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Answer:

The 16ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 9

Common Difference = (d) = 2

Now, For 16ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₁₆ = 7 + (16 - 1) × 2

a₁₆ = 7 + 15 × 5

a₁₆ = 7 + 75

a₁₆ = 82

Thus, The 16ᵗʰ term of this sequence is 82

-TheUnknownScientist

Answer: 7.44

Step-by-step explanation: DeltaMath

Answer:

1) because they are vertical angles

2) because SAS

3)  CPCTC

4) Converse of the Alternate Interior Angles

Answer:

Car A speed = 80 m/s

Car B speed = 60 m/s

Step-by-step explanation:

Let Speed of Car A be represented as x

Let Speed of Car B be represented as y

Let z represent the distance that Car A travels until it catches up to Car B

Since it takes 14 hours for Car B to cover the distance z,

Solving Equation 1 and Equation 2, we get:

Answer:

Car A speed = 80 km/h

Car B speed = 60 km/h

Step-by-step explanation:

Answer: 250

Step-by-step explanation:

Given

12% of the Pizzas had extra cheese

If those pizzas were 30 in number

Suppose, x be the total Pizzas

So, 12% of x is 30

[tex]\Rightarrow x\times \dfrac{12}{100}=30\\\\\Rightarrow x=250[/tex]

Thus, 250 Pizzas were maid last week

Answer:

Line I:y=5

Line m:y=_2×+5

Line n:y=×-1

Line p:×=_5

Step-by-step explanation:

Hope It Help

Brainliest Please

Answer:

Step-by-step explanation:

Please see diagram attached.

Moon A and C are 100,000km + 10,000 = 110,000km from center of planet.

So they are 110,000 + 110,000 = 220,000km apart.

Answer:

Step-by-step explanation:

AC is 220000km according to the drawing:

Answer:

21.4

Step-by-step explanation:

13^2 + 17^2 = c^2

169 + 289 = c^2

458 = c^2

The square root of 458 is 21.4.

Answer: gggggg
g the sum of values are 1

Step-by-step explanation: 8-7=1

The factorized form of the expression is A = ( x - 7 ) ( x + 8 ) and sum of the values in the blanks should be 1

Brackets should be expanded in the following ways to factorize an expression

For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the expression be represented as A

Now , the value of A is

A = x² + x - 56

On factorizing the equation , we get

A = x² + 8x - 7x - 56

8x - 7x = 1

So , A = ( x - 7 ) ( x + 8 )

Hence , the expression is A = ( x - 7 ) ( x + 8 )

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Answer:

≈ 5.4 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (2, 6)

d = [tex]\sqrt{(2+3)^2+(6-4)^2}[/tex]

   = [tex]\sqrt{5^2+2^2}[/tex]

   = [tex]\sqrt{25+4}[/tex]

   = [tex]\sqrt{29}[/tex]

   ≈ 5.4 ( to 1 dec. place )

Answer:

True

Step-by-step explanation:

[tex] \sqrt{144} [/tex]

is a rational number.

It is also a perfect square which means it is an integer.

:)

Answer:

Step-by-step explanation:

True.  √144 = 12 (an integer) or 12/1, which is rational.

Answer:

see explanation

Step-by-step explanation:

Substitute n = 7 into f(n)

f(7) = 5 + 8(7 - 1) = 5 + 8(6) = 5 + 48 = 53

f(n) = 5 + 8(n - 1) represents the nth term of an arithmetic sequence

f(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

By comparison, then

a₁ = 5 and common difference d = 8

Answer:

Approximately 1553.83

Answer:

=225

Step-by-step explanation:

The value of x² - 2xy + y² would be; 225

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

we are given that (x-y)=15

The identity (x + y)² - (x - y)² = 4xy.

(x + y)²= (x² + 2xy + y²)

we have been asked to find x² - 2xy + y²

x² - 2xy + y² = (x - y)²

x² - 2xy + y² = 15²

x² - 2xy + y² = 225

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Answer:

32 and 58.

Step-by-step explanation:

complementary angles add up to 90.

26+x=y

x+y=90

plug y=26+x into the above equation

x+26+x=90

2x=64

x=32

The angles are 32 and 58.

At the 95% confidence level, the margin of error for this survey, expressed as a proportion, is approximately 0.0288.

To calculate the margin of error for a survey expressed as a proportion, we need to use the formula:

Margin of Error = Critical Value [tex]\times[/tex] Standard Error

First, let's find the critical value.

For a 95% confidence level, we can refer to the standard normal distribution (Z-distribution) and find the z-value associated with a 95% confidence level.

