What are the first five terms of the following sequence a1=42, an=an-1-7

Answer:

y = (-2/3)x + 16/3

Step-by-step explanation:

Any line parallel to y = (-2/3)x has the same slope:  (-2/3).

Then, in this pattern, y = (-2/3)x + c, where c is the y-intercept.

If (4, -8) lives on this new line, then:

-8 = (-2/3)(4) + c, and

-8 = -8/3 + c

This last equation is equivalent to -24/3 + 8/3 + c  => -16/3 = -c.

Therefore the y-intercept is 16/3 = c, and the desired equation is

y = (-2/3)x + 16/3

Answer:

  11)  KI = 28

  12) PR = 22

Step-by-step explanation:

You want the base segment lengths KI and PR, given relations between those segments and the corresponding midsegment of the triangle.

A midsegment is a line segment that joins midpoints of other line segments, usually the midpoints of triangle sides or opposite sides of a quadrilateral. In the case of a triangle, the midsegment is parallel to the third side, and half its length. This relation is used to solve these problems.

  KI = 2·AB

  (x +37) = 2(x +23) . . . . substitute given expressions

  x +37 = 2x +46 . . . . . . eliminate parentheses

  37 = x +46 . . . . . . . . . . subtract x

  28 = x +37 . . . . . . . . . . subtract 9

The length of KI is 28 units.

  PR = 2·HG

  (x +30) = 2(19 +x) . . . . substitute given expressions

  x +30 = 38 +2x . . . . . eliminate parentheses

  22 = x +30 . . . . . . . . subtract (x+8)

The length of PR is 22 units.

__

Additional comment

As you can see here, there is no real reason to find the value of x, then substitute it back into the expression for the segment of interest. We can, and did, solve directly for the value of that expression.

As with any algebraic manipulation, any operation performed on one side of the equal sign must also be performed on the other side of the equal sign. When we say "subtract ()", we mean "subtract () from both sides of the equation."

In problem 11, x=-9. In problem 12, x=-8. Negative values of x work just fine, as long as the resulting segment lengths are positive.

Answer:W=16-3

Step-by-step explanation:

W is how many more weeks she has to work
she needs to work a total of 16 weeks and she has worked for 3 so far to find the total number of weeks she still needs to work she would take 16-3=13 13=W

The roots of the quadratic equation represented by the graph are;  x = -2.5 and x = 2.5.

The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.

The roots are located between -3 and 3.

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Answer:

a. Describe how the value of each statistic changes when 32 is subtracted from the temperature in degrees Fahrenheit.

a) The mean will change and other quantities remain same.

b) The mean, standard deviation and IQR change.

c) The standard deviation and IQR change.

a. When 32 is subtracted from the temperature in degrees Fahrenheit:

b. When the new values (obtained after subtracting 32) are multiplied by 5/9:

c. To find the value of each statistic when the temperature is measured in degrees Celsius:

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Answer:

$1425

Step-by-step explanation:

To find how much money you would make, we would first have to multiply the number of weeks worked by how many hours you work per week.

4 · 25 = 100

What this tells us is that in 4 weeks, you worked 100 hours in total. Now we can multiply total hours worked by how much you are paid per hour to get our answer.

14.25 · 100 = 1425

The value of the unknown variable, m in the equation 4m / 3 = 8 is 6. option B

4m / 3 = 8

4m = 8 × 3

4m = 24

m = 24/4

m = 6

let

three more than twice as many pounds of apples as bananas.

a = 2b + 3

If you bought seven pounds of apples, how many pounds of bananas did you buy?

b = 7 pounds

a = 2b + 3

7 = 2b + 3

7 - 3 = 2b

4 = 2b

b = 4/2

b = 2 pounds

So therefore, the correct equation and solution for this problem is 2p + 3 = 7; p = 2 pounds. option D

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Answer:

A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible​.

Answer:

No, it is not possible for a triangle to have two right angles because a triangle's angles add up to 180 degrees, and two right angles add up to 180. A triangle also has three angles, so the third angle cannot be 0 degrees.

Answer:

a = [tex]\frac{d}{M-N^3}[/tex]

Step-by-step explanation:

d = Ma - N³a ← factor out a from each term on the right side

d = a(M - N³) ← isolate a by dividing both sides by M - N³ )

[tex]\frac{d}{M-N^3}[/tex] = a

The equivalent expression is 5^(4) * 3^(-10)

Equivalent expressions are expressions having the same solution but different arrangement

Two expressions are said to be equivalent if they have the same value of solution irrespective of the variable(s) in them.

Now, let's represent the expression;

( 5^-2 × 3^5 )^-2

We simply by multiply the exponential value by the
5^-2(-2) × 3^5(-2)

5^4 × 3^- 10

Hence, the equivalent expression is 5^(4) * 3^(-10)

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Answer:

486,732 hope this helps

The order of the values from least to greatest is 8*1/ 100, 8 tens, 88

To determine the order of the values from least to greatest is to outline or arrange the value on the basis of the sizes or according to their magnitude

Given the values as;

Note that 8 ten is simply written as

=  8 × 10 = 80

= 8/ 100 = 0. 8

= 88

From the number system, the values can be arranged as;

0. 8, 80 , 88

Thus, the order of the values from least to greatest is 8*1/ 100, 8 tens, 88

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Answer:

455 is the answer of your question

Answer: (8, 8)

Step-by-step explanation:

y>x-7, y<=2x-8

1: 5>12-7

5>5 ==> Not true

2: 3>12-7

3>5 ==> Not true

3: -10>-6-7

-10>-13

-10<=2(-6)-8

-10<=-12-8

-10<=-20 ==> Not true

4: 8>8-7

8>1 ==> True

8<=2(8)-8

8<=16-8

8<=8 ==> True ==> (8, 8)

Yes, the pole will fit in the box when kept diagonally.

In order to fit the pole in rectangular prism or cuboid, it has to be kept diagonally. Now, we need to calculate the length of body diagonal of cuboid. The length of body diagonal of cuboid should be greater than pole to fit it.

The length of body diagonal of cuboid can be calculated by the formula -

Diagonal = √(l² + b² + h²)

Keep the values in formula to find the diagonal of rectangular prism

Diagonal = √(10² + 9² + 8²)

Taking square of the three numbers to find the diagonal of rectangular prism

Diagonal = √100 + 81 + 64

Taking sum of numbers present on Right Hand Side of the equation

Diagonal = √245

Taking square root of the number

Diagonal = 15.65 feet

Hence, as the diagonal of rectangular prism is greater than shower curtain pole, it will definitely fit.

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Answer:

1/4

Step-by-step explanation:

Let x = the scale factor

4x = 1  Divide both sides by 4

x = 1/4

The total cost is T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/).

Given:

T(x)={a if x≤2, b if x > 2}

let us take

a= 90x, 0≤x≤2

and, b = 180 + 50x  for x>2

Hence. the total cost be T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

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The equations of the lines in the form y=mx+b are-

A line's slope is described like the change in y coordinate to the change in x coordinate. The net y coordinate change is y, whereas the net x coordinate change is x.

Therefore the variation in y coordinate in relation to the variation in x coordinate is written as, dy/dx.

Now, as per the given conditions;

The equation of the line is y = (6 + 4x)²

Simplifying the equation;

y = (6 + 4x)²

  = 36 + 48x + 16x²

y = 16x² + 48x + 36

Now, differentiate the equation to find the tangent slope;

dy/dx = 32x + 48

At the point (6,900),

dy/dx = 32(6) + 48 = 240

Let equation of the tangent at point (a,b) is;

(y - b) = m(x - a)

a = 6, b = 900, m = 240

y - 6 = 240(x - 900)

Write this in y = mx + b form,

y - 6 = 240x - 216000

y = 240x - 215994 (Equation of Tangent line)

The slope of the normal line = -(1/slope of the tangent line) (since they're both perpendicular to each other)

Slope of the normal line = -1/240

The, equation of the normal will become;

y - 6 = (-1/240)(x - 900)

y - 6 = (-x/240) + 3.75

y = (-1/240)x + 9.75

y = - 0.00417x + 9.75 (Equation of Normal line)

Thus, the equation for the normal and tangent has be found.

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The complete question is-

Find the equation of the tangent line and normal line to the curve y = (6 + 4x)² at the point (6,900). Write the equations of the lines in the form y=mx+b. Tangent line: y=

Normal line: y=

Answer:

Mav bought 5 oranges.

Step-by-step explanation:

$2.34 ÷ 6 oranges = $0.39 ( Price per orange)

$0.39 x 5 oranges = $1.95

The computation shows that the average number of viewers over the two weeks will be 3.85 × 10⁴.

From the information given, the tv show had 3.6 x 10⁴ viewers in the first week and 4.1 x 10⁴ viewers in the second week.

Therefore, the average number of viewers over the two weeks will be:

= (3.6 × 10⁴ + 4.1 × 10⁴)/2

= 7.7 × 10⁴/2

= 3.85 × 10⁴

Therefore, the average is 3.85 × 10⁴

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The volume of the square frustrum is 1018791.667 cubic feet, the volume of the pyramid is 22019.625 cubic feet and the volume of the Washington Monument is 1040811.292 cubic feet.

