The ratio of keepers to animals in the city zoo is 2 : 7. The table shows the current numbers of animals and keepers in the zoo. If 21 more animals are added, how many total keepers are needed to maintain the ratio of keepers to animals?

City Zoo
Number of Keepers Number of Animals
12 42

Answer:

24.1 is a possibility for the perimeter

Step-by-step explanation:

The third side between 12+0.5 and 12-0.5, or 12.5 and 11.5.

The third side is between 11.5 and 12.5.

Simce it isn't isosceles third side can't be 12.

So it's asking you to choose a number between 11.5 and 12.5 with the exclusiion of 12 for the third side measurement in meters.

So let's choose 11.6.

So the perimeter is just the sum of all side measurements.

11.6+12+0.5

11.6+0.5+12

12.1+12

24.1

24.1 is a possibility for the perimeter

Answer:

x = 46

Step-by-step explanation:

Assuming DE is an angle bisector , then it divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{HD}{DG}[/tex] = [tex]\frac{EH}{EG}[/tex] , substitute values

[tex]\frac{x+4}{58}[/tex] = [tex]\frac{55}{63.8}[/tex] ( cross- multiply )

63.8(x + 4) = 3190 ( divide both sides by 63.8 )

x + 4 = 50 ( subtract 4 from both sides )

x = 46

Answer:

4 triangles and 1 square

Step-by-step explanation:

Required

The shapes in two-dimensional net of a square pyramid

To do this, I will attach an attachment of a 2D net of a square pyramid (see attachment)

From the attachment, we can see that:

The 2d shape of the pyramid is made of 4 triangles and 1 square

Answer:

D

Step-by-step explanation:

Answer:

126 was removed.

Step-by-step explanation:

The total before division took place was

Total = mean * 14

mean = 49

Total = 49 * 14

Total = 685

Now you subtract x from the total

685 - x

And divide by 13 [one number is missing]

(685 - x)/13

and the result = 43

(685 - x ) / 13 = 43                Multiply both sides by 13

685 - x  = 43 * 13

685 - x = 559                       Subtract 685 from both sides

- x = - 126                             Multiply by - 1

x = 126

Answer:

B

Step-by-step explanation:

As T is the midpoint of SU, ST=TU. 9x=5x+28, 4x=28, x=7. ST=TU=63 and SU=126

Using Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \sf\longmapsto P^2=11^2-9^2[/tex]

[tex]\\ \sf\longmapsto P^2=121-81[/tex]

[tex]\\ \sf\longmapsto P^2=40[/tex]

[tex]\\ \sf\longmapsto P=\sqrt{40}[/tex]

[tex]\\ \sf\longmapsto P=6.2cm[/tex]

Step-by-step explanation:

Given,

Hypotenuse = 11 cm

Base (One of the given leg) = 9 cm

Therefore,

According to Pythagoras Theorem,

[tex] {base}^{2} + {height}^{2} = {hypotenuse}^{2} [/tex]

[tex] = > {(9)}^{2} + {height}^{2} = {(11)}^{2} [/tex]

[tex] = > {height}^{2} = {(11)}^{2} - {(9)}^{2} [/tex]

[tex] = > {height}^{2} = 121 - 81[/tex]

[tex] = > {height}^{2} = 4 0[/tex]

[tex] = > height = \sqrt{40} [/tex]

=> height = 6.3245553203

When rounded to nearest tenth,

=> height = 6.3

Hence,

Required length of other leg is 6.3 (Ans)

Answer:

b1=7

Step-by-step explanation:

If we deal with geometric series, we should use the formulas for it. If there is the last term, it is not infinite geometric series. The sum of geometric series which isn't infinite is equal to b1(r^n-1)/(r-1)   where b1 is the first term and r is the common ratio.

