What is an equation of the line that passes through the point (-5,7) and is parallel
to the line x + 5y = 10?

Answer:  x=[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

There are special right triangles in this! First, you need to find out what I am saying.

45-45-90 triangle

The bottom triangle has angles measures of 45, 45, and 90 degrees. There is a theorem that states that the two legs are equal, and the hypotenuse is leg×[tex]\sqrt{2}[/tex].

Plugging it in will give you leg lengths of  [tex]4\sqrt{2}[/tex].

Plug in that number into the side that connects with our next very special triangle:

30-60-90 triangle

Another theorem states that the hypotenuse is shorter leg times 2, the longer leg is shorter leg times [tex]\sqrt{3}[/tex].

Great! We have the shorter leg. Now we need to find the hypotenuse. Multiply [tex]4\sqrt{2}[/tex] by 2, and you get [tex]8\sqrt{2}[/tex]. That is x!

The final answer to this problem is: x=[tex]8\sqrt{2}[/tex]

Hope this helped a lot!

Answer:

B. (1.5, 2)

Step-by-step explanation:

Hope it helps!

Answer:

B

Step-by-step explanation:

The intersection of the two lines looks to be about (1.5 , 2)

The average rate of change of the function f(x)=2(3)x from x = 2 to x = 4   =  72

The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input.

To calculate the average rate of change, use the slope formula:

y2−y1/x2−x1=m

f(4)−f(2)/4−2=m

Finding the values of f(4) and f(2) will help us to simplify this.

f(4)=2(3)4=2(81)=162

f(2)=2(3)2=2(9)=18

m=162−18/2

m=144/2

m=72

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Answer:

6

Step-by-step explanation:

Perimeter = 2l + 2w

48 = 2(18) + 2(w)

48 = 36 + 2w

12 = 2w

w = 6

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The snowfall of both towns by equal in 4/5 hours or 48 minutes.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Assuming the no. of hours to be x, therefore the expression for town 1 is

y = (7/2)x + 5 and the expression for town 2 is y = (9/4)x + 6.

The snowfall of both towns by equal when,

(7/2)x + 5 = (9/4)x + 6.

(7/2)x - (9/4)x = 6 - 5.

[(14 - 9)x]/4 = 1.

(5/4)x = 1.

x = 4/5 hours Or (4/5)×60 = 48 minutes the snowfall of both towns by equal.

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Answer:

Slope: 1

__________

y-intercept: (0,0)

Step-by-step explanation:

Answer:

-[tex]\frac{16}{49}[/tex]

Step-by-step explanation:

First do: (-[tex]\frac{4}{7}) ^{2}[/tex], which is -[tex]\frac{4}{7}[/tex]*-[tex]\frac{4}{7}[/tex] which is [tex]\frac{16}{49}[/tex] and then add in the other negative:   -[tex]\frac{16}{49}[/tex]

29.78% of customers will most likely probability be waiting between 4 and 9 minutes.

The formula for the z score is-

z = (x - μ)/σ

In which,

μ =  mean of 10. 3 minutes

σ = standard deviation of 2. 7 minutes.

z score for the x = 4 minutes.

z = (4 - 10.3)/2.7

z = -2.33

z score for the x = 9 minutes.

z = (9 - 10.3)/2.7

z = -0.48

Thus,

Probability that the customer will have to wait between 4 and 9 minutes.

P(4 < x < 9) = P(-0.48 < z <  -2.33)

Use z score table-

P(4 < x < 9) =  0.3085 - 0.0107

P(4 < x < 9) = 0.2978

P(4 < x < 9) = 29.78%

Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.

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At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _l = 30^{2} + x^{2}[/tex]

= x² + 900

Similarly for the 2nd part of the wire

[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]

= 256 + 2025 - 45x + x²

= x² + 2281 - 45x

We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]

√x² + 900 + √ x² + 2281 - 45x

we can take the first derivative of this and set it to 0

[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]

x = 30

Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

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The interquartile range of the data will be 13

When arranged from lowest to highest, the IQR reflects the median 50% of values. To calculate the interquartile range (IQR), firstly compute the median (middle value) of the data's lower and upper halves. All those are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The interquartile range is the difference between quarters three and then one.

first, let us sort the data from lowest to highest

25,25,29,31,33,37,38,42,46

Q1- median of the lower half of the data=(29+25)/2=27

Q3-median of the upper half of the data=(38+42)/2=40

the interquartile range of the data will be Q3-Q1

40-27= 13

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The given function f(x) = 2 cos (x) is an even function because the result of the cosine of negative angles are the same with those of positive angles.

To check if a function is odd or even, we have to calculate f(−x).

The function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function as; f(x) = 2 cos (x)

f(-x) = 2 cos (-x)

Now, we know that the cosine of a negative angle always gives the same value as the cosine of the positive angle and as such, we can say that;

2 cos (-x) = 2cos (x)

The same result as f(x) which tells us that it is an even function

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The angle of elevation of the sun is [tex]tan^{-1}[/tex](106/ 135).

The angle of elevation:

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

Here we have to find the angle of elevation of the sun.

Data given:

length of the tower = 106 feet

shadow form by the tower = 135 feet

The formula for the angle of elevation = height/base

tanФ = height/base

        = 106/ 135

Ф = [tex]tan^{-1}[/tex](106/135)

Therefore the angle of elevation is [tex]tan^{-1}[/tex]( 106/ 135).

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Using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Compound interest works by periodically adding collected interest to your main, which is the sum you first deposited into the savings account so that interest can then be earned on both.

In essence, your interest begins to generate interest of its own.

Compound interest formula: [tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]

Now, calculate the amount Danni will have after 4 years:

[tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]

A = 5700(1+0.021)⁴

A = 5700(1.0210⁴

A = $6,194.09

Therefore, using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.

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Answer:

A=6199.48

Step-by-step explanation:

Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=5700, r=0.021, and t=4. Substitute the values into the formula and simplify.

A=5700e0.021⋅4

A=5700e0.084

A=5700(1.0876...)

A=6199.48

The amount in the account after four years is A≈6199, to the nearest dollar.

The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.

A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.

An example of an unary expression is: 12

A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7

A trinomial is always of higher degree than a monomial is false statement .

A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.

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Answer:

Below

Step-by-step explanation:

Total pages read = 40 + 60 +43  = 143 pages read

  Total pages of all of the books  = 70 + 85 + x  

       percentage READ =   (143) / ( 70 + 85 + x)  * 100% =  ???  

            percentage NOT read = 100 - ???

              (since 'x' was not given in the question post)

Read pages:

40+60+43=143

All pages:

70+85+43=198

198-143=55

55/198=0,2778

0,2778×100%=27.78%

Pattern Recognition is defined as the pattern is a number, shape, or something repeated in a particular way. Analysis of patterns should consider on different basis. The correct option is option (d).

The main basis of Pattern Recognition are the following:

1. Color change

2. Shape change

3. Rotation change

4. Size change

we have given three shapes pattern and we have to find out the perfect shape for forth place and the required shape follow the order like others.

After examine the pattern, we can see that the first figure is a filled triangle and the second figure is a hollow circle. This pattern is maintained alternately. The last figure(3rd place) is an open circle, so the next figure is a filled triangle.

So, the correct option is d.

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The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.

A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.

Initial Pass: 2 9 8 7 6 5 1 4 3

The array's first two members are initially compared using an insertion sort.

Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.

Therefore, 2 is currently kept in a sorted sub-array.

Second Pass: Continue with the next two elements and compare them.

2 8 9 7 6 5 1 4 3

Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.

Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.

Moving on to the following two components, which are 9 & 7,

2 7 8 9 6 5 1 4 3

Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.

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Answer: 1

Step-by-step explanation:

We can rewrite the equation as

12x = 4x +8

8x= 8

x=1

Answer:

44

Step-by-step explanation:

Essentially there are 3 triangles

The top left has a base of 5 and a height of 4

Its area is 1/2 x b x h = 1/2 x 5 x 4 = 10

Then there are two triangles with the same base of 2.5 + 6 = 8.5 and same height of 4 feet. So each of the triangles has the same area as the other.

Total area of both triangles = 2 (1/2 x b x h) = bh = 8.5 x 4 = 34

Total area = 10 + 34 = 44

Answer:

44 ft²

Step-by-step explanation:

Here's how I divided the parts of the composite figure:

1. There is a triangle at the left with the vertex pointing down and base above. The base is 5 ft. The height is 4 ft.

2. There are 4 triangles left. I divided them into two triangles like this:

An upper triangle which has a base of 2.5 ft + 6 ft, and a height of 4 ft with a horizontal base on the bottom and a vertex on the upper side.

A lower triangle that is a mirror image of the triangle just above. The dimensions are the same.

Triangle on upper left:

base = 5 ft

height = 4 ft

Triangles at right (2 triangles with the same dimensions)

base = 2.5 ft + 6 ft = 8.5 ft

height = 4 ft

area of triangle = base × height / 2

Total Area = (5 ft)(4 ft)/2 + 2 × (8.5 ft)(4 ft)/2

Total Area = 10 ft² + 34 ft²

Total Area = 44 ft²

The polynomial that represents the area of the booth is 3[tex]t^3[/tex]-12t.

Polynomial is a expression of variable, coefficients, and constants with mathematics operation of subtraction, addition, multiplication, and powers (only positive integers) of variable.

So, basically to calculate polynomials is the same as normal calculations except that the numbers are changed to variables.

Base length = 2[tex]t^2[/tex]-8

Height length = 3t

Calculate the area of triangle. So,

Area of triangle = (1/2) × base × height

= (1/2) × 2[tex]t^2[/tex]-8 × 3t

= (1/2) × 6[tex]t^3[/tex]-24t

= 3[tex]t^3[/tex]-12t

Thus, the area of the booth can be written by this polynomial 3[tex]t^3[/tex]-12t.

Your question is incomplete, but most probably your full question was (image attached).

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Answer:

[tex]\huge\boxed{\sf v = 81}[/tex]

Step-by-step explanation:

Let Vidya's age be v.

v - 15 = 66

Add 15 to both sides

v = 66 + 15

[tex]\rule[225]{225}{2}[/tex]

The dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

Given, a rectangular vegetable patch.

The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.

We have a budget of $96 for the project.

Let the length of the rectangle be, l

and breadth of the rectangle be, b

according to the ques,

4l + 8b = 96

l + 2b = 24

l = 24 - 2b

Now, area of the rectangle be,

Area = length×breadth

Area = l×b

A = (24 - 2b)b

A = 24b - 2b²

On differentiating both sides, we get

A' = 24 - 4b

b = 6

l = 24 - 12 = 12

So, the dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

Hence, The dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

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The probability of Ultraviolet performing fourth and Abacus performing last is 1/20.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

In a tour, five bands agree to determine the order of performance on the basis of random selection.

Since, the name of 5 bands are pulled randomly.

The probability of Ultraviolet performing fourth = 1/5

And the probability of Abacus performing last = 1/4, since 1 place is fixed for Ultraviolet.

Probability of Ultraviolet performing fourth and Abacus performing last

= 1/5 x 1/4 = 1/20

The required probability is 1/20.

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Answer:

56

Step-by-step explanation:

Answer: (2,0)

Step-by-step explanation:

Answer:

C. x = -5/3 and x = 2

Step-by-step explanation:

Bring the 10 over to the other side of the equation.

3x² - x - 10 = 0

Factorise.

(3x + 5)(x - 2) = 0

3x + 5 = 0 or x - 2 = 0

3x = -5 or x = 2

x = -5/3 or x = 2

The total number of pizzas were made in 4 hour in pizza shop is 24.

For the stated question-

For one pizza-

Ounce of cheese required = 5.

Ounces of sauce required = 3.

Total requirement = 8 ounces.

After 4 hours,

Total ounces combined of sauce and cheese used = 192.

Thus,

Number of pizza = 192 / 8

Number of pizza = 24

Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.

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The probability that there will be at least 12 successes in the total 18 trials with 60% rate of success is ¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

Binomial Probability distribution, In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments.

We have given that :

Rate of sucess (p) = 60% = 0.6

Rate of failure (q) = 1 - 0.6 = 0.4

Number of trials (n) = 18

We want to find P(there will be at least 12 sucess)

Use binomial distribution to find given mentioned probability.

X ~ Bin( 18, 0.6)

P (X= x ) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Let, X= Number of success among 18

So that it suitable for binomial distribution with parameters are n and p.

P(there will be atleast 12 success)

= P(X>= 12)

18

= ∑ ⁿCₓ (p)ˣ(q)⁽ⁿ⁻ˣ⁾ =

x = 12

¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

= say x

Hence, the required probability is x

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After solving the area of the triangle PQR obtained will be equal to 273.6 m²

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information given in the question,

p= 16.2

q = 35.0 m and,

m ∠R = 75°

Find x by cosine rule,

cos 75° = (16.2² + 35² - x²)/(2 × 16.5 × 35)

x = 34.5 m

The value of r is 34.5 mm then the third side of the triangle pqr will be,

Use heron's formula,

s = (16.2 + 35 + 34.5)/2

s = 42.85

Area = [tex]\sqrt{s(s-p)(s-q)(s-r)}[/tex]

A = √42.85(42.85 - 16.2)(42.85 - 35)(42.85 - 34.5)

A = 273.6 m²

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