What are the measures of the missing angles x°, y° of a regular triangle if one angle measure equals 60°?​

Answer:

The present age of Michael is 33 years .

Step-by-step explanation:

Given as :

Michael is 17 years older than Brandon

And 17 years ago the age of Michael was 4 times as old as Brandon

Now,

Let the age of Michael = M years

And The age of Brandon = B years

So , According to question

M = B + 12                             .........A

And ( M - 17 ) = 4 × ( B - 17 )

Or, M - 17 = 4 B - 68

Or, 4 B - M = 68 - 17

or, 4 B - M = 51               ...........B

Solving Eq A and B

I.e 4 B - ( B + 12 )= 51

or, 4 B - B = 51 + 12

or, 3 B = 63

∴  B = [tex]\frac{63}{3}[/tex]

I.e B = 21 years

So, Now the age of Brandon = B = 21 years

Put the value of B in eq A

So, M = B + 12

∴   M = 21 + 12

I.e M = 33 years

So, Now the age of Michael = M = 33 years

Hence The present age of Michael is 33 years . Answer

[tex]\frac{1}{2}[/tex] of the grandmother's lawn Dan can mow per gallon.

Option C

Solution:

Given that, mowing [tex]\frac{1}{4}[/tex] uses [tex]\frac{1}{2}[/tex] gallon of gas.

To find: The fraction of the lawn can Dan mow per gallon

According to unitary method,

[tex]\frac{1}{2}[/tex] gallon of gas is required to mow [tex]\frac{1}{4}[/tex] of lawn that is [tex]\frac{1}{2}\rightarrow \frac{1}{4}[/tex]

Therefore, 1 gallon of gas will be required to mow [tex]\frac{1}{2}\times2\rightarrow \frac{1}{4}\frac2[/tex]

[tex]\Rightarrow1 \text{ gallon }\rightarrow \frac{1}{2} \text{ of lawn}[/tex]

Therefore, one gallon will be enough to mow [tex]\frac{1}{2}[/tex] of lawn.

Unitary method:

The unitary method is a technique to solve a problem by finding the value of a single unit first, and then finding the required value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

Answer:

B) (3/10)/(7/9)=(3/10)(9/7)

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

1/2*1/3

1*1/2*3

1/6

Answer:

1/6

Step-by-step explanation:

1/3*1/2 = 1/6

1/3 = 0.33333333  = 3/9 =1/3

1/6 = 0.1666666   = 15/90=1/6  

The minimum possible area of the rectangle is 19.25 m² and the maximum possible area is 29.25 m².

To find the minimum and maximum possible areas of the rectangle, we need to consider the possible values that the length and width can take.

Given that the measured dimensions are 6 m by 4 m to the nearest whole unit, the minimum possible length would be 5.5 m (6 m - 0.5 m) and the minimum possible width would be 3.5 m (4 m - 0.5 m).

Similarly, the maximum possible length would be 6.5 m (6 m + 0.5 m) and the maximum possible width would be 4.5 m (4 m + 0.5 m).

To calculate the minimum and maximum possible areas, we multiply the minimum and maximum possible lengths by the minimum and maximum possible widths respectively. The minimum possible area would be 5.5 m x 3.5 m = 19.25 m² and the maximum possible area would be 6.5 m x 4.5 m = 29.25 m².

Answer:

A- Overall, students are less interested in reading magazines than comics.

Answer:

Option A

Step-by-step explanation:

Answer:

[tex]\displaystyle 161[/tex]

Step-by-step explanation:

[tex]\displaystyle 159 = \frac{477}{3} \\ \\ 318 = 157 + 161 \\ \\ 161, 159, 157[/tex]

I am joyous to assist you anytime.

Answer:K=5D/f

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

the answer is D

Step-by-step explanation:

i did it on EDG

Answer:

Step-by-step explanation:

-(8x-9)/3 +6>=9

-(8x -9)/3 +18>=27

-8x +9 +18 >=27

-8x >= 27-9-18

-8x >=0

x>=0

Answer:

576

Step-by-step explanation:

8*8 = 64

If dimensions are tripled, you get 24. 24*24 = 576

Answer:

576

Step-by-step explanation:

A=L*W

8*8=64

8*3=24

24*24=576

Answer:

9/10

Step-by-step explanation:

Final answer:

The improper fraction [tex]\frac{19}{10}[/tex] is equal to the mixed number [tex]1\frac{9}{10}[/tex], where 1 is the whole number and [tex]\frac{9}{10}[/tex] is the proper fraction remainder after division.

Explanation:

The improper fraction [tex]\frac{19}{10}[/tex] can be converted into a mixed number by dividing the numerator by the denominator. The division [tex]\frac{19}{10}[/tex] equals 1 with a remainder of 9. Therefore, the mixed number is [tex]1\frac{9}{10}[/tex]. This illustrates that any improper fraction can be expressed as a combination of a whole number and a proper fraction, where the numerator is smaller than the denominator.

Answer:

The average of this pie chart is 33 1/3.

Step-by-step explanation:

To find the average (or mean) of this pie chart, we simply add all the numbers together then divide the sum by however many numbers there are:

71.4 + 14.3 + 14.3 = 100

100  ÷ 3 = 33.333... or 33 1/3

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

14

Step-by-step explanation:

13.65 is rounded to 14

Answer:

14

Step-by-step explanation:

since your looking for the nearest whole number the first number behind the decimal is what determines if it goes to 14 or 13. because the number is 6 and is higher than 5 the number would be 14 but if the number was 4 than it would be 13. any number above 5 goes and 4 and below makes the number go down.

Answer:

Step-by-step explanation:

D.

Answer:

Step-by-step explanation:

Its 56/8 or 7

The value of the number is 7 . There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Two expressions joined by the equals symbol ("=") form an equation. [2] The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero. Providing the generality is not diminished, this can be achieved by deducting the right-hand side from both sides.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Given ,

product =8

increased number =6

8(x+6)=104  

8x+48= 104

8x = 104 - 48 =56

x = 56/8

= 7

Therefore The value of the number is 7.

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Answer:

The ordered pair

(−4, 0)

is a solution to the system because it makes both equations true.

The ordered pair

(−4, 0)

is a solution to the first equation because it makes the first equation true.

The ordered pair

(−4, 0)

is a solution to the second equation because it makes the second equation true.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

8 - 6 = 10 - 8 = 2

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 2, thus

[tex]a_{n}[/tex] = 6 + 2(n - 1) = 6 + 2n - 2 = 2n + 4 ← explicit formula

Hence

[tex]a_{130}[/tex] = (2 × 130) + 4 = 260 + 4 = 264

Answer:

The amount of money in Victoria's account at the end of n-th year will be,

$ [tex] (965 \times (1.02)^{(n -1)} - 765)[/tex]

Step-by-step explanation:

The amount of money in Victoria's account at the end of n-th year will be,

$ [tex](200\times (1.02)^{(n-1)} + 15 \times ((1.02)^{(n-1)} + (1.02)^{(n -2)} + (1.02)^{(n-3)} + ........ + (1.02)))[/tex]

= $ [tex](200 \times (1.02)^{(n -1)} + 15 \times \frac{1.02 \times ((1.02)^{(n-1)} - 1)}{0.02})[/tex]

= $ [tex](200 \times (1.02)^{(n -1)} + 15 \times 51 \times ((1.02)^{(n-1)} - 1))[/tex]

= $ [tex] (965 \times (1.02)^{(n -1)} - 765)[/tex]

Since, the interest is compounded over that $ 200 (which was there in the account at the end of 1st year) for (n-1) years and for (n-1) years, (n-2) years, (n -3) years, ...... 1 year respectively over those $ 15 which are deposited in the account at the end of 1 , 2, 3, ...... (n-1) years.

Answer:

[tex]a_{n}=\left [ a\left ( n-1 \right )+15 \right ]*1.02\\[/tex]

Step-by-step explanation:

1) A Recursive formula always makes reference to the previous term, written as a function.

2) From $200 to $215 there was a 7.5% growth, so since the question states that from the beginning of the second year there will be a regular growth.

3) Since it is 2% of interest compounded annually q=1+ 0.02.

[tex]A=215(1+\frac{0.02}{1})^{1}\\A=219.3[/tex]

Or simply

215*1.02=219.3

4) We can write a Recursive formula this way:

[tex]a(n)=215[/tex]

[tex]a(n)=a(n-1)(1.02)[/tex]

5) But since we have a pattern, She will deposit $15 yearly then we must make a little adjustment then add $15. to that. Considering the first term to be 200

[tex]a_{n}=\left [ a\left ( n-1 \right )+15 \right ]*1.02\\a_{1}=200[/tex]

Answer:

The aquarium can be made by 83 sq. ft. of glass.

Step-by-step explanation:

The public library aquarium is in the shape of a hollow cuboid.

The dimensions of the hollow cuboid are 6 ft by 2.5 ft. by 4 ft.

Now, the total surface area of the aquarium will be given by 2(LW + WH + HL)

Where, L = length = 6 ft, W = width = 2.5 ft and H = height = 4 ft.

If the top of the aquarium is open, then the total surface area will be

= 2(WH + HL) + LW

= 2(2.5 × 4 + 4 × 6) + 6 × 2.5

= 83 sq. ft.

Therefore, the aquarium can be made by 83 sq. ft. of glass. (Answer)

To calculate the square feet of glass used for the aquarium, we find the total surface area of the rectangular prism excluding the top. The total surface area is 83 square feet.

To find out how many square feet of glass were used to build the aquarium, we need to calculate the surface area of the rectangular prism minus the top since it is open.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

Given the dimensions of the aquarium:

First, we calculate the areas of the sides:

Total surface area excluding the top is:

Total Surface Area = 2lw + 2lh + 2wh - (length * width)

Total Surface Area = 30 + 48 + 20 - (6 * 2.5) = 98 - 15 = 83 square feet

So, 83 square feet of glass were used to build the aquarium.

The ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement

Given:

Polenta:

Cups of water = 5

Cornmeal = 2

Ratio of cups of water to cornmeal = 5 : 2

= 5/2

= 2.5

Han:

Cups of water = 3

Cornmeal = 1 1/5

= 6/5

Ratio of cups of water to cornmeal = 3 : 6/5

= 3 ÷ 6/5

= 3 × 5/6

= 15/6

= 2.5

Tyler:

Cups of water = 7 1/2

= 15/2

Cornmeal = 3

Ratio of cups of water to cornmeal = 15/2 : 3

= 15/2 × 1/3

= 15/6

= 2.5

Therefore, the ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement.

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Final answer:

The question involves mathematical ratios to determine the correct proportions for a polenta recipe. By setting up proper proportions, we confirm that Han's and Tyler's calculations for the amount of cornmeal and water needed are correct.

Explanation:

The question discusses proportions used in a recipe which relates to mathematical ratios. Han and Tyler are trying to determine how much cornmeal and water they need for polenta based on a recipe that calls for a specific ratio of these ingredients. To solve this, we must set up a proportion that maintains the constant ratio given by the recipe.

For Han's statement, since the recipe calls for 5 cups of water for every 2 cups of cornmeal, we can set up the following proportion:

5 cups water / 2 cups cornmeal = 3 cups water / x cups cornmeal

Multiply across the equal fractions (5 * x = 2 * 3)

x = 6/5 or 1.2 cups cornmeal, which confirms Han's statement as correct.

For Tyler's statement, using the same ratio:

2 cups cornmeal / 5 cups water = 3 cups cornmeal / x cups water

Multiply across the equal fractions (5 * 3 = 2 * x)

x = 15/2 or 7.5 cups water, which confirms Tyler's statement as correct as well.

Because of the answers that you gave I'm going to assume the radians were 3pi/4. That would be A, 135 degrees.

If this is the wrong amount of radians please let me know.

The radian measures of the given degree measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

One radian is the measure of a central angle subtended by an arc that is equal in length to the radius of the circle. When no symbol is used, radians are assumed. When degrees are the unit of angular measure, the symbol "°" is written. Note that the radian is a derived unit in the International System of Units (SI).

Given are some degree measurements, 135° 180° 270° 360°, we need to convert them into radians.

Since, we know that,

1 Rad = 1 Deg × π / 180

Therefore,

1) 135° = 135 × π / 180

= 3π / 4 Rad

2) 180° = 180 × π / 180

= π Rad

3) 270° = 270 × π / 180

= 3π / 2 Rad

4) 360° = 360 × π / 180

= 2π

Hence, the radian measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

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Answer:

joe mama

Step-by-step explanation:

joemama

Answer:

810

Step-by-step explanation:

-21 + d = 789

d = 789+21

d= 810

Answer:

Approximately 4, exactly 3.786 liters.

Step-by-step explanation:

128/33.8=3.786

There are approximately 3.8 litres in a gallon.

There are 33.8 fluid ounces in a litre. Therefore,

33.8 fluid ounces = 1 litre

128 fluid ounces = ? litre

cross multiply

amount = 128 / 33.8

amount = 3.78698224852

amount ≈ 3.8 litres

There are 128 fluid ounces in a gallon. Therefore,

128 fluid ounces = 1 gallon

Since, 128 fluid ounces = 3.8 litre

Therefore,

Approximately 3.8 litres are in a gallon

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Answer:

x = 5.57

Step-by-step explanation:

c² = a² + b² − 2ab cos C

x² = 10² + 6² − 2(10)(6) cos 29°

x = 5.57

Your answer and steps are correct.

Answer:

The needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]

Step-by-step explanation:

The given equation is of the form [tex]p(x) = ax^2 + bx + c[/tex]

The given solutions of the equations are:

x = 3 +i, x = 3 - i

Now, if x = a is the zero of the polynomial p(x)

⇒(x -a ) is the root of the given polynomial.

⇒ (x - ( 3+i)) and (x - ( 3+i)) are the given roots for p(x)

P(X) = PRODUCT OF ALL ROOTS

⇒ p(x) = (x - ( 3+i))(x - ( 3-i))  = ( x-3 -i)(x -3+i)

Now, [tex](a-b)(a +b) = a^2 - b^2\\\implies ( (x-3)-i)((x-3)+i) = (x-3)^2 - (i)^2 = x^2 +9 - 3x -(-1)\\= x^2 +10 - 3x\\\implies p(x) = x^2- 3x + 10[/tex]

Hence, the needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]