Complete the expression so that it forms a perfect square trinomial--don't forget the sign for an operation. Then write the expression for the perfect square binomial using ^ to make an exponent. x^2+5 perfect square binomial

The value of x using the theorem of intersecting secants is 10

From the question, we have the following parameters that can be used in our computation:

intersecting secants

Using the intersecting secants equation, we have

8 * (8 + x) = 6 * (6 + 18)

Evaluate the like terms

So, we have

8 * (8 + x) = 6 * 24

Divide both sides by 8

8 + x = 6 * 3

So, we have

8 + x = 18

Subtract 8 from both sides

x = 10

Hence, the value of x is 10

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Answer:

length of the rectangle=27"

Step-by-step explanation:

length be = l; width be = b

2b-15= l

perimeter= 2(l+b)

=2(2b-15+b)=96

=2(3b-15)  =96

3b-15 .=48

3b=48+15=63

b=21. Therefore l = (2 x 21)  - 15=42-15  =27"

Answer: 6 plates

Step-by-step explanation:

18 ÷ 6 = 3

24 ÷ 6 = 4

3 blueberry muffins and 4 cranberry muffins for each plate.

Answer:

6 because there can be 6 plates of 2 blueberry muffins and 4 cranberry muffins

Step-by-step explanation:

The triangles ABD and CBD has equal angles because of the angle bisector property.

What is angle bisector?

DB is the angle bisector, So ADO = CDB(Angle)

DB = OB (Side)

AD = DC (Side)

So, triangles ABD and CBD has equal angles.

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Answer:

I think you may have this worded wrong Ben is 12 12 12 years older is it 12 years older and then four times older as?

Step-by-step explanation:

if so your answer is 7

Answer:

12.0396 meters

Step-by-step explanation:

Given that in 1 meter, there are 100 cm, we can write:

1 m = 100 cm   (divide both sides by 100)

1/100 m = 1 cm  

re-writing this equation, we get:

1 cm = 1/100 m  or,

1 cm = 0.01 m

2.54 cm = 2.54 x 0.01 = 0.0254 m, or

2.54 cm = 0.0254 m -----> equation 1

Also given that in 1 inch, there are 2.54 cm, we can write

1 inch = 2.54 cm (substitute equation 1 into this equation)

1 inch = 0.0254m

474 inches = 474 x 0.254 = 12.0396 meters (answer)

Answer:

Step-by-step explanation:

C

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

C

Step-by-step explanation:

use the points to find the slope (y-y1/x-x1) 3-5/3-6 = 2/3

the answers are all in point slope form so the slope is 2/3 and the point represented is 3,3

Answer: It’s A. Just did it

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

2/6*1/6=2*1/6*6 or 1/9.

Answer:

1/18

Step-by-step explanation:

1. multiply across

2*1 and 6*6

2/36

2. divide by 2 to simplify

2/2 and 36/2

1/18

Step-by-step explanation:

5x-2y=10 equation (1)

4x-3y=15 equation (2)

multiply equation 1 by-3 and equation 2 by 2

the equations become :

-15x+6y=-30 equation (1)

8x-6y=30 equation (2)

Eliminate y from the equations by adding the 2 equations to find x .

-15x+8y=0

-7x=0

x=0

Substitute x in equation (1) and solve for y

5x-2y=10 equation (1)

5(0)-2y=10

y=10/-2=-5

therefore ,x=0 and y=-5

The roots of the quadratic function f(x) = -3x² - 11x - 5 will be negative 3.14 and negative 0.53.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

\(\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\)

The quadratic function is given below.

f(x) = -3x² - 11x - 5

Then the roots of the quadratic function will be given as,

x = [-(-11) ± √{(-11)² - 4 × (-3) × (-5)}] / [2 × (-3)]

Simplify the equation, then the roots of the equation are calculated as,

x = [-(-11) ± √{(-11)² - 4 × (-3) × (-5)}] / [2 × (-3)]

x = [ 11 ± √{121 - 60}] / [-6]

x = - (11 ± 7.81) / 6

x = - (11 + 7.81) / 6, - (11 - 7.81) / 6

x = - 3.14, -0.53

The solution of the quadratic function will be negative 3.14 and negative 0.53.

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The surface area of the solid is 281 ft².

Given that, a solid figure made of a rectangular prism and a square pyramid,

We need to find its surface area,

To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,

So,

Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,

= 2×5×5 + 2(4·12+12·5+4·5)-5²

= 50+256-25

= 281 ft²

Hence the surface area of the solid is 281 ft².

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The question is not complete, so i have attached it.

Answer:

A) Option B: μ ≤ 19,000

B) Option C:

H0: μ ≤ 19,000

Ha: μ > 19,000

C) Option D: The null hypothesis H0: μ ≤ 19,000 is the claim

Step-by-step explanation:

A) From the question, we are told that an amusement park claims that the mean daily attendence at the park is at most 19,000 people.

Now, since it's at most 19000 people, it means that they are either 19000 or less. So the claim is;

μ ≤ 19,000 which is option B

B) Now, the claim is usually the null hypothesis. Thus, the null hypothesis is;

H0: μ ≤ 19,000

While the alternative hypothesis which states the opposite of the claim is;

Ha: μ > 19,000

So, option C is the correct answer

C) The claim is μ ≤ 19,000

Now, this also happens to be the null hypothesis.

Thus, the null hypothesis H0: μ ≤ 19,000 is the claim.

So option D is correct.

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

\(P(X<13.28)=P(\frac{X-\mu}{\sigma}<\frac{13.28-\mu}{\sigma})=P(Z<\frac{13.28-13}{0.2})=P(z<1.4)\)

And we can find this probability using the normal standard distribution table and we got:

\(P(z<1.4) =0.919\)

And the percentage faster than 13.28 seconds would be 91.9%

Step-by-step explanation:

Let X the random variable that represent the runtimes of a population, and for this case we know the distribution for X is given by:

\(X \sim N(13,0.2)\)  

Where \(\mu=13\) and \(\sigma=0.2\)

We want to find this probability:

\(P(X<13.28)\)

And we can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we have:

\(P(X<13.28)=P(\frac{X-\mu}{\sigma}<\frac{13.28-\mu}{\sigma})=P(Z<\frac{13.28-13}{0.2})=P(z<1.4)\)

And we can find this probability using the normal standard distribution table and we got:

\(P(z<1.4) =0.919\)

And the percentage faster than 13.28 seconds would be 91.9%

Answer:

Step-by-step explanation:

The formula for the area of a triangle gives a relationship between area, height, and base length. The problem statement gives the area, and it gives another relation between height and base length. Using these two relations, you can solve for the dimensions of the triangle.

__

The side to which the altitude is measured is called the "base" in the area formula. The altitude is called the "height." The relation between them given by the area formula is ...

  A = 1/2bh

  51 = 1/2bh . . . . . . using the given value for area

The other relation given by the problem statement is that the base is 1 less than 3 times the height:

  b = 3h -1 . . . . . . . base is 1 less than 3 times altitude

__

Using this second equation to substitute for 'b' in the first equation, we have ...

  51 = 1/2(3h -1)h

  102 = 3h² -h . . . . multiply by 2, eliminate parentheses

  3h² -h -102 = 0 . . . . . put in standard form

  3h² -18h +17h -102 = 0 . . . . . prepare to factor

  3h(h -6) +17(h -6) = 0 . . . . . factor pairs of terms

  (3h +17)(h -6) = 0 . . . . . . . . finish factoring

Solutions are the values of h that make these factors zero:

  3h +17 = 0   ⇒   h = -17/3

  h -6 = 0   ⇒   h = 6

We know that dimensions in a geometry problem must be positive, so the solution here is h = 6. Then b = 3h -1 = 3(6) -1 = 17. The dimensions are all in inches.

The length of the side is 17 inches; the altitude to that side is 6 inches.

Answer:

-14, 14

Step-by-step explanation:

\( {x}^{2} = 196 \\ x = \pm \sqrt{196} \\ x = \pm \: 14 \\ x = 14 \: \: or \: \: x = - 14 \\ x = \{ - 14, \: \: 14 \}\)

Answer:

\(x = 14\)

x= -14

Step-by-step explanation:

\( {x}^{2} = 196 \\ x = \sqrt{196} \\ x = 14\)

x= -14

To check whether the answer is correct,

\( {x}^{2} = 196 \\ \)

\(x = 14\)

\( {14}^{2} = 196 \\ 14 \times 14 = 196 \\ 196 = 196\)

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Answer:

Step-by-step explanation:

Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours

The class groups would be

1 to 5

5 to 10

10 to 15

15 to 20

The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are

(1 + 5)/2 = 3

(5 + 10)/2 = 7.5

(10 + 15)/2 = 12.5

(15 + 20)/2 = 17.5

The frequency table would be

Class group Frequency

1 - 5 4

5 - 10 8

10 - 15 6

15 - 20 2

The total frequency is 4 + 8 + 6 + 2 = 20

Answer:

perimeter is the length of all sides added together, since this a square and one side is 20 length, all sides must be 20 length. 20 + 20 + 20 + 20 = 80

The area is the length times width. 20 * 20 is 400.

Step-by-step explanation:

Answer:

Lateral area of the pyramid = 120 square units

Step-by-step explanation:

In the figure attached,

A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.

Lateral area of a pyramid = Area of the lateral sides

Area of one lateral side = \(\frac{1}{2}(\text{Base})(\text{Lateral height})\)

                                       = \(\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})\)  [Since l = \(\sqrt{r^{2}+h^{2}}\)]

                                       = \(\frac{1}{2}(6)(\sqrt{6^2+8^2})\)

                                       = \(3\sqrt{100}\)

                                       = 30 units²

Now lateral area of the pyramid = 4 × 30 = 120 square units

Answer: 240 units^2

Step-by-step explanation:

LA= 1/2 Pl

P= perimeter of base

l= lateral height

l= 8^2 + (12/2)^2 = 10^2

P= 12 x 4 = 48

48 x 10 = 480

480/2 = 240

240 units^2

Answer:

\(44\)

Step-by-step explanation:

The dimensions of the garden is 12 by 8. If we have a walkway that surrounds the garden, the dimensions of the walkway is 2. Since it surrounds the rectangle all sides add 2 to each of the dimensions so now the dimensions of the garden and walkway is 14×10.

The area of the garden is 96 square ft.

The area of the garden and walkway is 140 so let subtract the area of the garden from the total area of both the garden and walkway.

\(140 - 96 = 44\)

The area is 44.

Answer:

120 square feet

Step-by-step explanation:

(8+2*2)

(18+2*2) - 8*18 = 120 square feet.

The height of the window is 9-x feet, the perimeter of the window is 36-2x.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. Here, we refer to these letters as variables.

Given that,

A window is 9 feet long.

Its length exceeds its height by x feet.

The length of the window = 9 feet

Then, the height of the window,

x feet shorter than the length= 9-x feet

As a result, the window is 9-x feet tall.

The perimeter of the window is 2 (l+b)

2 (9+9-x),

2 (18-x),

36 - 2x.

Therefore, the perimeter of the window is 36-2x.

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Answer:

-65/125=-13/-25 (decimal -0.52)

Step-by-step explanation:

i hope this is right ,-,

Answer:

Step-by-step explanation:

Answer:

7.504, 8 1/2, 171/20, 8.89.

Step-by-step explanation:

Simplify the fractions to decimals.

171/20 = 8.55

8 1/2 = 8.50

Answer Key:

1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.

| I just want to help you with #2 anyway