Answer:
4, 6, 8
Step-by-step explanation:
Let the three consecutive integers be a, b, and c.
So, first, we know that they are three consecutive even integers. In other words:
[tex]a=2n,b=2n+2,c=2n+4[/tex]
N is any integer, but the 2n ensures that the outcome is even. Since we want to make the subsequent terms also even, we add 2.
We are told that when the first integer (a) is multiplied by the third integer (c), the result is 2 more than 5 times the second integer (b). In other words:
[tex]ac=2+5b[/tex]
Substitute:
[tex](2n)(2n+4)=2+5(2n+2)[/tex]
Distribute both sides:
[tex]4n^2+8n=2+10n+10[/tex]
Add on the right:
[tex]4n^2+8n=10n+12[/tex]
Subtract 10n and 12:
[tex]4n^2-2n-12=0[/tex]
Divide everything by 2:
[tex]2n^2-n-6=0[/tex]
Factor. Find two numbers that when multiplied equals (2)(-6)=-12 and when added equals -1.
3 and -4 works. Thus:
[tex]2n^2-4n+3n-6=0\\2n(n-2)+3(n-2)=0[/tex]
Combine:
[tex](2n+3)(n-2)=0[/tex]
Zero Product Property:
[tex]2n+3=0\text{ or } n-2=0[/tex]
Solve for n:
[tex]n=-3/2\text{ or } n=2[/tex]
So, n is either -3/2 or 2.
That means that a must be either:
[tex]a=2(-3/2)\text{ or } 2(2)[/tex]
Multiply:
[tex]a=-3\text{ or } 4[/tex]
The first answer is not even. So:
[tex]a=4[/tex]
Our first answer is 4.
And our sequence is 4, 6, and 8.
Checking:
4 times 8 is 32.
2 plus 5 times 6 is also 32.
So our answer is correct.
The sum of 2 composite numbers is never a prime number. Explain your answer.
Answer:
Step-by-step explanation:
Composite numbers are positive numbers that have factors, This means that they are divisible by numbers other than 1 and itself provided that number is a factor of the composite number. They possess at the bearest minimum level, a divisor other than 1 and itself. They are a natural number that is expressible as the product of two(or more) numbers other than 1 and itself.
For example:
4 is a composite number because its factors are 1, 2 and 4 which have another divisor apart from 1 and itself (4). That divisor is 2.
We all know that prime numbers are numbers that can be only be divided by 1 and itself.
Therefore, the sum of two composite number, for example:
4 + 6 = 10, We can now see that 10 is never a prime number.
Find the midpoint of the segment with the following endpoints.
(-2, 1) and (6,-3)
Answer:
The midpoint is ( 2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-2+6)/2 =4/2 =2
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
( 1+-3)/2 = -2/2 = -1
The midpoint is ( 2,-1)
Answer:
(2, -1)
Step-by-step explanation:
Let M is the midpoint of that segment with the endpoints A(-2,1) and B(6,-3)
x-coordinate of M:
xM = (xA + xB) / 2 = (-2 + 6) / 2 = 4 / 2 = 2
y-coordinate of M:
yM = (yA + yB) / 2 = ( 1 + -3) / 2 = -2 / 2 = -1
Answer: M(2, -1)
Determine the exponential regression of the data below using either a calculator or spreadsheet program. Round the values in the regression equation to two decimals.Then, estimate the y value when the x value is 100. Round your answer to one decimal place. (14,500),(23,320),(37,150),(41,87),(56,40),(70,21)
Answer:
Y = 1148.92(0.94^x) ; Y = 2.4
Step-by-step explanation:
Given the following data :
(14,500),(23,320),(37,150),(41,87),(56,40),(70,21)
X:
14
23
37
41
56
70
Y:
500
320
150
87
40
21
The exponential regression equation is expressed in the form :
Y = AB^x
A = Initial value
B = rate ; x = time
Using the online exponential regression calculator on the data provided :
Y = 1148.92(0.94^x)
Y = prediction
Estimate y, when x = 100
Y = 1148.92(0.94^100)
Y = 1148.92(0.0020548)
Y = 2.360800816
Y = 2.4
Answer:
2.4
Step-by-step explanation:
You ran 2 miles on Monday,2 miles on Tuesday, 3 miles on Wednesday ,2 miles on Thursday and 4 miles on Friday how many miles did you run during the week
Answer:
13 miles
Step-by-step explanation:
Add all of the number of miles you ran from each day to get your total mileage.
2+2+3+2+4
The product of two whole number is 462 and their sum is 43. What are the two numbers?
Answer:
21 and 22
Step-by-step explanation:
Let the two whole numbers be a and b.
