elimination method. please help

3x+4y=21
3x-2y=11

a) Using a system of equations, the amount invested in the mutual fund that earned 6% was $1,600.

b) The amount invested in the mutual fund that earned 4% was $200.

A system of equations is two or more equations solved concurrently.

A system of equations is also called simultaneous equations.

Total investment = $1,800

Profit from investment A = 6%

Profit from investment B = 4%

The total investment profit = $76

Let A = Investment A and B = Investment B

A + B = 1,800

A = 1,800 - B

0.06A + 0.04B = 76

0.06(1,800 - B) + 0.04B = 76

108 - 0.06B + 0.04B = 76

108 - 0.02B = 76

-0.02B = -32

B = 1,600

A = 200 (1,800 - 1,600)

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Answer:

∠ 1 = 25° , ∠ 2 = 155°

Step-by-step explanation:

∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is

x - 6 + 5x = 180

6x - 6 = 180 ( add 6 to both sides )

6x = 186 ( divide both sides by 6 )

x = 31

Then

∠ 1 = x - 6 = 31 - 6 = 25°

∠ 2 = 5x = 5 × 31 = 155°

The weight of all of the rocks to the nearest tenth is 6.085 pounds .

Given :

in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.

Let x be the total weight or all the weight of rocks .

3 = 49.3 % * x

3 = 49.3 * 1 / 100 * x

3 * 100 = 49.3 * x

300 = 49.3 * x

divide with 49.3 on both sides

300 / 49.3 = 1 * x

x = 300 / 49.3

= 6.085 pounds

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If m is the centroid of triangle abc, am = 44, ce =54, and dm = 23, then each missing measure fm=88 and ce=44.

The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Step 1: Identify each vertex's coordinates.

Step 2: Add together and divide by three all the x values from the coordinates of the three vertices.

Step 3: Add together all the y values from the three vertices and divide the result by three.

Step 4: The centroid coordinate is determined from the values collected in stages 2 and 3.

the ratio of both segments is 2:1.

where;

am = 44 and dm = 23

the longer segment is double of shorter one:

2*23 = 46.

Therefore,

fm = 46-23

= <<23=23>>23

now finding ce:

= 2*44

= 88, so

ce measures

= 88-44

=44.

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In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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Answer:

[tex]log_{9} 59,049=5[/tex]

Step-by-step explanation:

The equation in logarithmic form is ㏒₉59,049 = 5

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given is an equation, 9⁵ = 59,049, we need to convert it into logarithmic form.

So,

y = aˣ, then x = ㏒ₐY

Applying the same,

9⁵ = 59,049

㏒₉59,049 = 5

Hence, the equation in logarithmic form is ㏒₉59,049 = 5

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The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.

How to solve function?

h(x) = −3|x − 1| + 4

Substitute x = -5

h(-5) = −3|(-5) − 1| + 4

= -3|-6| + 4

= -18 + 4

= -14

h(-5) = -14

Hence, The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.

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the area will be fall in between 100≤ 20x ≤1000.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides

All the internal angles of a quadrilateral sum up to 360°.

The area of a rectangle is A = a*b

Here in the figure the length is given 4x and the breadth is 5.

The area is given in between 100≤A≤1000

So this area will be A = 5x*4 = 20x

Now the area will be lie in between 100≤ 20x ≤1000

hence, the area will be fall in between 100≤ 20x ≤1000.

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In linear equation, Clark rode 2 kilometres more than Denise .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                       Equations whose variables have a power of one are called linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Denise rode 3 kilometres .

Clark rode 5000 metres which is 5 kilometres .

So , Clark rode 2 kilometres more than Denise .

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Step-by-step explanation:

so pretty much replace -3, 0 and 3 into the equation

-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30

0 squared is 0 so the 2nd one would be 0

3 squared times 3 is 27 and subtracted by 3 is 24.

Answer: n= 1

Step-by-step explanation:

8n+7=-4n+19

First, subtract 7 from both sides

8n = 4n +12

Then add 4n from both sides

12n = 12

Then divide by 12 from both sides

n= 1

If you can please give me a Brainliest, thank you!

Answer: n = 1

Step-by-step explanation:

First, you could start off by bringing the -4n to the left side:

8n + 7 = -4n+19  →  12n + 7 = 19

Next, you take the 7 on the left side of the equals sign and subtract it from the 19:

12n + 7 = 19 → 12n = 12

Finally, you divide the 12 on the right by the 12 on the left:

12n = 12  →  n = 12/12

A number over itself will always be 1, so n = 1.

Based on the residual plot, is a linear model is not appropriate for summarizing this relationship. Therefore, the correct answer option is: C. A linear model is not appropriate because the residual plot shows a clear pattern.

In Mathematics, a residual plot is sometimes referred to as scatter plot and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation (relationship) between the data set.

Mathematically, a linear model can be represented by this mathematical expression; y = mx + b.

Where:

By critically observing the residual plot (scatter plot) which shows a relationship between the residuals and quarters since January 2011, we can reasonably infer and logically deduce that a linear model is not appropriate because there is a clear pattern between the data points.

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Step-by-step explanation:

First, you should translate everything into math. So,

"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)

"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)

Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:

(3C + 2) + C = 90

4C + 2 = 90

4C = 88

C = 22

Plugging C = 22 back into either equation (1) or (2) gives us

B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)

Thus, ∠B = 68º; ∠C = 22º

hope this helps

Answer:

x = -4

Step-by-step explanation:

(4x-5)/(3x+5) = 3

1. Multiply both sides by 3x+5

  4x-5 = 3(3x+5)

2. Expand

   4x-5 = 9x+15

3. -4x from both sides

   -5 = 5x+15

4. -15 from both sides

  -20 = 5x

   x = -4

It is greater than 3

x = 4

We can solve the equation as

(4x-5) = (3x+5)*3

4x-5=9x+15

x = 4

Let the cost of each gift card be x.

Three of them will cost 3x.

We need the total cost be no more than $2 above or below $60.

This can be represented as:

and

or as combined inequality:

There are 1240 students in the school.

What is Proportionalities (Ratios)?

It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day.  The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.

In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.

If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:

( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls

[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]

Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.

Now let's simplify the equation and solve for x :

[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]

If we have 558 girls, the number of boys is then:

x+124=558+124=682boys

Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students

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Answer:

The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.

To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:

sum = (n/2)(a1 + an)

where n is the number of terms in the series, a1 is the first term, and an is the nth term.

Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:

sum = (infinity/2)(-1 + infinity)

Since the series contains an infinite number of negative terms, it is divergent.

By applying the exterior angle of a triangle theorem, m<WUV = 19°

What is an exterior angle of a triangle?

The angle created by one side of a triangle and the subsequently extended side is known as the external angle of a triangle. A triangle has three exterior angles, and the sum of those three external angles is always 360 degrees.

Here, we have

The given parameters are;

ΔUVW with side UW extended to X

m∠UVW = (x + 19)°

m∠VWX = (5x +14)°

m∠WUV = (x + 13)°

Applying the exterior angle of a triangle theorem:

m∠WUV + m∠UVW = m∠VWX

(x + 13)° + (x + 19)° = (5x +14)°

2x + 32 = 5x + 14

32 - 14 = 5x - 2x

18 = 3x

x = 6°

Now, we put the value of x in m∠WUV = (x + 13)° and we get

m∠WUV = (6+13)°

m∠WUV = 19°

Hence, by applying the exterior angle of a triangle theorem, m<WUV = 19°

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Answer:

6

Step-by-step explanation:

RS and QT are parallel because it is a trapezoid. This means that the transversal applies. Look at the picture attached to understand what I mean.

So, we know that 18x - 13 = 180(degree of a line)-85. Then, solve the equation.

18x-13=95

18x=108

x=6

Practicing mathematics will bring Peace and Harmony in your life It provides us with a method for comprehending patterns, quantifying relationships, and making future predictions.

