C. 2500 = -(x) + 1243

Answer:

The total amount after five years =  $7,000

Step-by-step explanation:

Step(i):-

Given Esther deposited $5,000 into an account

Principal amount 'P' = 5000

Given rate of interest (R) = 8%

r = R / 100 = 0.08 per year

Step(ii):-

The total amount after 5 years

            [tex]A = P( 1 + r t )[/tex]

          [tex]A = 5000(1+ (0.08 X 5) = 7000[/tex]

Final answer:-

The total amount after five years =  $7,000

Answer:

The answer is C

Step-by-step explanation:

This is right because that's what I did

From the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO

The 3 lines are shown in the image attached below.

In the diagram, there are two linear pairs that are formed, they are:

Therefore, from the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO

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Answer:

C. [tex]\sqrt{18}[/tex]

Step-by-step explanation:

[tex]\frac{4\pi }{\pi }[/tex] = 4(whole number)

[tex]\sqrt{ 6^{2}}[/tex] = 6(whole number)

[tex]\sqrt{18}[/tex] = 4.2426406871192851464050661726291(goes on and on)

21.989(terminating number)

Irrational numbers are un-whole numbers that do not terminate and cannot be turned into a fraction.

The irrational number number in the options is C. √18.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

Given options are 4π/π, √(6²), √18 and 21.989.

4π/π can be written as 4, which is a whole number and thus a rational number.

So, 4π/π is a rational number.

√(6²) = 6, which is also a rational number since it is a whole number.

√18 does not have a decimal which is ending.

So it is an irrational number.

21.989 has only 3 decimal places and can be written as 21989/1000 and is thus a rational number.

Hence the correct option is C.

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Answer:

1) The length of the arc AB is approximately 21.99 cm

2) The perimeter of the figure is approximately 49.99 cm

3) The area of the figure is approximately 153.938 cm²

4) The area of the right triangle ΔAOB is 98 cm²

5) The area of the shaded segment is approximately 55.938 cm²

Step-by-step explanation:

The given parameters are;

The radius of the circle from which we have the quarter circle, r = 14 cm

Therefore, we have;

The length of segment OA = The length of segment OB = r = 14 cm

1) The length of the arc AB = 1/4 × The circumference of the circle with radius 14 cm and center O

The length of the arc AB = 1/4 × 2 × π × r = 1/4 × 2 × π × 14 c m= 7·π cm ≈ 21.99 cm which is approximately 22 cm, to the nearest whole number

2) The perimeter of the figure = The length of the arc AB + The length of segment OA + The length of segment OB

∴ The perimeter of the figure = 7·π cm + 14 cm + 14 cm ≈ 49.99 cm which is approximately 50 cm, to the nearest whole number

3) The area of the figure (sector AOB) = The area of the quarter of a circle = π × r²/4 = π × (14 cm)²/4 = 49·π cm² ≈ 153.938 cm²

4) Whereby we have arc AB and segment OA and OB form a quarter (1/4) of a circle, we have;

∠AOB = 360°/4 = 90°

Therefore, ΔAOB is a right triangle

The base length of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm

The height of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm

The area of the right triangle ΔAOB = 1/2 × The base length × The height

∴ The area of the right triangle ΔAOB = 1/2 × 14 cm × 14 cm = 98 cm²

The area of the right triangle ΔAOB = 98 cm²

5) The area of the shaded segment = The area of the quarter of a circle (Sector OAB) - The area of the triangle ΔAOB

The area of the quarter of a circle = 49·π cm² ≈ 153.938 cm²

∴ The area of the shaded segment = 49·π cm² - 98 cm² ≈ 55.938 cm²

The area of the shaded segment ≈ 55.938 cm²

The area of the shaded segment is approximately 55.938 square centimeters.

The length of the arc AB is approximately 21.991 centimeters.

The perimeter of the figure is approximately 49.991 centimeters.

The area of triangle AOB is 98 square centimeters.

The area of the circle segment is approximately 153.938 square centimeters.

The area of the shaded segment ([tex]A[/tex]), in square centimeters, is obtained by subtracting the area of the triangle from the area of the circle quarter, that is:

[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot \left(\frac{\sqrt{2}}{2}\cdot r \right)\cdot \left(\sqrt{2}\cdot r\right)[/tex]

[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot r^{2}[/tex]

[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot r^{2}[/tex] (1)

If we know that [tex]r = 14\,cm[/tex], then the area of the shaded segment is:

[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot (14\,cm)^{2}[/tex]

[tex]A \approx 55.938\,cm^{2}[/tex]

Where [tex]r[/tex] is the radius of the circle segment, in centimeters.

The area of the shaded segment is approximately 55.938 square centimeters. [tex]\blacksquare[/tex]

The length of the arc AB ([tex]s[/tex]) is determined by definition of circular arc:

[tex]s = \frac{\pi}{2} \cdot r[/tex] (2)

If we know that [tex]r = 14\,cm[/tex], then the length of the arc AB is:

[tex]s = \frac{\pi}{2} \cdot (14\,cm)[/tex]

[tex]s \approx 21.991\,cm[/tex]

The length of the arc AB is approximately 21.991 centimeters. [tex]\blacksquare[/tex]

The perimeter of the figure ([tex]p[/tex]), in centimeters, is the sum of the arc AB and the two legs of the right triangle, that is:

[tex]p = \frac{\pi}{2}\cdot r + 2\cdot r[/tex]

[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot r[/tex] (3)

If we know that [tex]r = 14\,cm[/tex], then the perimeter of the figure is:

[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot (14\,cm)[/tex]

[tex]p \approx 49.991\,cm[/tex]

The perimeter of the figure is approximately 49.991 centimeters. [tex]\blacksquare[/tex]

The area of the triangle ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:

[tex]A = \frac{1}{2}\cdot r^{2}[/tex] (4)

If we know that [tex]r = 14\,cm[/tex], then the area of the triangle AOB is:

[tex]A = \frac{1}{2}\cdot (14\,cm)^{2}[/tex]

[tex]A = 98\,cm^{2}[/tex]

The area of triangle AOB is 98 square centimeters. [tex]\blacksquare[/tex]

The area of the circle segment ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:

[tex]A = \frac{\pi\cdot r^{2}}{4}[/tex] (5)

If we know that [tex]r = 14\,cm[/tex], then the area of the circle segment is:

[tex]A = \frac{\pi\cdot (14\,cm)^{2}}{4}[/tex]

[tex]A \approx 153.938\,cm^{2}[/tex]

The area of the circle segment is approximately 153.938 square centimeters. [tex]\blacksquare[/tex]

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Answer:

x+y=2100

x(0.04) + y(0.02) = 62

(2100-y)(0.04)+ 0.02y = 62

84-0.02y = 62

22/0.02=y

y=1100

x=1000

Answer:

34 is the asnwer congruent thats why.

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

because you multiply 5 times 3 which is 15 times 7 equals 105

Answer:

200

Step-by-step explanation:

160/80 is 2. 2 times 100 is 200

Answer:

3a = [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

Given

2a + 4b = 5 ← substitute a = 3b into the equation

2(3b) + 4b = 5

6b + 4b = 5

10b = 5 ( divide both sides by 10 )

b = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]

Now

a = 3b = 3 × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] , thus

3a = 3 × [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]

Answer:

The value of 3a = 9/2

Step-by-step explanation:

Given the expression

[tex]2a+4b=5[/tex]

Given that a is equal to three times b. so,

[tex]a = 3b[/tex]

plug in a = 3b in the expression

[tex]2a+4b=5[/tex]

[tex]2(3b) + 4b = 5[/tex]

[tex]6b+4b = 5[/tex]

Adding like terms: 6b+4b = 10b

[tex]10b = 5[/tex]

Dividing both sides by 10

[tex]\frac{10b}{10}=\frac{5}{10}[/tex]

simplify

[tex]b=\frac{1}{2}[/tex]

so

a = 3b ⇒ a = 3(1/2) = 3/2

Therefore, the value of 3a can be determined by substituting a = 3/2 in 3a.

