Write 240 as a product of primes. Use index notation where appropriate.

Answer:

see below

Step-by-step explanation:

x² = 30

x = ±√30 (take the square root of both sides)

The value of X in the equation is:

√30 or 5.48

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

If X to the second power equals 30 can be written as:

X² = 30

To find the value of X, take the square root of both sides of the equation. That is:

√X² = √30

X = √30

X = 5.48

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Answer:

Fraction =  13/20

Decimal =  0.65

Percent = 65%

Step-by-step explanation:

Given:

13 out of 20 emails in mail inbox are junk emails

Solve for:

The experimental probability that next email is junk

Solution:

Step 1: Define the formula for calculating the probability

P = number of elements/total number of elements

Step 2: Perform the calculation

The number of elements (junk emails) = 13

The total number of elements (all emails) = 20

=> P(obtain odd number in experiment) in fraction form = 13/20

=> P(obtain odd number in experiment) in decimal from = 0.65

=> P(obtain odd number in experiment) in percent form = 0.65 x 100 = 65%

Hope this helps!

:)

Answer: 1/200 * (5a-2b)(5a+2b)

Step-by-step explanation:

a^2/8 - b^2/50

Factor out 1/200,

1/200 * (25a^2 - 4b^2)

Using a^2 - b^2 = (a-b)(a+b),

1/200 * (5a-2b)(5a+2b)

Answer:

1/2(a/2+b/5)(a/2-b/5)

Step-by-step explanation:

a²/8- b²/50= 1/2(a²/4- b²/25)= 1/2(a/2+b/5)(a/2-b/5)

Answer:

Your answer is 160

Step-by-step explanation:

Just did this on edg.

The measurement of asked arc is 160°.

An arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.

Given that. the two tangents intersect at a point outside the with circle center O

The angle formed between the two tangent = 20°

The first arc formed is measured as x°, which is the arc opposite the point where the two tangents meet = The arc the satellite can see (refer to the attached figure)

The angle x is given by the relationship;

x = 2 × (90 - v/2)

Where;

v = The angle formed at the point where the two tangent meet = 20°

Therefore;

x = 2 × (90 - 20/2) =  2 × (90 - 10) =  2 × 80  = 160°

The arc measure, x, that the satellite can see = 160°.

Hence, the measurement of asked arc is 160°.

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Answer:  [tex]\bold {1)\ \cos\ \theta}=\dfrac{\sqrt2}{2}\qquad 2)\ \tan \theta =\dfrac{1}{3}\qquad 3)\ \cos\ \theta=\dfrac{3\sqrt{13}}{13}\qquad 4)\ \cos\ \theta = \dfrac{2\sqrt5}{5}}[/tex]

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse

[tex]1)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt2}\quad =\large\boxed{\dfrac{\sqrt2}{2}}[/tex]

Note: 2² + 2² = hypotenuse²  →  hypotenuse = 2√2

[tex]2)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{2}{2\sqrt2}\quad =\dfrac{5}{15}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Note: hypotenuse not needed for tan θ

[tex]3)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3}{\sqrt{13}}\quad =\large\boxed{\dfrac{3\sqrt{13}}{13}}[/tex]

Note: 2² + 3² = hypotenuse²  →  hypotenuse = √13

[tex]4)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{2\sqrt5}\quad =\large\boxed{\dfrac{2\sqrt5}{5}}[/tex]

Note: hypotenuse given in problem

Answer:

y=2x-2-3

Step-by-step explanation:

First you will need graphing paper. Go ahead and locate the y intercept on each of these equations. Then locate the slope. (y=mx+b). If the slope is positive count the amount of blocks up the slope's value is. And if negative count down. Then count to the right depending on the denominator. (2/1) You will make a triangle draw the line on the hypotenuse of the triangle. Then you have the line. You can also just use desmos.

The equation of the graphed function is [tex]y = 2^{x-2} + 3[/tex]

Functions are used to represent equation, graphs and tables

The parent function of the graph is an exponential function represented by

[tex]y = 2^x[/tex]

First, the function is shifted 2 units right.

So, we have:

[tex]y = 2^{x - 2}[/tex]

Next, the function is shifted 3 units up.

This is represented as:

[tex]y = 2^{x - 2} + 3[/tex]

Hence, the equation of the graphed function is [tex]y = 2^{x-2} + 3[/tex]

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Answer:

Linear. While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x-value to only one y-value).

Answer:

see below

Step-by-step explanation:

do long division

for example 42/8 = 5 2/8 =5 1/4 =5.25

Answer:

6 is not a solution to the given equation.

Step-by-step explanation:

We are given the equation [tex]x^2-4=5x[/tex]

We need to know whether or not x=6 is a solution. This means that we should substitute in 6 for each instance of x. Then, if both sides of the equation are equal, then 6 is a solution to the equation.

