Question 3 help please

The next set of measurements for the triangle are as follows:

                        Triangle 1            Triangle 2           Triangle 3

Hypotenuse:    5.26                    7.89                     10.52

Opposite:          2.63                   3.945                   5.26

Adjacent:          4.556                  6.834                   6.834

This is done using the concept of similar triangles,

Similar triangles are two triangles that have the same shape but may be scaled to different sizes. In other words, similar triangles have the same angles, but their sides may be proportional.

In the problem, the proportion of the sides are equal and this will maintain the size of the angle

let the size of the angle be x

Sin x = opposite / hypotenuse

Sin x = 2.63 / 5.26 = 3.945 / 7.89 = 5.26 / 10.52 = 0.5

x = arc sin (0.5)

x = 30

To maintain same proportion the triangles where all a scaled version of the given triangle

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The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.

Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.

To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting,  r = 6 into the formula, we get:

C = 2π(6)

C = 12π

To approximate this value using 3.14, we can substitute π = 3.14 and get:

C ≈ 12(3.14)

C ≈ 37.68

Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

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The function notation that moves a pre-image 4 units right and 7 units down is f(x) ⇒ (x + 4, y - 7)

Translation is the movement of a point on the coordinate plane either left, right, up or down. Translation is a rigid transformation because it preserves the shape and size. Reflection and rotation are also rigid transformations.

If a point A(x, y) is translated a units right and b units down, then the new point is A'(x + a, y + b)

The function notation that moves a pre-image 4 units right and 7 units down is (x, y) ⇒ (x + 4, y - 7)

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Answer: (6y + 1) (y + 4)

Step-by-step explanation: (6y + 1) (y + 4)   (6y)(y) + (6y)(4) + (1)(y) + (1)(4) 6y^2 + 24y + 1y + 4 6y^2 + 25y + 4

Answer:

multiply 6×2 an you get 12

step:1 =4×12y⁴ ¹+25y¹ ¹

step:2=48y⁴ ¹ +25y¹ ¹

step:3=48y³+25y⁰

step:4=48y³+25×1

step:5=48y³+25

answer=48y³+25

The value of the wanted limit is:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = 64[/tex]

So the correct option is the third one.

Here we know that:

[tex]\lim_{x \to 0} f(x) = 4[/tex]

And we want to find the value of the limit:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4[/tex]

Notice that because neither the fraction nor the power depend on the value of x, we can put the limit inside the parenthesis to get:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = \frac{1}{4} (\lim_{x \to 0} f(x))^4[/tex]

And we know that the thing inside the parenthesis is 4, then:

[tex]\frac{1}{4} (\lim_{x \to 0} f(x))^4 = \frac{1}{4} (4)^4 = 4^3 = 64[/tex]

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As the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The graph of the function is given below.

From the graph, we can conclude that the value of the graph is always positive. So, the function will be an exponential function.

From the graph, as the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

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Answer:

Step-by-step explanation:

The middle one

There are 15 total blocks that is your denominator.

There are 5 shaded that is your numerator.

5/15

The volume of a rectangular prism is 320 m³.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

1) Given that, base area is 40 m² and height is 8 m.

So, the volume = 40×8

= 320 m³

2) 2) In the basketball game, Scott attempted 14 free throws.

He made half of them = 14/2

= 7

So, he made 7 throws

3) Today's high is 47 degrees Fahrenheit.

The weatherman says it will hit freezing tonight.

So, the temperature is represented as -47 degrees.

4) The given numbers are 5489 and 6752

Now, the sum is 5489 +6752

= 12241

Estimated to the nearest thousand as 12000.

5) Jace had 38 paper airplanes at home.

Christopher gave him 14 more paper airplanes to play with at home. Then Ameera gave him 29 paper airplanes.

So, total airplanes= 38+14+29

= 81

So, Jace had total 81 paper airplanes.

Therefore, the volume of a rectangular prism is 320 m³.

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The boat will coast a total distance of approximately 40/ln(0.5)/(-10) ft.