3a = 3(3/2) = 9/2

Therefore, the value of 3a = 9/2

Answer:

Mind if ya brainiest meh

Step-by-step explanation:

The volume of the hemisphere is 1071.78 ft^3

Answer:

P=5n/m-qr

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

14 and 5

Step-by-step explanation:

the range is 5 and the domane is 14

Answer:

28 blue marbles

Step-by-step explanation:

600 divided by 240 = 2.5

70 divided by 2.5 = 28

Answer:

y= -1/3x-4

y=2x+2

Step-by-step explanation:

the slope is rise over run

Answer:

6.26666666667, your welcome :)

Step-by-step explanation:

The given function f(x)=3x²=f(x)=3x²+0x+0 is a quadratic function

Answer: The answer is X= 9    Hope this helps :)  Please mark Brainliest

Step-by-step explanation:

Answer:

32 words per minute

Answer:

it will float!

Step-by-step explanation:

in order to find density, you must divide the mass by the volume. the volume is 56 ml, and the mass is 45.5. (45.5 / 56 = 0.8125) because we know the density of water is 1, and the density of this liquid is less than that of water, it will float because it is "lighter". hope it helped <33

Step-by-step explanation:

answer is you're question

Answer:

Step-by-step explanation:

Like terms: 10y, -2y, 3x, and x

These are all like terms since they have a similar variable

Simplifying the expressions:

10y + 3x + 10 + x -2y = [(10y + -2y) + (3x + x)] + 10

= 8y +  4x + 10

Like terms: 3x, 4x, y, and -2y

Same as first explanation, terms have a similar variable

3x - y + 4x + 6 - 2y = (3x + 4x) + (-2y - y) + 6

= -3y + 7x + 6

Hope I helped :)

Answer:

(ASA) Angle Side Angle

Step-by-step explanation:

Both triangles shown have the congruence line on an angle and an adjacent side. ASA proves congruence because in addition to the angle and side, the triangles ADE and CBE share the same angle on point E. Because the two lines are intersecting, their opposite angles are congruent and the triangles share the opposite angles.

The triangle congruence theorem that could be used to show that triangle ADE is congruent to triangle CBE is;

ASA Congruence theorem.

Looking at the given triangles we can say that;

∠AED = ∠CEB

This is because they are both vertically opposite angles and vertically opposite angles are equal.

Now, from the triangle, we are given that;

∠DAE = ∠BCE

We are also given that;

AE = CE

This means that we have 2 corresponding angles and 1 corresponding included side that are congruent.

Thus, the congruence theorem that this represents is ASA Congruence theorem.

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Answer:

The formula for perimeter is the sum of

twice the width and twice the length, so

the formula would be:

Perimeter = 2W + 2L

In this problem:

Width is unknown (x)

Length is twice the width (2x)

and Perimeter = 60, so to set it up:

60 = 2x + 2(2x)

60 = 2x + 4x

60 = 6x

x = 10

Width = 10; Length = 20

So then you do 20/10

= 2

2 is the answer

Step-by-step explanation:

Hope this helps,

Please give brainliest if you like my answer.

The equation 3x + 4 = 4x + 3 has one solution.

To determine the number of solutions for the equation 3x + 4 = 4x + 3, we can simplify and analyze the equation.

First, we can rearrange the equation by moving all the x terms to one side and the constant terms to the other side:

3x - 4x = 3 - 4

Simplifying further:

-x = -1

Next, we can multiply both sides of the equation by -1 to eliminate the negative sign:

x = 1

Therefore, we have found a single solution for x, which is x = 1. This means that when we substitute x = 1 into the original equation, both sides will be equal.

In summary, the equation 3x + 4 = 4x + 3 has one solution, which is x = 1. This can be verified by substituting x = 1 back into the equation and confirming that both sides are equal.

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Answer:

x = -4,  y = 3/2

Step-by-step explanation:

simplify the 1st equation by dividing each term by 4 to get:

x + 2y = -1

-5x + 2y = 23

Subtract to get: 6x = -24

x = -4

find 'y':    2y - 5(-4) = 23

               2y + 20 = 23

               2y = 3

                y = 3/2

Answer:

y is equal to 1.5, and x is equal to -4

Step-by-step explanation:

given:

[tex]4x + 8y = -4[/tex]

[tex]2y - 5x = 23[/tex]

We can start by factoring 4 out of the first equation:

[tex]x + 2y = -1[/tex]

Now let's multiply it by -5:

[tex]-5x - 10y = 5[/tex]

We'll rearrange the other equation to match that (just for clarity):

