Is 5 an acute angle?.

The lines which are parallel among the given answer choices are; line 1; y = 1/2x - 6 and line 2; x - 2y = -1.

Recall that parallel lines are described by the feature such that; they have equal slopes but different y-intercepts.

Hence, by representing the equations in slope-intercept form; we have;

line 1; y = 1/2x - 6

line 2; x - 2y = -1;. y = 1/2x + 1

line 3; y = 4x + 6

line 4; y + 3 = 1/4 (x-6);. y = 1/4x - 9/2.

By comparison with the slope-intercept form equation; it follows that the lines which have equal slopes but different y-intercepts is the pair; line 1 and 2.

Hence, the parallel lines are; lines 1 and 2.

Read more on parallel lines;

https://brainly.com/question/26961508

#SPJ1

Answer:

66

Step-by-step explanation:

First find AD:

AD² + 9² = 41²

AD² = 1681-61=1600

AD = √1600 = 40

Now find BD:

BD² + 40² = 85²

BD² = 7225-1600=5625

BD = √5625 = 75

BC = BD - 9 = 75 - 9 = 66

Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given. The f(x) is 1.2x.

Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given.

Detailed explanation:

Given:

f(x - 5) = 1.2x - 6

Required:Find f (x) In order to solve f(x), we must translate f(x - 5) into terms of f. (x). The procedure is as follows.

f(x - 5) = 1.2x - 6

The expression to the right should be factored.

f(x - 5) = 1.2(x - 5) (x - 5)

Now that we have changed x for x - 5 in the previous formula, we may solve for f(x) (on the right hand side and the left hand side).

To learn more about value refer

https://brainly.com/question/27923727

#SPJ1

A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zero.

How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0. The quadratic function doesn't have any real roots if b2 - 4ac is less than 0.

Formula for the quadratic 4x2-8x9=0

4x2−8x−9=0

The answers can be found using the quadratic formula.

−b±√b2−4(ac)/2a

Replace the values

a=4

, b=−8

, and

c=−9

Then enter it into the quadratic formula to find

x.8±√(−8)2−4⋅(4⋅−9)/2⋅4

Simplify.

To continue, tap...

x=2±√13/2

There are various ways to display the outcome.

precise form:

x=2±√13/2

Number Form:

x=2.80277563…,−0.80277563…

To learn more about real roots here:

https://brainly.com/question/28939945

#SPJ4

Full Question = What is the nature the roots of quadratic equation 4x²-8x+9=0?​

According to the given statement, If the principal was invested at 2.45% compounded weekly for 78 months, then The principal is 9521.

When you first take out a home loan, you borrow a certain amount of money, which is known as the principal. Simply deduct your deposit for a house from the final selling price of your home to determine your mortgage principal.The principal amount means the amount you owe at any point in time.

The formula is =

11139.58 = x (1 + 0.0245) ^6.5

11139.58 = x (1.0245) ^ 6.5

11139.58 = 1.17x

x = 11139.58/ 1.17

x = 9521 (approx)

Hence, the principal is 9521.

To learn more about principal visit :

https://brainly.com/question/23084620

#SPJ1

The radius of the circle created by the ice skater is 1 yard.

What is circle ?

A circle is a two-dimensional geometric shape that is defined by a set of points that are all the same distance from a central point called the center. The distance from the center to any point on the circle is called the radius. The distance across the circle, passing through the center, is called the diameter.

The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

To learn more about circle visit : brainly.com/question/29142813

#SPJ4

The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

Answer:

n = 28

Step-by-step explanation:

2^2 is equal to 4, so we can plug in 2^2 as 4. Then, 4 * 7 = 28, so n = 28.

Answer:

14

Step-by-step explanation:

35/100= .35

.35 x 40= 14

Not red skittles: 14

Answer:

14

Step-by-step explanation:

35/100= .35

.35 x 40= 14

Not red skittles: 14

Answer:

These two equations are equivalent to each other because they both represent the same mathematical operation and they both yield the same result.

The first equation, 88 + 32, is adding 88 to 32, which results in the sum of 120.

The second equation, 90 + 30, is adding 90 to 30, which also results in the sum of 120.

In other words, both equations represent the same mathematical operation (addition) of two numbers (88 and 32 or 90 and 30) and both yield the same result (120).

Step-by-step explanation:

a brainliest pls

Answer:

the number would be anything over 59.50

Step-by-step explanation:



The area of the rectangle is 20. The length of the base and the height are 2√10 and √10.

From the case, we know that each point's locations are:

A = (-7, 4)

B = (-1, 6)

C = (0, 3)

D = (-6, 1)

Since the graph is a rectangle then it has 2 kind of sides, the height and the weight. Based on the given graph, we can categorize each side as:

Height = BC = DA

Base = AB = CD

We can find the length of each sides by using the coordinates of each point.

Length of a side = √[(x2 - x1)² + (y2 - y1)²]

Lenght of AB = √[(xB - xA)² + (yB - yA)²]

Length of AB = √[(-1 - (-7))² + (6 - 4)²]

Length of AB = √[6² + 2²]

Length of AB = √(36 + 4)

Length of AB = √40

Length of AB = 2√10 --> Length of the base

Length of BC = √[(xC - xB)² + (yC- - yB)²]

Length of BC = √[(0 - (-1))² + (3 - 6)²]

Length of BC = √(1² + (-3)²)

Length of BC = √(1 + 9)

Length of BC = √10 --> Length of the height

The area of the rectagle would be:

Area = base x height

Area = 2√10 × √10

Area = 20

Learn more about Area of Rectangle here: brainly.com/question/28570018

#SPJ1

Answer:

no its incorrect

Step-by-step explanation:

-2(8m+8)=-16 is worng its m=0

The problem is incorrect.

The correct solution for the given equation is:

-2(8m +8) = -2(8m) -2(8) = -16m -16

You cannot simplify it to -16 as the equation is not a true equation.

Please let me know if there is something more I can assist you with.

The evaluation of the simultaneous equation is as follows;

a) The simultaneous equations, indicates by plugging in the value of the variable x in the first equation, that the first equation is; 7·x² + 5·y + 3 = 0

b) The equation has no real solutions

Simultaneous equations are set two or more equations that have common solution.

The simultaneous equations are;

y² + x·y + 3 = 0...(1)

x = 6·y + 5...(1)

Plugging in x = 6·y + 5, in equation (1) we get;

y² + x·y + 3 = y² + y × (6·y + 5) + 3 = 0

y² + 6·y² + 5·y + 3 = 0

b) The number of solutions the simultaneous equation has can be obtained by solving the equation, obtained in part (a), 7·y² + 5·y + 3 = 0, as follows;

7·y² + 5·y + 3 = 0

The quadratic formula for finding the solution of the equation; a·x² + b·x  + c = 0, is; -b±√(b² - 4·a·c)/(2·a)

Where the discriminant is; b² - 4·a·c

Comparing the equations, we get;

a = 7, b = 5, and c = 3

b² - 4·a·c is therefore; 5² - 4 × 7 × 3 = -59

The discriminant is less than 0, therefore, there are no real solutions to the equation, but there are to imaginary solutions

Learn more about quadratic equations here: https://brainly.com/question/17105224

#SPJ1

The player's chances of scoring a goal on their next shot are 0.205, or 20.5%.

This is calculated by dividing the number of goals they scored (16) by the number of shots they took (78).

The formula for finding the probability:

P(A) = number of favorable outcomes / total number of possible outcomes

16 / 78 = 0.205

Probability is a mathematical concept that quantifies the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is unavoidable.

A probability of 0.5 (or 50%) means that the event is equally likely to occur or not occur.

To learn more about Probability.

https://brainly.com/question/16722133

#SPJ4

The number is 10 more than 8910+89 = 99

given that

One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them. Three apples and two apples are combined to make five apples in the example in the adjacent image. This observation is analogous to the formula "3 + 2 = 5" in mathematics (that is, "3 plus 2 is equal to 5").

In addition to counting things, addition can also be defined and performed using abstractions known as numbers, such as integers, real numbers, and complex numbers. A branch of mathematics called arithmetic includes addition. Addition can also be done on abstract objects like vectors, matrices, subspaces, and subgroups in algebra, another branch of mathematics.

10 more than 89

more than means plus or addition or sum

10+89 = 99

To learn more about more than:

https://brainly.com/question/29172205

#SPJ4

The total area of metal that can be seen on the surface of the wood is 43.2 square millimeters.

To find the total area of metal that can be seen on the surface of the wood, we need to find the area of one nail head and then multiply that by the number of nails.

The area of a circle is given by the formula:

A = πr²,

where π is the mathematical constant pi (estimated as 3 in this case) and r is the radius of the circle (half of the diameter).

So, the area of one nail head in square millimeters is:

A = 3 ×(2.4/2)² = 3 × 1.2² = 3 × 1.44 = 4.32 square millimeters

As there are 10 nails, so the total area of metal that can be seen on the surface of the wood in square millimeters is:

Total area = 4.32 square millimeters/nail × 10 nails = 43.2 square millimeters

Learn more about area of circle on:

brainly.com/question/15673093

#SPJ1

The logarithmic function is a mathematical function that expresses the exponent of a number to produce a given value, with the property of simplifying multiplication to addition and it is the inverse of the exponential function.

A logarithmic function is a mathematical function that expresses the power to which a number (the base) must be raised in order to produce a given value. The logarithm of a number is the exponent to which the base must be raised to produce that number.

A logarithmic function can be represented in the form of log_b(x) or logb(x), where b is the base of the logarithm and x is the value being evaluated.

For example, the logarithm of 1000 to the base 10 is 3, because 10^3 = 1000. It can be written as log10(1000) = 3.

The logarithm function has the property that log_b(x*y) = log_b(x) + log_b(y), which means that logarithms simplify the multiplication of numbers to the addition of logarithms.

The logarithmic function also has an inverse function, which is the exponential function, that's why logarithms and exponents are inverses of each other.

To know more on logarithmic function

https://brainly.com/question/16017369

#SPJ4

The transformed equation is y = -1/(x + 2) - 3

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

y = -1/x

We have the transformation to be

(2, -3)

This implies that we transform the function be (x + 2, y - 3)

using the above as a guide, we have the following:

y = -1/(x + 2) - 3

The above represents the new equation when the previous is transformed

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The order pairs to the given equations are (-3, 18) and (3, 6)

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given are two equation, f(x) = x²-2x+3 and f(x) = -2x+12

For solving, equate them,

x²-2x+3 = -2x+12

x² = 2x-2x+12-3

x² = 9

x = ±3

Put x = -3 in f(x) = -2x+12

f(-3) = -2(-3)+12

f(-3) = 18

And, Put x = 3 in f(x) = -2x+12

f(3) = -2(3)+12

f(3) = 6

Therefore, the ordered pairs are (-3, 18) and (3, 6)

Hence, the order pairs to the given equations are (-3, 18) and (3, 6)

Learn more about equations, click;

https://brainly.com/question/29657983

#SPJ1

A 30-degree angle is a measure of an angle, which is one-sixth of a full rotation or circle.

The measure of an angle is the amount of rotation between the two rays that form the angle, measured in degrees. The full rotation of a circle is 360 degrees, so one-sixth of a full rotation is 360 degrees divided by 6, which equals 60 degrees. However, a 30-degree angle is half of a 60-degree angle, so it is half of one-sixth of a full rotation, which is 30 degrees. It's also a right angle's complement angle, meaning that the sum of the 30 and 60 degrees angles is 90 degrees, a right angle. In geometry, 30-degree angles are often used in various calculations and constructions, such as finding the measure of complementary and supplementary angles, solving trigonometric problems, and drawing geometric figures.

To learn more about the angle, visit:

brainly.com/question/28451077

#SPJ4

Antionette can purchase a maximum of 56 adult-sized t-shirts.

What is algebraic ?

Algebraic refers to anything that pertains to algebra, which is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.

