slove for the variable
2a-5=5a+23

Answer:

Simplifying

3u = 72

Solving

3u = 72

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Divide each side by '3'.

u = 24

Simplifying

u = 24

3u= 72

three will go to the other side so it will divide

and it well be

u= 24

The first five terms of the geometric sequence with a first term of 900 and a common ratio of -1/3 are: 900, -300, 100, -33.333..., and 11.111..

The explicit formula for a geometric sequence is given by the formula:

\(aₙ = a₁ * r^(n-1)\)

where aₙ represents the nth term of the sequence, a₁ is the first term, r is the common ratio, and n is the position of the term in the sequence.

In this case, we have the following values:

a₁ = 900 (the first term)

r = -1/3 (the common ratio)

Substituting these values into the formula, we get:

aₙ = 900 * (-1/3)^(n-1)

Now, let's list the first five terms of the sequence:

When n = 1:

a₁ = 900 * (-1/3)^(1-1) = 900 * (-1/3)^0 = 900 * 1 = 900

When n = 2:

a₂ = 900 * (-1/3)^(2-1) = 900 * (-1/3)^1 = 900 * (-1/3) = -300

When n = 3:

a₃ = 900 * (-1/3)^(3-1) = 900 * (-1/3)^2 = 900 * (1/9) = 100

When n = 4:

a₄ = 900 * (-1/3)^(4-1) = 900 * (-1/3)^3 = 900 * (-1/27) = -33.333...

When n = 5:

a₅ = 900 * (-1/3)^(5-1) = 900 * (-1/3)^4 = 900 * (1/81) = 11.111...

Therefore, the first five terms of the geometric sequence with a first term of 900 and a common ratio of -1/3 are: 900, -300, 100, -33.333..., and 11.111..

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Answer:

1 : 900

Step-by-step explanation:

18 m = 1800 cm

2:1800 reduced is 1:900

To show that | | | | | 1 1 1 a b c a 2 b 2 c 2 | | | | | = (b − a)(c − a)(c − b), we can use row reduction. We start by subtracting the first row from the second row and the first row from the third row, which gives:

| | | | | 1 1 1 a b c a 2 b 2 c 2 | | | | |

R2 - R1 | | | | | 1 0 b-a 0 b-a c-a a 2 b 2 c 2 | | | | |

R3 - R1 | | | | | 1 0 b-a 0 b-a c-a 0 b 2(c-a) | | | | |

Next, we multiply the second row by (c-a) and the third row by b-a, which gives:

| | | | | 1 0 b-a 0 b-a c-a a 2 b 2 c 2 | | | | |

(c-a)R2 | | | | | c-a 0 (b-a)(c-a) 0 (b-a)(c-a)(c-b) (c-a)a (c-a)2b (c-a)2c 2(c-a)2bc | | | | |

(b-a)R3 | | | | | b-a 0 (b-a)(c-a) 0 (b-a)(c-a)(c-b) 0 b(b-a) 2bc(b-a) (c-a)b2 | | | | |

Finally, we add (b-a) times the second row to the third row, which gives:

| | | | | c-a 0 (b-a)(c-a) 0 (b-a)(c-a)(c-b) (c-a)a (c-a)2b (c-a)2c 2(c-a)2bc | | | | |

(b-a)R3 | | | | | 0 0 (b-a)(c-a) 0 (b-a)(c-a)(c-b) b(b-a) 2bc(c-a) (c-a)b2+(b-a)2c | | | | |

Now, we can see that the determinant of the matrix is the same as the determinant of the last row, which is:

(b-a)(c-a)(c-b)(c-a)b2+(b-a)2c = (b-a)(c-a)(c-b)c

Therefore, we have shown that | | | | | 1 1 1 a b c a 2 b 2 c 2 | | | | | = (b − a)(c − a)(c − b).

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Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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Answer:

The farmers believed in the principal of federalism

Step-by-step explanation:

edge 2020

The tenth amendment reserved some powers to the states because the The framers believed in the principle of federalism.

The concept of federalism is a political term that describes the power of states or provinces to share power with the national government or the central government.

The 10th amendment agrees to federalism by providing that all powers that were not given to the federal government by the constitution, belongs to the states or the people.

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We have,

= -6(3x - 2/3)

= -6(3x × 3 - 2)/3

= -6(9x - 2)/3

= -2(9x - 2)

= (-18x + 4)

Your answer will be option number 4.

Answer:

- 18x + 4

Step-by-step explanation:

\(-6(3x-\frac{2}{3})\)

- 18x + 4

Answer: 6 cows,8 chickens,8 goose

Step-by-step explanation: Add 15+.25+1=16.25

16.25x4=65+35-32.5=2.5

6 animals each right now

6 cows

8 chickens

The angle of elevation of the point T on the top of the pole from the point A on the level ground, obtained using Pythagorean Theorem and the relationship between similar triangles is about 39.3°.

Similar triangles are triangles that have the same shape (the sizes may be different) and in which the ratio of the corresponding sides are equivalent.

The triangles ΔXBA, ΔXAC, and ΔABC are right triangles, such that the angles, ∠ABX in triangle ΔXBA is congruent to triangle ∠CAX in triangle ΔXAC, and ∠ABC in ΔABC.

The 90° angle in the right triangles are congruent (All 90° angle are congruent), therefore;

ΔXBA ~ ΔXAC ~ ΔABC by AA (Angle-Angle), similarity postulate

The length of the hypotenuse in the right triangle, ΔABC, \(\overline{BC}\), can be obtained using Pythagorean Theorem as follows;

\(\overline{BC}\)² = 14² + 25² = 821

\(\overline{BC}\) = √(821)

\(\overline{BC}\)/\(\overline{AC}\) = \(\overline{AB}\)/\(\overline{AX}\)

√(821)/25 = 14/\(\overline{AX}\)

\(\overline{AX}\) = 25 × (14/(√(821)) = 350/(√(821))

Let θ represent the angle of T from A, we get;

tan(θ) = 10/(350/(√(821)))

θ = arctan(10/(350/(√(821)))) ≈ 39.3°

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Answer:2.94

Step-by-step explanation:2.80*1.05=2.94

To find the solution for the system of linear equations shown in the graph, we need to find the point of intersection of the two lines.

The first line passes through the points (0,0) and (1,3). We can find the equation of this line using the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the two given points:

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

m = (3 - 0) / (1 - 0)

m = 3/1

m = 3

The y-intercept of the line is (0,0), so b = 0.

Therefore, the equation of the first line is:

y = 3x

The second line passes through the points (0,2) and (1,1). We can find the equation of this line using the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the two given points:

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

m = (1 - 2) / (1 - 0)

m = -1/1

m = -1

The y-intercept of the line is (0,2), so b = 2.

Therefore, the equation of the second line is:

y = -x + 2

To find the point of intersection of these two lines, we can set their equations equal to each other:

3x = -x + 2

Solving for x, we get:

4x = 2

x = 1/2

Substituting x=1/2 into either equation, we can find y:

y = 3x

y = 3(1/2)

y = 3/2

Therefore, the point of intersection of the two lines is (1/2, 3/2).

So, the solution for the system of linear equations shown in the graph is:

x = 1/2

y = 3/2

Therefore, the correct response is:

one half comma three halves

The perpendicular distance from R to PQ is; 184.47 ft

From the attached image, we see that;

Height of leaning tree = 185.5 ft

Distance from point Q to the base of the tower = 126 ft

Angle of elevation to the top of the tower = 60°

By using SSA Congruency postulate, we can say that;

(sin 60)/185.5 = (sin R)/126

making sin R the subject gives;

sin R = (126/185.5) * sin 60

sin R = 0.5882

R = sin⁻¹0.5882

R = 36.03°

Now, sum of angles in a triangle is 180 degrees. Thus;

∠RPQ = 180 - (60 + 36.03)

∠RPQ = 83.97°

The perpendicular distance from R to Q will be calculated as;

RQ = 185.5 sin 83.97°

RQ = 184.47 ft

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The initial value problem, 2y″ + y = f(t), y(0) = 0, y′(0) = −1, where f(t) is defined as {2, 0 < t ≤ 2, 0, t > 2}, can be solved using Laplace transforms.

