Solve the system of linear equations using any method

The length of ST obtained using Pythagorean Theorem is about 13.2 units

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is the sum of the square of the other two legs of the triangle.

The length of the segment [tex]\overline{PR}[/tex] = 18

[tex]\overline{RS}[/tex] = [tex]\overline{SP}[/tex] = 16 (Radial length of the same circle)

Triangle ΔSRP is an isosceles triangle, therefore, ∠SRP ≅ ∠SPR

[tex]\overline{ST}[/tex] ≅ [tex]\overline{ST}[/tex] (Reflexive property of congruence)

Triangles ΔRST and ΔPST are congruent by the Hypotenuse Leg, HL rule of congruent triangles

Therefore; RT ≅ PT

RT + PT = 18

RT + RT = 18

2 × RT = 18

RT = 18/2 = 9

RT = 9

Therefore, ST, can be obtained using Pythagoras Theorem as follows;

ST = √(16² - 9²) = 5·√7 ≈ 13.2

The length of the side ST is about 13.2 units long

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Answer:

arc length ≈ 37.7

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{135}{360}[/tex] ( r is the radius )

   = 2π × 16 × [tex]\frac{3}{8}[/tex]

   = 32π × [tex]\frac{3}{8}[/tex]

  = 4π × 3

  = 12π

  ≈ 37.7 ( to the nearest tenth )

The measure of angle C is 80°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It can also be called inscribed quadrilateral.

A theorem if circle geometry states that the opposite angles of a cyclic quadrilateral are supplementary. This means the sum of. opposite angles of a cyclic quadrilateral is 180°

Therefore 3x-59+2x-1 = 180

5x -60 = 180

5x = 180+60

5x = 240

x = 240/5

x = 48

angle A = 2x+4 = 2×48+4

= 100°

therefore angle C = 180-(angle A)

C = 180-100

= 80°

therefore the measure of angle C is 80°

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Answer: To calculate the mean square treatment (MST), we need to have the sums of squares for treatment (SST) and the degrees of freedom for treatment (dfT).

Assuming that there are k treatment groups and a total of n observations, we can calculate SST and dfT as follows:

SST = Σ(xi - x_bar)^2 - Σ(yi - y_bar)^2 / n

where xi is the dried weight of plants for the i-th treatment group, x_bar is the mean dried weight of plants for all treatments combined, yi is the dried weight of plants for the control group, and y_bar is the mean dried weight of plants for the control group.

dfT = k - 1

Once we have calculated SST and dfT, we can find MST by dividing SST by dfT:

MST = SST / dfT

Note that SST is the sum of squares for treatment, which represents the variation in the response variable that is due to the different treatment conditions. MST represents the average amount of variation in the response variable that can be attributed to the treatment conditions.

Without knowing the specific values for the dried weight of plants, it is not possible to calculate SST and dfT, and therefore the MST.

Step-by-step explanation:

The equation of a line perpendicular to line AB and passing through point (0,2) is y = -4x + 2.

The given line has a slope of 1/4, so the slope of any line perpendicular to it will be -4 (the negative reciprocal).

Using the point-slope form of a line, we can write the equation of the line passing through the point (0,2) with slope -4 as

y - 2 = -4(x - 0)

Simplifying, we get

y - 2 = -4x

Adding 2 to both sides, we get

y = -4x + 2

Therefore, the equation of the line passing through the point (0,2) which is perpendicular to the line y=1/4x+5 is y = -4x + 2.

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Carmen will be paid $36 in interest in the first 3 years on her deposit of $600 at a simple interest rate of 2% per year.

Given

Principal: $600

Annual interest rate: 0.02

Time period: 3

To Find

Interest ?

Solution

To calculate the interest that Carmen will be paid in the first 3 years on her deposit of $600 at a simple interest rate of 2% per year, we can use the formula:

I = P * r * t

where I is the interest, P is the principal (the initial amount deposited), r is the annual interest rate (as a decimal), and t is the time period (in years).

Substituting the given values, we get:

I = 600 * 0.02 * 3

I = $36

Therefore, Carmen will be paid $36 in interest in the first 3 years on her deposit of $600 at a simple interest rate of 2% per year.

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Answer:

17.7

Step-by-step explanation:

using the pythagorean theorem, plug in and solve.

hi

with Pythagoras we have :

13²+12² = 313

so answer is [tex]\sqrt{313}[/tex] ≈ 17.7  rounded.

The value of the surd form √14 is 3. 74

The square root of a number is a value that, when multiplied by itself, equals the original number.

It is represented by the symbol √ and is a way to find the side length of a square given its area or the length of a diagonal in a right triangle.

From the information given, we have that;

The expression is √14

We can see that the value √14 is a surd which can no longer be simplified into a whole or rational number.

To determine the square root, we use the calculator

√14

3. 7416

In the nearest tenth, we get;

3. 74

Hence, the value is 3. 74

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The coordinates of point U are (-h, 0).

To find the coordinates of point U in the parallelogram RSTU, we can use the properties of parallelograms. In a parallelogram, opposite sides are parallel, and hence they have the same slope.

Given that point S is at (0, 0), we can calculate the slope of RS as follows:

Slope of RS = (y2 - y1) / (x2 - x1)

= (0 - g) / (0 - (-f)) (Substituting coordinates of R and S)

= g / f

Since RS and TU are opposite sides of the parallelogram, they must have the same slope. Thus, the slope of TU is also g / f.

Given that point T is at (h, 0), we can calculate the equation of the line TU in point-slope form using the slope we just found:

y - y1 = m(x - x1) (Point-slope form of a line)

where;

Plugging in the values, we get:

y - 0 = (g / f)(x - h)

Simplifying, we get:

y = (g / f)x + gh / f

Now, we can substitute the coordinates of point U, which are (x, y), into the equation we just found:

y = (g / f)x + gh / f

y = (g / f)x + gh / f

Since U lies on the x-axis (i.e., y = 0), we can set y = 0 in the equation and solve for x:

0 = (g / f)x + gh / f

(g / f)x = -gh / f

x = -h

So, the x-coordinate of point U is -h.

Now, we can substitute the value of x = -h into the equation we found earlier to get the y-coordinate of point U:

y = (g / f)x + gh / f

y = (g / f)(-h) + gh / f

y = -gh / f + gh / f

y = 0

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The value of cos(2θ) is 1/2

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

If cos(tetha) = √3/2

this means the adjascent is √ 3 and the hypotenuse is 2

therefore ;

opp = √ 2²- √3)²

= √4-3

= √1

= 1

therefore sin(tetha) = 1/2

cos(2θ) = cos²(tetha) -sin²(tetha)

cos²(tetha) = (√3/2)² = 3/4

sin²(tetha) =( 1/2)² = 1/4

cos(2θ) = 3/4 - 1/4 = 2/4 = 1/2

therefore the value of cos(2θ) is 1/2

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Answer:

[tex]x^{2} + y^{2} = 36[/tex]

Step-by-step explanation:

The form of the equation for a circle is [tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex], where [tex](h, k)[/tex] is the center and [tex]r[/tex] is the radius. Here, (h, k) is (0,0) and r is 6, so the equation would just be [tex]x^{2} + y^{2} = 36[/tex].

Answer:

x² + y² = 36 (top right answer)

Formula for the circle:

(x - h)² + (y - k)² = r²

h = X center point  

k = Y center point

Answer: To write the equation of a line parallel to AB through a given point, we need to follow these steps:

Find the slope of the line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1)/(x2 - x1)

Let the coordinates of points A and B be (x1, y1) and (x2, y2) respectively. Then, the slope of the line AB is:

m = (y2 - y1)/(x2 - x1)

Since we want to find the equation of a line parallel to AB, the slope of this line will also be equal to m.

Let the given point be (x0, y0). Using the point-slope form of the equation of a line, we can write the equation of the line passing through (x0, y0) with slope m as:

y - y0 = m(x - x0)

Substituting the value of m found in step 1, we get:

y - y0 = (y2 - y1)/(x2 - x1) * (x - x0)

This is the equation of the line parallel to AB passing through the point (x0, y0).

Note that we assume that the line passing through A and B exists and is not vertical. If the line is vertical, then its slope is undefined, and we cannot find the equation of a parallel line using this method. In that case, we need to use a different method to find the equation of the line.

Step-by-step explanation:

Answer:

A circle graph would be appropriate here.

According to the given information, Julie's new bank balance was $1,609.01

To calculate Julie's new bank balance, we need to subtract the total amount of checks she wrote from her initial balance, and then add the total amount of deposits she made.

Total amount of checks = $62.41 + $224.14 + $12.92 + $357.16 = $656.63

Total amount of deposits = $197.34 + $879.13 = $1,076.47

New bank balance = Initial balance - Total amount of checks + Total amount of deposits

New bank balance = $1,189.17 - $656.63 + $1,076.47

New bank balance = $1,609.01

Therefore, Julie's new bank balance was $1,609.01.

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Answer:

22

i took this one

Answer:

17.5

Step-by-step explanation:

94 divided by 4 is 23.5 and I subtracted 6 from 23.5

The required, graph of both lines has been shown where the common solution is (0, 2).

I apologize for the error in my previous solution. Here's the corrected solution:

To solve the system of linear equations x + 2y = 4 and -2x + 5y = 10 graphically, we need to plot the graphs of the two equations on the same set of axes and find the point where they intersect.

The graph of both lines has been shown where the common solution is (0, 2).

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Answer:

y=2/3x-6 1/3

Step-by-step explanation:

y+1=2/3(x-8)

first do the distributive property.

2/3*x=2/3x

2/3*-8= -5 1/3

2/3x-5 1/3

then we subtract 1 from both sides

y=2/3x-6 1/3

According to arithmetic progression, the sum of the first 100 terms is 7500 and the common difference is 0.

