Reducing the fraction to the lowest terms

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:

3x+6y^3

Step-by-step explanation:

-First you add all the Xs

2x+x+x

-Then you multiply all the Ys

2y * 3y * y

* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3

*the numbers are multiplied making it a 6

Together it forms 6y^3

-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3

The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of 2x+x+x+(2y × 3y × y) can be done as,

2x + x + x + (2y × 3y × y)

= 4x + (2y × 3y × y)

= 4x + 6y³

Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.

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57-12= 3x+12-12

45=3x

Divide by 3

x=15

Check answer

57= 3(15)+12

57=57

Answer is correct.

x= 15

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:

1/8

Step-by-step explanation:

trust me

Answer:

m<A = m<D

Step-by-step explanation:

This is the correct answer to your question.

Hope this helps!!!

Kyle.

[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:

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]

Answer:

Derek:

Mean:1929

Median: 1930

range: 54

IQR: 48

MAD: 23.75

Paul:

Mean: 1929

Median: 1929.5

range: 15

IQR: 6

MAD: 3.5

Step-by-step explanation:

For the Derek's collection:

1.  Mean =  1930.375

2. Median =  1930

For the Paul's collection:

1.  Mean = 1929.75

2. Median = 1931

For Derek's collection:

Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8

          = 1930.375

Median:

The median is the middle value of the set, so we first need to put the numbers in order:

1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955

The median is the average of the middle two numbers, which are 1910 and 1950:

Median = (1910 + 1950) / 2

             = 1930

For Paul's collection:

Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8

          = 1929.75

Median:

The median is the middle value of the set, so we first need to put the numbers in order:

1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935

The median is the average of the middle two numbers, which are 1930 and 1932:

Median = (1930 + 1932) / 2

            = 1931

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Answer:

log (y)+ 8 log (z)

Step-by-step explanation:

use the rules of logarithm

The expanded form of the given function is log (x)+ 8 log (y).

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Given;

[tex]log(xy^8)[/tex]

use the rules of the logarithm;

log (x)+ 8 log (y)

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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:

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 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:

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:

Answer:

Step-by-step explanation:

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

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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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.

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:

Answer choice D, Infinitely many solutions.

Step-by-step explanation:

6x-24=6x-24

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:

V1 / T1 = V2 / T2

0.67 / (273 + 89) = 1.12 / (273 + t )

t = 332 °C

Given values:

Volume,

Temperature,

We know the relation,

→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]

By substituting the values, we get

→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]

→   [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]

          [tex]= 332^{\circ} C[/tex]

Thus the answer above is right.

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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:

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:

((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]

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:

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:

the answer is y=  9/2  x+7

Did you mean the interception or solve for? Anyway I'll do both.

Solve for y:

[tex]

2y-9x=14\Longrightarrow 2y=14+9x \\

2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}

[/tex]

Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]

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:

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: