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Answer:

(x - 4)² + (y - 5)² = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (4, 5) and r = 2, thus

(x - 4)² + (y - 5)² = 2², that is

(x - 4)² + (y - 5)² = 4 ← second option on list

The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

The standard equation of a circle is expressed as:

(x-a)^2  + (y-b)^2 = r^2

where:

(a, b) is the centre = (4, 5)

r is the radius = 3 units

Substitute to have;

(x-4)^2  + (y-5)^2 = 2^2

(x-4)^2  + (y-5)^2 = 4

Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

Learn more on equation of circle here: https://brainly.com/question/14150470

Answer:

21, 22 and 26

Step-by-step explanation:

To answer this question first we need to know which are the factors of 12:

[tex]12= 2^2(3)[/tex]

So, now, we need 3 numbers that are between 20 and 30 and that only have one common factor with 12, in other words, they need to have just a 2 or a 3 in their factorization.

Let's take number 21:

[tex]21= (7)(3)[/tex], we can see that 21 only has a 3 and a prime so therefore it has only one common factor with 12

Now, let's take the number 22,

[tex]22=11 (2)[/tex], thus since 22 has a 2 and a prime, it has only one common factor with 12.

Now, let's take the number 26

[tex]26= 13 (2)[/tex], thus, since 26 has a 2 and a prime, it has only one common factor with 12.

Thus, the three possible answers are 21, 22 and 26

This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.

Correct Question

A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.

A. What is the slant height of the pyramid?

B. What is the surface area of the composite figure?

HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

C. How many cubic yards of concrete are needed to make the planter?

Answer:

A. The slant height of the pyramid = 2.24 yards.

B. The surface area of the composite figure = 12.94 square yards.

C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.

Step-by-step explanation:

A. What is the slant height of the pyramid?

To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:

a² + b² = c²

Where a = Height of the square pyramid represent by h

b = radius of the square pyramid represented by r

c = Slant height of the square pyramid represented by s

Therefore, we have

h² + r² = s²

Looking at the attached diagram, we are given the side length = 2 yards.

The radius of the square based pyramid = side length ÷ 2

= 2÷ 2 = 1 yard.

The height of a square based pyramid = 2 yards

Since , h² + r² = s²

The slant height of the square pyramid is calculated as :

√h² + r² = s

√(2² + 1²) = s

√5 = s

s = 2.24 yards

B. What is the surface area of the composite figure?

We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

Step 1

We find the Lateral area of the faces of the insides of the inverted pyramid

We have 4 faces, Hence,

The formula is given as

a × √( a² + 4h²

a = 2 yards

h = 2 yards

So, = 2 × √( 2² + 4 ×2²

The Lateral area of the faces = 8.94 square yards.

Step 2

Area of the 5 faces of the cube

= a²

Where a = side length = 2 yards

= 2²

= 4 square yards.

Step 3

Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards

= 12.94 square yards.

C. How many cubic yards of concrete are needed to make the planter?

This is calculated by find the Volume of the Square based pyramid.

The formula is given as :

V = (1/3)a²h

Where a = side length = 2 yards

h = height of the square based pyramid = 2 yards

V = 1/3 × 2² × 2

V = 2.67 cubic yards

Answer:

D

Step-by-step explanation:

Firstly, to answer this question, we need to calculate the change in elevation.

Let’s just think of the question as, the distance from the foot of the mountain to the top is 4,418 meters. Now we have climbers starting at a height of 2,550 meters. We now need to know the difference or the distance to which they have climbed.

To calculate this is quite straightforward, all we need do is to subtract the starting point from the end position.

Mathematically that would be 4,418 - 2,550 = 1,868 meters

Now our answer need be in foot. we have a conversion system given in the question already.