In this case, we know that the first term (a1) is 75, and the 25th term (a25) is also 75. So we can use the formula with n = 25:

common difference = (a25 - a1) / (25 - 1)

common difference = (75 - 75) / 24

common difference = 0

Since the common difference is 0, this means that all the terms in the sequence are the same. In other words, this is not really an arithmetic progression - it's just a sequence of 100 terms, all of which are equal to 75.

To find the sum of the first 100 terms, we can use the formula:

sum = (n/2)(first term + last term)

where n is the number of terms, and the last term is the 100th term.

In this case, we know that the first term (a1) is 75, and all the terms are the same. So the last term (a100) is also 75. Therefore, we can use the formula with n = 100:

sum = (100/2)(75 + 75)

sum = 50 x 150

sum = 7500

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Answer:

1.5

Step-by-step explanation:

Move the decimal point two places to the left to go from a percentage to a decimal.

Answer:



Step-by-step explanation:

Answer:

I found a video that provides the answer key for the Ankara Güçlendiren

Step-by-step explanation:

The volume of the given cone with a height of 17.3 and a diameter of 10.4 is  489.87 cubic cm

The volume of any cone can easily be determined by the formula (pi*r*r)*(h/3) where pi has the value of 3.14, 'r' is the radius of the cone, and 'h' is the given height of the cone.

Here in the given question, we can see that the height(h) given here is 17.3cm and the diameter is 10.4cm with which we can find the radius because we know the radius is the half of diameter so 'r' will be 5.2cm.

Now just putting the values of 'h' and 'r' in the given formula (pi*r*r)*(h/3)  we get the volume of the cone which is 489.87 cubic cm.

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Answer:

Step-by-step explanation:

here,

height h= 17.3cm

diameter= 10.4cm

therefore, radius r will be 5.2cm

pi= 3.14

solution:

volume v of cone= 1/3*pi*r2*h

= 1/3*3.14*5.2*5.2*17.3 cm3

= 489.7 cm3

explanation:

here, it is given that the height is 17.3cm and the radius is 5.2cm. we know that the formula for finding the volume of a cone is 1/3*pi*r2*h.

On solving the provided query we have Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

The facts (3) ABCD and AB are insufficient to demonstrate that ABCD is a parallelogram.

The diagonals are bisected by each other, which is a characteristic of parallelograms, according to statement (1).

According to statement (2), opposing sides of a parallelogram are congruent and parallel, which is another characteristic of parallelograms.

Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

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The expression (4d + 7) + (4d² + 8d + 9) simplifies to 4d² + 12d + 16.

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

(4d + 7) + (4d² + 8d + 9)

We can simplify the expression by combining like terms:

(4d + 7) + (4d² + 8d + 9) = 4d² + (4d + 8d) + (7 + 9)

= 4d² + 12d + 16

Therefore, (4d + 7) + (4d² + 8d + 9) simplifies to 4d² + 12d + 16.

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The ratio for sin A, written as a fraction in simplest form, is 3 / (2√3).

The sine function is a mathematical function that takes an angle as its input and returns the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle

In a right triangle, the sine of an angle A is defined as the ratio of the length of the side opposite to angle A to the length of the hypotenuse. Therefore, we have:

sin A = Opposite / Hypotenuse

Substituting the given values, we get

sin A = CB / AB = 8√3 / 16 = √3 / 2

To simplify this fraction further, we can multiply both the numerator and denominator by √3:

sin A = (√3 / 2) × (√3 / √3) = 3 / (2√3)

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The given question is incomplete, the complete question is:
Which is the ratio for sin A, written as a fraction in simplest form?

The equation that represents the cost of the rental truck is y = 0.42x + 71. The Option C is correct.

Let x be the number of miles driven

Let y be the cost of the rental truck.

We can set up a system of equations to represent the given information:

For Bob:

y = mx + b

112.96 = 138m + b

For Carl:

y = mx + b

142.78 = 209m + b

Solving for b in both equations, we get:

b = 112.96 - 138m

b = 142.78 - 209m

Setting the two expressions for b equal to each other, we get:

112.96 - 138m = 142.78 - 209m

209m - 138m  = 142.78 - 112.96

71 m = 29.82

m = 0.42

Substituting m into equation for b:

b = 71.

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The answer of the given question based on the circle is ,  the answer is option (d) 8/3π.

In geometry, an arc is  portion of circumference of a circle. It is  curved line that connects two points on  circle. The length of arc is proportional to the angle that it subtends at the center of the circle.

Since EFB is a straight line and EB is a diameter of the circle, angle EFB subtends the entire circle at F. Therefore, the angle subtended by arc EFD is the difference between the angles subtended by arcs EF and EB.

Arc EF subtends a full circle at F, so its angle is 2π radians. Arc EB subtends a straight angle at F, so its angle is π radians.

Therefore, the angle subtended by arc EFD is:

2π - π = π

The length of arc is given by formula L = rθ, where r is  radius of  circle and θ is  angle (in radians) subtended by  arc at  center of  circle.

In this case, r = 4 and θ = π, so the length of the arc corresponding to angle EFD is:

L = rθ = 4π

Therefore, the answer is (d) 8/3π.

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