Their product is 462. Hence, we can write that:
[tex]ab=462[/tex]
Likewise, because their sum is 42:
[tex]a+b=43[/tex]
This yields a system of equations:
[tex]\displaystyle \begin{cases} ab = 462 \\ a + b = 43 \end{cases}[/tex]
We can solve the system using substitution.
Isolating one variable in the second equation yields:
[tex]a=43-b[/tex]
From substitution:
[tex](43-b)(b)=462[/tex]
Distributing yields:
[tex]-b^2+43b=462[/tex]
Solve for b by factoring:
[tex]\displaystyle \begin{aligned} b^2 - 43d & = -462 \\ \\ b^2 - 43d + 462 & = 0 \\ \\ (b-21)(b-22) &= 0 \\ \\ b = 21 \text{ or } b & = 22 \end{aligned}[/tex]
Solve for a:
[tex]\displaystyle \begin{aligned} a& =43-(21) & \text{ or } a& =43-(22) \\ a&=22&\text{ or } a&=21\end{aligned}[/tex]
In conclusion, the two whole numbers are 21 and 22.
What is the value of r in the equation 3r − 6 = 18?
6
8
18
24
Answer:
8
Step-by-step explanation:
3 [tex]x[/tex] 8 = 24
24-6=18
so its 8
2 Blood sugar levels are normally distributed with a mean of 100 milligrams per deciliter and a standard deviation of 10 milligrams per deciliter. Sam's blood sugar is 85 milligrams per deciliter. What is his Z-score? * (2 Points) O 1.5 0 -1.5 O 15 010
235 people are at RSM summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp? PLS DO IT QUICK
Answer:
Number of girls = 90
Number of boys = 125
Number of Adults = 20
Step-by-step explanation:
Let us represent:
The number of girls = g
The number of boys = b
Number of Adults = a
235 people are at RSM summer camp.
Hence,
g + b + a = 235 .......Equation 1
There are 35 more boys than girls, and 70 fewer adults than girls.
b = g + 35
a = g - 70
Hence we substitute g + 35 for b and g - 70 for a in Equation 1
g + b + a = 235 .......Equation 1
g + g + 35 + g - 70 = 235
3g + 35 - 70 = 235
3g - 35 = 235
3g = 235 + 35
3g = 270
g = 270/3
g = 90
Hence, there are 90 girls in the party.
Number of boys is calculated as:
b = g + 35
b = 90 + 35
b = 125
Number of Adults is calculated as:
a = g - 70
a = 90 - 70
a = 20
How many people of each group are at the camp?
Number of girls = 90
Number of boys = 125
Number of Adults = 20
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
When a number is increased by 26, the result is tripled. Then the result is increased by 72. If the final result is 1/2 of the number, what is the value of this number?
Answer:
-60.
Step-by-step explanation:
Let the unknown number be x.
Number is increased by 26 = x+26
Then result is tripled = 3(x+26)
Then the result is increased by 72 = 3(x+26)+72
Final result is [tex]\dfrac{1}{2}[/tex] of the number = [tex]\dfrac{1}{2}x[/tex]
[tex]3(x+26)+72=\dfrac{x}{2}[/tex]
[tex]3x+78+72=\dfrac{x}{2}[/tex]
[tex]3x+150=\dfrac{x}{2}[/tex]
Isolate variable terms.
[tex]3x-\dfrac{x}{2}=-150[/tex]
[tex]\dfrac{6x-x}{2}=-150[/tex]
Multiply both sides by 2.
[tex]5x=-300[/tex]
Divide both sides by 5.
[tex]x=-\dfrac{300}{5}[/tex]
[tex]x=-60[/tex]
Therefore, the required number is -60.
Can someone explain this to me?
Answer:
120/7
Step-by-step explanation:
You cross multiply120=7xDivide both sides x= 120/7Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)? Question 16 options: A) There isn't enough information given. B) g(x) and ƒ(x) have equal absolute maximums. C) g(x) D) ƒ(x)
Answer:
Answer C: g(x)
Step-by-step explanation:
I used a graphing calculator to graph f(x) = -x^2 + 4x - 5, and by doing so I immedately saw that the vertex of f(x) is at (2, -1).
The absolute max of g(x) is approximately (3.25, 6.1).
The absolute max of f(x) is approximately (2, -1).
Since the y-coordinate of the absolute maximum of g(x) is greater than the y-coordinate of the absolute maximum of f(x), we conclude that Answer C is correct: g(x) has the greater absolute maximum
For an apartment complex, the association collects $158,000 from all of its 211 residents. What is the average rent per capita for this apartment complex?
Solve the equation –4 In(6x) = 2.
O A. 0.101
B. 0.275
C 3.639
D. 67.238
Isolate the variable using algebraic manipulation.
[tex]-4 ln(6x)=2[/tex]
[tex]ln(6x)=-\frac{1}{2}[/tex]
[tex]6x=e^{-\frac{1}{2}}[/tex]
[tex]x=\frac{e^-\frac{1}{2}}{6}[/tex]
[tex]x=0.101[/tex]
Hope this helps.
頑張って!
Answer:
A) 0.101
Step-by-step explanation:
[tex]ln(6x) = -1/2[/tex] [tex]6x = e^(^-^1^/^2^)[/tex] [tex]6x = 1/\sqrt{e}[/tex] [tex]x = 1/(6\times \sqrt{e})[/tex]Using the calculator [tex]x = 0.101[/tex]
What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?
Answer:
The answer is
[tex]y = - \frac{3}{5} x + 13[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is 3x + 5y = 11
We must first write the equation in the general equation above
So we have
5y = - 3x + 11
Divide both sides by 5
[tex]y = - \frac{ 3}{5} x + \frac{11}{5} [/tex]Comparing with the general equation above
Slope = - 3/5
Since the lines are parallel their slope are also the same
Slope of parallel line = - 3/5
So the equation of the line using point
(15, 4) and slope - 3/5 is
[tex]y - 4 = - \frac{3}{5} (x - 15) \\y - 4 = - \frac{3}{5} x + 9 \\ y = - \frac{3}{5} x + 9 + 4[/tex]We have the final answer as
[tex]y = - \frac{3}{5} x + 13[/tex]Hope this helps you
Answer:D
Step-by-step explanation:Edge
ANSWER ASAP
In the diagram shown to the right, mGAF = x-6, mEAF=x+18, and mGAE=72. find the value of x and the numerical values of mGAF and mEAF
find x first 72-18+6=48
now make x=48
48-6=42
now x is 42
42+18=60
now x=60
Thnks!
|Brailiest!!!!!!!!!
Round $7.425.07 to the nearest dollars
All we need to do is round up so we don't have any decimal.
Remember:
4 and below rounds down
5 and above rounds up
Since we have the number "0" in the tenths place, its below 0 so we round down.
7,425.07 -> 7,425
Therefore, the answer is [ 7,425 ]
Best of Luck!
Question text
A recipe calls for 5 cups of flour to make 20 biscuits, how many cups of flour do you need to make 100 biscuits.
Findf '(3), where f(t) = u(t) · v(t), u(3) =1, 2, −2, u'(3) =8, 1, 4,andv(t) =t, t2, t3.
Answer:
[tex]f'(3)=100[/tex]
Step-by-step explanation:
Given:
[tex]f(t)=u(t)\cdot v(t)\\u(3)=\left ( 1,2,-2 \right )\\u'\left ( 3 \right )=\left ( 8,1,4 \right )\\v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
To find: [tex]f'(3)[/tex]
Solution:
[tex]v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v(3)=(3,3^{2},3^{3} )=(3,9,27)[/tex]
Differentiate with respect to t
[tex]v'(t)=\left ( 1,2t,3t^{2} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v'(3)=\left ( 1,2(3),3(3)^{2} \right )=\left ( 1,6,27 \right )[/tex]
Using product rule, differentiate [tex]f(t)=u(t)\cdot v(t)[/tex] with respect to [tex]t[/tex]
[tex]f'(t)=u'(t)\cdot v(t)+u(t)\cdot v'(t)[/tex]
At [tex]t=3;[/tex]
[tex]f'(3)=u'(3)\cdot v(3)+u(3)\cdot v'(3)\\=\left ( 8,1,4 \right )\cdot \left ( 3,9,27 \right )+\left ( 1,2,-2 \right )\cdot \left ( 1,6,27 \right )\\=24+9+108+1+12-54\\=100[/tex]
I need help with 1,2 and 3
Step-by-step explanation:
Hey there!!!
1. Ans.
The formula for quadratic equation,
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
2. Ans.
When, the quadratic equation is given, in the form of;
[tex]a {x}^{2} + bx + c = 0[/tex]
Then, "a" is the coefficient of x "b" is the coefficient of y. and c is the constant value.
3.Ans.
[tex] \sqrt{ {b}^{2} - 4ac } \: tells \: us \: the \: type \: of \: solutions.[/tex]
Hope it helps..
Help me please 2(x-4) = 6x - 6
Answer:
-1/2
Step-by-step explanation:
2(x-4)=6x-6
2x-8=6x-6
2x-6x-8=-6
-4x-8=-6
-4x=-6+8
-4x=2
x=2/-4
simplify
x=-1/2
Answer:
[tex]x = -\frac{1}{2}[/tex]
I hope this helps!
Write an equation in slope-intercept form (y = mx + b).
Passing through (2, -3) with a slope of 5/3.
Answer:
Step-by-step explanation:
y + 3 = 5/3(x - 2)
y + 9/3 = 5/3x - 10/3
y = 5/3x - 19/3
Plz help 7th grade math
Answer:
9feet
Step-by-step explanation:
B= -34 M=-25
-34-(-25)=-34+25=9
Answer:
9 feet
Step-by-step explanation:
Brett is -34 feet and Max is -25 feet from sea level.
In order to find how many feet Max is above Brett, we can change the numbers to be positive and subtract Brett's distance - Max's distance
34-25=9
Max is 9 feet above Brett
Solve the inequality 9y+5(y+3)<4y−35 and write the solution in interval notation.
Answer:
( −∞,−5) interval notation, and inequality solution y < -5 ,
Step-by-step explanation:
Answer:
y<-5
Your Interval Notation would be an open circle and the arrow would be pointing to the left. (<-- (-6) --- (-5) --- (-4) -->) This will be your # line.
Step-by-step explanation:
9y+5(y+3) < 4y-35
1) Distribute the 5 in 5(y+3).
9y+5y+15 < 4y-35
2) Combine like terms. 9y and 5y.
9y+5y= 14y
14y+15 < 4y-35
3) MY TIP is to keep the variables on the left side, bc if you don't at the end you will have to flip the sign. so.. Subtract 4y from both sides
14y+15 < 4y-35
-4 -4
10y+15 < -35
3) Then you will subtract 15 from both sides
10y+15 < -35
-15 -15
10y < -50
4) Last is to divide to get your variable by itself.
10y < -50
÷10 ÷10
Answer : y < -5
Interval Solution: Open circle, -5 in the middle of the line and you will shade in the numbers to the left. .
Identify the nonlinear graph A) B) C) D)
A linear function makes a straight line
A nonlinear graph is any curve that isn't a straight line. In this case, graph C is a parabola (from a quadratic function).
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
The non-linear graph is option D.
Option D is the correct answer.
What are coordin2ates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Graph A
Graph B
Graph C
Graph D
A linear graph is a graph that is a straight line.
A non-linear graph is a graph that is not a straight line.
Now,
With the given coordinates on each graph, we see that,
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
Thus,
The non-linear graph is option D.
Option D is the correct answer.
Learn more about coordinates here:
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Multiply 39.341 × 0.72 = _____ Numerical Answers Expected!
Answer:
28.32
Step-by-step explanation:
multply them with a calculator, then take away the numbers you dont need
PLEASE HELP
Consider the equation: 1/4x + 3y − 23 = 42
The variables are:
The coefficients are:
The constants are:
Answer:
The variables are x and y.The coefficients are 1/4 and 3.Lastly the constants are -23 and 42
Step-by-step explanation:
Variables are letters used to represent an unknown number.Coefficients are the numbers in front of the variables.Constants are numbers by themselves they can be positive and negative.
For the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
What is a variable?A quantity that may assume any one of a set of values or in simple words a quantity whose value changes may vary.
What is a coefficient?A numerical or constant quantity placed before and multiplying the variable in an algebraic expression
What is a constant?A constant is a value or number that never changes in expression
in the given equation: 1/4x + 3y − 23 = 42
x and y are variables as the changes for different set of values.
1/4 and 3 are coefficient as they are placed before and multiplying the variable.
-23, 42 is a constant as its value never changes in expression.
Thus for the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
To know more about variables , coefficients and constants click here
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5-1 + (-3) = 3 + (-1)
Answer: 1=2 so your answer would be false.
Step-by-step explanation:
Answer:
The answer is 1=2 which is false.
Step-by-step explanation:
5-1+(-3)= 3+(-1)
or, 5-1-3 = 3-1
or, 5-4 = 2
or, 1=2
Order the numbers in each list from least to greatest
-5,-7,0,-1
A. 0,-1,-5,-7
B. -1,-5-7,0
D. -7,-1-5,0
C. 7,-5-1-0
I really need help with this question
Answer:
-7,-5,-1,0
Step-by-step explanation:
The reason behind this is because if you think about it -7 is small number due to it being in the other side of the number line, and same goes with -5 and -1
which are possible names for the angle
Answer:
[tex] < JHP \\ < H[/tex]
Step-by-step explanation:
[tex] < [/tex]
Note the letter in the number carries the angle I
sign.
According to the diagram, H is the angle
Answer:
The answer to this one is <JHP and <H
Step-by-step explanation:
Math 1 3/8 1/4 a c= 2 5/8 11/16 a c= 3 4/6 6/9 a c=
Wen can turn both fractions into decimals.
1 1/3 = 1.333...
1/4 = 0.25
As we can see 1 1/3 is greater than 0.25.
Therefore, the answer is [ 1 1/3 > 1/4 ]
Best of Luck!