how much should your mom set aside and invest in a fund earning 3% compounded quarterly is she needs 85,000.00 in 20 months

i hope you guys didn't have to suffer thru the rest like I did c,:

here is THE REST OF THE ANSWERS!

Step-by-step explanation:

THE ENTIRE PICTURE ABOVE IS CORRECT, BUT AFTER THAT THE NEXT ANSWERS ARE.....

8. angle LNO is congruent to angle NLM because of CPCTC

9. segment ON is parallel to segment LM because of converse of the alt. int. angles theorem

10. segment LO is parallel to segment MN because of converse of the alt. int. angles theorem

11. LMNO is a parallelogram because of the def. of a parallelogram

I just did all of these on edg. 2022 and they're correct. have a great day/night you guys and good luck!

We will use the converse of alternate interior angles theorem  to prove LMNO is a Parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal measure.  

The proof is as follows:

Statements                                                   Reasons

1) LO ≅ MN                                                        Given

2) ON ≅ LM                                                       Given

3) LN ≅ LN                                                     Reflexive property

4) Δ LON ≅ Δ NML                                       SSS congruency rule

5) ∠ NLO ≅ ∠ LNM                                         CPCTC

and ∠ MLN ≅ ∠ LNO              

6) LM ║ ON and LO ║ MN   converse of alternate interior angles theorem

7) LMNO is a Parallelogram                  Property of Parallelogram  

For more references on Parallelogram, click;

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Answer:

the solutions of x^2=16x-28 are

2) 2 and 14

Answer:

(x - 2)^2 + (y + 2)^2 = 100

Step-by-step explanation:

We know that the equation for a circle with a center in the point (a, b) and a radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is the point (2, - 2) and that the point (-4, 6) lies on the circle.

Then the radius of this circle will be the distance between (2, - 2) and  (-4, 6)

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Then the distance between (2, - 2) and  (-4, 6) is:

[tex]D = \sqrt{(2 - (-4))^2 + (-2 - 6)^2} = \sqrt{6^2 + (-8)^2} = \sqrt{100} = 10[/tex]

Then the radius of the circle is R = 10

and we know that the center is (2, -2)

the equation for this circle is then:

(x - 2)^2 + (y - (-2))^2 = 10^2

(x - 2)^2 + (y + 2)^2 = 100

Answer:

O D. an = 2(5)"

Step-by-step explanation:

Given the expression/sequence below

2, 10, 50, 250, 1250, ...

O D. an = 2(5)"

The explicit formula is C

a0= 2*5^0= 2

a1=2*5^1= 10

a2= 2*5^2= 50

a3=2*5^3= 250

a4=2*5^4= 1250

Answer:

one solution only

Step-by-step explanation:

16y + 7 = -3y + 10 + 8y

16y + 3y - 8y = 10 - 7

11y = 3

y = 3/11

Step-by-step explanation:

[tex]a) \: 7 \sqrt{3} - 2 \sqrt{3} + \sqrt{3} - 3 \sqrt{3} [/tex]

[Taking sq.root 3 common]

[tex] = (7 - 2 + 1 - 3) \sqrt{3} [/tex]

[tex] = (8 - 5) \sqrt{3} [/tex]

[tex] = 3 \sqrt{3} (ans)[/tex]

[tex]b) \: 5 \sqrt{7} + 4 \sqrt{7} - 8 \sqrt{7} [/tex]

[Taking sq.root 7 common]

[tex] = (5 + 4 - 8) \sqrt{7} [/tex]

[tex] = (9 - 8)\sqrt{7} [/tex]

[tex] = 1 \sqrt{7} [/tex]

[tex] = \sqrt{7} (ans)[/tex]

Answer:

No, it cannot be correct.

Step-by-step explanation:

1/5 of 24 is 4.8.

This would mean that Mary would have identified 4.8 animals.

This is logically incorrect, because the number of animals has to be a full number. There cannot be any decimals, or parts of animals.

So, this cannot be correct.

Answer:

x = 13.2

Step-by-step explanation:

We know that

sin theta = opp / hyp

sin 27 = y/x

sin 27 = 6/x

x sin 27 =6

x = 6/sin 27

x=13.21613559

Rounding to 1 decimal place

x = 13.2

Problem 1, part (a)

For instance, 200 feet in real life can be reduced to scale down to say 2 inches on paper. So we have a reduction going on, and not an enlargement.

====================================================

Problem 1, part (b)

This is because a scale drawing involves similar polygons. This is true whenever any dilation is applied.

