how much more is 1.8 • 10^11 greater than 7.2 • 10^10

Answer:

a) The formula for the sequence is

[tex]a_n = 67,000 -3,000(n-1)[/tex]

b) [tex]a_7 = 49,000[/tex]

Step-by-step explanation:

Note that the difference between any two consecutive terms in the sequence is always equal to $3,000

[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]

Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.

The explicit formula for an arithmetic sequence is:

[tex]a_n = a_1 +d(n-1)[/tex]

Where d is the common difference between the consecutive terms of the sequence

[tex]d = -3,000[/tex]

[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]

n represents the number of years since the house was purchased

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

a) Then the formula for the sequence is

[tex]a_n = 67,000 -3,000(n-1)[/tex]

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

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

b) Now we can use the formula to find the price of the house after 7 years

[tex]a_7 = 67,000 -3,000(7-1)[/tex]

[tex]a_7 = 67,000 -3,000(6)[/tex]

[tex]a_7 = 49,000[/tex]

Final answer:

The equation cos(90°) = 4/x has no solution because cos(90°) is 0, and no value of x would satisfy the equation 0 = 4/x.

Explanation:

The student's equation is cos(90°) = 4/x. Knowing that the cosine of 90 degrees (or π/2 radians) is 0, we can substitute that into the equation, which simplifies to 0 = 4/x. This indicates that there is no value of x that would satisfy this equation, as no number multiplied by 0 can result in 4. Therefore, the solution is that there is no solution for x in this equation.

Oodoososososo o mi o mi o mi o my ha

Answer:

Step 3

Step-by-step explanation:

16-7=9 he just miscalculated this equation

Answer:

Option 3.

Step-by-step explanation:

It is given that Anani used 10 as an anchor to find the difference of 16 and 7.

The correct steps are

Step 1: The phrase "difference of" means subtraction.

Step 2: 16-6 = 10

Step 3: Since 7 is 1 more than 6, 1 more needs to be subtracted

to 10.

16-6-1 = 10-1

Step 4: Therefore, 16 - 7 = 9.

Anani did his first error in step 3.

Therefore, the correct option is 3.

Answer:

try and plug in number like 15 like and then find the answer that makes the 125

Step-by-step explanation:

Answer:

28/66 or 0.42 or 42%

Step-by-step explanation:

first find a

66-38=a

a=28

Answer:

18 in²

Step-by-step explanation:

Given 2 similar figures then

linear ratio = 9 : 12 = 3 : 4

area ratio = 3² : 4² = 9 : 16

let the area of the other figure be x

[tex]\frac{9}{x}[/tex] = [tex]\frac{16}{32}[/tex] [ [tex]\frac{ratio}{corresponding area}[/tex] ]

cross- multiply

16x = 288 ( divide both sides by 16 )

x = 18

Area of other figure is 18 in²

The area of two similar figures is related by the square of the ratio of their corresponding sides. Once you know the ratio of their sides, you can find the area of the second figure by squaring this ratio and multiplying it by the area of the first figure.

To figure out the area of the second figure, first you need to understand the concept of similarity. Two figures are similar if their corresponding sides are proportional. When two figures are similar, the ratio of their areas is the square of the ratio of their corresponding sides. If we let's say the ratio of their corresponding sides are in the ratio 1:R, then the ratio of their areas would be 1:R^2.

Suppose the area of the first figure is A and you're looking for the area of the second figure (let's call it A'). If the sides are in ratio 1:R, then A/A' = (1/R)^2. Or conversely, A' = A * R^2.

Once you find R (the ratio of their corresponding sides), you can find the area of the second figure by multiplying the area of the first figure by R^2.

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Answer:

The baby

Step-by-step explanation:

If you count the baby inside the pregnant woman, then he is the youngest.

hahha funny the baby of course

Answer:

Step-by-step explanation:

3x + 1 + 5x = 7 + 15 + 7x          combine like terms

(3x + 5x) + 1 = (7 + 15) + 7x

8x + 1 = 22 + 7x             subtract 1 from both sides

8x = 21 + 7x             subtract 7x from both sides

x = 21

Answer:

X= 21

Step-by-step explanation:

First you want to add alike terms which will get you 8x+1=22+7x. Next you want to get your x on one side so I subtracted 7x which you get x+1=22. Last you want to get rid  of your 1 to get x alone so you subtract 1 from both sides and you get x=21.

Answer:

72 ft

Step-by-step explanation:

4 x 4 = 16 ft

4 x 7 = 28

28/2 = 14

14 x 4 = 56 ft

56 + 16 = 72 ft

Answer:

The answer is 1.2

Step-by-step explanation:

1/5 it basicly stands for 1 ÷ 5

1 ÷ 5 = 0.2

plus the one you already have

1 + 0.2 = 1.2

1.2

Hope this helped!

~Lunar Rose. Moon

Answer:

1.2

Step-by-step explanation:

Take 1/5, or make it larger into 2/10 and divide those.

