Area of composite figures worksheet. How do you solve it. Step-By-Step​

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

\(4x+3y=1\) and \(-3x - 6y = 3\), we can look at which variable will be easiest to eliminate.

\(y\) looks like it might be easy to get rid of, we just have to multiply \(4x+3y=1\)  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation \(4x+3y=1\)  by 2.

\(2(4x + 3y = 1)\\8x + 6y = 2\)

Now we can add these equations

\(8x + 6y = 2\\-3x-6y=3\\\)

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

\(5x = 5\)

Dividing both sides by 5, we get \(x = 1\).

Now we can substitute x into an equation to find y.

\(4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1\)

Hope this helped!

Answer:

m<2 = 87

m<4 = 87

m<7 = 93

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

Answer:

so where is your question..I'm good in proving

Answer:

notation is the number 4

A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).

To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.

The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.

Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.

The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.

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Answer: 126 samples

Step-by-step explanation:

Given that :

Standard deviation (σ) = 0.7

Mean (m) = 7.3

Error (E) = 0.08

α = 80%

The sample size n can be obtained using the relation :

n = [(Zcrit * standard deviation) / Error]^2

The Zcritical at 80% = 1.282

Hence,

n = ((1.282 * 0.7) / 0.08)^2

n = (0.8974 / 0.08)^2

n = 11.2175^2

n = 125.83230625

n = 126

69

Step-by-step explanation:

angles 111 and 3 are the same. in a trapezoid bottom base angles are the same and the top base angles are the same. so in order to find angle 2 you must subtract 111 from 180 because the top angles are supplementary to the bottom

180 - 111 = 69

Answer:

The answer will be 69

This is because angle 3 would also be 111

Angles in a quadrilateral add up to 360

So, 360-(111+111)

=138

there are two angles left, angle 1 ND 2, THEY ARE THE SAME VALUE. So DIVIDE 138 by 2, and you would get your answer 69 degrees.

Hope this helps!!

Answer:

.125

Step-by-step explanation:

4 is one-eighth (1/8) of 32, which would be represented by the decimal .125 or 0.125

Answer:

D=360_180÷9

D=360_20

D=340

Answer:

the answer is 30

Step-by-step explanation:

10+10=20-5=15+10=25+5=30

Answer:

30!

Step-by-step explanation:

Answer:

23.

Step-by-step explanation:

You would multiply the 4 sizes of carpet by the 3 qualities, which equals 12. Then, you add 5+2+2+2. So it would end up being 12+11.

Answer:

20

Step-by-step explanation:

25 ÷ 1.25 = 20

Answer:

Types of numbers

Natural Numbers - Common counting numbers.

Prime Number - A natural number greater than 1 which has only 1 and itself as factors.

Composite Number - A natural number greater than 1 which has more factors than 1 and itself.

Whole Numbers - The set of Natural Numbers with the number 0 adjoined.

Integers - Whole Numbers with their opposites (negative numbers) adjoined.

Rational Numbers - All numbers which can be written as fractions.

Irrational Numbers - All numbers which cannot be written as fractions.

Real Numbers - The set of Rational Numbers with the set of Irrational Numbers adjoined.

Complex Number - A number which can be written in the form a + bi where a and b are real numbers and i is the square root of -1.

Step-by-step explanation:

The solution that makes both expressions true is x = 8.55556 and y = 10.31746.

To solve for x and y, we need to use a system of equations involves finding the values of x and y that satisfy both equations simultaneously.

We can start by using the first equation to solve for x:

2x + 7x = 77

Combining like terms:

9x = 77

Dividing both sides by 9:

x = 8.55556 (rounded to six decimal places)

Now that we know the value of x we can use either equation to solve for y. Let's use the second equation:

5x + 7y = 115

Substituting x = 8.55556:

5(8.55556) + 7y = 115

Simplifying:

42.7778 + 7y = 115

Subtracting 42.7778 from both sides:

7y = 72.2222

Dividing both sides by 7:

y = 10.31746 (rounded to six decimal places)

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The width RQ of the river is approximately 61.98 ft.

To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.

Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.

From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.

Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.

From the given information, we know that TU = 68 ft.

Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.

The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

UQ² = TU² - US²

UQ² = 68² - 28²

UQ² = 4624 - 784

UQ² = 3840

Taking the square root of both sides, we have:

UQ = √3840

UQ ≈ 61.98 ft

Therefore, the width RQ of the river is approximately 61.98 ft.

Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.

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Answer:

£17.92

Step-by-step explanation:

Harry : Jess

       1 : 4

£7.35 : £29.40

(for every 1 Harry has, Jess has 4, so Jess = 4 x 7.35 = 29.40)

PRESENT:

Harry uses 3/4 of his money = 0.75 x 7.35 = £5.51

So Jess pays:  16.99 - 5.51 = £11.48

Jess has left:  29.40 - 11.48 = £17.92

The values of H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 using the given equations by substituting the values.

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 expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.

Here,

H(x)= {-5x-13 for x<-7

          3 for -7<=x< 3

          x+2 for x=> 3}

when x=-7,

H(x)=3

when x=-2,

H(x)=3

when x=3,

H(x)=x+2

H(x)=5

when x=9,

H(x)=x+2

H(x)=11

H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 when the values are substituted under the conditions stated for the given equation.

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Answer: yes

Step-by-step explanation:

if u substitute 7 into the x for 4x - 28 then it would be the same as 4(7), because any variable next to a number means multiplication.

hope this was an easier way for u to understand

Answer:

Yes, 7 is still a solution.

Step-by-step explanation:

Answer:

\(4 \div 6 \times 12 = 4 \times 2 \\ \\ 4 \times 2 = 8\)

so, 8 laps

please mark it brainliest

Answer:

neither

Step-by-step explanation:

First we must determine if both x and -x are in the domain of the function

since it is a polynomial function our first condition is satisfied

Then we should calculate the image of -x :

2x(-x)^3 + 3*(-x)² = -2x^3+3x²

it is not equal to f(x) nor -f(x)

In linear algebra, the kernel of a linear transformation is the set of all vectors that map to the zero vector in the codomain. It is also known as the null space of the transformation.

(a) Range: The range of T is the set of all possible outputs of T, which is the set of all 2-dimensional vectors where the first and second components can be any real number. Therefore, the range of T is R².

Kernel: The kernel of T is the set of all vectors in the domain of T that get mapped to the zero vector in the codomain. In this case, T(v₁, v₂) = (v₂, v₁) = (0, 0) if and only if v₁ = v₂ = 0. Therefore, the kernel of T is {(0, 0)}.

(b) Range: The range of T is the set of all possible outputs of T, which is the set of all 2-dimensional vectors where the third component is zero. Therefore, the range of T is the x-y plane in R³.

Kernel: The kernel of T is the set of all vectors in the domain of T that get mapped to the zero vector in the codomain. In this case, T(v₁, v₂, v₃) = (v₁, v₂) = (0, 0) if and only if v₁ = v₂ = 0. Therefore, the kernel of T is the set of all vectors of the form (0, 0, v₃), where v₃ can be any real number.

(c) Range: The range of T is the set of all possible outputs of T, which is the singleton set {(0, 0)}.

Kernel: The kernel of T is the set of all vectors in the domain of T that get mapped to the zero vector in the codomain. In this case, T(v₁, v₂) = (0, 0) if and only if v₁ and v₂ are arbitrary real numbers. Therefore, the kernel of T is the entire plane in R².

(d) Range: The range of T is the set of all possible outputs of T, which is the set of all 2-dimensional vectors where the second component is the same as the first component. Therefore, the range of T is the line in R² that passes through the origin and has slope 1.

Kernel: The kernel of T is the set of all vectors in the domain of T that get mapped to the zero vector in the codomain. In this case, T(v₁, v₂) = (v₁, v₁) = (0, 0) if and only if v₁ = 0. Therefore, the kernel of T is the y-axis in R².

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The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

D. x ≤ 5

Step-by-step explanation:

The closed circle means greater than or equal to (≤) or less than or equal to (≥). The open circle is greater than (<) or less than (>).

And since the circle is closed and the arrow is going to the right, than x is either greater than 5 or equal to 5

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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