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By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

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Answer:

B is correct

Step-by-step explanation:

Cus I said so

The values for y are i, 0, √3 and 2√2

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Given:

F(x)= y = √(x-5) -1

At x=5,

y=  √(5-5) -1

y= i

At x= 6

y= √(6-5) -1

y=0

At x= 9

y= √(9-5) -1

y=√3

At x= 14

y= √(14-5) -1

y=√8= 2√2

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Answer:

Which of the following completes Ted's proof?

In square ABCD; angle ADC = angle BCD

In square ABCD; angle ADP = angle BCP

In triangles APD and BPC; angle ADC = angle BCD

In triangles APD and BPC; angle ADP = angle BCP\

Answer:

N: 30 B:150

Step-by-step explanation:

Supplementary angles add up to 180 meaning their equations must also add up to 180:

(3x + 18) + (2x + 142) = 180

Solve for x:

5x + 160 = 180

5x = 20

x = 4

Substitute 4 in all values of x to obtain the measure of the two angles:

N: 3(4) + 18 = 30

B: 2(4) + 142 = 150

The value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The question is incomplete.

The question is:

The area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant to be found.

The missing figure is attached; please refer to the picture.

As we can see in the figure we have given a rectangle.

Area of rectangle = (3 + x)(3 + x)

10 = (3 + x)(3 + x)

or

10 = (3 + x)²

10 = 9 + 6x + x²

After rearranging:

x² + 6x = 1

We have equation:

x² + 6x = a

After comparing:

a = 1

Thus, the value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.

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The simple interest is $24.75.

The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.

Simple interest = amount deposited x time x interest rate

$375 x 0.022 x 3 = $24.75

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Answer:

[tex]6y^1^6[/tex]

Step-by-step explanation:

I hope this has Helped :)

Step-by-step explanation:

sorry but I dont know

Answer: 654 grams

Step-by-step explanation:

that's the answer it gave it when I got it wrong.

Answer:

See below

Step-by-step explanation:

arrange to standard form   (x-h)^2   + (y-k)^2 = r^2     h,k = center   r = radius

x^2 - 4x        +    y^2 + 2y   =   4        complete the square for 'x' and 'y'

(x-2)^2    -  4    +    (y-1)^2  -1  = 4

(x-2)^2    +  ( y-1)^2  = 4 + 4 + 1 = 9           '9' is equal to r^2  so r = 3

center = 2,1     radius = 3

Answer:

you're welcome!!!

Step-by-step explanation:

The measure of the angle x is 117 degrees

To determine the value of x in the given diagram, we will use the alternate angles theorem

The value of x is expressed as shown;

p + q= x

If the value of p = 51, then;

51 + q. = x

Determine the value of. q

q = 108 - 42

q = 66

Determine the value of x

x = 66 + 51

x = 117 degrees

Hence the measure of the angle x is 117 degrees

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Considering the common factor, the most efficient way to factor the expression 2x³ - 18x² + 40x is given by:

C. Factor out 2x.

The most efficient way to factor the expression is factoring out the common factor.

In this problem, the expression is:

2x³ - 18x² + 40x

We have that:

Hence the common factor is of 2x, which means that option C is correct.

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Answer:

6√27 + √243

6√9 x 3 + √81 x 3  

6 x 3 √3 + 9√3

18√3 + 9√3

27√3

The inverse of the function f(x) = 2x - 10 is f-1(x) would be x/2 + 5.

Lets try to solve it,

We will be using the inverse function to solve this.

f(x) =[tex]2x - 10[/tex]

Replace f(x) with y.

[tex]y = 2x - 10[/tex]

Interchange x and y

[tex]x = 2y - 10[/tex]

Solve for y

[tex]y = (x + 10) / 2[/tex]

Replace y with f-1(x).

[tex]f-1(x) = x/2 + 5[/tex]

Thus, the inverse of the function f(x) = 2x - 10 is f-1(x) = x/2 + 5

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In the equation given, the quadratic inequality  that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).

Note that a quadratic function exist in factored form is as:

y = a(x - a)(x - b)

The zeros of the equation is seen at x = (-4, 10)

Therefore, one need to write an expression for the quadratic inequality and so it will be:

y ≥ a(x - a)(x - b)    

Also note that at At point (6, -8), we also have:

-8 = a(6 - (-4))(6 - 10)  

-8 = a(6 + 4)(6 - 10)

-8 = a(10)(-4)

-8 = -a(40)

a = 0.2.

Therefore, In the equation given, the quadratic inequality  that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).

See full question below

Which statement describes the quadratic inequality in factored form that represents the relationship greater than or

equal to the quadratic equation containing the point (6, -8) on the boundary and zeros-4 and 10?

Oy2-0.2(x + 4)(x - 10)

Oy≥ 0.2(x + 4)(x - 10)

O y 20.2(x-4)(x + 10)

Oy2-0.2(x-4)(x + 10)

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The value of f(x) when the value of x is 9 is 38.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The given data points are in a linear relation, therefore, if we find the slope of the line on which these data points will be located. Then the slope will be,

m = (17-5)/(2+2) = 3

Now, equate any point and the slope in the general equation of line, therefore, the equation will be,

y = 3x + c

17 = 3(2) + c

17 - 6 = c

c = 11

Further, the value of f(x) when the value of x is 9 will be,

f(x) = 3x + 11

f(9) = 3(9) + 11

f(9) = 38

Hence, the value of f(x) when the value of x is 9 is 38.

