-6+2y=10 and 6x-2y=-10

Answer:

b) 8 × 12 + 8 × 30

Step-by-step explanation:

Now we have to,

→ Find the equivalent expression.

The property we use,

→ Distributive property.

The expression is,

→ 8(12 + 30)

Let's simplify the expression,

→ 8(12 + 30)

→ 8(12) + 8(30)

→ (8 × 12) + (8 × 30)

→ 96 + 240

→ 336

Hence, the option (b) is correct.

Regarding the average rate of change of the function, it is found that:

a) 245 habitants per year between 1998 and 2001.

b) The average rate of change was of -328.5 habitants per year between 2002 and 2004.

c) The rate of population increase was greater between 1998 and 2001.

d) The rate of population decrease was greater between 2002 and 2004.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, we have that:

Hence the rate is:

(1591 - 856)/3 = 245.

The average rate of change was of 245 habitants per year between 1998 and 2001.

For item b, we have that:

Hence the rate is:

(826 - 1483)/2 = -328.5.

The average rate of change was of -328.5 habitants per year between 2002 and 2004.

Hence:

c) The rate of population increase was greater between 1998 and 2001.

d) The rate of population decrease was greater between 2002 and 2004.

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(a). The equation of the line L in the form of y = mx + b is y + 2x  = 0.

(b). The equation of the line K that passes through the point (0, -1) and is perpendicular to the line L is y = 2x - 1.

(c). The intersection of the lines and K is located at a location with the coordinates (0,-1).

The equation of a line has the usual form axe + by + c = 0. Here, x and y are the variables, a and b are the coefficients, and c is the constant term. You may also find and see the equation of a line in the slope-intercept form, point-slope form, two-point form, intercept form, and normal form.

The formula of slope is given by m = (y₂-y₁)/(x₂-x₁).

Here, m is the slope of the line.

(x₁, y₁) and (x₂, y₂) are the two points of the line.

Now put the value of x₁, y₁, x₂, y₂  in

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

m = [tex]\frac{3-1}{-1-1}[/tex]

m = 2/-1

m = -2  

The slope of the line perpendicular is:

mₐ = - 1/m

mₐ = -1/-2

mₐ = 2

(a) The equation (in the form y = mx + b) of the line L.

(y-y₁) = m(x-x₁)

(y-1) = -2(x-1)

y-1 = -2x-1

y = -2x

y + 2x  = 0        

(b) The equation of the line K that passes through the (0, -1) and is perpendicular to the line L.

x = 0 and y = -1

y = mx + b  

y = 2x + b  

-1 = 2×0 + b  

-1 = b

b = -1

Substituting the above in y = mx + b to get:

y = mx + b

y =2x + (-1)

y = 2x - 1

(c) The coordinates of the point at which the lines and K intersect.

y = 2x - 1

y+2x+1=0

(2x-1)+2x+1=0

4x =0    

x = 0, y = -1

The intersection of the lines and K is located at a location with the coordinates (0,-1).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

60

The equation that can represent the fee for x hours is y = 10 + 5x.

A mathematical equation that represents the relationship of two expressions on either side of the sign.

We have,

Initial fee = $10

Let the constant fee for each hour of work = M

Fee for 5 hours of work = $35

Every mowing job for 5 hours = Initial fee + constant fee for 5 hours
$35 = $10 + M x 5

35 = 10 + 5M

25 = 5M

M = 5

So,

If y represents Anumeha's fee (in dollars) for a single job that took x hours for her to complete.

We can write an equation as:

y = 10 + 5x

Thus the equation that can represent the fee for x hours is y = 10 + 5x.

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Answer:3

Step-by-ste

la respuesta es 3 porque si sumas -2x a 5 pues -2 es. un numero negativo y 5 es positivo restas 5-2 y obtienes 3

In simplest form, I believe it would be 4/75.

The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points

What is the desired annual percentage rate for the borrower?

The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%

difference in interest rate=4.15%-3.8%

difference in interest rate=0.35%

We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point

number of points required to buy down interest=1 point*0.35%

number of points required to buy down interest=0.350

In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%

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Answer:

0.66

Step-by-step explanation:

175 yards long is the 15th hole if the map shows 17.5 inches.

hole = c yards

1.5 / 15 = 17.5 / c

1.5 c = 15 * 17.5

1.5 c = 262.5

c = 175 yards

A length unit equal to 36 inches, or 3 feet (see foot), in the United States Customary System, or 0.9144 metre in the International System of Units. A cloth yard is 37 inches long, and it was also the standard length for arrows.

The yard is an English unit of length that equals 3 feet or 36 inches in both the British imperial and US customary measurement systems. Since 1959, it has been standardized as 0.9144 meter by international agreement. One mile is equivalent to 1,760 yards. The survey yard in the United States is slightly longer.

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Answer:

Step-by-step explanation:

13-b

put ixes in equations and see which is correct that b is correct.

14- c

in this question put   known points in equations.

The probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that an urn contains twenty chips, numbered 1 through 20. Two are drawn simultaneously.