[tex]x^2-4=5x\\\\(6)^2-4=5(6)\\\\36-4=30\\\\32=30[/tex]

As 32 ≠ 30, 6 is not a solution to the given equation.

Answer:

a) y = -5 b) y = -4 c) y = 4 d) y = 11

Step-by-step explanation:

a) (-2+2)²-5

b) (-1+2)²-5

c) (1+2)²-5

d) (2+2)²-5

Answer:

c) T(−1, 3) ° Rotation,180°

Step-by-step explanation:

Explanation:-

First we will apply transformation is

Rotation of 180°  then we will apply transformation is changes  

(x,y) to (-x ,-y)

a)

Given vertex T(  2 ,2 )

T( 2 ,2 )→ T( -2 ,-2)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

T( -2 ,-2) → T¹ ( -2 -1 ,-2 +3)

The new vertex is  T¹ ( -3 ,1)

b)

Given vertex U(  4 ,2 )

U( 4 ,2 )→ U( -4 ,-2)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

U -4 ,-2) → U¹ ( -4 -1 ,-2 +3)

The new vertex is  U¹ ( -5 ,1)

c)

Given vertex R(  3 ,5 )

R( 3 ,5 )→ R( -3,-5)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

R( -3 ,-5) → R¹ ( -3 -1 ,-5 +3)

The new vertex is  R¹ ( -4 ,-2)

d)

Given vertex S(  1 ,3 )

S( 1 ,3 )→ S( -1 ,-3)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

S( -1,-3) → S¹ ( -1 -1 ,-3 +3)

The new vertex is  S¹ ( -2,0)

Answer:

[tex]\angle PRQ = 50^\circ[/tex]

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:

We are given the following details:

[tex]\angle RPQ =99^\circ[/tex]

[tex]\angle PQR =31^\circ\\\text{Side QR} = 11\ units[/tex]

To find:

[tex]\angle PRQ =?\\Side\ PR = ?\\Side\ PQ = ?[/tex]

We know that the sum of all the angles of a triangle is equal to [tex]180^\circ[/tex]

i.e.

[tex]\angle PQR +\angle PRQ +\angle RPQ =180^\circ\\\Rightarrow 31^\circ +\angle PRQ +99^\circ =180^\circ\\\Rightarrow \angle PRQ = 180-130\\\Rightarrow \angle PRQ = 50^\circ[/tex]

To find the sides, we can use Sine rule:

As per Sine rule:

[tex]\dfrac{a}{sin A} =\dfrac{b}{sin B} =\dfrac{c}{sin C}[/tex]

Where a, b and c are the sides opposite to [tex]\angle A,\angle B,\angle C[/tex] respectively.

Using Sine rule in given triangle:

[tex]\dfrac{11}{sin 99} =\dfrac{b}{sin 31} =\dfrac{c}{sin 50}\\\\\text{Solving }\dfrac{11}{sin 99} =\dfrac{b}{sin 31} \\\Rightarrow b = \dfrac{11}{sin 99} \times sin31\\\Rightarrow b =5.74\ units\\\\\text{Now, Solving }\dfrac{11}{sin 99} =\dfrac{c}{sin 50} \\\Rightarrow c = \dfrac{11}{sin 99} \times sin50\\\Rightarrow c =8.53\ units[/tex]

So, sides are

PR = 5.74 units and

PQ = 8.53 units

Answer:

Answer:

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:

We are given the following details:

To find:

We know that the sum of all the angles of a triangle is equal to

i.e.

To find the sides, we can use Sine rule:

As per Sine rule:

Where a, b and c are the sides opposite to  respectively.

Using Sine rule in given triangle:

So, sides are

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:

Answer:

[tex]x = 20[/tex]

Step-by-step explanation:

[tex]3x + 2x + 80 = 180 \\ 5x + 80 = 180 \\ 5x = 180 - 80 \\ 5x = 100 \\ \\ x = \frac{100}{5} \\ \\ x = 20[/tex]

Answer:

x=20

Step-by-step explanation:

The 3 angles are on a straight line together. Therefore, they are supplementary. This means they must add to 180 degrees.

Therefore,

3x+80+2x=180

Combine like terms by adding 3x and 2x

(3x+2x)+80=180

5x+80=180

We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

80 is being added to 5x. The opposite of addition is subtraction, so subtract 80 from both sides.

5x+80-80=180-80

5x=180-80

5x=100

x is being multiplied by 5. The opposite of multiplication is division, so divide both sides by 5.

5x/5=100/5

x=100/5

x=20

x is equal to 20.

X-intercept is -4 and the Y-intercept is 5

Answer:

4 is a

Step-by-step explanation:

Answer:

[tex]x=-8[/tex]

Step-by-step explanation:

→All you need to do for this equation is, divide both sides by -300. You do this to get "x," by itself:

[tex]2400=-300x[/tex]

[tex]\frac{2400}{-300} =\frac{-300x}{-300}[/tex]

[tex]-8 = x[/tex]

Answer:

196

Step-by-step explanation:

196 is the perfect square number, because its square root is 14.