Let x be the number of adult-sized t-shirts that Antionette purchases.

We know that ,

The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

We can set up the equation to represent the total cost of all the t-shirts and the money Antionette has ,

(x6.25) + (454.50) = 550

To solve for x, we can simplify the equation by multiplying the number of adult-sized t-shirts by the cost per t-shirt and the number of youth-sized t-shirts by the cost per t-shirt, and then set it equal to the total money Antionette has ,

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

To learn more about algebraic visit : brainly.com/question/24875240

#SPJ4

The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

(x*6.25) + (454.50) = 550

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

The amount of natural numbers from m to k that Jane wrote is given as follows:

k - m + 1.

The natural numbers are the numbers that represent countable amounts, hence they are non-decimal and non-negative amounts.

The set of natural numbers can be represented as follows:

{0, 1, 2, 3, ...}

The number of natural numbers between 0 and 1 is given as follows:

2, which are 0 and 1.

2 = 1 - 0 + 1.

Hence the number of natural numbers between m and k is given as follows:

k - m + 1.

More can be learned about the natural numbers at https://brainly.com/question/24672369

#SPJ1

y = (1/3)x - 2 is an equation of a line where the slope of the line is 1/3 and the y-intercept of the line is -2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (1/3)x - 2

This is in the form of y = m + c

So,

This is an equation of a line.

The slope of the line = 1/3

The y-intercept of the line is -2.

Thus,

y = (1/3)x - 2 is an equation of a line.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

The square root of negative number can be negative imaginary number (complex number)

As we know the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.

Finding a square root of number is an inverse method of squaring a number.

A radical symbol '√' used to represent the square root of number.

If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],

We can write above relation as, m² = n

We know that square of any real number is positive.

For example, 3² = (3 × 3) = 9

(-3)² = (-3) × (-3) = 9

i.e., the square root of 9 is 3 and -3

Thus the square root of a negative number is undefined among the set of Real Numbers.

As we know the set of real numbers is subset of complex numbers.

In complex numbers, the imaginary number 'i' is the square root of negative 1.

When an imaginary number is squared, the result is negative number.

Consider example,

[tex]\sqrt{-16}\\\\ =\sqrt{16} \times \sqrt{-1}\\\\ =(\pm 4)\times i\\\\=\pm4i[/tex]

Learn more about square root here:

https://brainly.com/question/29286039

#SPJ4

The two chickens and a dog three animals won.

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.

Given that There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.

One dog speeds up 5mph and the chickens speeds up 10mph.

Then the dogs quit and the chickens keep going and speed up at 3 mph.

We have to find the winner.

The chicken win the race.

Hence, the two chickens and a dog three animals won.

To learn more on Speed click:

https://brainly.com/question/28224010

#SPJ1

7. 2n^2 - 5n + 10 = 7, is true.This means that if we substitute the value of n in the given equation we will get 7.

The Remainder Theorem states that if a polynomial is divided by a linear function, then the remainder is equal to the value of the polynomial at the root of the linear function.

In this case, we have the polynomial p(x) = 2x^2 - 5x + 10, which is being divided by x-n, and we are told that the remainder is 7. This means that when we substitute the root of x-n (which is n) into p(x), we get a remainder of 7. 2n^2 - 5n + 10 = 7, so this statement is true.

To learn more about Remainder Theorem:

https://brainly.com/question/27749132

https://brainly.com/question/30242306

#SPJ4

The numerator and denominator of a complicated rational expression must first be written as a single algebraic fraction in order to simplify the expression.

[tex]\frac{P(x)}{Q(x)}. Q(x)P(x)[/tex]

After that, simplify the result by multiplying the numerator by the reciprocal of the divisor. A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction. In other words, the overall fraction contains at least one small fraction.

There are two methods for reducing the complexity of fractions. For the numerator and denominator, identify common denominators. Make the numerators simpler. Add to the denominator and subtract the rational expressions from the numerator. Simplify.

Learn more about complex expression Visit: brainly.com/question/5564133

#SPJ4