After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Around the answer to the nearest penny.

Answers

Answer 1

The value of the principal investment would be = $12,500.75

What is a principal investment?

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

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Related Questions

Anna wants to buy 4 sweaters. The sweater come at a discount rate. If you buy one sweater regular price the other sweater is 40% off. How much percent is off of each sweater?

Answers

Answer:

20%

------------------------

If you buy a sweater, the second one is at 40% discount.

Divide the discount between the two to get:

40%/2 = 20%

You get a discount of 20% for each sweater.

Answer:

Discount percentage = 20%

Step-by-step explanation:

Discount of the sweaters,

→ first sweater = 0%

→ other sweater = 40%

The average discount percent is,

→ (first sweater + other sweater)/2

→ (0% + 40%) ÷ 2

→ (0 + 40)/2

→ 40/2

→ 20% off

Hence, the answer is 20% off.

9x+12y=-108 Please solve this, but it cannot be in fraction form!!!

Answers

All you have to do is solve this by using substitution or elimination. or in this case, because we don’t have a second equation, we would solve the x-intercept and y-intercept


X=-12

Y=-9

What is a remainder

Answers

I think you spelt it wrong

A remainder is the remaining amount of a number than comes out of a division. I'm not sure how to explain it better, so I'll give you an example:

Let's say you want to divide 5 by 2. We know that 5 can't be divided by 2 evenly, it won't give you a whole number. Instead it will give you a decimal 2.5.

In this case, 1 is the remainder and I will explain why! Do the long division for 5/2. 2 fits into 5 two times, so you multiply 2 * 2, which gives you 4. If you subtract that number from 5, you get 1. We know that 2 can't fit into one, therefore, 1 is the remainder. once you start getting into decimals, you can fit numbers into other numbers, which is why technically you can fit 2 into 5, but you can't fit it in evenly, if that makes sense!

I hope this example helps see what a remainder is. It's just the number in a long division that the divisor (in my example, 2 is the divisor) can't fit in!

Part A
GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
a. Write an expression for the area of the trapezoid.
A=(blank)x^2 +(blank)x ft^2

PART B Write an expression for the area of the trapezoid if its height is increased by 4 feet
A=(blank)x^2+(blank)x+(blank)ft^2

Answers

The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x

How to solve an equation?

An equation is an expression that shows the relationship between two or more numbers.

Let x represent the height of the trapezoid.

a) One base of trapezoid measures five feet greater than its height. Hence:

First base = x + 5

The other base is one foot less than twice its height, hence:

Second base = 2x - 1

Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x

b) The height is increased by 4 feet. New height = x + 4

First base = (x + 4) + 5 = x + 9

Second base = 2(x + 4) - 1 = 2x + 7

Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x

The area of the trapezoid is 1.5x² + 2x.

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Someone pls help!!


Construct a circle through points
X, Y, and Z.

Answers

By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.

What is a circle?

It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)

How can you create a circumcircle?

First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.

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Which equation is NOT true?

Parallelogram Q R S T with diagonal S Q. Angle R has measure (15 x + 55) degrees, angle R Q S is (6 x) degrees, angle S Q T is (4 x) degrees, and angle T is (26 x) degrees.
CLEAR CHECK

15+55=6+4
15
x
+
55
=
6
x
+
4
x



15+55=26
15
x
+
55
=
26
x



25+55=180
25
x
+
55
=
180



m∠=6+4

Answers

Answer: can you put them in order so i can read it better?

Step-by-step explanation:

Let a = (2, 1, 0), b = (3, -1, 2), c = (4, 0, 3).
Calculate the angle between a and the plane containing b and c.
Extra effort to show working will be awarded the brainliest.

Answers

The volume of the parallelopiped is 14 cubic units

What is the volume of a parallelopiped?

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

We know that the parallelopiped has sides

a = (2, 1, 0)b = (3, - 1, 2) and c = (4, 0, 3)

Thus, we proceed as follows

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

i × i = 0, j × j = 0, k × k = 0, i × j = k, j × i = -k, j × k = i, k × j = -i, k × i = j, i × k = -j,

So, we have

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2)

Since (a × b) = (5, -7, -2)

Thus, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14

So, the volume is 14 cubic units

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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4

Answers

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.

Answers

The density of the material is 1533.3 grams per quarts.

What is density?

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.

The formula to find the density is Density=Mass/Volume

Density =6900/4.5

Density= 1533.3 grams per quarts

Therefore, the density of the material is 1533.3 grams per quarts.