So 280= b1(3^n-1)/(3-1)

560= b1(3^n-1)

560= b1*3^n-b1

Then express bn=b1*r^(n-1)

189= b1*3^(n-1)

189= b1*3^n*1/3

567= b1*3^n when

560= b1*3^n-b1

560=567-b1

b1=7

Answer:

2^4 x 6^4

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

11a   -2(x^2 -3)

Distribute

-2*x^2 -2(-3)

-2x^2 +6

11b  2x(x+4)

 Distribute

2x*x +2x*4

2x^2 +8x

12 The perimeter is the sum of all sides

The top is equal to the bottom and the left side is equal to the right

x-10 + x+20+x-10+x+20

Combine like terms

4x +20

Answer:

4746

Step-by-step explanation:

Answer:

C(x)=40x+14, 6 days

Step-by-step explanation:

C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.

C(x)=254=40x+14, 40x=240, x=6

Answer:

D. Positively skewed

Step-by-step explanation:

Answer:

Step-by-step explanation:

The shorter arc is 22 cm.

Arc length formula:

Circumference formula:

Use the first formula to work out the value of C:

Length of arc=L=22cm

We know

[tex]\boxed{\sf L=\dfrac{\Theta}{360}\times πr}[/tex]

[tex]\\ \sf\longmapsto 22=\dfrac{45}{360}\times 2πr[/tex]

[tex]\\ \sf\longmapsto \dfrac{2πr}{8}=22[/tex]

[tex]\\ \sf\longmapsto {2πr=176}[/tex]

[tex]\\ \sf\longmapsto Circumference=176cm[/tex]

Answer:

(-150, 45)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

My best guess from the graph is

(-150, 45)

Answer:

true

Step-by-step explanation:

We are given that sides LM and NM, LO and NO, MO and MO are congruent. Since this describes 3 sides of the triangle, you can say ΔMNO is congruent to ΔMLO. From this, you can say ∠OMN is congruent to ∠OML. The two angles (∠OMN and ∠OML) form a straight line, meaning they add up to 180 degrees. We can write:

∠OMN + ∠OML = 180

And since ∠OMN = ∠OML, we can substitute and solve:

∠OMN + ∠OMN = 180

2∠OMN = 180

∠OML =∠OMN = 90

Since both these angles are 90 degrees, LN is perpendicular to MO by definition.

Answer:

The perimeter of a shape is the length around it.

Step-by-step explanation:

We will be using the x and y values and add them together to find the total perimeter.

To do this, let's find all the values of the 2 axis:

(2 to 4) = 2

(1 to 3) = 2

(4 to 10) = 6

(3 to 1) = 2

(10 to 12) = 2

(1 to 8) = 7

(12 to 2) = 10

(8 to 1) = 7

We now add these values together which gives us 38. Don't forget to add the units afterwards (cm, m and so forth).

Answer:

x = ¾-a

Step-by-step explanation:

x + a = ¾

Subtract a from each side

x + a -a= ¾-a

x = ¾-a

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]x+a=\dfrac{3}{4}\\\\x=\dfrac{3}{4}-a\\\\x=\dfrac{3-4a}{4}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

2y+3x-2=0

Step-by-step explanation:

The slope of the line is 3/2 and the equation of line is y=-1.5x+1

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3}{12}[/tex] ← divide numerator and denominator by 3

= [tex]\frac{1}{4}[/tex]

The angle the golfer went off line from the tee when they  drove the ball

is [tex]\phi=28.2 \textdegree[/tex] because the cosine rule has been applied to calculate the angle

From the question we are told that:

Distance of hole from tee [tex]d_h=340yards[/tex]

Distance to the right [tex]d_r=230yards[/tex]

Ball distance from hole [tex]d_b=175 yard[/tex]

Given that the three points form a triangle x,y,z respectively

Where

[tex]d_h=xz[/tex]

[tex]d_r=xy[/tex]

[tex]d_b=yz[/tex]

Using Cosine Rule

[tex]yz^2=xy^2+xz^2-2(xy)(xz)cos\phi[/tex]

Therefore

[tex]cos\phi=\frac{yz^2}{xy^2+xz^2-2(xy)(xz)}[/tex]

[tex]cos\phi=\frac{(175)^2}{230^2+340^2-2(230)(340)}[/tex]

[tex]cos\phi=0.88[/tex]

[tex]\phi=28.2 \textdegree[/tex]

In conclusion the angle the golfer went off line from the tee when they

drove the ball is mathematically deducted and give as

[tex]\phi=28.2 \textdegree[/tex]

For more information on this visit

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The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

Learn more about GeoGebra hear;

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Answer:

Step-by-step explanation: from edmentum

1.  - 62.34

2. - 1.4997

3. - $76.49

4. - 23.29

5. - 0.27

6. - $28.26

7. - 0.378

8. - 7.08

9. - 0.3

10. - 1.64

Answer:

1. 62.34

2. 1.4997

3. $76.49

4. 23.29

5. 0.27

6. $28.26

7. 0.378

8. 7.08

9. 0.3

10. 1.64

Answer:-3\2

Step-by-step explanation:

slope is difference y axis by x axis

4-12/-2+6=-6/4=-3\2

Answer:

b

Step-by-step explanation:

Answer:

d: 20

Step-by-step explanation:

alternative angle

Answer:

f(9) = - 59

Step-by-step explanation:

Substitute x = 9 into f(x) , that is

f(9) = - (9)² + 9 + 13

     = - 81 + 22

    = - 59

Answer:

-59

Step-by-step explanation:

f(x) =-x^2+x+13

Let x = 9

f(9) = - (9)^2 +9+13

       = -81 +9+13

      = -59

Answer:

C

Step-by-step explanation:

c

Answer:

13 and 17 units

Step-by-step explanation:

explaination is in pic.

The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.

The length between two given points (x₁, y₁) and (x₂, y₂) will be:

√[(x₂ - x₁)² + (y₂ - y₁)²] units

Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).

Therefore, the diagonals of the quadrilateral will be AC and BD.

The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).

Now, the length of the diagonal AC will be:

= √[(-8 - 4)² + (2 - (- 3))²] units

= √[(- 12)² + (5)²] units

= √[144 + 25] units

= √(169) units

= 13 units                                  (length can't be negative)

Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).

Now, the length of the diagonal BD will be:

= √[(-1 - 7)² + (- 5 - 10)²] units

= √[(- 8)² + (- 15)²] units

= √[64 + 225] units

= √(289) units

= 17 units                                  (length can't be negative)

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Answer:

The Empty set............

Answer:

There is no solution for the intersection of these two sets, as they do not intersect! They don't have any numbers in common and thus form an empty set. The correct answer choice is option D. the empty set.

Step-by-step explanation:

The solution for { x | x <-5} is ---> x < -5

The solution for { x | x >5 } is ---> x > 5

If you placed the two sets on a number line close to each other, you would see that they do not intersect. Thus there is no solution for the intersection of set A and set B as defined in the given problem.

See the graph for better understanding. You see how there's an empty space or area between -5 and 5? Yeah, this is called the empty set which is option D from your answer choices.

Answer:

eşnatto eşmatoroorlfld

Answer:

Now , Piyush age =3+Honey age

Step-by-step explanation:

Honey age=x

Piyush age=y

1 year ago,Honey age=x-1

Piyush age=y-1

the ratio of Honey and Piyush age=2:3

x-1:y-1=2:3

x-1/y-1=2/3

3(x-1)=2(y-1)

3x-3=2y-2

3x-2y= -2+3

3x-2y=1 eq _1

after 5 years from now,

Honey age=x+5

Piyush age=y+5

the ratio of them=4:5

x+5/y+5=4/5

5(x+5) =4(y+5)

5x+25=4y+20

5x-4y=20-25

5x-4y=-5 _eq2

eq1and 2_

5x-4y= -5

3x-2y= 1

-

2x-2y=-6

x-y =-3

-y=-3-x

y=3+x