Would $3.99$ million flies or $47,000,000$ ants have a greater mass? Approximately how much greater, in grams, would the greater mass be?

Given:

The line passes through (-3,-6) and (2,-2).

To find:

The equation of line.

Solution:

If a line passes through two points [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The line passes through (-3,-6) and (2,-2). So, the equation of line is

[tex]y-(-6)=\dfrac{-2-(-6)}{2-(-3)}(x-(-3))[/tex]

[tex]y+6=\dfrac{-2+6}{2+3}(x+3)[/tex]

[tex]y+6=\dfrac{4}{5}(x+3)[/tex]

[tex]y+6=\dfrac{4}{5}(x)+\dfrac{4}{5}(3)[/tex]

Subtract 6 from both sides.

[tex]y=\dfrac{4}{5}(x)+\dfrac{12}{5}-6[/tex]

[tex]y=\dfrac{4}{5}(x)+\dfrac{12-30}{5}[/tex]

[tex]y=\dfrac{4}{5}(x)+\dfrac{-18}{5}[/tex]

[tex]y=\dfrac{4}{5}(x)-\dfrac{18}{5}[/tex]

Therefore, the equation of line is [tex]y=\dfrac{4}{5}(x)-\dfrac{18}{5}[/tex].

Answer:

Step-by-step explanation:

Sum interior of triangles add up to 180 degrees. So add 103 + 43 to get 146 then subtract 180 - 146 to get 34 as the last missing angle of the triangle

Answer:

34

Step-by-step explanation:

103+43=146

a triangle always adds up to 180 degrees

180-146=34

so that's the workings hope the answers right

Answer:

B

Step-by-step explanation:

Expand to get -4y+2-3y. Combine like terms to get -7y+2.

Answer:

675

Step-by-step explanation:

If the price is 20 % off, then we will pay 100-20 = 80 percent of the original price

Let x be the original price

x* 80% = 540

Change to decimal form

x * .80 = 540

Divide each side by .80

.80x / .80 = 540/.80

x =675

The original price is 675

Answer:

A

Step-by-step explanation:

Assuming you mean the square root of five, then the answer is A.

You start by taking the square root of both sides.

√(x - 4)^2 = ±√5

x - 4 = ±5

x = 4 ±5

Answer:

2.2%

Step-by-step explanation:

Use the percent error formula:

% error = | (approx - exact) ÷ approx | x 100

Plug in the approx. and exact values:

| (8.9 - 8.7) ÷ 8.9 | x 100

| (0.2) ÷ 8.9 | x 100

= 2.2

So, the percent error is 2.2%

Answer:1.2%

Step-by-step explanation:

∣experimental−actual∣

​

×100

The formula

∣

8.7

−

8.6

∣

8.6

×

100

8.6

∣8.7−8.6∣

​

×100

Plug in values

∣

0.1

∣

8.6

×

100

8.6

∣0.1∣

​

×100

Subtract

0.1

8.6

×

100

8.6

0.1

​

×100

Take the absolute value

0.0116279

×

100

0.0116279×100

Divide

1.16279

1.16279

Multiply by 100

1.2

%

1.2%

Step-by-step explanation:

1. (4m² - 1.5m + 2) + (9m - 2m³ + 2m)

= 4m² - 1.5m + 2 + 9m - 2m³ + 2m

= 4m² + (-1.5m + 9m + 2m) + 2 + 2m³

= 4m² + 9.5m + 2 + 2m³

= 2m³ + 4m² + 9.5m + 2

2. (-3y + 2y² - 6) + (3y + 4y² + x)

= -3y + 2y² - 6 + 3y + 4y² + x

= (-3y + 3y) + (2y² + 4y²) - 6 + x

= 0y + 6y² - 6 + x

= 6y² - 6 + x

Answer:

Step-by-step explanation:

These types of problems can be solved with substitution.

We just have to translate the word problem into math.

#1:

F = family, I = individual

[tex]F + I = 188\\95F + 42I = 12,507[/tex]

[tex]F = 188-I\\95(188-I) + 42I = 12507\\17860 - 95I + 42I = 12507\\-53I = -5353\\I = 101\\\\F + I = 188\\F + 101 = 188\\F = 87[/tex]

87 Families, 101 individuals

#2:

The perimeter is 899 meters. The perimeter can be defined as:

[tex]2L + 2W = P\\2L + 2W = 899[/tex]

We are also given that

[tex]2L = W - 100\\so\\2L + 2W = 899\\W- 100 + 2W = 899\\3W = 999\\W = 333\\\\L = \frac{W-100}{2} = \frac{333-100}{2} = \frac{233}{2}[/tex]

W = 333 meters, L = 233/2 meters

Answer:

here is explanation by graph

Answer:

He can buy 5 pounds of peaches.

Step-by-step explanation:

2 pomegranates cost $3.18 so, subtract that from $10.00 and you get $6.82. Multiply the different number of pounds with the cost per pound until you go over $6.82. Then go back a pound and multiply. 5 pounds times $1.19 equals $5.95.

Answer:

no

Step-by-step explanation:

they are not

Answer:

Step-by-step explanation:

In fact, every function is a relation. However, not every relation is a function. In a function, there cannot be two lists that disagree on only the last element. This would be tantamount to the function having two values for one combination of arguments.

Answer: Answer= 480a^2

Step-by-step explanation

1. remove the parentheses =-16a*10*3a

2. Multiply the numbers 16*10*3= 480

3. Apply exponent rule =aa=a^1+^1  = -480a^1+^1

Answer= 480a^2

Step-by-step explanation:

a could be 3580 X 1.25^n

b could be 6992.19

dk c

Answer:

5x + 3y = 13 parallel.

6x - 10y = 7 perpendicular.

The equation which is parallel to the line JK is

a) Parallel is 5x + 3y = 13

b) Perpendicular is 6x - 10y = 7

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be J ( -5 , 5 )

Let the second point be K ( 1 , -5 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - ( -5 ) ) / ( -5 - 1 )

m = 10 / -6

m = -5/3

The parallel lines have same slope and the perpendicular lines have the negative reciprocal of slope

So , the equation of line parallel to JK is 5x + 3y = 13

And , the equation of line perpendicular to line JK is 6x - 10y = 7

Hence , the equation of line is solved

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Answer:

x=4

Step-by-step explanation:

-x=-3x+8

-x+3x=-3x+8+3x

2x=8

2x/2 = 8/2

x = 4

Answer:

side angle side. Seems contrary

Answer:

side angle side. Seems contrary

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

Answer:

A) t=5d

Step-by-step explanation:

Since the problem states "He rode 1 mile in 5 minutes",  that means for every mile Andre travels, it will take him 5 minutes for each mile.

Therefore, the equation that best works is t=5d because the coefficient is 5 where it's the slope representing 5 minutes per mile.

Answer:

the answer is 6

Step-by-step explanation:

Answer:

First one obv false

the second one since they all times 3/4 so yes

Answer:

C

Step-by-step explanation:

Both Holly and Emily have the same account balance thus it is equal to

Answer:

Dont listen to the person its actually B

Step-by-step explanation:

On a number line, smaller numbers are to the left of larger numbers.

Negative values are always less than positive values.

So, the following is true.

Holly's account balance < Emily's account balance

Answer:

d

Step-by-step explanation:

so at 5 hours he  was at a profit of 900 and 5 hours later he is at a profit 1500 then you can sub tract 900 from 1500 which gives you 600

$600 is the average rate of change in profit from Hour 5 to Hour 10

A rate of change is a rate that describes how one quantity changes in relation to another quantity

The given table is

Hour                Profit

0                        $0

2.5                     $500

5                        $900

7.5                     $1200

10                        $1500

5 hours the profit is 900 and 5 hours later he is at a profit 1500

We need to subtract 900 from 1500 to find the average rate of change.

1500-900=600

Hence $600 is the average rate of change in profit from Hour 5 to Hour 10

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Answer:

5563.85 But round the nearest whole number is 5564

Step-by-step explanation:

Formule is P=Ie^(r)(t)

If, In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously,  then 5563.85 is the population in 2022.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

In 2010 the Network Club membership was 2,500.

Annual growth rate of approximately 8%

8% is converted to decimal value by dividing 8 with 100

8/100=0.08

[tex]P=Ie^{rt}[/tex]

p is the final population

I is the initial population

[tex]p=Ie^{0.08(10)}[/tex]

[tex]p=2500e^{0.8}[/tex]

p=5563.85

Hence, 5563.85 is the population in 2020.

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Answer:

y = 2x + 1

Step-by-step explanation:

Let the equation of the line be y = mx + c

since it is parallel to y = 2x + 8, their slope/gradient is the same (aka m = 2)

sub (1, 3):

3 = 2(1) + c

c = 1

therefore, the equation is y = 2x + 1

This is a question on coordinate geometry. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Correction is the question: 6[tex]\frac{1}{2}%[/tex]% = 6.5%

Answer:

Amount to be repaid is $335798.833

Step-by-step explanation:

Amount of loan = $332,200

Rate of interest = 6.5%

time =  2months = 2/12 = 1/6 years

The amount of interest is simple interest

SI = [tex]\frac{P * R * T}{100}[/tex]

    =[tex]\frac{ 332200 * 6.5 *1 }{100 * 6}[/tex]

    = $3598.833

Final amount to be repaid = 332200+ 3598.833

                                            = $335798.833

Answer:

EF = 7 + 39 = 46

Step-by-step explanation:

EF = FG

x + 39 = 7x - 3

39 + 3 = 7x - x

42 = 6x

x = 42/6

x = 7

hope this helps :)

Step-by-step explanation:

Since we are not given the required parameters, we can use the following parameters

Given:  

∠ A  =  5 x + 30 °

∠ B  =  2 x

Since △ABC is isosceles with AB = BC, then ∠ A  = ∠ C (the base angles of an isosceles triangle are equal)

Since sum of angle in a triangle are the same, then;

∠ A  + ∠ B + ∠ C = 180°

Substitute the given functions and get x;

5x+30 + 2x + 5x+30 = 180

12x + 60 = 180

12x = 180-60

12x = 120

x = 120/12

x = 10°

∠ A  = 5x+30

∠ A  = 5(10)+30

∠ A  = 80°

Since ∠ A  =∠ C

∠ C = 80°

For ∠ B;

∠ B = 2x

∠ B = 2(10)

∠ B = 20°

Let AB = 1, since AB = BC, BC = 1

To get AC, use the sin rule;

a/sin∠ A  = b/sin∠ B

a/sin80 = 1/sin20

asin20 = sin80

a = sin80/sin20

a = 0.9848/0.3420

a = 2.879

Hence AC ≈ 3

Note that the values of the sides and angles are assumed.

9514 1404 393

Answer:

  interval notation for all numbers except those that are at least -1 and less than 2.

Step-by-step explanation:

The ∪ between the two sets of brackets indicates the "union" of two sets. The brackets on the left indicate the interval ...

  -∞ < x < -1 . . . . . for a value represented by x

The curved brackets ( ) indicate the end values of the interval are not included, which is why the < symbol is used, and not the ≤ symbol.

The brackets on the right indicate the interval ...

  2 ≤ x < +∞ . . . . . for a value represented by x

The square bracket [ ] is used to indicate the end value is included, which is why the ≤ symbol is used in relation to the end-value 2.

By convention, the interval notation lists the left end of the interval first, and always uses curved brackets for infinity.