
substitute
[tex]m=kg[/tex] -------> [tex]m=25g[/tex]
The graph represents the balance on Harrison’s car loan in the months since purchasing the car.
Which statement describes the slope of the line?
The loan balance decreases $500 per month.
Harrison makes a monthly payment of $250.
The loan balance increases $250 per month.
Harrison increases his monthly payment by $500 each month.
Answer:
B. Harrison makes a monthly payment of $250.
Step-by-step explanation:
We have been given a graph that represents the balance on Harrison’s car loan in the months since purchasing the car.
Let us see which of the given options describes the slope of the line.
Let us find slope of our given line.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Slope}=\frac{7000-5000}{0-8}[/tex]
[tex]\text{Slope}=\frac{2000}{-8}[/tex]
[tex]\text{Slope}=-250[/tex]
A. The loan balance decreases $500 per month.
We can see from slope of our given line that loan balance is decreasing $250 per month, therefore, option A is incorrect.
B. Harrison makes a monthly payment of $250.
We have seen that our slope is negative 250 this means that loan balance is decreasing $250 per month. This implies that Harrison makes a monthly payment of $250, therefore, option B is the correct choice.
C. The loan balance increases $250 per month.
We can see from our graph that our slope is negative, which means that loan amount is decreasing, therefore, option C is incorrect.
D. Harrison increases his monthly payment by $500 each month.
Since we know that linear functions have a constant rate of change, therefore, option D is not true regarding slope of the line.
Answer:
B. Harrison makes a monthly payment of $250.
Step-by-step explanation:
correct on edge ;))
The square root of 75 times the square root of 12.
A. the square root of 63
B. 3 times the square root of 7
C. 3 times the square root of 3
D. 8 times the square root of 3
option E) 30 is the answer for the square root of 75 times the square root of 12
We start by using the property of square roots that states the product of two square roots is the square root of the product of the numbers. This gives us:
[tex]\sqrt{75} \times \sqrt{12} = \sqrt {75 \times 12}[/tex]
Now we can simplify the expression by finding the product of 75 and 12. This gives us:
[tex]\sqrt {75 \times 12} = \sqrt{900} = 30[/tex]
Thus, the square root of 75 times the square root of 12 gives 30 as the answer. So, option E) 30 is the correct answer.
Correct question:
The square root of 75 times the square root of 12.
A. the square root of 63
B. 3 times the square root of 7
C. 3 times the square root of 3
D. 8 times the square root of 3
E. 30
Use the graph to find the cost of 8 hats.
If you look at the graph, the x axis the the number of hats and y axis is the cost.
So 8 hats will cost $60
Answer
D. The cost of 8 hats is $60
Answer: The cost of 8 hats = $60.
Step-by-step explanation:
In the given graph , the x-axis is representing the number of hats and y-axis is representing the cost of hats ( in dollars $).
To find the cost of 8 hats , just look at the x-axis and search for point x=8 on it .
Then , draw a straight line vertically passing through x=8 or just look at the dot marked above x=8 on the graph.
Then check the y-value associated with that dot or draw a horizontal line from that point , you will get y= 60
It means, the cost of 8 hats = $60.00.
See attachment below.
Need help one this one please answer quickly
what is the value of the 4 in 2.704
The value of 2.704 is .004 because it is 3 spaces to the right of the decimal point.
30 Points! Please answer each question or just answer one!
Answer:
1. See below for the table
2a. Early Pay: y = 45
2b. Deposit Plus: y = 12 + 4x
2c. Daily Pay: y = 6x
3. See the second attachment for a graph.
Step-by-step explanation:
1. The deposit (Deposit Plus) and the flat rate (Early Pay) are paid whether or not any days are spent swimming. For Early Pay, there are no additional charges, so the total cost is the same regardless of the number of days spent swimming.
For Deposit Plus, the $4 per day cost will add $20 for each 5 swimming days.
For Daily Pay, the $6 per day cost will add $30 for each 5 swimming days.
2. As described above, the Early Pay and Deposit Plus have charges when the number of swimming days is zero. The Daily Pay does not. The Deposit is only paid once, not each day.
a. Early Pay: y = 45
b. Deposit Plus: y = 12 + 4x
c. Daily Pay: y = 6x
3. The above equations are graphed in the second attachment. You will note that the plan that results in a minimum charge depends on the number of swimming days.
Answer:
2a. Early Pay: y = 45
2b. Deposit Plus: y = 12 + 4x
2c. Daily Pay: y = 6x
Step-by-step explanation:
the combined enrollment in the three grades at Jefferson Middle School is 977. there are 356 students in the 7th grade 365 in the 8th grade write and solve an equation to find how many students are in the ninth grade find an equation and a solution for the problem.
356 + 365 + x = 977 where x is the number of students in the third grade.
to find x subtract 356 and 365 from 977
x = 977-356-365 = 256
The equation of the given problem will be as; 356 + 365 + x = 977 . Therefore, there are 256 kids in the 9th grade.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
It is given that the combined enrollment in the three grades at Jefferson Middle School is 977. there are 356 students in the 7th grade 365 in the 8th grade.
Equation:
356 + 365 + x = 977
where x is the number of students in the third grade.
Since there are 977 kids in total, we have to add 356 and 365 to get 721.
356 + 365 + x = 977
721 + x = 977
Then subtract 721 from 977 to get how many kids are in 9th grade.
x = 977 - 721
x = 256
Therefore, there are 256 kids in the 9th grade.
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Find the values of x and y in the following equation.
(x+yi)+(4+9i)=9-4i
A. x = -9 and y = 4
B. x = 5 and y = -13
C. x = 5 and y = 13
D. x = 9 and y = -4
Answer:
B. x = 5 and y = -13
Step-by-step explanation:
Subtract the constant on the left:
... (x +yi) = (9 -4i) -(4 +9i)
... = (9 -4 +i(-4-9))
... = 5 -13i
Matching real and imaginary parts, we see that ...
... x = 5, y = -13
The excursion boat on the river takes 2 1/2 hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current? Which of the following equations can be used to solve for c, the rate of the current? (4c)(2.5) + (6c)(2.5) = 24 (4c)(12) + (6c)(12) = 2.5 [12/(4c)] + [12/(6c)] = 2.5
Answer:
[12/(4c)] + [12/(6c)] = 2.5
Step-by-step explanation:
time = distance/speed
You know the speeds upstream (5-1)c and downstream (5+1)c, the distance, and the total time for both trips. This information can be combined to give the equation above.
_____
The first equation assumes the trips upstream and down took 2.5 hours each.
The second equation is an incorrect combination of the numbers, as the units on the left are miles²/hour and are equated to hours on the right.
The third equation makes appropriate use of the relation between speed, distance, and time.
Answer:
Last option as
[tex][12/(4c)] + [12/(6c)] = 2.5[/tex]
Step-by-step explanation:
Time = distance/speed
Speed of boat = 5c (given)
Hence upstream speed = 5c+c =6c and
downstream speed = 5c-c =4c
Distance remains the same 12 miles for up and down
Total time = 2.5 hours
The first equation assumes total time as 5 hours when it is actually 2.5 hours.
The second equation is an incorrect because time x distance will not yield any result instead distance /time should have been done.
The third equation calculates time taken for upstream and downstream and add to equate to 2.5 hours.
So this is correct.
These are two angles that are located outside two parallel lines on opposite sides of the transversal.
Answer:
The answer is the angels will be the equivalent.
Explanation:
Lines on a plane that never meet. They are dependably a similar separation separated. Here the red and blue line sections are parallel.In different words, the slants of parallel lines are equivalent. Note that two lines are parallel if their slants are equivalent and they have distinctive y-blocks. As it were, opposite inclines are negative reciprocals of one another. Here is a fast survey of the slant/capture type of a line.
Answer:
Alternate Exterior Angles
Step-by-step explanation:
The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 2 pi cubic inches when the radius is 1 inch and the height is 6 inches, find the volume of a cone when the radius is 5 inches and the height is 3 inches. Please help!!!!!!! :(
The variation statement tells you that when the radius is multiplied by 5, the volume is multiplied by 5² = 25. When the height is multiplied by 1/2, the volume is multiplied by 1/2.
