the sum of vectors a and b where a = <3, 2> and b = <-1, 4> is

Answer:

24×1 equal 24 and multiply it by 1/6 is 24/6 and simplifying it would make 4.

answer=4

not sure if this is what u want

Step-by-step explanation:

hope it helps

Using fractions subtraction, we know that the original fraction in the given situation is -7/8.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.

So, we have the fraction:
1/8

Now, the original fraction would be:

1/8 - 4/4

1-8/8

-7/8

Therefore, using fractions subtraction, we know that the original fraction in the given situation is -7/8.

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If the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism. The correct answer would be an option (D).

When you make a horizontal slice through a solid, it cuts through the object along a plane and the shape that is produced is the cross-section of that plane.

A rectangular prism will produce a rectangle.

A pentagonal prism will produce a pentagon.

A square prism will produce a square.

A trapezium prism will produce a trapezium.

A hexagonal prism will produce a hexagon.

Therefore, if the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism.

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The amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.

Let x be the amount of the loan with 4% interest and y be the amount of the loan with 3.5% interest. Then, x + y = 6000, because the total amount borrowed is 6000.

The interest owed on the 4% loan after 5 years is 4% of x per year, so the total interest owed after 5 years is 5 * 0.04x = 0.20x.

Similarly,

The interest owed on the 3.5% loan after 5 years is 3.5% of y per year, so the total interest owed after 5 years is 5 * 0.035y = 0.175y.

The total interest owed after 5 years is $1062.50, so 0.20x + 0.175y = 1062.50.

Now we have two equations, so we can solve for x and y.

First, substitute x + y = 6000 into the second equation, and we get,

0.20x + 0.175(6000 - x) = 1062.50

Expanding the second term, we get,

0.20x + 1035 - 0.175x = 1062.50

0.025x = 27.50

Dividing both sides by 0.025,

x = 1100

So the amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.

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A soccer ball in the air for time 4.929 seconds.

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory

The vertical position of a projectile launched from the ground with velocity  v and angle  θ  is:

y(t)=−4.9t^2+(vsinθ)t

We can factor this as:

y(t)=t(−4.9t+vsinθ)

Now we know that  t=0  is one root, when you first kick it, so we only need to solve for the other root

−4.9t+vsinθ=0

t=vsinθ/4.9

Plugging in what we have:

t=25sin61/4.9

t = 25 *0.96611777 /4.9

t≈4.929 sec

So about  4.929 seconds.

A soccer ball in the air for time 4.929 seconds.

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Answer:

Mistake: From line 4 to 5

Correct Solution:

7x - 5 = 5x + 9

2x = 14

x = 7

Step-by-step explanation:

On line 4 to 5, Ms.Shreve should've subtracted 5 to 7, and add 5 to 9, not vice versa.

∠AGH = ∠GHD = 60° (alternating angles)

∠EGB = ∠AGH = 60° (Vertically Opposite Angles)

Coplanar infinite straight lines that are parallel have no points of intersection. In the same three-dimensional space, parallel planes are any planes that never cross. Curves that are parallel to one another and maintain a predetermined minimum distance do not touch or intersect.

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.

According to the alternative angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.

It is given that AB and CD are parallel to each other

EF is the transversal

∠GHD = 60°

∠AGH = ∠GHD = 60°(alternating angles)

∠EGB = ∠AGH = 60° (Vertically Opposite Angles)

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The numbers are classified as rational or irrational as follows:

Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.

The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.

Hence the numbers are classified as follows:

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The decimal equivalent of 1101.011 in base 7 is 343.14300.

The decimal system is a base 10 numbering system that is widely used in everyday life.

To convert 1101.011 from base 7 to decimal, we need to start by converting the whole number portion of the value. 1101 in base 7 is equivalent to

=> 1 x 7³ + 1 x 7² + 0 x 7¹ + 1 x 7⁰ = 343

Next, we need to convert the fractional portion of the value. The fraction 0.011 in base 7 is equivalent to

=> 0 x 7⁻¹ + 1 x 7⁻² + 1 x 7⁻³ = 0.143

Finally, we add the decimal equivalent of the whole number portion and the fractional portion to find the decimal equivalent of 1101.011 in base 7.

=> 343 + 0.143 = 343.143,

which is the decimal equivalent of 1101.011 in base 7.

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The 6n × 6n board can be tiled with trominoes if n is even.

A tromino is a geometric shape made up of three squares, and a 6n × 6n board is a grid of squares with 6n rows and 6n columns.

The question is whether it is possible to tile a 6n × 6n board with trominoes so that no two overlap and all squares are covered.

In order for a 6n × 6n board to be tiled with trominoes, n must be an even number. This is because each tromino covers three squares and there must be a whole number of trominoes to cover the entire board. If n is even, the board can be tiled with trominoes.

To do so, the board is divided into 2n rows of 3 squares each and 2n columns of 3 squares each. A tromino is placed in each of the resulting 3 × 3 squares, covering all of the squares in the board.

Each tromino covers three squares and the board can be divided into a grid of 3 × 3 squares that can each be filled with a tromino.

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The amount of fence needed to enclose a rectangular garden is 90 feet.

To determine the amount of fence needed to enclose a rectangular garden with length 14 feet and width 31 feet, you need to calculate the perimeter of the rectangle. The perimeter is the total length of all four sides of the rectangle.

The formula for the perimeter of a rectangle is given by

2 * (length + width)

In this case, the length is 14 feet and the width is 31 feet, so the perimeter is

2 * (14 + 31) = 2 * 45 = 90 feet

This means that 90 feet of fence is needed to enclose the rectangular garden.

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Answer:

3.125 cm

Step-by-step explanation:

cos50 ≈ 0.64 = b/h
b = 2
∴ h = 2/0.64 = 3.125 cm

Answer:

True

Step-by-step explanation:

the function is y = x/5

The linear inequality will be 2.5x+1.5y<=9, where x=boxes of popcorn and y=no. of drinks.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given that  Shiloh and Mario went to the movies. At the theater a small box of popcorn costs $2.50 each and each drink costs $1.25 each.

Shiloh and Mario only have $9 to spend.

So, let  x=boxes of popcorn and y=no. of drinks

Therefore, given statements can be satisfied by linear inequality given

as 2.5x+1.5y<=9.

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Half a kilogram of mixed nuts costs 36 cents.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Five-sixths of a kilogram costs 60 cents.

That means,

1 kilogram of mixed nuts costs = 60 x 6/5 = 72 cents.

So,

half a kilogram of mixed nuts costs = 72/2 = 36 cents.

Therefore, the required cost is 36 cents.

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Two week ago I bought 10 cupcake last week I bought 7 today id like to follow this pattern so 4 cupcakes are needed.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.

As per the given,

Number of cupcakes in two weeks ago = 10

Number of cupcakes in last weeks ago = 7

Decrement of cupcakes = 10 - 7 = 3

Thus,

Number of cupcakes in today = 7 - 3 = 4

Hence "The number of cupcakes is 10 - 7 = 3 thus with follow this pattern the number of cupcakes today will be 7 - 3 = 4 cupcakes".

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The present age of Lia is 35 and the present age of Myra is 5.

The sum of Lia's age and Myra's age is 40.

Let the present age of Myra is x and the present age of Lia is y.

So the equation should be

x + y = 40..................(1)

After 10 year the age of Myra is x + 10 and age of Lia is y + 10.

In 10 year Lia will be three time a older than Myra.

y + 10 = 3(x + 10)

Simplify

y + 10 = 3x + 30

Subtract 10 on both side, we get

y = 3x + 20

Now putting the value of y in the equation 1.

x + 3x + 20 = 40

4x + 20 = 40

Subtract 20 on both side, we get

4x = 20

Divide by 4 on both side, we get

x = 5

The present age of Myra is 5.

Now putting the value of x in equation 1

x + y = 40

5 + y = 40

Subtract 5 on both side, we get

y = 35

The present age of Lia is 35.

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The complete question is:

The sum of Lia's age and Myra's age is 40. In 10 year Lia will be three time a older than Myra. How old is each person?

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are  –6x + 15 < 10 – 5x  and an open circle is at 5 and a bold line that starts at 5 and is pointing to the right which is denoted as option C and D.

This is referred to as a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Workings:

-3(2x-5)<5(2-x)

-3(2x-5)<5(2-x)

-6x+15<10-5x --- C

Subtract 15 from both the sides of the inequality

-6x + 15 -15 < 10 -5x -15

-6x < -5 -5x

-6x +5x < -5

-x < -5

Multiply both sides by (-1) ,

x > 5 .

x> 5 on the number line depicts an open circle is at 5 and a bold line starts at 5 and is pointing to the right .

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The full question is:

Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.

(a) x < 5

(b) –6x – 5 < 10 – x

(c) –6x + 15 < 10 – 5x

(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.

(e) A number line from negative 7 to 3 in increments of 1,  An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.

Answer:

1 and 1/6

Step-by-step explanation:

You have to add together the growth of the 2 weeks. So, 1/3 + 5/6 but to add these you need to find the common denominator. I would change 1/3 to have a denominator of 6. To turn 3 into 6 you have to multiply by 2 and whatever you do to the bottom you do to the top so 1 x 2. Now that your fraction of 1/3 is 2/6, you can add the 2 weeks together. 2/6 + 5/6 = 7/6, which can also be written as 1 and 1/6.

Answer:

c.

the length of WZ is

[tex] \sqrt[3]{13} [/tex]

The greatest common monomial factor of this polynomial will be 14x²y³.

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The polynomial is given below.

⇒ 14x³y⁵z² - 98x²y⁴x² + 28x²y³

⇒ 14x²y³(xy²z² - 7x²y + 2)

The greatest common monomial factor of this polynomial will be 14x²y³.

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the dimensions of rectangle is  l = 23 and w = 14

Given,

A rectangle has perimeter 74 inches, and its area is 322 square-inches

To find the dimensions of this rectangle.

Steps:

With this question it is known that the perimeter of the rectangle is 74 inches and the area is 322 inches. the question is what is the length and width of the rectangle.

The formula for the perimeter of a square is P = l + l + w + w or P= 2(l + w) and the formula for the area of a rectangle is A = l x w.

the formula for the perimeter of a rectangle is P= 2(l + w) that means w=l(p/2-l) and the formula for the area of a rectangle is A = l x w, usually l is longer than w

insert the w equation with the perimeter formula into the area formula A = l (p/2-l) to

solve this equation:    [tex]l\\^{2}[/tex] - ([tex]\frac{P}{2}[/tex]) x l + A=0 to get l

 [tex]l\\^{2}[/tex] - (74/2) l +322=0

 [tex]l\\^{2}[/tex] - 37l + 322=0

(l-23)(l-14)=0 so

l =23 and l=14,

it can be concluded that l = 23 and w = 14

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No conclusion can be drawn with the given information regarding function.

No conclusion can be drawn about whether f is defined at x=1 or whether f(1)=5 based solely on the statement "lim f(x) = 5." The limit of a function only describes the behavior of the function near a particular value, not necessarily the value of the function at that point.

It is possible for a function to have a limit at a point without being defined at that point, or for a function to be defined at a point but have a different value there than its limit.

Hence, no conclusion.

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As per the initial-value problem, the formula for the solution is dy/dt = y³

An initial-value problem, which involves finding a formula for a solution based on an initial value and a differential equation.

In this specific problem, the differential equation is

=> dy/dt = y³

and the initial value is

=> y(0) = 1.

To solve for the formula, we will use mathematical techniques to find the solution for y based on the given conditions.

The domain of the definition of the solution refers to the set of all possible values for the independent variable (t in this case) for which the solution is valid. In this problem, the domain of the solution is determined by the conditions that ensure the solution is well-defined.

As the solution approaches the limits of its domain, certain properties of the solution may change.

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The x-coordinates of the inflection points of this function are −1 and −1/3.

In this case, we are looking for the open intervals on which the function f(x) = −x⁴ − 9x³ + 4x − 6 is concave up (down) and the x-coordinates of the inflection points of the function.

To find the open intervals on which f is concave up, we must first calculate the second derivative of the function.

The second derivative of the function f(x) is

=> f''(x) = −12x³ − 27x² + 4.

This means that the function f is concave up when f''(x) > 0 and concave down when f''(x) < 0. Solving the equation f''(x) > 0 will give us the intervals on which the function is concave up.

These are the intervals (−∞, −1), (−1, −1/3), and (−1/3, ∞).

Similarly, solving the equation f''(x) < 0 will give us the intervals on which the function is concave down. These intervals are (−1, −1/3) and (−1/3, 0).

We can now determine the x-coordinates of all inflection points of the function f by finding the x-values at which the second derivative is equal to zero.

Solving the equation f''(x) = 0 will give us the x-coordinates of the inflection points, in this case −1 and −1/3.

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Answer:

The zeroes of the function are: [tex]\frac{-1}{3}[/tex].

Option b would be the correct answer.

Step-by-step explanation:

The zeros of a function are defined as the point at which the value of the function is zero. We can say the zeros are the x values where the graph intersects the x-axis. We obtain these algebraically by setting the function equal to zero then solving.

Given

[tex]y=3x+1[/tex]

Lets find all real zeros of the function.

Replace [tex]y[/tex] with 0.

[tex]0=3x+1[/tex]

Subtract 1 from both sides of the equation

[tex]-1=3x[/tex]

Divide both sides of the equation by 3.

[tex]\frac{-1}{3} =\frac{3x}{3}[/tex]

Simplify the right side by cancelling the common factor of 3.

[tex]\frac{-1}{3} =x[/tex]

The box should have inches for its length, width, and height. 2. Divide the result of multiplying the length, breadth, and height by 1,728. In cubic feet, this represents the container's volume.

As such, it is listed here for documents that can simply be destroyed.

The instructions below can be used to calculate a container's cubic foot volume.

In cubic feet, this represents the container's volume.

A case in point

18"L x 11.5"W x 9"H = 1,863 cubic inches

1,863/1,728 equals 1.078 cubic feet.

The aforementioned container has a volume of 1.1 cubic feet (round to the nearest tenth).

The Complete Question.

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The center of dilation of the triangle is (7, 5)

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

Two triangles

The center of dilation of the triangles is the center of both triangles

From the figure, we can see that the center is located at (7, 5)

Hence, the center is (7, 5)

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Answer:

The answer is 18.

Step-by-step explanation:

You need to divide 144 by 8 to end up with 18.

Number of Excavation                                  Height of Soils(inches)

0                                                                       3 ins

1                                                                        5 ins

5                                                                       13 ins

10                                                                      23 ins

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

It is already noted that when Levi starts digging the hole is already 3 inches dip with soil

In each excavation he digs 2 inches of soil each

So, when number of Excavation is :

Zero :  the inches of soil is 3 inches

One : the inches of soil is 3+2 = 5 inches

Five : the inches of soil is 3+2*5 = 13 inches

Ten :the inches of soil is 3 + 2*10 = 23 inches

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