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Simplify. RADICAL 75 - RADICAL 12

A) RADICAL 63
B) 3 RADICAL 7
C) 3 RADICAL 3
D) 8 RADICAL 3

Answer:

x = 8 , x = - 2.5

Step-by-step explanation:

( x - 8 ) ( 2 x + 5 ) = 0

1. x - 8 = 0

2. 2 x + 5 = 0

x - 8 = 0

( + 8 on both sides )

x = 8

2. 2 x + 5 = 0

( - 5 from both sides )

2 x = - 5

( ÷ 5 on both sides )

x = - 2.5

[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=&sides'\\ &length\\ \cline{1-2} A=&150 \end{cases}\implies 150=s^2\implies \sqrt{150}=s~~ \begin{cases} 150=&2\cdot 3\cdot 5\cdot 5\\ &2\cdot 3\cdot 5^2 \end{cases} \\\\\\ \sqrt{2\cdot 3\cdot 5^2}=s\implies 5\sqrt{2\cdot 3}=s\implies 5\sqrt{2}\cdot \sqrt{3}=s[/tex]

well then, we have a couple of known fellows, √2 and √3.

now, let's bear in mind that 2 and 3 are both prime numbers, a prime number is not divisible by anything but itself or 1, so we will never find two same-values that will give us either 2 or 3, namely, there's no exact root for √2 or √3, which means they're both irrationals, and therefore since they're factors of the answer, the answer is irrational.

Answer:

1)he maximum height your feet will be above the ground is 2.25

2)Will you be able to dunk the ball= No

Step-by-step explanation:

Given:

In order to dunk the basket ball, height needed to jump= 2.5 feet

The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12t

1) the maximum height your feet will be above the ground=?

Given function of height,h(x)=-16t^2+12t

finding maximun of the above function

The maximum of any function written in form of ax^2+bx+c is given by

max= c - (b2 / 4a)

Putting values c=0, b=12 and a=16, we get

max= 0-(12^2/4(-16))

      = 144/64

      =2.25 feet

he maximum height your feet will be above the ground is 2.25 feet.

2)  Will you be able to dunk the ball=?

As the height needed to jump in the air to dunk the ball is 2.5 feet which is greater than the maximum height the feet will be above the ground i.e.

2.5>2.25

hence No you will not be able to dunk the ball !

The maximum height your feet will be above the ground is 2.25 feet. No, you will not be able to dunk the ball.

To find the maximum height your feet will be above the ground, we need to determine the vertex of the quadratic function h(t) = -16t^2 + 12t.

The vertex of a quadratic function of the form h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -16 and b = 12, so the vertex is t = -12/(2*(-16)) = 0.375 seconds.

Substituting this value back into the function h(t), we get h(0.375) = -16(0.375)^2 + 12(0.375) = 2.25 feet. Therefore, the maximum height your feet will be above the ground is 2.25 feet.

Since you need to jump 2.5 feet in the air to dunk the ball and the maximum height your feet will reach is only 2.25 feet, you will not be able to dunk the ball.

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20% of the students wore blue shirts

40 x 0.08 = 3.2

3.2% out of the 40 students wore blue shirts.

1. 3^4 x^3 z^2

2. 73 aabbbb

Rotations, translations and reflections are transformations that preserve areas, so they always produce congruent figures.

So, the only way you have to produce a similar but not congruent figure is to use dilation with a scale different than 1.

Your problem looks like this

[tex]11\sqrt{45}  - 4\sqrt{5}[/tex]

To make this problem easier, we need to simplify these square roots

[tex]11\sqrt{45}[/tex]    can be simplified

Here's how :

The factors of 45 are 9 and 5

9 is a perfect square root, but 5 is not

Think of the problem like this

[tex]\sqrt{9}     ×     \sqrt{5}[/tex]

The square root of 9 is 3, but 5 has no perfect square root

Now [tex]11\sqrt{45}[/tex] is simplified to [tex]33\sqrt{5}[/tex]

Now let's solve the problem, because we have a common square root of 5

[tex]33\sqrt{5}[/tex] - 4\sqrt{5}[/tex]

Our final answer is

[tex]29\sqrt{5}[/tex]

Feel free to ask questions if you are confused! Hope I helped :)

For this case we must simplify the following expression:

[tex]11 \sqrt {45} -4 \sqrt {5}[/tex]

So, we rewrite 45 as [tex]3 ^ 2 * 5[/tex]:

[tex]11 \sqrt {3 ^ 2 * 5} -4 \sqrt {5} =[/tex]

We have by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]11 * 3 \sqrt {5} -4 \sqrt {5} =\\33 \sqrt {5} -4 \sqrt {5} =\\29 \sqrt {5}[/tex]

Answer:

[tex]29 \sqrt {5}[/tex]

Answer:

Approximately 53

Step-by-step explanation:

This is a geometric progression, because each term is found by multiplying the previous one by a constant factor.

