Decide whether each equation is true or false.
1. 9 ⋅ 9 ⋅ 3 = 3 5
2. 7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3
3. 1 7 ⋅ 1 7 ⋅ 1 7 = 3 7
4. 4 1 = 4 ⋅ 1
5. 6 + 6 + 6 = 6 3

The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

Given the surd function expressed as:

[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]

Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]

Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]

Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

Learn more on rationalization here: https://brainly.com/question/14261303

Answer:

c; 63 square cm

Step-by-step explanation:

the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)

this means the height times base 1 and base 2 added together divided by 2

(1/2)(6)(8 + 13) is the equation

this can become 3(21)

which is ultimitaly 63

Answer:

it's gonna be 63cm^2

Step-by-step explanation:

First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2

Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.

Next, we have to find the area for the triangle. The formula is length x width / 2.

So, we have to multiply 6x5 to get 30.

Then, well divide it by 2, which will give us 15cm^2

Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.

Bada-bing, bada-boom, we got 63cm^2 as our answer :)

Step-by-step explanation:

Tn = a + (n-1)d

where a is the first term, d is the common difference and n is the nth term

For the 6th term: T6 = a + (6-1)d

= a + 5d

For the 8th term: T8 = a + (8-1)d

= a + 7d

From the question (a + 5d)/(a + 7d) = 7/9

From the Equation above, we can say that;

a + 5d = 7......1

a + 7d = 9.....2

Solving equations 1 & 2 simultaneously, we have that a = 2 and d = 1

Sn = n/2[2a + (n-1)d]

where Sn is the sum of nth terms, n is the nth term, a is the first term and d is the common difference.

By substituting the values gotten into this equation. You would be able to find the ration between the sum of the first 10 terms to the sum of the first 20 terms

Answer:

see analysis for detailed explanation

Answer:

B

Step-by-step explanation:

The slope of this function is obviously decreasing, and the point where it intersects the y axis, is (0,-2)

Answer B contains this information

Hope this helps!

Answer:

complete your question please

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

As we know :

Length of arc = Radius × Angle made by Arc at center [ in radians ]

[tex]\qquad \tt \dashrightarrow \: arc = radius \times angle \: \: ( in \: \: rad)[/tex]

[tex]\qquad \tt \dashrightarrow \: arc = 9 \times { \pi}{} [/tex]

[tex]\qquad \tt \dashrightarrow \: arc = 9\pi \dfrac{ }{} \: \: units[/tex]

or

[tex]\qquad \tt \dashrightarrow \: arc = 9 \times 3.14 = 28.26 \: \: units\dfrac{ }{} \: \: [/tex]

Arc length

Step-by-step explanation:

radius = 10 cm

volume = v

height h cm

[tex] {10 }^{2} = h - 10 + r { }^{2} \\ {10 = }^{2} h - 20 + r { }^{2} \\ r {}^{2} = 20h - h {}^{2} [/tex]

hope it's helpful thanks

Answer:

z = 600

Step-by-step explanation:

Method 1 - ratios

If 150 is 25% then z is 100%:

[tex]\begin{aligned} 150 : 25 & = z : 100\\\dfrac{150}{25} & = \dfrac{z}{100}\\150 \cdot 100 & = 25z\\15000 & = 25z\\z & = \dfrac{15000}{25}\\z & = 600 \end{aligned}[/tex]

Method 2

Calculate the amount for 1%, then multiply by 100% to find z:

25% = 150

⇒ 1% = 150 ÷ 25 = 6

⇒ z = 100% = 6 x 100 = 600

Answer:

The answer is 20p – 10 or 10(2p – 1)

Step-by-step explanation:

4(2p + 2) + 6(2p − 3)

8p + 8 + 12p – 18

20p – 10 or 10(2p – 1)

Answer: 80%

Step-by-step explanation:

or 85% but i think its 80%

Answer:

D

Step-by-step explanation:

We know the ratio of the cut string is 2 : 5 : 3. If we add 2, 5, and 3 together, we get 10. We can do 90 ÷ 10 = 9. Each number in the ratio should be multiplied by 9 to find the actual length after it is cut.

Left piece : 2 x 9 = 18 cm

Middle piece : 5 x 9 = 45 cm

Right piece : 3 x 9 = 27 cm

D is the correct answer.

I hope this helps and please mark me as brainliest!

Answer:

Ken's misunderstanding is that you have to round starting from the 1st number that is behind what your rounding to. In this case Ken needs to start from 1 and round instead of starting from 3. So  you would round the 9,000 by looking at the 1 and seeing if you should round up or down. You want to round down because 1 is less than 5. If Ken rounds from 1 the real answer should be 9,000

Step-by-step explanation:

Answer:

i}. Mango only (no(M))=30

ii}.Orange (n(O))= 20

Answer:

x=8 y=10

Step-by-step explanation:

x+y =18        x=(18-y)

3(18-y) +2y =44

54-3y+2y =44

54-y =44

-y=-10

y=10

                                     x+10=18

                                      x=8

Answer:

The answer is 24 cm.

Step-by-step explanation:

Since we know two sides, we can find the third side. Using the pythagorean theorm, a^2 + b^2 = c^2, this gives us:

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

Square root of 100 = c

10 = c.

Hope this helps!

Answer:

40

Step-by-step explanation:

10+10+10+10 = 40

A square has 4 sides which is why you add 10, 4 times.

Answer:

35 feet

Step-by-step explanation:

when the flare is fired , time t = 0

substitute t = 0 into the equation

f(0) = - 10(0)² + 60(0) + 35 = 0 + 0 + 35 = 35

Answer:

the correct answer would be 35  feet

Step-by-step explanation:

hope this helps

Answer:

(A)

Step-by-step explanation:

(D) is already out since the teachers may have favorites or unfavorites.

(C) is already out since you can't be in all the halls at once.

There is only (A) and (B).

I think it's (A) and not (B) because it might not be a classes/grades library day.

Answer:

Mean: 54
Median: 61.5
Mode: 0
Range: 54

Step-by-step explanation:

Mean: Add everything up and divide by the amount of numbers
(47 + 31 + 84 + 50 + 68 + 85 + 67 + 56 = 488/8 = 54)

Median: Put all numbers in order from smallest to largest, the middle number is the median. Since we have 2 middle numbers, we add both 67 and 67 together, then divide them by 2.
31, 47, 50, 56, 67, 68, 84, 85
(56 + 67 = 123/2 = 61.5

Mode: The mode is the number that appears most often in the set of given numbers.
(There are no numbers that appear more than once so the mode is 0)

Range: The range is the largest number subtracted by the smallest number.
(85 - 31 = 54)

Answer:

Math-Graphing Inequalities on a Number Line (the basics)

Step-by-step explanation:

Answer:

x=15
y=2

Step-by-step explanation:

the scale factor is 6:1

if you divide 12 by 6 you get 2
so y=2

if you multiply 6 by 2.5 you get 15
so x=15

Step-by-step explanation:

100%+5%=105%

105/100*200=210

100%-6%=94%

94/100*210

The area of the flower bed has a radius of 4 feet is 16π or 50.24 square feet.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

A circular flower bed in a botanical garden has a radius of 4 feet.

Then the area of the flower bed will be

Area = π r²

Area = π × 4²

Area = 16π

Area = 16 × 3.14

Area = 50.24 square feet.

More about the circle link is given below.

https://brainly.com/question/11833983

Yes they are proportional

Answer:

A- yes

Step-by-step explanation:

If you never buy the popcorn because you think that it is too expensive then the only thing you are paying for is the tickets therefore the price you pay is proportional to the number of tickets you buy.

Answer:

Step-by-step explanation:

The explicit rule for the sequence in simplified form is y = 30000(2)^n

The standard exponential equation is expressed as:

y = ab^n

Given the following parameters

a is the initial values = 30,000
If the amount doubles each year then b = 2

Substitute the parameters

y = 30000(2)^n

Hence the explicit rule for the sequence in simplified form is y = 30000(2)^n

Learn more on explicit rule here: https://brainly.com/question/2059043

Answer: Explicit Rule: a_n=30,000 • 2^n-1 Recursive Rule: a_n = 2a_n-1; a_1 =30,000

Step-by-step explanation: the Explicit Rule for a geometric sequence is a_n = r • a_n -1 and the Recursive Rule is a_n = a_1 • a_n-1

a_1 is the first term and r is the common ration. In this case, the first term is 30,000 as stated in the question and the common ration is 2 since it doubles each time. So substitute those numbers into the formulas and that’s what you’ll get! Hope this helps! God bless you all!!