====================================================

Problem 2

I'm not sure how your teacher wanted you to answer this question. S/he didn't give you any numbers for the side lengths of the polygon. The angle measures are missing as well.

Answer:

36 boys

Step-by-step explanation:

let x be the number of pupils in the class , then

[tex]\frac{3}{5}[/tex] x + 24 = x ( multiply through by 5 to clear the fraction )

3x + 120 = 5x ( subtract 3x from both sides )

120 = 2x ( divide both sides by 2 )

60 = x

Then

number of boys = [tex]\frac{3}{5}[/tex] × 60 = 3 × 12 = 36

Answer:

<NKM is the first.the second is <MKN

Answer:

< NKM and <MKN

Step-by-step explanation:

Answer:

x = 27

Step-by-step explanation:

3x - 4y = 65

3x = 65 + 4y

Find x, when y = 4

3x = 65 + 4 (4)

3x = 65 + 16

3x = 81

x = 27             [tex][ \ x = \frac{81}{3}\ ][/tex]                    

Answer:

αѕ hєrє thє ѕhσє rαngє íѕ gívєn = 3

αnd thє lєє fαmílч íѕ cσnѕíѕtєd σf thrєє pєσplє

thє ѕhσє ѕízє σf twσ pєσplєѕ = 6

wє knσw thαt rαngє = highest observation - lowest observation

so there are two probalities that lee s shoe size can be higher than the other two members by 3 units or greater than the other two members by 3 units

but one limitation given here that the lee shoe size is not smaller than the other two members by 3 units

so lee s shoe size = 6+3= 9 (ans)

Answer:

326.06 in^3

Step-by-step explanation:

Volume of the cylinder = [tex]\pi[/tex] · [tex]r^{2}[/tex] · h

Volume of the cylinder = [tex]\pi[/tex] · [tex]4^{2}[/tex] · 4

Volume of the cylinder = [tex]\pi[/tex] · 16 · 4

Volume of the cylinder = [tex]\pi[/tex] · 64

Volume of the cylinder = 201.06 in^3

Volume of the composite = length · width · height

Volume of the composite = 5 · 5 · 5

Volume of the composite = 125 in^3

201.06 + 125 = 326.06 in^3

Answer:

The answer to this question is C.

Answer: uhh 76t4

Step-by-step explanation: words here

Answer:

x=15 y=24

Step-by-step explanation:

This is because the rule is x goes up 3 y goes up 4

(9,12)->(x,20)

it skips one, so instead of adding 3 we add six

x=15

(15,20)->(18,y)

you follow the rule and 4.

Y=24

Answer:

A = 6.1 units²

Step-by-step explanation:

Δ ABC and Δ A'B'C' are congruent, since the translation only shifts their position , but does not change their dimensions, then

AB = A'B' = 6.1

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 2 and h = 6.1 , then

A = [tex]\frac{1}{2}[/tex] × 2 × 6.1 = 1 × 6.1 = 6.1 units²

Answer:

Step-by-step explanation:

An exponent or index is a number or letter written above and to the right of a mathematical expression called the base.

It indicates that the base is to be raised to a certain power.

Here,

3, 4 and 12 are the letters which are written above the base 2.

So,

3, 4 and 12 are exponent or index

Answer:

Step-by-step explanation:

First get everything on the same side of the equals sign and set the quadratic equal to 0:

[tex]x^2+x-5=0[/tex] where a = 1, b = 1, c = -5:

[tex]x=\frac{-1+-\sqrt{1^2-4(1)(-5)} }{2(1)}[/tex] which simplifies down a bit to

[tex]x=\frac{-1+-\sqrt{21} }{2}[/tex] and your 2 solutions are

[tex]x=\frac{-1+\sqrt{21} }{2}[/tex]  and  [tex]x=\frac{-1-\sqrt{21} }{2}[/tex]

Answer:

v = lhw

Step-by-step explanation:

[tex]\frac{v}{lh} = w[/tex]

v = lhw

Answer:

rolling a number cube with sides labeled 1-6 and tossing a coin

Step-by-step explanation:

Answer:

The average velocity of the particle is [tex]\vec {v}_{avg} = 4\,\hat{i} +24\,\hat{j}\,\left[\frac{m}{s} \right][/tex].

Step-by-step explanation:

In vector terms, the average velocity of a particle ([tex]\vec v_{avg}[/tex]), in meters per second, at a given time change ([tex]\Delta t[/tex]), in seconds:

[tex]\vec v_{med} = \frac{\Delta x}{\Delta t}\,\hat{i} + \frac{\Delta y}{\Delta t}\,\hat{j}[/tex] (1)

Where [tex]\Delta x[/tex] and [tex]\Delta y[/tex] is the change in position for x and y axes, in meters.

[tex]\Delta x = x(2) - x(1)[/tex]

[tex]\Delta x = (4\cdot 2 - 1)-(4\cdot 1 - 1)[/tex]

[tex]\Delta x = 4\,m[/tex]

[tex]\Delta y = y(2) - y(1)[/tex]

[tex]\Delta y = 8\cdot (2)^{2}-8\cdot (1)^{2}[/tex]

[tex]\Delta y = 24\,m[/tex]

[tex]\Delta t = 2\,s - 1\,s[/tex]

[tex]\Delta t = 1\,s[/tex]

[tex]\vec v_{avg} = \left(\frac{4\,m}{1\,s}\right)\,\hat{i} + \left(\frac{24\,m}{1\,s} \right) \,\hat{j}[/tex]

[tex]\vec {v}_{avg} = 4\,\hat{i} +24\,\hat{j}\,\left[\frac{m}{s} \right][/tex]

Answer:

13

Step-by-step explanation:

Prime numbers are only divisible by 1 or themselves.

No other factors

Answer:

[tex]x=7\\y=128\\z=128[/tex]

Step-by-step explanation:

Value of x:-

Form an equation:

[tex]4x+24=7x+3[/tex]  {opposite / vertical angles are equal}

Subtract 7x from both sides:

[tex]4x+24-7x=7x+3-7x[/tex]

[tex]-3x+24=3[/tex]

Subtract 24 from both sides:

[tex]-3x+24-24=3-24[/tex]

[tex]-3x=-21[/tex]

Divide both sides by -3

[tex]-3x/-3=-21/-3[/tex]

[tex]x=7[/tex]

Value of y and z:-

Value of x is 7 so replace x in the equations:

[tex]4(x)+24=52\\7(7)+3=52[/tex]

Now that we have the value of x, its easy to find y and z

[tex]52+52+y+z=360[/tex]

{complete circle makes 360°}

[tex]104+y+z=360[/tex]

[tex]y+z=360-104[/tex]

[tex]y+z=256[/tex]

Divide 256 by 2 to get value of each variable:

vertically opposite angles (y & z) are equal

[tex]256/2 = 128[/tex]

[tex]y=128\\z=128[/tex]

∴ CHECK: 128 + 128 + 52 + 52 = 360°

hope this helps...

Answer:

X=7

Y and Z = 128

Step-by-step explanation:

7X+3=4X+24

it is equal coz by the opposite angle

find the value of X

7x+3=4x+24--------------collect like term

3x=21----------divided by 3

x=7

then 7x+3=52

4x+24=52

SR is the line that measure 180°

that means (7x+3)+Z=180°

use the value of X into the equation

Z=180-52

Z=128

it means Z and Y are equal so Y= 128

Answer:

The answer is below

Step-by-step explanation:

A function shows the relationship between the set of inputs (independent variable) to the set of outputs (dependent variables).

The domain of a function is the set of possible inputs (independent variable) that satisfies the functions.

From the question, the domain of the function is the set of all possible vales of the inputs which is a (number of album sold).

Hence the domain of the function is:

0 < a < ∞

Answer:

y = 2x -11

Step-by-step explanation:

The equation of  a line that passes through point x1, y1 is given as

y - y1 = m (x - x1)

where m is the slope of the line

Given that the line passes through the point (8,5) and has a slope of 2, the equation of the line

y - 5 = 2 (x - 8)

y - 5 = 2x - 16

add 5 to both sides

y = 2x - 16 + 5

y = 2x -11

Answer:

x = 17

Step-by-step explanation:

(5x-23) + (7x-1) = 180

12x - 24 = 180

12x = 204

x = 17

Answer:

x = 17

Step-by-step explanation:

The 2 given angles are same- side interior angles and sum to 180° , then

7x - 1 + 5x - 23 = 180

12x - 24 = 180 ( add 24 to both sides )

12x = 204 ( divide both sides by 12 )

x = 17

Answer:

"-2" is the same in all expressions, and it's just plus or minus. so let's ignore the "-2" and look only at the rest

+1 is the greatest then

so -2+1 is the greatest

Answer:

x ≈ 43.3°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{11}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{8}{11}[/tex] ) ≈ 43.3° ( to 1 dec. place )