A'(- 4, 3 )
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
A(3, 4 ) → A'(- 4, 3 )
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...
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
Kim's age is three times that of her sister's age. When you add Kim's age to her sister's age, you get 40. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used. (b) Solve the equation from part (a). Show your work. State your solution as a complete sentence.
Please help I do not understand how to do this. Thank you
When solving a problem like this you will need to break down the equation. The answer is actually really simple and easy.
For Kim's age we will use X as the variable. For her sister we will use Y.
y*3=x and X+Y=40 and that will get us our answer.
Now we are going to break it down. Kim is three times the age of her sister. So what number under 40 can be evenly distributed into 3 parts since we need to find a number three times greater than another number that can be added one time to itself to equal 40.
The answer to that question would be x=10.
Which means her younger sister is going to be 10
So taking that and plugging it into our equation we will get the following;
10*3(y*3) = (x)30
Which now means Kim's age is 30.
Now we check to make sure. Does 30 + 10 = 40? If so then that's your answer explained and in depth.
Can I get some help on this problem? Thanks guys yo its really easy but I cant figure it out I need an explanation so dont post without one
Answer:
x = 15
Step-by-step explanation:
When figures are similar, the lengths of corresponding sides are in the same ratio.
In the figure, the side measuring 8 corresponds to the side measuring 20. The ratio of the lengths of those two corresponding sides is 8/20.
The side measuring 6 corresponds to the side measuring x. The ratio of the lengths of those two corresponding sides is 6/x.
Since the quadrilaterals are similar, the ratio 8/20 must equal the ratio 6/x.
We use that fact to write an equation, and then we solve for x.
8/20 = 6/x
Reduce the fraction on the left side.
2/5 = 6/x
Cross multiply.
2x = 5 * 6
2x = 30
x = 15
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
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.
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]
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]
Find the slope of the line passing through the two points.
Chapter Reference
b
(12, 1), (36, 42) and (–1, –8), (–7, –4)
These are different question
[tex]\frac{41}{24}[/tex] and - [tex]\frac{2}{3}[/tex]
calculate the slope m using the gradient formula
m = ( y₂ - y₁ )/ (x₂ - x₁ )
with (x₁, y₁ ) = (12, 1 ) and (x₂, y₂ ) = (36, 42 )
m = [tex]\frac{42-1}{36-12}[/tex] = [tex]\frac{41}{24}[/tex]
repeat with (x₁ y₁ ) = (- 1, - 8 ) and (x₂, y₂ ) = (- 7, - 4 )
m = [tex]\frac{-4+8}{-7+1}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex]
The slope of a line passing through the points (1, 0.1) and (7, 26.8) is found by subtracting the y-coordinates and the x-coordinates and then dividing the former by the latter, resulting in a slope of approximately 4.45, which is option 'b'.
Explanation:Finding the Slope of a Line Given Two PointsTo find the slope of a line passing through two points, you use the formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Lets calculate the slope for the points (1, 0.1) and (7, 26.8).
The slope of a line passing through these two points is therefore approximately 4.45, which matches option b.
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 number must you add to complete the square x^2+12x =16
A. 24
B. 12
C. 6
D. 36
Answer:
D. 36
Step-by-step explanation:
The square of half the x-coefficient must be added. That value is (12/2)² = 36.
_____
You're trying to create a trinomial of the form ...
... (a + b)² = a² +2ab +b²
where a = x, and 2b = 12.
The number you need to add is b² = (2b/2)² = (12/2)² = 36.
Answer:
D. 36 is the answer .. (ap ex)
Step-by-step explanation:
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.
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.
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.
PLEASE KNOW BEFORE YOU ANSWER.
Identify and EXPLAIN the ERROR
Show CORRECT WORK and SOLUTION
Show CORRECT WORK and SOLUTION
THE FIRST PIC IS THE QUESTION!!!!
Answer:
The error is the exponent in the answer should be 11.
Step-by-step explanation:
When you move the decimal place one spot as they do in the final step to move it from a base 10 to a base 1, we have to add a exponent on. Therefore, it should go from 10 to 11.
-5/3/10 as a improper fraction
A can holds 753.6 cubic centimeters of juice. The can has a diameter of 8 centimeters. What is the height of the can?
height = 15 cm
the volume (V) of a cylindrical can is
V = πr²h ( r is the radius and h the height )
here d = 8 cm ⇒ r = 4 cm
π × 4² × h = 753.6
16πh = 753.6 ( divide both sides by 16π )
h = 753.6 / 16π = 14.99 ≈ 15 cm
if michaels family has 210 acres and each cow takes 1/3 acre for grazing,then how many cattle could their farmland support?
there is enough acres to support 3 cattle on their farmland .
Michael's family's 210-acre farmland can support 630 cattle, with each cow needing 1/3 acre for grazing.
To find out how many cattle Michael's family's farmland can support, you would divide the total acreage by the amount of land each cow needs for grazing.
Given:
- Michael's family has 210 acres.
- Each cow requires 1/3 acre for grazing.
You can calculate it like this:
[tex]\[ \text{Number of cattle} = \frac{\text{Total acreage}}{\text{Acreage per cow}} \][/tex]
[tex]\[ \text{Number of cattle} = \frac{210 \, \text{acres}}{\frac{1}{3} \, \text{acre/cow}} \][/tex]
To divide by a fraction, you multiply by its reciprocal:
[tex]\[ \text{Number of cattle} = 210 \, \text{acres} \times \frac{3}{1} \, \text{cow/acre} \][/tex]
[tex]\[ \text{Number of cattle} = 630 \, \text{cows} \][/tex]
So, Michael's family's farmland can support 630 cattle.
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 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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Need help one this one please answer quickly
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!
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
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 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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At a gas station in Centerville, 19 gallons of gas cost $22.75. The same amount of gas at a station in Huntsville cost $26.30. How much more did this amount of gas cost in Huntsville than in Centerville? A) $4.65 B) $4.45 C) $3.55 D) $3.25
Answer:
The answer would be C) $3.55
Step-by-step explanation:
$26.30-$22.75=3.55
The gas in Huntsville is $3.55 more expensive than in Centerville for 19 gallons, so the correct answer is C) $3.55.
Explanation:To determine how much more the gas cost in Huntsville than in Centerville, you need to subtract the cost of gas in Centerville from the cost of gas in Huntsville. In math terms, the operation is as follows:
Huntsville cost ($26.30) - Centerville cost ($22.75) = Additional cost.
When you perform this subtraction, the result is $3.55. Therefore, the gas in Huntsville is $3.55 more expensive than in Centerville for 19 gallons.
So, the correct choice is C) $3.55.
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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 ;))
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".
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
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.