Instructions: Find the missing side. Round your answer to the nearest
tenth.
19
х
66°
X =

Given:

The function is:

[tex]f(x)=-(x+5)(x+1)[/tex]

To find:

The range of the function.

Solution:

We have,

[tex]f(x)=-(x+5)(x+1)[/tex]

It can be written as:

[tex]f(x)=-(x^2+x+5x+5)[/tex]

[tex]f(x)=-(x^2+6x+5)[/tex]

Add and subtract square of half of coefficient of x, i.e., [tex]\left(\dfrac{6}{2}\right)^2=9[/tex].

[tex]f(x)=-(x^2+6x+9-9+5)[/tex]

[tex]f(x)=-(x^2+2(x)(3)+3^2-4)[/tex]

[tex]f(x)=-(x^2+2(x)(3)+3^2)+4[/tex]

[tex]f(x)=-(x+3)^2+4[/tex]

On comparing this equation with [tex]f(x)=a(x-h)^2+k[/tex], we get

[tex]a=-1[/tex], it means the graph of the function is a downward parabola and the vertex is the point of maxima.

[tex]h=-3[/tex]

[tex]k=4[/tex]

The vertex of the function is (-3,4). So, the value of the function cannot be greater than 4.

Therefore, the range of the function is all real numbers less than or equal to 4.

Note: All options are incorrect.

Answer:

7 cannot be achieved

-1 + 6 = 5

-3 + 4 = 1

-5 + 2 = -3

as you can see, no combinations can form seven

The volume of the new cone would be 1331 times more than the volume of the original cone. Thus, The volume of the original cone is multiplied by 1331

The volume of the cone can be calculated by the given formula:

                       The volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

where r = radius of the cone

           h = height of the cone

Solution:

The volume of the original cone= .......1

It is given that the height and radius of a cone are multiplied by 11.

then volume

= [tex]\frac{1}{3} \pi (11r)^{2} (11h)[/tex]

= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex] .........2

The change in volume of the cone after multiplying 11 to r and h would be

dividing equation 2 by equation 1

=  [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex]/[tex]\frac{1}{3} \pi r^{2} h[/tex]

= 121*11

= 1331

Thus, The volume of the original cone is multiplied by 1331

Learn more about the volume of the cone:

https://brainly.com/question/1315822

Answer:

Step-by-step explanation:

The equation for an arithmetic sequence is

[tex]a_n=a_1+d(n-1)[/tex]  where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.

Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:

[tex]a_n=2+3(n-1)[/tex] which simplifies to

[tex]a_n=2+3n-3[/tex] and a bit more to

[tex]a_n=3n-1[/tex] (which should tell you that arithmetic sequences are lines!)

Finding the 13th number simply requires that we replace n with 13 and solve:

[tex]a_{13}=3(13)-1[/tex] so

[tex]a_{13}=38[/tex]

Answer:

38

Step-by-step explanation:

This isn't the most efficient way but it's the best I can do.

2, 5, 8, 11....

The pattern is that we add 3 every time.

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,

1 , 2, 3, 4, 5,  6,   7,    8,    9,   10,  11,   12,  13

We can see that 38 is the 13th term of the sequence.

Answer:

a is 1.58 and b is 0.42

Step-by-step explanation:

[tex]{ \sf{3 {x}^{2} - 6x + 2 = 0 }} \\ { \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} }} \\ \\ { \sf{x = \frac{ - ( - 6)± \sqrt{ {( - 6)}^{2} - (4 \times 3 \times 2) } }{(2 \times 3)} }} \\ \\ { \sf{x = \frac{6± \sqrt{12} }{6} }} \\ \\ { \sf{x = 1.58 \: and \: 0.42}}[/tex]

Answer:

(675°F − 32) × 5/9 + 273.15 = 630.372K

Hope it's right if not so sorry :)

Answer:

4

Step-by-step explanation:

1 5

2 10

3 15

4 20

i wrote it out

x+16=5x

16=4x

4=x

Marissa is currently four years old.

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.

Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

Let's represent Marissa's current age "x".

According to the given question, in 16 years she will be five times older than she is today, which we can express as:

x + 16 = 5x

Solving for x, we can subtract x from both sides:

16 = 4x

Dividing both sides by 4, we get:

x = 4

Therefore, Marissa is currently 4 years old.

To learn more about the Algebra link is given below.

brainly.com/question/953809

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

760

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\(35+5)[16+(12\div 4)]\\------------------\\\text{Follow \textbf{PEMDAS}}\\\\\rightarrow 35+ 5 = 40\\\\40[16+(12\div 4)]\\\\\rightarrow 12\div4 = 3\\\\\rightarrow 16 + 3 = 19\\\\40(19)\\\\\rightarrow 40 * 19\\\\\boxed{760}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

max: -4

Step-by-step explanation:

(x+3)^2 》0 mọi x

<=> -(x+3)^2 《0

<=> -(x+3)^2 -4 《 -4

Step-by-step explanation:

1/2 + 3/4

= 2/4 + 3/4

= 5/4

= 1 and 1/4 miles

Answer:

the correct answer to this question is b

Step-by-step explanation:

got it right

Answer:

1

(3,0)(0,-3)

-3 - 0 /0 - 3 = -3/-3 = 1

Step-by-step explanation:

Step-by-step explanation:

To find the slope of this line get any points along the straight line since the slope along a straight line is the same throughout, you can actually get (2,-1)(1,-2)

m=y2-y1/x2-x1

= -2+1/1-2

=-1/-1

=1

I hope this helps

Answer:129

Step-by-step explanation:(621 x 0.25) + (750 x 0.10) = 230.25

750 - 621 = 129 more dimes than quarters

Complete question is;

The outer radius of a cylindrical metal tube is R and t is the thickness of the metal.

A) Show that the volume, V, of metal in a length, l units, of the tube is given by V = πlt(2R - t)

B) Hence calculate V when R = 7.5. t = 1 and L = 20

Answer:

A)V = πlt(2R - t)

B)V = 879.65

Step-by-step explanation:

A) Formula for volume of a hollow cylinder is; V = π(R² - r²)h

Where;

R is outer radius

r is inner radius

h is height/length of tube

Now, we are told thickness is t.

Thus; R - r = t

Also, h = l

Thus;

V = π(R² - r²)h

Let's factorize this to get;

V = π((R + r)(R - r))l

V = π((R + r))lt

Since R - r = t

Then, r = R - t

Thus;

V = π(R + R - t)lt

V = πlt(2R - t)

B) when R = 7.5, t = 1 and l= 20;

V = ​πlt(2R - t)

V = ​π × 20 × 1(2(7.5) - 1)

V = 879.65

Answer:

y=-70

Step-by-step explanation:

10.4/10y=-28.10

4y=-280

y=-70

Answer: Distance = √170

Step-by-step explanation:

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Find the distance between M and P, where:

[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance = \sqrt{(-3+10)^2+(-12+1)^2}[/tex]

[tex]Distance = \sqrt{(7)^2+(-11)^2}[/tex]

[tex]Distance = \sqrt{49+121}[/tex]

[tex]Distance = \sqrt{170}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

(x₁ , y₁) = (-1 , -10)   & (x₂,y₂)=(-12,-3)

Distance = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

               [tex]= \sqrt{(-12-[-1])^{2}+(-3-[-10])^{2}}\\\\= \sqrt{(-12+1)^{2}+(-3+10)^{2}}\\\\=\sqrt{(-11)^{2}+(7)^{2}}\\\\= \sqrt{121+49}\\\\=\sqrt{170}[/tex]

               = 13.03

               = 13

Answer:

4.6

Step-by-step explanation:

tan(75) = 17/x

x = 17/tan(75)

x = 34-17√3

x = 4.6

Answered by GAUTHMATH

Answer:

The correct answer is 6.768.

Step-by-step explanation:

(4.23)(1.6) = 6.768

Answer:

6.768

Step-by-step explanation:

(4,23)(1.6)=6.768

The equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-a)²+(y-b)² = r²

Where (a, b) is the centre and 'r' is the radius

We have a circle with centre (0, 0) and radius of 5.

Now, Substituting these value into the equation form, we have

(x-0)²+(y-0)² = 5²

x² + y² = 25

Hence, the equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

Learn more about equation of a circle here:

https://brainly.com/question/10165274

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Answer:

The correct answer is (B)

Step-by-step explanation:

remember it is (x,y) so -4 would be on the x axis, whereas the 0, is on the y axis.

Answer: 5

Step-by-step explanation:

⇒ (x - 4) = 1

⇒ x = 1 + 4

⇒ x = 5

Therefore value of x = 5

Answered by Gauthmath must click thanks and mark brainliest

Answer:

The possible approximate frequencies of the guitar string are 516.82 Hz and 508.82 Hz

Step-by-step explanation:

The given period of the tuning fork, T₁ = 1.95 × 10⁻³ s

The number of beats in 6.0 s = 24 beats

Therefore, the beat frequency, [tex]f_{beat}[/tex] = 4 beats per second = 4 Hz

Let f₁ represent the frequency of the tuning fork, and let f₂ represent the frequency of the guitar string, we have;

f₁ = 1/T₁ = 1/(1.95 × 10⁻³) ≈ 512.82 Hz

We have;

[tex]f_{beat} = \left | f_2 - f_1 \right |[/tex]

[tex]\pm f_{beat} = f_2 - f_1[/tex]

Therefore, we get;

[tex]4 \, Hz= \left | f_2 - 512.82 \, Hz \right |[/tex]

f₂ - 512.82 = ± 4

∴ f₂ = 512.82 ± 4

The possible frequencies of the guitar string,  f₂ ≈ 516.82 Hz or f₂ ≈ 508.82 Hz

Answer:

There are 6 more girls than boys

Step-by-step explanation:

boys :girls : total

2         3       2+3 = 5

There are 30 total students

30/5 = 6

Multiply each number by 6

boys :girls : total

2*6     3*6     5*6

12          18      30

There are 18 girls and 12 boys

18-12 = 6

There are 6 more girls than boys

Answer:

Answer is 6.

Step-by-step explanation:

I will now explain the fastest way to solve this. First off, the ratio is 2:3 so the first thing I do is combine that for 5, then do 30/5 for an answer of 6. Then, I multiply 6 for the ratio, which comes out as 12:18, 12 boys and 18 girls. 18-12=6, so there are 6 more girls than boys in the class.

Answer: No solutions

Step-by-step explanation:

[tex]\large \bf \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex]                                   [tex]\large \boldsymbol{} \bf 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]

Answer: A. 20 is the answer.

Step-by-step explanation:

x+40 = 3x

or, 40 = 3x-x

or, 2x = 40

or, x = 40/2

so, x = 20

Answer: About 27.49

Step-by-step explanation:

You use the laws of tangent within a triangle to find x:

[tex]tan(32)=\frac{opposite}{adjacent}= \frac{x}{44}\\ \\x=44*tan(32)=27.49425...[/tex]

Answer:

c² = n²

Step-by-step explanation:

Given the 2 equations

a² + b² = c² → (1)

a² + b² = n² → (2)

Substitute a² + b² = c² into (2)

c² = n²

Answer:

C is correct

Step-by-step explanation:

a is wrong because: 1*-1*-1*-1 =1

b) 1*1*1*1 =1

d) 1*-1*1*1 =1

only c 1*-1*-1*1 =-1 at the end of polynomial

Answer:

I (-4, -3)

J (-4,-2)

K (-2,-2)

L (0,-4)