Use the perfect square trinomial identity to write this expression in factored form:
x2 + 10x + 25.

Answer:

B. (0, –1); maximum

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

( 0 , − 1 )

Focus:  

( 0 , − 5 /4 )

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

−

3

4

x

y

−

2

−

5

−

1

−

2

0

−

1

1

−

2

2

−

5

Use the formula  

x

=

−

b

2

a

to find the maximum and minimum.

( 0 , − 1 )

Answer : Yes the answer to your question is 2411.

Explanation : how I got the answer

To convert decimal number 356.625, we convert its integer and fraction part individually and then add them to get the equivalent quinary number, as below:

To convert integer 356 to quinary, follow these steps:

Divide 356 by 5 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent quinary number.

356 / 5 = 71 with remainder 1

71 / 5 = 14 with remainder 1

14 / 5 = 2 with remainder 4

2 / 5 = 0 with remainder 2

Here is the answer to 356 decimal to quinary number:

2411

Answer: 2000.25 ft

Step-by-step explanation:

Given

Height of lighthouse [tex]h=175\ ft[/tex]

Angle of elevation [tex]\theta=5^{\circ}[/tex]

Suppose, you are x feet away from lighthouse

From the figure, we can write

[tex]\Rightarrow \tan 5^{\circ}=\dfrac{175}{x}\\\\\Rightarrow x=\dfrac{175}{\tan 5^{\circ}}\\\\\Rightarrow x=2000.26\ ft[/tex]

Thus, the ship is 2000.25 ft away from the light-house

Answer:

15 is the missing side (hypotenuse)h

Step-by-step explanation:

A^2+b^2=c^2

9^2+12^2=c^2

81+144=c^2

225=c^2

15=c

Answer:

The volume of this rectangular prism is D. 60[tex]cm^{3}[/tex].    

Step-by-step explanation:

In order to find the volume of a rectangular prism, we need to multiply the length by the width, and then multiply their product by the height of the prism. We can write what I said above as a formula...

V = l × w × h    

(In the formula above "V" is the volume, "l" is the length, "w" is the width, and "h" is the height).

Now we just substitute the values into the formula and we get...

V = l × w × h    

V = 4cm × 3cm × 5cm

V = 60[tex]cm^{3}[/tex]

Therefore, the volume of this rectangular prism is D. 60[tex]cm^{3}[/tex].    

Step-by-step explanation:

everything can be found in the picture

Answer:

Area of the shades region = 244.6 ft²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

                                    = 29.8 × 13

                                    = 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                        = [tex]\frac{1}{2}(10.2)(28)[/tex]

                        = 142.8 ft²

Area of the shades region = 387.4 - 142.8

                                             = 244.6 ft²

Answer:

36

Step-by-step explanation:

She gets 6 question right for every 8 question that means a ratio of 6/8 which is equal to 3/4

so we can say the ratio multiplied by the number of questions equals the correct answers

while x is the number of questions:

solve for x

3/4 * x = 27

x = 27 / (2/3) = 36

Answer:

-10

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

A man is now 3 times as old as his son.

m = 3s

In 10 years time, the sum of their ages will be 76

(m + 10) + (s + 10) = 76

Subsitute for m = 3s

(3s + 10) + (s + 10) = 76

4s + 20 = 76

4s = 56

s = 14

m = 3s = 14 * 3

m = 42

------------------------

How old was the man when his son was born?

m - s = 42 - 14

m - s = 28

Answer:

-18

Step-by-step explanation:

fog(x) = -9(x-9) -9

=> f o g (10) = -9(10-9)-9 = -9-9 = -18

Answer:

Amount of simple interest in three year = 750

Step-by-step explanation:

Given:

Amount invested = 5,000

Number of year = 3 year

Rate of interest = 5% Annually

Find:

Amount of simple interest in three year

Computation:

Simple interest = (P){R)(T)

Amount of simple interest in three year = (5,000)(3)(5%)

Amount of simple interest in three year = (5,000)(3)(0.05)

Amount of simple interest in three year = (5,000)(0.15)

Amount of simple interest in three year = 750

Answer:

Step-by-step explanation:

Recall that the argument of the square root function y = √x must always be 0 or greater.

If you meant y=√x+8 -7, the domain is therefore [0, infinity).

But if you meant y=√(x+8) -7, the domain is [-8, infinity).

Those parentheses are important!

[tex]6 + (1 + ( - (3 + 5) - 8) + 2 \\ 6 + (1 + 2 - 8) + 2 + 10 \\ 6 + ( - 5) + 2 + 10 \\ 6 - 5 + 2 + 10 \\ \\ = 13[/tex]

Step By Step Explanation:

Answer:

C. 1

Step-by-step explanation:

2cos²(x) - cos(2x) = 1

Answer:

C

Step-by-step explanation:

Using the identity

cos2x = 2cos²x - 1 , then

2cos²x = cos2x + 1

Given

2cos²x - cos2x

= cos2x + 1 - cos2x

= 1 → C

Answer:

B.    m = [tex]\frac{3}{2}[/tex], y-int = 3

Step-by-step explanation:

To find the slope of the line, we need to plot two points

(2, 6) (-2, 0)

m = slope

Then use the Slope-Formula to Solve for the slope

m = [tex]\frac{y2-y1}{x2-x1}[/tex]        

m = [tex]\frac{0-6}{-2-2}[/tex]

m = [tex]\frac{-6}{-4}[/tex]

m = [tex]\frac{6}{4}[/tex]

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

The Slope is [tex]\frac{3}{2}[/tex]

The y-intercept is 3 because the line is going 3 units upwards on y axis!

Equation: y = 3/2x + 3

Slope: 3/2

y-intercept: 3

Answer:

m = 3/2      int- 3

Step-by-step explanation:

The line goes up 3 and goes right 2. The line crosses the y-intercept at 3.

Answer:

x = 15

Step-by-step explanation:

20^2 + x^2 = 25^2

400 + x^2 = 625

subtract each side 400

it results to 225

square root 225, to equals this -->

X = 15

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

your answer would be b

Answer:

x=9

Step-by-step explanation:

so the angles of a triangle add up to 180 and since it shows two angles of 60 which makes 120, you have 60 more degrees which means A has to be 60 degrees. so if all of the angles are the same then the side lengths are the same so since it already shows one side =9 then x=9

Answer:

x=9

Step-by-step explanation:

missing angle + 60 + 60=180 degree (sum of interior angles of a triangle

missing angle + 120 =180

missing angle =180 -120

missing angle =60 degree

since all angles are 60 degree it is an equilateral triangle and all sides of a equailateral triangle are equal .So, x is also 9

Answer:

160

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

VOLUME...

1) π*r^2*h

π*(2.5)^2 *h

(π)*(2.5)^2* 6

= 117.8

2) π*r^2*h + 1/2 *[(4/3) · π · r3]

(π)*(3)^2* 3 + 1/2 *[(4/3) · π · 3^3]

        84.8+ 56.5 = 141.41

3) (1/3) π*r^2*h

(1/3) π*3^2*h

3^2 + h^2 = 36

h = sqrt(27) = 5.1

(1/3) π*3^2*5.1

= 48.06

Answer: 1.28 cups of water per cup of milk

Step-by-step explanation:

0.8 divided by 5/8 equals 1.28

verified by my teacher :)

Answer: Almost 232 students going on the field trip.

Step-by-step explanation:

Let x be the number of students going on the field trip.

As per given,

[tex]2x+35 \leq500[/tex], where [tex]x\geq2[/tex].

To solve the inequality , subtract 35 from both sides

[tex]2x\leq465\\\\x\leq232.5[/tex] [divide both sides by 2]

i.e Almost 232 students going on the field trip.

Answer:

y=cx-b/a

Step-by-step explanation:

ay+b=cx

ay=cx-b

y=cx-b/a

Answer:

No it cant

Step-by-step explanation:

You have to use the Pythagoras theorem which is a^2 + b^2 = c^2. So 9^2 + 11^2= 202. Then 17 is the hypotenuse so 17^2= 289. They are not equal so they are not.

Answer:

a = x² + 11x + 30

Step-by-step explanation:

a = (x + 5)(x + 6)

multiply each term in the first set of parenthesis by each term in the second

a = x(x + 6) + 5(x + 6)

a = (x² + 6x) + (5x + 30)

combine like terms

a = x² + 11x + 30