50 Points! Multiple choice algebra question. Photo attached. Thank you!

The equation of this parallel line using point slope is  y = 4x - 31.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given that the equation of a line is y = 4x - 2.

Here, we observe that the slope m = 4

Parallel lines have the same slope. So, the slope of the new line is:

m = 4

Given that points (x1, y1) = (5, -11) are also in the new parallel line.

Using the Point-Slope form we can write:

y - y1 = m (x - x1)

Substitute the value of x and y coordinates in the above equation:

y - (-11) = 4 (x - 5)

y + 11 = 4x - 20

y = 4x - 20 -11

y = 4x - 31

Hence, the equation of this parallel line using point slope is  y = 4x - 31.

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When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be is 2000.

From the information, the biologist is researching a newly-discovered species of bacteria. At 8:00AM when she arrives at the lab, she puts a population of 600 bacteria into a favorable growth medium.

She measures the sample again before she goes home at 4:00PM and notes that the population is now 1300 bacteria. The difference in the population will be:

= 1300 - 600

= 700

When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be will be:

= 1300 + 700

= 2000

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The rearranged formulae with x as the subject is x=y-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here:

y=x+2

rearranging we get

x=y-2

Hence, The rearranged formulae with x as the subject is x=y-2

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The polynomial f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11 represents a cubic function equal to polynomial f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11 shifted up two units and left ten units.

Cubic equations are polynomials of grade 3, whose form is shown below:

y = a · x³ + b · x² + c · x + d

Where:

In this problem we need to apply horizontal and vertical translations to modify a given cubic polynomial:

Horizontal translation

f(x) → f(x - k)

Where k > 0 for a rightward translation.

Vertical translation

f(x) → f(x) + k

Where k > 0 for a upward translation.

First, assume a given cubic function:

(a, b, c, d) = (3, 2, - 4, 9)

f(x) = 3 · x³ + 2 · x² - 4 · x + 9

Second, apply a vertical translation two units up: (k₁ = 2)

f'(x) = 3 · x³ + 2 · x² - 4 · x + 9 + 2

f'(x) = 3 · x³ + 2 · x² - 4 · x + 11

Third, apply a horizontal translation ten units left:

f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11

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Answer: 9/4 (This a fraction)

Step-by-step explanation:

We do Keep. Switch. Flip aka KSF

we keep 3/4 and change the sign multiplication and flip 1/3 to 3/1

3/4 x 3/1 = 9/4

Note: I tried my best, don't hate me if it's wrong.

13.3 mg should be given to a patient who weighs 190lb.

What is the unitary method?

The unitary method determines the value of a unit and then the value of the required number of units.

Assume you go to the market to buy six apples. The shopkeeper informs you that he is selling ten apples for Rs one hundred. The apples are the units in this case, and the cost of the apples is the value. It is critical to recognise the units and values when using the unitary method to solve a problem.

Given that a patient weighs 40 lb, then he needs 2.8 mg of medication.

Now find how much medication is required for a  patient whose weight is 1 lb.

Apply unitary method:

A patient weighs 1 lb, then he needs 2.8/40 mg of medication.

Now find how much medication is required for a  patient whose weight is 190 lb.

A patient weighs 190 lb, then he needs (2.8×190)/40 mg of medication.

                                                                = 13.3mg

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A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in  dy/dx + sin^2(x) = cos^2(x)

B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.

D: Because there is only one function y and its derivative  dy/dx involved in the equation, first-order differential equations are what it is.

G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.

H: The equation may be written as dy / y =  (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .

I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as  (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .

J: The equation is self-sufficient; it is not dependent on any explicit function of t.

       Therefore, the differential equation  dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.

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Answer:

slope = - 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (0, 2 ) and (x₂, y₂ ) = B (2, 0 )

m = [tex]\frac{0-2}{2-0}[/tex]  = [tex]\frac{-2}{2}[/tex] = - 1

Answer: For the first number 40, one possible set of factors that have a product of 40 and a sum of 13 is (1,40) or (40,1) . Because 1*40=40 and 1+40 = 41

We can not have any other pair whose product is 40 and sum is 13 as it is not possible for any pair of factors of 40 to sum up to 13 as the only pair is (1,40) or (40,1) and their sum is 41

Step-by-step explanation:

The number of children that attend the fair on the day tha 350 were present in the fair is 200

The number of children in the fair is obtained by solve a simultaneous equation generated as follows

let x be the number if children be x and the number of adults be y. such that

x + y = 350

and from  the cost we  have

$3y + $2x = 900

the two equations are

x + y = 350

3y + 2x = 900

solving simultaneously with a calculator

x = 200 and y = 150

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Answer:

11.  TS = 123.8 cm

12.  SW = 108.8 cm

13.  m∠SVU = 123°

14.  m∠STU = 123°

15.  US = 217.6 cm

16.  m∠TUV = 57°

Step-by-step explanation:

Properties of a Parallelogram:

11.  Opposite sides are equal in length:

12. Diagonals bisect each other (divide into 2 equal parts):

13. Adjacent angles are supplementary (sum to 180°):

     ⇒ m∠SVU + m∠TSV = 180°

     ⇒ m∠SVU + 57° = 180°

     ⇒ m∠SVU = 123°

14. Opposite angles are equal:

15. Diagonals bisect each other (divide into 2 equal parts):

     ⇒ US = 2 × UW

     ⇒ US = 2 × 108.8

     ⇒ US = 217.6 cm

16. Opposite angles are equal:

The given equation is inconsistent equation.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Identity equations are those equations which are satisfied for every values of the variables.

Conditional equations are those which is only true for some values.

Inconsistent equations are those which does not have a solution.

Given equation is,

8 (x + 6) = 9 + 8x

8x + 48 = 9 + 8x

8x - 8x = 9 - 48

0 = -39

There is no solution for the variable x. So it is inconsistent equation.

Hence the equation is inconsistent.

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The amount of Brown material: 39 gallons and Green material: 13 gallons.

A proportion is a fraction of a total amount, and in problems involving it, basic arithmetic operations such as multiplication or division are used along with the unit rates to find the equivalent measures.

On the first column of the table, the total amount is:

12.75 + 4.25 = 17 gallons.

The fractions of each material are given as follows:

Brown material: 12.75/17 = 0.75

Green material: 4.25/17 = 0.22.

Therefore, the amount of brown material needed with 52 gallons is:

0.75 x 52 = 39 gallons.

The amount of green material needed with 52 gallons is:

0.25 x 52 = 13 gallons.

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The value of 98,060 × 4 = 392240.

The distributive property of multiplication states that when we multiply a number by the total of two or more addends, the outcome is the same as when we multiply the number by each addend separately.

The sum and difference of two more numbers are both subject to the distributive property of multiplication.

According to the Distributive Property of Multiplication:  

                            (A + B)C = AC + BC

Here we have

98,060 × 4

As we know 98060 = (98000 + 60)  

=  (98000 + 60) × 4  

=  (98000 × 4) + (60 × 4)      [ ∵ (A + B)C = AC + BC ]

=  392000 + 240

=  392240

Therefore,

The value of 98,060 × 4 = 392240.

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Answer:

[tex]\displaystyle x=\frac{1\pm\sqrt{5}i}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2x^2=2x-3\\2x^2-2x+3=0\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(3)}}{2(2)}\\\\x=\frac{2\pm\sqrt{4-24}}{4}\\ \\x=\frac{2\pm\sqrt{-20}}{4}\\ \\x=\frac{2\pm2\sqrt{5}i}{4}\\\\x=\frac{1\pm\sqrt{5}i}{2}[/tex]

Answer:

9) 11.18 feet

10) 6.14 inches

Step-by-step explanation:

The first problem sets up a situation with a right triangle. See image. Two sides are given, so you can use Pythagorean Theorem to find the last side. See image.

The second problem also sets up a right triangle. But here only one side length is given and one angle, so you use trigonometry. Sine is the ratio of the opposite side/hypotenuse. Use sine to find the missing length. See image.

