What is the surface area of the regular pyramid

Final answer:

To rewrite the given logarithm as a subtraction of logs, use the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

Explanation:

The given logarithm is log11 (29/11). To rewrite this as a subtraction of logs, we can use the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

So, log11 (29/11) can be rewritten as log11 (29) - log11 (11).

Answer: ΔHGF≅ ΔABC

Step-by-step explanation:

In the given figure ΔABC and ΔHGF have the pair of two corresponding angles and the included sides are congruent.

i.e.[tex]\angle{C}\cong\angle{F}[/tex]

[tex]\overline{GF}\cong\overline{BC}[/tex]

tex]\angle{G}\cong\angle{B}[/tex]

Therefore , by ASA congruence postulate:-

ΔABC ≅ ΔHGF

In  ΔTUV , there is only angle given . So there is no enough information to prove it by ASA.

Answer:
The smaller angle is 20 degrees. 

Explanation:
Complementary angles are two angles (or more) whose sum is 90 degrees.

If two angles have a sum of 90 degrees and their ratio is 2:7, we must determine which two numbers when added together would yield this proportion?

60 + 30 = 90 but 60:30 is a 6:3 ratio which simplifies to 2:1.

45 + 45 = 90 but 45:45 is a 1:1 ratio.

50:40 = 90 but 50:40 is a 5:4 ratio.

10 + 80 = 90, but 10:80 is a 1:8 ratio. We're getting closer!

20 + 70 = 90, and 20:70 can be simplified to 2:7 when you divide each number in the ratio their greatest common factor (GCF) of 10.

Therefore, the two complementary angles would be 20° and 70°, the smaller of which would be 20°

The decimal equivalent of the fraction 5/33 is option A. o.15....

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given fraction is 5/33.

We have to find the decimal corresponding to the given fraction.

For that divide 5 by 33.

5 is not divisible by 33.

So add 0 and it become 50.

50 = (33 × 1) + 17

And the quotient is 0.1 with remainder 17.

Now 17 is not divisible by 33.

Add 0 and it becomes 170.

170 = (33 × 5) + 5

Quotient becomes 0.15 with remainder 5.

Again the remainder is 5 and add 0 and becomes 50.

It continues.

So the quotient is 0.1515....

Hence the decimal form is 0.(15) repeating.

Learn more about Fractions here :

https://brainly.com/question/548650

#SPJ3

The height of the rectangular prism is 4 feet.

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]

Given that the volume of the rectangular prism is 192 cubic feet and the base area is 48 square feet, we can set up the equation as follows:

[tex]\[ 192 = 48 \times \text{Height} \][/tex]

To solve for the height, we divide both sides of the equation by the base area:

[tex]\[ \text{Height} = \frac{192}{48} \][/tex]

[tex]\[ \text{Height} = 4 \][/tex]

Therefore, the height of the rectangular prism is 4 feet.

Answer:

Q1:   The correct option is:   16

Q2:   The correct options are: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]

Q3:   The correct option is:  [tex]\overline{BC}=12; \overline{EF}=16[/tex]

Step-by-step explanation:

Question 1:

As here  [tex]\triangle RST\sim \triangle MNO[/tex], so the ratio of the corresponding sides will be equal. That means.....

[tex]\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16[/tex]

So, the length of the side [tex]x[/tex] will be 16.

Question 2:

If two triangles are similar, then the ratio of their corresponding sides should be equal.  So, here the ratios of the corresponding sides are............

[tex]\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}[/tex]

So we can see that the ratio of side [tex]AC[/tex] and side [tex]DF[/tex] is not equal with the other ratios.

Thus, the proportions that show the triangles are not similar:  [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]

Question 3:

Given that,  [tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]  

The ratio of [tex]AB[/tex] and [tex]DE[/tex] is given as [tex]\frac{3}{4}[/tex]

So, the ratio of [tex]BC[/tex] and [tex]EF[/tex] will be also [tex]\frac{3}{4}[/tex]

Among the four options, if [tex]BC=12[/tex] and [tex]EF=16[/tex], only then the ratio will be [tex]\frac{3}{4}[/tex]

[tex]\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}[/tex]

So, the lengths of [tex]BC[/tex] and [tex]EF[/tex] could be 12 and 16 respectively.

Answer:

the correct answer is c

Step-by-stepth explanation:

Answer:

The answer is D

Step-by-step explanation:

The percentage of the tickets for the dance that were purchased in advance is 9%.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %.

Percent of advance tickets bought = (number of advance tickets / total number of tickets) x 100

(18 / 200) x 100 = 9%

To learn more about percentages, please check: https://brainly.com/question/25764815

Answer

21.3 i think hope this can help

Explanation of dividing 4.5 by 0.5+0.1 in computation words.

4.5 divided by 0.5+0.1 can be written as:

4.5 / (0.5 + 0.1)

To solve this, we first add 0.5 + 0.1 to get 0.6. Then, we divide 4.5 by 0.6 to find the result.

The result of the computation is 7.35.

To compute the given expression[tex]\(14.5 \times 0.5 + 0.1\):[/tex]

Multiplication :

  - Multiply [tex]\(14.5\)[/tex]  by [tex]\(0.5\).[/tex]

  - [tex]\(0.5\)[/tex] represents half, so you're essentially halving 14.5.

Half of [tex]\(14.5\) is \(7.25\).[/tex]

Addition :

  - Now add [tex]\(0.1\) to \(7.25\).[/tex]

  - The addition gives [tex]\(7.25 + 0.1 = 7.35.[/tex]

Thus, the result of the computation is 7.35.

Complete question : Write the computation in words: 4.5 divided by 0.5+0.1

The given value h=16 ft is possible based on the quadratic equation model provided. By solving the equation h=[tex]-16t^2 + 35t[/tex] and substituting h=16, we find the possible values of t to be approximately 0.52 seconds or 1.48 seconds.

- For each given value of h, set [tex]\( h = -16t^2 + 35t \)[/tex] and solve for t.

- If you obtain real solutions, the given h is possible. If not, it isn't possible.

Checking for h=16:

1. Set h=16 and solve for t:

[tex]\[ 16 = -16t^2 + 35t \][/tex]

2. Rearrange to form a quadratic equation:

[tex]\[ -16t^2 + 35t - 16 = 0 \][/tex]

3. Solve for \( t \) using the quadratic formula:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

  where a= -16, b=35, c=16.

  - Find the discriminant:

   [tex]\[ b^2 - 4ac = 35^2 - 4 \times (-16) \times (-16) = 1225 - 1024 = 201 \][/tex]

  Since the discriminant is positive, this quadratic has real roots, indicating that h=16 is possible.

Checking for h=20:

1. Set h=20 and solve for t:

[tex]\[ 20 = -16t^2 + 35t \][/tex]

2. Rearrange to form a quadratic equation:

 [tex]\[ -16t^2 + 35t - 20 = 0 \][/tex]

3. Solve for t using the quadratic formula:

 [tex]\[ t = \frac{-35 \pm \sqrt{35^2 - 4 \times (-16) \times (-20)}}{2 \times (-16)} \][/tex]

  - Find the discriminant:

 [tex]\[ 35^2 - 4 \times (-16) \times (-20) = 1225 - 1280 = -55 \][/tex]

  Since the discriminant is negative, this quadratic has no real roots, indicating that h=20 is not possible.

Conclusion:

- The value h=16 is possible.

- The value h=20 is not possible.

Answer: B. Theoretical probability

Step-by-step explanation: Theoretical probability is based on calculations, and not actual tests.