To solve this problem, we can use the concept of exponential decay. If we let v(t) be the velocity of the boat as a function of time t, then we can write the differential equation that describes its motion as:

dv/dt = -kv(t)

where k is the proportionality constant between resistance and velocity. We can separate variables and integrate both sides to get the velocity as a function of time:

∫(dv/dt) = -k∫(v(t))dt

v(t) = Ce^(-kt)

where C is an arbitrary constant of integration. We can use the initial condition v(0) = 40 ft/s to find C:

C = 40

So the velocity of the boat as a function of time is:

v(t) = 40e^(-kt)

We can use the condition v(10) = 20 ft/s to solve for k:

20 = 40e^(-10k)

Taking the natural logarithm of both sides:

ln(0.5) = -10k

k = ln(0.5)/(-10)

Next, we can use the velocity as a function of time to find the distance traveled by the boat:

∫(v(t))dt = ∫(40e^(-kt))dt = 40/k * (1 - e^(-kt))

Let's call the total distance traveled by the boat "D". Then we can write:

D = 40/k * (1 - e^(-kt))

We can plug in the value of k we found earlier and evaluate the expression at t = ∞:

D = 40/ln(0.5)/(-10) * (1 - e^(-∞)) = 40/ln(0.5)/(-10)

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Visualizing Kruskal's algorithm involves representing the graph, its edges, and the minimum spanning tree in a visual format.

To visualize a Kruskal algorithm, you need to follow the steps below:

1. Sort all the edges in ascending order of weight.
2. Create a new graph G' with the same vertices as the original graph G, but no edges.
3. Start with the smallest edge and add it to G' if it doesn't create a cycle. Repeat this step until you have added all the edges or you have a minimum spanning tree.
4. If you have a minimum spanning tree, you can visualize it by drawing the graph with the edges included in G'.

Here is an example:

Original graph G:

A---2---B---3---C
|       |
4       1
|       |
D---5---E

Step 1: Sort the edges in ascending order of weight: 1, 2, 3, 4, 5

Step 2: Create a new graph G' with the same vertices as G, but no edges.

Step 3: Start with the smallest edge (1) and add it to G'. This doesn't create a cycle, so we can add it.

G':
A       B---1---C
|       |
4       1
|       |
D       E

Next, add the second smallest edge (2) to G'. This also doesn't create a cycle, so we can add it.

G':
A---2---B---1---C
|       |
4       1
|       |
D       E

Continue this process until you have added all the edges or you have a minimum spanning tree.

Step 4: Visualize the minimum spanning tree by drawing the graph with the edges included in G'.

Minimum spanning tree:

A---2---B---1---C
|       |
4       1
|       |
D       E

I hope this helps! Let me know if you have any further questions.

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The statement t < –3 or t > 4 is the inequality that the graph represents.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

The graph represents the inequality t < –3 or t > 4. This can be seen by the number line, which has the integers -5 to 5 incrementally marked, with the bars extending beyond the -3 and 4 markers. This indicates that the value of t is less than -3 or greater than 4, but not equal to either of these values. Therefore, the statement t < –3 or t > 4 is the inequality that the graph represents.

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Answer:

$0.30

Step-by-step explanation:

They tell you that a bag of 3 is $0.90. 3 can go into 90 a total of 30 times. 0.90/3 is 0.30

Answer:

first take a total price and then divided by the total bags to get price of each

Step-by-step explanation:

The rate of decrease is 89%.

The function shows exponential decay.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

An exponential function,

y = 8600(0.11)ˣ.

When we put x = 0,

we get,

y = 8600

And when we put x = 1

we get,

y = 946

So, 1 - r = 0.11

Rate of decrease, r = 0.89

Therefore, the function shows exponential decay.

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The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.

The length of the first secant in the image is x + 18, and the second is 24 + 16.

x + 18 times 18 = 40 times 16

18x + 324 = 640

18x = 316

x= approximately 17.6

Jimmy’s total income is the sum of all the incomes which is $91838.61 .

How to determine Jimmy's income?

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period .

Now in the given question ,

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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Answer: To multiply the expression, we first distribute the constant factors:

2p^3q^4r^2 * 2p^4q^2t^3 * 3r = 6p^3q^4r^3 * 2p^4q^2t^3

Next, we multiply the variables by combining like terms:

6p^3q^4r^3 * 2p^4q^2t^3 = 6p^7q^6r^3t^3

This is the final simplified expression, and we can circle or highlight it as the answer.

Step-by-step explanation:

Answer:

0.000154

Step-by-step explanation:

To find multiple of 3 and 5 we need to add 15 to the previous multiple of 15.

To find multiples of 3 and 5, you can use the following steps:

1. Start with the number 3 and 5, respectively.
2. Add 3 or 5 to the previous number to get the next multiple. For example, 3 + 3 = 6, 6 + 3 = 9, and so on. Similarly, 5 +    5 = 10, 10 + 5 = 15, and so on.
3. Repeat step 2 until you have found the desired number of multiples.

Here are the first 10 multiples of 3 and 5:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Note that some numbers, such as 15 and 30, are multiples of both 3 and 5. These are called common multiples.

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Answer:

x = 8

Step-by-step explanation:

Vertically opposite angles are congruent.

          5x + 9 = 57 - x

 Add x to both sides,

      5x +x + 9 = 57

           6x + 9 = 57

Subtract 9 from both sides,

                  6x = 57 - 9

                  6x = 48

Divide both sides by 6,

                 x = 48 ÷ 6

                x = 8

Answer:

x=7

Step-by-step explanation:

You graph it and find the middle point that would create a line through it and see where it his the x-axis.

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

Solution:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

According to question:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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Answer:

y = - 1 , y = 17

Step-by-step explanation:

y² - 16y + 64 = 81 ← y² - 16y + 64 is a perfect square

)y - 8)² = 81 ( take the square root of both sides )

y - 8 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 8 to both sides )

y = 8 ± 9

then

y = 8 - 9 = - 1

x = 8 + 9 = 17

The following expressions solved with the properties of exponents;

b³

ax

a³ × b⁵

b

b³ / b⁰

= b^(3-0)

= b³

a•x⁵ / a•x⁴

= ax⁵ / ax⁴

= ax^(5-4)

= ax¹

= ax

a • b²• a²•b³

= a^(1+2) × b^(2+3)

= a³ × b⁵

b^-2•b²•a⁰

= b^(-2+2) × a⁰

= b¹ × 1

= b

Therefore, the properties of exponents states that when numbers of the same base are divided, the exponent will be subtracted and

when numbers of the same base are multiplied, the exponent will be added.

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Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

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Using the distributive property to write the expression, we have:

12+4 = 4(3 + 1)

The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.

We can use this property to write an expression that is equivalent to 12 + 4 as follows:

12 + 4 = 4(3) + 4 (here, we have factored out 4 from 12 using the distributive property)

         = 4(3 + 1) (we have combined the terms inside the parentheses)

Therefore, 12 + 4 is equivalent to 4(3 + 1).

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The value of n is 443 inches when using the triangle rule and law of sine.

The formula is given as

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P

∠N + ∠O + ∠P = 180

57 + 55 + ∠P = 180  : Sum of angles in a triangle is equal 180 degrees

∠P = 180 - 112

∠P = 68

Using law of sine

p/sin P = n/sin N

490/sin68 = n / sin57

n = [(490 × sin 57) / sin 68]

n = 443 inches

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Answer:

y=2/3x+-1

Step-by-step explanation:

The given problems are solved:

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Question 4:

To calculate angle A,

Consider tan function.

[tex]tan A=\frac{opposite side }{adjacent side}[/tex]

[tex]tan A=\frac{9.6}{7.2}[/tex]⇒ 1.34

A= 53.26°

Question 7:

In triangle PQR, ∠Q=80°, PQ=8 and QR= 6,

PR=?

Area of triangle = 1/2 *a*b*sinC

                          = 1/2*8*6*sin°80

                          =24*0.984

Area of triangle = 23.616 square units.

Question 8:

Consider the triangle JKL, here two sides and one angle is given,

we can use cosine law,

The equation set us is given by,

           [tex]a^{2} = b^{2}+ c^{2} -2bcCos\alpha\\b ^{2} = a^{2}+c^{2} -2acCos\beta\\ c^{2} = b^{2} +a^{2} -2baCos\gamma[/tex]

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