Simplify −2√45+3√3+2√3 Question 4 options: A.−6√5+6√3 B.−2√5+6√3 C.−6√5+5√3 D.−18√5+5√3

Set (x+3) to 0. X+3=0. X=-3

Set (x+2) to 0 X+2=0. X=-2

an equation for a circle has formula

(x-m)² + (y-n)² = r²

where (m,n) is its center

and r is its radius

so, the equation has center (4,3) and radius 4

the equation is derived from the pythagorean theorem

Answer:

The shape includes a curve.

Step-by-step explanation:

A polygon consists of joined straight lines - no curves.

Answer:

A. 5/9    B. 1/6.

Step-by-step explanation:

Total possible events = 6*6 = 36.

A.  The possible combinations for the sum  being <= 6 are:

1 ,1  2,2   3,3   1,2  1,3  1,4  1,5  2,1   2,3  2,4  3,1   3,2  3,3  4,1  4,2  5,1

= 16

So Probability of Sum > 6 =  (36-16) / 36

= 20/36

= 5/9.

B.   Possible combinations where the sum is divisible by 6  are

3,3  2,4  4,2  1,5  5,1. 6,6   =   6.

So the required probability =  6/36

= 1/6.

Answer:

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step explanation:

1) * Lets study the pattern;

- 19 , 27 , 35 , 43 , ..................

∵ 27 - 19 = 8

∵ 35 - 27 = 8

∵ 43 - 35 = 8

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* Lets take about the arithmetic sequence

- If the first term is a and the constant difference is d

∴ a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........

∴ an = a + (n - 1)d, where n the position of the term in the sequence

* Now we will use this rule to find the expression of our pattern

∵ a = 19 , d = 8

∴ an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n

* Lets check it;

∵ a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true

∴ The expression to represent the pattern is 11 + 8n

2) * Lets study the pattern;

- 71 , 62 , 53 , 44 , ..................

∵ 62 - 71 = -9

∵ 53 - 62 = -9

∵ 44 - 53 = -9

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* We will use the same rule above to find the expression of the pattern

∵ a = 71 , d = -9

∴ an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n

* Lets check it;

∵ a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true

∴ The expression to represent the pattern is 80 - 9n

Answer:

Step-by-step explanation:

The first triangle is a 30-60-90 right triangle.  We have a Pythagorean triple associated with this type of triangle that is

 (x , x√3, 2x) which represent the side lengths across from the

(30°, 60°, 90°)

We have the side length across from the 30° as 14.  That means that x = 14.  In our figure, "y" is across from the 60° which means that the side length is

14√3, which has a decimal equivalency of 24.24871131; in our figure "x" is the hypotenuse which is 14(2) which is 28.

For the intents and purposes of keeping you not confused:

x = 28, y = 14√3 (or 24.24871131)

The next triangle is also a right triangle but this one is a 45-45-90.  The Pythagorean triple for that triangle is

( x , x , x√2 ) as the side lengths across from the

(45°, 45°, 90°)

We have a side length across from the 90° as 18 units long; therefore, according to our Pythagorean triple:

x√2 = 18 and

x = [tex]\frac{18}{\sqrt{2} }[/tex] and, rationalizing the denominator:

[tex]x=\frac{18\sqrt{2} }{2}[/tex] so

x = 9√2, which has a decimal equivalency of 12.72792206.

Summing up again:

x = 9√2 (or 12.72792206)

Answer:

I would think the answer would be 35

Step-by-step explanation:

Step 1: Round your answer to 2 decimal places.

Step2: Divide or Multiply your answer you got by 2.

cos42= 35/y

y=35/cos42

y= 47.10

is the answer

Answer:

[tex]18\ pieces[/tex]

Step-by-step explanation:

step 1

Divide each large candy bar into thirds

so

[tex]\frac{1}{3}[/tex]

Now for each large candy bar you have 3 pieces of [tex]\frac{1}{3}[/tex]

step 2

Find the total number of candy bars pieces by proportion

[tex]\frac{1}{3}\frac{bar}{pieces} =\frac{6}{x}\frac{bar}{pieces}\\ \\x=6*3\\ \\x=18\ pieces[/tex]

Final answer:

To determine the total number of candy bar pieces after splitting 6 large bars into thirds, you multiply 6 by 3 resulting in 18 pieces.

Explanation:

The student's question is about dividing candy bars into thirds. If you start with 6 large candy bars and want to split each one into thirds, you end up with 6 groups of 3 pieces. To find the total number of candy bar pieces, you multiply the number of candy bars by the number of pieces you want to make from each bar, which is:

6 bars × 3 pieces per bar = 18 pieces.

Therefore, after splitting all the large candy bars into thirds, you will have a total of 18 candy bar pieces.

Answer:

An angle showing a turn through 1/5 of a circle is greater

Step-by-step explanation:

we know that

A complete circle represent [tex]360\°[/tex]

so

An angle showing a turn through 1/6 of a circle is

[tex](360\°)*(\frac{1}{6})=60\°[/tex]

An angle showing a turn through 1/5 of a circle is

[tex](360\°)*(\frac{1}{5})=72\°[/tex]

therefore

An angle showing a turn through 1/5 of a circle is greater

Answer:

[tex]\large\boxed{A=x^2+23x+49}[/tex]

Step-by-step explanation:

Subtract the area of a square (x + 1) × (x + 1)

from the area of a rectangle (x + 10) × (2x + 5)

The area of a square:

[tex]A_s=(x+1)(x+1)[/tex]            use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]A_s=(x)(x)+(x)(1)+(1)(x)+(1)(1)=x^2+x+x+1=x^2+2x+1[/tex]

The area of a rectangle:

[tex]A_r=(x+10)(2x+5)[/tex]              use FOIL

[tex]A_r=(x)(2x)+(x)(5)+(10)(2x)+(10)(5)=2x^2+5x+20x+50=2x^2+25x+50[/tex]

The area of a figure:

[tex]A=A_r-A_s[/tex]

Substitute:

[tex]A=(2x^2+25x+50)-(x^2+2x+1)=2x^2+25x+50-x^2-2x-1[/tex]

combine like terms

[tex]A=(2x^2-x^2)+(25x-2x)+(50-1)=x^2+23x+49[/tex]

Answer:

d = 50 in.

Step-by-step explanation:

A = Pi*r^2

625Pi = Pi*r^2

625 = r^2

r = 25 in

Diamenter = 2(radius=

d = 50 in

Best regards

Answer:

none

Step-by-step explanation:

y = -4x^2 +3x-2

To find the x intercepts, let y =0

0 = -4x^2 +3x-2

Using the discriminant

a=-4, b=3  c=-2

b^2 -4ac

3^2 -4(-4)(-2)

9 -32

-23

Since this is negative all the roots are complex, so it has no real roots

none

To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we use formulas for a binomial distribution. The mean is 78 and the standard deviation is 6.34. The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.

To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we can use the formulas for a binomial distribution. The mean is found by multiplying the total number of trials (150) by the probability of success (0.52): mean = 150 × 0.52 = 78. The standard deviation is found by taking the square root of the product of the number of trials, the probability of success, and the probability of failure (1 - 0.52): standard deviation = √(150 × 0.52 × 0.48) = 6.34.

The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor, which in this case is 78.

It would not be unusual if 71 out of the 150 adults surveyed believe that the overall state of moral values is poor, as this value falls within one standard deviation from the mean.

Answer:

7.125 feet

Step-by-step explanation:

1. convert both fractions to decimals by dividing numerator by denominator

    10 1/2 = 10.5

    3 3/8 = 3.375

2. Subtract 10.5-3.375 = 7.125 feet left

Answer:

7.125 ft

Step-by-step explanation:

Answer:

9 hours.

Step-by-step explanation:

Average rate = distance / time

=  871 / 13

=  67 mph

So the time to travel 603 miles

=  distance / rate

= 603 / 67

=  9 hours.

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative is positive when x > 0 and negative when x < 0.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative of f(x) = ln(x^4 + 27) can be found using the chain rule: f'(x) = (4x^3)/(x^4 + 27).

The derivative is positive when (4x^3)/(x^4 + 27) > 0, which occurs when x > 0.

The derivative is negative when (4x^3)/(x^4 + 27) < 0, which occurs when x < 0.

Therefore, the interval of increase is (0, infinity) and the interval of decrease is (-infinity, 0).

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Answer:

[tex]\large\boxed{V=\dfrac{1600\pi}{3}\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 10cm and H = 16cm. Substitute:

[tex]V=\dfrac{1}{3}\pi(10^2)(16)=\dfrac{1}{3}\pi(100)(16)=\dfrac{1600\pi}{3}\ cm^3[/tex]

315 > 131.5 > 131.05 > 13.15 > 1

Rewrite y^4 as (y^2)^2

(y^2)^2 + 14y^2 +49

Rewrite 49 as 7^2

(y^2)^2 + 14y^2 +7^2

Factor using the perfect square rule.

Final answer: (y^2 + 7)^2

The factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

What is factorization ?

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

The given expression is [tex]y^{4}[/tex] + 14y² + 49.

Before factorization if we look at the given expression we can find out that it is a form of perfect square which is :

A² + B² + 2AB.

Let's convert the given expression in the perfect square form. This will be equal to :

(y²)² + (7)² + 2 × y² × 7

We know that the expansion A² + B² + 2AB is equal to (A+B)².

Here ; A = y² and B = 7.

So , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is equal to :

(y² + 7)²

Therefore , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

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Answer:

D

Step-by-step explanation:

We need to graph both  [tex]6^x[/tex]  and  [tex]3^x[/tex]  and figure out the x-value at which the graph of  [tex]6^x[/tex] is LESS THAN that of the graph of [tex]3^x[/tex].

The attached picture shows the graph of  [tex]6^x[/tex] in BLUE and the graph of  [tex]3^x[/tex] in RED.

We need to find x-value where the BLUE graph is "BELOW" the RED graph. We can see that this occurs when x < 0.

Thus the correct answer is  D

Answer:

3c=36

c = 12

Step-by-step explanation:

We have 36 sugar flowers

We put 3 on each cupcake

The number of cupcakes times the number of flowers per cupcake equals the total flowers

3*c = 36

Divide each side by 3

3c/3 = 36/3

c = 12

Answer:

12 cupcakes

Step-by-step explanation:

3 sugar flowers on each (1) cupcake

36 sugar flowers on c cupcakes

3c = 36 * 1

3c = 36

 c = 36/3

 c = 12 cupcakes

Answer:

The series is convergent ⇒ answer (a)

Step-by-step explanation:

* The series is 3/2 + 9/8 + 27/32 + ........

- It is a geometric series with:

- first term a = 3/2 and common ratio r = 9/8 ÷ 3/2 = 3/4

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = 3/4

∴ r < 1

∴ The series is convergent

Answer:

C. F(X) = (X - 3)⁴

Step-by-step explanation:

Hope this helps you.

The graph of F (x) will be;

⇒ F (x) = (x - 3)⁴

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The function G (x) is,

⇒ G (x) = x⁴

And, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

Now,

Here, The function G (x) is,

⇒ G (x) = x⁴

Since, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

So, The function of F(x) become;

⇒ F (x) = (x - 3)⁴

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The cost of painting a wall varies jointly with the length and width of the wall, represented by the formula C = k * l * w, where C is the cost, k is the cost per unit area, l is the length, and w is the width.

The cost of painting a wall varies directly with its area. The area of a rectangular wall is found by multiplying its length (l) by its width (w), giving the formula A = l * w for the area. If C represents the cost of painting, and k is the cost per unit area, then the cost formula can be written as C = k * A, which simplifies to C = k * l * w. This means the cost varies jointly with the length and width of the wall, as both dimensions contribute to the total area. Therefore, the cost does not vary directly with l or w alone, but with their product.

Answer:

C. y = -4x +10

Step-by-step explanation:

Equation of a line is found by the formula y = mx +b

Where m is the slope and b is the y intercept

we see that y-intercept is given as 10, so b = 10 and we plug in the coordinate (2,2) into the equation to find the slope (m). We plug in x = 2 and y = 2. Shown below:

[tex]y=mx+b\\2=m(2)+10\\2=2m+10\\2-10=2m\\-8=2m\\m=\frac{-8}{2}\\m=-4[/tex]

We know the value of m to be -4 and b to be 10, thus we can write the equation as:

[tex]y=-4x+10[/tex]

Answer choice C is right.

Answer:

c. y = -4x + 10

Step-by-step explanation:

y = mx + b where b = y -intercept = 10

so

y = mx + 10

Plug in (2,2) to find slope m

2 = 2m + 10

2m = -8

m = -4

Slope m = -4

Equation

y = -4x + 10

Answer:

its the third one i got that

For this case we must simplify the following expression:

[tex]\frac {12y ^ 7} {18y ^ {- 3}}[/tex]

We have that by definition of properties of powers, it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, we can rewrite the expression:

[tex]12y ^ 7 * 18y ^ 3[/tex]

By definition of multiplication properties of powers of the same base we have:

[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]

So:

[tex]12y ^ 7 * 18y ^ 3 = (12 * 18) * y ^ {7 + 3} = 216y ^ {10}[/tex]

Answer:

[tex]216y ^ {10}[/tex]

When y = 0 the expression is 0

Answer:

[tex]\frac{1}{2} (x+5)\leq 10[/tex]

Step-by-step explanation:

Half the sum of (1/2 * ) a number and five (x + 5) is a maximum of 10 (less than or equal to).

Answer:[tex]\frac{x+5}{2}\leq 10[/tex]

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

Yes, the right angle is angle C.

Step-by-step explanation:

The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).

Recall the slope formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of the line going through AC is

[tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]

The slope of the line going through BC s

[tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]

The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]

This means line AC is perpendicular to BC at C.

Hence the triangle ABC is right angled at C.

Answer:

Yes, the right angle is angle C.

Step-by-step explanation: