Which of the following is the conjugate of the expression below when x>-2?
6+√x+2
OA. 6+√x+2
B. 6-√x-2
C. 6-√√x+2
D. 6+√x-2

Answer: d

Step-by-step explanation:

divide 300 by 50 to get 6 then multiply 2.5 by 6 to get 15 therefore the answer is d 15ml

Answer: Right iscoleces triangle

Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.

Answer:

right isosceles

Step-by-step explanation:

the right angle and the two sides that are equal make the triangle a right isosceles

Answer:

The number in the green box should be 3.

Step-by-step explanation:

[tex]c + 4 {c}^{2} - 2 + 2c - {c}^{2} + 5 = 3 {c}^{2} + 3c + 3[/tex]

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Step-by-step explanation:

(9x³+5)/(2x - 3)

split up (9x³+5)

9x³/2x-3 + 5/2x-3

attached solution.

A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,

f(-3) = -(-3)² - 4(-3) + 5

f(-3) = -9 + 12 + 5

f(-3) = 8

Now, the value of f(x) when the value of x is 3 is,

f(3) = -(3)²-4(3)+5

f(3) = - 9 - 12 + 5

f(3) = -16

further, the value of f(3) + f(-3) is,

f(3) + f(-3) = -16 + 8

f(3) + f(-3) = -8

Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

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Answer:

1/4

Step-by-step explanation:

Since y/x = 3/12 = 1/4, the answer is 1/4.

Answer:

y=3x+8

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

you find the slope by using this formula:

then we figure out it is 3

then graph to find the y-intercept which is 8

Answer:

y = 3x + 8

Step-by-step explanation:

Below is the image for the formula of the slope.

1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.

Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).

When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8

Therefore, the equation is y = 3x + 8

Answer:

the value of x is between -4 and 4

Answer:

[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]

To find the zeros, set the function to zero and solve for x using the quadratic formula.

[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]

Quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore,

Substituting the values into the quadratic formula:

[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]

[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

The sum of the roots of a polynomial is -b/a:

[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]

The sum of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is:  c/a

[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]

The product of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

Answer:

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

Quadratic formula:

Therefore,

a = 2√3

b = 5

c = - 4√3

Substituting the values into the quadratic formula:

The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

The formula that should be entered in A3 is = A1 * B1

The question implies that:

A3 = A1 times B1

In mathematics, the term "times" means *

So, we have:

A3 = A1 * B1

Remove the variable A3

= A1 * B1

Hence, the formula that should be entered in A3 is = A1 * B1

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The range of the function on the graph is C. all the real numbers greater than or equal to –3 .

We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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Answer:

y=−6x−36

Step-by-step explanation:

ez math

Answer:

1. x - 1

2. [tex]\sqrt{x^2-1}[/tex]

Step-by-step explanation:

[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]

[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]

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Answer:  [tex]7.21[/tex]

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Given:  [tex]\textsf{(2, -3) and (-4, -7)}[/tex]

Find: [tex]\textsf{Find the distance between the two points}[/tex]

Solution:  Use the distance formula and the two points that were provided to determine the distance.

Plug in the values

Simplify and expand

If we are using square root we use the square root of 52 but if we simplify it to a decimal point we would use 7.21

The amount in the new checking account is 600 dollars

The operation (5 α 3) + (7 α 5) is 46.

She had 1000 dollars in her checking account. she had a loan of 800 dollars to pay.

After paying her loan form her checking account the balance of the loan reduce to half.

Therefore, she paid 800 / 2 = 400 dollars for her loan

Hence,

Her new checking account = 1000 - 400 = 600 dollars

a α b = ab - a + b

Therefore,

(5 α 3) + (7 α 5)

(5 α 3) = 5(3) - 5 + 3 = 13

(7 α 5) = 7(5) - 7 + 5 = 33

Therefore,

(5 α 3) + (7 α 5) = 13 + 33 = 46

Note: I can't use the at symbol because it is a swear word.

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Answer:

-3 and -7

Step-by-step explanation:

Factors of 21: 1, 3, 7, 21

3 and 7 add up to 10, but what about -10? Well, -3 * -7 is also 21, and -3 + -7 gives you -10.

Brainliest, please :)

The transformation that can be used to show that ABCDE and its image are congruent is a 90° counterclockwise.

It should be noted that when we rotate a point through 90° counterclockwise, the mapping will be: (x, y) to (-y, x).

In this situation, it van be deduced that the x and y coordinates swapped positions. This illustrates a 90° counterclockwise rotation about the origin..

In this situation, since the rotation is a rigid motion, the two shapes are congruent.

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Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

The best approximation for the median is 3.6.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

For the given density curve, the area under the density curve is

A=(1/2)×5×(1/2)=5/4

now, for the median, the area on the left and the area on the right of the median.

Let the median be x, then

The area criteria we get

(1/2)x(x/10)=(5/4)/2

⇒x²=5*20/4=25/2

So, we get x=5/([tex]\sqrt2[/tex])=3.5 ≈ 3.6

Hence the required answer is option 3.6

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Answer:

21 grandchildren

Explanation:

2/7ths + 5/7th = all

5/7ths = 15   <- divide both sides by 3 to get 1/7th

1/7th = 3 (multiply both sides by 7 to get "1")

  7/7ths    = 21

so, eva has 21 grandchildren

Answer:

21

Step-by-step explanation:

If 2/7th of Eva's grandchildren live in one location, we know that 5/7th (the remaining portion of Eva's grandchildren) must live in the other location

Wales + Australia = all of the kids (100% = 1/1  (which is equal to 7/7) )

Wales + Australia = 7/7ths

{x is the total number of kids}

Australia = 5/7ths

15 = [tex]\frac{5}{7}x[/tex]   {multiply both sides by 7 to get rid of fraction}

105 = 5x   {divide both sides to find 1x}

21 = x

check:

2/7th of 21 = 6

5/7th of 21 = 15  {which we know}

6 + 15 = 21

21 = 21

(TRUE)

So, Eva has 21 grandchildren

hope this helps!!

The part that represents the solution to the inequality will be Part B shaded below first line and above second line.

From the information given, the equation of the first line will be:

y - 3 = (-3 - 3/2 + 4)(x + 4)

y - 3 = -1(x + 4)

y + x = -4 + 3

x + y = -1

The equation of the second line will be:

y + 3 = -1(x + 4)

y = x + 4 - 3

y = x + 1

This is plotted on the graph attached.

From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

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Answer:

f = 4 [tex]\frac{5}{37}[/tex]

Step-by-step explanation:

divide 1000 on both sides.

f = 4.135 repeating (the 135 is repeating.)

Put the .135135135... over 999 because it is repeating. F becomes 4[tex]\frac{135}{999}[/tex]

Simplify. f = [tex]4\frac{5}{37}[/tex]

Answer:

2nd option

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]

         = [tex]\frac{3x+1}{3}[/tex]

         = [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]

        = x + [tex]\frac{1}{3}[/tex]

Answer:

f=- 6, x=-1

f = - 6, x=-3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

Tim is 8 years old.

Explanation:

8 is the cube number of 2, as 2 × 2 × 2 = 8. Additionally, 8 is double 4, which is the square number of 2, and half of 16, which is the square number of 4.

Tim who goes to school is 8 years old.

Good numerical ability describes your ability to think and conclude logical thoughts in your daily life also in your working role how you handle data in form of numbers, graphs, statements etc.

According to the given question Tim goes to school.

His age is a cube number let that number be x therefore age of Tim would be x³.

His age can also be defined as double of 1 square number which is 2x² and half of a different square of a numbers.

Let us equate x³ = 2x² and by hit and trial we get to know that x = 2 satisfies this condition.

So, Age of Tim could be 8 years,Now lets check our third statement half a different square number 16 is square of 4 so half of 16 is also 8.

Thus Tim is 8 years old.

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Answer:

54.6 ÷ 8.4 = 6.5 hours

6 hours, 30 minutes:)

There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle and a parabola:

As we know the standard form of a circle:

[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]

The standard form of the parabola:

[tex]\rm y = a(x-h)^2+k[/tex]  

If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)

The solution of the quartic equation will be 4.

Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

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If the geometric series has first term [tex]a[/tex] and common ratio [tex]r[/tex], then its [tex]N[/tex]-th partial sum is

[tex]\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}[/tex]

Multiply both sides by [tex]r[/tex], then subtract [tex]rS_N[/tex] from [tex]S_N[/tex] to eliminate all the middle terms and solve for [tex]S_N[/tex] :

[tex]rS_N = ar + ar^2 + ar^3 + \cdots + ar^N[/tex]

[tex]\implies (1 - r) S_N = a - ar^N[/tex]

[tex]\implies S_N = \dfrac{a(1-r^N)}{1-r}[/tex]

The [tex]N[/tex]-th partial sum for the series of reciprocal terms (denoted by [tex]S'_N[/tex]) can be computed similarly:

[tex]\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}[/tex]

[tex]\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}[/tex]

[tex]\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}[/tex]

[tex]\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}[/tex]

We're given that [tex]a=1[/tex], and the sum of the first [tex]n[/tex] terms of the series is

[tex]S_n = \dfrac{1-r^n}{1-r} = 364[/tex]

and the sum of their reciprocals is

[tex]S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}[/tex]

By substitution,

[tex]\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243[/tex]

Manipulating the [tex]S_n[/tex] equation gives

[tex]\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363[/tex]

so that substituting again yields

[tex]r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}[/tex]

and it follows that

[tex]r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}[/tex]