The property that justifies the following statement, 5(3 x+1)=15 x+5 is the distributive property.
Distributive property can be described as one of the properties of multiplication which states that if we multiply two or more values that are added together with a number then the result will be the same even if we multiply each value separately with that number and then add them together. This can be given as:
x(y + z) = xy + xz
Therefore, as 5 x 3 = 15 and 5 x 1 =5, we can write the equation 5(3x+1) as 15x + 5 as the result will be the same in both circumstances.
The distributive property not only justifies the equations when two or more values are added but also justifies the equations in which they are subtracted which can be given as:
x(y-z) = xy - xz
So, according to the distributive property, the statement, 5(3 x+1)=15 x+5 is valid.
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the temperature in Minnesota was -11 degrees Fahrenheit.In Los Angeles the temperature was 57 degrees Fahrenheit.How many degrees warmer was the temperature in Los Angeles.?
Answer:
68 degrees higher.
Step-by-step explanation:
You have to start at negative ( -11 to 0 ) which is already 11 degrees and then you need to count how much degrees from 0 to 57.
Answer: 68°F warmer was the temperature in Los Angeles
Step-by-step explanation:
[tex]57^0F-(-11^0F)=\\\\57^0F+11^0F=\\\\68^0F[/tex]
Unit rate 25 letters in 4 days
Answer:6.25
Step-by-step explanation:25/4=6.25 hope this helps
Part 1 of 3
Use the number line below, where RS= 8y + 2, ST = 4y + 5, and RT = 79.
a. What is the value of y?
b. Find RS and ST.
R
a. What is the value of y?
Please help me
Using the segment addition postulate, the values are:
a. y = 6
b. RS = 50
ST = 29
How to Apply the Segment Addition Postulate?Based on the segment addition postulate, the following equation is true which we can use in finding the missing measures:
RS + ST = RT.
Given:
RS = 8y + 2,
ST = 4y + 5,
RT = 79.
a. Plug in the given values into RS + ST = RT:
8y + 2 + 4y + 5 = 79
12y + 7 = 79
12y = 79 - 7
12y = 72
y = 6
b. RS = 8y + 2 = 8(6) + 2
RS = 50
ST = 4y + 5 = 4(6) + 5
ST = 29
Thus, using the segment addition postulate, the values are:
a. y = 6
b. RS = 50
ST = 29
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Jaya has a points card for a movie theater.
. She receives 70 rewards points just for signing up.
• She earns 7.5 points for each visit to the movie theater.
• She needs at least 175 points for a free movie ticket.
Use the drop-down menu below to write an inequality representing v, the number of
visits she needs to make in order to get a free movie ticket.
The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let v represent the number of visits she needs to make in order to get a free movie ticket.
She needs at least 175 points for a free movie ticket. Hence:
7.5v + 70 ≥ 175
The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175
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7 divided by 9 long division
Find the measure of the numbered angle, and name the theorems that justify your work. (Lesson 2-8)
∠2 and ∠3 are supplementary; m∠2=149
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠3 is 31°.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that ∠2 and ∠3 are supplementary angles. Therefore, the sum of the two angles will be 180°. Thus, we can write the sum of the two angles as,
∠2 + ∠3 = 180°
Also, it is mentioned in the question that the measure of ∠2 is 149°. Therefore, substitute the value of ∠2 in the above equation.
149° + ∠3 = 180°
∠3 = 180° - 149°
∠3 = 31°
Hence, the measure of ∠3 is 31°.
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The value of a certain stock tripled. If you knew what the stock used to be worth, how would you find how much it is
worth now?
Ricardo is talking to his parents about saving for retirement. Which of the following is NOT a good way to save for retirement, and why?
Answer:
There is nothing to refer to
Step-by-step explanation:
3 times a number is increased by 22, the result is 14 less than 7 times the number. What
is the number?
The value of the number is 9
Solving linear equationsFrom the question, we are to determine the number
From the given information,
"3 times a number is increased by 22"
Let the number be x
Thus,
3x + 22
"the result is 14 less than 7 times the number"
That is,
3x + 22 = 7x - 14
Now, solve the equation
3x + 22 = 7x - 14
22 + 14 = 7x - 3x
36 = 4x
x = 36/4
x = 9
Hence, the value of the number is 9
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how many ways can a student select 5 questions from an exam containing 9 questions
There are 126 ways a student can select 5 questions from an exam containing 9 questions
How to determine the number of selections?The given parameters are
Total questions, n = 9
Selected question, r = 5
The number of ways is calculated as
Ways = nCr
This gives
Ways = 9C5
Apply the combination formula
Ways = 9!/5!4!
Evaluate
Ways = 126
Hence, there are 126 ways a student can select 5 questions from an exam containing 9 questions
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Write an equation in slope-intercept form for a line parallel to y=4 x-5 containing (-1,5) .
The equation in slope-intercept form is y = 4x + 1
Given,
Points (x, y) = (-1, 5)
Parallel to y = 4x - 5
Now,
Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").
Therefore the equation of a parallel line has to be of the form:
y = 4x - b
5 = 4(-1) - b
5 = -4 - b
b = -4 - (-5)
b = -4 + 5
b = 1
So the equation now becomes:
y = 4x + 1
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Solve each inequality. Check your solution. 4x - 2 > 1/2
The inequality given by 4x - 2 > 1/2 has the solution x > 5/8 or (5/8 , +∞).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality 4x - 2 > 1/2, add 2 to both sides.
4x - 2 + 2 > 1/2 + 2
4x > 5/2
Multiply both sides by 1/4.
1/4(4x) > 1/4(5/2)
x > 5/8
To check, let x = 3/4
x = 3/4 ≥ 5/8
Substitute this value to the inequality.
4x - 2 > 1/2
4(3/4) - 2 > 1/2
3 - 2 > 1/2
1 > 1/2
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Please Help! Due in 20 minutes
Answers
1.1) So, we're given that 6cm is 15 ft to scale. That means that every 2cm = 5ft. So, the dimensions of her room are 5ft x 10ft.
1.2) In square feet that makes 15 (length*width)
1.3) We want a 3-foot wide couch (1/5 of 15) which means it will be 1/5 of 6cm, which equals 1.2 cm wide.
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Uranium-238 (U-238) has a half-life of 4.5 billion years. Geologists find a rock containing a mixture of U-238 and lead, and determine that 71% of the original U-238
remains; the other 29% has decayed into lead. How old is the rock?
The rock is ___ billion years old.
(Round to three decimal places as needed.)
Answer: 2.223 billion years old
Step-by-step explanation:
since 71 percent of the rock is remaining, the half life hasn't been reached yet. Hence, we know uranium isn't 4.5 billion years old yet. However, every-time 4.5 billions years pass, the rock get smaller by 2 times(a scale factor of 1/2). Hence, you can express that in a log equation:
[tex]\log_{2}(100/(percent of rock remaining))=[/tex] Fraction of 4.5 billions years of time passed
[tex]\log_{2}(100/50)=1[/tex] ==> 100% of 4.5 billion years passed. When 50% of rock remains, 4.5 billion years have passed.
[tex]\log_{2}(100/100)[/tex] =
[tex]\log_{2}(1)=0[/tex] ==> 0% of 4.5 billion years passed. When the rock hasn't decayed at all yet, that means that it is 0 years old.
[tex]\log_{2}(100/71)=0.494[/tex] ==> 49.4 % of 4.5 billion years passed
0.494*4.5 billion =2.223 billion years passed
2.223 billion years old
Evaluate.
5/4 ÷ 3/5
help pls!!!!!
Answer: 25/12
Step-by-step explanation:
Julia grows flowers in a garden that is the shape of a rectangle. the side lengths are 51/2 feet and 3 ft. which of these is equal to the area of the garden
Answer:
Step-by-step explanation:
an area of a rectangle is
A= LW
A=51/2 (3)
A= 153/2
A= 76.5 ft
Write each statement in if-then form. An acute angle measures less than 90 .
If-then form of the given statement : an acute angle measures less than 90 will be : If an angle is an acute angle, then the angle measures less than 90 degrees.
We can understand this problem by using the above statement as an example like :
If an angle is an acute angle, then the angle measures less than 90 degrees. The part after if : an angle is an acute angle is called a hypotheses and the part after then : the angle measures less than 90 degrees is called a conclusion.
Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.
This is noted as :
p → q
This is read - if p then q.
A conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said "If an angle is an acute angle, then the angle does not measure less than 90 degrees."
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Write an equation for each line. m=3 and the y -intercept is (0,2) .
The equation of a line with slope = 3 and y-intercept = (0,2) is: y = 3x + 2
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Now,
Given:
Slope of the given line = 3Coordinates of the y-intercept = (0,2)To find: Equation of the line
Finding:
Now, we know that the slope-point form method to find the equation of a line, requires only two things: slope of the line and coordinates of the y-intercept.The equation so given by the method: y = mx + c, wherem = slope of the linec = y-interceptOn substituting the given values in the above equation, we get:=> y = 3x + 2, which the required equation of the line.
Hence, The equation of a line with slope = 3 and y-intercept = (0,2) is: y = 3x + 2.
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Point D is located on line MV. The coordinates of D are (0,−3/4). What ratio relates MD to DV?
If you do solve this can you show your work so I know how to solve problems like this, too?
