Find the equation of the line that has a y-intercept of 1 and is perpendicular to the graph of the line 2x + y = 4.

The system of inequality the satisfies the given credit conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.

One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality's solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.

Given that to graduate the core credit must be at least 13 credits. This is represented as follows:

C ≥ 13.

The credit of the electives should be at least 6, this is represented as follows:

E ≥ 6

The total credits should be no more than 27, this is represented as:

C + E ≤ 27

Hence, the system of inequality the satisfies the given conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.

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The 53rd term of the arithmetic sequence is 584

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2

The nth term of an arithmetic sequence is given as : a(n) = a+(n-1) d

where a is the first term and d is the common difference.

The first term in the sequence is -12 and the common difference is -1-(-12) = 11

a(53) = -12+( 53-1) 11

= -12+ 52×11

= 12+ 572

a(53) = 584

Therefore the 53rd term is 584

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The next three terms of the alternating series are - 1 / 16, 1 / 32 and 1 / 64, respectively.

Herein we find an alternating series of the form:

sₙ = (- 1)ⁿ · rⁿ⁻¹, for n = {1, 2, 3, ..., n}

Where:

By direct inspection, we find that r = 1 / 2 and the next three terms are: n = {5, 6, 7}

n = 5

s₅ = (- 1)⁵ · (1 / 2)⁵⁻¹

s₅ = - 1 · (1 / 16)

s₅ = - 1 / 16

n = 6

s₆ = (- 1)⁶ · (1 / 2)⁶⁻¹

s₆ = 1 · (1 / 32)

s₆ = 1 / 32

n = 7

s₇ = (- 1)⁷ · (1 / 2)⁷⁻¹

s₇ = 1 · (1 / 64)

s₇ = 1 / 64

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Answer:

Translation, then Rotation

Step-by-step explanation:

It is first moved(translation), then rotated(rotation) around the left meeting point of the graph by about 90 degrees to the right.

So, on solving the provided question, we cans ay that value o the  quadratic equation (x+1)(x+1) => x = -1, -1

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation will be

[tex]y=(x+1)^2[/tex]

so,

(x+1)(x+1)

x = -1, -1

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The correct question is -

What is the restricted domain of the quadratic(y=(x+1)^2) that would ensure that the inverse is a function?

Establish,Set a condition and Include an iteration are the three action.

Looping math is a part of lion that starts and end at the same point. It can refer to a continuous curve like Circle or a or to a sequence of discrete Point like a polygonal line.

1. Establish a loop control variable - This is a variable that will be used to control the loop. It is typically assigned an initial value before the loop starts, and is then modified each time the loop runs.

2. Set a condition - The loop should include a condition that will be evaluated each time the loop runs. If the condition is true, the loop will continue, and if the condition is false, the loop will end.

3. Include an iteration - The loop should include an instruction that will be executed each time the loop is run. This instruction can modify the loop control variable, or it can perform some other action.

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The definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex] will be 11.515

The region beneath a curve between two set limits is a definite integral. For a function f(x), defined with reference to the x-axis, the definite integral is written as baf(x)dx a b f (x) d x, where an is the lower limit and b is the upper limit.

The upper limit and lower limit are the two stated limits that make up the definite integral.

As per the question,

We have the value: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

Given:-

[tex]I=\int_0^2 x^3 \sqrt{x^4+1} dx[/tex]

Let [tex]x^4+1=t[/tex]

[tex]\\& 4 x^3 d x=d t \\& x^3 d x=\frac{d t}{4}[/tex]

x=0, t=0^4+1=1

x=2,

t=2^4+1

t=16+1=17

Now evaluating the value of integration:

[tex]$$\begin{aligned}I & =\int_{t=1}^{17} \sqrt{t} \frac{d t}{4} \\I & =\frac{1}{4} \int_1^{17} t^{1 / 2} d t \\& =\frac{1}{4}\left[\frac{t^{1 / 2+1}}{\frac{1}{2}+1}\right]_q^{17} \\& \left.=\frac{1}{4}\left[\frac{17^{3 / 2}-1^{3 / 2}}{\frac{3}{2}}\right]^{17 \sqrt{17}-1}\right] \\& =\frac{1}{4} \times \frac{2}{3} \times[120]\end{aligned}$$[/tex]

[tex]I=\frac{1}{6}[17 \sqrt{17}-1]=11.51546594[/tex]

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The correct questions should be:

Evaluate the definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

The solution of the given equation is (i) x = 3 ,(iii) x=-1/2 .

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that satisfy the equation. In other words, if f() = 0, therefore x = is a root of the quadratic equation f(x). The x-coordinates of the points where the curve y = f(x) intersects the x-axis are the real solutions of an equation f(x) = 0.

So we can find the root of 2[tex]x^2[/tex]— 5x —3 = 0 by factorising them.

=> 2x² - 5x - 3 = 0

=> 2x² - 6x + x - 3 = 0

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

=> (x-3)(2x+1) = 0

so the value of x = 3 , - 1/2

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Complete question :

For 2[tex]x^2[/tex]— 5x —3 = 0, determine which of the following are solutions?

(i) x = 3 (ii) x= –2

(iii) x=-1/2 (iv) x=-1/3

The Simplification of the rational expression n[1/x - 1/(x + 2) / 2] gives 1/[x(x+2)] or 1/(x²+2x)

Simplification of a rational expression as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

[1/x - 1/(x+2)] /2

The LCM of x and (x+2) is x(x+2). Thus, we have:

[1/x - 1/(x+2)] /2 = [(x+2 - x) / x(x+2)] /2

                        = [ 2 / x(x+2)] /2

                        = 1 / [x(x+2)]

                        = 1/(x²+2x)

Thus, the expression simplifies to 1/[x(x+2)] or 1/(x²+2x)

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Therefore , the solution of the given problem of distance comes out to be D = 11.66.

An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the shortest distance a moving object can travel. We frequently take into account the concepts of distance et displacement.

Here,

provided parameters

Dimensions of A = (-4,5)

B's coordinate number is (2,-5)

Unknown:

Size of AB =?

Solution:

Use the formula below to calculate the distance between these two places;

D = √(y2-y1)²+(x2-x1)²

x₁ = -4

x₂ = 2

y₁ = 5

y₂ = -5

enter the parameters, then solve;

=> D = √(2-(-4))  ²+(-5-5)   ²

=>D = √6² + (-10)² = 11.66

Therefore , the solution of the given problem of distance comes out to be D = 11.66.

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Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The amount of Cashew nuts is 0.205

The amoun of Peanuts is 0.295

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Amount of Cashew nuts = x

Amoun of Peanuts = y

Now,

We can make two equations.

x + y = 1/2 ____(1)

x = 1/2 - y  _____(20

Substituting (2) in (3)

6.25x + 2.10y = 1.90 _____(3)

6.25 (1/2 - y) + 2.10y = 1.90

3.125 - 6.25y + 2.10y = 1.90

3.125 - 4.15y = 1.90

3.125 - 1.90 = 4.15y

y = 1.225/4.15

y = 0.295

And,

x = 1/2 - y

x = 1/2 - 0.295

x = 0.205

Thus,

Amount of Cashew nuts = 0.205

Amoun of Peanuts = 0.295

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Answer:

The original number is 8.

Step-by-step explanation:

(x + 8) x 3 = 48

x + 8 = 48/3

x = 16 - 8

x = 8

Dilation is a transformation that can be used to resize an item. Dilation can cause the items to grow or shrink.

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

You have most likely started labour when your cervix is 3 cm dilated. Your cervix slowly widens to around 6 cm during this phase. It can take anywhere from a few hours to a few days to complete this stage of labour, however it typically takes between 8 and 12 hours. An average woman can dilate between 0.5 and 0.7 cm per hour during the active stage of labour. Whether this is your first child or not will also influence how quickly your cervix dilates. Experienced mothers typically progress through labour more quickly.

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The equation of the line with given slope and passing through the given point is y = -5x - 6.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

General form of slope intercept form of line is,

y = mx + d

Here d is the y intercept, which is the value of y coordinate when x coordinate is 0. And m is the slope.

Given that slope, m = -5

Also we have a point on the line (-2, 4)

Substituting these,

4 = (-5 × -2) + d

4 = 10 + d

d = -6

So the equation is y = -5x - 6.

Hence the equation of the line is y = -5x - 6.

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The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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Triangles which are similar to triangle ABC is the triangle having same corresponding angles.

A) triangle DEF where angle D is 35º and angle E is 20°.

C) triangle JKL where angle J is 35º and angle L is 125°.

D) triangle MNO where angle N is 20° and angle O is 125°.

Triangle can be defined as a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

We know the sum of all the interior angles in a triangle is 180°.

A triangle ABC, angle A is 35º and angle B is 20º.

∴ m∠C is 180° - (35 + 20)°.

m∠C = 180° - 55°.

m∠C = 125°.

∴ Triangles which are similar to triangle ABC is the triangle having the same corresponding angles.

Triangle DEF where angle D is 35º and angle E is 20°.

Triangle JKL where angle J is 35º and angle L is 125°.

Triangle MNO where angle N is 20° and angle O is 125°.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: 3x + 11 = k[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x + 11 - 11 = k - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = k - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{k - 11}{3} [/tex]

A non-function inverse would be a mathematical operation that does not produce a new function.

A function inverse is a new function that can be used to "undo" the effects of an original function. An example of a function inverse would be the inverse sine function of sin(x).

A non-function inverse would be a mathematical operation that does not produce a new function. Examples of non-function inverses include division, subtraction, and multiplication. These operations can be used to undo the effects of an original function, but they do not create a new function. Division can be used to “undo” multiplication, for example. However, the end result is not a new function, but rather a number or set of numbers. Subtraction and multiplication can be used to “undo” addition and division, respectively, but again, the end result is a number or set of numbers, not a new function. Therefore, these operations are not function inverses.

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The line created by Alexa is not a good representation for this data

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

The graph

On the graph, we can see that the line divides the points on the line unevenly

A good line of best fit would have equal number of points on either sides

Hence, the line is not a good representation

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Answer:

[tex]\huge\boxed{\sf x = -100}[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}[/tex]

So the sin(z) is approximately 0.4866.

In a right triangle, the two non-right angles are complementary, meaning that their measures add up to 90 degrees.

So, if ∠x is complementary to ∠z, then we can write the equation ∠x + ∠z = 90°

We also know that in a right triangle, the cosine of one angle is equal to the ratio of the adjacent side to the hypotenuse.

And the sine of one angle is equal to the ratio of the opposite side to the hypotenuse.

Given that cos(x) = 0.6.

We can find sin(z) by using the trigonometric identity, sin²(z) + cos²(z) = 1

sin²(z) = 1 - cos²(x)

sin²(z) = 1 - 0.6²

sin²(z) = 0.24

sin(z) = √0.24

sin(z) = 0.4866

So the sin(z) is approximately 0.4866.

It's important to note that the result is an approximation since the value of cos(x) is given as 0.6, which is not exact.

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Answer:

0

Step-by-step explanation:

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.

Given-

Kylie uses the number 400 to represent 400 miles north of the equator.

Kylie uses the number -2000 to show 2000 miles south of the equator.

What is the direction?

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.

As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.

The area of the wall is 80.7293 square feet. The number of cans that Asher needs is 4.

What is a pentagon?

A pentagon is a five-sided polygon with five angles. The term "pentagon" is made up of two terms, Penta and Gonia, both of which mean five angles. All of the sides of a pentagon meet end to end to form a shape.

Given the wall on a storage shed is a pentagonal shape.

The area of a pentagon can be divided into two shapes. The shapes are one is a rectangle and another is a triangle.

The length of the rectangular shape is (1+1+1) = 3 meters.

The width is (1+1) = 2 meters.

The area of the rectangular shape is 3 × 2 = 6 square meters.

The length of the base of the triangle is 3 meters.

The height of the triangle is 1 meter.

The area of the triangle is 1/2× base× height = 1/2 × 3×1 = 3/2 square meter.

Total area of the pentagon is  6 + 3/2 = 7.5 square meters.

1 square meter = 10.7639 square feet

7.5 square meters = (7.5×10.7639) square feet

                              = 80.7293 square feet

1 can of paint covers an area of 24 square feet.

Therefore to cover 80.7293 square feet, he needs 80.7293/24 = 3.36.

Thus he needs a minimum 4 cans of paint.

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Answer: abrimos

Step-by-step explanation: That's what it is on my quiz.

In the sentence "Nosotros _____ la ventana", the correct verb form is "abrimos". The best answer is option D.

The verb "abrir" is a Spanish verb that means "to open", and the first person plural form of this verb is "abrimos". So the sentence "Nosotros abrimos la ventana" translates to "We open the window".

The other verb forms in the options ("compartimos", "abro", and "escribimos") do not fit the context of opening the window. "Compartimos" means "we share", "abro" means "I open" (first person singular), and "escribimos" means "we write". So these forms are not the correct form to complete the sentence.

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Answer:

(x+3) and (5x-2)

Step-by-step explanation:

first get everything onto one side

5x^2+13x-6=0

then multiply 5 by 6 to get 30 and 15 times 2 is thirty and 15-2=13

5x^2+15x-2x-6=0

then split in half and factor both sides

5x^2+15x factored is 5x(x+3)

-2x-6 factored is -2(x+3)

so the answer is (x+3) and (5x-2)

This means that C-Town flour is more expensive because it is only $1.88 per pound compared to Food Bazaar's $2.25 per pound.

Cost is the amount of money or resources needed to acquire, maintain, or produce something. It can refer to either the expense of buying a good or service, the expense of labor, or the expense of resources such as time and materials. In a business context, cost is often used to refer to the total amount of money a company has spent on a particular activity or product.

C-Town's smaller bag size may make it a more convenient purchase, but it is not a good price compared to Food Bazaar.

In order to get the best deal, the shopper needs to compare prices and consider all of the factors. The size and quantity of the bags, the number of servings in each bag, the cost per serving, and the store's location are all important considerations. For example, C-Town may be closer geographically, but if the shopper needs more servings for their recipe, the extra cost to buy multiple bags at C-Town may be more expensive than buying a larger bag of flour at Food Bazaar.

In addition to the cost of the flour, other costs such as the cost of transportation to the store, the cost of any necessary packaging, the cost of any other ingredients needed for the recipe, and the cost of any other items purchased should also be taken into account.

Finally, shoppers should take the quality of the product into consideration. The type of flour, the freshness and shelf life of the product, and any special features of the product should also be taken into account. A low-cost bag of flour may be far less desirable than a more expensive bag of flour with higher quality ingredients.

Overall, to get the best deal on flour, shoppers need to consider all of these factors and compare prices between stores.

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Colleen's velocity increased from the first section to the second section, while it remained constant from the second section to the third section.

The measures in this problem are obtained considering the relation between velocity, distance and time.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

For session 1, considering decimal numbers, the parameters are given as follows:

Hence the velocity is of:

v = 9.9/2.2 = 4.5 miles per hour.

For session 2, the parameters are given as follows:

Hence the velocity is of:

v = 11.875/2.5 = 4.75 miles per hour.

For session 3, the parameters are given as follows:

Hence the velocity is of:

v = 15.4375/3.25 = 4.75 miles per hour.

The table is given by the image presented at the end of the answer.

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The cost of each t-shirt is $20 and cost of each pair of pant is $12.

In the given question a shopper purchased 8 t shirts and 5 pairs of pants for $220

The next day he purchased 5 t shirts and 1 pair of pants for $112. We have to find the cost of each pair of t-shirts and pants.

Suppose that t is the price of a T-shirt and p is the price of a pair of pants.

For $220, a customer bought 5 pairs of pants and 8 T-shirts:

8t + 5p = 220...…..(1)

He spent $112 on 5 T-Shirts and 1 pair of slacks the following day:

Now the equation should be

5t + p = 112...…..(2)

From the equation 2, p = 112 - 5t

Now putting the value of p in equation (1)

8t + 5(112 - 5t) = 220

8t + 560 - 25t = 220

Subtract 560 on both side, we get

-17t = -340

Divide by -17 on both side, we get

t = 20

Now putting the value of t in p = 112 - 5t

p = 112 - 5(20)

p = 112 - 100

p = 12

Hence, the cost of each t-shirt is $20 and cost of each pair of pant is $12.

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If the expression be −2/5h+7h+6 then the value of h be -10/11.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.

An expression in mathematics is made up of a number of variables, functions, and other elements (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

Using mathematical operations like addition, subtraction, multiplication, and division, a combination of numbers and integers can be expressed numerically in mathematics.

Let the equation be -2/5h + 7h + 6 = 0

Move 6 to the right side

-2/5h + 7h = -6

Multiply both sides by 5

-2/5h × 5 + 7h × 5 = -6 × 5

Simplifying the above equation, we get

33h = -30

Divide both sides by 33

33h/33 = -30/33

Therefore, the value of h = -10/11.

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