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Which of the following shows the correct first step to solve x^2 - 16x = -21 by completing the square?

A)x^2 - 16x + 64 = -21

B) x^2 - 16x + 64 = -21 + 64

C) x^2 - 16x + 16 = -21 + 16

D) x^2 - 16x + 8 = -21 + 8

21b-32+7b-20b=

21b + 7b - 20b - 32

       8b            - 32

Hello!

21b-32+7b-20b=

21b +7b -20b -32

= 28b -20b - 32

= 8b -32

Answer:

J

Step-by-step explanation:

Start by labelling the sides of the triangle. The length of the ramp is the hypotenuse side, while the height of the ramp is the opposite side.

[tex]\textcolor{steelblue}{ \sinθ = \frac{opp}{hyp} }[/tex]

Let the length of the ramp be x.

[tex] \sin5° = \frac{3}{x} [/tex]

Multiply x on both sides:

x(sin5°)= 3

[tex]x = \frac{3}{ \sin5°} [/tex]

x= 34.4 (3 s.f.)

Thus, the length of the ramp is 34 ft. (nearest foot)

Answer:  3 out of 19  

Step-by-step explanation:

Answer:

P(caramel) = 3/10

P(raspberry) = 1/3

Step-by-step explanation:

Given:

⇒ Total chocolates = 3 + 3 + 4 = 10

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(picking \ caramel \ chocolate) = \dfrac{3}{10}[/tex]

If the picked caramel chocolate is NOT replaced then:

[tex]\sf \implies P(picking \ raspberry \ chocolate) = \dfrac39=\dfrac13[/tex]

Answer: -5x - 2

Step-by-step explanation:

Combine like terms: (3x - 8x) + (3 - 5) → -5x - 2 :)

Step-by-step explanation:

All Natural Number (1,2,3,4,5...) are integers

All Whole numbers (0,1,2,3,4...) are not natural numbers (1,2,3,4...)

All integers are rational numbers

All real numbers are not irrational numbers as real nimber contain both rational and irrational numbers hence it is false.

Hence statement 1 and statement 3 are true

Answer:

The answeris D

Step-by-step explanation:

All whole numbers are natural numbers; natural numbers are numbers we use for counting 1, 2, 3....and so on, so that makes them whole because thay have no fraction, or decimils.

Answer:

x= 5

Step-by-step explanation:

Since RQ= PQ,

3x= 15

Divide both sides by 3:

x= 15 ÷3

[tex]\textcolor{red}{x = 5}[/tex]

[tex]\textcolor{steelblue}{\text{Prove for RQ}= \text{PQ}}[/tex]

Let SP= x

RS= SP= x (given)

Let SQ= y

Applying Pythagoras' Theorem,

In triangle QRS

(RQ)²= (RS)² +(SQ)²

(RQ)²= x² +y²

[tex]RQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

In triangle QPS

(PQ)²= (SP)² +(SQ)²

(PQ)²= x² +y²

[tex]PQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

Thus, RQ= PQ.

Answer:

Step-by-step explanation:

3x = 15

3x/3 = 15/3

x = 5

3(5) = 15

Answer:

x=9

Step-by-step explanation:

divide 4 by 4 to get 1

x-1=8

9-1=8

Hey there!

x - 4/4 = 8

x - 1 = 8

ADD 1 to BOTH SIDES

x - 1 + 1 = 8 + 1

CANCEL out: -1 + 1 because it give you 0

KEEP: 8 + 1 because it give you the x-value

NEW EQUATION: x = 8 + 1

SIMPLIFY IT!
x = 9

Therefore, your answer is: x = 9

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

C, they are congruent.

Step-by-step explanation:

Rotation only changes the position of the image, not the size. :)

Answer:

C. They were rotated around the origin since that is the only point in the plane you can use as the center of rotation.

explanation:

when you think about it and look at the other problems, they are all going around the center of the grid when rotated, specifically the key word is when rotated, when they are translated they go anywhere they want.

Answer:-7/8>-0.60

C is not true

Answer:

rectangle

Step-by-step explanation:

the question is asking what the shape of the cross section would be if it was perpendicular to the base. imagine a cylinder that you could slide a piece of paper into. what would be inside the cylinder? perpendicular to the base, it would be a rectangle. if it was parallel to the base, you'd then have a circle.

======================================================

Explanation:

At 99% confidence, the z critical value is roughly z = 2.576 which is found using a Z table.

We're given that [tex]\hat{p} = 0.5[/tex] as the sample proportion and E = 0.05 is the desired error.

The min sample size n is:

[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{2.576}{0.05}\right)^2\\\\n \approx 663.5776\\\\n \approx 664\\\\[/tex]

Always round up to the nearest integer.

Unfortunately n = 664 isn't one of the answer choices. The next closest value is 700. It appears that your teacher wants to know a valid sample size that is the smallest of the answer choices, not necessarily the smallest ever possible.