Point M coordinates: (-6, 3)
Point V coordinates: (2, -2)
If point D is located on the line MV, then the ratio that relates MD to DV is 3 : 1
How to determine the ratio that relates MD to DV?The given parameters are
Point M coordinates: (-6, 3)Point V coordinates: (2, -2)Point D coordinates: (0, -3/4)Calculate the distance between point D and point M using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have
MD = √(-6 - 0)^2 + (3 + 3/4)^2
Calculate the distance between point D and point V using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have
DV = √(2 - 0)^2 + (-2 + 3/4)^2
The ratio that relates MD to DV is represented as
Ratio = MD : DV
So, we have
MD : DV = √(-6 - 0)^2 + (3 + 3/4)^2 : √(2 - 0)^2 + (-2 + 3/4)^2
This gives
MD : DV = √(-6)^2 + (3 3/4)^2 : √(2)^2 + (-1 1/4)^2
Evaluate the exponents
MD : DV = √[36 + 225/16] : √[4 + 25/16]
Evaluate the sum
MD : DV = √[801/16] : √[89/16]
Divide ratios by √[89/16]
MD : DV = √9 : √1
Evaluate the exponent
MD : DV = 3 : 1
Hence, the ratio that relates MD to DV is 3 : 1
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if a movie starts
at 7:45 and is
I hour and 43
mins what time
will it end
9:28 would be the time the movie ends
Answer:
9:28
Step-by-step explanation:
First, add an hour to 7:45. Then, find how much time there is until you reach the next hour. After that, take the remaining time and add it on. 7:45 plus one hour is 8:45. There is fifteen minutes until the next hour, so subtract that from the forty three minutes. Add that fifteen minutes on and you are at nine o'clock. There is twenty eight minutes left. Add it in to nine o'clock. You now have the time the movie will end
Hope this helps! :)
Solve for f. – 9+8f= – 6+5f
Answer:
f = 1
Step-by-step explanation:
-9 + 8f = -6 + 5f
move variables
-9 + 6 = -3
-3 + 8f = 5f
5f - 8f = -3f
-3 = -3f
divide by -3
f = 1
What is the domain of function f?
ƒ(x) = 2|x − 1| + 3
Find the value of n:
1/(3^√7)^5 = 7^n
Step-by-step explanation:
[tex]n = \frac{ - 5}{3} [/tex]
ATTACHED IS THE SOLUTION!!
542.84−39.93 pls help
Answer:
answer is 502.91
Step-by-step explanation:
answer is 502.91
Answer:
502.91
Step-by-step explanation:
Determine the slope of the line that contains the given points.
A(0,6), B(4,0)
The slope of the line that contains the given points A(0,6), B(4,0) is -3/2.
It is given in the question that the line contains the points A(0,6) and B(4,0).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (0,6)
(c,d) = (4,0)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points A(0,6), F(4,0) is given by:-
(0-6)/(4-0) = -6/4 = -3/2
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I need this answered please
X=2 if and only if |x| = 2
True or false? Please answer if you're 100 percent sure.
Answer:
False
Step-by-step explanation:
Let's just analyze it.
x=2 if and only if |x|=2
That can be rewritten as:
if x = 2 then |x| = 2
AND
if |x| = 2 then x = 2
Let's solve each one separately:
we have x = 2
we can simply get |x| by removing the sign, if any. There is none, so |x| = 2.
The first part checks out.
we have |x| = 2
As with absolute values, this means that either x = 2 or x = -2
So we know from |x| that x is either 2 or -2, but the logical statement said "if |x| = 2 then x = 2", which is too specific - it forgets about -2.
The second part is false.
Overall, we now know that "X=2 if and only if |x| = 2" is false because x = -2 is a counterexample. We get: "False if and only if True" which itself is false.
Write an equation of a parabola with its vertex at the origin and the given characteristics.directrix y=-1
Answer:
ue7e66eywgwgwgwjw7wh3he
If the probability that it will snow on Tuesday is 4/13, then what is the probability that it will not snow?
A 4/9 C 13/9 E 13/4
B 9/13 D 13/5
The correct option is (B) 9/13.
The probability that it will not snow on Tuesday is 9/13.
What is defined as the probability?The ratio of the quantity of favorable outputs to the overall number of possibilities of an event is defined as probability.
The number of favorable results for an experiment with 'n' outcomes is denoted by x.
The following formula is used to determine the probability of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.
Some properties of the probability are mentioned below-
The sum of the probability of an event occurring and not occurring is equal to one.The probability of any event occurring is always between 0 and 1.The probability about an impossible event occurring or of an event not occurring will always be equal to zero.A certain event's probability will always be equal to one.Now, for the stated question;
The probability that it will snow on Tuesday is 4/13.
Use property 1;
Then, the probability that it will not snow on Tuesday is;
= 1 - 4/13
= (13 - 4)/13
= 9/13
Therefore, the probability that it will not snow on Tuesday is 9/13.
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in exercises 14 and 15, the value of the surface area of the cylinder is equal to the value of the cylinder. Find the surface area of the cylinder
Considering that the surface area and the volume of the cylinders are equal, the surface areas are given as follows:
14. 108π ft².
15. 250π ft².
What are the surface area and the volume of a cylinder?For a cylinder of radius r and height h, the surface area is given by:
S = 2πr(h + r).
The volume is given by:
V = πr²h.
For item 14, the parameters are given as follows:
r = 6 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
36πx = 12π(x + 6)
3x = x + 6
2x = 6.
x = 3.
Hence the surface area is:
S = 12π(3 + 6) = 108π ft².
For item 15, the parameters are given as follows:
r = 10 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
100πx = 20π(x + 10)
5x = x + 10
4x = 10.
x = 2.5.
Hence the surface area is:
S = 20π(2.5 + 10) = 250π ft².
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