1 foot = 0.3048 meters

x foot = 1,868 meters

x = 1,868/0.3048

x = 6,128.6 feet which is approximately 6,129 feet

Answer:

i tried so i hope this helps you

Answer:

y = -3x - 9

Step-by-step explanation:

Equation of line in point slope form is given as:

[tex]y - y_1 = m(x-x_1) \\

y - 3= - 3\{x - (-4)\}\\

y - 3 = - 3(x + 4)\\

y =- 3x - 12 +3\\

y = - 3x - 9\\ is \: the \: required \: equation \\ [/tex]

Answer:

2 1/2

Step-by-step explanation:

take 25 and divide it by 10 giving you 5/2 but that equals 2.5 and 2.5 equals 2 1/2

Answer:

Keith; -5, -12

Step-by-step explanation:

Logic ( Subtract 12 from both sides, then factor it out)

Answer:

22/28 = 11/14

Step-by-step explanation:

no of socks other than blue = 22

total no of socks = 28

so probability= 22/28 = 11/14

Answer:

22

Step-by-step explanation:

8 black 6 blue and 14 white is equal to 28

and if 6 are blue the rest are not so 6-28=22

Answer:

The graph changes from the original position to right 3 units and down 1 unit.

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!

Answer: 47,520

Step-by-step explanation: 36 times 40 times 33

Answer:

920 ft^2

Step-by-step explanation:

area of triangles: base x height / 2 (2)

8 x 15 / 2

= 60 x 2

= 120

area of rectangular base: length x width

15 x 20 = 300

area of sloped rectangle: length x width

17 x 20 = 340

area of rectangle: length x width

8 x 20 = 160

Total: 120 + 300 + 340 + 160

=920 ft^2

Answer:

920 ft²

Step-by-step explanation:

2 triangles + 3 rectangles

2(½×15×8) + 20(17+8+15)

120 + 800

920

Answer:it’s 31.7 cm^2

Step-by-step explanation:

The approximate area of the shaded sector is 31.7 cm² (Option A).

To find the area of the shaded sector, we need to calculate the fraction of the entire circle that the sector represents and then multiply it by the area of the whole circle.

The formula to find the area of a sector is given by:

Area of sector = (θ/360) * π * r²

where θ is the central angle and r is the radius of the circle.

In this case, the radius (r) of the circle is given as 11 cm, and the central angle (θ) is given as 30 degrees.

Let's calculate the area of the shaded sector:

θ = 30 degrees

r = 11 cm

Area of sector = (30/360) * π * 11²

             = (1/12) * π * 121

             = π * 10.0833...

Now, we can approximate the value of π as 3.14:

Area of sector ≈ 3.14 * 10.0833...

             ≈ 31.7 cm²

Therefore, the approximate area of the shaded sector is 31.7 cm².

The correct option from the given choices is A. 31.7 cm².

To know more about sector, refer here:

https://brainly.com/question/12051312

#SPJ2

Answer:

1. $0.99

2. $1.98

Step-by-step explanation:

1. From the question we have

Cost of box = $2.48

Selling price = $1.49

That is the box is discounted from $2.48 to $1.49

Therefore, amount saved = $2.48 - $1.49 = $0.99

2. The amount saved from buying a second box is hence;

2 × $0.99 = $1.98

Hence, as the number of boxes bought increases, the amount saved increases

Answer:

The answers to both questions are

1. You save $0.99 on the box when it is purchased on sale

This is calculated by subtracting on-sale price from pre-sale price:

$2.48-$1.49 = $0.99

2. Total amount saved when a second box is purchased on-sale price is derived by multiplying the amount saved on-sale purchase by two:

$0.99 x 2 (boxes)

$0.99 x 2 = $1.98

Cheers!

Answer:

I think the correct answer is 27 so option c. :)

Answer & Step-by-step explanation:

If each fruit tree produces an average of 590 pounds of fruit, then that means we are going to multiply. For the apples, we are going to multiply 120 by 590. For the pears, we are going to multiply 90 by 590. After we multiply these numbers, we are going to add the products so we can find the total amount of pounds of fruit.

Apples:

120 × 590 = 70800

Pears:

90 × 590 = 53100

Now, we add 70800 to 53100.