In our case, the first term is know (a1 = 3), and the growth factor is also known (q = 1.333333).

What we are tasked to do is to find the 11th (n=11) term of the series, since it asks for AFTER the 10th roll..  That's easy with the base formula:

[tex]a_{n} = a_{1} q^{n-1}[/tex]

Let's place the values we have in the equation and solve it:

[tex]a_{10} = 3 * (1.333333)^{11-1} = 3 * (17.758) = 53.3[/tex]

So, after the 10th roll, you should need 53 dice, approximately.

Answer:

Step-by-step explanation:

f(x) = { 0, x<0; 0 <= x, (x +3) * 1000000 }

(Note the graph ought to flatten to zero for x < 0)

ANSWER:

You need to write it’s piecewise function if

x < -3, the term x+3 becomes negative. So , for all values of x < -3 , the term becomes -(x+3)

Piecewise will be

F(x) = square root of (x+3) when x is greater than or equal to -3

F(x) = square root of -(x+3) when x less than or equal to -3

For this case we must solve the following inequality:

[tex]3x <18[/tex]

Dividing between 3 on both sides of the inequality we have:

[tex]x <\frac {18} {3}\\x <6[/tex]

Thus, the solution of the variable "x" is given by all the numbers smaller than 6.

Answer:

All values of "x" less than 6.

(-∞, 6)

Answer:

Final answer is [tex]2y^4 \sqrt{5}[/tex].

Step-by-step explanation:

Given expression is [tex]\sqrt{20y^8}[/tex].

Now we need to smplify the given expression [tex]\sqrt{20y^8}[/tex].

So begin with factoring 20 into two parts so that one part is perfect square number.

[tex]\sqrt{20y^8}[/tex]

[tex]=\sqrt{4 \times 5y^8}[/tex]

[tex]=\sqrt{4 y^8} \times \sqrt{5}[/tex]

[tex]=2y^4 \times \sqrt{5}[/tex]

Hence final answer is [tex]2y^4 \sqrt{5}[/tex].

Answer:

8 ft

Step-by-step explanation:

let width = x

then length= x+2

Area = l(w)

        =x(x+2)

168  = x^2 + 2x

x^2 + 2x-168=0

Using quadratic formula we get roots :

x= 12, x=-14

x= 12 (as width cannot be in negative)

then length= x+2 = 14

length of rug= length of floor - 4

                     = 14- 4

                    = 10

width of rug= width of floor- 4

                    = 12-4

                    = 8

Hence the length (the shorter side) of the rug be 8 feet !

Answer:

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Step-by-step explanation:

We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;

(the number of times a 4 was rolled)/(total number of rolls)

8/20 = 0.4

0.4*100 = 40%

The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;

P(HT or TH or TT)

The above events are mutually exclusive, thus;

P(HT or TH or TT) = P(HT) + P(TH) + P( TT)

                               = (22+34+16)/(28+22+34+16)  

                               = 0.72 = 72%

On the other hand, the theoretical probability of obtaining at least one tails,

P(HT or TH or TT) = 3/4

                              = 75%

This is because there is at least one tail in 3 out of 4 possible outcomes.

Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.

Answer:

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Step-by-step explanation:

1. Lets define experimental probability first.

Experimental probability is the probability of an event's occurrence when the experiment was conducted.

The number cube is rolled 20 times, so our sample space is 20.

And the number 4 came in result 8 times, so the the event space is 8.

So,

Experimental Probability = 8/20

=> 0.4

Converting into percentage will give:

=> 40%

So the first option is correct.

2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed

The sample space is {HH, HT, TH, TT}

3 out of these 4 outcomes contain at least one tail

So the theoretical probability of getting at least one tail is: 3/4

=> 0.75 or 75%

Now for the experimental probability,

The total sample space is 28+22+34+16 = 100

The number of favorable outcomes are(Which contain at least one tail):

22+34+16 = 72

So, experimental probability of getting at least one tail = 72/100

=> 0.72 or 72%

We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..

