#15: m∠NST = ____°
need answer

Answer:

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We see the exterior angle measures given with one unknown.

Recall the sum all exterior angles of a polygon is 360°.

Set up equation and find the unknown value:

Step-by-step explanation:

completing the square means finding an expression

(x + a)² = b²

or

(x - a)² = b²

(x + a)² = x² + 2ax + a²

(x - a)² = x² - 2ax + a²

because of the "+ 18x" in the original equation we know that we are looking for (x + a)².

now, let's compare the different terms :

x² = x²

18x = 2ax

18 = 2a

a = 9

so, the complete square would look like

(x + 9)² = x² + 18x + 81

but we have only "+ 79" in the original equation.

so, we add the missing 2 (to both sides to keep the equation true)

x² + 18x + 79 + 2 = 0 + 2

x² + 18x + 81 = 2

(x + 9)² = 2

x + 9 = ±sqrt(2)

x1 = sqrt(2) - 9

x2 = -sqrt(2) - 9

x = sqrt(2) - 9, -sqrt(2) - 9

yes, every quadratic equation has 2 solutions.

as every cubic equation has 3 solutions.

and so on.

Answer:

35/4

Step-by-step explanation:

8*4=32

32+3

=35

35/4

Answer:

x=1

Step-by-step explanation:

18x+3=21

  -3 = -3

18x= 18

18x/18 = 18/18

x= 1

Answer:

x = 1

Step-by-step explanation:

[tex]18x + 3 = 21\\18x = 21 - 3\\18x = 18\\18x/18 = 18/18\\x= 1[/tex]

Answer:

9.6*10^-12

Step-by-step explanation:

To calculate this, you will do the mass of 2 times 10^(-12) gram. So, 2*(10)^-12. Then we know 30 hours = 480,000,000 bacteria.

So now now you calculate the mass, 480,000,000 * 2(10)^-12 which gives you 9.6*10^-4.

Sorry if it sounds confusing! I hope this helps, have a good day! :D

First of all let me tell you UPSC is the body which conducts the civil services examination in our country. To prepare for the civil services you must know it is the highest offered post by the government to an citizen of India.

You have many subjects in order to complete the syllabus of civil services.

The examination takes place in two parts. In the first part there are multiple choice questions and in the second part there are subjective questions which must be answered in a descriptive format.

The candidate also has to face interview after clearing both the examinations.

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Answer:

-1/5

y=-1/5 x-8

-1/5 is the slope

Step-by-step explanation:

-1/5

Formula-    y=mx+b

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Rewrite in slope-intercept form.

Simplify the left side

Simplify each term.

Combine 1/8 and x.

x/9+5y/8=-5

Subtract x/8 from both sides of the equation.

5y/8=-5-x/8

Multiply both sides of the equation by8/5.

8/5.5y/8=8/5(-5-x/8)

Simplify both sides of the equation.

Simplify the left side.

Simplify 8/5.5y/8

y=-x/5-8

y=-1/5 x-8

Step-by-step explanation:

Given equation:

1/8x + 5/8y =-5

Now write it in standard form like ax+by+c=0

1/8x + 5/8y + 5= 0

Now,slope of line (m) = -a/b

here value of a is 1/8 and value of b is 5/8

now by formula..

-(1/8)÷(5/8) = m(slope)

-1/8 × 8/5 = m

-1/5 = m

here ia your answer

The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is

What is a quadratic equation?

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .

formula: −b±√b2−4ac/2a

Given equation ,

2[tex]x^{2}[/tex] -12x-20=0

By comparing with the quadratic equation

Here, a=2, b= -12, c= -20.

X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a

X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)

X=12+-  [tex]\sqrt{144-160}[/tex]/4

X=12+- [tex]\sqrt{-16}[/tex]/4,

X=12+- (-4)/4

X=12+(-4)/4 and x=12-(-4)/4

X= 12-4/4 and x=12+4/4

X=8/4 and x= 16/4

X=2 and x= 4

Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.

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Answer:

At the 3rd day 160 students caught flu.

Step-by-step explanation:

Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6

The total number of students is represents by P.

We need to find the day that 160 students had the flu.

Substitute the value of P=160 in above formula.

Hence the value of t=10 or t=3

But it is given that 1 ≤ t ≤ 6, Therefore select t=3

Hence, at the 3rd day 160 students caught flu.

The solution associated with rational numbers is descriptively illustrated below with a detailed explanation.

What is a rational number?

Problems with the division of Rational Numbers:

(a) [tex]\frac{5}{7}[/tex] ÷ [tex]\frac{-11}{5} = \frac{5}{7} * \frac{5}{11} = \frac{25}{77}[/tex]

(b) [tex]\frac{\frac{-4}{5} }{\frac{3}{10} }[/tex]

[tex]\frac{-4}{5}[/tex]÷[tex]\frac{3}{10}[/tex]

[tex]\frac{-4}{5} *\frac{10}{3} \\=\frac{-8}{3}[/tex]

(c) [tex]\frac{-7}{17}[/tex]÷[tex]\frac{13}{34}[/tex]

[tex]\frac{-7}{17} X\frac{34}{13}[/tex]

(d) [tex]\frac{-2}{7}[/tex]÷[tex](\frac{-2}{21}[/tex] ÷ [tex]\frac{1}{7} )[/tex]

[tex]\frac{-2}{7}[/tex] ÷[tex](\frac{-2}{21} X\frac{7}{1} )[/tex]

[tex]= \frac{-2}{7} X \frac{-3}{2}[/tex]

[tex]=\frac{3}{7}[/tex]

He multiplied the denominator and numerator.

(e)

[tex]\frac{-1 \frac{1}{2} }{1\frac{2}{3} } \\\\=\frac{\frac{3}{2} }{\frac{5}{3} } \\\\=\frac{3}{2} X \frac{3}{5} \\\\=\frac{9}{10}[/tex]

(f) [tex]\frac{-3}{4}[/tex] ÷ [tex]\frac{2}{5} = \frac{-3}{4} X \frac{5}{2} =\frac{-15}{8}[/tex]

0.75÷0.4 = 1.875

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{2}{5} = \frac{3}{4} X \frac{-5}{2} =\frac{-15}{8}[/tex]

(g)

Reciprocal of [tex]-1\frac{1}{17} = \frac{-17}{18}[/tex]

Reciprocal of [tex]\frac{-17}{18} = \frac{-18}{17}[/tex]

The above expressions are multiplicative inverse as [tex]\frac{-17}{18} X \frac{-18}{17} =1[/tex]

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Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

Length of the house = 35 feet

width of the house = 28 feet

Height of the house = 6 feet

Total surface area = 2 l b + 2 b h + 2 h l

A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)

A = 1960 + 336 + 420

A = 2716 feet²

If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²

Gallon of paint required = 5432 / 225 = 24.14 gallons.

Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

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Using algebraic expressions and equations to solve this problem, a 19- inch piece of steel is cut into three pieces measuring 2 inches, 4 inches, and 13 inches.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

If the second piece is twice as long as the first piece, we can write this as an algebraic expression "2x" where x is the length of the first piece.

If the third piece is three inches more than five times the length of the first piece, we can write this as an algebraic expression "3 + 5x" where x is the length of the first piece.

If the three pieces were cut from a single piece of steel 19-inches long, we can write the equation for the sum using the algebraic expressions.

let x = length of first piece

2x = length of second piece

3 + 5x = length of third piece

x + 2x + 3 + 5x = 19 inches

Solving for x,

8x = 19 -3

8x = 16

x = 2 inches

length of first piece = 2 inches

Substitute the value of x in the expressions for the second and third piece.

length of second piece = 2x

length of second piece = 2(2)

length of second piece = 4 inches

length of third piece = 3 + 5x

length of third piece = 3 + 5(2)

length of third piece = 3 + 10

length of third piece = 13 inches

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Answer:

Can you provide more info? Like is there a graph that comes along with this question?

Step-by-step explanation:

Janet spent $230 on fuel

Janet rented a car to travel to Argentina

After the journey, she discovered that she had driven 1400 miles and used 56 gallons of gas

The gas costs $4.099 per gallon

Therefore the amount Janet spent thought out the journey for fuel can be calculated as follows

= 4.099 × 56

= 229.5

= 230

Hence when estimated, Janet spent $230 on fuel

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Answer:

[tex]x=27, \quad x= \dfrac{1}{27}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3.7 cm}\underline{Logs Laws}\\\\$\log_ba=\dfrac{\log_ca}{\log_cb}$\\\\\\$\log_ab=c \iff a^c=b$\\\end{minipage}}[/tex]

Given equation:

[tex]\log_3x=9\log_x3[/tex]

Change the base of  9logₓ3  to base 3:

[tex]\begin{aligned}\implies \log_3x & =9\log_x3\\\\& =\dfrac{9\log_33}{\log_3x}\\\\&=\dfrac{9(1)}{\log_3x}\\\\&=\dfrac{9}{\log_3x}\end{aligned}[/tex]

Therefore:

[tex]\implies \log_3x=\dfrac{9}{\log_3x}[/tex]

[tex]\textsf{Let }\log_3x=u:[/tex]

[tex]\implies u=\dfrac{9}{u}[/tex]

[tex]\implies u^2=9[/tex]

[tex]\implies u=\pm3[/tex]

[tex]\textsf{Substitute back in }u=\log_3x:[/tex]

[tex]\implies \log_3x=\pm3[/tex]

Case 1

[tex]\implies \log_3x=3[/tex]

[tex]\implies 3^3=x[/tex]

[tex]\implies x=27[/tex]

Case 2

[tex]\implies \log_3x=-3[/tex]

[tex]\implies 3^{-3}=x[/tex]

[tex]\implies \dfrac{1}{3^3}=x[/tex]

[tex]\implies x=\dfrac{1}{27}[/tex]

Answer: x=3   x=1/27

Step-by-step explanation:

[tex]log_3x=9log_x3\\[/tex]

The area of acceptable values:

[tex]x > 0\ \ \ \ x\neq 1\\Hence,\\x\in(0,1)U(1,+\infty)[/tex]

Solution:

[tex]\displaystyle\\log_3x=\frac{9}{log_3x} \ \ \ \ \ \boxed{ log_ab=\frac{1}{log_ba} }\\\\Multiply\ both\ parts\ of\ the\ equation\ by\ log_3x :\\\\log^2_3x=9\\log^2_3x=3^2\\ log_3x=б3\\\\log_3x=3\\\\x=3^3\\x=3*3*3\\x=27\\\\\\log_3x=-3\\x=3^{-3}\\\displaystyle\\x=(\frac{1}{3})^3\\ x=\frac{1}{3}*\frac{1}{3}*\frac{1}{3} \\ x=\frac{1}{27}[/tex]

If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be  3  and the constant term would be 12 .

What is  polynomial function?

f(x)=(x+1)(x+3)9x-4)

f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12

f(x) =  3x³ + 32 x² + 11x - 12

in above function highest degree would be 3 and constant -12 .

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If a delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.

Given:

Weight of the delivery person=160 lb

Weight of box of book=50 lb

Maximum capacity=1,000lb

Let b represent the number of boxes of books

Hence,

160+50b=1,000

Collect like terms

50b=1000-160

50b=840

Divide both side by

b=840/50

b=16.8 boxes of books

Therefore the maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.

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The Height of the drill after 15 hours was 18.75 feet deep or (-18.75) feet.

Given that in 24 hours

the water well drilling rig dig -30 feet .

we know that ,

24 hours = 1 day

So,

1 hour =1/24 day

15 hours = [tex]\frac{15}{24} =\frac{5}{8} day[/tex]

Now according to the question ,

in 1 day the drilling rig dug -30 feet

So in [tex]\frac{5}{8} day[/tex] the drilling rig will dig =[tex]\frac{5}{8} *(-30)=-18.75feet[/tex]

in 15 hours (5/8 days ) drilling rig dig -18.75 feet.

Therefore , The Height of the drill after 15 hours (5/8 days) was 18.75 feet deep or (-18.75) feet.

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Answer:

judging from the list of numbers i would pick a

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer: 80 degrees because a line is 180°.

So if you subtract

180 - 100 = 80°

Answer:

x=80°

Step-by-step explanation:

The measures of angle x and the 100° angle form a straight angle.

This straight angle is 180°.

You can subtract the measure of one angle from the whole to find the measure of the other angle.

180°-100°=80°

This means angle x is 80°.

Answer:

What is the question so I can answer

The cost of Robert purchase of books after the paid tax is $32.66.

For the given question;

The original cost of the book purchased by the Robet = $30.45.

The tax of 7.25% is applied on the original cost of the book.

7.25% of $30.45 = (7.25×30.45)/100

7.25% of $30.45 = $2.21

The final cost of the book = original cost + tax

The final cost of the book = $30.45 + %2.21

The final cost of the book = 32.66

Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.

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The complete question is-

Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?

Answer: -1536

Step-by-step explanation:

1: 4(3+3) (3+1) (3+5) (3-5)

2: 4(6) (4) (8) (-2)

3: 24 (4) (8) (-2)

4: 96 (8) (-2)

5: 768 (-2)

= -1536

Answer:

$110

Step-by-step explanation:

quarter is 1/4 of a thing

so $440 ÷ 4 = 110

hence we can conclude that if you get $440 in quarters you will get $110 each time

Hope it helps!!!

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Answer:An equation will not pass through the origin if the points are 0,0.

Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.

Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes

Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes

Total time combined = 30 minutes

Total days in a week Monday through Friday= 5 days

Total days in 2 weeks = 10 days

Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday  = 10*30 = 300 minutes

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Answer: A=32 B=19

Step-by-step explanation: