FACTOR....
x^2 + 10× - 2400 = 0​

Answer:

[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]

Step-by-step explanation:

we would like to solve the following using double-angle formula:

[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]

there're 4 double Angle formulas of cos function which are given by:

[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]

since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore

step-1: assign variables

to do so rewrite the given function:

[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]

so,

Step-2: substitute:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]

recall unit circle thus cos300 is ½:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]

simplify square:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]

reduce fraction:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]

simplify substraction and hence,

[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]

Answer:

[tex]f(x) = 3x - 5[/tex]

For a zero, f(x) = 0:

[tex]{ \tt{0 = 3x - 5}} \\ { \tt{x = \frac{5}{3} }}[/tex]

Answer:

ARC= 15.7

ARC= 2(3.14)10(90/36)

Step-by-step explanation:

Answer:

Jack

Step-by-step explanation:

convert the fractions to decimals to determine the person that painted the larger part of the wall

5/8 = 0.625

7/12 = 0.583

the fraction Jack painted is larger.

Answer:

Step-by-step explanation:

We know, for square

[tex](side)^2=(Area)\\=>X^2=8\\[/tex]

∴[tex]X=2\sqrt{2}[/tex] unit

[tex]Now, Side=3X[/tex]

[tex]Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit[/tex]

hope you have understood this...

pls mark my answer as the brainliest

The area of square of side 3X is 72 square unit.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

Area of square having side X is 8.

Since, formula for area of square having side X is X².

Implies that,

X² = 8

X = 2√2

The area of square having side 3X
side =3 × 2√2

side = 6√2

The area of square = (6√2)²

                                = 36 x 2

                                = 72

The area of square is 72 square unit.

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The equation with exactly one solution is  3x + 5 = 2x - 6. Option D is correct.

To determine which equation has exactly one solution, we need to solve each equation and see if we end up with a unique value for 'x'.

4x – 4 + 2x = 6x - 4

Combine the x terms on the left side: 6x - 4 = 6x - 4

This equation is an identity and holds true for all values of x. It doesn't have a unique solution.

B. 2(4x + 5) = 8x + 10

Distribute the 2 on the left side: 8x + 10 = 8x + 10

Similar to the previous equation, this equation is also an identity and holds true for all values of x.

It doesn't have a unique solution.

4x - 8 = 4(x - 4)

Distribute the 4 on the right side: 4x - 8 = 4x - 16

Subtract 4x from both sides: -8 = -16

This equation is contradictory and has no solution.

3x + 5 = 2x - 6

Subtract 2x from both sides: x + 5 = -6

Subtract 5 from both sides: x = -11

This equation has a unique solution, x = -11.

So, the equation with exactly one solution is  3x + 5 = 2x - 6. Option D is correct.

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Answer:

y = 1/2x + 5/2

Step-by-step explanation:

y = 1/2x + b

5 = 1/2(5) + b

5 = 5/2 + b

5/2 = b

Answer:

Step-by-step explanation:

If the coins are identical and not numbered, we need to find the number of patterns.

There are 4 rows and 4 columns. One cell remains empty in each row.

There are 4 options for the first row, 3 options for the second row, 2 options for the third row and 1 option for the fourth row.

The number of options reduces to avoid more than 1 empty cell in each row or column.

Number of options is:

_________

[tex] \: [/tex]

4rows, and 4columns.

Soo :

= 4!

= 4 × (4 - 1) × (4 - 2) × (4 - 3)

= 4 × 3 × 2 × 1

= 24

Answer:

1.5 per hour

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

Angle C = arccos((84²+13²-85²)/(2×84×13))

= arccos(0/2184)

= arccos(0)

= 90°

Answered by GAUTHMATH

Step-by-step explanation:

please mark this answer as brainlist

Answer:

1) X = 0

2) X = 0 or X = 1

Step-by-step explanation:

1)

[tex] \sqrt{6x} + 9 + 2 = 11 [/tex]

6x = 0 since root can only be = 0 if radicand is 0

X = 0

2)

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

[tex] \sqrt{x} = x[/tex]

X = x^2 ( We are squaring both sides to simplify)

x-x^2 = 0

x (1-x) = 0 (Factor the expression)

X = 0 or

1 -x = 0

X = 1

Answered by Gauthmath

Answer:

He ate 1/12 of the pizza

Step-by-step explanation:

Divide the pizza by 4 to get the share each friend got

1/4

Then Binli ate 1/3 of his share

1/4 * 1/3 = 1/12

He ate 1/12 of the pizza

Answer:

348 km³

Does the answer help you?

Let assume hours be x.

1 hour = 60 minutes

x hour = 330 minutes

[tex] \bf \large \rightarrow \: \: \frac{1}{60} \: \times \: \frac{x}{330} \: \: \: \small\rm({\red{ Cross \: \: Multiplying }}) \\ [/tex]

[tex]\bf \large \rightarrow \: \: 60x \: = \: 330[/tex]

[tex]\bf \large \rightarrow \: \: x \: = \: \cancel \frac{330}{60} \: = \: 5.5 \\ [/tex]

Total hours in a day is 5.5

The average American student is in class 5.5 hours a day.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

We have to given that;

The average American student is in class 330 minutes a day.

We know that;

⇒ 1 hours = 60 minutes

⇒ 1 minute = 1/60 hours

Hence, We can change the unit as;

⇒ 330 minutes = 330 / 60 hours

                        = 5.5 hours

Thus, It is equal to 5.5 hours.

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Answer:

x^2 +2x+xy +2y

Step-by-step explanation:

(x + y) (x + 2)

FOIL

first x*x = x^2

outer  x*2 =2x

inner y*x= xy

last = y*2 =2y

Add together

x^2 +2x+xy +2y

Answer:

Step-by-step explanation:

F - First ; O - Outside ;  I - inside  ; L -last

(x + y)(x + 2) = x*x + x*2 +y*x +y*2

                    = x² + 2x + xy +2y

Answer:

10t+2

Step-by-step explanation:

2-5t+8+5t-8

10t+2

Answer:

Step-by-step explanation:

Solve for a:

Answer:

The answer to your question would be x=12. Equation is worked out below

Step-by-step explanation:

5 /2 x−7= 3 /4 x+14

5 /2 x-3/4x − 7 =  3 /4 x-3/4x +14

7/ 4 x−7=14

7 /4 x−7+7=14+7

7/ 4 x=21

do the opposite of 7/4x (division)

7/4 / 7/4x = 21 / 7/4

4/7 / 7/4x (cross each other out) = 21 / 4/7

x=12

Answer:

[tex] \frac{5}{2}x - 7 = \frac{3}{4} x + 14 \\ \frac{5}{2} x - \frac{3}{4} x = 14 + 7 \\ \frac{7}{4} x = 21 \\ x = \frac{21 \times 4}{7} \\ x = 12[/tex]

I hope I helped you^_^

Answer:

[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1} = 2 \cdot x^2 - 9 \cdot x + 7 \ Remainder \ (x - 2)[/tex]

Step-by-step explanation:

Part I

The problem can be expressed as follows;

The dividend is 4·x⁴ - 5·x³ + 2·x² - x + 5

The divisor is x² + x + 1

[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1}[/tex]

Part II

The number of times x² goes into the larest term, 4·x⁴ = 4·x² times

2·x² - 9·x + 7

[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1}[/tex]

4·x⁴ + 4·x³ + 4·x²

-9·x³ - 2·x² - x + 5

-9·x³ - 9·x² - 9·x

7·x² + 8·x + 5

7·x² + 7·x + 7

x - 2

Therefore, we have;

[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1} = 2 \cdot x^2 - 9 \cdot x + 7 \ Remainder \ (x - 2)[/tex]

Answer:

Step-by-step explanation:

First step plug the numbers into the equation.

-10/(5+2) = (-10/5) + (-10/2)

Solve both sides of the equation separately.

-10/(5+2) Use distributive property, multiply both 5 and 2 by -10.

= -50 + (-20) = -70

-10/5 + -10/2 Multiply the fractions so they can be added together.

-10/5*2 = -20/10  -10/2*5 = -50/10

-20/10 + -50/10 = -70

Now you have solved both equations and they are both equal to -70, so you have verified that the equations are equal to each other because they both equal -70.

Answer:

28.26 in ^2

Step-by-step explanation:

The diameter is 6 inches

The radius is 1/2 of the diameter

r = 1/d = 1/2(6) = 3 inches

A = pi r^2 = 3.14( 3)^2  = 3.14 (9) =28.26 in ^2

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Question isn't well formatted, a picture if the question is attached below.

Answer:

1 / 4

Step-by-step explanation:

From the plot, each dot represent a gamer ; therefore, the total number of gamers will be counting all the dots ;

Total number of gamers = 24

Fraction of gamers that have 7 / 8 of the way to go ;

This means that they have 7/8 of the way left to proceed to next level ;

The fraction is : 1 - 7/8 = 1 /8

This means the number of of people whose progress are on 1/8 ; this is 6

Hence, fraction of gamers that have 7/8 of the way to go :

6 / 24 = 1 / 4

Answer:

b = 55°

Step-by-step explanation:

The angle at the centre is twice the angle on the circle subtended by the same arc, then

a = 0.5 × 110° = 55°

Angles on the circumference subtended by the same arc are congruent, so

b = a = 55°

Answer:

12/13

Step-by-step explanation:

we know this is a right triangle, and we know that the hypotenuse is the longest side. so we can already say that the hypotenuse of the triangle is DF or 78.

when you draw it out, you find that the shortest leg is 30 and the second is 72 and the hypotenuse is 78. we also know that cosine is adjacent/hypotenuse. once you draw the triangle and notice which side is adjacent to angle F, just fit it into the formula and you get:

cos F = 72/78

cos F = 12/13

Answer: Choice C. [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Answer:

Min = -16; max = 0

Step-by-step explanation:

I plotted the inequalities for the constraints (see pic).

Sub in the coordinates of the vertices into the optimisation equation.

z = -(-4) + 5(-4) = -16

z = 0

z = -3 + 5(-1) = -8

Therefore, the max value of z is 0, and the min value is -16

Answer:

2 miles per hour

Step-by-step explanation:

To find her walking pace in 'miles per hour' we need to divide the distance (in miles) by the time (in hours).

Speed = Distance/ Time

The time is given in minutes , but 50 minutes = 50/60 hours

=5/6 hours

1 2/3 ÷ 5/6

=5/3 × 6/5 miles per hour

Now cut it

= 2 miles per hour

Answer:

d=2

Step-by-step explanation:

We are given equation:

sqrt(4y-3)=d-y

Squaring both sides gives:

4y-3=(d-y)^2

Applying the identity (x+y)^2=x^2+2xy+y^2 on right:

4y-3=d^2-2dy+y^2

Now let's y=7:

4(7)-3=d^2-2d(7)+(7)^2

Simplify:

25=d^2-14d+49

Subtract 25 on both sides:

0=d^2-14d+24

Factor left:

0=(d-12)(d-2) since -2+-12=-14 and -2(-12)=24

This gives d=12 or d=2.

The d that makes d-y or I mean d-7 negative will give us y=7 as extraneous

Since 2-7 is -5, then d=2 is what we are looking for.

Check:

sqrt(4y-3)=d-y

Set d=2: sqrt(4y-3)=2-y

Now solve for y:

Square both sides: 4y-3=4-4y+y^2

Subtract 4y and 3 on both sides: 0=7-8y+y^2

Reorder right side: 0=y^2-8y+7

Factor: 0=(y-7)(y-1) since -7+-1=-8 and -7(-1)=7

This gives y=7 or y=1.

Plugging in y=7 for a check to this equation gives:

sqrt(4×7-3)=2-7

Sqrt(25)=-5

5=-5 which is not true which is what we wanted

Answer: 75th term

Step-by-step explanation:

If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.