The equation of a line through the origin and (-5,6) is y = -1.2x
How to determine the equationIt is important to note that the equation of a line is expressed as;
y = mx + c
Where;
y is the point on the y - axism is the slope of the linex is the point on the x - axisc is the intercept on the y axisFrom the information given, we have the points;
(0, 0) and ( -5, 6)
The formula for slope is given as;
slope, m = y₂ - y₁/ x₂ -x₁
slope, m = 6 - 0/ -5 - 0
slope, m = 6/ -5
slope, m = - 1. 2
To determine the intercept, we have;
6 = -1. 2(-5) + c
expand the bracket
c = 6 - 6
c = 0
The equation is given as;
y = -1.2x
Hence, the equation is y = -1.2x
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Find the coordinates of the vertices of each figure after a reflection over the given axis.
triangle ABC with vertices A(2,3)B(4,-5), and C(-1,2); x-axis
The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
Given,
A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)
To find the coordinates of the vertices of each figure after a reflection over the given axis.
Now, According to the question:
We should know that:
You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin = (-x, y)
So here's our set of points.
A(2,3) , B(4,-5), and C(-1,2)
Here's those points reflected over the x axis.
A' (2, -3) B' (4, 5) and C' (-1, -2)
Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
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how do I right this in numeral formsix thousand, five hundred eighty-two ten-thousandths
Which line on the xy-plane has a positive slope?
Line 1
Line 2
Line 3
Line 4
Please only answer with the options provided
Line 2 has a positive slope with respect to the angle made with the x-axis.
What is the slope?Slope refers to the tan of the angle with the x-axis. For example. if the line makes an angle β with the x-axis, then the slope is the tan β.
Now taking line 1,
The line is parallel to the x-axis, therefore the line makes 0 angles with the axis which gives slope 0.
Now taking line 2,
The line passes to the origin and has the equation x=y, thus the slope is 1
Now taking line 3,
The line is parallel to the y-axis, therefore the line makes 90°, thus the slope is 1/0 which gives infinity.
Now taking line 4,
The line is making an angle of 60°, therefore the line is having a slope: - [tex]\sqrt{3}[/tex]
Hence considering the above values, line 2 has a positive slope only.
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Consider the inequality y > -1.25. Which if the following statements are the?
we have the inequality
y > -1.25
the solution is the interval (-1.25, infinite)
Note that the number -1.25 is not included in the solution
so
Verify each statement
1) 1 is a solution --------> true2) -1.75 is a solution ------> false
3) all the solutions are negative -------> false
4) they're are infinitely many solutions to this inequality -----> true5) the inequality -1.25 < y represents the same solution set to given the inequality ----> trueThe ratio between Siu's height and the height of her brother Tai is 5:6. If
Tai is 145 cm tall, how tall is Siu, to the nearest centimetre?
With the concepts of ratio, Siu's height is 121 cm tall.
What is a ratio?We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part to part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.
A ratio is a comparison between two amounts that often uses a fraction.
Considering that the fraction has been simplified,
Given that Siu's height is 5x
Tai's height is 6x.
Now, 6x= 145
Thus, x= 145/6
Now, Siu's height is 5x
Then, its height is (145 ×5)/6= 120.8 cm
Siu's height is 121 cm because it must be rounded to the closest centimeter.
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Hi, can you help me to solve this problem please!!!
The Solution:
Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.
An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.
From the given graph of f(x), the function f(x) is ODD.
The degree of the function f(x) is odd since the f(x) itself is odd.
Emily is designing a t-shirt logo for her company. The t-shirt printing company offers 11 colors to choose from for the logo design. If any number of colors can be chosen, how many different color combinations are possible?
39,916,800 color combinations are possible
Here, we want to get the possible number of color combinations possible.
Since any number of colors can be chosen, there are no restrictions here
That means the number of possible color combinations will be;
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations
Shawn designs a rectangular garden as shown below. He will design both rock sections to have the same width (x). A. Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Shawn's garde .