Number of favorable outcomes = ( 4 - 2 ) , ( 3 - 1 ) , ( 6 - 4 ) , ( 10 - 8 ), ( 11 - 9 ), ( 7 - 5 ), ( 14 - 12), ( 15- 13 ) , ( 18 - 16 ), ( 19 - 17 ) = 10

Number of samples = 20

Probability = Number of favorable outcomes / Number of sample

Probability = 10 / 20

Probability = 1 / 2

Therefore, the probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).

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Answer:

101

Step-by-step explanation:

Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.

Hope this helps!

Answer:

1 revolution is 360 degrees

1 hour = 60 minutes

360/60 = 6

so it rotates 6 degrees every minute

135/6 = 22.5 minutes

Answer:

-13 13/35

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation: Just took it

Answer:

1/9

Step-by-step explanation:

When the quantities are proportional, you are able to find the constant of proportionality by y/x.  If you take each one of the y's listed and divide it by x, you will get 1/9.

For example 1 2/9 ÷11

1 2/9 is the same at 9/9 + 2/9 or 11/9

[tex]\frac{11}{9}[/tex] ÷ 11 is the same as [tex]\frac{11}{9}[/tex] ÷ [tex]\frac{11}{1}[/tex] To divide with fractions, you multiply by the reciprocal.

[tex]\frac{11}{9}[/tex] x [tex]\frac{1}{11}[/tex] The 11 can cancel out and we are left with [tex]\frac{1}{9}[/tex]

Answer: r = [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

y = rx

finding r (substitute y and x):

5 = r x 45

5/45 = r

r = [tex]\frac{5}{45} = simplify = \frac{1}{9}[/tex]

checking:

rx = y

   [tex]\frac{1}{9}[/tex] x 11 = 1 [tex]\frac{2}{9}[/tex]

[tex]\frac{11}{9}[/tex] = 1 [tex]\frac{2}{9}[/tex]

convert mixed fraction into improper fraction

[tex]\frac{11}{9}[/tex] = [tex]\frac{11}{9}[/tex]

correct

The radius of the spherical tank of capacity 750 gallons to the nearest hundredth is 2.88 ft.

How much s a gallon?

In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L[1] (231 cubic inches); and the US dry gallon ("usdrygal"), which is defined as 18 US bushel (exactly 4.40488377086 L).

Given data: 1 gallon ≈ 0.1337 ft³

Then, 750 gallons = 0.1337 x 750 ≈ 100.275 ft³

We know, Volume of sphere,  [tex]V=\frac{4}{3}\pi r^{3}[/tex]

then, r = [tex]\sqrt[3]{\frac{3}{4\pi }V }[/tex]

           = [tex]\sqrt[3]{\frac{3}{4\pi } 100.275}[/tex]

           = [tex]2.88 ft.[/tex]

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Step-by-step explanation:

[tex]y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20[/tex]

you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.

Answer:

3/5, 9/15 - some equivalent fractions for 6/10

If you invest a 100% in stocks however, you stand to make an average of 9.2% but a chance of a worst return of -40.40%.

In the given statement is:

Your friend tells you he is going to start investing and would like to earn a 10% return. He says stocks make him nervous, so he will only be investing 10% in stocks and the remaining 90% will be invested in bonds.

Based on the graph given on bond and stock returns, the average return if one invested 100% in bonds or in stocks is 5.0% and 9.2% respectively.

What happens if you invest 100% in either stocks or bonds?

The graph shows that when you invest a 100% in bonds, the average return you stand to make it 5.0% while the worst return is -2.1%.

If you invest a 100% in stocks however, you stand to make an average of 9.2% but a chance of a worst return of -40.40%.

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Step-by-step explanation:

perimeter=s+s+s

p=x/2+x-5+x-2

13=x/2+x-5+x-2

26=x+x+x-10-4

26=3x-14

26+14=3x

3x/3=40/3

x=13.3cm

b.

x/2=6.65

x-5=8.3

x-2=11.3

longest side=11.3cm

Answer: 9 and -5

Step-by-step explanation:  2+7=9 and 2-7=-5

Answers:

E ' = (0, 1)

F ' = (0.5, 0.5)

G ' = (0, 0)

D ' = (-1, 0.75)

Notes: 0.5 = 1/2 and 0.75 = 3/4

================================================

Explanation:

Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25

For instance, the point E(0,4) moves to E ' (0, 1) since

Do the same for the other points.

Answer:

14x+11

Step-by-step explanation:

The 95% confidence interval estimate for the mean number of absences for clerical workers during the year is (8.132, 11.268).

It should be noted that the mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given a = 0.05, Z(0.025) = 1.96 (from standard normal table).

The 95% confidence interval will be:

xbar +/- Z*s/vn

= 9.7 +/- 1.96*4/✓(25)

= (8.132, 11.268)

Therefore, the 95% confidence interval is (8.132, 11.268).

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Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.

It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.

It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.

Hence, an example of a number that is ten times greater is; 10 × 80,000.

Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.

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