If the pattern rule is defined by the equation `t = 6n`, where `t` is the term value and `n` is the term number, what is the one hundredth term?

Answer:

x = 12, y = 16

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AD}{PS}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values

[tex]\frac{20}{2x+6}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

-------------------------------------------

and

[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values

[tex]\frac{y}{24}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16

Answer:

The number sentence is false.

Step-by-step explanation:

The inequality given is

20 > 86 − ℎ

We are to substitute the value of h as 46 to see if the inequality is true or false.

20 > 86 - 46

20 > 40

Since 20 is not greater than 40, the number sentence is false.

Answer:

14^2/15

Step-by-step explanation:

70/15 simplifies to 14/3

14/3 X 14/5

= 14^2/15

Complete Question

Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the accoutnt after t years can be calculated using the expression below.

[tex]250(1+\frac{0.018}{2})^{2t}[/tex]

Use the given expression to complete the statements below.

The expression is the___(Product , Sum  , Quotient , Square) of the amount initially deposited and the____(Quotient , Product , Difference , Sum)  of one and the rate of increase raised to the number of ___.(Compounding Periods , Years, Months)

Answer:

Step-by-step explanation:

For an amount invested at compound interest at a rate of r% with period for t years,

Amount [tex]=P(1+\frac{r}{k})^{tk}[/tex]

Comparing with the given expression: [tex]250(1+\frac{0.018}{2})^{2t}[/tex]

Period =2

Rate =0.018

Total Compounding Period =2 X t, where t=Number of years

Therefore:

The expression is the Product of the amount initially deposited and the Sum of one and the rate of increase raised to the number of Compounding Periods .

Answer:

- 3

Step-by-step explanation:

Calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 2) and (x₂, y₂ ) = (- 3, - 8)

m = [tex]\frac{-8-(-2)}{-3-(-5)}[/tex] = [tex]\frac{-8+2}{-3+5}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

Answer:

d = [tex]\frac{2S-2an}{n(n-1)}[/tex]

Step-by-step explanation:

Given

S = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]

Multiply both sides by 2 to clear the fraction

2S = n [ 2a + (n - 1)d ] ← distribute the bracket by n

2S = 2an + n(n - 1)d ( subtract 2an from both sides )

2S - 2an = n(n - 1)d ← divide both sides by n(n - 1)

[tex]\frac{2S-2an}{n(n-1)}[/tex] = d

Answer:

Hope this helps:)

If so please mark me as Brainliest.

Answer:

242

Step-by-step explanation:

Here, we want to calculate t15 + t25

Mathematically, nth term is

a + (n-1)d

here, a = 26 and d = 31-26 = 5

t15 = 26 + (15-1)5

t15 = 26 + 70

t15 = 96

t25 = 26 + (25-1)5

t25 = 26 + 120

t25 = 146

t15 + t25 = 96 + 146 = 242

Answer:

Irrational

Step-by-step explanation:

[tex]7\sqrt{3}+2\sqrt{9}= \\\\7\sqrt{3}+2(3)= \\\\6+7\sqrt{3}[/tex]

Therefore, this is irrational. Hope this helps!

Answer:

200 kg

Step-by-step explanation:

To satisfy the ratio 1:2:3, Mark must use 100 kg cement, 200 kg sand, and 300 kg gravel

Answer:

6 kg

Step-by-step explanation:

Answer:

The correct answer is B!

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

(b+1)/2b

quotient = divided by

we're dividing a number that is 1 more than b (b + 1), with a number twice as large as b (2b).

Answer:

Step-by-step explanation:

slope = [tex]\frac{vertical}{horizontal}[/tex] = - [tex]\frac{3}{10}[/tex] → A

The slope is negative as the ramp slopes down from left to right

The slope of the ramp shown in the diagram given is 3/10.So option D is the correct answer.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given is a diagram of a ramp.

It can be picturized as a right angled triangle.

We know that,

Slope = Change in y coordinates / change in x coordinates.

Horizontal distance = change in x coordinates = 10

Vertical distance = change in y coordinates = 3

Substituting,

Slope = 3/10

Hence the slope of the ramp is 3/10.

Learn more about Slope here :

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Answer: 4 feet < Length < 21 feet

Step-by-step explanation:

From the question, the length of the rectangular fence is 4 feet more than its width and the perimeter of the fence is less than 42 feet. The range of the lengths of the fence will be:

Length is greater than 4 feet (4 feet more than the width. This means that the length must be at least 4 feet) and less than 21 feet i.e the length must be less than 1/2 of the perimeter which is 42/2 = 21. Therefore, the answer will be:

4 feet < Length < 21 feet

Answer:

12.5

its right

Step-by-step explanation:

Answer:

[tex]y=-5/8x+6[/tex]

Step-by-step explanation:

[tex]m=\frac{7/2 - 11}{4--8}[/tex]

[tex]m=\frac{-15/2}{12}[/tex]

[tex]m=-5/8[/tex]

[tex]y=-5/8x+b[/tex]

[tex](-8,11)[/tex]

[tex]11=-5/8 \times -8+b[/tex]

[tex]b=11-(-5/8)(-8)[/tex]

[tex]b=6[/tex]

Answer:

15

17

Step-by-step explanation:

x/5=3 ⇒ x=5*3=15

x/2=8.5 ⇒ x= 2*8.5=17

Options:

Answer:

(C)The graph of f(x) has exactly two x-intercepts.

Step-by-step explanation:

Given a linear function f(x)=ax+b where the domain of f(x) is the set of all real numbers, x.

(A)If f(x)=y, the graph of f(x) will have zero x-intercepts except at y=0 which is the equation of the x-axis.

(B)A linear function can only intersect the x-axis at exactly one point.

(D)When the linear function is f(x)=0, all points of x are x-intercepts of f(x). Therefore f(x) will have infinitely many x-intercepts at this point.

However:

A straight line cannot intersect the x-axis twice, therefore the graph of f(x) cannot have two x-intercepts.

The statement which cannot be true is Option C.

Answer:

C

Step-by-step explanation:

yes

Answer:

-2

Step-by-step explanation:

To find the slope we use the formula

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

   = (-3-1)/(0- -2)

  = -4 / (+2)

  = -2

Complete Question:

sierrac3000

06/28/2019

Select the correct answer from each drop-down menu.

Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.

250(1+0.018/2)^2t

Use the given expression to complete the statements below.

The expression is the *blank* of the amount initially deposited and the *blank* of one and the rate of increase raised to the number of *blank*

1st Blank:

Product

Sum

Quotient

Square

2nd Blank:

Quotient

Product

Difference

Sum

3rd Blank:

Compounding Periods

Years

Months

Answer:

1st blank = product

2nd blank = sum

3rd blank = years

Step-by-step explanation:

The expression given above is :

250(1+0.018/2)^2t

The expression can thus be explained as:

The *product* of the amount initially deposited and the *sum* of one and the rate of increase raised to the number of *years*

Answer: 2/3xy^-2z

Step-by-step explanation:

18/27 = 2/3

x^2 / x = x

y / y^3 = y^-2

z isn’t changed

Put the variables together after dividing and you get 2/3xy^-2z.

Step-by-step explanation:

do you mean like this?

18x²y/27xy³z =

if yes the answer is like this

18/27 = 2/3

x²/x = x

y/y³ = 1/y²

1/z = 1/z

multiply all and that's the answer

⅔ * x * 1/y² * 1/z =

[tex] \frac{2x}{3 {y}^{2} z} [/tex]

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers. Irrational numbers can also be expressed as non-terminating continued fractions and many other ways.

The answer is True

The statement that all irrational numbers are real numbers is true.

Real number is a union of rational number and irrational numbers.

An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. All the root values, repeating values, comes under irrational numbers.

Since irrational numbers can still be plotted on the number line, they are considered real numbers. Therefore, all irrational numbers are also real numbers.

Thus, all irrational numbers are also real numbers.

Yes, the given statement is true.

Learn more about irrational numbers here:

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Answer:

Rational

Step-by-step explanation:

Can convert it to a ratio (-415/1)

Answer:

Rational

Step-by-step explanation:

-415 is an integer. All integers are rational. It can be written as a fraction p/q, where p and q are integers and q is not equal to zero.

-415 can be written as [tex]-\frac{415}{1}[/tex].

Answer:

y = 8-3x and y = -11/3 + x/3

For the first equation you have to subtract 3x from both sides of the equation. for the second equation you have to move all terms that doesn't contain y to the right side and solve

Answer:

185 -> Spent on new CD's

$ 555 -> Savings Account

Steps:

37*20 = 740/4 = 185 -> Spent on new CD's

740 - 185 = $ 555 -> Savings Account

Description:

The 2 question is asking that how much money did she spend on her CD. We times 37 and 20 = that will equal 740 then we divide 740 by 4 = 185. Meaning we just solved for question 2. Answer is 185 spent on new CD.

For question 3 this time we get 740 again we do it by 37 times 20 equal 740. we minus it by 185 the spent on new CD answer. so 740-185= $555. So answer for question 3 is $555 to her saving account.

Please mark brainliest

Hope this helps.

Answer:

Only the second equation is an identity

Step-by-step explanation:

1)

[tex]1+\dfrac{\cos^2\theta}{\cot^2\theta(1-\sin^2\theta)}= \\\\\\1+\dfrac{\cos^2\theta}{\cot^2\theta(\cos^2\theta)}= \\\\\\1+\dfrac{1}{\cot^2 \theta}= \\\\\\1+\tan^2\theta=\sec^2\theta\neq 2\sec^2 \theta[/tex]

This one is not an identity.

2)

[tex]19\cos \theta\left( \dfrac{1}{\cos \theta}-\dfrac{\tan \theta}{\csc \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1-\sin^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta \left( \dfrac{\cos^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta (\cos \theta)= \\\\\\19\cos^2 \theta = 19\cos^2 \theta[/tex]

This one is an identity. Therefore, only the second equation is an identity. Hope this helps!

Answer:

the person above me is right :)

Step-by-step explanation:

Answer:

343 cubic inches

Step-by-step explanation:

7 times 7 times 7 is 343

Answer:

Option (3). (5, 9.2)

Step-by-step explanation:

If Point P divides the line segment QR in the ratio of m : n.

Let the coordinates of the point P are (x, y)

Since coordinates of the point P are given by,

x = [tex]\frac{m(x_2)+n(x_1)}{m+n}[/tex]

y = [tex]\frac{m(y_2)+n(y_1)}{m+n}[/tex]

Where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the ordered pairs representing points Q and R.

If [tex](x_1,y_1)[/tex] represents (2, 5) and [tex](x_2,y_2)[/tex] represents (7, 12),

Coordinates of point P(x, y) which divides the segment in the ratio of 3:2.

x = [tex]\frac{3(7)+2(2)}{3+2}[/tex]

x = [tex]\frac{25}{5}=5[/tex]

y = [tex]\frac{3(12)+2(5)}{3+2}[/tex]

y = [tex]\frac{46}{5}=9.2[/tex]

Therefore, Point P will be represented by (5, 9.2)

Option (3) will be the answer.

Answer:

y=1x

Step-by-step explanation:

theirs no b because it goes through (0,0)

to find slope you do 2-4 over 2-4 and it equals 1

hope this helps:)

Answer:

4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = s / 4 sqrt(2)

Multiply each side by 4 sqrt(2)

4 sqrt(2) *sin 45 = s

4 sqrt(2) * 1/ sqrt(2) =s

4

Answer:

z = 6√2 = 8.49

Step-by-step explanation:

In this question, we are to find the value of the length z.

Mathematically, using Pythagoras’s theorem we can do this.

The Pythagoras’ theorem states that the square of the length of the hypotenuse equals the sum of the length of the squares of the two other sides.

Kindly note that the hypotenuse is the side that faces the angle 90

These are the points needed to solve for z

Using Pythagoras,

z^2 = y^2 + 4^2

z^2 = y^2 + 16 •••••••(i)

x^2 + z^2 = 20^2

x^2 + z^2 = 400 •••••••••(ii)

z^2 + 16^2 = x^2. ••••••••(iii)

Substitute iii into ii

z^2 + 16^2 + z^2 = 400

2z^2 + 256 = 400

2z^2 = 400-256

2z^2 = 144

z^2 = 72

z = √(72)

z = 6√2

Answer:

4[tex]\sqrt{5}[/tex]

Step-by-step explanation: