Answer:
[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]
Step-by-step explanation:
Given that:
r < 5
To simplify:
|3r−15|
Solution:
First of all, let us learn about Modulus function:
[tex]f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.[/tex]
In other words, we can say:
Modulus function has a role to make its contents positive.
If the contents are positive, the result will be equal to its contents only.
If the contents are negative, it will add a negative sign to the contents to make it positive.
Now, let us consider the given condition:
[tex]r < 5[/tex]
Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)
[tex]3r < 15[/tex]
Subtracting 15 from both sides:
[tex]3r-15<15-15\\\Rightarrow 3r-15<0[/tex]
Now, we know that [tex]3r-15<0[/tex], let us use the definition of Modulus function.
Add a negative sign to the contents because the contents are already negative.
[tex]\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15[/tex]
So, the answer is:
[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]
Describe how to translate the graph of y = square root of X to obtain the graph of y = square root of X + 1
Answer:
Translated up by 1 unit.
Step-by-step explanation:
According to the diagram below, if you were to do the (square root of X + 1), then the graph would be translated to the left by 1 unit. If you were to do the square root of X + 1, the graph would be translated up by 1 unit.
Hope this helps!
Which equation has the steepest graph?
A. y = 10x-5
B. y=3/4x-9
c. y = -14x+1
D. y = 2x + 8
The equation that has the steepest slope is y = -14x + 1
What is a slope?A slope is the ratio of the change in the y-coordinates to the change in the x-coordinates of a line segment.
Analysis:
A line is said to be the steepest if it has the highest absolute value of the gradient or slope.
From the equations, the coefficient of x in the equations is taken as the slope. y = -14x+ 1 is the equation with the highest absolute value 14. The absolute value means ignoring the minus sign, since it indicates a negative slope.
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Answer:
Y=-14x+1
Step-by-step explanation:
PLZ HELP!! I WILL NAME BRAINLIEST thxs
Answer:
1.) f(-2)=g(4)
2.) f(0) = g(-2)
3.) f(-4)=g(-2) and f(4)=g(4)
4.) -9
Step-by-step explanation:
Estimate the value of the function at x = 2. Can someone help me with this?
Answer:
y ≈ 2.1
Step-by-step explanation:
If you look at the graph and locate on the x axis 2, you can see that directly above on the line is a little more than 2.
Can you help me round these to significant figures (:
Answer:
a) 2
b) .05
c) 6.07
d) 0.002
When using a debit card: A:There are always fees. B:Identification is always required. C:You still need to record transactions in your checkbook. D:You are not personally liable for more than $50 if it is stolen.
Please answer ASAP :)
Answer:
D.
Step-by-step explanation:
Since this isn't a credit card, there are no interests or fees on a debit card, so A is incorrect. B is also incorrect. You only need identification when you are withdrawing or depositing at a bank, but purchases made in stores or online do not need your identification. You also don't need to record transactions in your checkbook (but it is recommend to keep track of purchases). Modern day technology already records transaction history and all you need to do is access it online.
D is correct because if someone steals your PIN for your debit card, they could go to stores and use that money. You can dispute charges and report to the bank if that happens.
Answer:
B
Step-by-step explanation:
When you get a Debit card, you also get a PIN and everytime you make a purchase, you have to use that PIN. C is wrong because Debit is an electronic form of payment and transactions can be viewed online. A is wrong because there aren't always fees. D is wrong because unless you call the bank provider, you will be held liable for every purchase you make.
Lucio quiere repartir su colección de estampillas entre la mayor cantidad de amigos pero de manera que todos reciban la misma cantidad tiene parar repartir 30 estampillas de animales 75 estampillas de flores y 160 de ciudades del mundo cuantos grupos iguales puede armar
Answer:
Lucio podrá armar 5 grupos iguales de estampillas.
Step-by-step explanation:
El problema plantea un caso de distribución mediante la aplicación del divisor común mayor a todos los números involucrados. Para ello, primero debemos analizar los divisores de cada uno de estos números:
-30: divisible por 2, 3, 5, 6, 10, 15 y 30.
-75: divisible por 3, 5, 15, 25 y 75.
-160: divisible por 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 y 160.
Así, podemos ver que el divisor común mayor a los tres números es 5, ya que 30, 75 y 160 dan como resultado un número entero tras ser divididos por 5.
