The value pi/16 is a solution for the equation 2cos^2(4x)-1=0

True or false?

Answer:

2.6 hours

2 hours 36 minutes.

Step-by-step explanation:

Let the time be x hours

we know

distance = speed*time

speed of one train = 85 miles/hour

time = x hours

distance traveled by one train = 85*x = 85x miles

speed of one train = 95 miles/hour

time = x hours

distance traveled by other  train = 95*x = 95x miles

__________________________________________________

Given that

Two trains leave stations 468 miles apart at the same time and travel toward each other

Thus, together cover 468 miles.

distance traveled by one train + distance traveled by other train = 468

85x+95x = 468

=> 180x = 468

=> x = 468/180 = 2.6

Thus, it will take 2.6 hours to meet each other

we know 1 hour = 60 minutes

0.6 hour = 60*0.6 minutes = 36 minutes

Thus, we can also say that it took 2 hours 36 minutes to meet each other.

Answer: $112.50 ; $4612.5

Step-by-step explanation:

a) Determine how much interest Christine paid at the end of 1 year.

This will be:

Simple interest = PRT/100

where

P = principal = $4500

R = rate = 2.5%

T = time = 1 year

Interest = (4500 × 2.5 × 1)/100

= 11250/100

= $112.50

b) Determine the total amount Christine will repay the bank at the end of 1 year.

Total amount = Principal + Interest

= $4500 + $112.50

= $4612.5

Complete the squares to get

[tex]x^2+y^2=2x-6y+6[/tex]

[tex]\implies(x^2-2x+1)+(y^2+6y+9)=16[/tex]

[tex]\implies(x-1)^2+(y+3)^2=4^2[/tex]

which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.

The area of the region enclosed in the graph x²+y² =2x-6y+6 is 50.26 square units.

The area of the circle can be calculated by the product of π times square of the radius or the product of π/4 times square of diameter.

Area of the circle= A= πr²= πd²/4

where r is radius of the circle and d is diameter of the circle.

Here given that

the equation of circle is given by

x²+y² =2x-6y+6

⇒ x²+y² -2x-6y = 6

⇒ x²-2x+y²-6y = 6

Adding 1 on both sides

⇒ x²-2x+1+y²-6y = 6+1

Adding 9 on both sides

⇒ x²-2x+1+ y²-6y+9 = 6+1+9

⇒x²-2x+1+ y²-6y+9 = 16

⇒ (x-1)² + (y-3)²= 4²

which is similar to equation of the circle

(x-a)² + (y-b)²= r²

This is the equation of the circle in center and radius form where (a,b) is the center of the circle and r is the radius of the circle.

here in the equation of the circle the center of the circle is (1,3)

radius is 4 units.

then the area of the circle is = πr²= π4²= 16π= 50.26 square units.

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Answer:A rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get -7/12 . What is the number.

Step-by-step explanation:Let p/q (q ≠ 0) denote the rational number. Multiplying it by 5/2 gives (p/q)(5/2). Add 2/3 to the product and we get (p/q)(5/2) + 2/3 . The result is given to be -7/12.

∴ (p/q)(5/2) + 2/3 = -7/12 …………………………..……………………………………..(1)

Transposing 2/3 to right-hand-side and changing the sign to negative,

(p/q)(5/2) = -2/3 -7/12 = -(2/3 + 7/12) =- (2 x 4 + 7)/12 (Taking L.C.M.)

Or, (p/q)(5/2) = -(8+7)/12 = - 15/12

Multiplying both sides by 2/5,

(p/q)(5/2) x (2/5) = -15/12 . 2/5 = -(3x5)/(3x4) . 2/5 =- 5/4 .2/5

Since 2/5 is the multiplicative inverse of 5/2, 5/2 x 2/5 = 1 and we obtain

(p/q).1 = -1/4 . 2/1 = -1/2

⇒ p/q = -1/2 which is a negative rational number in which p = 1 and q = 2 ≠ 0 .

∴ the rational number = -1/2

Answer:

x = 10

Step-by-step explanation:

a² + b² = c²

6² + 8² = c²

36 + 64 = 100

√100 = ±10

x = 10

Answer:

10

Step-by-step explanation:

We can use the Pythagorean Theorem to find the value of x.

It states that in a right triangle, [tex]a^2 + b^2 = c^2[/tex].

A and b are the sides, while c is the hypotenuse.

We already know the measure of a and b, so we can find the measure of c easily.

[tex]6^2 + 8^2 = c^2\\\\36+64=c^2\\\\100=c^2\\\\10=c[/tex]

Hope this helped!

Answer: A = 6.5

B = 10.

Step-by-step explanation:

First, remember that when we have a triangle of height H and base B, the area of the triangle is:

Area = B*H/2.