The equivalent expression of the perimeter in two terms is 44 + 4x
How to determine the equivalent expression of the perimeter?From the question, the area of the garden is given as
A = 15(2x + 7)
The area of a rectangle is calculated using
A = LW
Where
Length = L
Width = W
This means that
L = 15
W = 2x + 7
The perimeter of the rectangular garden is then calculated as
P = 2 * (L + W)
So, we have
P = 2 * (15 + 2x + 7)
Evaluate
P = 2 * (22 + 2x)
This gives
P = 44 + 4x
Hence, the perimeter is 44 + 4x
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Complete question
Shawn designs a rectangular garden as shown below. He will design both rock sections to have the same width (x). A. Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Shawn's garden.
The area in, square feet, of Shawn’s garden is found be calculating 15(2x + 7).
the cost of a computer repair is worked out using the formula C = 35 + 15h.
C represents the cost in dollars.
H is the time taken in hours.
use the formula to find the cost of repair that takes 3 hours.
Answer: C = 35 + 15 x 3 = 80
Step-by-step explanation:
15h = 15 x (h) = 15 x 3 = 45 + 35 = $80
C = (15 x 3) + 35 = 80
with pic. Which of the following functions is graphed below?
The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)
How to derive the absolute function associated with the picture
Absolute values are functions defined by the following piecewise function:
f(x) = |x| = x for x ≥ 0.f(x) = |x| = - x for x < 0.The function in the picture is the consequence of the following rigid transformations:
Horizontal translation 5 units in the + x direction.Vertical translation 4 units in the - y direction.Now we proceed to obtain the image of f(x):
Horizontal translation
f'(x) = |x - 5|
Vertical translation
g(x) = |x - 5| - 4
The picture is represented by the function g(x) = |x - 5| - 4.
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Help me with these two question please!!!
Question 10
Lines a and b by the converse of the consecutive interior angles theorem
Question 11
Lines e and f by the converse of the alternate interior angles theorem
Enola bought 14 chicken wings for $29.40. How much would it cost for 5 wings?
Answer:
10.5
Step-by-step explanation:
The 5 chicken wings will cost $10.5 to Enola.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Price of 14 chicken wings bought by Enola = $29.40.
To find the price of 5 wings,
Use ratio property,
Price of 14 chicken wings = $29.40
Price of 1 chicken wing = 29.40 / 14
= 2.1
Price of 5 chicken wings = 2.1 x 5 = 10.5
The price of the 5 chicken wings is $10.5.
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in a basketball game Tatiana May 23 baskets each of the baskets was worth either two or three points and Tatiana scored a total of 53 points let x represent the number of two-point baskets she made and why represent the number of three-point baskets she made.part a write a system of equations represent the situation.part b would you use graphing or substitution to solve the system and determine the number of 2.3 point baskets Tatiana made? explain.part c use the method you chose in part b to solve the system and find out how many two point and 3-point baskets Tatiana made.
Part A
start by naming the variables you will be using in the system of equation
x= number of two-point baskets
y= number of three-point baskets
since she did 23 baskets the first equation representing the number of baskets she made will be
[tex]x+y=23[/tex]the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.
[tex]2x+3y=53[/tex]Part B
Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.
However both methods could be used.
Part C
[tex]\begin{gathered} x+y=23 \\ 2x+3y=53 \end{gathered}[/tex]Brynn rides her bike 84 miles in 4 hours.
a. Create a ratio of Brynn's miles per hour.
b. Using the ratio you found in part a, determine
how far Brynn can ride in 7 hours.
c. If Brynn rides 57 miles at the rate indicated,
how long will she ride? Justify your response.
Part (a)
distance = rate*time
rate = distance/time
rate = 84/4
rate = 21
Answer: 21 mph
==================================================
Part (b)
distance = rate*time
distance = 21*7
distance = 147
Answer: 147 miles
==================================================
Part (c)
distance = rate*time
time = distance/rate
time = 57/21
time = 2.71428571428571
time = 2.714
Answer: Approximately 2.714 hours
Answer;
A.21:1
B:147 Miles
C.2.7 hours or 182 minutes
A truck rental company charges $90 plus $20 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 5, and what does it represent?
Of(h) = 20h + 90
$470, which is the total charge in dollars for renting a truck for 5 hours
Question 6 of t
Of(h) = 90+20h
$190, which is the total charge in dollars for renting a truck for 5 hours
Of(h) = 20 +90h
$470, which is the total charge in dollars for renting truck for 5 hours
Of(h) = 90h + 20
$190, which is the total charge in dollars for renting a truck for 5 hours / pls help lol
The function that represents the total charge for renting a truck for a certain number of hours is f(h) = 90 + 20h What is the value of the function for an input 5 represent : $190, which is the total charge in dollars for renting a truck for 5 hours.