Both of these variations together will multiply the volume by 25·(1/2) = 25/2.
So, the revised volume is (2π in³)·25/2 = 25π in³.
The number of cubic feet of water in a curved container can be approximated by V = 0.95h2.9. Find the amount of water in the container when h = 8 feet. Round to the nearest tenth.
We are given
[tex]V=0.95h^2[/tex]
we can plug h=8
and then we can find volume
[tex]V=0.95(8)^2[/tex]
[tex]V=60.8ft^3[/tex]
so,
the amount of water in the container when h = 8 feet is 60.8 ft^3........Answer
Answer:
395.1
Step-by-step explanation:
Simplify
0.95 ( 8 ) ^2.9= v
395.07956558
corresponding solution for 6=1/3x+5
Let's solve your equation step-by-step.
6=
1
3x
+5
Multiply all terms by x and cancel:
6x=
1
3
+5x
6x=5x+
1
3
(Simplify both sides of the equation)
6x−5x=5x+
1
3
−5x(Subtract 5x from both sides)
x=
1
3
Check answers. (Plug them in to make sure they work.)
x=
1
3
(Works in original equation)
Answer:
x=
1
3
6 -5 = 1/3x
1 =1/3x # divided both side by 3/1 to isolate x by itself
then you get x = 3
What is the slope of this line?
slope = [tex]\frac{1}{4}[/tex]
to calculate the slope m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (8, 8 ) and (x₂, y₂ ) = (- 4, 5 ) ← 2 poinys on the line
m = [tex]\frac{5-8}{-4-8}[/tex] = [tex]\frac{-3}{-12}[/tex] = [tex]\frac{1}{4}[/tex]
What is the slope of the line on the graph?
Enter your answer in the box.
Answer:
The answer is -2
Step-by-step explanation:
m= y2-y1/x2-x1
m= -6-6/3+3
m= -12/6
m= -2
What does the equal? Keep getting it wrong
Answer:
A) -9/4
Step-by-step explanation:
The answer ends up becoming -2.25.
So if you do the math, that's -9/4. or add up 4 until you're at 9.
4, 8. Now we know we have 2 whole. What's left? 1/4.
So now we have, -2 1/4. or "-9/4".
Select all that apply. Which of the following are not quadrantal angles? 90° 180° 210° 260° 270°
[tex]210^{o} and 260^{o}[/tex] are not quadrantal angles.
A quadrantal angle is formed by two lines which lie on x-axis and y-axis.
For this reason, angles like;
[tex]0^{o},90^{o},180^{o},270^{o} and also -90^{o},-180^{o},-270^{o}[/tex] are quadrantal.
However, on the other hand,
[tex]210^{o} and 260^{o}[/tex] are not quadrantal because these angles are not formed by lines lying along x-axis and y-axis.
Answer:
210 and 260 degrees are not quadrantal angles
Step-by-step explanation:
quadrantal angles are angles that directly fall on the x or y axis. They're also multiples of 90 degrees. Quadrantal angles are 0, 90, 180, 270 degrees. hope this helps!
Juan is participating in a 40 mile bike race. He will pedal at a steady rate of 11.5 miles per hour. He pedaled for 1 hour and 45 minutes with the wind and for 2 hours and 30 minutes against the wind and finished the race in 4 hours and 15 minutes. What was rate at which the wind was blowing in miles per hour?
To work this problem, you must assume that Juan's pedaling speed adds to the wind speed when going downwind, and that the wind speed subtracts from Juan's pedaling speed going upwind. (In other words, Juan's pedaling speed is relative to the air, not the ground.)
Let w represent the wind speed in miles per hour.
... distance = speed × time
Juan's total distance is 40 miles, so we have ...
... 40 = (11.5 +w)×1.75 + (11.5 -w)×2.50
... 40 = 48.875 - 0.75w . . . . . simplify
... -8.875/-0.75 = w . . . . . . . . subtract 48.875, divide by -0.75
... w = 11.833... = 11 5/6
The wind was blowing 11 5/6 miles per hour.
