What is the best approximation of the solution to the system to the nearest integer values?

Answer: x = 6

NS = 8.5

Step-by-step explanation:

JK = KL= KP + LP

26 = 13 + 2x + 1

2x = 12

x = 6

NS = PS

PS = 8.5

NS = 8.5

The total interest on the mortgage loan  is $219,249.60

What is a mortgage loan?

It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.

Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.

PV=monthly repayment*(1-(1+r)^-N/r

PV=loan amount=$210,000

monthly repayment=unknown(assume it is X)

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly payments in 30 years=30*12=360

$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-0.19277525234572900)/0.00458333333333333

$210,000=X*0.80722474765427100/0.00458333333333333

$210,000=X*176.12176312456800000

X=$210,000/176.12176312456800000

X=monthly payment=$1,192.36

total repayments(360 months)=$1,192.36*360

total repayments(360 months)=$429,249.60

Total interest=total repayments(360 months)-loan amount

Total interest=$429,249.60-$210,000

Total interest=$219,249.60

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The greatest common factor from the given information is 12h³.

The greatest common factor (GCF) of a given set of whole numbers is the largest value that can be divided by the set of numbers.

From the information given, we are to find the GCF of:

12h³ = (1 , 2, 3, 4, 6 , 12 )h³

36h³ = (1, 2, 3, 4, 6, 9, 12, 18, 36)h³

12h⁶ = (1, 2, 3, 4, 6, 12)h³ * h³

Therefore, we can conclude that the greatest common factor is 12h³.

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The simplification of the expression 5(6 ÷ 2² × 3 - 1) using the proper order of operation is 3.75

5(6 ÷ 2² × 3 - 1)

Bodmas

= 5(6 ÷ 4 × 3 - 1)

= 5(6 ÷ 4 × 2)

= 5(6 ÷ 8)

= 5(0.75)

= 3.75

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Answer:

D

Step-by-step explanation:

I assume that for C and D, you meant e^x.

Since the function is defined at 0, eliminate A and B (since ln 0 is undefined)

Between C and D, we know that when x=0, e^x = 1. Since the y intercept of the graph is -3, this means the equation is y = e^x - 4.

Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:

p = 5/25 = 0.2 = 20%.

20% probability that a customer ordered a large given that he or she ordered a cold drink.

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Answer:

53 times per second

Step-by-step explanation:

There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.

3180 / 60 = 53

Answer:33

Step-by-step explanation: The expressions have equivalent values when x + 6

The expressions have equivalent values for any value of x.

When x=10 , both expressions have a value of 33.

The integers are therefore -2, -2, 0, 1 and 2

Let the five consecutive integers be x-3, x-2, x-1, x and x+1

If the  sum of five consecutive integers equals 5.5 times the middle integer, then;

x-3+x-2+x-1+x+x+1 = 5.5(x-1)

5x - 5 = 5.5x - 5.5

Collect the like terms

5x-5.5x = -5.5 + 5

-0.5x = -0.5

x = 1

The integers are therefore -2, -2, 0, 1 and 2

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Area

Answer:

1725 ft²

Step-by-step explanation:

The formula to find the area of a trapezoid is :

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Let us solve it now.

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30

Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30

Area = [tex]\frac{1}{2}[/tex] × 3450

Area = 1725 ft²

The [tex]n[/tex]-th term is

[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]

so the 39th term is

[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]

Observe that

[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]

which suggests that

[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]

Answer:

telephone was $45, utility was $135

Step-by-step explanation:

Let the telephone bill be x, then the utility bill is 3x

3x+x = 180

4x = 180

x = 45

3x = 135

The exponential growth formula is 3,400,000 x (1.09^t).

The year in which the grove would reach one billion board feet is  63.16 years.

The exponential growth formula usually has this form:

FV = P (1 + r)^n

3,400,000 x (1.09^t).

The year in which the grove would reach one billion board feet  = (In 1,000,000,000 / 3,400,000) / 0.09 = 63.16 years

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The missing length of given right triangle is equal to 25.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean  Theorem.