Answer: 17.320508075689

Step-by-step explanation:

Answer:

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A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

Easy

Solution

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Verified by Toppr

Radius of the wheel =r=

2

60

=30 cm

Circumference of the wheel =2πr=2×

7

22

×30=

7

1320

cm

Distance covered in 1 revolution =

7

1320

cm

Distance covered in 140 revolutions =

7

1320

×140=26400 cm=264 m=

1000

264

km

Distance covered in one minute = Distance covered in 140 revolutions =

1000

264

km

Distance covered in 1 hour =

1000

264

×60=15.84 km

Hence, the speed with which the boy is cycling is 15.84km/hr.

Answer:

Step-by-step explanation:

the area of this rectangle is

(10 + 2x)(8 + 2x) = 168

80 + 20x + 16x + 4x² = 168

4x² + 36x = 88

Step-by-step explanation:

A quadratic equation is an equation whose leading coefficient is of the second degree. The correct option is A.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

Let the width of the frame be represented by x. Therefore, the length and the breadth of the photographer be represented by (10+2x) inches and (8+2x) inches. Therefore, the total area of the photograph can be written as,

Area = Length × Breadth

168 inches² = (10+2x) inches × (8+2x)inches

168 = (10+2x)(8+2x)

168 = 80 + 20x + 16x + 4x²

0 = 80 + 20x + 16x + 4x² - 168

0 = 4x² + 36x - 88

4x² + 36x - 88 = 0

4x² + 36x = 88

Hence, the following quadratic equations that would be used when solving the width of the frame is 4x² + 36x = 88.

Learn more about Quadratic Equations:

https://brainly.com/question/2263981

#SPJ5

Given -

To find -

Solution -

We know to find the perimeter of the quarter of a circle we use the formula,

1/4 × circumference of the circle

= 1/4 × 2πr

= 1/4 × 2×3.14×3.57

= 2.8 yards

The word or phrase that describes the chances of Elizabeth winning the mountain bike if she buys all the tickets is likely.

If Elizabeth buys all the tickets, then she will most definitely win the raffle because she will have the winning ticket.

In probability, when an event is certain to happen, it is said that the event is "likely." It is therefore likely that Elizabeth will win the raffle.

Find out more on likely events at https://brainly.com/question/7130419.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$34000\\ P=\textit{original amount deposited}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ t=years\dotfill &9 \end{cases} \\\\\\ 34000=Pe^{0.049\cdot 9}\implies 34000=Pe^{0.441}\implies \cfrac{34000}{e^{0.441}}=P\implies 21875.35\approx P[/tex]

Answer:

  B

Step-by-step explanation:

The first step of any problem solution is look at the given information. Here, we are given the equation of a line in (almost) standard form, and we want to match the equation with a graph. We notice that the coefficients of the variables are factors of the constant, so the intercepts are integer values easily found.

We can compare the line's intercepts to those shown on the graphs to choose the correct graph.

x-intercept

The x-intercept is found by setting y=0 and solving for x:

  -3x +5(0) = -15

  x = -15/-3 = 5

Only one graph shows a line with an x-intercept of (5, 0): graph B.

y-intercept

We can confirm graph B by finding the y-intercept. For this, we set x=0 and solve for y.

  -3(0) +5y = -15

  y = -15/5 = -3

Graph B also has a y-intercept of (0, -3), confirming it is the correct choice.

_____

Additional comment

Part of "look at the given information" is "look at the answer choices." What you look for is what makes one choice different from the others. Here, the lines have x- and y-intercepts of ±3 and ±5. The y-intercepts are the same for graphs A and B, and for graphs C and D.

However, the x-intercepts are different for all of them. This tells you that finding the x-intercept is the fastest way to find the correct graph.

Answer:

-4

Step-by-step explanation:

if you divide a negative number by a positive number, you will get a negative number

Answer:

-4

Step-by-step explanation:

-(4×3)/3

by crossing both 3 out

-(4) remains

Step-by-step explanation:

2 × 10⁸ - 7 × 10⁷

= 200,000,000 - 70,000,000

=130,000,000

= 1.3 × 10⁸

Answer:

130 million

Step-by-step explanation:

200 million in N

70 million in F

200-70 = 130 million

Hope this helps have a great day

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Answer:

Step-by-step explanation:

16 ticks, the pointer is on 12. there fore it is the second answer.

2 3/4 lb

Answer:

2 eggs

Step-by-step explanation:

Use a proportion.

48 cupcakes is to 8 eggs as 12 cupcakes is to x eggs.

48/8 = 12/x

Reduce the left fraction.

6 = 12/x

Multiply both sides by x.

6x = 12

Divide both sides by 6.

x = 2

Answer: 2 eggs

Answer:

im terreb.le at math

Step-by-step explanation:

Answer:

285 dancers

Step-by-step explanation:

[tex]\frac{acrobats}{dancers}[/tex] = [tex]\frac{13}{15}[/tex] = [tex]\frac{247}{x}[/tex]

After cross-multiplication:

13x = ( 15 )( 247 )

13x = 3705

x = 285 dancers

Answer: -2, 0

Step-by-step explanation:

The graph this represents this system is the second graph since the vertex of the absolute value function is at x=-2.

So, to find the solutions, we can find the intersection points. These are at x=-2 and x=0.

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

12

Step-by-step explanation:

[tex] \sqrt{ - 72k} \\ \\ = \sqrt{ - 72( - 2)} \\ \\ = \sqrt{144} \\ \\ = 12[/tex]

Answer:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

=12