_____
Compared with real-life experience, and working through the details, this problem makes no sense whatever. Pedaling a bicycle is not like rowing a boat, where the current of the medium directly affects speed.
If you work through the segments of the problem, you find that Juan traveled 40.833 miles with the wind in the first 1.75 hours, so actually finished the race and then some. He spent the next 2.5 hours being blown backward by the wind, even though he was pedaling forward at 11.5 mph. (How much sense does that make?)
At an animal rehabilitation center the baby armadillos need to be fed every four hours and the baby bats need to be fed every three hours if the bats and armadillos are both fed at 7:00 AM when will they be fed again at the same time
Answer:
19:00 or 7:00 PM
Step-by-step explanation:
Baby armadillos need to be fed every four hours.
Baby bats need to be fed every three hours.
So we need to figure out when will they be fed again at the same time:
Basically, we need to find the LCM of two numbers i.e. 4 and 3. And the reason why are we finding the LCM is because that time difference will is the least common multiple of both the time differences, it is the smallest non-zero number that is the multiple of both 4 and 3.
The LCM of 4 and 3 is 12. So the time when they will be fed again at the same time will be 12 hours after 7:00 AM that is 19:00 hours or 7:00 PM.
In ΔPQR shown below, segment QS is an altitude:
Triangle PQR with segment SQ drawn from vertex Q and intersecting side RP.
Which of the following is a justification used while proving the similarity of triangles ΔPSQ and ΔQSR?
a. Transitive Property of Equality
b. Addition Property of Equality
c. Definition of an Altitude
d. Definition of Supplementary Angles
Answer:
c. Definition of altitude.
Step-by-step explanation:
We are given that segment QS is an altitude in ΔPQR and we are asked to find a justification used while proving the similarity of triangles ΔPSQ and ΔQSR.
Since we know that altitude meets opposite side at right angles. When QS will intersect line PR we will get two right triangles QSR and QSP right angled at S.
ΔPQR is similar to ΔPSQ as they both share angle P and right triangle. So their third angle should also be similar.
ΔPQR is similar to ΔQSR as they both share angle R and both have a right triangle at Q and S respectively. So they will have their third angle equal.
ΔPQR is similar to triangles ΔQSR and ΔPSQ. Therefore, ΔQSR is similar to ΔPSQ.
Therefore, by definition of altitude triangles ΔPSQ and ΔQSR are similar as ΔPSQ and ΔQSR are created from ΔPQR by altitude QS.
Paula has a dog that weighs 3 times as much as Carlos dog total weight of the dogs is 48 lb how much does a dog weigh
Paula's dog : Carolos' dog = 3 : 1
The total number of ratio units is 3+1 = 4, so each one stands for (48 lb)/4 = 12 lb.
Paula's dog weighs 3·12 lb = 36 lb.
Carlos' dog weighs 1·12 lb = 12 lb.
what is an equation of the line with slope 3 that goes through point (-1/2, 5/2)?
a.) y=4x+3
b.) y=-3x+4
c.) y=4x-3
d.) y=3x+4
The only equation that has 3 as the coefficient of x (a slope of 3) is ...
... d.) y = 3x+4
_____
Happily, it also goes through the given point.
... 5/2 = 3(-1/2) +4
... 5/2 = -3/2 + 8/2 . . . . true
The equation of the line with a slope of 3 that passes through the point (-1/2, 5/2) is y = 3x + 4, which corresponds to answer option (d.) y = 3x + 4.
To find the equation of a line with a given slope and that passes through a specific point, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the given point. So, for a line with a slope of 3 that goes through the point (-1/2, 5/2), we can plug in the values to get the equation.
Substituting into the point-slope form, we get y - 5/2 = 3(x + 1/2). Simplifying and solving for y will give us the equation of the line in the form of y = mx + b. After distributing and rearranging, the equation will be y = 3x + 4.
Therefore, the correct answer is (d.) y = 3x + 4.