simultaneous equation -- 4x+3y=16 .. 5x-y=1

Answer:1.7

Step-by-step explanation:

One Decimal Place Rule #1: If the last digit in 1.74 is less than 5, then remove the last digit.

One Decimal Place Rule #2: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is less than 9, then remove the last digit and add 1 to the second to the last digit.

One Decimal Place Rule #3: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.When rounding 1.74 to one decimal place we use

One Decimal Place Rule #1. Therefore, the answer to "What is 1.74 rounded to 1 decimal place?" is:

The estimated answers by rounding each number to a 1 decimal place and then adding them together are 14.3, 35.9, 30.6, respectively.

Here are the estimated answers to the following calculations:

12.55 and 1.74 rounded to 1 decimal place are 12.6 and 1.7. The sum is 14.3.

30.38 and 5.49 rounded to 1 decimal place are 30.4 and 5.5. The sum is 35.9.

19.16 and 11.42 rounded to 1 decimal place are 19.2 and 11.4. The sum is 30.6.

The sum of all three calculations is 14.3 + 35.9 + 30.6 = 80.8.

To estimate the answers, we simply rounded each number to 1 decimal place. This means that we lost some precision, but the overall accuracy of the estimates is still good. For example, the actual sum of 12.55 and 1.74 is 14.29, which is very close to our estimate of 14.3.

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Simple bivariate correlations, which measure the strength and direction of the linear relationship between two variables, are not sufficient for establishing causation for several reasons:

1. Correlation does not imply causation: Just because two variables are correlated does not mean that one causes the other. There could be a third variable, known as a confounding variable, influencing both the variables in the correlation. A correlation only indicates that the variables co-vary, but it does not explain the direction or the reason behind this relationship.

2. Reverse causation: Correlation cannot determine the direction of causation. It is possible that the relationship between two variables is bidirectional, and one variable causes changes in the other, but the reverse is also true. Without further evidence or experimental manipulation, we cannot determine which variable is causing changes in the other.

3. Spurious correlations: Sometimes, two variables may show a significant correlation, but this relationship is purely coincidental and does not have a meaningful causal connection. These spurious correlations may arise due to chance or data anomalies, leading to incorrect assumptions about causation.

4. Omitted variable bias: Bivariate correlations do not account for all the potential variables that could influence the relationship between the two variables being studied. Omitting relevant variables could lead to biased estimates and incorrect conclusions about causality.

5. Experimental control: Establishing causation typically requires conducting controlled experiments where the researcher can manipulate one variable and observe its effects on the other while controlling for other confounding factors. Bivariate correlations do not involve experimental manipulation, making it challenging to establish causal relationships.

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Answer:

4/9

Step-by-step explanation:

Hello!

We need to convert the repeating decimal to a fraction.

Let x = 0.44444.....

Therefore, the fraction is 4/9.

The fraction which represent the given decimal number is 4/9.

The given recurring decimal is 0.4444........

Let x=0.4444........ -------(i)

Multiply the given equation (i) by 10, we get

10x=4.4444........ -------(ii)

Subtract equation (i) from (ii), we get

10x-x=4.4444........ - 0.4444........

9x=4

x=4/9

Therefore, the fraction which represent the given decimal number is 4/9.

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The equation of the linear trendline is y = 18.1x + 51.97

The linear trendline is the line which best minimizes the sum of squared error for the data. The linear trendline is usually written in slope-intercept form ; mx+b.

m= slope of the equation

b = Intercept

The equation of the trendline obtained using a regression calculator is y = 18.1x + 51.97. With a slope value of 18.1 and intercept value of 51.97.

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Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

\(r = \frac{1}{4}\)

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

\(s_n=\frac{a_1(1-r^n)}{1-r}\)

common ratio, n=4 and equate to 170.

\(\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170\)

\(\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128\)

Answer:

The first term is 128

The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:

The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

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The question is incomplete:

A farmer sells 8.1 kilograms of apples and pears at the farmer's market. 2/5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answer:

She sold 4.86 kg of pears at the farmer's market.

Step-by-step explanation:

With information provided, you know the amount of kilograms of  apples and pears sold and that 2/5 of this weight is apples, so you can find first the number of kilograms of apples sold by multipying 2/5 for 8.1 kilograms:

2/5*8.1=3.24 kg

Now, you can find the kilograms of pears that the farmer sold by subtracting the kilograms of apples sold from the total amount of apples and pears sold:

8.1-3.24=4.86 kg

According to this, the answer is that she sold 4.86 kg of pears at the farmer's market.

The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.

A linear equation is represented by ax + b = 0. The solution for this equation is

ax + b = 0

⇒ ax = -b

⇒ x = -b/a

The given equation is

7/8 + x = 1/4

On simplifying,

x = 1/4 - 7/8

⇒ x = -5/8

Therefore, the solution of the given equation is -5/8.

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Answer:

\( \frac{ \sqrt{ - 75} }{ \sqrt{25} } \\ \\ \frac{ - 5625}{625} \\ \\ - 9\)

The solutions are:

sin(a)  = 24/25

tan(a) = 24/7

For a given point (x, y) and an angle "a" measured counterclockwise from the positive x-axis to a ray that connects the origin with our point, we can think on the situation as a triangle rectangle.

Where the ray is the hypotenuse, the x-component is the adjacent cathetus, and the y-component is the opposite cathetus.

So we have:

x = adjacent cathetus

y = opposite cathetus

h = hypotenuse = √(x^2 + y^2)

Then the trigonometric relations become:

cos(a) = x/√(x^2 + y^2)

sin(a) = y/√(x^2 + y^2)

tan(a) = y/x

Now, we know that we have:

cos(a) = 7/25

then we can see that:

x = 7

and

h = 25 = √(7^2 + y^2)

We can solve the above equation for y:

25 = √(7^2 + y^2)

25 = √(49 + y^2)

25^2 = 49 + y^2

625 - 49 = y^2

√576 = y = 24

Then we have:

x = 7

y = 24

h = 25

Now we can return to our known trigonometric relations and get:

sin(a) = y/√(x^2 + y^2) = 24/25

tan(a) = y/x = 24/7

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Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are  obtuse, scalene, equilateral, isosceles etc.

An isosceles triangle is a triangle with two equal sides, the base angles of an isosceles triangle is equal.

Since ΔMNP is an isosceles triangle with MN = PN, then:

∠QMN = ∠QPN (base angles of an isosceles triangle are equal)

∠MNQ = ∠PNQ (NQ bisects ∠MNP producing two equal angles)

∠MQN = ∠PQN (right angles)

There is no mode of the number of girl in the three classes.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.

Given:

The data for boys: 15, 12, 12

The data for Girls: 14, 12, 16

As, mode is the most repeating data.

We can see that the data repeats in boys but not for the Girls.

So, number of boys have the mode but the number of girls do not have the mode.

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Answer:

13

Step-by-step explanation:

2^2x13 is right

Answer:

128

Step-by-step explanation:

Step-by-step explanation:

Answer:

correct answer is B hope this helps :)

Step-by-step explanation:

The statement describes Sal’s purchase

Sal used a debit card and paid a total of $324.80 for the stereo.

The statement includes deposits, charges, and withdrawals, as well as the period's initial and ending balances. Account holders typically scan their bank statements once a month to assist keep track of their costs and spending, as well as to look for any fraudulent charges or errors.

Sal and Jen went shopping together and bought the same vehicle stereo. Sal made the purchase with a credit card, and the full money was instantly deducted from his bank account.

Jen used a credit card to complete the purchase, and she received a statement within 15 days.

She made monthly payments of $21.30 for the next 18 months until the account was paid in full. The total payment included interest of $58.60.

Sal used a debit card and paid a total of $324.80 for the stereo," says the document that explains Sal's purchase.

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The answer is 19 because it an easy question

a and b are correct

c is wrong

d can't be decided, because it can be true for one case, but not for others.

so only go for a and b

Answer:

B. The function is linear. (A and D COULD work)

Step-by-step explanation:

If the graph of a direct variation function has a slope of -3, then we know that the function is linear, and that m in the equation y = mx + b is -3. However, option A could be incorrect since we don't know if there is a y-intercept or not. C is wrong because of -3 being the slope, and D would only be true if A was also correct. So that leaves B. (If you know that there is more than one option, then A, B, and D are correct.)

Answer:

Step-by-step explanation:

4) ∠CTB , ∠PTA are vertical angles

If sum of two angles add up to 90, then they are Complementary angles.

If sum of two angles add up to 180, then they are Supplementary angles.

∠FTA and ∠ATR are supplementary angles

5) ( 1 , 2 )  & (3 , 6)

\(Midpoint=\left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)\)

                \(= \left(\dfrac{1+3}{2},\dfrac{2+6}{2}\right)\\\\=\left(\dfrac{4}{2} \ , \dfrac{8}{2}\right)\)

             \(\=\left(\dfrac{4}{2},\dfrac{8}{2}\right)\)

             = (2 , 4)

6) Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

                  \(=\sqrt{(3-1)^{2}+(6-2)^{2}}\\\\=\sqrt{2^{2}+(4)^{2}}\\\\=\sqrt{4+16}\\\\=\sqrt{20}\\\\= 4.47\)

The solution to the system of equations 6x - y = 21 and -5x + y = -18 is x = 3 and y = -3.

To solve the system of equations:

6x - y = 21   ...(1)

-5x + y = -18  ...(2)

We can use the method of elimination by adding the two equations together to eliminate the variable y:

(6x - y) + (-5x + y) = 21 + (-18)

Simplifying the equation:

6x - y - 5x + y = 21 - 18

Combining like terms:

x = 3

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation (1):

6x - y = 21

6(3) - y = 21

18 - y = 21

Subtracting 18 from both sides:

-y = 3

Multiplying by -1 to isolate y:

y = -3

Therefore, the solution to the system of equations is x = 3 and y = -3.

To verify this solution, we substitute these values back into the original equations:

6x - y = 21

6(3) - (-3) = 21

18 + 3 = 21

21 = 21

The equation holds true for x = 3 and y = -3.

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Let's denote the radius of the red circle by r, then the circumference of the red circle is 2πr. We know that the perimeter of the red circle is 37.7 inches, so:

2πr = 37.7

Solving for r, we get:

r = 37.7 / (2π) = 6.002 inches (rounded to three decimal places)

The radius of the yellow circle is 6 inches larger than the radius of the red circle, so:

r_yellow = r_red + 6 = 12.002 inches

Therefore, the circumference of the yellow circle is:

2πr_yellow = 2π(12.002) = 75.4 inches (rounded to one decimal place)

So the perimeter of the next-largest (yellow) circle is approximately 75.4 inches.

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The standard form of the quadratic equation is:

y = 3x² + 24x + 45

To do it, we just need to expand the product in the right side of the given quadratic, here we start with:

y = 3(x + 3)(x + 5)

Expanding the product we will get:

y = 3*(x + 3)*(x + 5)

y = (3x + 9)*(x + 5)

y = 3x*x + 3x*5 + 9x + 9*5

y = 3x² + 15x + 9x + 45

y = 3x² + 24x + 45

That is the standard form.

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To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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Answer:

the square root of 100 is 10

10x10=100

Answer:

the square root of 100 is 10

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D 4x2-8x+20

The correct answer is r = 3/2.

What is Common ratio?

The common ratio in geometric progression is the ratio of any phrase in the series divided by the previous term. As stated in the definition, we can compute the common difference of a geometric progression by dividing any word by its preceding term.

The common ratio of a geometric sequence is the factor by which each term is multiplied to obtain the next term. In this case,

The common ratio is,

r = 27/2 / 9

r = 3/2.

The correct answer is r = 3/2.

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The bottom is moving at a rate of \(4\sqrt{3}\) ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.

Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.

We have AB = y = distance of top of the ladder from the wall

BC = x = distance of bottom of the ladder from the wall

AC = z = height of the ladder = 12 ft (given)

The top of the ladder AB is sliding down at a rate of 4 \(ft/s\)

∴ \(\frac{dy}{dt}\) = - 4 ft/s (negative sign indicates that the top is sliding downwards)

Let the rate at which the bottom of the ladder is sliding be \(\frac{dx}{dt}\)

Now in the right angled triangle \(ABC\) by using Pythagoras theorem we have,

\(AB^{2} + BC^{2} =\)\(AC^{2}\)

\(y^{2} +x^{2} = z^{2}\)    (equation 1)

When x = 6ft and z = 12 ft,

\(y^{2} +6^{2} = 12^{2}\)

⇒ \(y^{2} = 144 - 36\)

⇒ \(y^{2} = 108\)

⇒ y = √108

⇒ y = 6 √3 ft

Differentiating equation 1 with respect to \(time\) we get,

\(\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})\)

⇒ 2y\(\frac{dy}{dt}\) + 2x\(\frac{dx}{dt}\) = 2z\(\frac{dz}{dt}\)

Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,

∴ 2(6√3) (-4) + 2(6)\(\frac{dx}{dt}\) = 2(12)(0)

⇒ -48√3 + 12\(\frac{dx}{dt}\) = 0

⇒ 12\(\frac{dx}{dt}\) = 48√3

⇒ \(\frac{dx}{dt} = \frac{48\sqrt{3} }{12}\)

⇒ \(\frac{dx}{dt} = 4\sqrt{3}\) ft/s

Hence the rate at which the bottom of the ladder is sliding is \(\frac{dx}{dt} = 4\sqrt{3}\) ft\s

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Answer:

Step-by-step explanation:

Multiplication and division are closely related, given that division is the inverse operation of multiplication. When we divide, we look to separate into equal groups, while multiplication involves joining equal groups. ... If we divide this product by one of the factors, we get the other factor as a result.