[tex] \sqrt{196} = 14[/tex]

Answer:

This means that she will be 16.35 ft away from the rim in 15 minutes at this current rate.

Step-by-step explanation:

What we are asked here is imply to state how long in terms of distance would be Arielle position after 15 minutes

Now, 55 ft will take her 234 minutes

x ft will take her 15 minutes

x * 234 = 55 * 15

234x = 3825

x = 3825/234

x = 16.35 ft

This means that she will be 16.35 ft away from the rim in 15 minutes at this current rate.

After 15 minutes, Ariele would be 3.5 feet away from the rim.

Speed is the ratio of distance travelled to total time taken. It is given by:

Speed = distance / time

Ariele is hiking down into the canyon. She starts at the rim and hikes down 55 feet in 234 minutes. Hence;

Ariele speed = 55 feet / 234 minutes

In 15 minutes, the distance covered is:

Distance = (55 feet / 234 minutes) * 15 minutes = 3.5 feet

After 15 minutes, Ariele would be 3.5 feet away from the rim.

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Answer:

Between 1997 and 2004, Baffin Bay’s polar bear population  

decreased

.

528 is about  

25

percent of 2074.

Step-by-step explanation:

Answer:

decreased

25

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is easy, just multiply 3.8 by 7.

3.8 x 7 = 26.6

I'm always happy to help :)

Answer:

  80 feet

Step-by-step explanation:

The smallest value of f(x) in the table is f(x) = 0. It occurs where x = 80.

Since x is the horizontal distance in feet from the wall, the minimum point (drain) is 80 feet from the wall.

Answer:

c

Step-by-step explanation:

edge2020

Answer:

see below

Step-by-step explanation:

1 2 3 4 5 6 7 8 9 10  = 10 cards

9 of them have 1 digit on them  ( 10 has 2 digits)

P( 1 digit) = number with 1 digit) / total = 9/10

P(  not have 1 digit)= number not  with 1 digit) / total = 1/10

Answer:

B)

Step-by-step explanation:

If two square matrix, with same dimensions, are inverse of one another, their product will always be the identity matrix with the same dimensions.

The matrix A and B are 2x2, so the result of the product A * B is a 2x2 identity matrix, that is represented as follows:

I = [1 0 ; 0 1]

(First line: 1 0, second line: 0 1)

So the correct option is B)

Answer:

3811.21

Step-by-step explanation:

volume of sphere is 4188.79 using the formula for the volume of a sphere.

volume of the box is=20x20x20=8000

8000-4188.79=3811.21

Answer:

A) -6x+3y = 27

B) -5x-3y = -16 We add the 2 equations

-11x = 11

x = -1

Putting 1 into equation B)

5 -3y = -16

-3y = -21

y = 7

Step-by-step explanation:

Answer:

R = {-9, -5, -1, 3}

Step-by-step explanation:

To find the range, plug in each value of the domain into the given equation for x.

g(-2) = 2 (-2) - 5 = -9

g(0) = 2 (0) - 5 = -5

g(2) = 2 (2) - 5 = -1

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

Answer:

R = {-9, -5, -1, 3}

Step-by-step explanation:

We can determine the range of the function g by inputting each given domain value into the function itself.

g(x) = 2x - 5 and D = {-2, 0, 2, 4}

g(-2) = 2(-2) - 5 = -4 - 5 = -9

g(0) = 2(0) - 5 = 0 - 5 = -5

g(2) = 2(2) - 5 = 4 - 5 = -1

g(4) = 2(4) - 5 = 8 - 5 = 3

Therefore, R = {-9, -5, -1, 3}.

I hope this helps!

Answer:

The answer is C

Step-by-step explanation:

got it right

The graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

The equation is given as:

y = - 3x + 1

The above equation is a linear function

A linear function is represented as:

y = mx + c

Where m represents the slope and c represents the y-intercept

This means that the graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

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Answer:

x= -12

Step-by-step explanation:

∠2= (180°-36°)÷2 (base ∠s of isos. △)

∠2= 72°

m∠2= x +84

72= x +84

x= 72 -84

x= -12

Answer:

The value if x is -12.

Step-by-step explanation:

Given that isosceles triangle have a same pair of angle. So in order to find the angles, you have to subtract it from 180° and 36°.

[tex]θ + θ + 36 = 180[/tex]

[tex]2θ = 180 - 36[/tex]

[tex]2θ = 144[/tex]

[tex]θ = 144 \div 2[/tex]

[tex]θ = 72[/tex]

Next, the expression for ∠2 is x + 84 which is also 72°. So you have to solve it by comparing :

[tex]x + 84 = 72[/tex]

[tex]x = 72 - 84[/tex]

[tex]x = - 12[/tex]