How to find the total charges?Given data :
Charges = $90 + $20 per hour
Value = 5
Now let formulate an equation
f(h) = 90 + 20h
Where,
h = 5
So,
Total charge = 90+ 20 ×5
Total charge = 90 + 100
Total charge =190
Therefore the correct option is B.
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i need help with my homework please check work when done I NEED HELP WITH THE QUESTION IN BLUE
Amount invested by Katelyn = $4000
rate = x%
time = x + 2 years
n = number of times compounded
n = annually = 1
We need to find the function that models the total amount
To find the function, we will apply the compound interest formula:
[tex]\begin{gathered} $$FV\text{ = P(1 +}\frac{r}{n})^{nt}$$ \\ \\ P\text{ = 4000} \\ t\text{ = x + 2} \\ n\text{ = 1} \\ \text{ r = x\% = x/100} \\ FV=\text{ total amount } \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} FV=\text{ 4000\lparen 1 + }\frac{\frac{x}{100}}{1})^{1\times(x\text{ + 2\rparen}} \\ \\ FV=\text{ 4000\lparen1 + }\frac{x}{100})^{x+2} \end{gathered}[/tex][tex]FV=\text{ 4,000\lparen}\frac{100+\text{ }x}{100})^{x\text{ +2}}\text{ }[/tex]let the function that represents the total amount = f(x)
[tex]f(x)=\text{ 4000\lparen}\frac{\text{ }x+\text{ 100}}{100})^{x\text{ +2}}\text{ }[/tex]Please help I don’t know what it is
Which methods correctly solve for the variable r in the equation 3/8r+ 2 = 14?
Select all that apply.
The third option is the correct method that solves for the variable r in the equation
Which method will solve for the variable in the equation correctly?Given the equation: 3/8r+ 2 = 14
Subtract 2 from both sides:
3/8r = 12
Multiply both sides by 8:
3r = 12 x 8
3r = 96
Divide both sides by 3:
r = 96/3 = 32
Therefore, the method that solve the variable r in the equation correctly is the third option.
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Can someone help me i will give brainlest :)
The solution to the inequalities given are graphed in the diagram attached below.
How to Solve and Graph Inequality?When graphing an inequality, a full circle is used when the sign involved is "≤ or ≥", while an empty circle is used to indicate the point on the graph when the inequality sign is "< or >".
The inequalities would be solved as shown below:
15. ¾x + 5 > 11
Subtract 5 from both sides
¾x > 11 - 5
¾x > 6
3x > 24
Divide both sides by 3
3x/3 > 24/3
x > 8
16. -5/6x - 1 ≥ 14
Add 1 to both sides
-5/6x ≥ 14 + 1
-5/6x ≥ 15
-5x ≥ 90
Divide both sides by -5
x ≤ -18
17. 5x - 2 ≤ -7
Add 2 to both sides
5x ≤ -7 + 2
5x ≤ -5
x ≤ -1
18. 6 - x ≤ 14
Subtract 6 from both sides
-x ≤ 14 - 6
-x ≤ -8
x ≥ 8
19. 4 - 1/3x > 11
Subtract 4 from both sides
-1/3x > 11 - 4
-1/3x > 7
-x > 21
x < -21
20. (x + 11)/-2 < -2
x + 11 < 4
Subtract both sides by 11
x < 4 - 11
x < -7
See the image below for the graph of the solution to each inequality given.
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=What is 623 divided by 7
623 / 7 = 89
Result = 89
I need this answered please
If they meet in 2 hr the rate of the slower car is 86.
What is rate?
rate is the ratio between two of related quantities in the different units. If the denominator of the ratio is expressed as of a single unit of one of those quantities.
Sol- as per the given question
{d =380
{t=2
Substitute {d=380 formula
{t=2
d=v×t
380=2v
=2(18+2x)=380
Apply the distributive property
36+4x=380
Rearrange variables to the left side of the equation
4x=380-36
4x=344
Divided both side of the equation by the coefficient of variable
X=344/4
By cross out the common factor we get
X=86
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Write the equations of the following lines. A line that is parallel to y=2x-4 and passes through the point (1, 1)
Considering the definition of parallel line, a line that is parallel to y=2x-4 and passes through the point (1, 1) is y= 2x -1.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and never touch.
Two lines are parallel if they have the same slope "m" and different y-intercepts "b".
Equation of parallel line in this caseIn this case, the line is y=2x -4
where:
The slope m is 2The y-intercepts b is -4.Since two lines are parallel if they have the same slope, the parallel line has a slope of 2 and has a form of: y= 2x + b
The line passes through the point (1, 1). Replacing in the expression for parallel line:
1= 2×1 + b
1= 2 + b
1 -2= b
-1 = b
Finally, the equation of parallel line is y= 2x -1 .
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Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. The speed of the tennis ball is...
The speed of the tennis ball is 6.2 metres per seconds.
How to find the speed of the tennis?Speed is measured as the ratio of distance to the time in which the distance was covered.
Therefore, speed can be represented mathematically as follows;
speed = distance / time
Hence, the table tennis travels 12.4 metres south in 2 seconds.
The speed of the tennis can be computed as follows:
distance = 12. 4 metres
time = 2 seconds
Therefore,
speed = 12.4 / 2
speed = 6.2 meters per seconds.
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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given that,
Katie and her best friend Liam play tennis every Saturday morning.
When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.
The speed of the tennis can be found by using formula
speed=distance/time
distance = 12. 4 metres
time = 2 seconds
Now speed=12.4/2
speed=6.2
Hence speed of the tennis ball is 6.2m/s
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A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate, in
pounds per hour, does the machine make nails? Show your work.
The rate of pounds per hour of the machine is 1.5 pounds per hour
How to determine the rate of pounds per hour?From the question, we have the following parameters:
Pounds of nails = 2 1/4 pounds of nail
Number of hours = 1 1/2 hour
From the above parameters, the rate of pounds per hour can be calculated using the following formula of constant of proportionality
The constant of proportionality is calculated as
Constant of proportionality = Pounds of nails/Number of hours
In this case, we have
Rate of pounds per hour = Pounds of nails/Number of hours
Substitute the known values in the above equation
Rate of pounds per hour = (2 1/4)/(1 1/2)
So, we have
Rate of pounds per hour = 1.5
Hence, the rate is 1.5 pounds per hour
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Answer:
1 1/2
Step-by-step explanation:
2 1/4 divide 1 1/2 is 1 6/12
1 6/12 simp —-> 1 1/2 (1.5)
A pet hotel charges $25 per night to keep a dog. When the dog arrives, there is a mandatory $15 examination fee. Part A: Write a function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days. Part B: How much would a 6 night stay cost? Part C: Does a 3 night stay cost half as much as a 6 day stay since it is half the time? Explain in detail!
A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15
B) The total cost to stay for 6 nights is; $165
C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.
How to solve algebra word problems?We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.
A) If the number of nights spent is n, then the function rule here for the total cost is;
T = 25n + 15
B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;
T(6) = 25(6) + 15
T(6) = $165
C) The cost of 3 nights would be;
T(3) = 25(3) + 15
T(3) = $90
This is more than half of the cost of 6 nights.
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The area of the arctic ocean is about 5 millon square miles. this is about 16% of the area of which ocean pacific 64 million square miles or indian 25 million square miles
The answer of this question is Indian Ocean
It is the Arctic Ocean.
18% of the Indian Ocean's surface, and the size of 12% of the Atlantic Ocean.
These two oceans are the closest to the Arctic Ocean in terms of size. It depends on whose answers are listed in the table because they are both close to the 16% mark. The closest is the Indian.
Of the five major oceans in the globe, the Arctic Ocean is the smallest and shallowest. It is regarded as the coldest ocean and covers an area of roughly 14,060,000 km2 (5,430,000 sq mi). Despite some oceanographers referring to it as the Arctic Mediterranean Sea, the International Hydrographic Organization (IHO) classifies it as an ocean. Approximately, it has been compared to an estuary of the Atlantic Ocean. In addition, It's been analogized to roughly an estuary of the Atlantic Ocean.
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3 halves times 3 halves
Answer:
2.25
Step-by-step explanation:
Answer:
2.25
Please:
Please Give Brainlist
WILL GIVE BRIANLSIT AND EXTRA POINTS TO BEST ANSWER!! HELP
Eva wants to buy a bicycle.
.The bicycle costs $250.
Eva already has $125 saved.
She plans on washing cars for $25 per car.
Ereed wash c cars to have enough to purchase the bicycle.
Select the 3 orrect equations below that can be used to represent when she will be able to purchase the bicycle she wants
The correct equations which can be used to represent when she will be able to purchase the bicycle she wants are:
250 = 125+25c125 = 25cc = 5Given, Eva wants to buy a bicycle.
The cost of bicycle is = $250
Saving's of Eva = $125
Eva plans on washing cars for $25 per car.
Eva wash 'c' cars to have enough to purchase the bicycle.
cost of bicycle = saving's of Eva + Eva washing 'c' cars for $25 per car.
⇒ 250 = 125 + 25c
arrange the like terms on one side.
⇒ 250 - 125 = 25c
⇒ 125 = 25c
⇒ 25c = 125
⇒ c = 125/25
⇒ c = 5
hence Eva washes 5 cars to earn $125 which gets added to the savings and becomes the cost of the bicycle she wants to purchase.
⇒ cost of bicycle = 125+25(5)
⇒ cost of bicycle = 125+125
⇒ cost of bicycle = $250
Hence we got the required answers.
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Mia needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 690 knives. There are currently 208 knives. If each set on
sale contains 10 knives, write and solve an inequality which can be used to determine
x, the number of sets of knives Mia could buy for the restaurant to have enough
knives.
Using inequality, we know that Mia needs to buy 41 sets of knives.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >, <, ≤, ≥, and ≠ has the meaning "7 is greater than" (or "is less than 7," when read left to right).So, the number of sets of knives Mia could buy:
There are currently 248 knives in the restaurant.There are 10 knives in each set that is for sale, so there are 10s knives added to each set.If s sets are purchased, there will be a total of, T = 248 + 10s.At least 657 knives are required by the restaurant, so:
T ≥ 657The difference is:
10s + 248 ≥ 657Now, solve as follows:
10s ≥ 409s ≥ 409/10s ≥ 40.9Rounding off: 41
Therefore, using inequality, we know that Mia needs to buy 41 sets of knives.
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Trigonometry question
- Refer to the table below if needed.
- Choose the correct graph
1. Given that cos0 = -8/17 and sin0 is negative.
2. Given sec0 = -13/12, choose the two possible angles with domain 0 degrees 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
3. 0 = 315 degrees
Using trigonometry, it is found that:
1. Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.
2. The angles are θ = 157.38º and θ = 202.62º, as shown in Graph 1.
3. Graph 3 shows an angle of θ = 315º.
Sine and cosine negativeIn item 1, it asks for an angle in which both the sine and the cosine of the angle are negative. This happens in the third quadrant, hence Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.
SecantThe secant of an angle is given by one divided by the cosine of the angle, that is:
sec(θ) = 1/cos(θ)
Considering the numeric value of the secant in this problem, we have that:
-13/12 = 1/cos(θ)
-13cos(θ) = 12
cos(θ) = -12/13
The cosine is negative in the second and the third quadrant, hence graph 1 shows these equivalent angles.
Applying the inverse cosine, the angles are given as follows:
θ = arccos(-12/13)
θ = 157.38º and θ = 202.62º. (two equivalent angles).
Angle of 315ºAn angle of 315º is on the fourth quadrant of the unit circle, hence Graph 3 shows this angle.
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x^2-8x+9
find x using the quadratic formula
Answer:
[tex]x = 4 \pm \sqrt7[/tex]
Step-by-step explanation:
Hello!
Standard form of a Quadratic: [tex]ax^2 + bx + c= 0[/tex]
Given the Equation: [tex]x^2 -8x+9=0[/tex]
a = 1b = -8c = 9Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex]
Solve by substituting the values into the Quadratic Formula.
Solve for x[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex][tex]x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(9)}}{2(1)}\\[/tex][tex]x = \frac{8 \pm \sqrt{64 - 36}}{2}\\[/tex][tex]x = \frac{8 \pm \sqrt{28}}{2}\\[/tex][tex]x = \frac{8 \pm 2\sqrt{7}}{2}\\[/tex][tex]x = 4 \pm \sqrt7[/tex]The solution to the quadratic is [tex]x = 4 \pm \sqrt7[/tex].