I rounded these answers to the nearest hundredth (two decimal places) Check directions if they should be rounded more or less.

Frank is going to plant d vegetable seeds in one garden, and 3d + 6 vegetable seeds in another. So Frank is going to plant 4d + 6 vegetable seeds in total.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebra is used to solve problems and to describe patterns and relationships between variables. It is a powerful tool for modeling and understanding many types of real-world situations.

In algebra, letters or other symbols are used to represent numbers or quantities that are not known. These symbols can be manipulated using mathematical operations, such as addition, subtraction, multiplication, and division. Equations and inequalities involving these symbols can be solved to find the values of the unknowns. Algebraic equations can also be graphed to visualize the relationship between the variables.

To find the total number of vegetable seeds Frank is going to plant, we can add the number of seeds he is planting in each garden:

d + (3d + 6) = d + 3d + 6 = 4d + 6

So Frank is going to plant 4d + 6 vegetable seeds in total.

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The Pythagorean theorem states that the square of a right-angled triangle's hypotenuse is equal to the sum of the squares of its other two sides.

You can demonstrate the congruence of two right triangles using the Hypotenuse-Leg (HL) Triangle Congruence Theorem, which is a particular instance. A right triangle is congruent with another right triangle if its hypotenuse and one of its legs are congruent with its hypotenuse and one of its legs.

The hypotenuse (longest side) square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem (base and perpendicular).

The right triangles are said to be congruent if their respective hypotenuses and legs are congruent with one another, according to the hypotenuse-leg (HL) theorem. By the HL theorem, these triangles are congruent.

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Step-by-step explanation:

[tex] - 1 > - 2(x - 4) - 5(4x - 7) \\ - 1 > - 2x + 8 - 20x + 35 \\ - 1 > - 2x - 20x + 8 + 35 \\ - 1 > - 22x + 43 \\ 22x > 43 + 1 \\ 22x > 44 \\ \frac{22x}{22} > \frac{44}{22} \\ x > 2[/tex]

The resulting quadratic equation is x^2 - x - 7 = 0.

The x-values for which f(x) < 1 can be determined by solving the inequality f(x) < 1.

Since f(x) is not given in the question, we must first define it. Let's assume f(x) = x^2 - 2x + 1.

The resulting equation is (x - 1)^2 < 0.

The function f(x) is defined as f(x) = x^2 - x - 6.

From here, the equation can be solved for x using the quadratic formula, which gives us x = [7 + sqrt(73)]/2 and x = [7 - sqrt(73)]/2.

Therefore, the x-values for which f(x) < 1 can be expressed in interval notation as (-∞, [7 - sqrt(73)]/2) U ([7 + sqrt(73)]/2, ∞).

(-∞, -3/2] ∪ [-3/4, 1)

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An equivalent expression of the expression 22/- 4 is,

⇒ - 11/2

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 22/-4

Now, We can simplify as;

⇒ 22 / - 4

⇒ - 22/4

⇒ - 11/2

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To fulfill all of the orders, they must pay their employees a total of $9600 as 480 * 20 = $9600 .

This unit technique is a way of problem-solving that entails calculating the value of a specific unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single model value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mechanics of matrices or operators, abstract algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

given

Each employee is paid $12 per hour for the first 40 hours,

therefore $480 must be paid to all of their employees in order to fulfill all orders (20 * 3 = 60 days for 20 automobiles

, or 5 employees working 8 hours per day).

480 * 20 = $9600

To fulfill all of the orders, they must pay their employees a total of $9600.

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The right triangle having the hypotenuse has x = 17.88.

Since a right triangle's three interior angles always add up to 90 degrees and a triangle's three interior angles always add up to 180 degrees, the other two interior angles must also always add up to 90 degrees (they are complementary).

Hypotenuse refers to the side across from the right angle. The legs are the sides extending from the right angle. If applying the Pythagorean Theorem, the hypotenuse or its length is frequently denoted with a lowercase c. A and B are typically used to denote the legs' lengths.

Using trigonometry rule

Cos 33° = 15/x

x = 17.88

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From the following set of points, 26 is a trapezoid but not a isosceles trapezoid while 27 is not a trapezoid at all.

