Sam wants to invest the same amount at the end of every 3 months so that he will have $5000 in 9 years. The account will
pay 3.1% compounded quarterly. How much interest will he earn after 9 years? (Round to the nearest hundredth if
necessary.)

Answer:

answer is 32

Step-by-step explanation:

Answer:

D=32.204≈32  ∘

Step-by-step explanation:

deltamath

Answer:

4x^2+20x+25

Step-by-step explanation:

(2x+5)^2 = (2x+5) (2x+5)

Using the foil method : 2x(2x) = 4x^2

(2x) (5) = 10x

(2x) (5) = 10x

5 (5) = 25

Combine like terms

Answer:

x = 2/3

Step-by-step explanation:

Since it's a parallelogram, the bisected parts of the diagonal must be equal

So 6x must equal 3x + 2:

-Chetan K

Answer:

26 lb is 11.8 kg.

Step-by-step explanation:

A pound (lb) is a unit of mass used in the imperial and US customary systems of measurement.

A kilogram (kg) is the base unit of mass in the International System of Units (SI).

To convert 26 lb to kg.

First, use the conversion factor between pounds and kilograms.

1 kg = 2.2046 lb

Next, write the following equation to find the weight in kg:

weight in kg = weight in lb x (1 kg / 2.2046 lb)

The pounds cancel out, leaving kilograms.

weight in kg = 26 lb x (1 kg / 2.2046 lb)

weight in kg  = 11.7935 kg

Rounding to the nearest tenth.

weight in kg  = 11.8 kg

Answer:

Step-by-step explanation:

152

Answer:

Step-by-step explanation:

If

n

is a positive integer that is greater than

x

and

a

is a real number or a factor, then

a

x

n

=

n

√

a

x

.

a

x

n

=

n

√

a

x

Use the rule to convert

x

5

7

to a radical, where

a

=

,

x

=

, and

n

=

.

7

√

x

5

The radical expression of \(x^(5/7)\) is \(\sqrt[7]{x^5}\).

A radical expression is "an expression that contains square root and a radicand contains number or expression inside a radical or square root".

According to the question,

In order to write \(x^(5/7)\)  as radical expression.

Formula for radical expression \(a^x/n\) = \(\sqrt[n]{a^x}\)  

From given  'a' = x; 'x'=5; 'n'=7 using above formula we can written radical expression as \(\sqrt[7]{x^5}\).

Hence, the radical expression of \(x^(5/7)\) is \(\sqrt[7]{x^5}\).

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Answer:

-7/25

Step-by-step explanation:

Could be in fraction:

-7/25

or in decimal expression:

-0.28

Answer:$0.85

Step-by-step explanation:

.95x17= 16.15    17.00-16.15=0.85

9514 1404 393

Answer:

  15.46 m

Step-by-step explanation:

Side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. That is, the height of the tree above eye-height is √3 times the distance from the trunk. The top of the crown will be at a height of ...

  1.6 m + (8 m)√3 ≈ 15.46 m

The value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

The correct question is

Which values of a, b, and c represent the answer in simplest form?

7/9 divided by 4/9 = \(\rm a\dfrac{b}{c}\)

1: a = 1, b = 4, c = 3

2: a = 1, b = 3, c = 4

3: a = 1, b = 63, c = 36

4: a = 1, b = 36, c = 63

Reducing to simplest form means to reduce to an extent where the numerator and denominator have nothing in common to be cancelled out.

It is given in the question that

(7/9) / (4/9) =  \(\rm a\dfrac{b}{c}\)

It can also be written as

(7*9)/(4*9) =  \(\rm a\dfrac{b}{c}\)

7/4 = \(\rm a\dfrac{b}{c}\)

\(\rm 1 \dfrac{3}{4} = a\dfrac{b}{c}\)

Therefore the value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

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Answer:

well, I don't have the computer in front me with this question on it, but i can explain how you would do it.

all points, or in this case vertices, are written like this : (x , y)

the x-axis is the one that lies flat and the y-axis is the one going up and down.

in this graph, the y-axis and x-axis are more than likely not centered. so where the y-axis intersects the x-axis is known as the origin. you will start at the origin for plotting all points.

to plot point A : start at the origin and count to the left 3, and then down 5 and thats point A

for point B : start at the origin, count left 1 and then down 5, that's point B

point C : start at the origin, count left 1 and then down 1, that's point C

point D : count left 3 and then down 1, that's point D

after plotting the points, you just need to play "connect the dots" and make the shape a rectangle.

Start at point A, go right point B, up to point C, left to point D then down back to point A again

Step-by-step explanation:

I hope this helps :)

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

\(\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}\)

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

\(\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}\)

Therefore:

\(\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}\)

\(\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}\)

The amount Howie will pay back at the end of one year is $26000.00

The given parameters are:

\(P =25000\) -- the principal amount

\(R = 4\%\) -- the interest rate

\(T=1\) --- the duration

The amount to pay back in this duration is then calculated using:

\(A = P(1 + RT)\)

So, we have:

\(A = 25000(1 + 4\% \times 1)\)

\(A = 25000(1 + 4\% )\)

Express percentage as decimal

\(A = 25000(1 + 0.04)\)

\(A = 25000(1 .04)\\\)

Multiply

\(A = 26000\)

Hence, the amount to pay back is $26000.00

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Answer:

the first answer is commutative property of addition and the second answer is commutative property of multiplication

Step-by-step explanation:

hope this helps

have an awesome day -TJ

if you need anymore help just let me know

pls mark brainliest :)

Answer:

no

Step-by-step explanation:

8a+8b are not equivalent 6a+5b

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Answer:-3x - 12 + 5x

Step-by-step explanation:

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

605.85 (ft 2)

Step-by-step explanation:

5 1/4 * 115.4 = 605.85 (ft 2)

Answer:

0.9 cubic centimeters

Step-by-step explanation:

Answer:

82 units.

Step-by-step explanation:

The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs.

In this case, 18 and 80 are the legs.

18^2 + 80^2 = c^2

324 + 6,400 = c^2

6,724 = c^2

c^2 = 6,724

c^2 = 82^2

c = plus or minus 82

Since measurements cannot be negative, the length of the hypotenuse is 82 units.

Hope this helps!

Answer:

82 units   indeed!

Step-by-step explanation:

c = \(\sqrt{ 18^{2} + 80^{2} }\)

c = 82

Answer:

it should be 16

Step-by-step explanation:

Answer:  d. 40°

Step-by-step explanation:

Use the Cofunction Identity:    sin Ф = cos (90° - Ф)

sin Ф = cos (Ф + 10) = cos (90° - Ф)

⇒                   Ф + 10 = 90 - Ф

                   2Ф + 10 = 90

                          2Ф  = 80

                             Ф = 40

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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A graph of this quadratic equation x² + x - 6 = 0 is shown below.

The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).

In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.

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Answer:

17

Step-by-step explanation:

angle one and angle three are equal to each other

so if you set the equations equal to each other

(4x+2)=( 5x-15)

move the 4x the right by subtracting it giving you 1x

then add 15 to 2 giving you 17

17=1x

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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Answer:

498

Step-by-step explanation:

so first multiply -100 by -5 to get 500

the word "by" indicates multiplication

Next subtract -4 and 6 by 500

so 500 - 6 - (-4) = 498