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A circle is centered at the point (-3, 2) and passes through the point (1,5). The radius of the circle is (blank) units. The point (-7 (blank) lies on this circle

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Step-by-step explanation:

1. DF≅EF ⇒ Reflexive property

2. ∠1≅∠2 ⇒Given

3.FG bisects ∠DFE ⇒Definition of a bisector

4. FG ≅ FG ⇒Given

5.ΔDFG ≅ΔEFG-SAS Congruence

The reflexive property of congruence simple means that any geometric figure is equal to itself. Line DF equals line FE because triangle ΔDFG≅EFG

A line segment that divides a angle into two equal parts in called an angle bisector. Line segment FG is bisects angle  ∠DFE

The Side Angle Side Postulate requires that two sides and included angle of one triangle are congruent to two sides and included angle of another triangle. In this case, angle ∠1 , ∠D and side DF equals ∠2, ∠E and side FE

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Keyword : proof, congruence,reflexive

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Answer:

The base is 11 inches long

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides and two equal interior angles

Let

y -----> is the length of the base of the isosceles triangle

x ----> is the length of each of the congruent sides

The perimeter of the triangle is equal to

[tex]P=y+x+x[/tex]

[tex]P=y+2x[/tex]

we have

[tex]P=55\ in[/tex]

so

[tex]55=y+2x[/tex] ----> equation A

[tex]y=\frac{x}{2}[/tex] ----> equation B

solve the system by substitution

substitute equation B in equation A

[tex]55=\frac{x}{2}+2x[/tex]

solve for x

[tex]55=\frac{5}{2}x[/tex]

[tex]x=55(2)/5\\x=22\ in[/tex]

Find the value of y

[tex]y=\frac{x}{2}[/tex] ----> [tex]y=\frac{22}{2}=11\ in[/tex]

therefore

The base is 11 inches long

88.8 acres are used for exhibits

Step-by-step explanation:

Given

Total area of Greenfield = 24 acres

Percentage of lad for exhibits = 37%

Now,

[tex]Acres\ used\ for\ exhibits = 37\%\ of\ 240\\= \frac{37}{100} * 240\\=0.37*240\\=88.8\ acres[/tex]

Hence,

88.8 acres are used for exhibits

Keywords: Percentage, percent

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Answer:

To drain the water tower it will take 36 hours.

Step-by-step explanation:

Given:

A 72,000 water tower is being drained, and in an hour 2000 gallons are drained.

Now, to calculate the hours it would take to drain total 72,000 gallons of water, we should divide the gallons of water drained in one hour by total gallons of water in the tower.

Gallons of total water in the tower ÷ Gallons of water drained per hour

[tex]72000\div 2000[/tex]

[tex]=\ 36[/tex]

Therefore, to drain the water tower it will take 36 hours.

Answer:

Every person in the US.

Step-by-step explanation:

Answer:

Step-by-step explanation:

100%-54%=46%

46%*25.6m=11,776,000

25,600,000+11,776,000=

37,376,000 Answer

Answer:

[tex]\large \boxed{\text{A. $\sqrt{194}$}}[/tex]

Step-by-step explanation:

We can use Pythagoras' Theorem.

[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 5^{2} + 13^{2}\\& = & 25 + 169\\& = & 194\\a & = & \sqrt{194}\\\end{array}\\\text{The length of the hypotenuse is $\large \boxed{\mathbf{\sqrt{194}}}$}[/tex]

Note that this is the equation of a line, since you can rewrite it as

[tex]3x-4y=6 \iff 4y=3x-6 \iff y=\dfrac{3}{4}x-\dfrac{3}{2}[/tex]

Now just choose two values for x and compute the correspondent y values:

[tex]x=0 \implies y=-\dfrac{3}{2}[/tex]

So, the line passes through the point (0, -3/2).

[tex]x=2 \implies y=\dfrac{3}{2}-\dfrac{3}{2}=0[/tex]

So, the line passes through the point (2, 0)

Now, draw on a coordinate plane the two points and connect them, and you'll have the line.