Entonces, para poder repartir equitativamente sus estampillas entre la mayor cantidad de amigos posibles, deberá repartir 6 estampillas de animales, 15 estampillas de flores y 32 estampillas de ciudades a 5 amigos. De esta manera, Lucio podrá armar 5 grupos iguales de estampillas.
2hours 45minutes in minutes
Answer:
165 minutes
Step-by-step explanation:
1hour--> 60 minutes
60+60+45=165 minutes
Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 825 and 900 hours
Answer:
P(825 to 900 hours) = 0.4772-0.3413=0.1359
Step-by-step explanation:
We are given that the life-span of the bulbs are normally distributed.
First we need to find the z-values, where
z(x)=(x-mean)/standard deviation
=(x-750)/75
therefore
z(825)=(825-750)/75=1
z(900)=(900-750)/75=2
Now we need to find the probabilities of the given z-values, from a probability table or from software.
P(z=1) = 0.3413
P(z=2)=0.4772
So probability that the life-span falls between 825 and 900 hours would be P(825 to 900 hour) = 0.4772-0.3413=0.1359
Please help thanks
a(n)=−6+3(n−1)
Answer:
a=-1
Step-by-step explanation:
a(n) = -6+3(n-1)
a(n) = -6+3n-3
a(n) -n=-6+3n-n-3
a=-6+3-3
+3 +3
a3=-3
---- ----
3 3
a=-1
what are the roots of the quadratic equation below 2x ^ 2 - 12x + 13=0 PLEASE HELP
Answer:
messy... but hope it helps you.
Factoring without Combining Like Terms
Try it
Complete the steps to factor 2x2 + 6x + 5x + 15 by grouping.
2x2 + 6x + 5x + 15
Step 1: Group the first two terms and the second two terms.
(2x2 + 6x) + (5x + 15)
Group 1 Group 2
Step 2: What is the greatest common factor of Group 1?
2
Ox
O 2x
Answer:
(x + 3)(2x + 5)
Step-by-step explanation:
Given
2x² + 6x + 5x + 15 ← grouping the terms
= (2x² + 6x) + (5x + 15) ← factor each group
= 2x(x + 3) + 5(x + 3) ← factor out (x + 3) from each term
= (x + 3)(2x + 5) ← in factored form
Answer:
EDG 2021
Step-by-step explanation:
Step 2: C. 2x
Step 3: B. 5
Step 4: C. x + 3
Step 5: A. (x + 3) (2x + 5)
Here's a graph of a linear function. Write the
equation that describes that function. Express it in slope-intercept form.
Answer:
y = -2x -5
Step-by-step explanation:
The line crosses the y-axis at -5. So, b = -5.
It goes down 2 units for each 1 unit to the right, so has a slope of ...
m = rise/run = -2/1 = -2
__
The slope-intercept form of the equation of a line is ...
y = mx +b where m is the slope and b is the y-intercept
For the slope and y-intercept shown, the equation is ...
y = -2x -5
Suppose you want to learn more about the heights of the buildings in New York City. How would you choose a sample of the buildings? Would your sample be representative of the whole city? Why or why not?
Answer:
I'd use a Non-probability Sampling Method.
Explanation:
The question is already laced with criteria - Heights of Buildings in New York.
This means that there are certain buildings that won't fit in the sample. In a non-probability sample, objects or subjects are elected based on specified criteria that are not random. This means that not all objects/subject have a chance of being included in the sample.
It is assumed that the question/assignment centers around high rise buildings.
Therefore, one storey buildings and bungalows that are within and outside New York will not be included in the sample.
Under the Non-Probability Sampling Method, it is essential to note that there are other subgroupings of sampling techniques. They are:
Convenience SampleVoluntary SamplePurposive SampleSnowball SampleCheers!
Vincent made a sketch that measures 10 inches by 15 inches. If he creates a new drawing where each of the dimensions is tripled, what will be the perimeter of the new drawing?
Answer:
150 inches
Step-by-step explanation:
Vincent sketch is a rectangle
10 inches by 15 inches
Length=15 inches
Width=10 inches
If each dimension is tripled
Then,
Length=15*3=45
Width=10*3=30
Perimeter of the new drawing=2(length+width)
=2(45+30)
=2(75)
=150 inches
Work out the size of angle x: 38° is at the top of the triangle, 101° is at the bottom right of the triangle, work out the size of angle x which is at the bottom left of the triangle.
Answer: x = 41°
Step-by-step explanation:
The sum of the angles in a triangle equals 180°.
To find the missing angle, subtract the sum of the two given angles from 180.
101 + 38 = 139
180 - 139 = 41
x = 41°
The size of the angle at the bottom left of the triangle is 41°.
What is a triangle?A triangle is a geometric figure which has three edges and three vertices. The sum of a triangle's three angles is 180°.
How to solve this problem?Given that the two angles of the triangle are 38° and 101°. We have to find the size of the other angle which is at the bottom left of the triangle. Let the size of the angle be x°.
We have to solve the equation:
x + 38 + 101 = 180
i.e. x = 180 - (38 + 101) = 180 - 139 = 41°
Therefore, the size of the angle at the bottom left of the triangle is 41°.
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Which relation is a function?
Answer:
C is the only one that looks right
6
5
WEM
-8-8-54-2-10
2
-2
3
c
B
-5
Which of the four images was formed by a reflection of the letter M?
А
Answer:
The answer is option A.
Hope this helps you
I don’t quite understand what to do or how to solve it. Can someone explain please ?
Answer:
True.
Step-by-step explanation:
Remember the vertical line test. Anywhere on that graph, you can draw a vertical line, and it will not touch the function two times. Because of this, it is true.
could anyone help me???? I WILL GIVE THE BRAINLIEST!!!!!!! PLEASE PLEASE PLEASE!!!! or could anyone tutor me on how to do it?????? 27 points!!!!!!!!
Answer:
see attached
Step-by-step explanation:
The attachment is my effort to complete the proof. It appears to me the idea is to show that B=3+1 and that 1=3+C. Then you substitute (3+C) for 1 and you've got the proof you want.
_____
The given statements and reasons are intended to give you enough clues that you can figure out the logic that is being used. Once you have done that, you fill in the missing details.
Amir wants to buy a $1382 Apple iPhone that is 12% off. What is 1 point
the discounted price before tax? *
Answer:
1273
Step-by-step explanation:
C) the answer on edg is C.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
c.) x-2
Step-by-step explanation:
Answer:
X-2
Step-by-step explanation:
Rewrte the expression with a ratational exponent as a radical expression (4^2/5)^1/4
Answer:
Step-by-step explanation:
(4^2/5)^1/4
first multiply the exponent
2/5*1/4=2/20=1/10
4^1/10= 10√4(the ten is on the top to the square root)
They can leave tonight by bus, or they can save two hours by leaving tomorrow morning and using the express train which travels 20 km/h faster than the bus. If the distance between South Central High and Calgary is 800 km, determine how long it will take to travel by bus, rounded to the nearest hour.
Answer:
The bus will take 10 hours to travel from South Central High to Calgary.
Step-by-step explanation:
Let suppose that both bus and express train travels at constant speed, whose kinematic formula is now described:
[tex]v = \frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]v[/tex] - Speed, measured in kilometers per hour.
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
The transportation time is cleared afterwards:
[tex]\Delta t = \frac{\Delta s}{v}[/tex]
The kinematic expressions for the bus and the express bus are, respectively: ([tex]\Delta s = 800\,km[/tex])
Bus
[tex]\Delta t = \frac{800\,km}{v}[/tex]
Express train
[tex]\Delta t - 2\,h = \frac{800\,km}{v + 20\,\frac{km}{h} }[/tex]
By eliminating [tex]\Delta t[/tex]:
[tex]\frac{800\,km}{v} -2\,h = \frac{800\,km}{v+20\,\frac{km}{h} }[/tex]
[tex]\frac{800\,km}{v} - \frac{800\,km}{v+20\,\frac{km}{h} } = 2\,h[/tex]
[tex]800\cdot (v+20)-800\cdot v = 2\cdot v\cdot (v+20)[/tex]
[tex]16000 = 2\cdot v^{2}+40\cdot v[/tex]
[tex]2\cdot v^{2}+40\cdot v -16000 = 0[/tex]
Which is a second-order polynomial and whose roots are:
[tex]v_{1} = 80\,\frac{km}{h}[/tex] and [tex]v_{2} = -100\,\frac{km}{h}[/tex]
Only first root is physically reasonable, as speed is a scalar, that is, a number that is represented only by magnitude. Then, the time taken by the bus to travel from Central High to Calgary is: ([tex]v = 80\,\frac{km}{h}[/tex])
[tex]\Delta t = \frac{800\,km}{80\,\frac{km}{h} }[/tex]
[tex]\Delta t = 10\,h[/tex]
The bus will take 10 hours to travel from South Central High to Calgary.
Fiona's school is in the shape of a triangle, with three hallways connecting the corners. Fiona enters the building and walks 90 yards through the first hallway to the first corner. Then, she walks 60 yards through the second hallway to the second corner. A triangle is shown. The side lengths are 60 yards, 90 yards, and question mark. The top point is labeled exit and the bottom right point is labeled entrance. The distance between exit and entrance is question mark. What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answer:
bettween 30 and 150 yards
Step-by-step explanation:
test
Answer:
Between 30 yds and 150 yds.
Step-by-step explanation:
Got it right Edge 2021
If the sum of all interior angles of a regular polygon is 1080 degrees then number of sides of the polygon is?
Answer: 8
Step-by-step explanation:
The formula for the sum of the angles of a polynomial is:
[tex]S_n=180(n-2)[/tex]
1080 = 180(n - 2)
1080 = 180n - 360
1440 = 180n
8 = n
Answer:
8
Step-by-step explanation:
It's an octagon
write the ratio 4.5: 2.25 in the form n:1
Step-by-step explanation:
you will divide both sides of the ratio I.e the 4.5 and 2.25 by 2.25
Instructions: Find the equation of the line through point (5, 1) and
perpendicular to 5x - y = -3. Use a forward slash (i.e. "/") for fractions
(e.g. 1/2 for).
make y the subject
y= 5x + 3
perpendicular line needs the reciprocal of the gradient
y = 1/5x + c
substitute in the point
1 = 1/5(5) + c
5/5 = 1 so the answer is y = 1/5x
hope this is helpful!
The required equation of the line is [tex]\bold{y=-\frac{1}{5}x+2}[/tex]
What is the slope-point form of equation of the line?"The equation of the line having slope m and passing through points (p, q) is (y - q) = m(x - p)"
What is the slope-intercept form of the line?"y = mx + c, where m is the slope and c is the Y-intercept of the line."
For given question,
We have been given a point (5, 1)
The required line is perpendicular to the line 5x - y = -3
⇒ 5x - y = -3
⇒ - y = -5x - 3
⇒ y = 5x + 3
Comparing above equation with slop-intercept form of the line.
m = 5
Let m1 be the slope of the required line.
We know that the product of the slopes of perpendicular lines is -1.
⇒ m1 × m = -1
⇒ m1 = [tex]\frac{-1}{5}[/tex]
Now we find the equation of the required line by using slope-point form.
Let (p, q) = (5, 1)
By using slope-point form,
⇒ (y - q) = m1(x - p)
⇒ (y - 1) = [tex]-\frac{1}{5}[/tex] (x - 5)
⇒ y - 1 = [tex]-\frac{1}{5}x[/tex] + 1
⇒ y = [tex]-\frac{1}{5}x[/tex] + 2
Therefore, the required equation of the line is [tex]\bold{y=-\frac{1}{5}x+2}[/tex]
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(04.03 LC
Given the following system of equations:
3x + 5y = 30
X + 3y = 10
Which action creates an equivalent system that will eliminate one variable when they are combined?
Answer:
multiply second equation by (-3)
new system of equations:
3x + 5y = 30
-3x - 9y = -30
Step-by-step explanation:
x + 3y = 10
multiplied by (-3):
-3x - 9y = -30
combinig:
3x+5y + (-3x-9y) = 3x - 3x + 5y - 9y = -4y
10 + (-30) = -20
so: -4y = -20
Answer:
Multiply the second equation by −3 to get −3x − 9y = −30.
Step-by-step explanation:
write 26/39 simplest form
Answer:
2/3
Step-by-step explanation:
26/39
26 and 39 are multiples of 13.
Simplify the fraction.
26 ÷ 13 / 39 ÷ 13
⇒ 2/3