15/4 and x/3 as a proportion

Answer:

BC = 56 units

Step-by-step explanation:

since the main diagonal AK bisects the diagonal BC , then the figure is a kite.

• the disjoint pairs of consecutive sides are congruent in a kite, that is

AB = AC and BK = CK

using the pair AB = AC  to solve for x

9x - 14 = 6x + 7 ( subtract 6x from both sides )

3x - 14 = 7 ( add 14 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Since m bisects BC , then

CP = PB and

BC = CP + PB = 4x + 4x = 8x

then

BC = 8x = 8 × 7 = 56

First product:

\(AB=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\end{bmatrix}=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\)

Notice how multiplying A by B produces A again, because B is an identity matrix.

The second product cannot be carried out because A has more columns that B has rows.

The third product also cannot be computed because A is not a square matrix.

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Answer:

g= −5x+2/x

x = 2/g+5

Step-by-step explanation:

Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

Answer:

see explanation

Step-by-step explanation:

2x + 3y = 12 → (1)

x - 2y = 4 ( add 2y to both sides )

x = 2y + 4 → (2)

now he can substitute x = 2y + 4 into (1)

Answer:

0.529

Step-by-step explanation:

1) Use the algorithm method.

       2    .     3

+  0   .    2    3

---------------------------

0 .    0   6    9

0 .   4   6  0

-----------------------------

                 1

0.    5  2  9

2) Therefore, 2.3 × 0.23 = 0.529.

0.529

Answer:

$1,045

Step-by-step explanation:

40×22=880

22÷2=11

11+22=33

33×5=165

165+880=1,045

Answer:

The answer is C or 44/12

Step-by-step explanation:

1/2 is equivalent to 3/6

1 4/6 is equivalent to 1 4/6 or 10/6

1 2/4 is equivalent to 1 3/6 or 9/6

When you add all of these together you get 22/6

Then you multiply 22/6 by 2 to get 44/12

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

Mei is correct because -9 is to the left of -3 on the number line.

Step-by-step explanation:

This is because -9 is LESS than -3, when you add or subtract using negative numbers, such as 7-9, you get -2. However when you subtract 7-13, you get -6. Because you subtracted a greater number from 7, your answer is -6 is LESS than -2. This is the same with inequalities, greater negative numbers will always be smaller and smaller negative numbers will always be greater.

Hope this helps!

Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Answer:

v = 8.6

Step-by-step explanation:

The first step to solve for x in the equation v + 1.26 = 9.86​  is to isolate the variable (v) on one side of the equation.

Looking at the equation, this can be done by subtracting 1.26 from both sides of the equation.

Shown below:

v + 1.26 - 1.26 = 9.86​ - 1.26      

v  = 8.6

As a result, v = 8.6

xKavinsky

Answer:

Step-by-step explanation:

\(\mathrm{v + 1.26 = 9.86}\)

Subtract -1.26 to both sides:-

\(\mathrm{v + 1.26-1.26 = 9.86-1.26}\)

Simplify :-

\(\mathrm{v=8.6}\)

_____________________

Hope this helps!

Answer: Let's draw a diagram to visualize the problem:

    C      D

    |      |

    |h     |

    |      |

    |_ _ _ |_ _ _ _ _ _

    A       10m      B

In the diagram, A represents the top of the platform, B represents the bottom of the building, C represents the bottom of the building as seen from the top of the platform, D represents the top of the building as seen from the top of the platform, h represents the height of the building, and the angles of depression and elevation are labeled.

We can use trigonometry to solve for h. Let x be the distance from point A to point C, as shown in the diagram. Then we have:

tan(39°) = h/x (1)

tan(56°) = (h + 10)/x (2)

We can rearrange equation (1) to get:

x = h/tan(39°)

Substituting this into equation (2), we get:

tan(56°) = (h + 10)/(h/tan(39°))

Simplifying this expression, we get:

tan(56°) = (h + 10)tan(39°)/h

Multiplying both sides by h, we get:

h tan(56°) = (h + 10)tan(39°)

Expanding the right side, we get:

h tan(56°) = h tan(39°) + 10 tan(39°)

Subtracting h tan(39°) from both sides, we get:

h (tan(56°) - tan(39°)) = 10 tan(39°)

Dividing both sides by (tan(56°) - tan(39°)), we get:

h = 10 tan(39°) / (tan(56°) - tan(39°))

Using a calculator to evaluate this expression, we get:

h ≈ 17.5 meters

Therefore, the height of the building is approximately 18 meters to the nearest whole number.

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.

The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15

x² - y² is common in both polynomials, let's factor it out.

x² - y² = (x-y)(x+y)

so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3

and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15

So the HCF of these two polynomials is (x-y)(x+y)

It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.

Answer:

(-1,4)

Step-by-step explanation:

to find out we just fill in the values to see if it’s true

(x,f(x))

4=-1^2+3

4=1+3

4=4

True

-4=-1^2+3

-4=1+3

-4=4

Not true

-4=1^2+3

-4=1+3

-4=4

Not true

-1=-4^2+3

-1=16+3

-1=19

Not true

Hopes this helps please mark brainliest

Answer:

m∠3 = 119°

Step-by-step explanation:

All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.

Answer:

K12 answer

Step-by-step explanation:

Answer:

Let me take 2,3,3 be 2x, 3x, 3x

Colin = 2x

Natasha = 3x

Angad = 3x

The equation forms to find out the value of x

2x + 3x + 3x = 48

=> 8x = 48

=> x = 48/8

=> x = 6

So share of Colin = 2x = £(2×6) = £12

Share of Natasha = 3x = £(3×6) = £18

share of Angad = 3x = £(3×6) = £18

For proof

£12 + £18 + £18 = £48

Hope it helps

Hello there. To solve this question, we have to remember some properties about geometry.

First, given a rectangle with side length L and width W:

Parallel sides have the same length, hence its perimeter, given by the sum of the measures of all its sides, is equal to

In this case, we were given the side length and width of the rectangle:

Plugging the values, we get

This is the answer to this question.

Answer:

transversal

Step-by-step explanation:

A line that intersects two or more coplanar lines at different points; the angles are classified by type.

Answer:

Step-by-step explanation:

3.9875

Answer:

\(5x - 20\)

Step-by-step explanation:

Product means the result of the multiplication of two numbers. A part of our expression will include the product of five and a number. We don't know what number it is, therefore, we'll call it \(x\). The product of those two numbers can be algebraically expressed as \(5x\) (we usually eliminate the multiplication sign between numbers and variables).

We are then asked to express the number that is 20 less than the product we found earlier. To find this expression, we should subtract 20 from the product, giving us \(5x - 20\).

On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

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Answer:

The vertex of this parabola, \((-2, 3)\), can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

\(g(x) = a\, (x - h)^2 + k\),

where \(a\), \(h\), and \(k\) are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at \((h,\, k)\).

The vertex form can be expanded to obtain:

\(\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}\).

Compare that expression with the given equation of this parabola. The constant term, the coefficient for \(x\), and the coefficient for \(x^2\) should all match accordingly. That is:

\(\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right.\).

The first equation implies that \(a\) is equal to \(3\). Hence, replace the "\(a\!\)" in the second equation with \(3\!\) to eliminate \(\! a\):

\((-2\times 3)\, h = 12\).

\(h = -2\).

Similarly, replace the "\(a\)" and the "\(h\)" in the third equation with \(3\) and \((-2)\), respectively:

\(3 \times (-2)^2 + k = 15\).

\(k = 3\).

Therefore, \(g(x) = 3\, x^2 + 12\, x + 15\) would be equivalent to \(g(x) = 3\, (x - (-2))^2 + 3\). The vertex of this parabola would thus be:

\(\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}\).

Answer:56

Step-by-step explanation:

We already have the lengths of the given sides:

5+7=12

12+5=17

17+5=22

22+11=33

33+7=40

40+(5+11)=56