Recursive formula of the arithmetic sequence 4,9,14,19

The values of a and b if they are integers are -10 and 3

Surd functions are square root of prime numbers. Given the following equation;

10 - √18 = a +b√2

Equate the real and surd part to form the equation

b√2 = √18

2b² = 18

b² = 9

b = 3

Similarly

a = -10

Hence the values of a and b if they are integers are -10 and 3

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Answer: 196m squared

Step-by-step explanation: A square has equal sides, so if one side were to be equal to 14m, the other would too. 14 x 14 = 196.

Answer:

  X = 91.50

Step-by-step explanation:

The relation that defines a Z value can be used to find an X value when the appropriate parameters are given.

The equation for finding the Z-score associated with an X-value is ...

  Z = (X -μ)/σ

Solving this for X using the values given, we have ...

  3.15 = (X -60)/10

  31.5 = X -60 . . . . . . . multiply by 10

  91.5 = X . . . . . . . . add 60

The random variable value is ...

  X = 91.50

The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.

A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.

When a line divides letter T vertically, it means that two mirror images will be created.

Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

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The number which represent tens digit of a number is twice the ones digit is;

Complete question:

The tens digit of a number is twice the ones digit. The sum of the digits in the number is

12. What is the number?

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The ordered pairs that represent functions are:

For a set of ordered pairs to represent a function, the following must be true:

The x value must point to only one y value

In {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)}, the x value point to only one y value

Hence, {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)} are functions

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The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

0.408 = (n - 1) * 0.058

n - 1 = 0.408/0.058

n = 7.03 + 1

n ≈ 8 months

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Answer: The base graph has been shifted down 90 units.

Step-by-step explanation:

See attached image.

Hello

42. ?

100 17

We use cross product.

[tex] \frac{42 \times 17}{100} = 7.14[/tex]

42% of 17 => 7.14

Have a nice day ;)

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{What is 42\% of 17?}[/tex]

[tex]\huge\textbf{Answering your question}[/tex]

[tex]\mathbf{42\% \ of \ 17}[/tex]

[tex]\huge\textbf{Translating it to easier to terms}[/tex]

[tex]\mathbf{42\% \ of \ 17}[/tex]

[tex]\mathbf{= 42\%\times 17}\\[/tex]

[tex]\mathbf{= \dfrac{42}{100}\times 17}[/tex]

[tex]\mathbf{= \dfrac{42\div2}{100\div2}\times17}[/tex]

[tex]\mathbf{= \dfrac{21}{50}\times17}[/tex]

[tex]\mathbf{= \dfrac{21}{50} \times \dfrac{17}{1}}[/tex]

[tex]\mathbf{= \dfrac{21\times17}{50\times1}}[/tex]

[tex]\mathbf{= \dfrac{357}{50}}[/tex]

[tex]\mathbf{= 357 \div 17}[/tex]

[tex]\mathbf{= 7.14}[/tex]

[tex]\huge\textbf{Answer }\bf \huge\boxed{\downarrow}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{7.14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The slope is m=6 and length of line is 3.5√37.

The slope of a line is a measure of its steepness.

Given:

endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5

slope= 8-2/3-2= 6

Now, using distance formula,

d= √(3-2)² + (8-2)²

d= √1+ 36

d= √37

As, Line AB is dilated by a scale factor of 3.5.    

So, new d= √37*3.5

new d= 3.5√37

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Answer: Line 3 to line 4

Step-by-step explanation:

When dividing by a negative, you need to flip the inequality sign.

Answer:

•3✓7

✓3.✓21

=✓3×✓3✓7

=3✓7

Answer:

3rd answer is correct

Step-by-step explanation:

√3 × √21

√3 × √(7 × 3)

√( 3 × 3 × 7 )

√ ( 3 × 3 ) × √7

3√7

Answer:

Step-by-step explanation:

Solution

The factored form is going to be the HCF (highest common factor)

The fest way to do this is to turn this into primes.

8x^2 + 12x

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

Now bold the HCF.

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

The HCF = 2*2*x

Divide that into the original question to determine the second factor.

8x^2 / 4x = 2x

12x / 4x = 3         Notice how the x-s cancel

Answer

4x (2x + 3)

The total amount of interest Dominick will pay throughout the life of the loan is $1350

Simple Interest is the interest applied only on the Principal amount invested or borrowed .

It is calculated by the formula

I = ( P * R * T ) /100

P is the Principal

R is the Rate of Interest

T is the Time Period

Here

P = $ 6000

R= 9 %

T = 30 months = 30/12 year = 2.5 years

I = ( 6000 * 9 * 2.5 ) / 100

Interest = $1350

Therefore , the total amount of interest Dominick will pay throughout the life of the loan is $1350

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After 20 years of depositing and investing there will be 168474.01 dollars in your account.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:

P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]

[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]

A = 1502.287 + 166971.717

A = $168474.01

Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.

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Answer:

[tex]-5x-5[/tex]

Step-by-step explanation:

original functions:

[tex]f(x)=3x-8\\g(x)=8x-3[/tex]

Subtract the polynomials:

[tex]f(x)-g(x) = (3x-8) - (8x-3)[/tex]

Distribute the negative sign:

[tex]3x-8-8x+3[/tex]

Combine like terms:

[tex](3x-8x)+(-8+3)[/tex]

Add like terms:

[tex]-5x-5[/tex]

Step-by-step explanation:

this is an arithmetic sequence :

a1 = 1

an = an-1 + 2 = a1 + (n-1)×2

the sum of n terms of an arithmetic sequence is

S = n×(a1 + an)/2

n = 5000

an = a1 + 4999×2 = 9999

S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000

The bisection method will converge to the solution after three iterations.

It should be noted that after one iteration, x1 will be:

= (1 + 9)/2

= 10/2

= 5

Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.

After the second iteration, x2 will be:

= (1 + 5)/2

= 3

Also, this is greater than 0. The third iteration will be:

m= (1 + 3)/2

= 2.

Now, f(2) = 2⁴ -2³ - 2² - 4

= 0

Therefore, the method converges exactly to the root in 3 iterations.

Complete question:

The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.

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Answer:

Every natural number is also a rational number but not every rational number is a natural number because the set of natural numbers is a subset of the set of rational numbers.

Explanation:

Since all natural numbers, n can be written as n/1. Thus all natural numbers are rational. Since 3/4 is a rational number but not natural thus all rational numbers are not natural.

Hint:

Natural numbers : All positive numbers except zero.

Rational numbers: All numbers in the form of p/q, where q ≠ 0 (p,q are integers)

The vertical stretch of f(x) to g(x) is a factor of 5

The functions are given as:

f(x) = x

g(x) = 5x

Substitute f(x) = x in g(x) = 5x

g(x) = 5f(x)

In th above equation, the factor is 5.

5 is greater than 1 (this means vertical stretch)

Hence, the vertical stretch of f(x) to g(x) is a factor of 5

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Answer:

Option (2)

Step-by-step explanation:

cos 50° = y/z

z = y/cos 50°

Answer:(4,7/2)

Step-by-step explanation:

Given: f(x) = 3x² -5x + 4

To find f(-2), simply substitute x = -2 in function f(x).

f(-2) = 3(-2)² -5(-2) + 4

f(-2) = 12 + 10 + 4

f(-2) = 26

Answer: 26

For an ordered pair (x, y) in a relation, the y element represents the range.

Answer: range

In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Trigonometric Functions: SOH-CAH-TOA

Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.

tan(23) = x / 2

x = tan(23) * 2

x = 0.8489

x = 0.8

Hope this helps!

Step-by-step explanation:

The measure of angle x from the diagram is 100 degrees

The formula for calculating the sum of interior angle of a polygon is given as:

s = (n-2)180

Since hexagon has 6 interior angles, the sum of the interior will be 720 degrees. Hence

x  + 620 = 720

x = 720 - 620

x= 100

Hence the measure of angle x from the diagram is 100 degrees

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Answer: according to my work i got

LCM - Lowest Common Factor

HCF - Highest common factor

Step-by-step explanation:

please mark brainlest!!

yw! =^.^=

Final answer:

Area of tile is 14 cm².

Step-by-step explanation:

Area of triangle is:

[tex]\frac{1}{2} base.height[/tex]

Putting [tex]b=3.5[/tex] and [tex]h=8[/tex] in [tex]\frac{1}{2} base.height[/tex]

[tex]\frac{1}{2}bxh=\frac{1}{2}3.5x8[/tex]

[tex]=3.5x4[/tex]

[tex]=14[/tex]

The conclusion will be; Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes. Option B.

Parameters

Group 1

n1=10

x=18.47

[tex]s^2_1[/tex]=2.12

Group 1

n2=15

x2=10.01

[tex]s^2_2[/tex]=0.62

Generally, the equation for the hypothesis is mathematically given as

[tex]H_0=\mu_1 =\mu=2 \\\\H_a= \mu_1 \neq \mu=2[/tex]

Therefore

[tex]t=\frac{12.47-10.01}{\sqrt{\frac{2.12}{10}+\frac{0.61}{15}}}[/tex]

t=4.8966

In conclusion, The pvalue from table is

p-value (4.8966, [tex]\alpha[/tex] =0.06)

[tex]p-value < \alpha=0.05[/tex]

since [tex]p-value < \alpha=0.05[/tex] we reject the null hypothesis and state that there is no difference b/w the two means.

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Zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

A polynomial graph can be defined as a type of graph that can be used to represent only positive (non-negative) integer exponents of a variable in an equation.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, solutions, roots, x-intercepts, and factors with even multiplicities.

In conclusion, we can logically deduce that zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

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