The critical value for a 95% confidence level is approximately 1.96.

Next, we need to calculate the standard error.

The standard error for a proportion can be computed using the formula:

Standard Error [tex]= \sqrt{((p \times (1 - p)) / n)}[/tex]

Where:

p = proportion of respondents in favor of the plan

n = sample size

In this case, the proportion in favor of the plan is 37/185 = 0.2 (rounded to the nearest thousandth).

The sample size is 185.

Now we can calculate the standard error:

Standard Error [tex]= \sqrt{((0.2 \times (1 - 0.2)) / 185)}[/tex]

Simplifying further:

Standard Error ≈ [tex]\sqrt{((0.04) / 185)}[/tex]

Standard Error ≈ [tex]\sqrt{(0.0002162)}[/tex]

Standard Error ≈ 0.0147 (rounded to the nearest thousandth)

Finally, we can calculate the margin of error:

Margin of Error = 1.96 [tex]\times[/tex] 0.0147

Margin of Error ≈ 0.0288 (rounded to the nearest thousandth)

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The volume of the rectangular prism is 4180in^3.

"A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles".

For the given situation,

Length of the rectangular prism = 19 in

Width of the rectangular prism = 20 in

Height of the rectangular prism = 11 in

The formula for volume of the rectangular prism,

[tex]V=l[/tex] × [tex]w[/tex] × [tex]h[/tex]

On substituting the values,

⇒[tex]V= 19[/tex] × [tex]20[/tex] × [tex]11[/tex]

⇒[tex]V=4180[/tex]

Thus the volume of the rectangular prism is [tex]4180 in^{3}[/tex].

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Answer:

Step-by-step explanation:

Unless we set x^2 + 8x + 15 equal to zero, we don't have an equation to be solved.  I will assume that the problem is actually x^2 + 8x + 15 = 0.

The coefficients of this quadratic are {1, 8, 15}, and so the "discriminant" b^2 - 4ac is (8)^2 - 4(1)(15), or 4.  Because the discriminant is positive, we know that there are two real, unequal roots.

Continuing with the quadratic formula and knowing that the discriminant is 4, we get:

      -8 ± √4           -8 ± 2

x = ---------------- = --------------- , or x = -2 ± 1:  x = -3 and x = -5

          2                       2

Answer:

Leo: 3n Dimes

Leo: 72 Dimes

Stacy: 72/3 Dimes

Stacy: 24 Dimes

Answer:

d= (-11-2)^2 + (-12--12)^2

d= (-13)^2 + (0)^2

d=169

square root the 169

answer is 13

that's the distance from (2, -12) (-11, -12)

hope that helps

Step-by-step explanation:

The distance between the points A ( 2 , -12 ) and B ( -11 , -12 ) is 13 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the distance between the two points be = D

Let the first point be represented as = A

The value of A = A ( 2 , -12 )

The second point be represented as = B

The value of B = B ( -11 , -12 )

Now , the distance between the points A and B is given by the equation of distance formula

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values in the equation , we get

[tex]Distance D = \sqrt{(-12-(-12)^{2} + (2-(-11))^{2} }[/tex]

On simplifying the equation , we get

[tex]Distance D = \sqrt{(0 + (2+11))^{2} }[/tex]

[tex]Distance D = \sqrt{(13)^{2} }[/tex]

[tex]Distance D = 13[/tex]

Therefore , the value of D is 13

Hence ,

The distance between the points A ( 2 , -12 ) and B ( -11 , -12 ) is 13 units

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Answer:

The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet

Step-by-step explanation:

The given coordinates of the clues for the treasure hunt are

The location of the first clue = 5 units north of the flag pole

The coordinates is (0, 5)

The location of the second clue = 6 units east of the flag pole

The coordinates is (6, 0)

The location of the final clue = 5 units south of the flag pole

The coordinates is (0, -5)

The flagpole is at the origin

The coordinates of the flagpole is (0, 0)

Each unit on the graph = 50 feet

From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;

The shortest distance between 2 points is a straight line

Therefore

The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units

The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet

The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units

The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet

By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61

The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet

Answer:

Step-by-step explanation:

tanα=h/d, where α=angle of elevation, h=height, d=horizontal distance.

d=h/tanα, we are given that h=4ft and α=4.76° so

d=4/tan4.76° ft

d≈48.04 ft  (to nearest hundredth of a foot)

Answer:

75

Step-by-step explanation:

did it 5 mins ago

Answer:

3.24

Step-by-step explanation: