what is the simplifed form of the following expression? (3/5)^3

The value of x in 5 - x < 4/7 based on the information given will be x < 4 3/7.

It should be noted that based on the information given in the question, the expression will be:

5 - x < 4/7

Therefore, collect like terms

5 - x <4/7

x < 5 - 4/7

x < 4 3/7

Therefore, the value of x is less than 4 3/7.

Learn more about expressions on:

brainly.com/question/25968875

#SPJ1

The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, K = 1 to n.

What is Geometric series?

A geometric series is a list of numbers having a common ratio. Each term after the first is gotten by multiplying the previous one by the common ratio.

Given that;

The first term is 3 and the common ratio is 10/9.

Now, A geometric sequence has the form:

a, ar , ar², ar³, . . .

Hence, The nth term of a geometric sequence is;

⇒ ∑ [tex](ar^k^-^1)[/tex]     where, k = 1 to n.

Therefore, the sum of geometric series with a first term of 3 and a common ratio of 10/9 is:

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

So, The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

Learn more about the geometric series visit:

https://brainly.com/question/9891309

#SPJ1

Answer:

x = 3 ± √23

Step-by-step explanation:

Simplify the quadratic equation.

[tex]3x^2-18x+5 = 473x^2-18x+5-47 = 0\\3x^2-18x-42 = 0\\\\a = 3\\b = -18\\c = -42\\\\x = (-(-18)\pm\sqrt{ (-18)^2-4(3)(-42) )} \div 2(3)\\x = (18\pm\sqrt{ 324+504)} \div 6\\x = (18\pm\sqrt{ 828}) \div 6[/tex]

Simplify further.

[tex]x = (18\pm\sqrt{ 23\times 36}) \div 6\\x = (18\pm6\sqrt{ 23}) \div 6\\x = 6(3\pm\sqrt{23}) \div 6[/tex]

Thus, the solution is

x = 3 ± √23

Hope this helps.

x = 3 + √23 and x = 3 - √23 are the two solutions of the given quadratic equation.

ax²+bx+c=0, with a not equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To solve for x in the equation 3x^2 - 18x + 5 = 47, we can begin by simplifying the equation:

[tex]3x^2 - 18x - 42 = 0[/tex]

Next, we can divide both sides of the equation by 3 to get:

[tex]x^2 - 6x - 14 = 0[/tex]

To solve for x, we can use the quadratic formula:

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

In this case, a = 1, b = -6, and c = -14, so we have:

[tex]x = \frac{(-(-6) \pm \sqrt{((-6)^2 - 4(1)(-14)))}}{2(1)} \\x = \frac{(6 \pm \sqrt{(36 + 56))}}{ 2} \\x = (6 \pm \sqrt{92}) / 2[/tex]

Simplifying the radical, we get:

x = (6 ± 2√23) / 2

Dividing both the numerator and denominator by 2, we get:

x = 3 ± √23

Therefore, the two solutions to the equation [tex]3x^2 - 18x + 5 = 47[/tex] are x = 3 + √23 and x = 3 - √23.

Learn more about Quadratic equations here:

https://brainly.com/question/22364785

#SPJ5

Answer: A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.

Step-by-step explanation:

The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

The given points are;

(-3, -3), (-2, 2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

(-3, 3), (-3, -3), (1, -4), (1, 1)

Now, For an ordered pair to be a function, either of the following must be true:

Each x-value have exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value have multiple corresponding y-values.

More than one x-values have the multiple corresponding y-values.

From the given options, only ordered pair (-3, -3), (-2, 2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

Learn more about ordered pairs visit:

https://brainly.com/question/19267542

#SPJ1

Approximately 7.4 is 1.9 times larger than 3.9.

[tex]10^{-8}[/tex]  is 3 times smaller than [tex]10^{-5}[/tex] .

7.4 x [tex]10^{-8}[/tex] is 1.9 x x [tex]10^{-3}[/tex] smaller than 3.9 x [tex]10^{-5}[/tex].

Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, when 100 is written in scientific notation it becomes 1 x 10².

For negative numbers, the sign in front of the power would be negative. For example, 0.0012 becomes 1.2 x [tex]10^{-3}[/tex] in scientific notation.