2/10 is obviously .2, while 1/5 is also .2.

now take the .2+ the 1 we had and you get 1.2

Answer:

Step-by-step explanation:

the expression is equivalent to (cd)5 : c^5×d^5

Answer:

Answer choice D, Infinitely many solutions.

Step-by-step explanation:

6x-24=6x-24

Answer:

Option B. [tex]116\ m[/tex]

Step-by-step explanation:

Let

x------> the height of the building

we know that

using proportion

[tex]\frac{2}{6}=\frac{x}{348} \\ \\x=348*2/6\\ \\x=116\ m[/tex]

Answer:

Step-by-step explanation:

y = 6x - 1

f(n) = 6n - 1

f(n + 1) = 6(n + 1) - 1 = 6n + 6 - 1 = 6n + 5

f(n + 1) - f(n) = (6n + 5) - (6n - 1) = 6n + 5 - 6n + 1 = 6 = constant

Answer:

b) -6x - 3

Step-by-step explanation:

3(-2x-1)=3*(-2x)+3*(-1)= -6x - 3

B. -6x - 3

Distribute the 3, or multiply it by everything in the parentheses.

You multiply 3 times -2x to get -6x, and you multiply 3 times -1 to get -3.

Put these together to get -6x-3.

Answer:

m<A = m<D

Step-by-step explanation:

This is the correct answer to your question.

Hope this helps!!!

Kyle.

Answer:

(x − 7)² + (y + 2)² = 52

Step-by-step explanation:

The equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center and r is the radius.

We know that (h, k) = (7, -2).  But we need to find the radius.  To do that, find the distance from the center to a point on the edge:

r² = (x₁ − x₂)² + (y₁ − y₂)²

r² = (7 − 1)² + (-2 − -6)²

r² = 6² + 4²

r² = 36 + 16

r² = 52

So the equation of the circle is:

(x − 7)² + (y + 2)² = 52

The equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.

To write the equation of a circle, we need to know the center and the radius of the circle. We can see from the diagram that the center of the circle is the point (2, -3), and the radius is 5 units.

The equation of a circle is given by the formula (x-h)^2 + (y-k)^2 = r^2,

where (h, k) is the center and r is the radius. Therefore, the equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.

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Answer:

((2 x + 1) (4 x^2 - 2 x + 1))/8

Step-by-step explanation:

Factor the following:

x^3 + 1/8

Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:

(8 x^3)/8 + 1/8

(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:

(8 x^3 + 1)/8

8 x^3 + 1 = (2 x)^3 + 1^3:

((2 x)^3 + 1^3)/8

Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):

((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8

1^2 = 1:

((2 x + 1) ((2 x)^2 - 2 x + 1))/8

Multiply each exponent in 2 x by 2:

((2 x + 1) (2^2 x^2 - 2 x + 1))/8

2^2 = 4:

Answer:  ((2 x + 1) (4 x^2 - 2 x + 1))/8

[tex]x^3+\dfrac{1}{8}=\\ \\ =x^3+2^{-3} = \\ \\ =x^3+(2^{-1})^3 =\\ \\ = (x+2^{-1})(x^2-2^{-1}x+2^{-2}) = \\ \\ = \Big(x+\dfrac{1}{2}\Big)\Big(x^2-\dfrac{x}{2}+\dfrac{1}{4}\Big)\\ \\ \\ \boxed{a^3+b^3 = (a+b)(a^2-ab+b^2)}[/tex]

Answer:

30.) B

I wasn't able to figure 29 out as some of the tables are cut off.

Hope this helps you out!

If 7 people share 3 cookies, a part of a cookie that each person gets is 3/7 cookies.

In Mathematics and Euclidean Geometry, a unit rate refers to the quantity of material that is equivalent to a single unit of product or quantity.

In this context, the unit rate can be calculated by using the following formula;

Unit rate = Total cookies/Total number of people

Unit rate = 3/7 cookies.

In this context, we can reasonably infer and logically deduce that the unit rate indicates 3/7 cookies per person.

Complete Question:

7 people share 3 cookies, what part of a cookie does each person get?

Answer:

Louise is missing the term [tex]30x^3[/tex]

Step-by-step explanation:

Remember that the formula for squaring a binomial is:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Where

[tex]a[/tex] is the first term of the binomial

[tex]b[/tex] is the second term of the binomial

Our binomial is [tex](5x^3+3)^2[/tex], so [tex]a=5x^3[/tex] and [tex]b=3[/tex].

Replacing values

[tex](5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2[/tex]

[tex](5x^3+3)^2=5^2x^6+6(5x^3)+9[/tex]

[tex](5x^3+3)^2=25x^6+30x^3+9[/tex]

Since Louise’s answer is [tex](5x^3+3)^2=25x^6+9[/tex], we can conclude that she is missing the term [tex]30x^3[/tex]

Answer:

Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Step-by-step explanation:

Answer:

18 cm

Step-by-step explanation:

find the hypotenuse using 30, 60, 90 rule then divide it by 2 to find the radius

P.S. posting all of the RSM questions aren't you

Answer:

The radius is 18 cm

Step-by-step explanation:

Given that a right triangle △ABC with right angle C  is inscribed in a circle.

Also, AC = 18 cm, m∠B = 30°

we have to find the radius of this circle.

In ΔABC

[tex]\sinB=\frac{AC}{AB}=\frac{18}{AB}[/tex]

[tex]AB=\frac{18}{\sin 30}=\frac{18}{\frac{1}{2}}=36cm[/tex]

As given right angle i.e angle C is of 90° which is angle formed in the semicircle. Hence, the hypotenuse side must be the diameter of circle.

Diameter=36 cm

[tex]Radius=\frac{1}{2}\times diameter=\frac{1}{2}\times 36=18 cm[/tex]

Answer:

1/8

Step-by-step explanation:

trust me

Answer:

the radius is 13

the diameter is 40.82 inches squared

the area is 530.66

Step-by-step explanation:

well, the radius is 13

Answer:

-17/10 is 1.7 is a rational number

Step-by-step explanation:

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. ... Moreover, any repeating or terminating decimal represents a rational number.

Rational numbers are numbers that can be expressed as a fraction with an integer numerator and denominator, where the denominator isn't zero. -17/10 is a rational number because it fits this definition, as -17 is the integer numerator and 10 is the integer denominator.

The number -17/10 refers to a specific type of number known as a rational number. Rational numbers are numbers that can be written as a fraction where both numerator and denominator are integers and the denominator is not zero. Therefore, -17/10 is indeed a rational number because it can be expressed as a fraction as the definition suggests. The numerator is -17 and the denominator is 10, both of which are integers and the denominator is not zero. Thus, when dealing with content-loaded rational numbers like -17/10, you can be confident that you are indeed working with a rational number.

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Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex]4^2\times2^3-(14-16)\div2\\\\=16\times8-(-2)\div2\\\\=128+2\div2\\\\=128+1\\\\=129[/tex]

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

[tex]\text{Find the area of the circle}[/tex]

[tex]\text{r = 6ft}[/tex]

[tex]\text{Use the pi formula to find it\ } (\bf{\pi})[/tex]

[tex]\text{Pi equals 3.14}[/tex]

[tex]\text{A =\ }\pi r^2 \approx \text{3.14}\times (6)^2[/tex]

[tex]\text{6}^2 =6\times6=36[/tex][tex]\text{3.14}\times\text{36 = 113.04}[/tex]

[tex]\approx\text{Which is rounded to 113}[/tex]

[tex]\boxed{\boxed{\text{Answer: A. 113.04 ft}^2}}\checkmark[/tex]

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

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

Answer:

i think its the first one but i'm not sure

Step-by-step explanation:

Answer: The slope is  [tex]\frac{-2}{5}[/tex] and the y-intercept is [tex]\frac{-1}{3}[/tex]

Step-by-step explanation:

We know that the intercept form of a linear function is given by :-

[tex]y=mx+c[/tex], where m is the slope of the line and c is the y intercept point.

The slope of a function is given by :-

[tex]m=\dfrac{\text{change in y}}{\text{change in x}}\\\\\\\Rightarrow\ m=\dfrac{\frac{-2}{15}-\frac{-1}{30}}{\frac{-1}{2}-\frac{-3}{4}}\\\\\\\Rightarrow\ m=\dfrac{\frac{-3}{30}}{\frac{1}{4}}=\dfrac{-2}{5}[/tex]

Put the value of m in the general intercept equation , we get

[tex]y=\frac{-2}{5}x+c[/tex]

Put [tex]x=\frac{-1}{2}[/tex] and [tex]y=\frac{-2}{15}[/tex] in it , we get

[tex]\frac{-2}{15}=\frac{-2}{5}\times \frac{-1}{2}+c\\\\\Rightarrow\ c=\frac{-2}{15}\times\frac{5}{1}=\frac{-1}{3}[/tex]

Hence, The slope is  [tex]\frac{-2}{5}[/tex] and the y-intercept is [tex]\frac{-1}{3}[/tex]

Answer:

The missing side length is 27 in

Step-by-step explanation:

see the attached figure

we know that

1 ft= 12 in

step 1

Convert ft to in

2 ft=2*12=24 in

Note ----> the given measure is 13 in instead of 13 ft

step 2

Find the missing side length

The perimeter of a quadrilateral is the sum of its four side lengths

Let

x------> the missing side length

P=x+24+13+15

P=79 in

so

79=x+24+13+15

x=79-52=27 in

The missing side length is 27 in

Answer:

27 in

Step-by-step explanation:

Answer:

The best possible answer for this would be: D. Mode.

This is because mode measures how many times each number appears.

Answer:

mine said c is the correct answer

Step-by-step explanation: