evaluate the following expression: 2(1,1) -4(0,1). enter your answer as a vector.

For this case we can make a change of variable, to obtain a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Making the change:[tex]u = 3x + 2[/tex]

Substituting the change we have:

[tex]u ^ 2 + 7u-8 = 0[/tex]

Thus, the correct option is:[tex]u ^ 2 + 7u-8 = 0[/tex]where [tex]u = 3x + 2[/tex]

Answer:

Option B

Answer:

second option: [tex]u^{2}+7u-8=0[/tex]

Step-by-step explanation:

We have the equation given:

[tex](3x+2)^{2}+7(3x+2)-8=0[/tex]

We can replace the variable in the quardatic equation.

So,

[tex]Putting\\u=3x+2[/tex]

Putting u in place of 3x+2 will give us:

[tex](u)^{2}+7(u)-8=0[/tex]

So the answer is:

[tex]u^{2}+7u-8=0[/tex]

So, the second option is correct ..

Answer:

The answer is b.

Step-by-step explanation:

Have a great day!!

Answer:

A. 68°

Step-by-step explanation:

sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

= 68°

The sum of angles inside a triangle is 180°. so option is A. 68°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Given angles are; 75 and 37.

The sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

x = 68°

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Answer: Addition property of equality

Step-by-step explanation: You added the x to the other side, which is clearly using addition. Hope this help!

units like radius, height, width, length or segments are single units, like meter or feet.

areas are double units, so they'd be in say meter² or feet².

volumes are triple units, namely like meter³ or feet³.

Answer:

The unit of measuring volume of the sphere is cubic meter.

Step-by-step explanation:

Given  :  Sphere with a  radius of 2 meters.

To find : Which unit of measure would be appropriate for the volume of sphere.

Solution : We have given Radius = 2 meter .

Volume = [tex]\frac{4}{3}\pi (radius)^{3}[/tex].

Volume  =  [tex]\frac{4}{3}\pi (2 meter)^{3}[/tex].

Volume of sphere =   [tex]\frac{32}{3}\pi[/tex] meter³ .

Therefore, The unit of measuring volume of the sphere is cubic meter.

Answer: Number of pizzas would be less than 5 but not more than 50.

Step-by-step explanation:

Since we have given that

Number of pizzas so far = 25

His principal asked him to make at least 30 pizzas but no more than 75.

According to question, we have

30 ≤ x + 25 ≤ 75

First we subtract 25 from both the sides:

[tex]30-25\leq x \leq 75-25\\\\=5\leq x\leq 50[/tex]

Hence, number of pizzas would be less than 5 but not more than 50.

The solution to the compound inequality is 5  x 50.

The compound inequality given is 30 x 25  75, where x represents the number of additional pizzas Billy needs to make to satisfy the principal's request. To solve for x, we need to isolate x in the inequality.

First, we subtract 25 from all parts of the compound inequality to shift the 25 pizzas already made to the other side of the inequality. This gives us:

30 - 25 x + 25 - 25 75 - 25

Simplifying the inequality, we get:

5  x  50

This means that Billy needs to make at least 5 more pizzas to reach the minimum requirement of 30 pizzas (since 25 + 5 = 30) and no more than 50 additional pizzas to not exceed the maximum allowed number of 75 pizzas (since 25 + 50 = 75).

Therefore, the number of additional pizzas Billy should make is any integer value between 5 and 50, inclusive. This ensures that the total number of pizzas made will be within the principal's specified range of 30 to 75 pizzas."

Answer:

8

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, 2) and (x₂, y₂ ) = (- 9, 9)

d = [tex]\sqrt{(-9+5)^2+(9-2)^2}[/tex]

  = [tex]\sqrt{(-4)^2+7^2}[/tex]

  = [tex]\sqrt{16+49}[/tex] = [tex]\sqrt{65}[/tex] ≈ 8 ( nearest unit )

Answer:  The required distance between my house and the subway stop is 8 units.

Step-by-step explanation:  Given that a grid shows the positions of a subway stop and my house. The subway stop is located at (-5,2) and my house is located at (-9,9).

We are to find the distance, to the nearest unit, between my house and the subway stop.

We will be using the following formula :

Distance formula :  The distance between the points (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points (-5, 2) and (-9, 9) is given by

[tex]D\\\\=\sqrt{(-9-(-5))^2+(9-2)^2}\\\\=\sqrt{(-9+5)^2+7^2}\\\\=\sqrt{4^2+49}\\\\=\sqrt{16+49}\\\\=\sqrt{65}\\\\=8.06.[/tex]

Rounding to the nearest units, we get

D = 8 units.

Thus, the required distance between my house and the subway stop is 8 units.

Answer:

A

Step-by-step explanation:

We can see that the slope is positive, which means that the x-term must be positive.

If you expand and simply both equations into the form y = mx + b, you will find that m is positive for A and negative for B, hence A is the correct answer.

Answer:

The statement is True

Step-by-step explanation:

The Isosceles Triangle Theorem states that;

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse of this statement is;

if two angles are congruent, then sides opposite those angles are congruent.

Answer:

True.

Step-by-step explanation:

To start with , remember that congruent angles have the same degree of measurement. For example, in an isosceles triangle, the base angles are congruent angles because they both measure 45°

The base angles  theorem states that the sides next to congruent angles are equal.The statement is therefore True.If sides of the triangle are congruent, the opposite angles in the triangle are congruent .

Answer:

Step-by-step explanation:

By observation, you can see that the irregular polygon can be split into 4 triangles (see attached image). We know that the sum of the internal angles of 1 triangle is always 180 degrees. Hence the sum of all the internal angles of the polygon is,

180 degrees x 4 triangles = 720 degrees.

Therefore Angle B,  

= sum of internal angles - sum of all other known angles

= 720 - (133 +102+117+90+170)

= 108 degrees.

The measure of angle B is 108 degrees.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

We can divide the given polygon in split into 4 triangles.

Using, angle sum property,

The sum of the internal angles of triangle is always 180 degrees.

Hence the sum of all the internal angles of the polygon is,

=180 x 4 triangles

= 720 degrees.

Now, angle B

= 720 - (133 +102+117+90+170)

=720 -612

= 108 degrees.

Hence, angle B is 108 degrees.

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Answer:  5

Step-by-step explanation:

f(5) = 2 means that when x = 5, y = 2 --> (5, 2)

f⁻¹(2) is the inverse (when the x and y are swapped) --> when x = 2, y = 5

Answer:

486 - 160l

Step-by-step explanation:

m = 90 - 32l

s = -48 + 18l

l = stationary

Combine like-terms, evaluate, then you will arrive at this crazy answer.

Answer:

3x^2+x-9

Step-by-step explanation:

f+g

means you are going to add whatever f equals to what g equals

so you have

(-3)+(3x^2+x-6)

Combine like terms

3x^2+x+(-3+-6)

3x^2+x+-9

or

3x^2+x-9

This is False

That is because the Arcs can only be congruent if the Chords are also Congruent

Answer:

FALSE

Step-by-step explanation:

its (8,6)

to get your x, you set what's in the absolute value to 0

so

x-8=0

then subtract 8 on both sides to get

x=8

then your y is just the number to the right of the absolute value so

y=6

Answer: Option B

(8, 6)

Step-by-step explanation:

By definition, for an absolute value function of the form

[tex]f (x) = | x-h | + k[/tex]

the vertex of f(x) will always be at the point

(h, k)

In this case we have the function of value ansoluto:

[tex]g(x) = |x - 8| + 6[/tex]

Therefore in this case

[tex]h=8\\k=6[/tex]

Finally the vertex of the function g(x) is: (8, 6)

The answer is the option B

Answer:

The graph that represent direct variation in the attached figure

Step-by-step explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

The graph that represent direct variation in the attached figure

Answer:

option d

Step-by-step explanation:

Answer:  15,600,000

Step-by-step explanation:

26 x 25 x 24 =15,600 combinations of letter with no repeats

10 x 10 x 10 = 1000 with repeating numbers

15,600 x 1000 = 15,600,000

The total number of possible license plates is 26*25*24*10*9*8.

The number of possible license plates with no repeated letters can be calculated by multiplying the number of choices for each position. Since no letter can be repeated, the choices for the first position would be 26 letters, then 25, and then 24 for the three positions. For the digits, there are 10 choices for each position.

So, the total number of possible license plates would be 26*25*24*10*9*8.

Answer:

Step-by-step explanation:

1 group = 10 students

x group = 240 students.

1/x = 10/240              Cross multiply

10x = 240                  Divide by 10

10x/10=240/10          Do the division

x = 24

An answer is

  [tex]\displaystyle f\left(x\right)=\frac{\left(x+1\right)^3}{\left(x+2\right)^2\left(x-1\right)}[/tex]

Explanation:

Template:

  [tex]\displaystyle f(x) = a \cdot \frac{(\cdots) \cdots (\cdots)}{( \cdots )\cdots( \cdots )}[/tex]

There is a nonzero horizontal asymptote which is the line y = 1. This means two things: (1) the numerator and degree of the rational function have the same degree, and (2) the ratio of the leading coefficients for the numerator and denominator is 1.

The only x-intercept is at x = -1, and around that x-intercept it looks like a cubic graph, a transformed graph of [tex]y = x^3[/tex]; that is, the zero looks like it has a multiplicty of 3. So we should probably put [tex](x+1)^3[/tex] in the numerator.

We want the constant to be a = 1 because the ratio of the leading coefficients for the numerator and denominator is 1. If a was different than 1, then the horizontal asymptote would not be y = 1.

So right now, the function should look something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{( \cdots )\cdots( \cdots )}.[/tex]

Observe that there are vertical asymptotes at x = -2 and x = 1. So we need the factors [tex](x+2)(x-1)[/tex] in the denominator. But clearly those two alone is just a degree-2 polynomial.

We want the numerator and denominator to have the same degree. Our numerator already has degree 3; we would therefore want to put an exponent of 2 on one of those factors so that the degree of the denominator is also 3.

A look at how the function behaves near the vertical asympotes gives us a clue.

Observe for x = -2,

Observe for x = 1,

We should probably put the exponent of 2 on the [tex](x+2)[/tex] factor. This should help preserve the function's sign to the left and right of x = -2 since squaring any real number always results in a positive result.

So now the function looks something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{(x+2 )^2(x-1)}.[/tex]

If you look at the graph, we see that [tex]f(-3) = 2[/tex]. Sure enough

  [tex]\displaystyle f(-3) = \frac{(-3+1)^3}{(-3+2 )^2(-3-1)} = \frac{-8}{(1)(-4)} = 2.[/tex]

And checking the y-intercept, f(0),

  [tex]\displaystyle f(0) = \frac{(0+1)^3}{(0+2 )^2(0-1)} = \frac{1}{4(-1)} = -1/4 = -0.25.[/tex]

and checking one more point, f(2),

  [tex]\displaystyle f(2) = \frac{(2+1)^3}{(2+2 )^2(2-1)} = \frac{27}{(16)(1)} \approx 1.7[/tex]

So this function does seem to match up with the graph. You could try more test points to verify.

======

If you're extra paranoid, you can test the general sign of the graph. That is, evaluate f at one point inside each of the key intervals; it should match up with where the graph is. The intervals are divided up by the factors:

So we need to see if -2 < x < -1 matches up with the graph. We can pick -1.5 as the test point, then

  [tex]\displaystyle f(-1.5) = \frac{\left(-1.5+1\right)^3}{\left(-1.5+2\right)^2\left(-1.5-1\right)} = \frac{(-0.5)^3}{(0.5)^2(-2.5)} \\= (-0.5)^3 \cdot \frac{1}{(0.5)^2} \cdot \frac{1}{-2.5}[/tex]

We don't care about the exact value, just the sign of the result.

Since [tex](-0.5)^3[/tex] is negative, [tex](0.5)^2[/tex] is positive, and [tex](-2.5)[/tex] is negative, we really have a negative times a positive times a negative. Doing the first two multiplications first, (-) * (+) = (-) so we are left with a negative times a negative, which is positive. Therefore, f(-1.5) is positive.

[tex]\bf (WY+4)-Y=6\implies \stackrel{\textit{nope}}{WY+4-Y=6}[/tex]

recall, a quadratic has a polynomial with a degree of 2.

Answer:

a = 3 ,  b = -2 ,  c = 0

Step-by-step explanation:

The given equation is:

1 = -2x + 3x^2 + 1

To find the correct substitution values of a, b and c. We need to convert t into the standard form first.

Standard form of a Quadratic equation is written as:

ax^2 + bx + c = 0        (where a is not equal to zero)

Converting the given equation into its standard form:

1 = -2x + 3x^2 + 1

-2x + 3x^2 + 1 - 1 = 0

3x^2 - 2x + 0 = 0  

OR 3x^2 - 2x = 0

According to the equation

a = 3 ,  b = -2 ,  c = 0

Answer:

The answer is 6.

Step-by-step explanation:

Plug in:  f(-5)=|-5+1|

Because this an absolute problem -5 is positive within |x|

so therefore f(-5)= |6|

[tex]\bf |x-6|<4\implies \begin{array}{llll} +(x-6)<4\\ -(x-6)<4 \end{array}\implies \begin{cases} x-6<4\implies &\boxed{x<10}\\ \cline{1-2} -(x-6)<4\\ \stackrel{notice}{x-6\stackrel{\downarrow }{>}-4}\implies &\boxed{x>2} \end{cases}[/tex]

Let n be a number

2n - 3 = 55

Add 3 to both sides

2n + (-3 + 3) = 55 + 3

2n = 58

Divide 2 to both sides

2n/2 = 58/2

n = 29

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

X=30, Scalene

Step-by-step explanation:

A circle is 360, The triangle is in the circle.

Part A:3x+30+2x+20+5x+10=360

10x+60=360

-60=-60

10x=300

x=30

Part B:Side BA is 3(30)+30=120

Side BC is 2(30)+30=90

Side AC is 5(30)+10=160

All three sides are unequal

Answer:

2x+5

because you are subtracting it is basically multiplying (5x-6) by negative one so you have to distribute it out so you are basically adding (7x-1) and (-5x+6) by adding like terms you get 7x-5x= 2x and -1+6=5

so the answer is 2x+5

Answer:

-2x + 8y - 5z

Step-by-step explanation:

-1/2*4x = -2x

-1/2 * - 16y = 8y

-1/2 * 10z = - 5z

Combine

-2x + 8y - 5z

If you break the question apart like this, you will never get confused by what the signs do. What is left for signs is what you put in the answer.

the answer is not 65 and not 4

Answer:

option 3 is the answer

Step-by-step explanation:

A polynomial  in two variables is said to be in standard form if exponent of one variable is keep decreasing  and another variable keep increasing

only option 3 follows it

As here exponent of x start from 5 and decreases up to 0

and exponent of y start from 0 and keep increasing up to 5

rest of the option do not follow this rule

Answer:

c)5x^5 - 9x^2y^2 - 3xy^3 + 6y^5

Step-by-step explanation: