the figures below are similar. the labeled sides are corresponding. what is the area of the larger triangle?

The radius of sphere is r = 4 cm.

Substitute the value in the formula to determine the surface area of sphere.

So answer is S.A = 201.1

The equation of the line will be equal to 3y = -x + 21.

A line may be defined as the straight figure drawn which has no end points. The equation of a line can be written in slope intercept form as y = mx + c where m is the slope of line, c is y intercept an x and y are independent and dependent variables. If a point (x₁, y₁) is given then equation of line is (y - y₁) = m (x - x₁). The slope of line which is perpendicular to a given line having slope m is equal to -1/m.

Now, equation of line is y = 3x + 3. If we compare with slope intercept form then, m = 3. Now, slope of line perpendicular to this line is equal to -1/3. Now, equation of line passing through point (-6, 9) is given as

(y - 9) = -1/3 (x + 6)

3y - 27 = -x - 6

=> 3y = -x + 21 which is the required equation of line.

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Answer:

(7,3.5)

Step-by-step explanation:

Midpoints

x = (x1 + x2)/2 = (9 + 5)/2 = 14/2 = 7

y = (y1 + y2)/2 = (2 + 5)/2 = 7/2 = 3.5

The values coming in the interval (-3,1] are -2, -1, 0, and 1.

The given interval notation is;

(-3,1], it is the case of half open half close.

-3 comes with the open interval, it means its value will not be included in the interval.

1 is with the closed interval, it means its value will be included in the interval.

Thus, the values lying between the interval (-3, 1] are  -2, -1, 0, and 1.

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The unknown angles of the triangle and trapezium are as follows:

A triangle is a polygon with three sides.

The sum of angles in a triangle is 180 degrees.

Therefore, angle 1 can be found as follows:

∠1 = 180 - 40 - 30

∠1 = 180 - 70

∠1 = 110 degrees.

Therefore, angle 2 can be found as follows:

∠2 = 180 - 40 - 40 - 30 - 30

∠2 = 180 - 80 - 60

∠2 = 180 - 140

∠2 = 40 degrees.

A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.

Therefore, the triangle in the trapezium is an isosceles triangle. The base angles are equal.

Hence,

∠1 = 180 - 30 - 30

∠1 = 180 - 60

∠1 = 120 degrees

Sum of angles in the same transversal is supplementary.

Therefore,

90 + 30 + ∠2 = 180

∠2 = 180 - 120

∠2 = 60 degrees

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The actual area of the park when a scale drawing of the park had a scale of 1 cm = 100 m is 4879m².

From the information, the scale drawing of a rectangur park had a scale of 1 cm = 100 m.

It should be noted that the dimensions are given as 4.1 cm and 11.9cm. The area of the scale will be:

= 4.1 × 11.9

= 48.79cm²

Therefore, the actual area of the park will be:

= 48.79 × 100

= 4879m²

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Answer:

13 ⅓.

Step-by-step explanation:

The area of a rectangle is given by

Area = Length × Breadth

Length = 2 7/9 = 25/9 and breadth = 4 4/5 = 24/5

.: Area = 25/9 × 24/5 = 600/45 (15 can go to both the numerator and denominator)

We have 40/3 but to convert it to a mixed fraction we get 13 ⅓ as your area.

The function f(x) = 2x² - x + 3 equals to 9 when x is equal to 2.

What is function in mathematics?

In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and another variable (the dependent variable). In mathematics, functions exists everywhere, and they are crucial for constructing physical links in the sciences.

The function given in the question is:

f(x) = 2x² - x + 3

We have to find f(x) when x = 2,

We are replacing x with 2 in given function, we get:

f(x) = 2(2)² - 2 + 3

f(x) = 2(4) -2 + 3

f(x) = 8 -2 +3

f(x) = 9

Hence the given function equals to 9 when x is equal to 2.

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Complete question

Given f(x) = 2x² -x+3

Find f(x) when x = 2

Answer:

See picture

Step-by-step explanation:

A) g(x)= (x-5)(x-9)

This is the answer because basically you need to find the roots of the function, since the function g intersects the x-axis at x=5 and x=9 you can conclude easily that those are the roots.

If:

x=5

g(5)=(5-5)(5-9)=0(-4)=0

and

If:

x=9

g(9)=(9-5)(9-9)=(4)(0)=0

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

[tex]\mathsf{6.07 \times 10^7}\\\mathsf{= 6.07(10^7)}\\\mathsf{= 6.07(10\times10\times10\times10\times10\times10\times10)}\\\mathsf{= 6.07(100\times100\times100\times10)}}\\\mathsf{= 6.07(10,000\times1,000)}\\\mathsf{= 6.07(10,000,000)}\\\mathsf{= 60,700,000 \rightarrow 6.07\times 10^7}\\\\\huge\text{Therefore, your answer should be: }\boxed{\mathsf{60,700,000}}}}\huge\checkmark[/tex]

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

Answer:

the answer has to be b

Step-by-step explanation:

answer:

the y-intercept is 15 which is the initial total depth of the snow at t=0 hours.

The rate of melting is 1.5inches per hour. It will take 10 hours at the melting rate given of 1.5 to melt all the snow.

Step-by-step explanation:

the y-intercept is 15, and it might mean that the total depth of the snow is 15 inches.

The rate of melting is 1.5inches per hour.

At time = 0, S=15 - 1.5t = 15 - 1.5(0) = 15 inches to start

At time = 10, S=15 - 1.5t = 15 - 1.5(10) = 0 inches; meaning all snow has melted and it took 10 hours.

Answer:

20a + 12c = 6000

Step-by-step explanation:

a = adult tickets

c = child tickets

$20 for adults, $12 for children, for a total of $6000

20a + 12c = 6000

a + c = 400

A = amount of sales

so hmmm The Furniture Barn gives only 5% of "A" then, that means

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of A}}{\left( \cfrac{5}{100} \right)A}\implies 0.05A[/tex]

whilst The Furniture Warehouse gives you 350 bucks per week and only 1% of "A", well, that means you gross pay there will 350 + 0.01A.

hmmm how much will "A" be for both offers to pay the same amount?

[tex]\stackrel{Furniture~Barn}{0.05A}~~ = ~~\stackrel{Furniture~Warehouse}{350 + 0.01A} \\\\\\ 0.04A=350\implies A=\cfrac{350}{0.04}\implies \boxed{A=8750}[/tex]

Answer: See attached.

Step-by-step explanation:

       We can look at the values given in the equation to graph it.

➜ The -3 shows the line will intercept the y-axis at -3.

➜ The equation has a slope of -4, so for everyone right we move four down.

The equation of the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2 is  y = - 2 / 7x - 2 / 3

The equation of a line can be represented as follows:

y = mx + b

where

Therefore, the equation of the line is perpendicular to  −7x+2y=3.

−7x+2y=3

2y = 7x + 3

y = 7 / 2 x + 3 / 2

Perpendicular lines follows the rule below:

m₁ m₂ = -1

7 / 2 m₂ = -1

7m₂ = -2

m₂ = - 2 / 7

Therefore, the equation of the line also haver the same y-intercept as

9x + 3y = −2.

3y = - 9x  - 2

y = -3x - 2  /3

The y-intercept of the equation is - 2 / 3.

Hence

the equation of the line is y = - 2 / 7x - 2 / 3

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y = 1 / 3 x + 5 is the linear equation for the first table.

The system of equations' answer is (3, 6).

A linear equation is an algebraic equation of the form y= mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."

based on the available facts;

Equation of a point slope:

y = mx + b,

where m = slope and b = y-intercept

As a result, the equation for the second table is y = - 1 /3 x + 7.

With the help of the table's (0, 5)(3, 6) values, the equation for the first table may be solved. Therefore,

m = 6 - 5 / 3 - 0 = 1 / 3

let's find b using (0, 5)

5 = 1 / 3(0) + b

b = 5

Therefore, the equation of the first table is as follows:

y = 1 / 3 x + 5

The solution to the system of equation can be calculated as follows:

y + 1 /3 x  = 7

y - 1 / 3 x  = 5

2y = 12

y = 12 / 2

y = 6

6 - 1 / 3 x = 5

- 1 / 3 x = 5 - 6

- 1 / 3 x = - 1

x = 3

Therefore, the solution to the system of equation is (3, 6)

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The first number is 8.33 percent more than the second number.

Let m be the first number, n be the second number and p be the third number.

Two numbers are respectively twenty percent and ten percent more than a third number.

m = (100 + 20)% of p

m = 120 percent of p

m = 120 % of p

m = (120 / 100) × p

m = 1.2 p

And the second number would be,

n = (100 + 10)% of p

n = 110 percent of p

n = (110 / 100) × p

n = 1.1 p

We need to find by how much number the first number more than the second.

Consider the difference,

1.2 p - 1.1p = 0.1 p

So the required percentage noting but the difference is what percent of the first number.

(0.1 p / 1.2 p) × 100 = 8.33%

Therefore, the first number is 8.33 percent more than the second number.

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By algebra properties, the rational expression [(- 2 / 3) · (- 5 / 7)] · (- 9 / 4) is equivalent to the following rational expression in simplest form: - 15 / 14.

In this problem we find a product of three rational numbers, which we must simplify by using algebra properties, especially those of related to rational numbers:

[(- 2 / 3) · (- 5 / 7)] · (- 9 / 4)                               Given

[(2 / 3) · (5 / 7)] · (- 9 / 4)                                   (- a) · (- b) = a · b

(10 / 21) · (- 9 / 4)                                              Multiplication of fractions

- [(10 / 21) · (9 / 4)]                                            (- a) · b = - a · b

- 90 / 84                                                          Multiplication of fractions

- 45 / 42                                                          Simplification of fractions

- 15 / 14                                                            Simplification of fraction / Result

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The probability that the sum of the number's digit is odd is 1/5.

Probability is used to determine how likely it is that a random event would happen.

An odd number is a number that is not perfectly divisible by 2. Examples of odd numbers include 1, 3, 5.

Sum of the number's digits:

1 + 0 = 1 (odd number)

1 + 7 = 8

1 + 9 = 10

2 + 2 = 4

2 + 4 = 6

2 + 8 = 10

3 + 2 = 5 (odd number)

3+ 9 = 12

4 + 2 = 6

4+ 4 = 8

4 + 4 = 8

4 + 6 = 10

5 + 1 = 6

5 + 4 = 9 (odd number)

5 + 7 = 12

6 + 0 = 6

6 + 4 = 10

6 + 6 = 12

7 + 1 = 8

7 + 4 = 11 (odd number)

7 + 7 = 14

7 + 9 = 16

8 + 4 = 12

9 + 3 = 12

9 + 7 = 16

9 + 8 = 17 (odd number)

The probability that the sum of the digits is odd = number of odd digits / total number

5 / 25 = 1/5

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Answer:

Step-by-step explanation:

d

1km = 1000 m

12.03 km = 12.03 x 1000

12.03 km = 12030 m

1km = 100000 m

12.03 km = 12.03 x 100000

12.03 km = 1203000 cm

Answer:

8a(3a + 1)

Step-by-step explanation:

24a² + 8a

8a(3a + 1)

I hope this helps!

Your answer is correct.

Integer - 19 (1/8)inch board would be left after cutting from 34(1/4) inch board

What is an Integer ?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. When expressed in mathematical terms,

34 (1/4) inch board = 137/4 ----(1)

Cut piece = 14 3/4 = 59/4 ----(2)

saw cut 3/8 = 3/8 --------(3)

To calculate the board which is left after cutting will be

                                                          = 137 / 4 - 59 / 4 - 3/8

                                                          = 137 - 59 / 4 - 3 / 8

                                                          = 39 / 2 - 3 / 8

                                                          = 312 - 6 / 8

                                                          = 306 / 16

                                                          = 153 / 8

or,                                                       = 19 (1/8)inch

Hence, 19(1/8)inch board will be left after cutting

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If Zeke learned that he could earn another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000

The extra amount he could make if he learn Spanish = $2000

The number of years he works = 10 years

To find the extra amount, we have to use multiplication

The extra amount he could make if he learn Spanish = The extra amount he could make if he learn Spanish × The number of years he works

Substitute the values in the equation

= 2000×10

Multiply it

= $20000

Hence, if Zeke learned that he could make another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000

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