Congruency please help!
Are these two triangles congruent? Show your reasoning.
I think these two triangles aren't congruent because the side length is between different angles. Please tell me if I am correct or not!

To perform a partial fraction decomposition of the rational expression (x² + 2x + 7) / (x³ - 2x² + x), we need to factor the denominator first.

The denominator x³ - 2x² + x can be factored as follows:

x³ - 2x² + x = x(x² - 2x + 1)

= x(x - 1)²

Now, we can write the partial fraction decomposition as:

(x² + 2x + 7) / (x³ - 2x² + x) = A / x + B / (x - 1) + C / (x - 1)²

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator:

(x² + 2x + 7) = A(x - 1)² + Bx(x - 1) + Cx

Expanding and collecting like terms:

x² + 2x + 7 = A(x² - 2x + 1) + B(x² - x) + Cx

Now, we can equate the coefficients of corresponding powers of x:

For the coefficient of x²: 1 = A + B

For the coefficient of x: 2 = -2A - B + C

For the constant term: 7 = A

Solving these equations, we find:

A = 7, B = -6, C = 9

Therefore, the partial fraction decomposition of (x² + 2x + 7) / (x³ - 2x² + x) is:

(x² + 2x + 7) / (x³ - 2x² + x) = 7 / x - 6 / (x - 1) + 9 / (x - 1)²

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Answer:

D) 3x + y = 5 and 2x -3y = 7

Step-by-step explanation:

You can plug in the x and y values into the equations, and see if they work. In this case, 3x + y = 5 and 2x -3y = 7 both satisfy (2, -1).

Answer:

the answer it D

Step-by-step explanation:

3(2)-1=5

and 2(2)+3=7

Answer:

the surface area of the solid is 76m²

Step-by-step explanation:

Based on the information you provided, it seems like you are asking about the surface area of a rectangular prism with dimensions 2m x 4m x 5m. The surface area of a rectangular prism can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

Substituting the given dimensions into the formula, we get:

Surface Area = 2(2m)(4m) + 2(2m)(5m) + 2(4m)(5m) = 16m² + 20m² + 40m² = 76m²

Therefore, the surface area of the solid is 76m².

Answer:

Step-by-step explanation:

\((2x -3)(x-1) = 2x(x-1) -3(x-1)\)

                     \(=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3\)

Answer:

3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Step-by-step explanation:

Given that,

(3). Distance = 35 km

Angle = 42°

Let distance in north is y km.

We need to calculate the distance

Using vertical component

\(y = d\cos\theta\)

Put the value into the formula

\(y = 35\cos42\)

\(y=26.0\ km\)

Let distance in east is x  km

We need to calculate the distance

Using horizontal component

\(x =d\sin\theta\)

Put the value into the formula

\(x = 35\sin42\)

\(x=23.4\ km\)

(4). A ship sails 200 km on a bearing of 243.7°

Let distance in south is y km.

We need to calculate the distance

Using vertical component

\(y = d\cos\theta\)

Put the value into the formula

\(y = 200\cos243.7\)

\(y=-88.61\ km\)

Let distance in west is x  km

We need to calculate the distance

Using horizontal component

\(x =d\sin\theta\)

Put the value into the formula

\(x = 200\sin243.7\)

\(x=-179.29\ km\)

Hence, 3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Answer:

67

Step-by-step explanation:

Answer:

Statements 1, 3, and 5

1) Two rays joined at the same end point form an angle.

3) A continuous section of the circumference of a circle is a circular arc.

5) A circle is the locus of all points a fixed distance from a given center point.

Step-by-step explanation:

Statement 2 is false because it says that intersecting lines that form right angles are parallel lines.  Actually, intersecting lines that form right angles are perpendicular lines.

Statement 4 is false because it says that lines that never intersect of cross each other are perpendicular.  Actually, lines that never intersect or cross each other are parallel.

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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Answer: 12

11x - 2 = 130

11x = 130 + 2

11x = 132

x = 132/11

x = 12

Now with value x the angle will be 130 and using converse of corresponding angles theorem line v and u will be parallel

Answered by Gauthmath must click thanks and mark brainliest

Answer:

24 units² and 6 units²

Step-by-step explanation:

shape A

is composed of 2 rectangles , left and right

the rectangle on the left has dimensions 8 by 2

the rectangle on the right has dimensions 4 by 2

total area = (8 × 2) + (4 × 2) = 16 + 8 = 24 units²

shape B is a triangle with area (A) calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

here b = 4 and h = 3 , then

A = \(\frac{1}{2}\) × 4 × 3 = 2 × 3 = 6 units²

Answer:

99.9

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

Equation: y = 7x + 11

67 = 7x + 11

Subtract 11 from both sides;

56 = 7x

Divide both sides by 7;

x = 8

Answer:

12 cm

Step-by-step explanation: i think if its not im sorry

In a class of statistics course, there are 50 students, of which 15 students scored b, 25 students scored c and 10 students scored f. If a student is chosen at random from the class, the probability of scoring not f is 80%.

Given that there are 50 students, out of which 15 scored b, 25 scored c and 10 scored f. Now, let's calculate the number of students who did not score f.

Number of students who scored f = 10

Number of students who did not score f = 50 - 10

= 40

Hence, the probability of scoring not f is:

Probability of scoring not f= Number of students who did not score f

Total number of students= 4049

Therefore,Probability of scoring not f=4080

=0.80

=80%

Hence, the probability of scoring not f is 80% which means out of 50 students, 10 scored f and the remaining 40 students did not score f. Therefore, the probability of choosing any student out of the class who did not score f is 80%.

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The largest possible area of one of the circles would be 314. 2 cm²

It is important to note that the formula for finding the area of a circle is given as;

Area = \(\pi r^2\)

From the information given, we have the sides of the square to have a value of 20cm

Also note that the measure of the sides of the square is the size of the diameter of the circle

But we need to find the radius

radius = diameter/2

radius = 20/ 2 = 10cm

Substitute value of radius into the formula for area

Area = 3. 142 × 10^2

Area = 3. 142 × 10 × 10

Area = 314. 2 cm²

The area of the circle is 314. 2cm^2

Thus, the largest possible area of one of the circles would be 314. 2 cm²

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Answer:

y = (x + 5)/3

Step-by-step explanation:

To make y the subject, you need to isolate y on one side of the equation.

x = 3y - 5

Add 5 to both sides:

x + 5 = 3y

Divide both sides by 3:

y = (x + 5)/3

Therefore, y is the subject of the formula when it is expressed as:

y = (x + 5)/3

Answer:

\(\frac{\sqrt{2} }{2\\}\)

Step-by-step explanation:

A triangle has a total of 180° (B is a 90° angle)

Take 180° - 90° to find the angle of A + C which equals 90°

take 90°/2 to get the angle of C which is 45°

and to check that take 45°+45°+90°= 180°

Now...

cos (C)

cos(45°) = \(\frac{\sqrt{2} }{2}\) [Answer]

Please rate!!

Answer:

A) convex B) convex C) concave D) concave

Step-by-step explanation:

concave means going in on itself and convex is going outwards.

Step-by-step explanation:

A) 4(3) + 2 = 14

True

B 3(5) - 8 = 7

False

C 2 - 10 = - 8

False

D 6 - 2(7) = 6 - 14 = - 8

True

Answer:

13

Step-by-step explanation:

-1--14

-1+14

13

The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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Answer:

k = 0.25

Step-by-step explanation:

The standard equation of a proportional relationship is

y = kx ← k is the constant of proportion

y = 0.25x ← is in this form

with k = 0.25

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

Answer:

B. X⁴+2X²+2

Step-by-step explanation:

If f(x) = x²+1, we are to find ff(x)

F(f(x)) = f(x²+1)

to get f(x²+1), we will have to substitute x as x²+1 in the function f(x) as shown;

F(x²+1) = (x²+1)²+1

Expand the expression

f(x²+1) = (x²+1)(x²+1)+1

f(x²+1) = (x⁴+x²+x²+1)+1

f(x²+1) = x⁴+2x²+1+1

f(x²+1) = x⁴+2x²+2

Hence f(f(x)) = x⁴+2x²+2

Explanation:

If lines m and n are parallel, then the same side interior angles shown are supplementary. They add to 180.

(x+12) + (4x-7) = 180

(x+4x) + (12-7) = 180

5x+5 = 180

5x = 180-5

5x = 175

x = 35

The probability (to the nearest percent) of a randomly thrown dart landing somewhere in the red shaded regions is approximately 2%.

To find the probability of a randomly thrown dart landing somewhere in the red shaded regions, we need to determine the ratio of the area of the red shaded regions to the total area.

Let's break down the problem step by step:

We are given that the area of the inner circle is 256π. Let's denote this area as A_inner.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius. From the given information, we can determine the radius of the inner circle.

A_inner = πr^2

256π = πr^2

r^2 = 256

r = 16

So, the radius of the inner circle is 16 units.

Now, let's consider the area of the red shaded regions. These regions consist of the area between the inner circle and the outer circle, as well as the five triangular regions formed by the sides of the pentagon.

The area between the two circles can be calculated as the difference between the areas of the two circles:

A_red = A_outer - A_inner

To find the area of the outer circle, we need to determine its radius. Since the outer circle is inscribed in the pentagon, the distance from the center of the circle to any vertex of the pentagon is the radius.

Let's denote the radius of the outer circle as R. The distance from the center of the circle to a vertex of the pentagon is also the apothem (a) of the pentagon.

Using trigonometry, we can calculate the apothem of a regular pentagon:

a = Rcos(36°)

Since the pentagon is regular, each interior angle is 108°, and the central angle of the isosceles triangle formed by the radius, apothem, and one side of the pentagon is 36°.

From the given information, we know that the apothem (a) is equal to the radius of the inner circle, which is 16 units.

16 = Rcos(36°)

Solving for R:

R = 16 / cos(36°)

R ≈ 19.82

The radius of the outer circle is approximately 19.82 units.

Now, we can calculate the area of the red shaded regions:

A_red = πR^2 - A_inner

= π(19.82)^2 - 256π

= 1238.22π - 256π

= 982.22π

Finally, we can calculate the probability of a randomly thrown dart landing somewhere in the red shaded regions by dividing the area of the red shaded regions by the total area, which is the area of the outer circle:

Probability = (A_red / A_outer) * 100

Plugging in the values:

Probability = (982.22π / πR^2) * 100

= (982.22 / 19.82^2) * 100

≈ 2.51%

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The answer is OC. Minimum: -12.48; maximum: 64.48.

The minimum usual value - 20 and the maximum usual value y + 20 for the given values of n and p, n = 100; p = 0.26 are found below.

Minimum usual value = np - z * sqrt(np(1 - p)) = 100 × 0.26 - 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 - 1.645 × sqrt(100 × 0.26 × 0.74) = 26 - 1.645 × sqrt(19.1808) = 26 - 1.645 × 4.3810 = 26 - 7.2101 = 18.79 ≈ 18.80

Maximum usual value = np + z * sqrt(np(1 - p)) = 100 × 0.26 + 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 + 1.645 × sqrt(100 × 0.26 × 0.74) = 26 + 1.645 × sqrt(19.1808) = 26 + 7.2101 = 33.21 ≈ 33.22

Therefore, the minimum usual value - 20 is 18.80 - 20 = -1.20.The maximum usual value y + 20 is 33.22 + 20 = 53.22.

Hence, the answer is OC. Minimum: -12.48; maximum: 64.48.

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Answer:

1.05 miles per hour

Step-by-step explanation:

m = y2 - y1/ x2 - x1 (It doesn't matter which you choose to be y2 and y1, just make it consistent)

m = 4.2 - 2.1/ 4 - 2

m = 2.1 / 2

m = 1.05