[tex]-5x + 2y = 23[/tex]

Now let's subtract the modified equation from that:

[tex]\begin{array}{c}-5x + 2y = 23\\-5x - 10y = 5\\ \ \ \ \ \ \ \ \ \ \ 12y = 18\end{array}[/tex]

So y is equal to 18/12, or 1.5

Let's plug that into one of the first equations and see what we get:

[tex]2y - 5x = 23\\2(1.5) - 5x = 23\\3 - 5x = 23\\-5x = 20\\x = -4[/tex]

Giving us an x value of negative four.  Let's plug that into the other equation to confirm:

[tex]4x + 8y = -4\\4(-4) + 8y = -4\\-16 + 8y = -4\\-4 + 2y = -1\\2y = 3\\y = 1.5[/tex]

That matches up, so our answer is correct.

I believe it would be 60, 60 is the only multiple for 6.

Final Answer: [tex]x = \frac{5y}{3}[/tex], [tex]y = 15[/tex]

Steps/Reasons/Explanation:

Question: [tex]\frac{x}{5} = \frac{y}{3}[/tex] and [tex]\frac{12}{y} = \frac{4}{5}[/tex]. What does [tex]x[/tex] equal and what does [tex]y[/tex] equal and how?

Solving for [tex]x[/tex] in the equation [tex]\frac{x}{5} = \frac{y}{3}[/tex].

Step 1: Multiply both sides by [tex]5[/tex].

[tex]x = \frac{y}{3} * 5[/tex]

Step 2: Simplify [tex]\frac{y}{3} * 5[/tex] to [tex]\frac{y * 5}{3}[/tex].

[tex]x = \frac{y * 5}{3}[/tex]

Step 3: Regroup terms.

[tex]x = \frac{5y}{3}[/tex]

Solving for [tex]y[/tex] in the equation [tex]\frac{12}{y} = \frac{4}{5}[/tex].

Step 1: Multiply both sides by [tex]y[/tex].

[tex]12 = \frac{4}{5}y[/tex]

Step 2: Simplify [tex]\frac{4}{5}y[/tex] to [tex]\frac{4y}{5}[/tex].

[tex]12 = \frac{4y}{5}[/tex]

Step 3: Multiply both sides by [tex]5[/tex].

[tex]12 * 5 = 4y[/tex]

Step 4: Simplify [tex]12 * 5[/tex] to [tex]60[/tex].

[tex]60 = 4y[/tex]

Step 5: Divide both sides by [tex]4[/tex].

[tex]\frac{60}{4} = y[/tex]

Step 6: Simplify [tex]\frac{60}{4}[/tex] to [tex]15[/tex].

[tex]15 = y[/tex]

Step 7: Switch sides.

[tex]y = 15[/tex]

~I hope I helped you :)~

Answer:  They spent $100 on ice cream.

Step-by-step explanation:

Given : Total friends  = 5

They bought each $24 worth of toppings.

Total price of toppings = (Total friends ) x (Worth of each topping)

= 5 x ($24)

= $ 120

Total expense = $220

Money amount on ice cream = (Total expense) - (Total price of toppings)

= $220 - $120

= $100

Hence, they spent $100 on ice cream.

Answer:

2/5

Step-by-step explanation:

2/10+2/10=4/10

4/10 divided by 2/2= 2/5

Hope this helps!

Answer;

2/10 + 2/10 is 4/10 and then simplified it would be 2/5 because 2 goes into both 4 and 10.

2/10 + 2/10 = 4/10

4/10 = 2/5

Hope this Helps!

Answer:

Trey lives 384 feet.

Step-by-step explanation:

Let the average rate be represented by s, and the distance by d.

speed = [tex]\frac{distance}{time}[/tex]

⇒ distance = speed x time

i.e d = s x t

On his first trip,

d = s x 8

d = 8s ............ 1

on his trip home, the average rate was 16 miles per hour faster, so that;

d = (s + 16) x 6

d = 6s + 96 ............ 2

Equation 1 and 2, we have;

8s = 6s + 96

8s - 6s = 96

2s = 96

s = 48

The average rate is 48 miles per hour.

Thus from equation 1 (also equation 2 can be used),

d = 48 x 8

  = 384

Therefore, Trey lives 384 feet from the mountains.