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Answer:

D

Step-by-step explanation:

x = 5y²

x = 3y²

Here x is a function of y and so the parabola is open either to right or left.

The coefficient of y² is positive. So the parabola is open to right.

Both parabolas are open to right and  x = 5y² is wider than x = 3y².

Answer:

98

Step-by-step explanation:

There are 180 degrees in a triangle.

180 - 53 - 29 = 98

Answer:

The answer is figure A, B, C, D.

Step-by-step explanation:

Because, polygon means a shape with more then 1 side, and in your pic all of the figures have more than one side, so that's the answer.

Answer:

10x + 332

when, x=0

Step-by-step explanation:

Please give me brainlist.

Answer:

8x

Step-by-step explanation:

Greatest common factor is the factor of 24, 56 and 16. Since 16x only has the power of 1, then then the answer should be on power of 1.

Answer:

Given the 24x⁵ - 56x³ + 16x contains numbers and variables, there are two steps to finding the GCF. Find the GCF for the numeric part, then find the GCF for the variable part.

Steps to find the LCD of 24x⁵ - 56x³ + 16x

Find the common factors of the numerical part: 24, −56, 16

The factors for 24 are −24,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,24.

The factors for −56  are−56,−28,−14,−8,−7,−4,−2,−1,1,1,2,2,4,4,7,7,8,8,14,14,28,28,56,56.

The factors for 16  are −16,−8,−4,−2,−1,1,2,4,8,16.

List all the factors 24,−56,16 to find the common factors.

The common factors for 24,−56,16 are −8,−4,−2,−1.−8,−4,−2,−1

The GCF of the numerical part is 8.

[tex]\bf{GCF_{Numerical}=8 }[/tex]

Then find the common factors for the variable part:

x⁵, x³, x

The factors for x⁵ are:

x · x · x · x · x

The factors for x³ are:

x · x · x

The factors for x¹ are:

x

List all the factors x⁵, x³, x¹ to find the common factors.

x⁵ = x · x · x · x · x

x³ = x · x · x

x¹ = x

The common factor of the variables x⁵, x³, x¹ is x.

The LCD of the variable part is x.

[tex]\bf{GCF_{Numerical}=x }[/tex]

Multiply the LCD of the numerical part 8 and the GCF of the variable part x.

8x

Clayman is 10 years old and Ato is 15 years old

Let the age of Clayman be x

Let the age of Ato be y

If the sum of ages of Clayman and Ato is 25 years. then;

x + y = 25

x = 25 - y ...... 1

In five years time;

Age of Clayman = x + 5

Age of Ato = y + 5

If in five years' time, the age of Ato will twice the age of Clayman now, then;

y+5 = 2x ............. 2

Substitute equation 1 into 2

y +5 = 2(25-y)

y + 5 = 2(30 - y)

y + 5 = 50 - 2y

3y = 45

y = 15

Since x + y = 25

x = 25 - 15

x = 10

Therefore Clayman is 10 years old and Ato is 15 years old

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Answer:

72

Step-by-step explanation:

8 x 3² = 8 x 3 x 3

          = 8 x 9

          = 72

[P.S. If you meant (8 x 3)² the answer is:

(8 x 3)² = (24)²

            = 24 x 24

            = 576     ]  

Answer:

Step-by-step explanation:

cost of 25 kg =262.50x25

                      =6562.5

Hope this helps you

........

Answer:  $30

Step-by-step explanation:

So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30

(I'm assuming what you mean by "how much money he will have" is profit)

Answer:

The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.

Step-by-step explanation:

     125

×    24

  --------

    500

+ 2500

-----------

  30.00

Answer:

x(x - 2)

Step-by-step explanation:

x² - 2x ← factor out x from each term

= x(x - 2)

A function assigns the values. The correct options are A, B, and E.

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

The situations that can be best modelled by exponential functions are:

A) The yearly depreciation of a car.

B) An investment compounded annually.

E) The annual growth rate of a city's population.

Hence, the correct options are A, B, and E.

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The equation of the line in slope-intercept form is [tex]\bf{y= \frac{3}{2} x + \frac{9}{4}} [/tex].

The first step is to calculate the slope of the line.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Slope

[tex] = \frac{ - 3 - 0}{ - 5 -( - 3)} [/tex]

[tex] = \frac{ - 3}{ - 5 + 3} [/tex]

[tex] = \frac{ - 3}{ - 2} [/tex]

[tex] = \frac{3}{2} [/tex]

Substitute the value of m into y= mx +c:

[tex]y = \frac{3}{2} x + c[/tex]

Next, substitute a pair of coordinates that the line passes through. Here, I will substitute (-3, 0) into the equation.

When x= -3, y= 0,

[tex]0 = \frac{3}{2} ( - 3) + c[/tex]

Find the value of c:

[tex]0 = - \frac{9}{2} + c[/tex]

[tex]c = \frac{9}{2} [/tex]

Substitute the value of c into the equation:

Thus, the equation of the line is [tex]y = \frac{3}{2} x + \frac{9}{2} [/tex].

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