1. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Answer:

0

Step-by-step explanation:

Given a polynomial p(x) divided by (x + h), then the remainder is

p(- h)

Here divisor is (x + 1), so evaluate p(- 1) for remainder

p(- 1) = [tex](-1)^{5}[/tex] + [tex](-1)^{4}[/tex] + (- 1)³ + (- 1)² + 2(- 1) + 2

        = - 1 + 1 - 1 + 1 - 2 + 2

        = 0

This means that (x + 1) is a factor of p(x)

Answer:

None are equivalent

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.

The area of a parallelogram is given as (1/2) × (sum of parallel sides) × (distance between parallel sides).

Area = (1/2) × (5 + 5) × h

30 = 10h/2

5h = 30

h = 6 units.

Hence "The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units".

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Given the question missing the figure attached below,

Answer:

2, -2, -6, -10

Step-by-step explanation:

In this graph, the x value represents the count of the terms, while the y represents the value of each term. This means that the value of the first one is 2, the value of the second one is -2, the third one -6, and the fourth one -10. Hope this helps!

Answer:

13

Step-by-step explanation:

Use the distance formula to determine the distance between two points.

d=√((x_2-x_1)²+(y_2-y_1)²)

√((10)-(-2))^2+(-1)-(4)^2)

√(144+25)

√(169)

13

Answer:

13

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

(2x + 4) – (3x + 6)

Distribute the minus sign

2x +4 -3x -6

-x -2

Let x = 4

-4-2

-6

Answer:

-6

Step-by-step explanation:

(2x + 4) – (3x + 6) =

= 2x + 4 - 3x - 6

= -x - 2

= -(4)  2

= -6

Answer:125.66cm

Step-by-step explanation:

Circumference formula is C=2pi (r)

So C=2(pi or 3.14) (20)

Just plug the 20 (radius for the r) and you have the answer.

Answer:

7

Step-by-step explanation:

Fish caught by Carlton= 21+7=28

Fish caught by Will= 13+8=21

Therefore, Carlton caught more fish

By how much=28-21=7

Answer:

down by 1 units

right/left by 4 units

Answer:

down by 1 units

right/left by 4 units

Step-by-step explanation:

Answer:

It'd be $4,700

Step-by-step explanation:$500 + $2,400 + $1,800 = $4,700. Minus that amount from her savings account total and that's how much money she has left.

Answer:

A

Step-by-step explanation:

Given

x + yi + 6i = 2 ( subtract 6i from both sides )

x + yi = 2 - 6i → A

Answer:

The building is 13.91 m tall

Step-by-step explanation:

The parameters given are;

Angle of elevation to the top of the building = 71°

Angle of depression to the bottom of the building = 26°

Height of the man = 2  m

Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:

The hypotenuse side = The sight of the man to the bottom of the building

Hence;

In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building

∴ ∠A + Angle of depression to the bottom of the building = 90°

∠A = 90° - 26° = 64°

∠B = 90° and ∠C = 26° (Sum of angles in a triangle)

[tex]Tan(C) = \frac{AB}{BC}[/tex]

Distance of the man from the building = BC

[tex]Tan(26) = \frac{2}{BC}[/tex]

[tex]BC= \frac{2}{ Tan(26) } = 4.1 \, m[/tex]

Given that the angle of elevation to the top of the building = 71°, we have;

ΔAET

Where:

A is at the head level of the man,

E is the point on the building directing facing the man and

T is the top of the building

Hence AE = BC and ∡TAE = 71°

TE + AB= The height of the building

[tex]Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}[/tex]

∴ TE = tan(71°) × 4.1 = 11.91 m

Hence the height of the building = 11.91 + 2 = 13.91 m.

You can compute the slope of a line by using the slope formula. This is given by:

slope,m=(change in y-axis)/(change in x-axis)

           =(Δ y-axis)/(Δ x-axis)

Given the points (x1,y1) and (x,y) from a linear graph, then:

slope m will be:

          m=(y-y1)/(x-x1)

You can compute the slope of a line by using the slope formula.

Given Information:

Volume of candle = V = 75 in³

Height of candle = h = 6 in

Required Information:

Radius of candle = r = ?

Answer:

Radius of candle = r = 2 in

Step-by-step explanation:

Recall that the volume of a cylindrical shape is given by

[tex]V = \pi \times r^{2} \times h[/tex]

Where V is the volume, r is the radius and h is the height

Re-arrange the above equation for radius

[tex]r^{2} = \frac{V}{\pi \times h} \\\\r = \sqrt{\frac{V}{\pi \times h}}[/tex]

Now substitute the given values into the above equation

[tex]r = \sqrt{\frac{75}{\pi \times 6}}\\\\r = 1.99 \: in[/tex]

Rounding to the nearest inch

[tex]r = 2 \: in[/tex]

Therefore, the radius of this candle is 2 inches.

Answer:

Diameter of the circle is 8.4 units

Step-by-step explanation:

To find the diameter of a circle with area of 56 square units, we will follow the steps below:

write the formula for calculating the area of a circle

area of a circle = πr²

from the question area= 56 units .

π is a constant which is ≈ 3.14

we can now proceed to substitute the values into the formula and solve for r

area of a circle = πr²

56 = 3.14×r²

divide both-side of the equation by 3.14

17.83 = r²

take the square root of both-side

√17.83 = √r²

4.2 =r

r= 4.2 units

but diameter = 2 r

diameter = 2×4.2

diameter = 8.4 units

Diameter of the circle is 8.4 units

Answer:

1/5 =  0.2

0.3 = 1/3

1/2 = 0.5

Answer:

1/5 =0.2

3/10 = 0.3

1/2 =0.5

Answer:

47.8

_____

1

Step-by-step explanation:

Answer:

she got it by breaking up the problem step by step  for

Step-by-step explanation:

she has done this putting the form like so

10 - 478

I hope this

Answer:

92 ft  

Step-by-step explanation:

Assume the garden has the shape shown below.

The length of fencing equals the distance around three sides of the rectangle plus that around the semicircle.

1. Around the rectangle

Distance = 28 ft + 14 ft + 28 ft = 70 ft

2. Around the semicircle

For a circle.

C = 2πr

For the semicircle,

½C =½(2πr) = πr  

D = 14 ft, so

r =    7 ft

[tex]\text{Distance} = \dfrac{22}{7} \times \text{7 ft} = \text{22 ft}[/tex]

3. Total distance

Distance = 70 ft + 22 ft = 92 ft

Jordan will need 92 ft of fencing.

Answer: 9

Step-by-step explanation:

The reason for this answer, is because when you decide 18 by 6 it gives you 3. Which means that when you devide 27 by 3 it will give you your answer. 9. You can make sure it’s correct when you do the math. 27/9=3. 18/6=3.

This way, your answers are equivalent to each other.

If you found this answer helpful, give it a five-star rating and a thanks! It would really mean a lot!

(Even a brainliest if you want ;D)

Answer:

a=9

Step-by-step explanation:cross multiply

Answer:

2291

Step-by-step explanation:

Given: Radius of a city's town hall is equal to 5-mile and about 180,000 people live in a city's town hall

To find: population density per square mile

Solution:

Population density refers to the number of people per unit of area.

Let r denotes radius of the town hall = 5 miles

Area of the town hall = [tex]\pi r^2=\pi (5)^2=25\,\pi[/tex] square miles

Population density per square mile = Population of a city's town hall/area of the town hall = 2290.9 [tex]\approx 2291[/tex]

Answer:

4 cm and 2cm

Step-by-step explanation:

Volume of the rectangular prism is 10.5 cm³.

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

Given three dimensions of a rectangular prism as given below in the image.

Length = 3 cm

Width = 7/4 cm

Height = 2 cm

Volume of a rectangular prism = Length × Width × Height

                                                   = 3 × 7/4 × 2

                                                   = 3 × 7/2

                                                   = 10.5 cm³

Hence the volume of the rectangular prism is 10.5 cm³.

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Answer:

D. d^2 - πd^2/4.

Step-by-step explanation:

The sides of the square are equal to the diameter of the circles so the area of the square = d^2.

The shaded area = area of the square -  4 * the area of a quarter circle

= area of the square - area of 1 circle

= d^2 - π r^2

r = d/2 so

Area of the shaded part = d^2 -  π (d/2)^2

= d^2 -  π (d^2/4)

Answer:

2

Step-by-step explanation:

You are trying to find (f' o f)(2).  This means that you need to put f(x) into f'(x) and solve for 2.