The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x),  cos (x) and tan (x) , where:

[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]

There is another important property, where h²=m*n. See the attached image.

From the previous informations presented, you can solve the given question.

From Pythagorean Theorem you can find h (heigth). Thus,

15²=9²+h²

h²=225-81

h²=144

h=12

If h=12 and m=9, from  h²=m*n you can find n.

h²=m*n

12²=9*n

144=9n

n=144/9

n=16

Therefore, x= m+ n= 9+16=25.

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Answer:

35 2/3

Step-by-step explanation:

49 1/3 - 13 2/3

First convert both into improper fractions, which is

148/3 - 41/3

Then subtract!

107/3

Next simplify the fraction.

35 2/3

Answer:

the number of 1 dollars bills was 5 si make 1 more 5 dollars so 8n total it is 10 dollars.

The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.

A fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).

Time spent practicing his multiplication facts = 1/4 of 1 1/4 hours

= 1/4 × 1 1/4

= 1/4 × 5/4

= (1 × 5) / (4 × 4)

= 5/16 hours

Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.

Complete question:

Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.

How many hours did Carlos spend practicing his multiplication facts?

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The equations which completes the left-hand column of the table are;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

The given expression on the right is written as follows;

First row;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

The definition of the sum and difference of cosine are;

cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)

cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)

Therefore;

Second row;

cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)

Which gives;

[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

Third row;

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Answer:

8) - 8z^3 - 3z^2 - 2z + 13

9) g^3 - 3g^2 + 3g + 6

10) (14n + 21) - (8n + 7) = 6n + 14

Answer:

$217.88

Step-by-step explanation:

12% of 194.95 plus the original cost of 194.94 equals the total

1.12*194.54 = $217.8848

Rounded: $217.88

Answer:

0.7

Step-by-step explanation:

Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7

Answer:

y=-2x+12

Step-by-step explanation:

First, subtract 1/2 from each side

1/4y = -1/2x + 3 --> multiply each side by 4

y = -2x + 12 is your final answer

The domain of the composite function is given as follows:

[–3, 6) ∪ (6, ∞)

The composite function of f(x) and g(x) is given as follows:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

The composite function is of the given functions f(x) and g(x) is:

[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:

[tex]x + 3 \geq 0[/tex]

[tex]x \geq -3[/tex]

The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:

[tex]\sqrt{x + 3} - 3 \neq 0[/tex]

[tex]\sqrt{x + 3} \neq 3[/tex]

[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]

[tex]x + 3 \neq 9[/tex]

[tex]x \neq 6[/tex]

Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:

[–3, 6) ∪ (6, ∞)

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Answer:

Step-by-step explanation:

10yy'=x

[tex]10y\frac{dy}{dx} =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\\frac{10y^2}{2} =\frac{x^2}{2} +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=\frac{60}{2} =30\\10y^2=x^2+60\\10y^2-x^2=60[/tex]

The divisor of the expression 2/3 ÷ 6/5 is 9.

We have,

Expression:

2/3 ÷ 6/5

The concept used.

a/b ÷ c/d = ad / bc

Now,

2/3 ÷ 6/5

This can be written as,

= 2/3 x 5/6

= (2 x 5) / (3 x 6)

= 10 / 18

= 2 x 5 / 2 x 9

Cancel the common factor.

= 5 / 9

This can be read as,

Dividend = 5

Divisor = 9

Thus,

The divisor of the expression is 9.

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Answer:

what do you need person jjff

The additional information needed to calculate ORS are the measures of SPR and PSR

The lines are given as:

Lines a, b, c and d

The special names of the lines are as follows:

The angle is given as:

OPS= 139 degrees

Start by calculating SPR using

SPR = 180- 139

SPR = 41 degrees

So, the additional information needed to calculate ORS are the measures of SPR and PSR

The theorem 65 is not stated.

So, the question cannot be answered

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