Answer:

x = [tex]\frac{14}{45}[/tex]

Step-by-step explanation:

10 - 2 + 6 = 3x (7 + 8)​

3x (7 + 8) = 10 - 2 + 6

21x + 24x = 8 + 6

45x = 14

x = 14 ÷ 45

x = [tex]\frac{14}{45}[/tex]

Answer:

b

Step-by-step explanation:

Both graphs end or start at at x = 2

The lower graph has an open circle at 2 meaning that x cannot equal 2

Thus y = x + 1 for x < 2

The upper graph has a solid circle at x = 2 meaning that x can equal 2

Thus y = x + 2 for x ≥ 2

Answer:

x=3

Step-by-step explanation:

16-x=x+10

16-x-x=10

16-2x=10

2x=16-10

2x=6

x=6/2

x=3

Answer:

Helene invested $ 400 at 6% and $ 600 at 7%.​

Step-by-step explanation:

Let

x -----> the amount invested at 6%

y -----> the amount invested at 7%

we know that

The interest earned with the amount invested at 6% plus the interest earned by the amount invested at 7% must be equal to $66

Remember that

[tex]6\%=6/100=0.06\\7\%=7/100=0.07[/tex]

so

[tex]x+y=1,000[/tex] ----> equation A

[tex]0.06x+0.07y=66[/tex] ----> equation B

Solve the system of equations by graphing

The solution of the system is the intersection point both graphs

using a graphing tool

The solution is the point (400,600)

see the attached figure

therefore

Helene invested $ 400 at 6% and $ 600 at 7%.​

The central angle created by an arc length of 6.9813 in a circle with a radius of 4 is approximately 100 degrees when rounded to the nearest whole number.

The student is asking about the relationship between the arc length of a circle, the radius of the circle, and the central angle created by this arc. To find the central angle from the arc length and the radius, we use the formula:

arc length (As) = radius (r) x central angle (θ)

Here, we're given the arc length as 6.9813 and the radius as 4. Since the central angle is usually given in radians, we first perform the calculation in radians and then convert it to degrees if necessary.

The central angle in radians is:

θ (in radians) = arc length / radius

θ = 6.9813 / 4 ≈ 1.7453 radians

To convert radians to degrees, we multiply by,

(180/π).

Thus,

θ (in degrees) ≈ 1.7453 x (180/π) ≈ 100 degrees

And when rounded to the nearest whole number:

θ ≈ 100 degrees

So, the central angle created by the arc is approximately 100 degrees.

[tex]\Huge{\underline{\underline{\mathttt{Answer \colon}}}}[/tex]

Acceleration of the object

Since,

[tex] \huge{ \boxed{ \boxed{\texttt{f = ma}}}}[/tex]

[tex] \leadsto \: \sf{a = \frac{f}{m} } \\ \\ \leadsto \: \sf{a = \frac{30}{6} } \\ \\ \huge{ \green{ \leadsto \: \mathtt{f = 5 \: ms {}^{ - 2} } }}[/tex]

Answer:

5 meters per second

Step-by-step explanation:

its basic math people

Answer:

There are 60t liters of water in the bathtub after t minutes.

After t minutes, [tex]\( 60t \)[/tex] liters of water fill the bathtub.

The amount of water in the bathtub after t minutes can be expressed as the product of the rate of filling (60 liters per minute) and the time (t minutes):

[tex]\[ \text{Amount of water} = \text{Rate of filling} \times \text{Time} \][/tex]

[tex]\[ \text{Amount of water} = 60 \text{ liters/minute} \times t \text{ minutes} \][/tex]

[tex]\[ \text{Amount of water} = 60t \text{ liters} \][/tex]

So, after [tex]\( t \)[/tex] minutes, there will be [tex]\( 60t \)[/tex] liters of water in the bathtub.

Answer:The perimeter of parallelogram PQRS = 2\sqrt{10}+8\sqrt{2} ⇒

2nd answer

Step-by-step explanation:* Lets revise some properties of the parallelogram

- Each two opposite sides are parallel

- Each two opposite sides are equal

- Its perimeter is the twice the sum of two adjacent sides

* Lets solve the problem

∵ PQRS is a parallelogram

∵ The length of side SR is

∵ The length of side QR is

∵ SR and RQ are two adjacent sides

∵ The perimeter of parallelogram PQRS = 2(RQ + SR)

∴ The perimeter of parallelogram PQRS =

∵  =

∵  =

∴ The perimeter of parallelogram PQRS =

Answer:

Option B.

Step-by-step explanation:

It is given that the sides of an equilateral triangle are 8 units long.

Draw an altitude of the triangle.

Altitude of an equilateral triangle is perpendicular bisector.

Let x be the length of the altitude of the triangle.

According to the Pythagoras theorem

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

Using Pythagoras theorem we get

[tex]8^2=4^2+x^2[/tex]

[tex]64=16+x^2[/tex]

[tex]64-16=x^2[/tex]

[tex]48=x^2[/tex]

Taking square root on both sides.

[tex]\sqrt{48}=x[/tex]

[tex]4\sqrt{3}=x[/tex]

The length of the altitude of the triangle is 4√3 units.

Therefore, the correct option is B.

The solutions of the system of equations are (0 , -6) , (-1 , -8)

Step-by-step explanation:

To solve a system of equations, one 1st degree and the other 2nd degree, do that:

∵ The system of equations is:

y = x² + 3x - 6 ⇒ (1)

y = 2x - 6 ⇒ (2)

Equate (1) and (2)

∴ x² + 3x - 6 = 2x - 6

- Add 6 to both sides

∴ x² + 3x = 2x

- Subtract 2x from both sides

∴ x² + x = 0

- Take x as a common factor in the left hand side

∴ x(x + 1) = 0

- Equate each factor by 0 to find the values of x

∵ x = 0

∴ The first value of x is 0

∵ x + 1 = 0

- Subtract 1 from each side

∴ x = -1

∴ The second value of x is -1

Substitute each value of x in equation (2) to find the values of y

∵ y = 2(0) - 6

∴ y = 0 - 6 = -6

The first value of y is -6

∵ y = 2(-1) - 6

∴ y = -2 - 6 = -8

∴ The second value of y is -8

∴ The solutions are (0 , -6) , (-1 , -8)

The solutions of the system of equations are (0 , -6) , (-1 , -8)

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Answer:

Yeah I'm here harmony plz tell

Step-by-step explanation:

Answer:

The solution of expression in the simplest form is 8

Step-by-step explanation:

Given as :

The expression is written

( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) - 2 ( - [tex]\dfrac{11 }{4}[/tex]x - [tex]\dfrac{5 }{2}[/tex])

Or, ( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) +[tex]\frac{11\times 2}{4}[/tex]x+  [tex]\frac{5\times 2}{2}[/tex]

Now, separate the variable terms

Or, ( [tex]\dfrac{-11 }{2}[/tex] + [tex]\frac{11\times 2}{4}[/tex]) x +  3 + 5

Or, ( 0) × x + 8

or , 0 + 8

∴ 8    

The simplest form if expression is 8

Hence The solution of expression in the simplest form is 8 . Answer

Answer:

285, 629, 7392, 15708,43695

Step-by-step explanation:

If you add the digits of the number together, it should be divisible by 9. If it isn't, then it must be a multiple of only 3, not 9.

Step-by-step explanation:

We need to find which of the numbers 285, 629, 5490, 7392, 15708, 43695 are divisible by 3 but not by 9.

      285

              285 ÷ 3 = 95  Divisible

              285 ÷ 9 = 31.66    Not divisible.  

              Correct

      629

              629 ÷ 3 = 209.67  Not divisible

              629 ÷ 9 = 69.89    Not divisible.  

              Not correct

      5490

              5490 ÷ 3 = 1830  Divisible

              5490 ÷ 9 = 610    Divisible.  

              Not correct

      7392

              7392 ÷ 3 = 2464  Divisible

              7392 ÷ 9 = 821.33    Not divisible.  

              Correct

      15708

              15708 ÷ 3 = 5236  Divisible

              15708 ÷ 9 = 1745.33    Not divisible.  

              Correct

      43695

             43695 ÷ 3 = 14565  Divisible

             43695 ÷ 9 = 4855    Divisible.  

              Not correct

Divisible by 3 and not by 9 are 285, 7392 and 15708.

Answer:

{a}p + 0.2m = 6

   0.8m = 4

or 5p + m = 30

   m = 5

{b} 5 lb peanuts and 5 lb mixture

Step-by-step explanation:

m1 → desired mixture with composition : 60% peanuts and 40% almonds and weight : 10 lb

⇒weight of peanuts in m1 = 60% × 5 = 6 lb

and weight of almonds in m1 is 4 lb

m2 → mixture with composition : 20% peanuts and 80% almonds and weight : m pounds

⇒weight of peanuts in m2 = 0.2m

and weight of almonds in m2 = 0.8m

p → weight (in pounds) of peanuts added to m2 to make m1

{a}

add p pounds of peanuts to m2 to make m1

equating weights of peanuts and almonds:

p + 0.2m = 6

0.8m = 4

{b}

equation gives m = [tex]\frac{4}{0.8}[/tex] ⇒ m = 5 lb

Using this in the [tex]1^{st}[/tex] equation:

p + 1 = 6 ⇒ p = 5 lb

Answer:

a) p + m = 10 and [tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex]

b) The mixing amount is 5 lb peanut and 5 lb mixture.

Step-by-step explanation:

Given that p pounds of peanuts and m pounds of the 80% almond and 20% peanut mixture are used to make 10 pounds of 60% peanuts and 40% of almonds mixture.

Now, we can write that p + m = 10 ........ (1)  

Now, m pounds of 80% almond and 20% peanut mixture contain 0.2m pounds of peanuts and 0.8m pounds of almonds.

Now, from the condition given it can be written that  

[tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex] .......... (2)

⇒ [tex]\frac{p + 0.2m}{0.8m} = \frac{3}{2}[/tex]

⇒ 2p + 0.4m = 2.4m

⇒ 2p = 2m

⇒ p = m  

Now from equation (1) we get p = m = 5 pounds.

a) Therefore, equations (1) and (2) are the system of equations that models the situation.

b) The mixing amount is 5 lb peanut and 5 lb mixture. (Answer)

You add 1/6 to both sides

Step-by-step explanation:

Answer:

A is the correct answer

Step-by-step explanation:

Add 1/6 to both sides

Answer:

20%

Step-by-step explanation:

Answer:

y=-4x+5

Step-by-step explanation:

the line goes down 4 for every 1 that x changes. the line crosses the y axis at 5.

(this might not be accurate, I can't really see if the line is on the exact point or not)

Answer:

[tex]\displaystyle y = -4x + 5[/tex]

Step-by-step explanation:

Starting from the y-intercept of [tex]\displaystyle [0, 5],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving four blocks north over one block west or four blocks south over one block east [west and south are negatives].

I am joyous to assist you anytime.

Answer:

42 Blades

Step-by-step explanation:

So 6 blades on each windmill

6=1 Windmill

so 7 windmills

so do

7 times 6 = 42 Blades

The total number of blades in 7 windmills is required.

42 blades are the total number of blades.

The number of blades in 1 windmill is 6 blades

[tex]1\ \text{windmill}=6\ \text{blades}[/tex]

There are 7 windmills

[tex]7\ \text{windmills}=7\times 6[/tex]

Using five fact

[tex]=(5\times 8)+(2\times 1) =42\ \text{blades}[/tex]

The total number of blades of the windmills are 42.

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Answer:

hypotenuse is not a rational number

Step-by-step explanation:

In a Right angled triangle , if a, b are the sides and h be the hypotenuse then relationship between them is given by

[tex]h^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

Here,

         a= 4 in.        [Given]

          b = 6 in.       [Given]

Thus ,

  [tex]h^{2}[/tex]  = [tex]4^{2}[/tex] + [tex]6^{2}[/tex]

  [tex]h^{2}[/tex]  =  16 + 36

  [tex]h^{2}[/tex]  = 52.

   h = [tex]\sqrt{52}[/tex]  = 7.21110255......

Clearly, h is not a rational number

Answer:

Each boy would get 59 seeds

Step-by-step explanation:

Aiden and his three friends = 4 people

236 divided by 4 = 59

Each boy will get 59 pumpkin seeds.

In this problem, Aiden and his three friends are sharing 236 pumpkin seeds equally. To find out how many pumpkin seeds each boy will get, we can divide the total number of seeds by the number of boys.

Divide the total number of pumpkin seeds, 236, by the number of boys, which is 4.

So, each boy will get 236 ÷ 4 = 59 pumpkin seeds.

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Answer:

-2/3

Step-by-step explanation:

m=(6-4)/(-2-1)=2/-3=-2/3

Answer:

3

Step-by-step explanation:

There are 15 shells all together

there is 5 friends

15 divided by 5 is 3

Therefore  the answer is three

Answer:

Each friend got 3 sea shells

Step-by-step explanation:

8+7=15 then they divided it up equaly to their 5 friends so 15/5=3 so each friend got 3 sea shells

Answer:

Everest and k2

Step-by-step explanation:

Answer:

its k2 and lhotse

Step-by-step explanation: 28,250 + 27, 940= 56, 190 because 0+ 0 =0

4+5 =9  9+ 2 = 11 carry the 1 8 + 7 +1 = 16 carry the 1 2+2+1 =5 so that equals 56,190 ft