1.
Which of the following is acute angle?
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Answer:

[tex]x = 8\±\sqrt{10[/tex]

[tex]a =8[/tex]    [tex]b = 10[/tex]

Step-by-step explanation:

Given

[tex]x^2 - 16x + 54 = 0[/tex]

Required

Complete the square

[tex]x^2 - 16x + 54 = 0[/tex]

Subtract 54 from both sides

[tex]x^2 - 16x + 54 -54= 0-54[/tex]

[tex]x^2 - 16x = -54[/tex]

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Take half of - 16

[tex](-16/2) = -8[/tex]

Square the result

[tex](-8)^2 = 64[/tex]

Add the squared result to both sides of the equation

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

So, we have:

[tex]x^2 - 16x +64= -54+64[/tex]

[tex]x^2 - 16x +64= 10[/tex]

Expand

[tex]x^2 - 8x - 8x + 64 = 10[/tex]

Factorize

[tex]x(x - 8) - 8(x - 8) = 10[/tex]

Factor out x - 8

[tex](x - 8)(x - 8) = 10[/tex]

[tex](x - 8)^2 = 10[/tex]

Take square roots

[tex]x - 8 = \±\sqrt{10[/tex]

Solve for x

[tex]x = 8\±\sqrt{10[/tex]

We have:

[tex]x = a - \sqrt{b}[/tex]

[tex]x = a + \sqrt{b}[/tex]

By comparing the above with: [tex]x = 8\±\sqrt{10[/tex]

Answer:

Step-by-step explanation:

Answer:

A or g(x) = f(x − 3) + 3

Step-by-step explanation:

Answer:

Suppose the one number be x

And the other number be 6x

The sum of two numbers is 5

x+6x=5

7x=5

X=5/7

Therefore

One number be 5/7

And other number be 6 * 5/7=30/7

If you are helped with my answer pls tag me brianliest I really want it

THANK YOU...............

Answer:

10.5, 31.5,  and 6.

Step-by-step explanation:

So to find the answers here, we must find the  value of t, when h equals 1.

To do this, lets take a h-t value we already know, and solve.

We can use: when h=2 t equasl 21:

2h=21t

So if we divide both sides by two we get:

2h/2=21t/2

=

h=10.5t

So know we know for every one h, t is 10.5

This can be verifyed with 4h = 42t. Which after solving, equals 1h=10.5t

So now that we have a value for t, lets get our solutions.

First off, we have 1h=__t?

Well, we have already made this one clear. It would be 10.5t, since for every 1h we have 10.5t

Next up, we have 3h=___t

All we have to do it multiply 10.5 by 3 to solve this:

10.5*3

=

31.5

So this is our second fill in answer.

Finally we have ___h=63t

We must divide both sides by 10.5, which is equal to 1t, to find this answer:

63/10.5

=

6

So our last fill in answer is 6.

Hope this helps!

Answer:

The domain that makes sense for this function is all values greater than or equal to 0.

Step-by-step explanation:

A ball is thrown into the air from a height of 4 feet at time t = 0. It is modeled by the function:

[tex]h(t)=-16t^2+64t+4[/tex]

The domain of the function is time t. The range of the function is the ball's height in the air h.

Since time is our domain, we must restrict our domain to values equal to or greater than 0 since time cannot be negative.

Therefore, the domain that makes sense for this function is all values greater than or equal to 0.

In interval notation, this is:

[tex][0, \infty)[/tex]

And as an inequality:

[tex]t\geq 0[/tex]

Answer:

easy what's 5% of 3000 that's just for one year then multiple it by 4

Answer:

30 Step-by-step explanation:

Answer:

Its 60

Step-by-step explanation:

I took the test

Answer:

249.60

Step-by-step explanation:

300 x .8 (100%-20%)=240

240 x .04 (4% sales tax)=9.60

price = 240+9.60=249.60

Answer:

22 days = 3 weeks and 1 day

454 minutes = 7 hours and 34 minutes

4 years and 4 months = 148 months

12 pounds and 13 ounces = 205 ounces

Answer:

Question?

Step-by-step explanation:

?

Answer:

C) (-4,2)

Step-by-step explanation:

It would be in quadrant II, so (-4,2)

Answer:

using 3.14 for pi the volume is 502.4

Step-by-step explanation:

The standard deviation of the distribution is 1.08.

Option B is the correct answer.

The standard deviation measures how spread out the data is from the mean, and it is a measure of the average distance of the data points from the mean.

We have,

To find the standard deviation of the distribution, we first need to calculate the expected value (mean) of X.

The expected value of X is:

E(X) = (4)(0.4) + (3)(0.32) + (2)(0.17) + (1)(0.08) + (0)(0.03)

= 1.6 + 0.96 + 0.34 + 0.08 + 0

= 2.98

Next, we need to calculate the variance of X:

Var(X) = (4 - 2.98)²(0.4) + (3 - 2.98)²(0.32)

+ (2 - 2.98)²(0.17) + (1 - 2.98)²(0.08) + (0 - 2.98)²(0.03)

= 0.64(0.4) + 0.0004(0.32) + 0.7921(0.17) + 5.4084(0.08) + 8.6404(0.03)

= 0.256 + 0.000128 + 0.134257 + 0.432672 + 0.259212

= 1.082

The standard deviation of X is the square root of the variance:

So,

SD(X) = √(Var(X))

= √(1.082)

= 1.04 (approximately)

Thus,

The standard deviation of the distribution is 1.08.

Learn more about standard deviation here:

brainly.com/question/23907081

#SPJ7

Answer:

we need 6 scoops of sugar

Answer:

Point B is to the right of point A

Step-by-step explanation:

On a number line, the mid value is usually 0 with positive and negative numbers positioned to the either sides of the midpoint 0, the negative numbers are arranged to the left and the positive numbers are written to the right. With this in mind and the knowledge that positive numbers are always greater than negative numbera. Then we can conclude that point B is greater than point A because point B is positive and point A is negative because point B is to the right of Point A.

Answer:

x = 4

Step-by-step explanation:

i am smart

Answer:

X=4

Step-by-step explanation:

Simplifying

8x + 7 = 6x + 15

Reorder the terms:

7 + 8x = 6x + 15

Reorder the terms:

7 + 8x = 15 + 6x

Solving

7 + 8x = 15 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

7 + 8x + -6x = 15 + 6x + -6x

Combine like terms: 8x + -6x = 2x

7 + 2x = 15 + 6x + -6x

Combine like terms: 6x + -6x = 0

7 + 2x = 15 + 0

7 + 2x = 15

Add '-7' to each side of the equation.

7 + -7 + 2x = 15 + -7

Combine like terms: 7 + -7 = 0

0 + 2x = 15 + -7

2x = 15 + -7

Combine like terms: 15 + -7 = 8

2x = 8

Divide each side by '2'.

x = 4

Simplifying.                Hope this helps :D

x = 4.                              Plz brainly and like

Answer:

The answer should be $57000(1.025)²⁰ = $93,401

Step-by-step explanation:

Answer:

i think the answer is 12 and 18

9514 1404 393

Answer:

  C. 6 > 3

Step-by-step explanation:

It is true that 6 is greater than 3.

__

All negative numbers are less than any positive numbers.

We hope you are sufficiently familiar with numbers and counting to be able to tell which positive numbers are more or less than any other positive number.

Answer:

[tex]x = 55°[/tex]

Step-by-step explanation:

L1 and L2 are parallel, so that the 2 interior angles are equal to 180°.

[tex](2x + 10) + (x + 5) = 180° \\ 2x + x + 10 + 5 = 180° \\ 3x = 165° \\ x = 55°[/tex]

Answer:

A

Step-by-step explanation:

Answer:

3.

Step-by-step explanation:

15 - 12 = 3.

The ends of the box are the lower and upper quartiles.

The difference  upper - lower = the interquartile range.

Answer:

28

[tex]\frac{7}{2} \\\\\frac{x}{8}[/tex]

[tex]2 * x = 8\\x = 4[/tex]

[tex]7 * 4 = x\\x = 28[/tex]

PLZZ GIVE BRAINLIEST

Answer:

180°

Step-by-step explanation:

it's half of a circle

The angle AXG is a straight line. The measure of a straight line would be 180

The measure is 180

9514 1404 393

Answer:

  (3, 2)

Step-by-step explanation:

Reflection across y=x swaps the coordinates:

  (x, y) ⇒ (y, x)

Dilation by a factor of 1/2 multiplies each coordinate by 1/2.

  (x, y) ⇒ (x/2, y/2)

The combination of these transformations gives you ...

  (x, y) ⇒ (y/2, x/2)

  (4, 6) ⇒ (3, 2)