In the absence of animosity and violence, peace is the idea of communal friendship and harmony.

Critical thinking about our surroundings is referred to as analytical thinking. Our capacity for reasoning is what allows us to approach problems logically. The ability to think critically and rationally is crucial since it aids in issue solving and solution seeking.

Understanding the world through mathematics also helps us develop mental discipline. Math fosters logical reasoning, critical analysis, inventiveness, abstract or spatial thinking, problem-solving aptitude, and even good communication abilities.

Therefore, It gives us a way of understanding patterns, measuring relationships, and forecasting the future.

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When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:

(1) The rectangle's diagonals will line up exactly with one another.

(2) A rectangle's diagonals are symmetry lines.

We deduce from the question that the rectangle is mirrored across the symmetry line.

When done, the rectangle's half will fall directly on the other half.

This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.

According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.

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Step-by-step explanation:

The diagram is very helpful, so really go off of that. Coordinates are written in the form (x,y). If you look at the signs (either there's a negative sign, - , or no sign at all, meaning it's +) for each number in a coordinate pair, you can see where each coordinate should go.

If you look at the last example (3, -3), the first digit is positive + and the second digit is negative - . When you look at the diagram, coordinates in the form of (+, -) are put in quadrant 4.

The number of feet of light used by Chad is 176 feet

From the question, we have the following parameters that can be used in our computation:

Length = 55 feet

Width = 48 feet

We start by calculating the distance from the end of the width till the beginning of the length

This is represented by the following Pythagoras theorem

Distance = √(Length² + Width²)

So, we have

Distance = √(55² + 48²)

Evaluate

Distance = 73

The number of feet is then calculated as

Feet = Length + width + distance

So, we have

Feet = 55 + 48 + 73

Evaluate

Feet = 176

Hence, the total distance is 176 feet

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The fraction of the cake that was ron's pieces is 1/5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:

= 1 - 1/5

= 4/5

The fraction of the cake that was ron's pieces will be:

= 2/(1+3+4) × 4/5

= 2/8 × 4/5

= 8/40

= 1/5

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Answer:

a - April

b - may

c - they neither made nor lost money that month

hope that helps :)

Step-by-step explanation:

Answer: a) - March

              b) - May

              c)- it neither made nor lost money that month

Step-by-step explanation:

a) - because -386 is the least out of all of them

b) - because 271 was the most out of all of them

c) - it didn't lose or make it just stayed the same as it was

Sean's real average speed was less than his predicted 40 mph.

Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.

Hence, Sean's real average speed was less than his predicted 40 mph.

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The dividend yield per stock share per year is 9.88 %

What Is the Dividend Yield?

The dividend yield, expressed as a percentage, is a financial ratio (dividend/price) that shows how much a company pays out in dividends each year relative to its stock price.

Given,

The stock price per share is = $85

Quarterly dividend is = $2.10

Now, for to find Dividend yield

Dividend Yield = Annual Dividends Per Share / Price per share

Annual Dividends Per Share = 4 * $2. 10

                                                = $8.4

Price per share = $85

Now, plug in the values

Dividend Yield = 8.4 / 85

                         = 0.0988

Now, in percentage is

Dividend Yield = 0.0988 * 100

                          = 9.88 %

Hence, the dividend yield per stock share per year is 9.88 %

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35 is  diagonals does a convex decagon have .

What does a pentagon basic definition entail?

A geometric figure with five sides and five angles is called a pentagon. Here, "Penta" stands for five, while "gon" is an angle.

                      One of the different kinds of polygons is the pentagon. For a standard pentagon, the total internal angles come to 540 degrees.

There are a total of  ¹⁰C₂  ways to connect two different vertices. But connecting neighbouring vertices doesn't count, so we have to exclude the sides from our consideration. There are 10 sides, so we need to take away 10 ways from the 45 ways possible to get the number of diagonals.

 Number of diagonals in a decagon = 35

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