0.000039 becomes 3.9 x [tex]10^{-5}[/tex]

Difference between 7.4 and 3.9 : 7.4 / 3.9 = 1.9

Difference between [tex]10^{-8}[/tex] and x [tex]10^{-5}[/tex]

= [tex]10^{-8 - (-5)}[/tex]

= [tex]10^{-8 + 5}[/tex]

= [tex]10^{-3}[/tex]

[tex]10^{-8}[/tex]  is three times smaller than  [tex]10^{-5}[/tex]

To learn more about scientific notation, please check: https://brainly.com/question/25334755

#SPJ1

Answer:

0.4oz

Step-by-step explanation:

conversion factor 1oz = 28.35g

(10g/1)(1oz/28.35g) cross out grams

    10/28.35oz = 0.3|527 = 0.4oz

The missing steps of the expression are as follows;

The expression can be solved as follows:

step 1

[tex](\frac{3^{2} + 4 }{|-0.25|} ) - 10.4[/tex] ÷ 4

Step 2

The absolute value will remove the minus sign of the denominator.

[tex](\frac{3^{2} + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 3

We have to find the square of the 3 in the numerator. Therefore, the step 3 will be as follows:

[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 4

We have simplify the numerator.

[tex](\frac{13 }{0.25} ) - 10.4[/tex] ÷ 4

Step 5

52 - 10.4 ÷ 4

Step 6

Using PEMDAS rule, we have to solve the division sign. Therefore, the step 6 is as follows;

52 - 2.6

Step 7

49.4

learn more on expression here: https://brainly.com/question/28393820

#SPJ1

The sequence is an arithmetic sequence due to the presence of a common difference.

An arithmetic sequence is a sequence that has a common difference while a geometric sequence is a sequence with a common ratio. For instance, given the sequence below:

a, b, c, d...

The sequence is an arithmetic sequence if;

common difference = b - a = c - b = d - c

The sequence is a geometric progression if;

common ratio = b/a = c/b = d/c

Given the sequence 17, 13, 9, ...

d = 13 - 17 = 9 - 13

d = -4

Since the sequence has a common difference, hence the given sequence is an arithmetic progression.

Learn more on arithmetic progression here: https://brainly.com/question/24191546

#SPJ1

Answer:

a 1760.

b 32.1

c 8.5 × 10^8

d 5.09×10^-5

Step-by-step explanation:

for positive numbet (2, 4, 6, 8, 10, 12, 14)

 2, 4, 6, 8, 10, 12, and 14.

Step-by-step explanation:

even number is 2,4,6,8.....

odd number is 1,3,5,7.......

wish you have a great day

The measure of the central angle m∠VWU is 69 degrees

Central angle is the angle formed by two arms and having the vertex at the centre of a circle.

The diameter of a circle runs from the centre of a circle.

The diameter SU and RT intersect each other at point Q.

Therefore,

m∠VWS = m∠TWU (Vertically opposite angles)

m∠VWU = m∠SWT (Vertically opposite angles)

Hence,

m∠TWU = 111 degrees.

Therefore,

m∠VWU = 360 - 111 - 111  /2

m∠VWU = 360 - 222 / 2

m∠VWU = 138 / 2

m∠VWU = 69 degrees

Therefore, the measure of the central angle m∠VWU is 69 degrees

learn more on central angle and diameter here: brainly.com/question/15272508

#SPJ1

Answer:

2

Step-by-step explanation:

2^2 is 4 and two more than 2, which is 4, is 16 when squared. 16+4=20

[tex]f(x) = ae {}^{bx} \\ f(2) = 5 \: \: \: \: \: f(3) = 4[/tex]

[tex]5 = ae {}^{2b} \: \: \: \: \: \: \: 4 = ae {}^{3b} \\ divide \: both \: systems \\ e {}^{b} = \frac{4}{5} \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = \frac{125}{16} [/tex]

[tex]f(x) = \frac{125}{16} e {}^{ln(0.8)x} [/tex]

[tex]f(10) = \frac{125}{16} e {}^{10ln(0.8)} = \frac{65536}{78125} \approx0.838861 \\ f(100) = \frac{125}{16} e {}^{100ln(0.8)} = \frac{4 {}^{98} }{5 {}^{97} } \approx1.59 \times 10 {}^{ - 9} [/tex]

Answer:

19

Step-by-step explanation:

Arrange into parentheses and start at the innermost parentheses

[tex]5 + (2 \times (6 + (3 \div 3)))[/tex]

Start with 3 ÷ 3

[tex]3 \div 3 = 1[/tex]

Continue with the other parts of the equation in order

[tex]1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19[/tex]

Hope this helped you understand better, have a great day!

Applying the triangle sum theorem, the value of x is: 4.

When we add the three interior angles of a triangle together, the sum must be equal to 180 degrees according to the triangle sum theorem.

Given the triangle with the following interior angles, 35°, (22x - 3)°, and 60°. Therefore:

35 + (22x - 3) + 60 = 180 [triangle sum theorem]

Solve for x

35 + 22x - 3 + 60 = 180

Combine like terms

92 + 22x = 180

Subtract 92 from each side of the equation

92 + 22x - 92 = 180 - 92

22x = 88

Divide both sides by 22

22x/22 = 88/22

x = 4

Thus, applying the triangle sum theorem, the value of x is: 4.

Learn more about the triangle sum theorem on:

https://brainly.com/question/7696843

#SPJ1

It should be noted that simplifying 5¹⁰ × 5² will be 5^12.

It should be noted that these values have to do with powers. In this case, since that have same base and we want to multiply, we will add their powers.

Therefore, 5¹⁰ × 5² will be:

= 5¹⁰ × 5²

= 5^12

In conclusion, the value will be 5 raise to power 12

Therefore, based on the information, it should be noted that the value of 5¹⁰ × 5² will be 5^12.

Learn more about numbers on:

brainly.com/question/24644930

#SPJ1

Simplify 5¹⁰ × 5²

Answer:

Step-by-step explanation:kfn

The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Triangle ABC is dilated with a scale factor of 3. Then the scale factor will be 3.

If the side BC is 5.4 units long, then the length of the side B'C' will be

B'C' = 3 x BC

B'C' = 3 x 5.4

B'C' = 16.2 units

If the side A'B' is 8.2 units long, then the length of the side AB will be

AB = A'B' / 3

AB = 8.2 / 3

AB = 2.7 units

If the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

There is no effect of dilation on the angle. Then the angles will remain the same.

The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ1

Answer:

A is the answer of the question

Answer:

22/10

=2.2

22-2.2=19.8

Stephanie pays £19.8

The area of the triangle with the given dimensions are 77cm.

According to the statement

We have to find that the area of the triangle.

So, For this purpose, we know that the

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

From the given information:

15 cm

7 cm

22 cm

Then

The base of the triangle is 7 cm and the height of the triangle is a 22cm.

Then

A = 1/2 × b × h.

A = 1/2 × 7 × 22.

Now solve it then

A = 154/2

A = 77cm.

So, The area of the triangle with the given dimensions are 77cm.

Learn more about area of a triangle here

https://brainly.com/question/8409681

#SPJ9

The radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

Radioactive decay is the spontaneous disintegration of atoms with the emission of radiation.

The half life of a radioactive isotope is the time it takes for half the number of atoms in a given sample to disintegrate.

To model the situation, we use the equation for radioactive decay which is given below

[tex]N = N_{0}e^{-{\lambda}t}[/tex] where

Given that the half life of the isotope dubnium-263 is 29 seconds and  sample of dubnium-263 was first measured to have 1024 atoms. Then, after t seconds, there were only 32 atoms of the isotope remaining. we have that

So, λ = 0.693/29 s = 0.0239 /s

So, susbtituting the values of the variables into the equation, we have

[tex]N = N_{0}e^{-{\lambda}t}[/tex]

[tex]32 = 1024e^{-(0.0239/s)t}[/tex]

So, the radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

Learn more about radiactive decay equation here:

https://brainly.com/question/27542728

#SPJ1

Answer:

16 + n

Step-by-step explanation:

Whenever something says "more" it typically includes addition.

It says 16 more than a number, meaning that you add 16 to an number (n)

*Please mark brainliest

Answer:

16 + n

Step-by-step explanation:

I got 100% on the test

In combination, 56 ways can Nick choose topping can only be chosen .

What is permutation and combination?

given that Nick choose pizza = 5

menu of toppings if each topping =8

chosen once  = 8c5

                        =>   8! / (5!(8−5)!)

                         =>  56

Learn more about permutation and combination

brainly.com/question/16837159

#SPJ9

Answer:

-4920.75 or 18

Step-by-step explanation:

I'm not quite sure if this is correct because I got two diffrent soultions for a.

In a1=3 I got a=3

In a8= -6561 I got a= -820.125

So i plugged my two solutions in to find a6

I got

18

or

-4920.75

That doesn't really seem correct, but I tried!!

Answer:

None of these

Step-by-step explanation:

We can estimate f'(9) by finding the slope of the secant through the two points closest to (9, f(9)).

[tex]\frac{f(10)-f(8)}{10-8}=\frac{16-10}{2}=3[/tex]

Answer:

$1 x 4

$20 x 3

$5 x 6

Step-by-step explanation:

$94

at least 4 $1 bills

$90

at least 3 $20  ($60)

$30

the remaining $30 can be made up of 6 $5 bills

4 + 3 + 6 = 13 bills total

Step-by-step explanation:

the €300 as current price is 125% relative to the original price. in other words : 1.25 times the original price.

to get the amount of the increase we need to get the original price first and then subtract the original price from the current price.

to get the original price we need now to divide the actual price by 1.25 to undo the increase.

the original price

OP = 300/1.25 = €240

the price increase (of 25%) was then

300 - 240 = €60