To solve the initial value problem using Laplace transforms, we first take the Laplace transform of the given differential equation. Applying the Laplace transform to the equation, we get 2s²Y(s) + Y(s) = F(s), where Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectively.

Next, we substitute the initial conditions y(0) = 0 and y′(0) = −1 into the transformed equation. Using the Laplace transform property for initial value conditions, we have Y(s) = Y(s) - 1/s.

Simplifying the equation, we can express Y(s) in terms of F(s) as Y(s) = F(s) / (2s² + 1) + 1/s.

Finally, we need to take the inverse Laplace transform of Y(s) to obtain the solution y(t). The inverse Laplace transform of F(s) / (2s² + 1) can be determined using partial fraction decomposition, and the inverse Laplace transform of 1/s is simply a ramp function.

Thus, by taking the inverse Laplace transform of Y(s), we can obtain the solution y(t) for the given initial value problem.

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The number of ways would be 2.68367259e14 for selecting 15 candidates out of  66 candidates.

Generally speaking, an arrangement of objects is just a collection of them. The sequence of the n items has no bearing on the number of "arrangements" that can be made of them (order is significant).

Total Candidates for software engineer = 66

Total Short listed candidates = 15

To find:

Number of 15 Candidates set possible

  ⁶⁶C₁₅ = \(\frac{66!}{51! 15!}\)

After Calculating from calculator we get,

2.68367259e14.

Hence the number of ways would be 2.68367259e14.

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Answer:

???

Step-by-step explanation:

sorry can you format it?

Answer:

151 cm² (i don't know what unit you were given so im going to use cm)

Step-by-step explanation:

Part One: finding the missing side (h)

h = a² = b² + c²

13² = 12² + c²

169 = 144 + c²

169 - 145 = c²

= 25

square root of 25 = c

5 = c

area of top triangular area = ½ b × h

= ½ × 12 × 5

= 30 cm²

Part Two

area of rectangle = l × b

= 12 × 8

= 96 cm²

Part Three

area of square = l × l

= 5 × 5

= 25 cm²

total surface area = (30 + 96 + 25) cm²

= 151 cm²

Answer:

\(\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }\)

Step-by-step explanation:

\(\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }\)

\(\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}\)

\(\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}\)

\(\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }\)

\(250=2 \cdot 5^3\)

\(\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}\)

Once

\(\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}\)

We have

\(5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}\)

We can proceed considering the common base of exponentials

\(\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}\)

Therefore,

\(5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}\)

Answer:

1.2 ft

Step-by-step explanation:

2*0.6 ft=1.2 ft

Answer:

50°

Step-by-step explanation:

angle ABE and angle CBD are vertical angles and has same measure so <ABE = 50°

Answer:

6 5/12

Step-by-step explanation:

Given the expression :

4 2/3 + 1 3/4

The sum of the numbers :

4 2/3 + 1 3/4

14/3 + 7/4

L.C.M of 3 and 4 = 12

(56 + 21) / 12

77 / 12

= 6 5/12

In the past year, 16 salespeople have sold between 45 and 65 cars.

Given that the accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center, and we need to determine how many of these salespeople have sold at least 45 but fewer than 65 cars in the last year.

As per the given distribution, Car Sales Relative Frequency3 5 up to 450.0745 up to 550.1555 up to 650.3165 up to 750.2275 up to 850.25

The relative frequency of cars sold between 45 and 65 is: Relative Frequency of cars sold between 45 and 65 = 0.31 - 0.15 = 0.16

Since there are 100 salespeople at Kelly's Mega Used Car Center, the number of salespeople who have sold at least 45 but fewer than 65 cars in the last year is: Number of salespeople who have sold at least 45 but fewer than 65 cars in the last year = 0.16 x 100= 16 cars

Therefore, the number of salespeople who have sold at least 45 but fewer than 65 cars in the last year is 16.

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Answer:

A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.

Answer:

The answers are (-10, -4) and (0, 1)

Step-by-step explanation:

The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.

Hope this helps!

Part (i)

Angle ABC is 150 degrees. The angle CBX is supplementary to this, so,

(angleABC)+(angleCBX) = 180

angle CBX = 180-(angleABC)

angle CBX = 180-150

angle CBX = 30 degrees

Because of the right angle marker at point X, we can find that triangle CBX is a 30-60-90 triangle. This special type of right triangle has its hypotenuse twice as long as the short leg, which we'll call y. The long leg is equal to y*sqrt(3) units.

The diagram shows BC = 6 is the hypotenuse, so the short leg is y = 6/2 = 3. The longer leg is y*sqrt(3) = 3*sqrt(3) which is the distance from B to X.

In summary so far,

CX = 3

BX = 3*sqrt(3)

We have enough information to find the tangent of angle CAB, and then find the actual angle itself.

tan(angle CAB) = opposite/adjacent

tan(angle CAB) = (CX)/(AX)

tan(angle CAB) = 3/(4+3*sqrt(3))

angle CAB = arctan(  3/(4+3*sqrt(3))  )

I'm using arctan in place of tan^(-1) which is the same basic function, just different notation.

========================================================

Part (ii)

Focus on triangle AXC. The legs we found were

AX = 4+3*sqrt(3)

CX = 3

Use the Pythagorean theorem to find the hypotenuse AC

a^2 + b^2 = c^2

(AX)^2 + (CX)^2 = (AC)^2

(AC)^2 = (AX)^2 + (CX)^2

(AC)^2 = (4+3*sqrt(3))^2 + (3)^2

(AC)^2 = (4+3*sqrt(3))(4+3*sqrt(3)) + 9

(AC)^2 = 4(4+3*sqrt(3))+3*sqrt(3)(4+3*sqrt(3)) + 9

(AC)^2 = 16+12*sqrt(3)+12*sqrt(3)+27 + 9

(AC)^2 = 52+24*sqrt(3)

AC = sqrt( 52+24*sqrt(3) )

Note that AC is a length so AC is positive. We don't have to worry about the plus minus.

This is known as a nested radical since one square root is buried in another.

We can write that as \(AC = \sqrt{52 + 24\sqrt{3}}\) if you're curious as to how that looks on paper.

Using your calculator, you should find that,

\(\sqrt{52+24\sqrt{3}} \approx 9.673118\)

Answer:

260

Step-by-step explanation:

100/5=20

8*20=160

100+160=260

The surface area of the mentioned rectangular prism is calculated to be 168 yd².

The surface area of ​​a three-dimensional object is the total area of ​​all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.

Area of rectangle 1

= 6 × 2

= 12 yd²

Area of rectangle 2

= 9 × 2

= 18 yd²

Area of rectangle 3

= 9 × 6

= 54 yd²

Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:

Area of prism = (12 × 2) + (18 × 2) + (54 × 2)

Area of prism = 24 + 36 + 108

Area of prism = 168 yd²

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Answer:

A

Step-by-step explanation:

The kite is about 16.5 yards above the edge of the pond.

You are flying a dragon kite. It's connected to 36 yards string. The kite is directly above the end of the pond. The edge of the pond is 32 yards where the kite is tied to the ground.

Therefore, the height of the kite above the ground can be calculated as follows:

This situation form a right angle triangle. Hence, using Pythagoras's theorem,

Therefore,

h² = 36² - 32²

h² = 1296 - 1024

h = √272

h = 16.4924225025

Hence, the height of the kite is 16.5 yards.

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We have to estimate the the arc and then the angle made by an arc. Here the ∠DBC will be 66°. Option b is correct.

Arc is the part of the circumference of a circle. Here arc CB is given as 48 degrees.

Here Arc CB + Arc DC = Arc DB

     Arc formed by a diameter is called semicircle arc and will be equal to 180 degrees.

48 + Arc DC = 180

Arc DC = 180- 48 = 132 degrees.

∠  DBC = 1/2 × Arc DC

             = 0.5 × 132 = 66°

So ∠DBC will be 66°. Option b is the right answer.

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