First, find f'(x).  To do this, take the original function and switch the x and y values.

y = 2x⁵ + 12

x = 2y⁵ + 12

x - 12 = 2y⁵

(x - 12)/(2) = y⁵

y = ⁵√(x - 12)/(2)

Now, you need to put f(x) into the inverse function through the x-value.  Simplify completely.

y = ⁵√((2x⁵ + 12) - 12)/(2)

y = ⁵√((2x⁵)/(2)

y = ⁵√x⁵

y = x

Now plug in the value given to you.

(f⁻¹ o f)(2) = 2

The answer is 2.

Answer:

71

Step-by-step explanation:

Take the cost of the item and multiply by the commission percent

800 * 8.875%

Change to decimal form

800*.08875

71

Answer:

71

Step-by-step explanation:

Simon earns 8.875 for a commission. yet for him to sold a rowboat that cost $800.

800*8.875

=$71

you have two walls that are  10 by 7.5 so 75 feet ^2 in area each

you have another two walls that are 14 by 7.5  so 105 feet^ 2 each

so all of that together is 360 feet^2 to cover for one coating, so you have 720 feet^2 to cover for 2 coats on the walls. so take that and divide it by the area that one gallon would cover, then round up giving you how many gallons you would have to buy

for the ceiling you do the same, the area is 140 and you only need one coat

Answer:

3.06

Step-by-step explanation:

[tex]\log_{5}(\dfrac{2}{3}x-2)+2=0\\\\\log_{5}(\dfrac{2}{3}x-2)=-2\\\\[/tex]

This means that 5 to the power of -2 is [tex](\dfrac{2}{3}x-2)[/tex], meaning that:

[tex]\dfrac{2}{3}x-2=5^{-2}=\dfrac{1}{25} \\\\\dfrac{2}{3}x=\dfrac{51}{25} \\\\2x=\dfrac{153}{25} \\\\x=\dfrac{153}{50}=3.06[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Let the number be x

Therefore the expression is 2(x-5)

Hope this helps

Plz mark it as brainliest!!!!

Answer:

2(x-5)

Step-by-step explanation:

x = number

then you subtract 5 from that number so that would look like

x-5

Then you double the result so then it would end up being:

2(x-5)

Please mark me brainliest :)

Answer:

42 feet.

Step-by-step explanation:

h=-10t² + 40t +2

The vertex of the quadratic function described by the equation is located at

 t = -(40)/(2(-10)) = 2

Next is to find the value of height at t=2 will be

 h = -10(2²) +40(2) +2 = -40 +80 +2 = 42feet

The maximum height is 42 feet.

Answer:

Option A shows the image of RST after the rotation

Step-by-step explanation:

Coordinates of S=(1,3)

Coordinates of R = (-2,1)

Coordinates of T = (-1,7)

We are given that after rotation(x,y)→(y,-x)

So, The new coordinates after rotation will be :

Coordinates of S'=(3,-1)

Coordinates of R'= (1,2)

Coordinates of T'= (7,1)

These are the coordinates of triangle of Option A

So, Option A is true .

Hence Option A shows the image of RST after the rotation

A. shows the image of RST after the rotation.

In the geometry, an equilateral triangle is the triangle in which have all 3 sides have same length. an equilateral triangle is also equiangular; that is, all 3 internal angles are also congruent to each other and are each 60 degrees It is also a regular polygon, so it is also referred to as the regular triangle.

Which plane does the triangle RST belong to?

The XY-coordinate plane or triangle RST are equilateral. Points R or In the x y -coordinate plane, triangle R S T is equilateral. Points R and T had coordinates ( 0, 2) and ( 1, 0), respectively.

Coordinates of S=(1,3)

Coordinates of R = (-2,1)

Coordinates of T = (-1,7)

We are given that after rotation(x,y)→(y, -x)

So, The new coordinates after the rotation will be :

Coordinates of S'=(3,-1)

Coordinates of R'= (1,2)

Coordinates of T'= (7,1)

These are the coordinates of the triangle of Option A

So, Option A is true.

Hence Option A shows the image of RST after the rotation.

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