70800 + 53100 = 123900

So, the orchard produces 123900 pounds of fruit in one year.

Answer:

The median is NOT the same thing as a quartile.

The median is a measure of center.

Answer:

-3/4

Step-by-step explanation:

Point A is at (-4,3) and Point B is at (4,-3)

The slope is at

m = (y2-y1)/(x2-x1)

   = (-3 -3)/(4 - -4)

   = (-3-3)/(4+4)

    = -6/8

     = -3/4

Answer:

756 is evenly divisible by 2, 3, 4, 6, and 9.

Step-by-step explanation:

756 is evenly distributed by the numbers (above).

Answer:

210 adult tickets were sold

Step-by-step explanation:

let x be the number of adult tickets sold

let y be the number of children tickets sold

x+y=260 equation 1

9x+5y=2140 equation 2

multiply equation 1 by 5

multiply equation 2 by 1

5x+5y=1300

9x+5y=2140

subtract equation 1 from 2

4x=840

x=840/4 =210  tickets

substitute for x in equation 1

210+y=260

y=260-210=50

Answer:

1/8

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

divide 6/42

Answer:

64

Step-by-step explanation:

To get the answer, just perform the reverse operation of what the question said. In this case, you would want to multiply by the reciprocal, which is (8/3). So the answer is found by just solving 24*(8/3).

Answer:

The number is 64

Step-by-step explanation:

Let the number be x

3/8 of x = 24

x = 24 ÷ (3/8)

[tex]x=24*\frac{8}{3}\\\\x=8*8[/tex]

x = 64

We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

[tex]\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex]

[tex]\angle R+123^{\circ}+28^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}[/tex]

[tex]\angle R=29^{\circ}[/tex]

[tex]\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})[/tex]

[tex]r=\frac{93}{0.838670567945}\cdot (0.484809620246)[/tex]

[tex]r=110.889786233799179\cdot (0.484809620246)[/tex]

[tex]r=53.7604351[/tex]

Upon rounding to nearest tenth, we will get:

[tex]r\approx 53.8[/tex]

Therefore, the length of r is approximately 53.8 inches.

Answer:

C

Step-by-step explanation:

Is is a one-tailed test

P(z < 2.45) = 0.9929

1 - 0.9929 = 0.0071

Significant at both 0.05 and 0.01 because both are greater than 0.0071

Answer:

The finding is significant at both α = 0.05 and α = 0.01.

Answer:

the answer is B

Step-by-step explanation:

hope it help

To find the slope of thine that passes through these points, use the slope formula. It can be read as “slope equals the second y-coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate.”

So we have [tex]\frac{-4 - 5}{-3 - 2}[/tex] and this simplifies to -9/-5 or 9/5.

Remember, a negative divided by a negative is a positive.

Answer:

Look at the attachment

Answer:

Richard gets 15 more sweets than Natasha.

Step-by-step explanation:

Given that the ratio of Sarah's sweets is 5 and she has 75 sweets. So firstly, you have to find out how many sweets in a ratio of 1 :

Let ratio be units,

[tex]5 units = 75 sweets[/tex]

[tex]1 unit = 75 \div 5[/tex]

[tex]1 unit = 15 sweets[/tex]

Now we have to find how many sweets does Natasha and Richard has :

Richard (ratio of 3),

[tex]3 units = 15 \times 3[/tex]

[tex]3 units = 45 sweets[/tex]

Natasha (ratio of 2),

[tex]2 units = 15 \times 2[/tex]

[tex]2 units = 30 sweets[/tex]

In order to find how many sweets Richard has more than Natasha, you have to substract :

[tex]45 - 30 = 15 sweets[/tex]

Answer:

15

Step-by-step explanation:

the answer is 15

Answer:

cosx= 35. Use Trignometrical identity cosx = √1−sin2x . cos x = √1−1625 = √925 = 35 to be the ...

Missing: =0.82 ‎| Must include: =0.82

Step-by-step explanation: