z varies directly with x4 and inversely with y.
When x = 2 and y = 4, z = 3.
What is the value of z when x = 4 and y = 9?

Answer:

u + v = <7 , 1>

║u + v║ ≅ 7

Step-by-step explanation:

* Lets explain how to solve the problem

- We can add two vector by adding their parts

∵ The vector u is <-4 , 7>

∵ The vector v is <11, -6>

∴ The sum of u and v = <-4 , 7> + <11 , -6>

∴ u + v = <-4 + 11 , 7 + -6> = <7 , 1>

∴ The sum u and v is <7 , 1>

* u + v = <7 , 1>

- The magnitude of the resultant vector = √(x² + y²)

∵ x = 7 and y = 1

∵ ║u + v║ means the magnitude of the sum

∴ The magnitude of the resultant vector = √(7² + 1²)

∴ The magnitude of the resultant vector = √(49 + 1) = √50

∴ The magnitude of the resultant vector = √50 = 7.071

* ║u + v║ ≅ 7

Answer:

The second one, with the 0-5 having 7 students.

Step-by-step explanation:

Add up the number of students who fell into each category (0-5, 6-11, etc), then plot them as shown.

The second one, with the 0-5 having 7 students.

Add up the number of students who fell into each category (0-5, 6-11, etc), then plot them as shown.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:

B (3x − 14)(2x − 7)

Step-by-step explanation:

6(x − 4)^2 − (x − 4) − 2

Replace x-4 with m

6m^2 − m − 2

(3m -2  )    (2m+1)

Now replace m with x-4

(3 (x-4) -2)   (2(x-4) +1)

Distribute

(3x-12 -2) (2x-8+1)

Combine like terms

(3x-14) (2x-7)

Answer:

A

Step-by-step explanation:

Given the 2 equations

y = x² - 4x + 8 → (1)

y = 2x + 3 → (2)

Since both express y in terms of x we can equate the left sides, that is

x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 6x + 5 = 0 ← in standard form

(x - 1)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 5 = 0 ⇒ x = 5

Substitute these values into (2) for corresponding values of y

x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)

x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)

Solutions are (1, 5) and (5, 13)

Answer:

A. [tex](1,5)[/tex] and [tex](5,13)[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to find the solution of our given system.

[tex]\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.[/tex]

Equate both equations:

[tex]x^2-4x+8=2x+3[/tex]

[tex]x^2-4x-2x+8-3=2x-2x+3-3[/tex]

[tex]x^2-6x+5=0[/tex]

Split the middle term:

[tex]x^2-5x-x+5=0[/tex]

[tex]x(x-5)-1(x-5)=0[/tex]

[tex](x-5)(x-1)=0[/tex]

Use zero product property:

[tex](x-5)=0\text{ (or) }(x-1)=0[/tex]

[tex]x=5\text{ (or) }x=1[/tex]

Now, we will substitute both values of x, in our given equation to solve for y.

[tex]y=2x+3[/tex]

[tex]y=2(1)+3[/tex]

[tex]y=2+3[/tex]

[tex]y=5[/tex]

One solution: [tex](1,5)[/tex]

[tex]y=2x+3[/tex]

[tex]y=2(5)+3[/tex]

[tex]y=10+3[/tex]

[tex]y=13[/tex]

2nd solution: [tex](5,13)[/tex]

Therefore, option A is the correct choice.

Answer:

z stays the same

Step-by-step explanation:

From the statements

z ∝ x and z ∝ 1/y

Combining both proportions

z ∝ x/y

z = k * (x/y)

The above equation defines the relationship between x,y and z

k is the proportionality constant.

Lets say that x and y are doubled

Then

z = k * (2x/2y)

2 in the numerator and denominator will be cancelled out

z = k * (x/y)

Therefore we can conclude that z will stay the same if x and y are doubled ..

Answer:

z stays the same

Step-by-step explanation:

We have been given that z varies directly with x and inversely with y.

Thus, we have the equation

[tex]z=\frac{kx}{y}...(i)[/tex]

Here k is constant of proportionality.

Now, x and y both are doubled, thus, the equation becomes

[tex]z=\frac{k(2x)}{2y}[/tex]

Cancel 2 from numerator and denominator

[tex]z=\frac{kx}{y}[/tex]

This is same as equation (i)

Hence, we can conclude that z remains same.

first option is correct.

Answer:

C.  2x - 3(-3x - 4) = -21.

Step-by-step explanation:

y + 3x = -4

2x - 3y = -21

From the first equation y = -3x - 4.

Substituting this for y in the second equation, we have:

2x - 3(-3x - 4) = -21.

Final answer:

To determine if one triangle is a dilation of another, ratios of corresponding sides must be compared and set up as proportions to see if they are equivalent. When the proportions are equivalent, it indicates a consistent scale factor, confirming a dilation.

Explanation:

To determine if one triangle is a dilation of the other, we compare the ratios of corresponding sides from each triangle. A dilation occurs when all sides of one triangle are in proportion with the sides of a second triangle by the same scale factor. For example, if one triangle has sides of length 3, 4, and 5, and the second triangle has sides of length 6, 8, and 10, then the ratios of the corresponding sides (3/6, 4/8, 5/10) all simplify to 1/2, indicating that the second triangle is a dilation of the first.

To use ratios to determine if one triangle is a dilation of another, you need to set up proportions. For instance, we can express the ratios of corresponding lengths as fractions, and then set each of these ratios equal to the unit scale to form proportions. If the lengths of the triangles are given as 1 inch to 50 inches and 0.5 inches to 5 inches, we can set up the proportion 1/50 = 0.5/5 to show that they are equivalent.

In problems like this, proper notation and maintaining consistency across corresponding dimensions (e.g., width to width and length to length) is essential for accurate comparison.

Answer:

34 square units

Step-by-step explanation:

Step 1 : Write the formula for area of rectangle

Area of rectangle = length x breadth

From the graph:

AB = DC

AD = BC

Step 2 : Find the distance between AB and AD to find the length and breadth.

Coordinates : A (-1, 4), B (3, 3)

Distance between two points on AB

Formula : √(x2-x1)² + (y2-y1)²

= √(3-(-1))² + (3-4)²

= √17

Distance between two points on AD

Coordinates of A (-1, 4), D = (-3,-4)

Formula : √(x2-x1)² + (y2-y1)²

= √(-3-(-1))² + (-4-4)²

= √68

Area of rectangle = length x breadth

Area of rectangle = √17 x √68

Area of rectangle = 34

Therefore the area of rectangle = 34 square units

!!

Answer:

34

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Consider the list of multiples

multiples of 4 are 4, 8, 12, 16, 20, ....

multiples of 6 are 6, 12, 18, 24, ....

The least common multiple is 12

the answer is 63 because 63*2=126 and 126+54=180 and all triangles add up to 180

Answer:

B) 63 degrees

Step-by-step explanation:

All triangles equal up to 180 degrees so you would subtract the lengths you are given by 180.

So 180 - 54 = 126

Now you would divide 126 by 2 since this is an isosceles triangle. Isosceles triangles have two equal sides so 126 divided by 2 equals 63 degrees.

So y = 63 degrees

Answer:

The dimensions of the living room is the scale drawing are 16 in by 10 in

Step-by-step explanation:

we know that

The scale drawing is equal to

[tex]\frac{4}{6}\frac{in}{ft}[/tex]

That means ----> 4 inches in the drawing represent 6 feet in the real

so

Find the dimensions of the living room in the scale drawing

using proportion

For 24 ft

[tex]\frac{4}{6}\frac{in}{ft}=\frac{L}{24}\frac{in}{ft}\\ \\L=4*24/6\\ \\L=16\ in[/tex]

For 15 ft

[tex]\frac{4}{6}\frac{in}{ft}=\frac{W}{15}\frac{in}{ft}\\ \\L=4*15/6\\ \\W=10\ in[/tex]

therefore

The dimensions of the living room is the scale drawing are 16 in by 10 in

Answer:

D

Step-by-step explanation:

To find the critical values , that is the zeros

Solve the quadratic

x² - x - 20 = 0 ← in standard form

Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)

The factors are - 5 and + 4, since

- 5 × 4 = - 20 and - 5 + 4 = - 1, hence

(x - 5)(x + 4) = 0

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 4 = 0 ⇒ x = - 4

Thus the critical values are - 4, 5 → D

Answer:

D. -4, 5

Step-by-step explanation:

x² - x - 20 factorised = (x - 5) (x + 4)

In order to get the answers, you have to make each bracket equal zero.

(x - 5) = x = 5

(x + 4) = x = -4

The crucial numbers are -4 and 5.

Hope this helps!

Answer:

The percent of error in her measurement is 1.3%

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

we have

[tex]D=5\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]C=(3.14)(5)=15.7\ in[/tex] ----> This value represent the 100% (theoretical value)

Find the difference between the theoretical value and the measured value

[tex]15.7-15.5=0.2\ in[/tex]

Find the percentage by proportion

[tex]15.7/100=0.2/x\\ x=100*0.2/15.7\\ x=1.3\%[/tex]

Answer:

c

Step-by-step explanation:

You can find that 22-6=38-22=54-38=70-54=16

so the answer is c 16

Answer:  The correct opion is

(C) 16.

Step-by-step explanation:  Given that the values in the following table represent a linear function.

x:       1,     2,    3,     4,    5

y:       6,    22,  38,  54,  70.  

We are to find the common difference of the associated arithmetic sequence.

If y = f(x) is the given function, then we see that

f(1) = 6,  f(2) = 22,  f(3) = 38,  f(4) = 54 and f(5) = 70.

So, the common difference of the associated arithmetic sequence is given by

[tex]f(2)-f(1)=22-6=16,\\\\f(3)-f(2)=38-22=16,\\\\f(4)-f(3)=54-38=16,\\\\f(5)-f(4)=70-54=16,~~~\cdots.[/tex]

Thus, the required common difference of the associated arithmetic sequence is 16.

Option (C) is CORRECT.

Answer:

The Answer is A, a line segment that has both endpoints on a circle.

Step-by-step explanation:

Answer:

Option A: A chord is a line segment that has both endpoints on a circle.

Step-by-step explanation:

A chord of a circle is a line segment whose endpoints both lie on the circle.

In general a chord is a line segment that connects two distinct points on a circle. Its also called a secant in a circle, that intersects the circle at exactly two points.

Here, option A is correct.

Answer:

4x+5y-34=0

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

My goal is to put in in this form first.  Then I will aim to put it in general form, ax+by+c=0.

So let's give it a go:

m is the change of y over the change of x.

To compute this I'm going to line my points up and subtract vertically, then put 2nd difference over 1st difference.  Like this:

( 1 , 6)

-(6 , 2)

----------

-5   4

So the slope is 4/-5 or -4/5.

So m=-4/5.

Now we are going to find b given y=mx+b and m=-4/5 and we have a point (x,y)=(1,6) [didn't matter what point you chose here].

6=-4/5 (1)+b

6=-4/5    +b

Add 4/5 on both sides:

6+4/5=b

30/5+4/5=b

34/5=b

So the y-intercept is 34/5.

The equation in slope-intercept form is:

y=-4/5 x + 34/5.

In general form, it is sometimes the goal to make all of your coefficients integers so let's do that.  To get rid of the fractions, I'm going to multiply both sides by 5.  This clears the 5's that were on bottom since 5/5=1.

5y=-4x+34

Now add 4x on both sides:

4x+5y=34   This is standard form.

Subtract 34 on both sides:

4x+5y-34=0

Answer:

segment SV

Step-by-step explanation:

Observing the figure

we know that

The side that is common to triangle SUV and triangle VTS is only the segment SV

There are no common angles to triangle SUV and triangle VTS

therefore

The answer is the segment SV

Answer:

Step-by-step explanation:

If you're asking for the equation of a line that goes through (1,-5) and is perpendicular to y=18x+26 here's what you do.

1. find the slope of the new line by taking the negative reciprocal of the slope of the first line ([tex]-\frac{1}{18}[/tex])

2. plug in the point (1,-5) and the new slope into the point slope form equation

[tex]y_{2} -y_{1}=m(x_{2}-x_{1})[/tex]

3.Now that you have y-(-5)= -1/18(x-1) simplify

3.a y-(-5)= -1/18x + 1/18

3.b y=-1/18x - 89/18

4. final equation you get is y = -1/18 - 89/18

Answer:

The correct  answer is the option "B":

B.(-x-6i)(x-6i)

The expression -x^2-36 can be factored as a difference of squares and is equivalent to -(x+6)(x-6).

The expression -x^2-36 can be equivalent to other algebraic forms depending on the manipulation or factoring techniques applied. To simplify or manipulate this expression, one can factor it as the difference of squares. The difference of squares is a pattern where you have an expression in the form of a^2 - b^2, which can be factored into (a+b)(a-b). In the case of -x^2-36, it can be written as -(x^2 - 36), which then can be factored as -(x+6)(x-6). This follows the pattern of a difference of squares since x^2 is the square of x, and 36 is the square of 6.

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Answer:

90 degree clockwise rotation about (0,0).

Step-by-step explanation:

That would be a clockwise rotation of 90 degrees about the origin (0,0).

The rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To find the rotation that maps point K(8,-6) to K(-6,-8), we can use the following steps,

Plot the points K(8,-6) and K(-6,-8) on a coordinate plane.

Since point K(8,-6) is being mapped to point K(-6,-8), the rotation must be counterclockwise. As rotation about the origin with angle 90 gives the transformation equation,
(x, y) ⇒ (y, -x)

Therefore, the rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).

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Answer:

is the equal sign supposed to be there? if it wasnt then answer would be 42x^6y^11

Step-by-step explanation:

Answer:

-3± √5

Step-by-step explanation:

It is given that,

m² + 6m = -4

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± v(b² - 4ac)]/2a

To find the solution of given equation

m² + 6m = -4

⇒ m² + 6m  + 4 = 0

Here a = 1, b = 6 and c = 4

m =  [-b ± v(b² - 4ac)]/2a

  =  [-6 ± √(6² - 4*1*4)]/2*1

  = [-6 ± √(36 - 16)]/2

  = [-6 ± √20]/2

  = [-6 ± 2√5]/2

 = -3± √5

Answer:

A: 0

B: There is one real root with a multiplicity of 2.

Step-by-step explanation:

[tex]\bf{x^2+2x+1=0}[/tex]

The discriminant of the quadratic equation can be found by using the formula: [tex]b^2-4ac[/tex].

In this quadratic equation,

I found these values by looking at the coefficient of [tex]x^2[/tex] and [tex]x[/tex]. Then I took the constant for the value of c.

Substitute the corresponding values into the formula for finding the discriminant.

Simplify this expression.

The answer for part A is [tex]\boxed{0}[/tex]

The discriminant tells us how many real solutions a quadratic equation has. If the discriminant is

Since the discriminant is 0, there is one real root so that means that the first option is correct.

The answer for part B is [tex]\boxed {\text{There is one real root with a multiplicity of 2.}}[/tex]

Answer:

A: 0  

B: There is one real root with a multiplicity of 2 .  

Step-by-step explanation:

Given a quadratic equation:

 [tex]ax^2+bx+c=0[/tex]

You can find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

In this case you have the following quadratic equation:

[tex]x^2+2x+1=0 [/tex]

Where:

[tex]a=1\\b=2\\c=1[/tex]

Therefore, when you substitute these values into the formula, you get that the discriminant is this:

[tex]D=(2)^2-4(1)(1)\\\\D=0[/tex]

Since [tex]D=0[/tex], the quadratic equation has one real root with a multiplicity of 2 .

Answer:

i think the answer is 7776

for two dice its 6x6 36 then 36×6 216 then 216×6 1296 then 1296×6 7776

Answer: 7776 possible outcomes

Step-by-step explanation:

You know that each dice has 6 possible results.

1, 2, 3, 4 , 5 , 6

Then, if you throw 2 dice, the possible results are 6(for the first one)*6(for the second one) = 6*6 = 36

then, as you add another die, you add another 6 to that equation, this means that for 5 dice we have

combinations = 6*6*6*6*6 = 6^5 = 7776

But in this situation most of the numbers can be repeated, for example, then number 6, can be made from (1 + 1 + 1 + 1 + 2), (1 + 2 + 1 + 1 + 1), (1 + 1 + 1 + 2 + 1 +1)

etc, this means that the die that rolls a 2 can change, but the end result of the addition is the same, in this case the total range of possible values is the amount of dice times the biggest value minus the amount of dice times the smallest value:

5*6 - 5*1 = 30 - 5 = 25 possible results

So you have 7776 combinations that give a only 25 possible results (a number between 5 and 30)

Answer:

It's asking for you to calculate the volume of a cylinder and multiply it by 2/3. This is because the question is asking how much water is in a cylindrical vase with the height and radius.

The formula to calculate the volume of a cylinder is : 3.14 (r^2) (h)

R being the radius and H being the height.

Plug in the values then multiply it all by 2/3

Hoped this help you solve your problem.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=5\\ h=14 \end{cases}\implies V=\pi (5)^2(14)\implies V=350\pi \\\\\\ \stackrel{\pi =3.14}{V=1099}~\hfill \stackrel{\textit{how much is }\frac{2}{3}\textit{ of that?}}{1099\cdot \cfrac{2}{3}\implies \cfrac{2198}{3}}\implies \stackrel{\textit{rounded up}}{732.7}[/tex]

Answer:

y = 4sin [(1/2)t - (4/3)π ]  - 2

Step-by-step explanation:

For this question, do not be intimidated by the terminology, just realize the following:

for y = a sin [ (2π/T) t ]

a = amplitude = given as 4

T = period = given as 4π

phase shift is simply horizontal shift, positive values means the graph moves by that amount to left and negative values means the graph moves to the right.

vertical shift ... is well a shift vertically. positive values move the graph up vertically and negative values move the graph down vertically.

so... if we start with the basic formula:

y = a sin [ (2π/T) t ]

given a = 4 and T = 4π (substitute these values into the formula)

y = (4) sin [ (2π/4π) t ] = (4) sin [ (1/2) t ]

y = 4sin [(1/2)t ]

Now for the shifts:

given phase shift, aka horizontal shift is -(4/3)π, equation becomes

y = 4sin [(1/2)t - (4/3)π ]

given vertical shift is -2, the equation simply becomes

y = 4sin [(1/2)t - (4/3)π ]  - 2

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