Answer: 17x = 85

Step-by-step explanation:

X is the number in which you'd multiply 17 by to equal 85, therefore x = the number of years.

Answer: Equation would be,

17x = 85

Where, x represents the number of year.

Step-by-step explanation:

Let x represents the number of year after which the cliff erodes 85 centimeters,

Since, the cliff on the seashore is eroding at the rate of 17 centimeters per year,

So, the total eroding of cliff after x years = 17x

[tex]\implies 17x = 85[/tex]

Which is the required equation..

Answer:

x verse y on the map

Step-by-step explanation:

It shows what the x and the y cordinates are

-2^2÷ -2^2=1

(-2)(-2)÷ (-2)(-2)=1

4 ÷4=1

Answer is 1

Answer:

Any number divided by itself is 1.

Step-by-step explanation:

One of the nice parts about algebra is that -- if a number appears more than once -- you can make things a lot cleaner looking by throwing them in a variable. Let's let x = -2² . Our equation then becomes x ÷ x = 1, and it's much clearer here that, since we're dividing x by itself, the answer should clearly be one.

You just need to factor a to get

[tex]a(1+2+3+4) = 10a[/tex]

P(x) to P(x+2), you need to graph the same but shift 2 units to the left.

New function :

Max = 4 ,coordinate points (-5, 0) and (5,0)

Answer:

Shirts = $7

Shorts $17

Step-by-step explanation:

Let:

T - shirts

S - shorts

We can make two equations out of this problem:

4T + 3S = $79

7T + 8S = $185

Through substitution we can solve for one of the unknowns. We make one equation to solve for an unknown

[tex]4T+3S=\$79\\\\3S = \$79-4T\\\\S=\dfrac{\$79-4T}{3}[/tex]

We use the formula of S and insert it into the other equation:

[tex]7T+8(\dfrac{\$79-4T}{3}) = \$185\\\\7T + \dfrac{\$632-32T}{3}=\$185\\\\\dfrac{\$632-32T}{3}=\$185-7T\\\\\$632-32T=3(\$185-7T)\\\\$632-32T=\$555 - 21T\\\\-32T+21T=\$555-\$632\\\\-11T=-\$77\\\\\dfrac{-11T}{11}=\dfrac{-\$77}{11}\\\\T = \$7[/tex]

Thus T-shirts are $7 each.

Now that we know T, we can use it to solve for the other unknown. You can use it on any of the formulas.

[tex]4T+3S=\$79\\\\4(\$7) + 3S = \$79\\\\\$28+3S =\$79\\\\3S=\$79-\$28\\\\3S=\$51\\\\S=\dfrac{\$51}{3}\\\\S = \$17[/tex]

We know then that Shorts are $17 each.

Answer:

The correct answer is for sure 100 % =33,490

Step-by-step explanation:

34,100-610= 33,490

610+33,490=34,100

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Answer:

y=1/2x-2.5

Step-by-step explanation:

4x-8y=20

Subtract 4x from both sides to get the 8y on on side.

-8y=-4x+20

divide -8 from both sides to get the y by itself.

y=1/2x-2.5

Answer:

C. [tex]\frac{32g^2}{3h^4}[/tex]

Step-by-step explanation:

Answer:

Option C is correct

Step-by-step explanation:

[tex]\frac{\frac{h}{3g^2}}{\frac{h^5}{32g^7}}[/tex]

We need to simplify the above expression.

We can write the above expression as:

[tex]\frac{h}{3g^2}\div\frac{h^5}{32g^7}[/tex]

Changing division sign into multiplication and reciprocating the second term we get,

[tex]\frac{h}{3g^2}*\frac{32g^7}{h^5}[/tex]

Applying the power rule: a^m/a^n = a^{m-n}

Solving:

[tex]\frac{h*32g^7}{3g^2*h^5}\\\\\frac{32g^{7-2}}{3h^{5-1}}\\\frac{32g^5}{3h^4}[/tex]

So, Option C is correct.

It’s either d or A but I’m sure it’s A

Answer: Last option

inverse property

Step-by-step explanation:

The property of the inverse sum says that if we have a number b and we add it with its negative -b then

[tex]b - b = 0[/tex]

In this case we have that:

[tex]x = a + bi[/tex]

and

[tex]y = -b - bi[/tex]

Note that

[tex]y = -x[/tex]

Therefore:

[tex]x + y = x -x= a + bi - a - bi = 0[/tex]

the answer is the last option

The answer is X= 2a+2

Answer:

a = 1/2x - 1

Step-by-step explanation:

-8a + 3a = -9a + 2x - 4

-8a + 3a + 9a = 2x - 4

4a = 2x - 4

a = (2x - 4) ÷ 4

a = 1/2x - 1

Answer:

q(x)= 2x+5

r(x)= 6

Step-by-step explanation:

Given:

2x^2+13x+26 /x+4

Re-writing in the form of q(x) + r(x)/d(x)

Let

Polynomial P(x)= 2x^2+13x+26

Polynomial d(x)= x+4

Using remainder theorem, putting -4 in P(x) to find r(x)

P(-4)= 2(-4)^2+13(-4)+26

       =6

i.e r(x)= 6

Finding q(x) by long division

q(x)= 2x+5

Hence given expression in the form q(x) + r(x)/d(x)

= (2x+5) + 6/x+4 !

Answer:

28

Step-by-step explanation:

We can see that all the angles are inside of a triangle and the sum of the interior angle of the triangle is 180 degrees.

Knowing this, we know that the sum of all the angles present is 180 degrees.

1st angle can be seen as 90 degrees, 2nd angle is x+6 and the 3rd is 2x.

The sum can be written as ( 90 + x + 6 + 2x ) and this equals to 180 degrees.

90 + x + 6 + 2x = 180

96 + 3x = 180

( subtract 96 on both sides )

3x = 180 - 96

3x = 84

( divide by 3 on both sides )

x = 84 / 3

x = 28

Answer:

x = 28

Step-by-step explanation:

Consider the lower right triangle

The 2 given angles sum to 90° ( sum of angles in a triangle = 180° )

Hence

x + 6 + 2x = 90

3x + 6 = 90 ( subtract 6 from both sides )

3x = 84 ( divide both sides by 3 )

x = 28

Answer: [tex]\frac{x}{5}+9[/tex]

Step-by-step explanation:

Let be "x" the number mentioned in the given phrase.

"...the quotient of a number and five" indicates a division. In other words, the number "x" is divided by 5. This can represented as:

[tex]\frac{x}{5}[/tex]

Now,  "Nine more than the quotient of a number and five" indicates that you need to add 9 to the quotient of a number and five ( [tex]\frac{x}{5}[/tex]).

Knowing this, you can conclude that the translation of "Nine more than the quotient of a number and five" into  a math expression is:

[tex]\frac{x}{5}+9[/tex]

Final answer:

The word phrase 'nine more than the quotient of a number and five' translates to the math expression '(x/5) + 9', where 'x' represents the number.

Explanation:

To translate the word phrase 'nine more than the quotient of a number and five' into a math expression, we first identify the quotient of a number and five, which is denoted as ‘x ÷ 5’ or ‘x/5’ where x represents the number. Next, we address the phrase 'nine more than', which indicates that we need to add nine to that quotient. So, the phrase translates to the algebraic expression ‘(x/5) + 9’.

Therefore, as per the above explaination,  the correct answer is (x/5) + 9

Answer:

1)center =(-2,3)

2) Vertices = (8,3) and (-12,3)

3) foci =(4,3) and (-8,3)

Step-by-step explanation:

As the general equation of ellipse with center at (h,k) is given by:

(x-h)^2/a^2 +(y-k)^2/b^2 = 1

where a=radius of the ellipse along the x-axis

b=radius of the ellipse along the y-axis

h, k= the x and y coordinates of the center of the ellipse.

Given equation of ellipse:

(x+2)^2/100 + (y-3)^2/64 = 1

1)

Finding center:

comparing with the general formula

h=-2 and k=3

Center of given ellipse is at (-2,3)

2)

Finding vertices:

comparing given equation of ellipse with the general formula:

a^2= 100 and b^2=64

then a = 10 and b=8

As a>b, it means the ellipse is parallel to x-axis

hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)

The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)

3)

Finding Foci, c:

From equations of general ellipse we have a^2 - c^2=b^2

Putting values of a^2=100 and b^2=64 in above

100-c^2=64

c^2=100-64

     = 36

taking square root on both sides

c=6

foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!

The formula for the area of a rhombus is s^2=A.  Plug in and solve:

s^2=25

*Take the square root of both sides*

s=5

Hope this helps!!

Answer:

The side length is 5 mm

Step-by-step explanation:

Since it is square, we know the area of a square is given by

A = s^2 where s is the side length of the square

25 = s^2

Take the square root of each side

sqrt (25) = sqrt(s^2)

5 = s

The side length is 5 mm