I'll give brainliest if you answer 11 and 12

The required, solution set to the given equation is {4}. Option A is correct.

A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).

Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:

log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)

So the given equation becomes:

log2(x² - 2x) = 3

2³ = x² - 2x

8 = x² - 2x

x² - 2x - 8 = 0

Factor this quadratic equation as:

(x - 4)(x + 2) = 0

x - 4 = 0, which gives x = 4

x + 2 = 0, which gives x = -2

However, the logarithm function is only defined for positive values of x, so the only possible solution is:

x = 4

Therefore, the solution set to the given equation is {4}.

Learn more about logarithmic function here:

https://brainly.com/question/30284289

#SPJ2

Answer:

[tex]y =112[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find y

The attached triangle is isosceles; so:

[tex]x - 5=34[/tex]

Also, we have:

[tex]y + x - 5 + 34=180[/tex] --- angles in a triangle

Substitute: [tex]x - 5=34[/tex]

[tex]y + 34 + 34=180[/tex]

Collect like terms

[tex]y =- 34 - 34+180[/tex]

[tex]y =112[/tex]

Answer:

1448

Step-by-step explanation:

24 × 63-64

Multiply 24 and 63 to get 1512.

1512-64

Subtract 64 from 1512 to get 1448.

answer

1448

Answer:

36 cm

Step-by-step explanation:

if p is perimeter then 10+13+13=36 is the correct answer

Answer:

0.46017

Step-by-step explanation:

Given :

Mean score = 75

Standard deviation, s = 10

Areum's score = 76

Probability of scoring higher than Areum is given by :

P(x > 76)

The standardized score : (x - mean) / standard deviation

P(x > 76) = P[Z > (76 - 75) / 10]

P[(Z > 0.1)] = 0.46017 (Z probability calculator)

= 0.46017

Answer:

-3/2

Step-by-step explanation:

Additive inverse of 2 = -2

Multiplicative inverse of 2 = ½

→ Sum = -2 + ½

→ Sum = (-4 + 1)/2

→ Sum = -3/2

Answer:

6000

Step-by-step explanation:

7500x4/5=6000

or

7500/5=1500

1500x4=6000

Answer:

No , it is not a right angle triangle

Step-by-step explanation:

according to the pythagoras theorem in right angled triangle sum of square of two sides is equal to the square of it's hypotenuse.

using pythagoras theorem

a^2 + b^2 = c^2

9^2 + 16^2 = 25^2

81 + 256 = 625

337 = 625

since sum of square of two smallest sides of a triangle is not equal to the square of it's hypotenuse it can be concluded that the given figure does not form right angle triangle.

Answer:

3a)1680

b)2620

4a)2130

b)13300

c)460

d)7540

Step-by-step explanation:

3a)1500+180

b)2800-170

4a)1800+330

b)7300+6000

c)670-210

d)8000-460

Answer:

a) 1600

b) 2600

c) 2200

d) 13200

e) 500

Step-by-step explanation:

a) 1463 + 179

1400 + 200

1600

b) 2806 - 176

2800 - 200

2600

c) 1831 + 329

1900 + 300

2200

d) 7345 + 5893

7300 + 5900

13200

e) 665 - 213

700 - 200

500

Answer:

1 . EF is a secant of OX

2. DF is a chord of OX.

3. AABC is made of tangents to OX

4. ∠DEF is an inscribed angle of OX.

Step-by-step explanation:

Secant is line which intersects a circle from two distant points. Locus is a set of points which is same distance from the center of a circle. Chord is a straight line whose end points lie on circular arc of a circle. Tangent is a line which touches the circle at one point only.

Answer:

640

Step-by-step explanation:

pleas check my answer

Answer:

112

Step-by-step explanation:

If you add all the triangle faces and the square.

Answer: 320ft^3

Step-by-step explanation:

Assuming the pyramid is just a normal rectangular pyramid and isn't made of stairs...

10x8x12/3 = 320 ft^3

The solution of the inequality will be;

⇒ x ≤ 9

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 15 + x ≤ 24

Now,

Since, The inequality is,

⇒ 15 + x ≤ 24

Solve the inequality as;

⇒ 15 + x ≤ 24

Subtract 15, we get;

⇒ 15 + x - 15 ≤ 24 - 15

⇒ x ≤ 9

Thus, The solution of the inequality will be;

⇒ x ≤ 9

Learn more about the inequality visit:

https://brainly.com/question/13777972

#SPJ1

Answer:

60 kg of 40% and 90 kg of 60%

Step-by-step explanation:

Let the amount of 40% chocolate be x.

Let the amount of 60% chocolate be y.

x + y = 150

0.4x + 0.6y = 0.52 * 150

x + y = 150

4x + 6y = 780

     -4x - 4y = -600

(+)   4x + 6y = 780

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

               2y = 180

y = 90

x + y = 150

x + 90 = 150

x = 60

Answer: 60 kg of 40% and 90 kg of 60%

Answer:

To convert kilometres to metres, divide the value by 1000.

0.7 ÷ 1000 = 700 metres

Kayli swam 700 meters in the swimming pool

Hope this helps!

Answer:

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured by machine A.

Six percent of all the parts are defective.

This means that [tex]P(A) = 0.06[/tex]

Probability that a part is defective and was manufactured on machine A

3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So

[tex]P(A \cap B) = 0.03*0.5 = 0.015[/tex]

Find the probability that a part was manufactured on machine A, given that the part is defective.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25[/tex]

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.

Answer:

[tex]252[/tex] cubic yards

Step-by-step explanation:

[tex]V=lwh[/tex]

Volume = length * width * height

[tex]V=7*4*9[/tex]

[tex]V=252[/tex]

Answer:

252 yd³

Step-by-step explanation:

Volume of rectangular prism = length * width * height

= 9 * 7 * 4 yd³

= 252 yd³

Step-by-step explanation:

the answer is in the above image

Answer:

314.2 cubic meters

Step-by-step explanation:

Volume of cone = 1/3 × pi × radius² × height

To find the radius we divide the diameter by two = 5 inches

1 × 3.142 × 25 × 12

               3

Ans= 314.2 cubic meters

I hope this helps u

Answer: 9 gallons

Step-by-step explanation:

How many gallons needed for small car: 375/32 = 11.7 or 12

How many gallons for large car: 375/18 = 20.8 or 21

21-12 = 9

Answer:

trffhuuuygreertttf 5

Step-by-step explanation:

fffffffftfdeerrr10

Answer:

[tex](f+g)(x) = x^2 + 4x - 4[/tex]

Step-by-step explanation:

We are given these following functions:

[tex]f(x) = 4x + 2[/tex]

[tex]g(x) = x^2 - 6[/tex]

(f+g)(x)

We add the common terms. Thus:

[tex](f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4[/tex]

Thus:

[tex](f+g)(x) = x^2 + 4x - 4[/tex]

Answer:

an exterior angle is equal to the sum of the two opposite interior angles.

3y + 11 + 4y = 116

Step-by-step explanation:

First combine like terms 7y + 11 = 116

Then undo addition or subtraction.

Then undo multiplication and division to get the value of y.

Answer:

The inequality that represents the graph must have the following form:

[tex]y > -4\cdot x + 6[/tex]

Step-by-step explanation:

First, we need to determine the equation of the line which represents the "lower" bound of the inequality:

[tex]y = m\cdot x + b[/tex] (1)

Where:

[tex]x[/tex] - Independent variable, horizontal axis.

[tex]y[/tex] - Dependent variable, vertical axis.

[tex]m[/tex] - Slope.

[tex]b[/tex] - Intercept.

Given two distinct points of the line, we can solve for both slope and intercept: [tex](x_{1}, y_{1}) = (1, 2)[/tex], [tex](x_{2}, y_{2}) = (0, 6)[/tex]

[tex]m + b = 2[/tex] (2)

[tex]b = 6[/tex] (3)

The solution of the system is: [tex]m = -4[/tex], [tex]b = 6[/tex]

Then, the inequation must have the following form:

[tex]y > -4\cdot x + 6[/tex]

Answer:

The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]

Step-by-step explanation:

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.

At the null hypothesis, we test if the mean is of 8 hours, that is:

[tex]H_0: \mu = 8[/tex]

At the alternative hypothesis, we test if the mean is different of 8 hours, that is:

[tex]H_1: \mu \neq 8[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

8 is tested at the null hypothesis:

This means that [tex]\mu = 8[/tex]

From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.

This means that [tex]n = 101, X = 7.3, s = 2.6[/tex]

What is the t-statistic that Jacob calculates?

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]

[tex]t = -2.71[/tex]

The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]

Answer:

17degrees

Step-by-step explanation:

The sum of two supplementary angles is equation 180degrees. Hence:

5x+95 = 180

5x = 180-95

5x = 85

x = 85/5

x = 17

Hence the value of x is 17

Answer:

The equation must include -8 as the slope

Step-by-step explanation:

Hi there!

Two key points to keep in mind:

Given the equation y=-8x+6, we can identify that -8 is in the place of m in y=mx+b, making it the slope.

For a line to be parallel to y=-8x+6, it would have to have a slope of -8 as well. This is the only quality a line needs to be parallel to this given line.

I hope this helps!

Answer: 63 miles

Step-by-step explanation: 21 miles x 3 = 63 miles

you times it by 3 because to get 3 gallons to 9 gallons, you have to multiply it by 3

Answer:

1 hour 56 minutes

Step-by-step explanation:

Given :

Time taken by Lucy = 3 hours 15 minutes = 3.25 hours

Time taken by brother = 4 hours 45 minutes = 4.75 hours

Rate = 1 / time taken

Lucy's rate = 1 / 3.25

Brother's rate = 1 / 4.75

Combined rate = Lucy's rate + brother's rate

Combined rate = 1/3.25 + 1/4.75

Combined rate = 0.5182186

Time taken if they work together = 1/ combined rate

= 1 / 0.5182186

= 1.9296 hours

= 1 hour (0.9296 * 60) minutes

= 1 hour 56 minutes (approximately)

Answer:

N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)

Step-by-step explanation:

To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.

The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the square be represented as KLMN

Now , the coordinates of the square KLMN is

K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )

Now , let the translated square be represented as K'L'M'N'

When translating the square to three units to the left , the x coordinate of the square gets reduced by 3

So , the new coordinate of the square will be ( x - 3 , y )

Substituting the values in the equation , we get

K' = K ( -5 - 3 , 3 )

L' = L ( 1 - 3 , 3 )

M' = M ( 1 - 3 , 9 )

N' = N ( -5 - 3 , 9 )

So , on simplifying the equation , we get

The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )

To learn more about translation click :

https://brainly.com/question/19007400

#SPJ2