A closed, four-sided trapezoid in two dimensions has a perimeter and an area. Two of the sides are considered the bases of the trapezoid because they are parallel to one another.

The non-parallel sides of a trapezoid are referred to as its legs or lateral sides. The altitude is that distance between two parallel sides that is shortest. The area of a trapezoid can be easily calculated because the opposite sides are parallel to one another.

If the given points make an isosceles trapezoid then AB and CD must be equal and BC and AD must not be equal

Lets solve

26. AB =  [tex]\sqrt{(-4-(-4))^2+(-1-6)^2}[/tex]  = 7

CD =  [tex]\sqrt{(2-(2))^2+ (6-(-4))^2}[/tex] = 10

BC = [tex]\sqrt{(-4-2)^2+ (6-6)^2}[/tex] = 6

AD = [tex]\sqrt{(-4-2)^2+ (-1-(-4))^2}[/tex] = 3√5

Thus, this not an isosceles trapezoid.

27. AB =  [tex]\sqrt{(-5-2)^2+(2-6)^2}[/tex]  = 8.06

CD =  [tex]\sqrt{(-1-2)^2+ (6-1)^2}[/tex] = 5.83

BC = [tex]\sqrt{(-5-(-1))^2+ (6-6)^2}[/tex] = 6

AD = [tex]\sqrt{(2-(-5))^2+ (-1-2)^2}[/tex] = 3√5

None of the side make an trapezoid and it is not a isosceles trapezoid

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The derivative of the function F(x) =x2 et4dt is e−x4(2x)−e−x2.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative.

Take the derivative to differentiate anything.

Finding the slope at any point is the same as taking the derivative of a function, so differentiating is just finding the slope.

You may be aware that is typically indicated by either

I'm assuming you mean to determine the derivative of F(x)

F(x)=∫x2xe−t2dt

Let G(x)=∫x0e−t2dt

According to the calculus fundamental theorem

F′(x)=ddx(G(x2)−G(x))

=G′(x2)(2x)−G′(x)

=e−x4(2x)−e−x2.

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Answer: The correct answer is choice A. 5.4

Step-by-step explanation:

I hope this helps! :D

Factor of x ^2+7x−18 is (x−2)(x+9)

What is factorization?

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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The value of K so that the line passing through (-4, 1) and (k, 3) is perpendicular to 8x + 13y = 26 is solved to be

A linear function consists of functions where the variables has exponents of 1. the relationship is expressed in the slope intercept form as below.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The given equation is rewritten in slope intercept form as follows

8x + 13y = 26

13y = 26 - 8x

y = 2 - 8/13 x

the slope is 8/13

For a perpendicular line the slope = -1/m

= -1/(8/13)

= -13/8

For a line to have a slope of -13/8, the points will be

-13/8 = (1 - 3) / (-4 - k)

cross multiplying

-13(-4 - k) = 8(1 - 3)

52 + 13k = -16

solving for k

13k = -16 - 52

13k = 68

k = 68/13

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The perimeter of this figure, to the nearest unit, is 21.9 units, and the area of this figure, to the nearest square unit is 62.53 square units.

What is a square?

It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.

We have a figure shown in the picture made with squares and circles.

To find the perimeter of the figure.

First, calculate the circumference of the circle portion.

The circumference of the 1/4 circle = (1/4)2πr

The radius of the circle r = 5 units

The circumference of the 1/4 circle = (1/4)2π(5)

The circumference of the 1/4 circle = 7.85 units

The perimeter of the figure = 2 + 5 +7.85 + 2+ 5

The perimeter of the figure = 21.85 units ≈ 21.9 units

The area of the figure = area of the square - an area of the square(5×5) +

area of the 1/4 circle

The area of the figure = 3×3 - 5×5 + π(5)²

The area of the figure = 9 - 25 + 78.53

The area of the figure = 62.53 square units

Hence, the perimeter of this figure, to the nearest unit is 21.9 units, and the area of this figure, to the nearest square unit is 62.53 square units.

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