Which of the following represents the factorization of the binomial below?
49x2 - 81y2
A. (x-9y)7x-9y)
B. (7x+9yX(7x+9y)
C. (7x+y)(x-97)
D. (7x+9y)(7x-9y)

Answer:

[tex]y=\dfrac{1}{8}x^2+1[/tex]

Step-by-step explanation:

Since the vertex is right between the vertex and the directrix, the y value of the vertex must be (3+(-1))/2=1. The x coordinate will just be the same as that of the focus, or in this case 0. This means that the vertex will be at (0,1). Since the graph opens toward the focus, it will be opening up, and since its vertex is at (0,1), it will have an equation of:

[tex]y=\dfrac{1}{8}x^2+1[/tex]

Hope this helps!

Answer:

y = one eighth x^2 + 1

Step-by-step explanation:

i took the test and got it right

Answer:

Moving 4 to the right on the x axis

Step-by-step explanation:

Answer:

Let the first equation be x + y = 10

x = 10 -y

2nd equation will be 1x + 1.2y = 11

Substituting in 2nd equation

(10 - y) + 1.2y = 11

10 - y + 1.2y = 11

.2y = 1

y = 5

If y = 5, x = 5: coz x + y = 10

She have buy 5 stamps of each $1 stamps and  5 stamps of each $1.20 stamps.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

Let the first equation be;  

x + y = 10

x = 10 -y

2nd equation will be,

1x + 1.2y = 11

Substituting in 2nd equation;

(10 - y) + 1.2y = 11

10 - y + 1.2y = 11

0.2y = 1

y = 5

If y = 5, x = 5:

x + y = 10

Hence, She have buy 5 stamps of each $1 stamps and  5 stamps of

each $1.20 stamps.

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Answer:

54.56

Step-by-step explanation:

Given:

Mean, u = 48

Standard deviation, [tex] \sigma[/tex] = 4

Test score = 5%

Required:

Find the raw score, X.

Having a test score of 5% means the Zscore has to correspond to 95%, ie, 1 - 0.05 = 0.95.

Thus, [tex] Z_0_._9_5 = 1.64[/tex]

To get X, use the formula:

[tex] mu + z * \sigma [/tex]

= 48 + (4 * 1.64)

= 48 + 6.56

= 54.56

The anxiety test score that would put someone in the top 5% is 54.56

Answer:

2.75

Step-by-step explanation:

3/4 is .75 in decimal

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve [tex](x+a)^2[/tex] and replace the result in the initial equation as:

[tex]x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b[/tex]

Then, this equality apply only if the coefficient of [tex]x[/tex] is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

[tex]3x=2ax\\4=a^2+b[/tex]

So, using the first equation and solving for a, we get:

[tex]3x=2ax\\3=2a\\a=\frac{3}{2}=1.5[/tex]

Finally, replacing the value of a in the second equation and solving for b, we get:

[tex]4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75[/tex]

Answer:

Number of cookies sold in March= 46

Number of cookies sold in April= 92

Step-by-step explanation:

Number of cookies made in Feb= 2×14= 28

Number of cookies sold in Feb= 28-5= 23

Number of cookies sold in March= 2× number of cookies sold in Feb

Number of cookies sold in March= 2× 23= 46

Number of cookies sold in April= 46×2= 92

Answer:

Step-by-step explanation:

The 2 smaller triangles are proportionate to one another because they are 2 parts of the same larger triangle. Setting up the proportion, one triangle at a time:

[tex]\frac{x}{8.3} =\frac{11.6}{6.7}[/tex] and cross multiply to get

6.7x = 96.28 so

x = 14.37 or 14.4, choice A.

Answer:

27 smoothies

Step-by-step explanation:

if you have 27 cups and one requires one cup, it would be 27 smoothies Katherine can make :)

Answer:

Step-by-step explanation:

1. The end time on the graph is 150 minutes. That is ...

  (150 min)(1 h)/(60 min) = (150/60) h = 2.5 h

It took Bella 2.5 hours to reach the grocery store.

__

2. Bella is stopped at the places in the curve where the vertical coordinates are not changing. That is, where the graph is horizontal. The total time that the graph is horizontal is 10 min + 20 min = 30 min.

Bella was on the phone for 30 minutes.

__

3. Bella walked 5 km in the first 50 minutes, 2 km (toward home) in the next 20 minutes, and 3 km in the last 60 minutes before she got to the grocery store. Her total distance was ...

  5 km + 2k + 3 km = 10 km

Bella traveled a total of 10 km.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 5000

For the alternative hypothesis,

H1: µ > 5000

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 5000

x = 5430

σ = 600

n = 40

z = (5430 - 5000)/(600/√40) = 4.53

Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001

Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.

Since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.

Given that it was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps, to determine if at = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day the following calculation must be made:

Therefore, since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.

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Answer:

Side a is 35/5=7 inches long

Side b is 30/5=6 inches long

Side c is 15/5=3 inches long

The square root of 81/625 = 0.36

The square root of x^2 = x

The square root of y^2 = y

25 x 0.36 = 9

X *x = x^2

Y*y = y^2

Final answer = 9x^2y^2

Answer:

The answer is option d. 9x²y²

Step-by-step explanation:

25xy√81/625x²y²

= 25xy × 9/25xy

= 9x²y²

Hope this helps.

Answer:

The answer is 2.

Step-by-step explanation:

3 - 2 = 1

7 - 5 = 2

2 x 1 = 2

Answer:

80° is the correct answer

Step-by-step explanation:

The angle B is 100° because of the property of  the vertically opposite angle.

As we know the property consecutive interior angle that the sum of two angle is 180°

So

Angle B + Angle X  =180°

100 °+ Angle X =180°

Angle X=180°-100°

Angle X = 80°

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D is the only answer with the correct distance formula format and the correct numbers inside the parentheses

Answer:

Step-by-step explanation:

Value of firm = Number of shares×Market price per share

= 450,000 × $15

= $6,750,000

Value of debt = $825,000

Weight of debt = $825,000 / $6,750,000 = 12.22%

Number of shares continue to own = 20,000 × (1 - 12.22%) = 17,555.56 or 17,556 shares

Number of shares continue to own = 17,555.56 or 17,556 shares

Answer:

Step-by-step explanation:

Pattern 6 will have 35

Answer: 8 times

Step-by-step explanation:

Youre essentially doing 3 divided by 3/8.

3 is equivalent to 3/1. And when you divide fractions, you have to multiply by the reciprocal. the reciprocal of 3/8 is 8/3.

[tex]\frac{3}{1} *\frac{8}{3} = \frac{24}{3} = 8[/tex]

There are eight (8) 3/8’s are in 3

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Answer:

P(Take the bus | Sophomore) = 0.83

Step-by-step explanation:

For a conditional probability (As given in the example),

P(A|B) is read as,

"The probability of event A occurring given that event B has occurred"

Here event A = Sophomore take a bus

Event B (occurred) = (Drive to school + Take the bus + Walk)

Therefore, P(Take a bus | Sophomore) = [tex]\frac{25}{(2+25+3)}[/tex]

                                                                = [tex]\frac{25}{30}[/tex]

                                                                = 0.833

                                                                ≈ 0.83

P(Take the bus | Sophomore) = 0.83 will be the answer.

Answer:

A and C

Step-by-step explanation:

A. \

(4.0 x 5.0)(10^3 x 10^5)

20 x 10^8

2.0 x 10^9

B. doesn't work, do not understand last number

C.

(2.1 + 2.7) (10^5 + 10^5) since powers are the same, do not need to change anything

4.8 x 10^5

D.

(3.1 - 2.7) (10^5 - 10^2) since powers are not the same, you need to make them equal

Do not need to subtract powers, hence D is untrue

Answer: B

Step-by-step explanation:

For this problem, we can use Integration by Parts to find f(u).

∫(ln u) du                 x=ln u             dx=1/u du

                               dv=du               v=u

u(ln u)-∫u(1/u)du

u(ln u)-∫1 du

u(ln u)-u+C

Looking at the placement of f(u), we know that f(u) is u (underlined above).

Answer:

C.

Step-by-step explanation:

Look at the image

Answer:

Step-by-step explanation:

You need the value of one of angles. If height angle is 90°, then you have 2 90° angles. So you have 2 triangles SAS.

I hope I've helped you.

Answer:

70 degrees

Step-by-step explanation:

Answer:

70 that my answer and so they can reach

Answer:

153.9 ft²

Step-by-step explanation:

The area for a circle formula is πr².

Using the radius, we get:

π×7² =

49π ≈

153.938 ≈ (Using the π key)

153.9 ft²

Answer:153.86

Step-by-step explanation:area of a circle is πr square

That is 3.14×49

=153.86

Answer:

The equation of the line is y = 2.

Step-by-step explanation:

When a line is horizontal, it's gradient will be 0. So you have to substitute the coordinates into the equation, y = mx + b, to find the b :

[tex]y = mx + b[/tex]

[tex]let \: m = 0 \\ let \: x = 5 \\ let \: y = 2[/tex]

[tex]2 = 0(5) + b[/tex]

[tex]b = 2[/tex]

[tex]y = 2[/tex]

Answer:

it would be Y=2 as it's a horizontal line at y=2

[tex]answer \\ option \: a \\ 3 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]