The sum of 4 consecutive multiples of 6 is 540. What is the greatest of these numbers?

9514 1404 393

Answer:

Step-by-step explanation:

An easy way to tell if the equation is true is to multiply it by the product of the denominators (cross multiply).

  7×7 ≠ 12×4 . . . . proportion is False

  9×8 = 36×2 . . . . proportion is True

  8×9 = 24×3 . . . . proportion is True

  5×104 = 8×65 . . . . proportion is True

Answer:

y = -6x + 1

Step-by-step explanation:

y = mx + b

b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6

y = -6x + b

-5 = -6(1) + b

b = 1

y = -6x + 1

Answer:

[tex]y=-6x+1[/tex]

Step-by-step explanation:

The linear equation with slope m and intercept c is given as follows:

[tex]y=mx+c[/tex]

The formula for slope of line with points [tex](x_{1} ,y_{2} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] can be expressed as,

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The line passes the points that are [tex](1,-5)[/tex] and [tex](3,-17)[/tex]

The slope of the line can be obtained as follows:

[tex]m=\frac{-17-(-5)}{(3)-1}[/tex]

[tex]m=\frac{-12}{2}[/tex]

[tex]m=-6[/tex]

The slope of the line is [tex]-6[/tex]

The line passes through the point [tex](3,-17)[/tex]

Substitute 3 for x, - 6 for m and -17 for y in equation [tex]y=mx+c[/tex] to obtain the value of c.

[tex]-17=-6(3)+c[/tex]

[tex]-17=-18+c[/tex]

[tex]-17+18=c[/tex]

[tex]1=c[/tex]

The equation is [tex]y=-6x+1[/tex]

Hence, the equation of the line that passes through the points [tex](1,-5)[/tex] and [tex](3,-17)[/tex] is [tex]y=-6x+1[/tex]

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]

[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]

[tex]y = \frac{269573}{1+985*0.08509}[/tex]

[tex]y = \frac{269573}{84.81365}[/tex]

[tex]y = 3178[/tex] --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]

[tex]y = \frac{269573}{1+985*0.01824}[/tex]

[tex]y = \frac{269573}{18.9664}[/tex]

[tex]y = 14213[/tex] --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]

[tex]y = \frac{269573}{1+985*0.00724}[/tex]

[tex]y = \frac{269573}{8.1314}[/tex]

[tex]y = 33152[/tex] --- approximated

Answer:

The sum is 2275

Step-by-step explanation:

Given

[tex]75,76,77....99,100[/tex]

Required

The sum

Using arithmetic progression, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where:

[tex]T_1 = 75[/tex] --- first term

[tex]T_n = 100[/tex] --- last term

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 100 - 75 + 1 = 26[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]

[tex]S_n = 13*175[/tex]

[tex]S_n = 2275[/tex]

Answer:

x + y = 30

y = 2x

Step-by-step explanation:

x = number of ounces of lemon juice

y = number of ounces of linseed oil

How much of each ingredient is needed to make 30 oz of floor wax?

x + y = 30

The amount of oil should be twice the amount of lemon juice.

y = 2x

Answer:

x + y = 30

y = 2x

Answer:

Y = 2/3X + 4/3

Step-by-step explanation:

(1,2) (4,4)

M = 2/3

Y = 2/3X + b

4 = 8/3 + b

12 = 8 + 3b

4 = 3b

B = 4/3

Y = 2/3X + 4/3

Step-by-step explanation:

Here, two angles i.e, (x + 13)° and (4x + 2)° are forming a straight line, thus the sum of these two angles will be 180° because they are forming a linear pair.

[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°

[tex]\longrightarrow[/tex] x + 13 + 4x + 2 = 180°

[tex]\longrightarrow[/tex] 5x + 15 = 180°

[tex]\longrightarrow[/tex] 5x = 180° ― 15

[tex]\longrightarrow[/tex] 5x = 165°

[tex]\longrightarrow[/tex] x = 165° ÷ 5

[tex]\longrightarrow[/tex] x = 33°

Therefore, the value of x is 33°.

Quick Check!

[tex]\longrightarrow[/tex] x + 13

[tex]\longrightarrow[/tex] (33 + 13)°

[tex]\longrightarrow[/tex] 46°

And, another angle :

[tex]\longrightarrow[/tex] (4x + 2)°

[tex]\longrightarrow[/tex] {4(33) + 2}°

[tex]\longrightarrow[/tex] (132 + 2)°

[tex]\longrightarrow[/tex] 134°

★ Sum of the angles should be 180° :

[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°

[tex]\longrightarrow[/tex] 46° + 134° = 180°

[tex]\longrightarrow[/tex] 180° = 180°

L.H.S = R.H.S, hence verified!

The value of x is 33

"It is  a mathematical statement which consists of equal symbol between two algebraic expressions."

"Two angles are supplementary angles if the sum of the angles is 180° "

For given question,

angle (x + 13) and angle (4x + 2) form linear pair of angles.

So, these angles are supplementary angles.

⇒ (x + 13)° + (4x + 2)° = 180°

We solve above equation to find the value of x

⇒ x + 4x + 13 + 2 = 180

⇒ 5x + 15 = 180

⇒ 5x = 165

⇒ x = 33

Therefore, the value of x is 33

Learn more about the supplementary angles here:

https://brainly.com/question/13045673

#SPJ2

D. 2.3.5 is the correct answer

Answer:

No se me puedes ayudar por fa

Answer: Let the number be x

3-2x is the equation.

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

Step-by-step explanation:

Given:

Substitute x= -3:

Answer:

5 years

Step-by-step explanation:

Answer:

18 hours

Step-by-step explanation:

Forst u must find out how much u get for 1 hour which is 198/11=18 so every hour u get 18 dollars.

Next, Ypu must divide 324/18 to see how many hours he worked which we get 18

Finally 18 is the answer!

Step-by-step explanation:

If he made $198 in 11hrs

how many hours will he take to make $324

Let hours be x

$198=11hours

$324= x hours

= $324 *11hours / $198

= 18 hours

I hope this helps.

Answer:

£1054.729

Step-by-step explanation:

To find compound interest you need to use the equation 1000(1.027)^x.

To find the interest rate (1.027):

100 + 2.7 = 102.7

102.7 / 100 = 1.027

The value of x is the amount of months if no payment is made in this situation, so 2 would be the x value for this problem.

Hope this helps!  

Answer:

60 miles/hour

Step-by-step explanation:

960÷16

=60 hours

Answer:

see graph...

B On a coordinate plane, a line goes through (0, 0) and (1, negative 4).

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the graph that represents the linear equation 4x + y = 0, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

Starting with the given equation:

4x + y = 0

Subtracting 4x from both sides:

y = -4x

Now we have the equation in the form y = mx + b, where m = -4 (the coefficient of x) and b = 0.

Looking at the given graphs:

Graph A: The line goes through (0, 0) and (1, 4). This graph does not represent the equation y = -4x, as the slope is 4, not -4.

Graph B: The line goes through (0, 0) and (1, -4). This graph does represent the equation y = -4x, as it has a slope of -4 and passes through the origin.

Graph C: The line goes through (0, 0) and (4, -1). This graph does not represent the equation y = -4x, as it does not have the correct slope.

Graph D: The line goes through (0, 0) and (4, 1). This graph does not represent the equation y = -4x, as it does not have the correct slope.

Therefore, the best graph that represents the linear equation 4x + y = 0 is:

b. Graph B

Answer:

The mean proportional between 1/36 and 1/9 would be 1/18.

Answer:

9*x*x*x*x*x*x.

Step-by-step explanation:

(3x^3)^2

= 3^2 * x^(3*2)

= 3^2 * x^6

= 9*x*x*x*x*x*x

Answer:

Step-by-step explanation:

I always advise my students to make a table of information for these story problems because trying to keep track of the information otherwise is a nightmare. The table will look like this:

           d      =      r      *      t

m

c

m is motorcycle and c is car.

First thing we are told is that the ratio of m's speed to c's speed is 5:4; that means that we can divide 5/4 to find out how many times faster m is going than c.

5/4 = 1.25 so we have a couple of values to put into the table right away, along with the fact that they are both traveling the same distance of 160 miles.

             d      =     r      *      t

m        160     =   1.25r

c         160     =     r

The last thing we have to fill in is the time. If m travels a half hour less than c, c is driving a half hour more than m, right? Filling that in:

            d      =      r      *      t

m       160     =   1.25r   *     t

c        160     =      r       *  t + .5

Now we have our 2 equations. Looking at the top row of the table gives us the formula we need to solve this problem. It tells us, in other words, what we are going to be doing with these columns of numbers. Distance equals the rate times the time. For the motorcycle, the equation is:

160 = (1.25r)t  and that seems pretty useless since we still have 2 unknowns in there and you can only have 1 unknown in 1 equation. Let's see what the equation for the car is.

160 = (t + .5)r  Same problem.

Let's go back to the equation for the motorcycle and since we are looking for the rates of each, let's solve that equation for time in terms of rate (solve it for t):

[tex]t=\frac{160}{1.25r}[/tex] and sub that into the car's equation in place of t:

[tex]160=r(\frac{160}{1.25r})+.5r[/tex] and simplify. The r's to the left of the plus sign cancel out leaving us with:

[tex]160=(\frac{160}{1.25})+.5r[/tex] and divide those numbers inside the parenthesis to get:

160 = 128 + .5r and subtract 128 from both sides to get:

32 = .5r and finally divide by .5 to get

r = 64 miles/hour

The car goes 64 mph and the motorcycle goes 1.25 times that so,

m = 1.25(64) and

m = 80 mph

Answer:

Sine Theta is a negative number, Tan Theta is a greater number then zero.

Step-by-step explanation:

If Sine Theta is less then zero, she is a negative number. So 0 - y = -y.

So if Tan Theta is a greater number than zero, her number is not negative. So 0 + y = y

I hope this helped! I didn’t really understand the question though.

Answer:

-00

OKAY

OKAY

OK

OK

DGSOTSITS6EUEYEYTITUTUTIT

Answer:

factor???

Factored Form:  y= (-1)(8x+1)(2x-3)    

Step-by-step explanation:

Step-by-step explanation:

Option B is correct. Refer to the attachment!

Answer: 9

Step-by-step explanation:

[tex]\frac{1}{4} (c^{3}+d^{2})[/tex]

Substitute in the values into the expression:

[tex]\frac{1}{4} ((-4)^{3}+10^{2})\\\\=\frac{1}{4}(-64+100)\\\\=\frac{1}{4}(36)\\\\=\frac{36}{4} =9[/tex]

Answer:

a simple random sample (SRS).

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Systematic sampling.

2. Convenience sampling.

3. Stratified sampling.

4. Cluster sampling.

5. Random sampling.

Random sampling also referred to as simple random sample (SRS) involves randomly selecting a subset of a larger population.

In this scenario, an elected government official randomly selected five schools at random from the 20 schools in her area and then interviews each of the teachers in those five schools, in order to get their opinions about voting. Thus, the government official is using a simple random sample (SRS).

Answer:

-15 -3.45 -3.15 -3.0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.

AnsweStep-by-step explanation:

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