19)
Solve the quadratic equation x2 − 18x + 81 = 64 for x.

A)
x = 17 or x = 1


B)
x = 11 or x = −5


C)
x = 9 or x = −8


D)
x = 2 or x = 9

Answer:

Yes

Step-by-step explanation:

We need to determine the sides of the squares

Area = 9

A = s^2

9 = s^2

Taking the square root of each side

sqrt(9)= sqrt(s^2)

3 =s

Perimeter of a square = 16

P =4s

16 =4s

Divide each side by 4

16/4 =4s/4

4 =s

Side = 5 in

Right triangles obey the Pythagorean theorem

a^2 + b^2 = c^2

Putting the smaller sides in for a and b

3^2 +4^3 = 5^2

9+16=25

25=25

Since this is true, we can arrange the squares to make a right triangle

Answer:

Yes, due to the Pythagorean theorem.

Leg A would be 3

Leg B would be 4

Hypotenuse C would be 5

Explanation:

When making the right triangle, only one side length value is needed.

If the area of square one is 9, 9 divided by 2 is 3.

If the perimeter of square two is 16, 16 divided by 4 is 4.

The single side length for square three is given, which is 5.

The Pythagorean theorem consists of a^2 + b^2 = c^2.

Plug in the values.

3^2 + 4^2 = 5^2

9 + 16 = 25

Hope this helps! :)

Answer:

Step-by-step explanation:

(1) 4x = 200

(2) 50

Answer:

4x = 200

50

Step-by-step explanation:

One scarf = $4

Number of scarves = x

Amount she needs to earn = $200

Equation

4x = 200

Number of scarves

= 200 ÷ 4

= 50

Answer:The starting value is 20,300, and the value is decreasing by 9.5% each year.

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.

A decrease by 9.5% corresponds to multiplying by 91.5% each year.

We write . We plug in 11 years for t.

$7,671.18

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Step-by-step explanation:

Answer:

The starting value is 20,300, and the value is decreasing by 9.5% each year.

Step-by-step explanation:

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.A decrease by 9.5% corresponds to multiplying by 91.5% each year.We write . We plug in 11 years for t.

Answer:

B 1/5 1/4 1/3

Step-by-step explanation:

The first digit Maggie's bank picked from the 5 digit available, so 1/5.

The second digit will be picked from the 4 remaining digits available, so 1/4.

For the final digit, the bank will have only 3 options to choose from, so 1/3.

So the possibility for the 3-digit assigned PIN to be 123 is

[tex]\frac{1}{5} * \frac{1}{4} *\frac{1}{3} =\frac{1}{60}[/tex]

1/60, so the formula is the one presented in the B option: 1/5 1/4 1/3

Answer:

Step-by-step explanation:

b+s=18

s=18-b

1.50 b+2.50 s=38

multiply by 4

6.00 b+10.00 s=152

divide by 2

3 b+5 s=76

3 b+5(18-b)=76

3 b+90-5 b=76

-2b=76-90

-2b=-14

divide by -2

b=7

s=18-7=11

There are total 11 packets of squash seeds and 7 packets of basil seeds.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.

According to the given question.

Cost of one packet of basil seeds = $1.50

Cost of one packet of squash seeds = $2.50

Cost of 18 packets of seeds = 38

Also, b represents the number of packets of basil seeds and s represents of numbers of squash seeds.

Therefore, from the given conditions we get some system of equations

[tex]s + b = 18..(i)[/tex]

and [tex]b(1.50) + s(2.50) = 38...(ii)[/tex]

From equation (i)

[tex]s = 18-b[/tex]

Substitute the value of s in the equation (ii)

⇒[tex]1.50b+(18-b)2.50 =38[/tex]

⇒ [tex]1.50b + 45 - 2.50b = 38[/tex]

⇒[tex]-b = 38-45[/tex]

⇒ [tex]-1b =- 7[/tex]

⇒[tex]b = 7[/tex]

So, [tex]s = 18 - 7 =11[/tex]

Hence, there are total 11 packets of squash seeds and 7 packets of basil seeds.

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The correct answer is b

Answer:

The third table

Step-by-step explanation:

A linear function must increase or decrease at a constant rate. All the tables either add 1 or subtract 1 each time x increases except for the third one which at one point adds two. This is not a consistent increase and therefore is not linear

Answer:

3ed tabel

Step-by-step explanation:

adds 1 to both sides so its a non leirn

Answer:

Part 1) The area of the shaded region is [tex]2.1\pi\ m^{2}[/tex]

Part 2) The length of the arc AB is [tex]2.5\pi\ in[/tex]

Part 3) The area of the shaded region is [tex]56.53\pi\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the area of the shaded region

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=3\ m[/tex]

substitute

[tex]A=\pi (3)^{2}[/tex]

[tex]A=9\pi\ m^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of 84 degrees

[tex]\frac{9\pi }{360} =\frac{x }{84}\\ \\x=(9\pi)*84/360\\ \\x=2.1\pi\ m^{2}[/tex]

Part 2) What is the length of arc AB?

step 1

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

we know that

The length of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the length of the arc AB with a central angle of 90 degrees

[tex]\frac{10\pi }{360} =\frac{x }{90}\\ \\x=(10\pi)*90/360\\ \\x=2.5\pi\ in[/tex]

Part 3) Find the area of the shaded region given that XY measures 8 in

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]XY=r=8\ in[/tex]

substitute

[tex]A=\pi (8)^{2}[/tex]

[tex]A=64\pi\ in^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of (360-42)=318 degrees

[tex]\frac{64\pi }{360} =\frac{x }{318}\\ \\x=(64\pi)*318/360\\ \\x=56.53\pi\ in^{2}[/tex]

Answer:

1) d. 2400

2) d.4200

Step-by-step explanation:

As per given data:

F(x) represents number of fish

x represents number of weeks

Relation between F(x) and x is given as

F(x)= 500 (1.2)x

Now part 1:

How many fish are in the pond after 4 weeks=?

x=4

Putting in given equation  F(x)= 500 (1.2)x

F(x)= 500(1.2)(4)

     = 2400

Now part 2:

How many fish are in the pond after 7 weeks?

x=7

Putting in given equation  F(x)= 500 (1.2)x

F(x)= 500(1.2)(7)

     = 4200 !

Answer:

Correct choice is b. 1036 fish.

and c. 1791 fish.

Step-by-step explanation:

Given equation is [tex]f(x)=500(1.2)^x[/tex].

There x represents number of weeks. We need to find about wow many fish are in the pond after 4 weeks.

To find that we will plug x=4 into above formula and simplify

[tex]f(x)=500(1.2)^x[/tex]

[tex]f(x)=500(1.2)^{4}[/tex]

[tex]f(x)=500(2.0736)[/tex]

[tex]f(x)=1036.8[/tex]

Which is approx 1036

Hence correct choice is b. 1036 fish.

------

We can repeat same process with x=7 for 2nd problem

[tex]f(x)=500(1.2)^{7}=1791.5904[/tex]

Hence correct choice is c. 1791 fish.

Answer:

35 in²

Step-by-step explanation:

The irregular shaped can be divided into two squares and one rectangle, so the area will be the additions of the area of the squares and the rectangle

area of square A = L *B = 3 *3 = 9in²

area of square B = L * B = 4*4 = 16in²

area of rectangle C = L * B = 5 *2 = 10in²

th area of the irregular shape = 9 in² + 16 in² + 10 in² = 35 in²

2x+6=20

move 7 to the right side.

The sign changes from positive to negative. whenever moving a number to the other side the sign changes.

2x+6-6=20-6

2x= 14

Divide by 2 for both of the numbers

x=7

check answer:

Substitute x into the equation

2(7)+6=20

20= 20

Answer: x=7

The solution of the given linear equation in one variable is x = 7.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.

Given is a linear equation in one variable, 2x+6 = 20,

We need to find its solution,

Since, the given linear equation has only one variable, so it will have only one solution.

The equation is =

2x+6 = 20

Solving for x,

2x = 20-6

2x = 14

x = 7

Hence, the solution of the given linear equation in one variable is x = 7.

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Answer:

see explanation

Step-by-step explanation:

0.97 is the value of cos14° to 2 dec. places

Use your calculator ( ensuring it is in degree mode )

press cos14 then = to obtain value 0.97

Find the jets speed per hour by dividing distance by time:

600 miles /  5 hours = 120 miles per hour. ( Rate of speed)

Now multiply the speed by time:

120 miles per hour x 14 hours = 1,680 miles.

Answer:

120 miles per hour

Step-by-step explanation:

Final answer:

The range of a cosine function is the set of output values the function can take, which is always between -1 and +1. This applies to the standard cosine function and is unaffected by horizontal or phase shifts. This range is consistent with the definition of the cosine function as the ratio of the adjacent side to the hypotenuse in a right triangle.

Explanation:

The range of a cosine function refers to the set of possible values that the function can output. In mathematical terms, the cosine function oscillates between +1 and -1 irrespective of any horizontal shifts or phase shifts. A horizontal shift, demonstrated in Figure 15.8 (b), where the function is shifted by an angle φ (phase shift), does not alter the range of values of the function, which remain – from its minimum value of -1 to its maximum of +1.

Similarly, in Figure 16.10, a sine function, which is related to the cosine function, also oscillates between +1 and -1 every 2π radians (a complete cycle). This oscillation represents the wave function amplitude, which in cases other than a cosine can fluctuate between +A and -A.

As illustrated in Figure 2.18, the cosine function can be visualized as the ratio of the adjacent side to the hypotenuse (Ax/A = cos A) in a right triangle, further highlighting that this ratio (and thus the range of the cosine function) is between -1 and 1.

For example, when √(1+1)* approaches 1, it is indicative that cos 0 = 1, representing one end of the cosine function's range.

The surface of the ocean is 0 meters.

Because the fish is below the surface it would be a negative number. ( it is less than 0)

The elevation of the fish would be -12 meters.

Answer:

-12 meters

Step-by-step explanation:

Elevation is the height above a given level, most often the sea. Therefore, elevation is like a vertical numerical line. If the sea level is 0, and to the right of the 0 is positive numbers, then the left has to be negative.

Therefore, the fish is -12 meters below sea level.

Answer:

42.5

Step-by-step explanation:

110 - 25 divided by 2 because

angle ABC = (angle AC- angle DE)÷2

Answer:

(x + 3)^2 + (y + 1)^2 = 25

Step-by-step explanation:

Equation of a circle with center (h, k) and radius, r.

(x - h)^2 + (y - k)^2 = r^2

The center is (-3, -1), so h = 1, and k = 2.

(x - (-3))^2 + (y - (-1))^2 = r^2

(x + 3)^2 + (y + 1)^2 = r^2

Now we substitute x and y with the values of x and y from the given point, and we solve for r^2.

(1 + 3)^2 + (2 + 1)^2 = r^2

4^2 + 3^2 = r^2

16 + 9 = r^2

r^2 = 25

Now that we know r^2, we substitute it into the equation above.

(x + 3)^2 + (y + 1)^2 = 25

Answer:

The correct answer is,

(x + 3)² + (y +1)² = 25

Step-by-step explanation:

It is given that, What is the equation of a circle with center (-3,-1) that contains the point (1,2)

Formula;-

Equation of the circle passing through the point ( x₁,y₁) with radius r is given by,

(x - x₁)² + (y - y₁)² = r²

To find the radius of circle

r =√[ (1 --3)² + (2 --1)²]

 =√(4² + 3²)

 = √(16 + 9)

 =√25 = 5

To find the equation of the circle

(x₁, x₁) = (-3, -1) and r = 5

(x - x₁)² + (y - y₁)² = r²

(x - -3)² + (y - -1)² = 5²

(x + 3)² + (y +1)² = 25

Answer:

C.

Step-by-step explanation:

A - Perpendicular lines always touch each other at least once.

B - Parallel lines never touch.

D- Not always true.

C is true. If they are not in the same plane they are skewed lines.

The true statement is C: Parallel lines are always in the same plane. Perpendicular lines do intersect, while parallel lines do not, and perpendicular lines can certainly be in the same plane. Hence, correct option C.

The question seeks to determine the accuracy of given statements about geometric relationships between. Perpendicular lines and parallel lines. Based on the provided theorems, the true statement is: C. Parallel lines are always in the same plane.

This is because if two lines are parallel, they will be equidistant from each other at all points, which can only occur if they are in the same plane. Statements A, B, and D are false.

Perpendicular lines do intersect at a 90-degree angle.

Parallel lines, by definition, never intersect as they are always equidistant.

Perpendicular lines can be in the same plane or in different planes, although a line that is perpendicular to a plane must lie in another plane.

Answer:

Option A.

Step-by-step explanation:

step 1

we know that

The equation of the solid line is

[tex]y=5[/tex]

The solution is the shaded area above the solid line

so

The equation of the first inequality is

[tex]y\geq 5[/tex]

step 2

The equation of the dashed line is

[tex]y=x^{2} -5x+6[/tex]

The solution is the shaded area above the dashed line

so

The equation of the second inequality is

[tex]y>x^{2} -5x+6[/tex]

therefore

The system of inequalities could be

[tex]y\geq 5[/tex]

[tex]y>x^{2} -5x+6[/tex]

Answer:

option b

1 , 16, 121 , 13456

Step-by-step explanation:

Given in the question a function, f(x) = (x - 5)²

initial value [tex]x_{0}[/tex] = 4

First iteration

f(x0) = f(4) = (4 - 5)² = (-1)² = 1

x1 = 1

Second iteration

f(x1) = f(1) = (1 - 5)² = (-4)² = 16

x2 = 16

Third iteration

f(x2) = f(16) = ( 16 - 5)² = (11)² = 121

x3 = 121

Fourth iteration

f(x3) = f(121) = (121 - 5)² = (116)² = 13456

x4 = 13456

Answer:

336 ft squared

Step-by-step explanation:

Looking for face area, not volume

So...

10*12=120

6*12=72

8*12=96

6*8/2=24

6*8/2=24

24+24+120+72+96=336ft squared

Answer:

number2

Step-by-step explanation:

Answer:

f(x) = |x|

Step-by-step explanation:

function is even if and only if f(-x) = f(x)

f(x) = |x| ; regard to its sign f(x) = x

f(-x) = |-x| ; regard to its sign f(-x) = x

So answer is f(x) = |x| is the even function

Answer:

a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

Step-by-step explanation:

The given vector is v= 4i - 5j

The magnitude of this vector is;

[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]

[tex]|v|=\sqrt{16+25}[/tex]

[tex]|v|=\sqrt{41}[/tex]

The unit vector u in the direction of v is;

[tex]u=\frac{v}{|v|}[/tex]

[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]

[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]

We rationalize to get

[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

Answer:

The radius of circle is 5 cm

Step-by-step explanation:

Given a right triangle △ABC with right angle C is inscribed in a circle in which

m∠C = 90°, AC = 8 cm, BC = 6 cm

we have to find the radius of circle.

As ACB is right angles triangle where angle C is right angle.

⇒ side AB must be the diameter of circle as angle made at semi circle is 90°

[tex]Radius=AO=\frac{1}{2}AB[/tex]

By Pythagoras theorem

[tex]AB^2=AC^2+CB^2[/tex]

[tex]AB^2=8^2+6^2=64+36=100[/tex]

[tex]AB=10cm[/tex]

[tex]Radius=AO=\frac{1}{2}AB=\frac{1}{2}\times 10=5cm[/tex]

Hence, the radius of circle is 5 cm

Answer:

D

Step-by-step explanation:

5 divided by 3 is 1.6666 which is the same as 1 and 2/3

The correct answer is D

Is the answer 25? Thats what I got.

Answer:

x=30

Step-by-step explanation:

Add up all of the values of the angles and set it equal to 180 degrees since a triangle is always made up of angles that have a sum of 180 degrees.

x+2x+3x=180

6x=180

x=30

C.yes, because of ASA or AAS

Answer: option C

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=l*w*h[/tex]

Where "V" is the volume of the prism "l" is the lenght, "w" is the width and "h" is the height.

You know that the volume of this prism is 93 cubic centimeters and you need to find the height. Then, you have to solve for "h":

[tex]h=\frac{V}{l*w}[/tex]

You can observe that the volume is in the numerator and the product of the lenght and the width of the rectangular prism is in the denominator, then, the option that matches this form is the option C:

[tex]h=\frac{93}{15.5}[/tex]

Answer:

H= 93/15.5

Step-by-step explanation:

First plug in g(x) into f(x)

F((g(x))=2(2x+3)

And now you plug in -8

F(g(-8))=2(-16+3)

F(g(-8))=2(-13)

F(g(-8))=-26