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5432
-2
X
Which linear inequality is represented by the graph?
Oy< ²x + 3
Oy> ²x+3
Oy> ²x + 3
Oy< ²x + 3

Help please

Answers

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.

How do you find the linear inequality of a graph?

The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.

To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.

When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.

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Which graph is defined by the function given below?
y=(x + 2)(x+7)
10-
A.
-10
OA. Graph A
OB. Graph B
C. Graph C
OD. Graph D
10+
B.
10-
10
10-
D.

Answers

Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .

what is function ?

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

The function's zeros are

0=x+2 x=-2

and

0=x+7 x=-7

Consequently, the graph at y=0 where the function crosses those two points .

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[-12] + [4] find the absolute value of each integer then add them

Answers

Hello there!

Answer:

16

Step-by-step explanation:

[tex] |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0[/tex]

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

question 12 to find the shaded portion

Answers

12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.

What is a trapezoid?

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,

= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].

= [8×8 - 4×4] cm².

= 64 - 16 cm².

= 48 cm².

10. Similarly the figure in (10) is twice the area of the two trapezoids.

11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.

12. The total area is the sum of the areas of the trapezoid and the parallelogram.

13. The larger figure is a rectangle with a right-angle triangle on top.

We have to subtract two rectangles from this to obtain the area of the shaded region.

14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.

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A chef makes small and large snacks to sell at a local art show. He cannot make more than 30
snacks before the show, with no more than 6 large snacks. The chef must make at least 10 small snacks to
earn a profit.
Part A
Let x represent the number of small snacks and y represent the number of large snacks. Given x ≥ 0 and
y 20, select all the inequalities that represent the situation.
0 x≤6
O y ≥ 10
Ox+y≤ 30
O 10x+6y≤ 30
0y≤6
0 x ≥ 10
-01:25

Answers

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

Here, given that,

A chef makes small and large snacks to sell at a local art show.

He cannot make more than 30

snacks before the show, with no more than 6 large snacks.

The chef must make at least 10 small snacks to earn a profit.

Let,

x represent the number of small snacks

and y represent the number of large snacks.

Given x ≥ 0 and y 20

So, we get,

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

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Someone HELPPppp for tmr

Answers

Answer:

y=1x-6

Step-by-step explanation:

First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.

-Hope this helped

My new year's resolution using mathematics word essay 200 words

Answers

This year, I have resolved to improve my mathematical skills. I understand that mathematics is a fundamental skill that is used in many aspects of life, and I want to be more proficient in it.

To achieve this goal, I plan to set aside time each week to practice and study math. I will start by reviewing basic concepts and then move on to more advanced topics. I will also try to find real-life situations where I can apply my mathematical knowledge, such as budgeting and calculating distances and speeds.

In addition to self-study, I plan to seek out opportunities to learn from others. This might involve taking a math class at a local college or finding a tutor to help me with specific concepts that I struggle with.

I am confident that with dedication and hard work, I can make significant progress in my mathematical abilities. By the end of the year, I hope to have a stronger foundation in math that will benefit me in both my personal and professional endeavors.

Britney bought 4 apples, 5 bananas, and 8 oranges at the grocery store.

Which is the ratio of apples to oranges written as a decimal?
A.
1.6
B.
0.4
C.
0.8
D.
0.5

Answers

Answer:

Step-by-step explanation:

The question asks for apples to oranges.

So put the number of apples as a numerator and the number of oranges as a denominator.  Simply put 4 on top and 8 on the bottom:

4/8 then divide:  4 divided by 8 = .5

There is the ratio as a decimal.

0.5

Option D

PLS HELP ASAPPAPA
Type the correct answer in the box. If necessary, use / for the fraction bar.
If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the volume of the prism is
cubic centimeter.

Answers

Answer:  105/512

Explanation:

Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.

(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512

This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.

Answer:

105/512

Step-by-step explanation:

hope this helps

renee spent 1/8 of the day landscaping around the house. she spent 1/2 of that time pulling weeds. what fractions of the day did renee spend pulling the weed? PLS HELP IM HAVING A UNIT TEST ON MONDAY

Answers

Answer:

Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.

Select all the correct answers. The manufacturer of a popular brand of markers is planning to release a new color. To determine which color to add, it mailed out surveys to 5,000 of its customers regarding the general color family they prefer. The returned results are shown in this pie chart. A Pie Chart with four sections representing the color preferences Blues, Greens, Yellows, and Pinks Based on the results, one member of the management team says they should choose the new color from the blue family of colors since a majority of people prefer those colors. Another member doesn’t agree and thinks they should do more research. Which statements would support her request? The difference among the percentages is not statistically significant enough to make the claim of majority. A majority of the management team prefers the yellow family of colors. Not all color families were represented in the survey, which could cause a nonresponse bias. The mail-in survey may have resulted in an undercoverage bias. Since only existing customers were surveyed, the results were not random.

Answers

The statements that would support her request include:

The difference among the percentages is not statistically significant enough to make the claim of majority.Not all color families were represented in the survey, which could cause a nonresponse bias.The mail-in survey may have resulted in an undercoverage bias.Since only existing customers were surveyed, the results were not random.

How to illustrate the information?

A well-known marker brand's manufacturer intends to introduce a new shade. It mailed surveys to 5,000 of its customers asking them which general color family they preferred in order to decide which color to add.

The percentage difference is not statistically significant enough to support the majority claim. The survey did not include families of every color, which might have led to nonresponse bias.

It's possible that the mail-in survey had an undercoverage bias. Also, the results were not random because only current clients were polled.

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Answer: the other guy is correct except for the "since only existing customers...".

Step-by-step explanation:

Just took the test, the others he mentioned were right

The table shows the types and numbers of prizes at a carnival game what is the ratio of stuffed animals to posters

Answers

Answer:

Step-by-step explanation:

3

if α and β are the zero of polynomial p(x) = 3x^2 +2x + 1, find the polynomial whose zeroes are 1-α /1+α and 1-β/1+β.​

Answers

Therefore , the solution of the given problem of function comes out to be 2.

Function Definition

A function connects various inputs together or produces a single output from each input. Simply explained, a function is a collection of equations that are linked to a single, identifiable output. A statement, rule, or law which explains the connection between two variables is known as a function in mathematics (the dependent variable). When a rule of this type is applied, there is just one output. by photographer Alex Federspiel. 

Here,

=> (1−α)(1−β)(1+α)(1+β)

​=>(1−α−β+αβ)​ /(1+α+β=αβ)

=> (1−(α+β)+αβ ) / ( 1+(α+β)+αβ)

=>(1 + 2/3 + 1/3 )/ (1 -2/3 + 1/3)

​=> 2 x 3 /2  =3

=> (1−α)(1+β)+(1−β)(1+α) / (1+α+β+αβ)

=> 3(2−2αβ)/2

=>3(1−αβ)

=>3(1− 1/3 )

=>2

Therefore , the solution of the given problem of function comes out to be 2.

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Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20-to-34 age group are approximately normally distributed with μ = 110 and σ = 25. What percent of people aged 20 to 34 have IQs between 125 and 150?

Answers

The percentage of people aged 20 to 34 that  have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%

What is percentage?

Percentage simply means a proportion of the number as a fraction of 100

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

This implies that  X ~ Normal(x=110, б² = 25)

The z-score probability distribution for the normal distribution is given by;   Z  =   (x-ц)/б ~ N(0,1)

Recall that  population mean = 110 and standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X  125)

 P(X < 150) = P(  <  ) = P(Z < 1.60) = 0.9452

 P(X  125) = P(    ) = P(Z  0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

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Write three ratios that are equivalent to 75% and three
ratios that are equivalent to 100%.

Answers

The three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

First we have to write the equivalent ratios for 75%.

Since, 75% can be written as,

75/100

Simplifying this, 15/20

Again simplifying this, 3/4

Hence, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4.

Now to write the equivalent ratios for 100%.

Since, 100% can be written as,

100/100

Simplifying this, 20/20

Again simplifying this, 4/4

Hence, the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

Therefore,  the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

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How much more interest would be earned on a 100,0000 CD for 9 months than for 6 monthd

Answers

There is a $1,000 additional interest earned on a $100,000 CD (Commercial Paper) for 9 months than for 6 months.

How is the additional interest determined?

The additional interest earned for a 9-month CD over a 6-month CD can be computed using the subtraction operation.

Firstly, the interests on the 9-month CD and 6-month CD are worked out separately, using the interest formula: Principal x Rate x Time.

The interest for the 6-month CD is subtracted from the interest for the 9-month CD.  The result is the difference or additional interest earned.

Commercial Deposit = $100,000

Annual Percentage Rate = 4%

Monthly Percentage Rate = 0.333% (4%/12)

Interest for 9 months = $3,000 ($100,000 x 4% x 9/12)

Interest for 6 months = $2,000 ($100,000 x 4% x 6/12)

The difference in interest earned = $1,000 ($3,000 - $2,000) or ($100,000 x 4% x 3/12)

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Question Completion:

APY = 4%

ASAP! PLEASE HELPP!!
SHOW ALL WORK PLS

Answers

Answer:

  (a, b, c) = (-3, -2, -4)

Step-by-step explanation:

You want to solve the system of 3 equations in 3 variables shown in the attached figure.

Solution

The easiest solution is one provided by a suitable calculator (attached). It tells you ...

a = -3b = -2c = -4

The "work" is entering the problem into the calculator.

Ad hoc

We notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...

  (4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)

  7b +3c = -26 . . . . . simplify

Multiplying the third equation by 4 and adding that to the first equation gives ...

  4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)

  21b +2c = -50 . . . . . simplify

Now, we have two equations in two unknowns.

Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...

  3(7b +3c) -(21b +2c) = 3(-26) -(-50)

  7c = -28 . . . . . simplify

  c = -4 . . . . . . . divide by 7

Using this in the first "ad hoc" equation, we can find b:

  7b +3(-4) = -26

  7b = -14 . . . . . . . . add 12

  b = -2 . . . . . . . . divide by 7

And the values of b and c can go into the last of the original equations to give ...

  -a +4(-2) +2(-4) = -13

  -a = 3 . . . . . add 16

  a = -3 . . . . . multiply by -1

The solution is (a, b, c) = (-3, -2, -4).

__

Additional comment

The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.

The third equation suggests we could make a substitution for 'a':

  a = 4b +2c +13

That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.

The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.

Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.

Use the picture below to answer the question.
6 ft
The angle of elevation from the swimmer to the lifeguard is 35*
Find the distance x from the swimmer to the base of the lifeguard chair.
Find the distance y from the swimmer to the lifeguard.
Round to the nearest tenth as needed.
Select the correct response
x=7.3ft, y= 3.4ft
x=8.6 ft y=10.5 ft
x=3.4ft, y=73 ft
x=10.5 ft, y= 8.6 ft

Answers

Answer: x = 8.6 y=10.5

Step-by-step explanation:

This is a question about trig identities, familiarize yourself with sin, cos, tanIn this problem, our value for degrees is 35 and our opposite side is 6ftOur variables to solve are x and y, x being the adjacent size and y being the hypothenusey has to be the longest size, it being the hypothenuse, so eliminate the first and last optionstan = opposite/adjacent so,  tan(35)=6/x.solve this equation for x, yielding 8.6For y, using the fact that sin=opposite/hypothenusesubstitute and get the equation sin(35)=6/ysolve and get y =10.5x=8.6 and y= 10.5

identify the part of following expression 4x-2y + 6/ 2x

Coefficients:

Constants:

Variable Terms:

Like Terms:

Answers

identification of the expression 4x- 2y + 6 = 2x is

Coefficient: 4, -2, 2Constant: 6Variable term: 4x, -2yLike terms: 4x and 2x

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, a linear expression 4x-2y + 6 = 2x

Coefficient:

Coefficients are the numbers by which the variables in an equation are multiplied

Thus, the Coefficient terms for this equation = 4x, -2y, 2x

Constants:

the constant is the part of the expression that does not vary with the value of x and y.

Thus, constant terms for this equation = 6

variable terms:

These are the terms that vary at the different values of x and y.

Thus, variable terms for this equation = 4x, -2y

Like terms:

Terms that have identical variable parts (same variable(s) and same exponent(s))

thus, Like terms for this expression = 4x, 2x

Learn more about Expressions here:

https://brainly.com/question/14083225

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a) Find the total mass in kilograms of 3500 books, each with mass 800.
b) If the total mass of 8000 apples is 1.04 tonnes, what is the average mass of one apple?​

Answers

A) Total mass of 3500 books is 2,800 kilograms.

B) The average mass of one apple is 130 grams.

A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:

Total mass = (3500 books) * (800 grams/book)

= 2,800,000 grams

= 2,800 kilograms

Therefore, the Total mass of 3500 books is 2,800 kilograms.

B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:

Average mass = (1.04 tonnes) / (8000 apples)

= 130 grams/apple

Therefore, the average mass of one apple is 130 grams.

Learn more about average:

https://brainly.com/question/27193544

Complete the graph
Red Paint 4, 8, 12, 16
Blue Paint 6, _, _, _
Please help

Answers

Answer:

Step-by-step explanation:

10,14,18

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