9. Here is a graph of the equation 2x - 3y = 15.
Please help I’m so confused

Dilating the given triangle with a magnitude of 3, the number corresponding to the question mark is 18.

Therefore the answer is 18.

Dilating a triangle means to scale it up or down by a certain factor, in this case, by a factor of 3. To dilate a triangle, you need to multiply the each elements of the matric by the dilation factor.

On multiplying a matrix by a scalar number, each element of the matrix is multiplied by that scalar number.

3 × [3 6 3 | -3 3 3] =  [3×3 6×3 3×3 | -3×3 3×3 3×3]

=[ 9 18 9 | -9 9 9]

That is

[tex]3\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right] = \left[\begin{array}{ccc}-3*3&6*3&3*3\\-3*3&3*3&3*3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}9&18&9\\-9&9&9\end{array}\right][/tex]

So the element corresponding to the question mark is 18.

--The question is incomplete, complete question is given below--

"Dilate the given triangle with a magnitude of 3.

[tex]\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}9&?&-\\-9&-&-\end{array}\right][/tex]"

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We can call a scatter diagram as a scatter plot, Scatter graph, or correlation chart. By including two variables a scatter diagram is drawn where the first variable is independent and the second variable is dependent on the first. Depending on the correlation between them, scatter diagrams can be divided into the following categories :

1) Scatter diagram with no correlation - we can call this diagram the 'Scatter Diagram with Zero Degree of Correlation ' as the variables do not correlate with each other.

2) Scatter diagram with moderate correlation - we can call this diagram as the 'Scatter Diagram with a Low Degree of Correlation' as here the data points are a little closer and a relationship between these variables can be found.

3) Scatter diagram with strong correlation - we can call this diagram as the 'Scatter Diagram with a High Degree of Correlation' as here the data points are closer and a line can be drawn by following their pattern.

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The solution to the system of equations is x = 0, y = 0.

What is substitution algebraic expression?

Substitution means replacing the variables in an algebraic expression with their numerical values. We can then work out the total value of the expression.

To use algebraic substitution to solve for x and y, we can substitute one equation into the other and solve for one of the variables.

Given that y = -8x, we can substitute this into the second equation, 2x + 4y = 0

So, 2x + 4(-8x) = 0

Simplifying this we get,

2x - 32x = 0

30x = 0

Dividing both sides by 30

x = 0

Now we have x = 0, we can substitute this value back into the equation y = -8x

So y = -8(0)

y = 0

Hence, the solution to the system of equations is x = 0, y = 0.

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The formula for Area of Hexagon is written as : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]

The formula for Perimeter of Hexagon is written as : [tex]6a[/tex] .

A Regular Hexagon is defined as a two dimensional shape which has 6 sides, 6 angles and 9 diagonals, and sum of its interior angles is 720°.

When one side length of the regular hexagon is given as "a" units ,

A regular hexagon comprises of six equilateral triangles, formula for finding area of a hexagon is derived from formula of area of equilateral triangle .

So,  the Area can be calculated by the formula : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]  square units ;

and Perimeter of hexagon be calculated by the formula : [tex]6a[/tex] units .

The given question is incomplete , the complete question is

What is the formula for area and perimeter of a hexagon ?

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Answer:

-3

Step-by-step explanation:

22-25=-3 because if the first number is smaller than the second number, then the answer is a negative number

No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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Evaluating the given expressions, A) 10^14 (option a), B) 10^-6 (option b), C) 10^27 (option b) D) 10^-8 (option c).

A) 10^5 x 10^9

Using the product of power rule, when the base is same, the exponents are added together. Hence,

10^5 x 10^9 = 10^(5 + 9) = 10^14

B) 10^4 x 10^-10

Using the product of power rule,

10^4 x 10^-10 = 10^(4 – 10) = 10^-6

C) 10^30 ÷ 10^3

Using the quotient power rule, when the base is the same, the exponents are subtracted.

10^30 ÷ 10^3 = 10^(30 – 3) = 10^27

D) 10^-12 ÷ 10^-4

Using the quotient power rule,

10^-12 ÷ 10^-4 = 10^(-12 –(-4) = 10^(-12 + 4) = 10^-8

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The graph of the resulting line of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

A graph is a pictorial representation of a figure formed by connecting set of points.

We have to find the points through which the line y = 1/2 x + 4 passes through to draw the graph of the line.

Let x = 0 ⇒ y = 4

A point P is found as P (0, 4), which is the y intercept where the line touches with the Y axis.

Let y = 0, then 1/2 x = -4 or x = -8

A point Q is found as Q (-8, 0) which is the x intercept where the line touches with the X axis.

Let x = 2, then y = 5

A point R is found as R (2, 5).

So graph of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

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the volume of rectangular shape is 8 cm³ and density is 4 gm/cm³

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6-sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Given sides of the rectangular cube are 1 cm, 2c.m, and 4c.m

The volume will be the product of all three sides = 1*2*4 = 8 cube cm

The density will be mass/volume.

= 32gm/8 = 4 gm/cm³

Hence volume of the rectangular shape is 8 cm³ and density is 4 gm/cm³

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Answer:

None

Step-by-step explanation:

Evaluate each answer option, following the order of operations (PEMDAS).

[tex]\begin{aligned}\textsf{A.} \quad (6^2+2)-18\sqrt{81}&=(36+2)-18\sqrt{81}\\&=(36+2)-18(9)\\&=38-18(9)\\&=38-162\\&=-124\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{B.} \quad 6^2(2-8)\sqrt{81}&=36(2-8)\sqrt{81}\\&=36(2-8)(9)\\&=36(-6)(9)\\&=(-216)(9)\\&=-1944\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{C.} \quad (6^2+2-8)\sqrt{81}&=(36+2-8)\sqrt{81}\\&=(36+2-8)(9)\\&=(38-8)(9)\\&=(30)(9)\\&=270\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{D.} \quad 6^2 +2(8\sqrt{81})&=36+2(8\sqrt{81})\\&=36+2(8\cdot 9)\\&=36+2(72)\\&=36+144\\&=180\end{aligned}[/tex]

Therefore, none of the answers has a value of -18.

1) Remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2) Their difference will be divisible.

The amount that remains after division is known as the Remainder. The result of division is a value if a number (dividend) cannot be divided entirely by another number (divisor).

1. Suppose the a random number is x and 4 consecutives number are x, x+1, x+2, x+3

Given that,

x² + (x+1)²+ (x+2)²+ (x+3)²

x² + (x² +2x+1) + (x² +4x+4)+ (x²+6x+9)

4x² + 12x + 14

is divisible by 4 with remainder 2

[tex]$ \frac{4x^2 + 12\text x + 14}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 +2}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 }{4} $[/tex] [tex]$+\frac{2}{4}[/tex]

Hence proved, remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2. As both 14 and 21 is divisible by seven, their difference is also divisible by 7, i.e. 70-42 = 28, all the numbers are divisible by 7 and hence the squares of the number are also divisible by seven as well as their numbers.

14²⁰ - 21²

(7 × 2)²⁰ - (7 × 3)²

Thus, their difference will be divisible.

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The value of x that makes the sentence 1/7 + x = 1/2 true is (d) 5/14

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

A mathematical sentence

The mathematical sentence is given as

1/7 + x = 1/2

Next, we make x the subject of the formula

This is done by subtracting 1/7 from both sides of the equation

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

1/7- 1/7 + x = 1/2 - 1/7

Evaluate the like terms on the left-hand side

So, we have the following representation

x = 1/2 - 1/7

Take the LCM of the fractions

x = (7 - 2)/14

Evaluate the difference on the right-hand side

So, we have the following representation

x = 5/14

Hence, the solution is (d) 5/14

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The solution of the equation is "True for all value of x".

In the given question, two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats.

The equation 4(x + 1) = 4x + 4 models the paths of the boats.

We have to solve for x.

The equation is 4(x + 1) = 4x + 4

Using the Distributive property

4x + 4 = 4x + 4

Subtract 4 on both side, we get

4x = 4x

Subtract 4x on both side, we get

0 = 0

As we can see that the equation is true for all the value of x.

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The two boats are traveling exactly 0 feet apart in the canal.

The equation 4(x + 1) = 4x + 4 can be rearranged to solve for x. First, subtract 4x from both sides of the equation so that the equation becomes 4(x + 1) - 4x = 4x + 4 - 4x. This simplifies to 4 + 4x = 4, and when 4 is subtracted from both sides of the equation, the result is 4x = 0. To solve for x, divide both sides of the equation by 4, so that x = 0.

This means that the two boats are traveling exactly 0 feet apart in the canal.

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The amount to be paid by Chet if The flight he selected was $229.99, but he got 20% off because he booked it online through a new travel website, is $184.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance.

Given:

The flight he selected was $229.99 but he got 20% off because he booked it online through a new travel website,

Calculate the amount of discount as shown below,

Discount = 20% of 229.99

Discount = 20 / 100 × 229.99

Discount = 0.2 × 229.99

Discount = 45.998

Thus, the amount to be paid = 229.99 - discount

the amount to be paid = 229.99 - 45.99

the amount to be paid = 184

Thus, the amount to be paid is $184.

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The value of unknown v from the given equation 8v - 4(v + 8) = 8 is

v = 10.

Simplifying the given algebraic equation :

8v - 4(v + 8) = 8

Rearrange the terms in equation :

8v - 4(8 + v) = 8

8v - (8 * 4 + v * 4) = 8

8v - (32 + 4v) = 8

Expand and rearrange the terms:

-32 + 8v - 4v = 8

Combine like terms: 8v - 4v = 4v ( on left side )

                                  8 + 32 = 40 (on right side )

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

4v = 8 + 32

4v = 40

Divide each side by '4'.

Simplifying

 v = 10.

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The number of pennies are 80 and number of nickels are 160.

Two or more expressions with an Equal sign is called as Equation.

Given that $8.80 in pennies and nickels.

The total number of coins are 240.

x+y=240

x is pennies and y is nickel.

0.01x+0.05y=8.8

Now from equation 1, x=240-y

Plug in equation 2

0.01(240-y)+0.05y=8.8

2.4-0.01y+0.05y=8.8

2.4+0.04y=8.8

Subtract 2.4 on both sides

0.04y=6.4

y=160

x+160=240

x=80

Hence, the number of pennies are 80 and number of nickels are 160.

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The estimated value of y when x1=12, x2=1, and x3=-1 is -204. This is calculated by substituting the given values into the equation ˆy=−184−7x1+47x2+20x3.

ˆy=−184−7(12)+47(1)+20(-1)

ˆy=−184-84+47-20

ˆy=−204

In the multiple regression equation

ˆy=−184−7x1+47x2+20x3

the estimated value of y can be determined by substituting the given values of x1, x2, and x3 into the equation. For example, given

x1=12, x2=1, and x3=-1,

the estimated value of y can be calculated as follows: ˆy=−184−7(12)+47(1)+20(-1). This simplifies to

ˆy=−184-84+47-20, or ˆy=-204.

The equation takes the form of a linear equation, with each independent variable x1, x2, and x3 multiplied by a coefficient, and then added together to give the estimated value of y. In this example, the coefficient for x1 is -7, for x2 is 47, and for x3 is 20. This means that if x1 increases by 1 unit, then the estimated value of y will decrease by 7 units; if x2 increases by 1 unit, then the estimated value of y will increase by 47 units; and if x3 increases by 1 unit, then the estimated value of y will increase by 20 units. Using the multiple regression equation, therefore, the estimated value of y can be calculated when the values of the independent variables are known. In this example, given x1=12, x2=1, and x3=-1, the estimated value of y is -204.

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The complete question is

In the following multiple regression equation, what is the value of x2 when x1 = 15.5 and ˆy is estimated to be -412?ˆy=78−20x1−10x2x2=2)Given the following multiple regression equation:ˆy=−184−7x1+47x2+20x3Determine the estimated value of y whenx1=12x2=1x3=−1ˆy=−204

Answer:

Step-by-step explanation:

The required answer is w-z = √2[cos(3π/4) + i sin(3π/4)]

A complex number is a number of the form a + bi, where a and b are real numbers.

Given that,

w = √2cos(π/4) +  i sin(π/4) and z = 2[cos(π/2)+i sin(π/2)]

On simplification we get,

w = √2cos(π/4) +  i sin(π/4)

w = √2(1/√2 + i · 1/√2)

w = 1+i

And,

z = 2[cos(π/2)+i sin(π/2)]

z = 2(0+i)

Now, the value of (w - z)

w - z = (1 + i) - (0 + 2i)

w - z = 1 - i

Polar form of the complex number:-

r = √1²+(-1)² = √2

And, θ would b,

θ = tan⁻¹(-1/1)

= tan⁻¹(-1)

θ = 3π/4

Therefore, polar form =  w-z = √2[cos(3π/4) + i sin(3π/4)]

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Answer:

? = 60.

Step-by-step explanation:

Multiply 3/5 by 20. The answer will yield that 3/5 = 60/100

Answer:

Missing number = 60

Step-by-step explanation:

★ Let the missing number be x.

Forming the equation,

[tex] \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} [/tex]

Now the value of x will be,

[tex] \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} [/tex]

[tex] \sf \rightarrow \: x = \frac{3}{5} \times 100 [/tex]

[tex] \sf \rightarrow \: x = \frac{300}{5} [/tex]

[tex] \sf \rightarrow \boxed{ \sf x = 60}[/tex]

Hence, the value of x is 60.

Answer:
Yes

If this help please set brainliest.

Step-by-step explanation:

Yes, a line with a slope of 0 is a horizontal line. It will always intersect the y-axis at a single point, which is known as the y-intercept. The y-intercept is the point where the line crosses the y-axis, and it is represented by the equation y = b, where b is the y-intercept.

For example, consider the line y = 2. This line has a slope of 0 and an y-intercept of 2. It is a horizontal line that passes through the point (0, 2) on the coordinate plane.

Answer:

Foci:  (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

   Write the equation of hyperbola in the form,

              [tex]\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}[/tex]

9x² - 16y² = 144

Divide the entire equation by 144,

          [tex]\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1[/tex]

a = 4 and b =3

  Eccentricity: e

           [tex]\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}[/tex]

                [tex]\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}[/tex]

Foci:

         (ae, 0)  & (-ae , 0)

          [tex]\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)[/tex]

Vertex of hyperbola:

       The vertex of the hyperbola is a point where the hyperbola cuts the axis.  (-a , 0)  ; (a , 0)

 Vertex : (-4 , 0) ; (4 , 0)

The solution for this question is as follows:

Vertices ≈ (±4 , 0)

Foci ≈ (±5 , 0)

Eccentricity: e = 5/4

Asymptotes: y=  ±(3/4)x

Hyperbola:

The location of all the points on a plane where the distance between them and two fixed points in the plane is always equal to zero is called a hyperbola.

Step by step solution:

Given: [tex]9x^{2} -16y^{2} =144[/tex]      

The given equation of hyperbola can be written as:

⇒[tex]\frac{x^{2} }{16} -\frac{y^{2} }{9} =1[/tex]

On comparing with standard equation of hyperbola; [tex]\frac{x^{2} }{a} -\frac{y^{2} }{b} =1[/tex]

We get; a=4 and b=3

The eccentricity of hyperbola is given by:

      9=16(e^2 - 1)

So; e^2 = (9/16) + 1

       e^2 = 25/16

       e = 5/4

The vertices of hyperbola are given by (±a , 0) ≈ (±4 , 0)

The foci of hyperbola are given by (±ae , 0) ≈ (±5 , 0)

The asymptotes of hyperbola are given by y= ± (b/a)x  

                                                                        y=  ±(3/4)x

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An inequality that represents the possible dimensions for the garden is ab < 80. And the three different sets of allowable dimensions for the garden are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

The maximum area that is available for a rectangular garden is 80 square feet.

Let a and b are the length and width of the rectangular garden.

And A be the area.

(a).

So, A < 80

That means, ab < 80.

(b).

To find the dimension of the rectangle:

We find the numbers whose product is less than 80.

Let the three number sets are,

{5, 10}, {10, 5} and {6, 6}.

(c).

So, the area of the rectangles are:

5 x 10 = 50 square feet,

10 x 5 = 50 square feet,

And 6 x 6 = 36 square feet.

Therefore, the inequality is ab < 80, three number sets are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

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Both Teresa and Leon have constructed regular hexagons. Teresa drew a circle and marked a point on it, then used a compass set to the radius to construct a regular hexagon. Leon drew a segment, then used a circle with the segment as the radius and a compass set to the length of the segment to construct a regular hexagon.

It is important to note that a regular hexagon is a polygon with six congruent sides and six congruent angles, and is constructed by using a compass to draw six equidistant points on a circle, connecting the points with straight lines, forming the hexagon. In both cases described above, it appears that Teresa and Leon were using a compass and the appropriate measurements to construct regular hexagons.

Using substitution method, the solution of the system of equation 9x + y = 65, y = 3x - 19 is x = 7 and y = 2.

The system of equation can be solved using substitution method, elimination method and graphical method. Let's solve the system of equation using substitution method as follows:

9x + y = 65

y = 3x - 19

let's substitute the value of y in the equation(i)

9x + (3x - 19) = 65

9x + 3x - 19 = 65

12x - 19 = 65

add 19 to both sides of the equation

12x - 19 + 19 = 65 + 19

12x = 84

divide both sides by 12

x = 84 / 12

x = 7

Let's find y

y = 3(7) - 19

y = 21 - 19

y = 2

Therefore, the solution are x = 7 and y  =2.

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The limit of g(x) as x approaches 4 negative is 2 and the limit of g(x) as x approaches 4 plus is negative 4.

To calculate the limit of g(x) as x approaches 4 negative, let us consider the function g(x) = -2x + 8.

We can calculate the limit of g(x) as x approaches 4 negative by plugging in the value 4 into the function.

When x = 4, g(x) = -2(4) + 8 = -8 + 8 = 0.

Therefore, the limit of g(x) as x approaches 4 negative is 0.

To calculate the limit of g(x) as x approaches 4 plus, let us consider the function g(x) = -2x + 8.

We can calculate the limit of g(x) as x approaches 4 plus by plugging in the value 4 into the function.

When x = 4, g(x) = -2(4) + 8 = -8 + 8 = 0.

Therefore, the limit of g(x) as x approaches 4 plus is 0.

In conclusion, the limit of g(x) as x approaches 4 negative is 2 and the limit of g(x) as x approaches 4 plus is negative 4.

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The difference between the diameters of the two cells G and H will be;

⇒ 70.43 × 10⁻² centimeters

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

Two cells are measured using this method,

Cell G: 1.87 x 10⁻² centimeters

Cell H: 7.23 x 10⁻³ centimeters

Now,

Since, Two cells are measured as;

Cell G: 1.87 x 10⁻² centimeters

Cell H: 7.23 x 10⁻³ centimeters

Hence, The difference between the diameters of the two cells G and H is,

⇒ 7.23 x 10⁻³ - 1.87 x 10⁻²

⇒ 72.3 × 10⁻² - 1.87 × 10⁻²

⇒ (72.8 - 1.87) × 10⁻²

⇒ 70.43 × 10⁻² centimeters

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Answer:

what is the regular price of the soda? 1.59$