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The solution to the system of equations is ( 1 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = -6x + 5   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = x - 2   be equation (2)

On simplifying the equations , we get

Substitute the value of y from equation (2) in equation (1) , we get

x - 2 = -6x + 5

Adding 6x on both sides of the equation , we get

7x - 2 = 5

Adding 2 on both sides of the equation , we get

7x = 7

Divide by 7 on both sides of the equation , we get

x = 1

Substitute the value of x in equation (2) , we get

y = 1 - 2

y = -1

Hence , the value of x and y is 1 and -1 respectively

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The approximate sales price for a home in 2020 would be 480

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

Year Avg. Sales Price (Thousands)

1990 149

1995 158

2000 207

We can see that there is an upward trend as the year increases

However, the table does not follow a linear or an exponential pattern

From 2000 and 1990, the change in price is 58

Using this as a guide, we have

2020 = 207 + 58 * 2

2020 = 323

The closest to 323 in the option is 480

Hence, the sales price is 480

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Answer:

Step-by-step explanation:

\(14^2 = b^2+6^2\\b^2 = 14^2-6^2\\b = \sqrt{14^2-6^2} \\ = \sqrt{160}\\ = 12.6491106407\)

Rounding off to nearest tenth:

b ≈ 12.6

tanθ = 6/12.6

\(tan^{-1} (6/12.6)\\ = 25.46334506\\\)

Hence angle A ≈ 25.5

Angle B = 180-25.5-90

Angle B = 64.53665494

Hence, Angle B ≈ 64.5

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Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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The probability that randomly selected person either has high blood pressure or is runner or both is 0.5.

Given:

P(H) = 0.2

P(R) = 0.4

P(H and R) = 0.1

The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.

Favorable Results/Total Results = x/n, where Probability(Event)

P(H or R) = P(H+P(r)-P(H and R)

= 0.2+0.4-0.1

= 0.5

Hence we get the probability as 0.5

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Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

Answer:

(a) 34 cm

Step-by-step explanation:

The formula for perimeter of a rectangle is

P = 2l + 2w, where

Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:

P = 2(12) + 2(5)

P = 24 + 10

P = 34

Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

Yes

Step-by-step explanation:

This relation is a function. Functions must have unique x-values for every y-value, this relation meets those requirements. Also, since this is a graph you can use the vertical line test. To pass the vertical line test you must be able to draw a vertical line on the graph and have it intersect with the function in no more than one place.

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

Based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

In statistics, a dataset is a collection of data that is organized in a specific way. Typically, a dataset consists of multiple data points, where each data point represents an observation or measurement of a particular variable or set of variables.

We can make some general observations to match the data sets to the appropriate MAD value without actually calculating them:

The MAD measures the average distance between each data point and the median of the data set.

Therefore, the larger the MAD value, the more spread out the data set is.

Data set 1 will have the smallest MAD value, since it is the most tightly clustered around the median.

Data set 3 will have the largest MAD value, since it is the most spread out around the median.

Data set 2 will have a MAD value between those of data sets 1 and 3.

Based on these observations, we can match the data sets to the appropriate MAD value as follows:

Data set 1 has the smallest MAD value (7).

Data set 2 has a medium MAD value (9).

Data set 3 has the largest MAD value (11).

Of course, without actually calculating the MAD values, we can't say for certain whether these matches are correct.

Therefore, based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

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Answer:

x = 15 & y = 35

Step-by-step explanation:

\(y = x + 20\)

\(x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15\)

\(y = x + 20 = (15) + 20 = 35\)

The present value of the investment in the fund is $2,455.32.

In order to calculate the present value of the investment in a fund, which is expected to generate $3,000 per year for the next 5 years with an interest rate of 4% per year compounded continuously,

we can use the formula for the present value of an annuity:

PV = A / r,

where PV is the present value, A is the annuity payment, and r is the interest rate.

However, since the interest rate is compounded continuously, we need to use the formula PV = A / e^(rt),

where e is the constant 2.71828, t is the time period in years, and r is the interest rate.

In this case, A = $3,000, r = 4%, and t = 5 years.

Therefore, the present value of the investment is:

PV = $3,000 / e^(0.04 x 5)

= $3,000 / e^(0.2)

= $3,000 / 1.2214

= $2,455.32 (rounded to the nearest cent).

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Answer:

The value is  \(\r p  =  2.9\%\)

Step-by-step explanation:

From the question we are told that

   The  number of singers is  \(N  =  1542\)

   The  sample  size is  \(n  =  650\)

    The  number the number of singers who are professional is k =  19

The  proportion of professional singers is mathematically represented as

       \(p  =  \frac{k}{n}\)

=>      \(p  =  \frac{19}{650}\)

=>    \(p  =  0.029 \)

The  percentage estimate of singers who are professional is

      \(\r p  =  100 * 0.029\)

       \(\r p  =  2.9\%\)

Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

Answer:

\(your \: answer \: is \: option \: a\)

I am sure about this answer.

Step-by-step explanation:

2/3 and 5/12

hope it helps..

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Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

Answer:

91

Step-by-step explanation:

96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Given that, Lena must choose a number between 67 and 113 that is a multiple of 4,6, and 8.

Start listing the multiples of 4 between 67 and 113, which are 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, and 108.

We can then narrow down the list by looking for the multiples of 6, which are 72, 78, 84, 90, 96, and 102, and the multiples of 8, which are 72, 80, 88, 96, 104, and 112.

Since 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Therefore, 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

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Answer:

6

Step-by-step explanation:

because its the middle number

Answer:

C: EAF Is the correct answer

Answer:

Niko purchased 31 raffle tickets.

Step-by-step explanation:

$23.25 ÷ 0.75 = 31.00

The equation for the cost y birr in terms of the distance X driven is y = 20 + 2x.

When the car is leased for 5 days, the cost is 100 + 2x.

From the information, the car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km.

The equation for the distance x will be:

= 20 + (2 × x)

= 20 + 2x.

When the car is leased for 5 days, this will be:

= 5(20) + 2x.

= 100 + 2x

= 100 + 2x

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Answer:

x=78

Step-by-step explanation:

q is 90 degrees since it is a right angle,

p=12

90 plus 12 =102

x=180-102

x=78

y=3x³-x²+5x+10 is the solution of the initial value problem.

A differential equation is an equation that contains one or more functions with its derivatives.

y'=9x²-4x+5 where y(-1)=0

dy/dx=9x²-4x+5

dy=9x²-4x+5 dx

Apply integration on both sides

∫dy=∫9x²-4x+5 dx

y=9x³/3-4x²/2+5x + c

When x = -1, y = 0.

0=9(-1)³/3-4(-1)²/2+5(-1) + c

0=-3-2-5+c

c=10

y=3x³-x²+5x+10

Hence, y=3x³-x²+5x+10 is the solution of the initial value problem.

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Solve the initial value problem

y'=9x²-4x+5 where y(-1)=0

Answer:

\( - \frac{1}{3} \)

Step-by-step explanation:

The slope of a line passing through two points is given by

\(\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }\)

where \((x_1,y_1)\) is the 1st coordinate and \((x_2,y_2)\) is the 2nd coordinate

Given: (3, 0) and (0, 1)

Slope

\( = \frac{0 - 1}{3 - 0} \)

\( = - \frac{1}{3} \)

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