Find three consecutive even integers such that when the first integer is
multiplied by the third integer, the result is 2 more than 5 times the
second integer. [Only an algebraic solution will be accepted.]

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.

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

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:

Answer:

Step-by-step explanation:

y + 3 = 5/3(x - 2)

y + 9/3 = 5/3x - 10/3

y = 5/3x - 19/3

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!

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.

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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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

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

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

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:

Using the calculator [tex]x = 0.101[/tex]

Answer:

120/7

Step-by-step explanation:

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

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

A quantity that may assume any one of a set of values or in simple words a quantity whose value changes may vary.

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression

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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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!!!!!!!!!

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!

Answer:

The answer is

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

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

We have the final answer as

Hope this helps you

Answer:D

Step-by-step explanation:Edge

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

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. .

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..

Answer:

8

Step-by-step explanation:

3 [tex]x[/tex] 8 = 24

24-6=18

so its 8

Answer:

28.32

Step-by-step explanation:

multply them with a calculator, then take away the numbers you dont need

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.

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!

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)

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:

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]

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.