The Washington Monument is an obelisc and the volume of the obelisc is the sum of the volumes of the square frustrum and the pyramid, that is:

V = V' + V''                                             (1)

V' = (1 / 3) · (a² + a · b + b²) · h              (2)

V'' = (1 / 3) · b² · h'                                 (3)

Where:

If we know that a = 55 ft, b = 34.5 ft, h = 500 ft and h' = 55.5 ft, then the volume of the Washington monumement is:

V' = (1 / 3) · (55² + 55 · 34.5 + 34.5²) · 500

V' = 1018791.667 ft³

V'' = (1 / 3) · 34.5² · 55.5

V'' = 22019.625 ft³

V = 1040811.292 ft³

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No the expression x³.x³.x³ is not equivalent to expression x³ˣ³ˣ³.

Given the expression:

x³.x³.x³

here we apply the law of exponent that, when bases are same powers are added.

Two exponential terms with the same base are multiplied, and while the base doesn't change, their powers are added. On the other hand, their powers are removed when two exponential expressions with the same base are split.

therefore, x³.x³.x³ = x ³⁺³⁺³

= x⁹

and in the second expression x³ˣ³ˣ³.

In this expression powers are multiplied.

= x³ˣ³ˣ³.

= x²⁷

therefore both expressions are not equivalent.

Hence the expressions are not equivalent.

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The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $⁢85.52 and a standard deviation of $10.81 are subsequently computed.

Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.

So, the 90% confidence interval for the true mean repair cost, μ is ;

⇒ P(-2.015 < t₅ < 2.015) = 0.90  

{As the critical value of t at 5 degrees of  freedom are -2.015 & 2.015 with P = 5%}

⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90

⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90

⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90

90% confidence interval for

⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))

Here, x = $85.52, s  = $10.81, and n = 13

⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))

⇒ μ = (79.47, 91.56)

Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

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198 of the 275 customers can be expected to prefer soda

A restaurant manger surveyed a random sample of costumers to determine which drink they prefer. Fourteen chose tea and 36 chose soda.

Based on the results , we have to find how many of the 275 customers can be expected to prefer soda?

total customers x = 275

customers chose soda y= 36

customers chose tea z= 14

therefore out of 275 customer who prefer soda = (x * y)/(y+z)

Based on the given conditions, formulate: [tex]: \frac{275 * 36}{14+36} \\\\[/tex]

Calculate the product or quotient:[tex]\frac{9900}{14+36}[/tex]

Calculate the sum or difference:[tex]\frac{9900}{50}[/tex]

Cross out the common factor: [tex]198[/tex]

Hence ,198 of the 275 customers can be expected to prefer soda

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Answer:

the prime factorization of 252 is. 252 = 2 × 2 × 3 × 3 × 7 = 22 × 32 × 7.

The 2 missing numbers are not given, so I'm unsure about the 2 missing numbers.

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

Definitions

Prime number: A whole number greater than 1 that cannot be made by multiplying other whole numbers.

Prime Factorization: Prime numbers that multiply together to make the original number.

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 252, begin by dividing 252 by the first prime number, 2:

⇒ 252 ÷ 2 = 126

As 126 is not a prime number, we need to divide again.  

⇒ 126 ÷ 2 = 63

As 63 is not a prime number, and 63 is not divisible by 2, try dividing it by the next prime number, 3:

⇒ 63 ÷ 3 = 21

As 63 is not a prime number, divide again.  

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 252 is the product of:

⇒ 252 = 2 × 2 × 3 × 3 × 7

As 2 and 3 appear twice, we can write these using exponents:

⇒ 252 = 2² × 3² × 7

Answer:

x = 96 degrees

Step-by-step explanation:

49 + 35 + x = 180

84 + x = 180

x = 180 - 84

x = 96 degrees

Based on the rowing speed of the team when rowing with the current and when rowing against, the team rowing speed when there is no current is 14 km/h.

Assuming that x is the rowing rate and y is the rate of the current, the equations needed will be:

2 (x + y) = 40

2 (x  - y) = 16

We can add the x-values of the equation to find the value of x which will be the rowing speed without current:

2x + 2x = 40 + 16

4x = 56

x = 56 / 4

x = 14 km /h

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Answer:

144.288

Step-by-step explanation:

yes because I just took the tes

Answer:

[tex]r \times \cos( 0) = - 6 \\ r = - \frac{6}{ \cos(0) } \\ r = - 6 \sec(0) \\ \\ r \times \cos(0) = 10 \\ r = \frac{10}{ \cos(0) } \\ r = 10 \sec(0) [/tex]