which is equivalent to......... algebra II engenuity

Answer:

x = 7

Step-by-step explanation:

-10 + 5 + 3x = 16

-5 + 3x = 16

3x = 21

x = 7

Answer:

A

Step-by-step explanation:

From the diagram:

The general rule of this reflection is

(x,y)→(-x,y)

and this is reflection across the y-axis. The y-axis has the equation x=0.

The values of x that make the expression (x - 6)(x + 2) equal to zero are -2 and 6. This is based on the Zero Product Property in Mathematics, which states that if the product of two factors is zero, then at least one of the factors must equal zero.

In Mathematics, the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this property in the expression (x - 6)(x + 2) = 0, one can conclude that either (x - 6) = 0 or (x + 2) = 0.

The expression (x−6)(x+2) equals 0 when either (x−6)=0 or (x+2)=0. Solving each equation separately:

For (x−6)=0, add 6 to both sides to get x=6.

For (x+2)=0, subtract 2 from both sides to get x=−2.

So, the values of x that make (x−6)(x+2)=0 are x=−2 and x=6.

Solving both equations, we get two possible solutions, x = 6 or x = -2. So, the values of x that would result in the expression being equal to zero are -2 and 6, listed in order from least to greatest.

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Answer:

True.

Step-by-step explanation:

These are sets containing the same exact elements so they are the same set of elements.

They both contain 4 elements.

The 4 elements in each are c, f , j , and k.

It matters not of the arrangement.  It also doesn't matter if they repeat an element.  

For example these sets are also the same:

{a,a,b} and {a,b}.

They both contain 2 elements and those elements are a and b.

People don't normally write something like {a,a,b} because it is redundant (because of the repetition of a).  

Here is an example of some sets that are equal:

{1,2,3}={1,3,2}={2,1,3}={2,3,1}={3,1,2}={3,2,1}.

These are all the same because they all contain the elements: 1 , 2 , and 3. It doesn't matter the order in a set.

Answer:

F 24

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

10^2 + EF^2 = 26^2

100 + EF^2 = 676

Subtract 100 from each side

100-100 + EF^2 = 676-100

EF^2 = 576

Take the square root of each side

sqrt(EF^2) = sqrt(576)

EF = 24

Answer:

F 24

Step-by-step explanation:

You have to use the Pythagorean Theorem

a²+b²=c²

(a and b are the legs of the triangle and c is always the hypotenuse)

a²+10²=26²

a²+100=676; now isolate the a² by subtracting 100 from both sides.

a²=576; now square root each side (gets rid of the squared)

a=24

Answer:

The degree is 2.

Step-by-step explanation:

We are given f(x)=-3x^2 and g(x)=-4x+1.

(f o g)(x)

f(g(x))

f(-4x+1)

This means the old x in f will be replaced with -4x+1 like so:

-3(-4x+1)^2

-3(-4x+1)(-4x+1)

Use foil!

-3(16x^2-4x-4x+1)

-3(16x^2-8x+1)

-48x^2+24x-3

The degree is 2. The degree is the highest exponent on the variable if you only have one variable and your polynomial is written in standard form.

Answer: C.

Step-by-step explanation:

The value of inverse function f⁻¹(3)  is 13, option (D) is correct.

Function is a combination of different types of variable and constants.

A function is generally denoted by f(x).

The given function is,

f(x) = (2x+1)/(x-4)

To find the value of f⁻¹(3),

Let  f⁻¹(3) = y

⇒3 = f(y)

⇒3 = (2y+1)/y-4

⇒3(y-4) = 2y+1

⇒3y-12 = 2y+1

⇒ y = 13

⇒ f⁻¹(3) = 13

Therefore, the value of  f⁻¹(3)  is 13.

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Answer:

[tex]\large\boxed{(f+g)(x)=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\\text{We have}\\\\f(x)=\dfrac{1}{3}-\dfrac{1}{2}x,\ g(x)=2x^2+x+4.\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{3}-\dfrac{1}{2}x\right)+(2x^2+x+4)\\\\=\dfrac{1}{3}-\dfrac{1}{2}x+2x^2+x+4\qquad\text{combine like terms}\\\\=2x^2+\left(-\dfrac{1}{2}x+x\right)+\left(\dfrac{1}{3}+4\right)\\\\=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}[/tex]

Answer:

Z=1.055

Step-by-step explanation:

Z is inversely proportional to X: [tex]Z=\frac{K}{X}[/tex] Where K is a constant

X=18, Z=1.583333333333 we can find K value

K=Z*X =1.58333333333*12= 19

So, Using X=18 We have the following

[tex]Z=\frac{19}{18}[/tex]= 1.055

Answer:

b. 5x^2 + 9x - 1

Step-by-step explanation:

A quadratic expression had the highest power of the variable at 2

x^2

b. 5x^2 + 9x - 1

a  has the highest power as x

c and d goes higher than x^2

The expression that represents a quadratic expression is 5x^2 + 9x - 1 (option b), which is in the form ax^2 + bx + c, where a, b, and c are constants.

The expression that represents a quadratic expression is option (b), which is 5x^2 + 9x - 1. A quadratic expression is generally in the form ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero. This type of equation represents a parabola when graphed on a coordinate plane. The examples provided in the question show how various terms relate to the constants a, b, and c in the quadratic equation, and the use of the quadratic formula for solving such equations. Option (a) is linear, option (c) is cubic, and option (d) is quartic, as indicated by the highest powers of x.

Answer:

3(5n -6)

Step-by-step explanation:

15n -18

Both 15 and 18 can be divided by 3

Factor out a 3

3(5n -6)

Anwser

3(5n -6)

Step-by-step explanation:

15n -18

Both 15 and 18 can be divided by 3

Factor out a 3

3(5n -6)

With $5 and pencils priced at 25 cents each, the student can buy 20 pencils. This is obtained by dividing $5 by $0.25 (the cost of one pencil).

Let's break down the calculation step-by-step:

Identify the given information.

The student has $5 to spend.

Each pencil costs 25 cents, which is equivalent to $0.25.

Set up the formula for the number of pencils.

Number of pencils = Total money / Cost per pencil

Substitute the given values into the formula.

Number of pencils = $5 / $0.25

Simplify the expression.

Dividing $5 by $0.25 is the same as multiplying $5 by the reciprocal of $0.25, which is 4.

Number of pencils = 5 * 4

Calculate the result.

Number of pencils = 20

So, the student can buy 20 pencils with $5.

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Answer:

[tex]\huge \boxed{123}[/tex]

Step-by-step explanation:

This question is about the order of operations. The order of operations stands for parenthesis, exponent, multiply, divide, add, and subtract.

Do parenthesis.

[tex]\displaystyle (35+25)=60[/tex]

[tex]\displaystyle 60*2+3[/tex]

Multiply from left to right.

[tex]\displaystyle 60*2=120[/tex]

Add numbers from left to right.

[tex]\displaystyle 120+3=123[/tex]

123 is the correct answer.

Answer:

r=7

Step-by-step explanation:

We have the equation

(x+5)^2 + (y+8)^2 =

We know that this is equal to the radius squares

(2+5)^2 + (-8+8)^2 = r^2

We know a point  on the circle (2,-8)

Substitute this point into the equation

(2+5)^2 + (-8+8)^2 = r^2

(7)^2 + (0)^2 = r^2

7^2 = r^2

The radius is equal to 7

Answer:

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

__

The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

  cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

  cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

  cos(2θ) = 7/25

__

  tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

  tan(2θ) = -24/7

Answer: tan(2θ) = -24/7

Step-by-step explanation: N/A

Answer:

Icosahedron

Step-by-step explanation:

Icosahedron has 20 faces and all the faces are equilateral triangle. Also the faces are congruent and the Icosahedron is one of the five Platonic solids.

Icosahedron has twenty faces that are equilateral triangles.

Icosahedron is one of the 5 Platonic solid which has 20 faces, 12 vertices, 30 edges.

All the faces of Icosahedron is an equilateral triangle at each vertex. also all the faces are congruent and are of the same size.

From the picture given below, it is also clear that

Icosahedron has twenty faces that are equilateral triangles.

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To determine the probability that Harold buys an ice-cream on Wednesday, we consider the probabilities for each day. Given that he bought an ice-cream on Monday, there is a 40% chance that he will buy an ice-cream on Wednesday.

To determine the probability that Harold buys an ice-cream on Wednesday, we need to consider the probabilities for each day.

Given that he bought an ice-cream on Monday, there is a 30% chance that he will buy a drink on Tuesday and a 40% chance that he will buy an ice-cream on Tuesday.

Using the probabilities, we can calculate the probability that Harold buys an ice-cream on each day:

Monday: 1 (since he bought an ice-cream)

Tuesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)

Wednesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)

Answer: .012

Step-by-step explanation:

We know that when two events A and B are independent of each other , then the probability of their intersection is given by :-

[tex]P(A\cap B)=P(A)\ \cdot\ P(B)[/tex]

Given : The probability that a shopper buys shoes is 0.12

The probability that a shopper buys a book is 0.10

Since, both the events are independent , then the probability that a shopper buys shoes and a book is given by :-

[tex]0.12\times0.10=0.012[/tex]

Hence, the probability that a shopper buys shoes and a book is .012 .

Answer:

0.012 is the answer

Answer:

The arcs form a circle ⇒ answer C

Step-by-step explanation:

* Lets explain some facts in the circle

- The chord in a circle is a segment whose endpoints lie on the circle

- Any chord of a circle intersects it into 2 arcs

- The minor arc which its measure lies between 0° and 180°

-The major arc which its measure lies between 180° and 360°

- The sum of the measures of the minor arc and the major arc is equal

  to the measure of the circle

- The measure of the circle is 360°

* Lets solve the problem

∵ The measure of arc XY + the measure of arc YZX = 360°

∵ The arcs do not overlap

- That means the endpoints of the arcs are X and y

∵ The measure of the circle is 180°

∴ The arcs form a circle

Answer:circle

Step-by-step explanation:

im lookin it on a question rn

Answer:

=19.81 in²

Step-by-step explanation:

We use the sine formula to find the area of the triangle in question.

In this formula we find the product of two adjoined sides with the sine of the angle between them.

The sides b and c are bound by the angle A.

Therefore area=1/2bcSin A

A=1/2×13.2 in×5.3 in× Sin 34.5

=19.81 in²

Answer:19.812

Step-by-step explanation:

 Given

angle A=34.5

b=13.2 in.

c=5.3 in.

Area of triangle when two sides and angle between them is given

[tex]A=\frac{1}{2}bcsina[/tex]

[tex]A=\frac{1}{2}\left ( 13.2\right )\left ( 5.3\right )sin\left ( 34.5\right )[/tex]

[tex]A=19.812 in.^2[/tex]

Answer:

The answer is 31.83....

Step-by-step explanation:

If you divide 191 by 6 we get:

=31.8333333333

Rounding to the nearest hundredth:

Underline the hundredths place: 31.8333333333

Look to the right. If it is 5 or above 5 then we give it a shove.

If it is 4 or less than 4, we let it go.

In our case it is 3.

Round to 31.83

Therefore the answer is 31.83....

Answer:

[tex]f(x)=-x^{2} +8x-16[/tex]

Step-by-step explanation:

we know that

A polynomial function that has a leading coefficient of -1 and root 4 with multiplicity 2 is equal to

[tex]f(x)=-(x-4)^{2}[/tex]

Expand the function

[tex]f(x)=-(x^{2}-8x+16)\\ \\f(x)=-x^{2} +8x-16[/tex]

Answer: B

Step-by-step explanation:

Answer:

-7/4

Step-by-step explanation:

Line A is the blue one.

I see two points they have identified for me:

(-7,0) and (0,4).

To find the slope of the line A given two points we could use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

We could also line up the points vertically and subtract, then put 2nd difference over 1st difference.

Like this:

(-7,0)

-(0,4)

-------

-7   -4

So the slope is -4/-7=4/7

So the slope of a line that is perpendicular will have opposite reciprocal slope. That is the opposite reciprocal of 4/7 is -7/4.

Therefore the slope of a line that is perpendicular to A will have slope -7/4.

Answer:

[tex] - \frac{7}{4} [/tex]

Step-by-step explanation:

We use the slope formula to fine the slope of line A.

[tex] m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Line A passes through (-7,0) and (0,4)

[tex]m = \frac{4 - 0}{0 - - 7} [/tex]

[tex]m = \frac{4}{7} [/tex]

The slope of a line that is perpendicular to line A is the negative reciprocal of the slope of line A

[tex] - \frac{7}{4} [/tex]

Answer:

B

Step-by-step explanation:

what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry

Answer:

B) 2

Step-by-step explanation:

Given that a rectangle is not a square.

Hence we find that opposite sides are equal.

If we mark midpoints on all sides then the vertical line joining mid points and horizontal lines joining next pair of midpoint of opposite sides are the lines of symmetry

There can be no other line of symmetry

Hence no of lines of symmetry for a rectangle = 2

Answer: 32°

Step-by-step explanation:

m∠BAC = m∠CDE, therefore m∠CDE = 32°

Answer:

Option B, 58°

Step-by-step explanation:

In the given figure AB ║ CD and BC ║ DE ( given )

Since BC ║ DE and BC ⊥ AC

So DE will also be perpendicular to CE

m ∠ BAC = 32° [given]

Since AB ║ CD and line AE is transverse

Then ∠BAC ≅  ∠DCE ≅ 32°

Now in ΔDEC.

∠DCE + ∠CED + ∠EDC = 180°

32° + 90° + ∠EDC = 180°

122° + ∠EDC = 180°

∠EDC = 180 -122

          = 58°

Option B, 58° is the answer.

Answer:

b =45

Step-by-step explanation:

A full circle is 360 degrees

b+315 = 360

Subtract 315 from each side

b+315-315 = 360-315

b =45

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given the slope of a line m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

B) 0,-2  (x = 0 , y = -2)

Step-by-step explanation by elimination:

Solve the following system:

{2 x + 6 y = -12 | (equation 1)

{5 x - 5 y = 10 | (equation 2)

Swap equation 1 with equation 2:

{5 x - 5 y = 10 | (equation 1)

{2 x + 6 y = -12 | (equation 2)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 5 y = 10 | (equation 1)

{0 x+8 y = -16 | (equation 2)

Divide equation 1 by 5:

{x - y = 2 | (equation 1)

{0 x+8 y = -16 | (equation 2)

Divide equation 2 by 8:

{x - y = 2 | (equation 1)

{0 x+y = -2 | (equation 2)

Add equation 2 to equation 1:

{x+0 y = 0 | (equation 1)

{0 x+y = -2 | (equation 2)

Collect results:

Answer:  {x = 0 , y = -2

Answer:

Explicit formula is 2(5)^(n-1).

Step-by-step explanation:

This is a Geometric Sequence  with common ratio 10/2 = 50/10 = 250/50 = 5.

The  nth term  an = a1 r^(n - 1)

= 2(5)^(n-1).

Formula for sequence tells about getting its specific term by putting its index. The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is  [tex]a[/tex]  and the term by which we multiply the previous term to get the next term is  [tex]d[/tex]

Then the sequence would look like

[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)

Thus, the nth term of such sequence would be

[tex]T_n = ad^{n-1}[/tex]

For the given sequence, it can be seen that each previous term is multiplied by 5 to get the next term to that term.

Like, we got

[tex]10 = 2 \times 5\\50 = 10 \times 5[/tex] and so on.

This shows that there is single constant used which is multiplied to previous terms to get the next term. This is the property of a geometric sequence. Here, we got

[tex]a = 2\\d = 5[/tex]

Thus, sequence is

[tex]a, ad, ad^2, ad^3, ...\\\\or\\\\2, 2\times 5, 2 \times 5^2, 2 \times 5^3 ...\\\\or\\2, 10, 50, 250, 1250,...[/tex]

Its nth term is given as: [tex]T_n = ad^{n-1} = 2(5)^{n-1}[/tex]

A sequence with n terms, and its nth term formula being [tex]a_n[/tex] is written as [tex]\{a_i\}_{i=1}^n[/tex] (showing that put i = 1, 2, ... n) to get its terms.

Here, sequence is not limited, so infinite terms.

or, we get the formula for the sequence as: [tex]\{a_i\}_{i=1}^n = \{2(5)^{i-1}\}_{i=1}^\infty[/tex]

Thus,  The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]

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