Solve the quadratic equation by square roots:

1. 4x²= 81
2. (4x-3)²+7=39

The slant height of a cone with a radius of 3 inches and a surface area of 16.8π square inches is 2.6 inches.

In order to find the slant height of a cone, we need to understand the formula for calculating the surface area of a cone. The formula is πrs + πr². The given surface area is 16.8π and the radius is 3 in. This area consists of the area of the base (which is a circle of radius 3 in, hence area πr² = π(3)² = 9π) and the area of the side, which is πr times the slant height (s).

So, we subtract the base area from the total area to isolate the side area: 16.8π - 9π = 7.8π. This is equal to πrs, so we can set up the equation: 7.8π = 3πs (we replace 'r' with its given value 3). Solving for 's', we divide both sides of the equation by 3π, getting slant height 's' = 7.8π / 3π, which simplifies to 2.6 inches.

https://brainly.com/question/19863050

#SPJ12

Answer: (1,2)

Step-by-step explanation:

You must:

- Multiply the first equation by 3.

- Add both equations.

- Solve for the variable left. In this case will be x.

Then:

[tex]\left \{ {{39x +3y = 45} \atop {-9x - 3y = -15}} \right.\\------\\ 30x=30\\x=1[/tex]

Substitute x=1 into any of the original equtions and solve for y:

[tex]13(1)+y=15\\y=2[/tex]

The solution is: (1,2)

Answer:

The solution of the system of equation is (1 , 2)

Step-by-step explanation:

The system of equation is:

* 13x + y = 15 ⇒ (1)

* -9x - 3y = -15 ⇒ (2)

- By using elimination ⇒ we must make on of the

 two variables in the two equations has the same value

 with different sign

- So we will multiply equation (1) by 3 to eliminate y

∴ 3(13x) + 3(y) = 3(15)

∴ 39x + 3y = 45 ⇒ (3)

- Now add (2) and (3)

∴ 39x + -9x = 45 + -15

∴ 30x = 30 ⇒ ÷ 30 both sides

∴ x = 1

- Substitute the value of x in equation (1) or (2)

- Lets use (1)

∴ 13(1) + y = 15

∴ 13 + y = 15 ⇒ subtract 13 from both sides

∴ y = 15 - 13  

∴ y = 2

∴ The solution of the system of equation is (1 , 2)

Answer:  [tex]\bold{\bigg(\dfrac{1}{3}x+\dfrac{1}{5}y\bigg)^2}[/tex]

Step-by-step explanation:

The square of the trinomial exists only if (a + b)² = a² + 2ab + b²

[tex]\dfrac{1}{9}x^2+\dfrac{2}{15}xy+\dfrac{1}{25}y^2\\\\\\a=\sqrt{\dfrac{1}{9}x^2}=\dfrac{1}{3}x\\\\\\b=\sqrt{\dfrac{1}{25}y^2}=\dfrac{1}{5}y\\\\\\2\cdot a\cdot b=2\cdot \dfrac{1}{3}x\cdot \dfrac{1}{5}y = \dfrac{2}{15}xy\\\\\text{So, }\dfrac{1}{9}x^2+\dfrac{2}{15}xy+\dfrac{1}{25}y^2=\bigg(\dfrac{1}{3}x+\dfrac{1}{5}y\bigg)^2\\[/tex]

Answer:

Step-by-step explanation:

Answer:

If you do not pay the entire credit card bill, you are charged an interest on the unpaid part.

Step-by-step explanation:

If you do not pay the entire credit card bill, you are charged an interest on the unpaid part.

When you do not pay the entire bill or pay less than minimum or minimum amount, an interest is charged on the remaining balance.

The amount increases each month as the interest is added with the unpaid amount.

Answer:

A

Step-by-step explanation:

We can use trigonometric ratios to solve this.

With respect to the angle given, the building's height is the side that is "opposite".

Also, the given length of 63 feet is the "adjacent" side with respect to the angle given.

Which trigonometric ratio relates "opposite to adjacent" side?

It is TAN.

Now, let's write the ratio and solve for the height of the building (let h be height of the building). We have:

[tex]Tan(\theta)=\frac{Opposite}{Adjacent}\\Tan(59)=\frac{h}{63}\\h=Tan(59)*63\\h=104.85[/tex]

Rounding this, we get h = 105 feet, correct answer A

Answer:

The height of the building = 105 feet ⇒ answer (A)

Step-by-step explanation:

* To find the height of the building use the trigonometry functions

- Lets consider the height (h) of the building as a side of right angle triangle

 and the other side is the distance from the bottom of the building

- Now we have right angle triangle one of its acute angle is 59°

- The length of one leg of the right angle = 63 feet

- We have the adjacent side of angle 59°

- we need to find the opposite side of angle (h)

∴ Lets use the function tan to find h

∵ tanФ = opposite to Ф/adjacent to Ф

∵ Ф = 59°

∵ The length of the side adjacent to Ф = 63 feet

∴ tan59 = h/63 ⇒ by using cross multiplication

∴ h = 63 × tan 59 = 104.849 ≅ 105 feet

∴ The height of the building = 105 feet answer (A)

c. 18 is the answer you get

Answer:

1017.87602

Step-by-step explanation:

A = π R squared = π · 18 squared ≈ 1017.87602

Answer:

$83.75

Step-by-step explanation:

To find the future value, we first need to define our variables.

P = 187.45 x 0.10 = 18.745

r = 5% or 0.05

t = 30 years

n = 12

Now we can use the formula:

[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]

[tex]A=18.745(1+\dfrac{0.05}{12})^{12(30)}[/tex]

[tex]A=18.745(1+\dfrac{0.05}{12})^{360}[/tex]

[tex]A=83.75[/tex]

So the future value after 30 years is $83.75.

The  future value of the 10% savings from earnings of $187.45 is $83.75.

Principal= 187.45 x 0.10 = 18.745

rate = 5%

time = 30 years

n = 12

Hence:

Future value=18.745 (1+0.05/12)^30×12

Future value=18.745 (1.05/12)^360

Future value=$83.75

Inconclusion the  future value of the 10% savings from earnings of $187.45 is $83.75.

Learn more about future value here:https://brainly.com/question/24703884

Sure, but with what question

Answer:

B

Step-by-step explanation:

If an equation of the form [tex]x^2-y^2=a[/tex] goes through a translation T (p,q), the transformed equation has the form  [tex](x-p)^2-(y-q)^2=a[/tex]

Using this, we can write the equation given as:

[tex](x-(-4))^2-(y-2)^2=9\\(x+4)^2-(y-2)^2=9\\x^2+8x+16-y^2+4y-4-9=0\\x^2-y^2+8x+4y+3=0[/tex]

So, B is the right answer.

Answer:

b. [tex]x^2-y^2+8x+4y+3=0[/tex]

Step-by-step explanation:

The given hyperbola has equation [tex]x^2-y^2=9[/tex].

This hyperbola is centered at the origin.

If this hyperbola is translated, so that its center is now at (-4,2), its equation now becomes;

[tex](x+4)^2-(y-2)^2=9[/tex]

We now expand to obtain;

[tex]x^2+8x+16-(y^2-4y+4)=9[/tex]

[tex]\Rightarrow x^2+8x+16-y^2+4y-4-9=0[/tex]

[tex]\Rightarrow x^2-y^2+8x+4y-4-9+16=0[/tex]

The correct choice is B.

[tex]\Rightarrow x^2-y^2+8x+4y+3=0[/tex]

Answer:

The frequency = 5/2π

Step-by-step explanation:

* Lets revise some facts about the trigonometry function

- If the function is f(x) = A sin (B x + C) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

 divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

- Period and Frequency are related where frequency = 1/period

* C is the horizontal shift  

- The horizontal shift is how far the function is shifted to left  

 (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

* Lets solve the problem

∵ f(x) = 3 cos (5x) + 2

∵ f(x) = A sin (B x + C) + D  

∴ A = 3 , B = 5 , C = 0 , D = 2

∵ The period = 2π/B

∴ The period = 2π/5

∵ The frequency = 1/period

∴ The frequency = 1/(2π/5) ⇒ multiply up and down by 5

∴ The frequency = 5/2π

The frequency of the function f(x) = 3cos(5x) + 2 is 5/2π, represented as 5 cycles per unit interval on the x-axis.

The frequency of the function f(x) = 3cos(5x) + 2 is determined by the coefficient of x inside the cosine function. In this case, the coefficient is 5, which represents 5 cycles per unit interval on the x-axis. The standard form for a cosine function's frequency is given when the function is written as cos(2πft), with f representing the frequency. To match this form, we can rewrite the function as cos(2π(5/2π)x), making it clear that f = 5/2π cycles per unit interval, which is the frequency.

In simplest fraction form, the frequency of the function f(x) is 5/2π.

The 21 consonants are :

b c d f g h j k l m n p q r s t v w x y z

The 5 vowels are :

a e i o u

Now, to arrange the consonants there are 21! ways.

Now the vowels can be arranged in 22 ways because one vowel can be placed before 'b' and one after 'z' also.

It can be shown like this : (V represents vowels)

V b V c V d V f .......................

Therefor the ways to put vowels will be : [tex]22P5[/tex]

The complete order to place consonants without repeating vowels becomes: [tex]22P5*21![/tex]

There are 22! x 6! x 5! ways to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively.

In order to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively, we can consider the vowels as a single block that needs to be placed in between the consonants. Firstly, let's count the number of ways to arrange the consonants C (21 consonants + 1 y) and the block of vowels V (5 vowels) as separate entities. This can be done in 22! x 6! ways. However, we need to consider that within the V block, the vowels can be rearranged in 5! ways. Therefore, the total number of arrangements is 22! x 6! x 5!.

https://brainly.com/question/26994598

#SPJ3

Answer: any number

Step-by-step explanation: 3x+2y=6, 2y=6-3x, we want y by itself, so divide by 2 from both sides, y=3-1.5x, then we plug it into the equation,3x+2(3-1.5)=6, then solve. 3x+6-3x=6, 3x-3x=0,so 6=6, y could be any possible answer

The expression for y in terms of x is y = 3 - (3/2)x the linear equation 3x+2y=6 .

To express y in terms of x using the linear equation 3x + 2y = 6, we need to isolate y on one side of the equation.

Step 1: Move the 3x term to the other side of the equation.

Subtract 3x from both sides:

3x + 2y - 3x = 6 - 3x

2y = 6 - 3x

Step 2: Now, to solve for y, divide both sides by 2:

y = (6 - 3x) / 2

Step 3: We can further simplify the equation:

y = 6/2 - (3x/2)

y = 3 - (3/2)x

So, the expression for y in terms of x is y = 3 - (3/2)x.

To know more about linear equation click here :

https://brainly.com/question/32634451

#SPJ2

Answer:

up

Step-by-step explanation:

Since this is written as y = function of x, it will open up or down

y = 3x^2 -5x -10

The coefficient of x^2 is positive so it will open up

Answer:

The Answer is C!! (With two L's pointing right)

Step-by-step explanation:

Answer:

Give the other person brainliest they deserve it!

Step-by-step explanation:

Answer: 20 picks

Step-by-step explanation: because orange is picked 3 out of every 5 picks, and 12 picks are orange, you multiply 3 by 4 to get 12, and 5 by 4 to get 20.

Answer:

I think the answer would be 20 picks. Good luck :)

Answer:

q = -25[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]

Step-by-step explanation:

Grab the generic solution of the equation. [tex]\frac 52 = \frac{-5 \pm \sqrt{5^2-4*2*q}}{2*2}[/tex]. Let's isolate the radical, and square both sides.[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]

Answer:

since we know that x1=2.5

we can just just use vieta's theorem

x1+x2=-b/a

x1*x2=c/a

Answer:

There are only two parameters needed to define any normal distribution curve.

Step-by-step explanation:

The two parameters are mean and standard deviation. This will allow us to see how far from the mean the curve exists and where the center is.

Subtract the mean from Jake's score:

520 - 500 = 20

Divide by the standard deviation:

20/60 = 0.33

Jake scored 0.33 standard deviation above the mean.

From the Z-table, 0.33 = 0.6293 = 62.93% of students scored below Jake.

Round to 63%

Answer:

z score is 0.33

( 0.6293) is the answer the next slot)

and 62.93% is last

Step-by-step explanation:

Answer:

9 cups

Step-by-step explanation:

12-3 = 9

Answer:

Bryan needs 9 cups more.

Step-by-step explanation:

Bryan is cooking cupcakes for a bake sale at his club. The recipe calls for 12 cups of flour.

Number of cups of flour, he already has = 3

Lets say he needs x cups more.

So, equation forms = [tex]12=x+3[/tex]

=> [tex]12-3=x[/tex]

x = 9

Hence, Bryan needs 9 cups more.

Answer:

c

Step-by-step explanation:

cause i am a math mttition

It is a rhombus because when we join the different coordinates which forms a rhombus

The answer is rhombus

Answer:

The answer is A. 3 1/3

Step-by-step explanation:

Simplify:

10/3

Then, convert to a mixed fraction:

3 1/3

Hope this helped.

The mathematical expression 5x2/3 = 15/3 x 2/3 = 30/9 = 5 2/3.

Option C is correct.

an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Step 1: Simplify 5x2/3

5x2/3 = (5 x 2)/3

5x2/3 = 10/3

Step 2: Simplify 10/3

10/3 = 3 + 2/3

10/3 = 5 2/3

An expression in math  can also be described as a statement having minimum of two numbers, or variables, or both and an operator connecting them.

Therefore, the correct answer is C.

Learn more about mathematical expression at:

https://brainly.com/question/1859113

#SPJ6

Answer:

1. Greater than

2 less than

3. More

Step-by-step explanation:

Answer:

55 centimeters

Step-by-step explanation:

Ok buddy, just say like 55 centimeters, and say you used a measuring tape.

Answer:

[tex]\log_{25}(\frac{1}{5})=-\frac{1}{2}[/tex]

Step-by-step explanation:

Let

[tex]\log_{25}(\frac{1}{5})=x[/tex]

We rewrite as an exponential equation to obtain;

[tex]\frac{1}{5}=25^x[/tex]

We rewrite both sides of the equation as an index number to base 5.

[tex]5^{-1}=5^{2x}[/tex]

Since the bases are the same, we equate the exponents to obtain;

[tex]-1=2x[/tex]

Divide both sides by 2;

[tex]x=-\frac{1}{2}[/tex]

Answer:

  No

Step-by-step explanation:

The magnitude of the distance from the origin to the point (8, 17) will be more than 17. That point is not on a circle of radius 9 centered at the origin. It is well outside the circle.

Answer:

B 40 yards for $45 is the best deal at $1.13 per yard

Step-by-step explanation:

Break it down by finding the unit price per yard (divide cost by yardage)

A. 30/20 = $1.50 per yard

B. 45/40 = $1.125 per yard

C. 70/50 = $1.40 per yard

D. 85/65 = $1.30 per yard

Answer:a

Step-by-step explanation:

Answer:

45, 60, 75

Step-by-step explanation:

The ratio of the angles are 6:8:10

Multiply by x to get the angle measures

6x, 8x,10x

We know the sum of the angles is 180 for a triangle

6x+8x+10x = 180

Combine like terms

24x = 180

Divide each side by 24

24x/24 = 180/24

x =7.5

Each angle is

6x = 6(7.5) =45

8x = 8(7.5) =60

10x = 10*7.5 = 75

The measures of the angles of the given triangle are 54 degrees, 72 degrees, and 90 degrees.

To find the measures of the angles of a triangle whose angles have measures in the ratio 6:8:10, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since the ratio of the angles is 6:8:10, we can set up the equation 6x + 8x + 10x = 180, where x is a common factor. Solving this equation, we find that x = 9. Therefore, the measures of the angles are 6x = 54 degrees, 8x = 72 degrees, and 10x = 90 degrees.