Answer:
length is 28,breadth is 29
Step-by-step explanation:
firstly we need to know the definition of consecutive integers:-Consecutive integers are those numbers that follow each other . They follow in a sequence or in order.
let the length and breadth be represented by n and n+1
since we are given in perimeter
perimeter of a rectangle =2(length+breadth)
114=2(n+n+1)
114=2n+2n+2
114=4n+2
114-2=4n
112=4n
n=28
:-n=28,(n+1)=28+1=29
:-the length is 28 and the breadth is 29
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The table shown gives values of the function y=g(x) for selected values of x. Which represents g(x)
Given:
A table with the given values of the function y=g(x).
To find the function that represents g(x), we substitute a value of x into the given options.
For:
g(x =3+2x:,:
Let x=3
[tex]\begin{gathered} g(x)=3+2x \\ =3+2(3) \\ =9 \end{gathered}[/tex]Based on the given table, the value g(x) is 24 when x=3. So g(x)=3+2x is not the function that represents g(x).
For
[tex]\begin{gathered} g(x)=3\cdot2x \\ =3\cdot2(3) \\ =18 \end{gathered}[/tex]The value of g(x) =18 when x=3, so this is not the function.
For g(x)=3x^2:
[tex]\begin{gathered} g(x)=3x^2 \\ =3(3)^2 \\ =27 \end{gathered}[/tex]Hence, this is not the function as well.
For g(x)=3(2)^x:
[tex]\begin{gathered} g(x)=3\cdot2^x \\ =3\cdot2^3 \\ =3(8) \\ g(x)=24 \end{gathered}[/tex]We can notice that when x=3, the value of g(x) =24 which is the same as the value of g(x) in the given table.
To double check this, we plug in the other values of x.
Therefore, the answer is:
[tex]g(x)=3\cdot2^x[/tex]Algebraic expression
2(x-7) + 10
Answer:
2(x-2)
Step-by-step explanation: distribute, add the numbers, common factor
The coordinates of the vertices of the triangle shown are P(2, 13), Q(7, 1) and R(2, 1).
What is the length of segment PQin units?
Answer:
13
Step-by-step explanation:
A scale on a map shows that 3 centimeters represents 10 kilometers. what nuber of centimeters on the map represents an actual distance of 25 kilometers
if you answer this question and the one before this question you will ahve good luck for 7 years!
if you dont, you will have bad luck. see attachment below and my question b4 this
Answer:x=32°
y=35°
Step-by-step explanation:
23°+32°+y=90°
55°+y=90°
y=35°
35°+23°+x=90°
58°+x=90°
x=32°
Answer:
Angle AOE = angle FOB = 32° (vertically opposite angles)
x = 32°
Since GH is a straight line, angle COH = angle COG = 90°
Angle BOD = angle COA = y° (vertically opposite angles)
y = 90-32-23 = 35°
the probability of the event that 0
Answer:
basically the even twill not happen as the probability of that is 0
I need help answering this question
If this is an arithmetic sequence, each of the terms will have a common difference. Let's check.
[tex]\begin{gathered} 3-21=-18 \\ 21-147=-126 \end{gathered}[/tex]As we can see, each of the terms does not have a common difference. The first one is -18 while the other one is -126. Therefore, this is not an arithmetic sequence.
Now, let's check if this is a geometric sequence. If it is, each of the terms will have a common ratio.
[tex]\begin{gathered} 3\div21=\frac{1}{7} \\ 21\div147=\frac{1}{7} \end{gathered}[/tex]As we can see, each of the terms has a common ratio which is 1/7. Therefore, 147, 21, 3 is a geometric sequence and the common ratio is equal to 7.
Use the drop-down menus to complete the statements to match the information shown by the graph.
Using the concept of the slope of a linear function, it is found that:
Pool A is filing up slower than Pool B because the slope of the graph for Pool A is less than that of the graph for Pool B.The slope of the graph tells you the unit rate in gallons per minute.What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have that Pool B starts with significantly less water than Pool A, but their volumes get closer, meaning that Pool B fills faster and has a higher slope, that is, it fills more gallons per minute into the pool.
The information above it what we use to complete the statements.
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whats 324/378 simplfy
Answer:6/7
Step-by-step explanation:
Answer:
162/189
Step-by-step explanation:
Divide by 2...................
answer both questions if possible or just the main questions
ASAP
Answer: Domain: [-4,infinity)
Range: (-infinity,6]
f(-1) is 3
Step-by-step explanation:
Answer: Domain: [tex]x\geq -4[/tex]
Range: [tex]y\leq 6[/tex]
f(-1) = 3
Step-by-step explanation:
(-4,6) and (0,2) are both points on the line, so the equation of the line is
y = -x + 2
1 + 2 = 3
Mario can save 40% on headphones at Best Buy with a coupon from the paper. Circle all of
the expressions he can use to find the discounted price of the headphones with an original
price of p.
a. 0.40p b. 0.60p c. p – 0.40 d. p – 0.40p
Answer: B and D.
Step-by-step explanation:
1) Find 40% as a decimal
100% = 1
40% = 0.4
2) It's -40% of its total value. So minus its value time 40%.
p - 0.4p
3) Simplify
0.6p
A) 0.4p not equal 0.6p X
B) 0.6p = 0.6p
C) p - 0.4 not equal 0.6p X
D) p-0.4p = 0.6p
The sum of three numbers is 135. The second number is 4 times the third. The first number is 9 less than the third. What are the numbers?
First number:
Second number:
Third number:
Answer:
First number: 21
Second number: 84
Third number: 30
21 times 4 = 84 which checks out.
30 - 21 = 9 which also checks out
21 + 84 + 30 = 135 so they are correct!
Step-by-step explanation:
Hope it helps! =D
For each equation, choose Rational or Irrational to show your answer.
Use the sequence below to complete each task. -5, 15, -45, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 12th term (22)
you get he common ratio by dividing a term by the previous term
so,
15/-5 = -3
common ratio = -3
Geometric seuqence has a general term of:
[tex]a_n=ar^{n-1}[/tex]Wher
r is common ratio
a is first term
Given,
a = -5
r = -3
We have:
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=-5(-3)^{n-1} \\ a_n=-5\times-3^n\times-3^{-1} \\ a_n=-5\cdot-3^n\times-\frac{1}{3} \\ a_n=-\frac{5}{3}(3)^n \end{gathered}[/tex]12th term is basically n = 12
So, we have:
[tex]\begin{gathered} a_n=-\frac{5}{3}(3)^n \\ a_{12}=-\frac{5}{3}(3)^{12} \\ a_{12}=-885735_{} \end{gathered}[/tex]A biased dice is rolled and the results are recorded in a table. The dice is rolled once more. a) Use the table to estimate the probability that a 3 will be rolled. b) If the dice is rolled another 500 times, how many sixes would you expect to roll? Score 1 2 3 4 5 6 Frequency 12 35 11 23 7 12
The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The events' estimated probabilities are as follows, according to the exponential probability theory:
P(3) = 0. 125
P(6 in 500 rolls) = 68 rolls
Number of times event occurs / number of trials
A number of attempts = sum of frequency:
(12+35+11+23+7+12) = 88
So the probability that a 3 will be rolled as
⇒ number of 3's / number of attempts
⇒ 11/88 = 0.125
The number of 6's probable in 500 rolls
⇒ (12 /88) × 500
⇒ 68.18 = 68
Therefore, the expected number of 6's roll would be 68.
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15. Write the conditional statement that the Venn diagram represents. Be sure to use
the "if, then" format (2 points).
Flower
Rose
Answer:
The conditional statement that the Venn diagram represents is:
"If it is a rose, then it is a flower".
How to write the conditional statement?
Here we have a Venn diagram, in it we can see that the set called "roses" is included in the set called "flowers".
So, the conditional statement is:
"if it belongs to the smaller set, then it belongs to the larger set"
This is kinda trivial.
For our case, it will be written as.
"If it is a rose, then it is a flower".
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The life expectancy of a new born kid increases at a rate of 1.5 years for every day the kid is alive during the first 60 days after being born. The expectancy reduces by 0.5 year for every day the kid is ill during these first 60 days. The initial life expectancy of a new born kid is 10 years. What is the life expectancy of a kid born on a Tuesday, after 37 days of being born (assume the kid is alive on the 37th day) if the kid falls ill on every Sunday?
The total life expectancy of the kid is 45.5 years.
rate of increase of life expectancy = 1.5 years per day
The rate of reduction of life expectancy = 0.5 years per day
37 days will mean ((7x5)+2), i.e., 5 complete weeks and 2 extra days.
Let the 2 extra days be Tuesday and Wednesday, now the 5 complete weeks will start from Thursday and after 37 days, the day will be Wednesday.
In this duration 5 Sundays will come on which the kid falls ill, so the reduction in life expectancy will be: 0.5 x 5= 2.5 years.
The remaining days will be: 37 - 5 = 32
So, the increase in life expectancy will be: 1.5 x 32= 48 years.
Thus, the total life expectancy of the kid is found to be : (48-2.5)years=45.5 years.
What are linear equations?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables.
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Rewrite 4/9 and 7/15 so that they have a common denominator
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-2, 4) and (-8,-6).
The equation for the perpendicular bisector of the line segment whose endpoints are (-2, 4) and (-8,-6) is 3x + 5y + 20 = 0.
What is a perpendicular bisector?A line segment known as a perpendicular bisector is at a right angle (90°) to another line segment and divides the line segment that was intersected into two equal pieces.The midpoint of a line segment is the location where the perpendicular bisector intersects it.Given:
Endpoints of the line segment are (-2, 4) and (-8,-6).
Midpoint of the line segment = ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
= [tex]\frac{-2 +(-8) }{2}[/tex] , [tex]\frac{4 +(-6) }{2}[/tex]
=( [tex]\frac{-10}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (-5, -1)
Slope of the line segment = [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{(-6) - 4 }{(-8) - (-2) }[/tex]
= [tex]\frac{-10}{-6}[/tex] = [tex]\frac{5}{3}[/tex]
The line perpendicular to the line segment will have a slope of the negative reciprocal of the line segment which is -3/5.
Therefore, the perpendicular bisector passes through (-5,-1) and has a slope of -3/5.
Equation of the line will be,
y - y₁ = m(x - x₁)
⇒ y - (-1) = -3/5(x -(-5))
⇒ 5( y + 1) = -3(x + 5)
⇒ 5y + 5 = -3x - 15
⇒ 3x + 5y + 20 = 0
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Please answer Part A and B
Answer:
Part A is Figure D
Part B is 3 units left
Zevel overheard Bradley say he got a 66% on the last test. If Zevel only got one-third whatBradley got, what is Zevel's score?
Let the total marks are 100.
And Bradely got 66% marks.
So the marks of Bradely are:
[tex]\begin{gathered} M_B=\frac{66}{100}\times100 \\ M_B=66 \end{gathered}[/tex]And Zevel got one third of Bradely's marks so:
[tex]\begin{gathered} M_Z=\frac{1}{3}M_B \\ M_Z=\frac{1}{3}\times66 \\ M_Z=22 \end{gathered}[/tex]Jason is putting crown molding in his master bedroom. The length of the room is 22 feet, and the width is 20 feet.How much crown molding will Jason need if he wants to have 20% extra in case of mistakes or damage?
SOLUTION:
Step 1:
In this question, we are given the following:
Jason is putting crown molding in his master bedroom. The length of the room is 22 feet, and the width is 20 feet.
How much crown molding will Jason need if he wants to have 20% extra in case of mistakes or damage?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Perimeter\text{ of the Rectangle = Length + Breadth + Length + Breadth} \\ Perimeter\text{ of the Rectangle = 22 + 20 + 22 + 20 = 84 feet} \end{gathered}[/tex]Then, we need to calculate 20% increase of 84 feet, we have that:
[tex]\begin{gathered} =(\frac{100\text{ + 20 \rparen}}{100}\text{ x 84 feet} \\ =\text{ }\frac{120}{100}\text{ x 84} \\ =1.\text{ 2 x 84} \\ \text{= 100. 8 feet} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]100\text{ . 8 feet}[/tex]find the equation of the line
Answer:
y = 1/2x + 1/2
Step-by-step explanation:
I'm going to give me answer is gradient/slope form :
To work out the gradient we make a triangle from the line and do :
change in y / change in x
You should get 1/2
Now we have y=1/2x + c
to work out c we substitute a point from the line and solve for c :
Point (1 , 1)
1 = 1/2(1) + c
1 = 1/2 + c
c = 1/2
So our final answer is y = 1/2x + 1/2
Hope this helped and have a good day
ben bowled 157 and 193 in his first two games. what must he bowl in his third game to have an average of at least 160?
Ben must bowl 130 in his third game so that the average will be of at least 160.
Given that, Ben bowled 157 and 193 in his first two games. So, we have to calculate the average of his third bowl to have an average of at least 160.
Let the average of third bowl be x.
The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:
Average = Sum of the Observations/Number of Observations
160 = 157+193+x/3
⇒ 160×3 = 157+193+x
⇒ 480 = 350+x
⇒ 480-350 = x
⇒ 130 = x
Therefore, Ben must bowl 130 in his third game so that the average will be of at least 160.
Hence, 130 is the required answer.
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What is a separate-variance t-test
Answer:
it is often known as the unequal variance t test. It assumes that both groups of data are drawn from Gaussian populations, but does not assume that their standard deviations are the same.
Carlos drives 161 kilometers at a speed of 70 kilometers per hour. For how many hours does he drive?
He drove for 2.3 hours.
What is speed?The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
A body's speed is the amount of distance it travels in one unit of time.
Therefore, the SI Unit for speed is the meter per second, abbreviated as m/s
Formula
Speed = [tex]\frac{distance}{time }[/tex]
Time = [tex]\frac{distance}{speed}[/tex]
Given Data
Distance = 161km
Speed = 70km
Putting values in the formula
Time = [tex]\frac{161}{70}[/tex]
Time = 2.3
He drove for 2.3 hours.
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Solve the quadratic equation by factoring Write the answer in reduced fraction form, if necessary.
Given:
The quadratic equation ,
[tex]42x^2-29x-5=0[/tex]The solution of the given quadratic equation can be obtained as,
[tex]\begin{gathered} x=\frac{-(-29)\pm\sqrt[]{(-29)^2-4(42)(-5)}}{2\times42} \\ \text{ =}\frac{29\pm41}{84} \\ x=\frac{29+41}{84}\text{ or x=}\frac{29-41}{84} \\ x=\frac{70}{84}\text{ or x=}\frac{-12}{84} \\ x=\frac{10}{12}\text{ or x=}\frac{-3}{21} \\ x=\frac{5}{6}\text{ or x=}\frac{-1}{7} \end{gathered}[/tex]Hence, the solutions are,
[tex]x=\frac{5}{6},\text{ }\frac{-1}{7}[/tex]Which is the better buy: 1 liter of soda for $1, or 1 gallon of soda for $4? Justify your answer.
It is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4 .
As given in the question,
1 liter of soda for $1 ____(1)
1 gallon of soda for $4
Relation between gallons and liters is given by:
1 gallon is equal to 3.785 liters
1 gallon of soda = $4
⇒ 3.785 liter = $4
⇒ 1 liter = $ ( 4 / 3.785 )
⇒ 1 liter = $ 1.056 _____(2)
From (1) and (2)
$1.056 > $1
It shows $1.056 is little bit higher than $1.
Therefore, it is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4 .
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Which inequality in standard form represents the shaded region?Find all the solutions to the equation 4x3 + 16x2 + 28x = 0.
0, negative 4 + 2 i StartRoot 3 EndRoot, negative 4 negative 2 i StartRoot 3 EndRoot
0, 4 + 2 i StartRoot 3 EndRoot, 4 minus 2 i StartRoot 3 EndRoot
0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRoot
0, 2 + StartRoot 3 EndRoot, 2 minus i StartRoot 3 EndRoot
All solutions to the cubic equation, 4•x³ + 16•x² + 28•x = 0, are presented as follows;
0, -2 + i•√(3), -2 - i•√(3), which is the option;
0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRootWhat are the solutions to a cubic function?The solutions of a cubic function are given by the values at which the graph intersects the horizontal axis.
First Part
The graph showing the shaded region of the inequality is left out
Second part;
The given equation can be presented as follows;
4•x³ + 16•x² + 28•x = 0
Required;
To find all the solutions of the equation
Solution;
The solutions of the equation are given by the locations on the graph where the equation intersects the x–axis, which are therefore, the points where the function is equal to 0
The equation 4•x³ + 16•x² + 28•x = 0 can therefore be used to find the solution as follows;
4•x³ + 16•x² + 28•x = 0
x•(4•x² + 16•x + 28) = 0
x•(4)•(x² + 4•x + 7) = 0
x•(x² + 4•x + 7) = 0 ÷ (4) = 0
x•(x² + 4•x + 7) = 0
Which by the multiplicative identity of 0, gives;
x = 0 or x² + 4•x + 7 = 0Therefore;
x = 0 is a solution to the equation
The other solutions are found from the quadratic equation, x² + 4•x + 7 = 0, using the quadratic formula that gives the solution to the general quadratic equation, a•x² + b•x + c = 0, as follows;
[tex] \displaystyle{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a }}[/tex]
Comparing the general form of the quadratic equation to the quadratic equation from the question;
a•x² + b•x + c = 0
x² + 4•x + 7 = 0
Gives;
a = 1
b = 4
c = 7
Plugging in the above values of a, b, and c, we get;
[tex] \displaystyle{x = \frac{ - 4 \pm \sqrt{ {4}^{2} - 4 \times 1 \times 7 } }{2 \times 1} = \frac{ - 4 \pm 2 \cdot\sqrt{ - 3} }{2} }[/tex]
Which gives;
x = -2 ± √(-3) = -2 ± i•√(3)
The other solutions are therefore;
x = -2 + i•√(3) and x = -2 - i•√(3)The solutions of the equation, 4•x³ + 16•x² + 28•x = 0, are therefore;
x = 0, x = -2+i•√(3), and x = -2 - i•√(3)
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can somebody help me please with this problem in mathematics.
Answer:
$15 × .8 = $12
$12 × .75 = $9