A:

First, count the complete squares:

We have 6 complete squares.

Now the diagonal part:

The diagonal connects a section of 1 by 3 squares, and the shaded area is a right triangle

Then the shaded area will be half of 1 by 3.

this is 1.5 squares.

The total area of A is:

6 + 1.5 = 7.5 squares.

B:

This is more complicated.

At the beginning, we have 4 completed squares in the top right.

At the left, we have a 2 by 4 = 8 square region, where the shaded part is only a triangle rectangle.

Then the area of this triangle is half of 8 squares:

8/2 = 4 squares.

Last, at the bottom, we have two times a 2 by 1 = 2 square region, where the shaded part is a triangle rectangle.

Then the area of each triangle is 2/2 = 1 square.

And we have two of them, so there are 2 squares here.

Then the total area is:

A = 4 + 4 + 1 + 1 = 10 squares.

Each small square In the graph paper represents 1 square unit

Answer:

6103.07 inches ^ 3

Step-by-step explanation:

Step 1: Find the volume of the head

d = 12

r = d/2

r = 6

[tex]=\frac{4}{3} (3.14)6^{3} \\=904.78 inches^{3}[/tex]

Step 2: Find the volume of the body

d = 16

r = d/2

r = 8

[tex]=\frac{4}{3} (3.14)8^{3} \\=2144.66inches^{3}[/tex]

Step 3: Find the volume of the legs

d = 18

r = d/2

r = 9

[tex]=\frac{4}{3} (3.14)9^{3} \\=3053.63 inches^{3}[/tex]

Step 4: Add the volumes together

[tex]904.78 +2144.66+3053.63=Volume[/tex]

[tex]6103.07=Volume[/tex]

Therefore the volume of the snowman is 6103.07 inches ^ 3

Answer:

a=6 x=1

Step-by-step explanation:

4x1=4 4-2=2

2+6=8

Answer:

a=3 i think, sorry if i'm wrong

Step-by-step explanation:

4x-2(x+a)=8     ~parenthesis first.

4*7-14-2a=8     ~4 times 7= 28 and just bring down the rest.

28-14-2a=8      ~ add 14 to negative 14 and 8, the positive and negative 14 would cancel out each other.

28-2a=22        ~ subtract 28 from both positive 28 and 22.

-2a=-6             ~ divide by 2 on both sides.

  a=3               ~ The reason why it is 3 is because negative 2 times positive 3 equals  negative 6.

Answer:

- 55

Step-by-step explanation:

a = −6, b = −5

Answer:

-10

Step-by-step explanation:

g(x) = -3x^2 +4x+5

Let x = 3

g(3) = -3*(3)^2 +4*3+5

     = -3*9 +12+5

     = -27+12+5

     = -10    

Answer:

g(3) = -10

Step-by-step explanation:

g(x) = -3x^2 + 4x + 5

g(3) = -3(3^2) + 4(3) + 5

g(3) = -3(9) + 12 + 5

g(3) = -27 + 12 + 5

g(3) = -15 + 5

g(3) = -10

Answer:

The graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).

Step-by-step explanation:

It is given that p(x) and q(x) are two functions such that

[tex]q(x)=2p(x+3)-6[/tex]    ...(1)

The translation is defined as

[tex]q(x)=kp(x+a)+b[/tex]              .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2) we get

k=2>1, so the graph of p(x) stretch vertically by factor 2.

a=3>0, so the graph of p(x) shifts 3 units left.

b=-6<0, so the graph of p(x) shifts 6 units down.

Therefore, the graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).

Greetings from Brasil...

Let us solve by parts. Power first

(X + 2)² = X² + 2.2.X + 2² = X² + 4X + 4

Rewriting

(X - 3).(X² + 4X + 4)             applying distributive property

X³ + 4X² + 4X - 3X² - 12X - 12

Answer:

1.53 £

Step-by-step explanation:

9×17 = 153p

we know this because there are 5 days left in November and 12 days in December (hence the 17).

Answer:

The correct answer would be No fine is paid if the DVD is returned by the due date, because the first 0 means it is 0 days overdue, so it is returned on time, and the second 0 means the fine would be $0

Step-by-step explanation:

Answer:

30 terms

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here d = 5 and a₃ = 13, thus

a₁ + 2d = 13

a₁ + 2(5) = 13

a₁ + 10 = 13 ( subtract 10 from both sides )

a₁ = 3

Thus

[tex]a_{n}[/tex] = 3 + 5(n - 1) = 148 ( subtract 3 from both sides )

5(n - 1) = 145 ( divide both sides by 5 )

n - 1 = 29 ( add 1 to both sides )

n = 30

The progression has 30 terms

Answer:

work is shown and pictured

Answer:

Answer is A

Step-by-step explanation:

[tex]m = y2 - y1 \div x2 - x1 \\ y2 = m(x2 - x1) + y1[/tex]

Answer:

2-(-3)=2+3=5

-7+4=-3

Step-by-step explanation:

Answer:

2 - (-3) is 5 because (-) × (-) is (+)

And for -7 + 4 is 3 because (-) × (+) is (-).

Answer:

[tex]\Huge \boxed{\mathrm{0.45}}[/tex]

Step-by-step explanation:

1/5 in decimal form is 0.2

1/4 in decimal form is 0.25

1/5 + 1/4

0.2 + 0.25 = 0.45

Answer:

1/5 + 1/4 = 9/20.

9/20 = 0.45

Answer:

Step-by-step explanation:

[tex]1-5\left(3+2\cdot \:3\right)=-44\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3+2\cdot \:3\right)\::\quad 9\\\\=1-5\cdot \:9\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:5\cdot \:9\::\quad 45\\\\=1-45\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:1-45\:\\\\:\quad -44[/tex]

Answer:

-36

Step-by-step explanation:

1-5(3+2x3)

-4(3+2x3)

-4(3+6)

-12-24

-36

Hope this helps ;) ❤❤❤

Hey there! I'm happy to help!

We want to find how much more 5/6 is than 1/2. To do this, we simply subtract 1/2 from 5/6. This will show us how much more 5/6 is.

First, we multiply 1/2 by 3/3 so that the denominator is 6.

1/2×3/3=3/6

Now, we subtract this from 5/6.

5/6-3/6=2/6

We can simplify this to 1/3.

Therefore, Methuki used 1/3 scoop more of brown sugar than white sugar while making desserts for Fun Day.

Have a wonderful day! :D

Answer:

Below

Step-by-step explanation:

● -7x + 5y = 35

Add 7x to both sides

● -7x +7x + 5y = 35+7x

● 5y = 7x + 35

Divide both sides by 5

● 5y/5 = (7x+35)/5

● y = 1.4x + 7

The graph of the function:

Answer:

Step-by-step explanation:

-7x+5y=35

write the equation in the form : y=mx+b

5y=35+7x ( divide both sides by 5)

y=7/5 x +35/5

y=7/5 x +7

if y=0   then 7/5 x+7=0 ⇒7/5 x=-7 ⇒x=-35/7 ⇒x=-5

x=0 then y=7

two points  (0,7) and (-5,0)

Answer:

  √89

Step-by-step explanation:

The distance formula is good for this.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = ((6 -(-2))^2 +(-1-4)^2) = √(64 +25)

  d = √89

The distance between the point is √89 units.

Answer:

Step-by-step explanation:

The equation is not properly formatted presumably here is the format.

Given

[tex]f(x) = 2x^2 + 4[/tex]

determine f(2) , and f(−1).

So we are expect to perform substitution operation and return an answers for values of x= 2 and x= -1

1. When x= 2 we have

[tex]f(2) = 2*2^2 + 4\\\\f(2)= 2*4+4\\\\f(2)= 8+4\\\\f(2)= 12[/tex]

2. When x= -1 we have

[tex]f(-1) = 2*-1^2 + 4\\\\ f(-1)= 2*1+4\\\\ f(-1)= 2+4\\\\ f(-1)= 6[/tex]

Answer:

213 x 112

Step-by-step explanation:

You have to multiply the recipe with the amount of times it's made.

Answer:

213 cups of beans.Keith is making 112 times the recipe.

Step-by-step explanation:

Answer:

x ≤ - 27

Step-by-step explanation:

[tex]\frac{x}{-9}\ge \:3\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\frac{x\left(-1\right)}{-9}\le \:3\left(-1\right)\\\\Simplify\\\\\frac{x}{9}\le \:-3\\\\\mathrm{Multiply\:both\:sides\:by\:}9\\\\\frac{9x}{9}\le \:9\left(-3\right)\\\\\mathrm{Simplify}\\\\x\le \:-27[/tex]

The solution of the given inequality is x ≤ -27.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given inequality ( x / -9) ≥ 3 is solved as:-

( x  / -9 ) ≥ 3

Multiply both sides by ( -1 ).

-1 ( x  / -9 ) ≥ -3

x / 9 ≤ -3

x ≤ -27

Hence, the solution is x ≤ -27.

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Step-by-step explanation:

the opposite side is AC

the building is twenty feet

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

You wont have any coins left. You will have a negative number of coins because 20 x 4 = 80. 80 - 50 = 30. You will need to owe 30 coins

We can distribute the outer x to each term inside

x(x-6) = x^2-6x

So the original equation turns into

x^2-6x = 20

Then you could subtract 20 from both sides to get everything to the same side

x^2-6x-20 = 20-20

x^2-6x-20 = 0

This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.

The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.