8/26 - Equation Review
Which is the solution that makes the equation - 8x = true?

The length of one edge of the triangular pyramid is 6 cm

The area is given as:

Area = 240 square centimeters

The net of the triangular pyramid consists of:

So, the area of the net is:

Area = 4 * Base * Height

This gives

240 = 4 * L * 10

Divide both sides by 40

L = 6

Hence, the length of one edge of the triangular pyramid is 6 cm

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It should be noted that for a standard normal distribution, the probability of (z > 0.97) will be 0.1660

It should be noted the normal distribution explains the symmetrical plot of data around its mean value, where the width of the curve is illustrated by the standard deviation and us visually depicted as the "bell curve."

In this case, the normal distributions are important in statistics and usually used in the natural and social sciences to represent real-valued random variables

Given that ,

P(z <-0.97 )

Using standard normal distribution

P(z <-0.97 )

Probability = 0.1660

Therefore, it should be noted that for a standard normal distribution, the probability of (z > 0.97) will be 0.1660

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Option (b) is the correct option i.e. The height is 5 units.

The height of an object is determined by measuring the distance between its base and its top.

As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."

Given, V = πr².H

          V/πr² = H

So, It can be written in terms of height, H as V/πr².

Now, If r = 3 units and V= 45π then,

H =   V/πr² = 45π / π(3)²

                = 45π/9π

                = 5 units.

Hence, height is 5 units.

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Answer:

Your answer is A <3

Step-by-step explanation:

Answer:

400 thousand people > 300 thousand people, so there are more people living in Miami.

The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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The first five terms of the arithmetic sequence are 5, 8, 11, 14, and 17.

We have,

In an arithmetic sequence, each term is obtained by adding a fixed constant, called the common difference (d), to the previous term.

To find the common difference, we can use the formula:

a_n = a_1 + (n-1)*d

where a_n is the nth term of the sequence, a_1 is the first term, and n is the position of the term in the sequence.

Using the given information, we can write two equations:

a_2 = a_1 + d = 8

a_6 = a_1 + 5d = 15

Solving these equations simultaneously.

a_1 = 5

d = 3

Now, we can use the formula for the nth term to find the first five terms of the sequence:

a_1 = 5

a_2 = a_1 + d = 5 + 3 = 8

a_3 = a_2 + d = 8 + 3 = 11

a_4 = a_3 + d = 11 + 3 = 14

a_5 = a_4 + d = 14 + 3 = 17

Therefore,

The first five terms of the arithmetic sequence are 5, 8, 11, 14, and 17.

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Answer:

C) A = \(3w^{2} - 4w\)

Step-by-step explanation:

First, read through what the question is asking.

Now, read it again, but slowly and take in everything it is saying (Don't read into it too slowly, or else you will over-complicate the problem and get frustrated - told from experience :) )

Alright, 4 less than 3 times the width. So, lets rearrange this and give width a variable (w).

So, the length is equal to:

l = 3w - 4

and the width is equal to:

w = w

The area of a rectangle is A = l * w

Let's plug in the values.

A = (3w - 4) * w

Now, simplify:

A = \(3w^{2} - 4w\)

A = \(3w^{2} - 4w\) is your final answer.

I hope this helps!

Answer:

the x value is 41

x=77

y=62

z=41

Step-by-step explanation:

part 1:

2y-5+y+21+y=180

4y+17=180

4y=164

y=41

part 2:

w-2(41)-5=77

x-41+21=62

y-41

To solve this question we must use the concept of the sum of the internal angles of the triangles and therefore the measures of each angle are x = 62º, y = 41º, w = 76º.

The sum of the internal angles of a triangle is of 180º. In this problem, the angles are w, x and y, hence:

x + y + w = 180.

The measure of angle w is five less than twice the measure of angle y, hence:

w = 2y - 5.

The measure of angle x is 21 more than the measure of angle y, hence:

x = y + 21.

Replacing in the first equation, we can find angle y as follows:

y + 21 + y + 2y - 5 = 180.

4y = 164.

y = 164/4

y = 41.

Then:

w = 2y - 5 = 2(41) - 5 = 76.

x = y + 21 = 41 + 21 = 62.

Therefore the measures of the angles are given as follows:

x = 62º, y = 41º, w = 76º.

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Answer:

StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction

Solve the proportion for x.

After using cross products, the proportion becomes the equation

✔ 4x = 10

.

Isolate the variable by dividing both sides of the equation by

✔ 4

.

x = ✔ 2.5

.

The value of x is 2.5 for the given proportion.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The proportion is given in the question, as follows:

4/2 = 5/x

Using cross-product, the proportion becomes the equation as:

4x = 2 × 5

4x = 10

Divide by 4 into both sides of the above equation,

x = 10/4

x = 2.5

Thus, the value of x is 2.5 for the given proportion.

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Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

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The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Answer:

???

Step-by-step explanation:

1. 52 + 5 = 57

2. 57 × 12 = 684

3. Test it out

684 ÷ 12 = 57

which is wrong because of the remainder.

BUT the remainder is not possible because 12 was the number it was divided by and 12 can not go into 5

so either your question is wrong or my solution is wrong

Answer:

44

Step-by-step explanation:

The required capacity of the mug is 12/5 cups of water.

The fundamental function of a ratio is to compare quantities, i.e., to illustrate the relative importance of one quantity to another.

If a and b are two values, their ratio will be a:b,

Given that,

The mug is 1/6 full of the water.

Also,

The mug contains 2/5 of the cup of water.

To find the capacity of the mug,

Use ratio property,

1/6 full mug contains = 2/5 cup of water,

1 full mug contains = (2/5) x 6 cup of water

1 full mug contains = 12 / 5 cup of water.

Hence, the capacity of the mug equal to 12/5 cup of water.

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Answer:

60 and -60

Hope this helps! :)

Hi!

I can help you with joy!

Let's list 10 multiples of 40 and 10 multiples of 28.

The first 10 multiples of 40 are:

40, 80, 120, 160, 200, 240, 280, 320, 360, 400...

The first 10 multiples of 28 are:

28, 56, 84,112, 140, 168, 196, 224, 252, 280

I have highlighted it. Guess why!

Because it's the LCM (LEAST COMMON MULTIPLE) of 40 and 48.

\(*RosalindCordelia*\)

Answer:

25 rows

Step-by-step explanation:

Because if you divide 350 by 14 it gives you 25

Answer:

25

Step-by-step explanation:

350÷ 14 = 25.........

Answer:

X=80.4

Step-by-step explanation:

Lol

Step-by-step explanation:

x= 78 approximately

hope this is correct

The answer to your question is C. -10. You can find this by knowing that a negative time a negative is a positive, and 5 time 2 is 10. And then you carry over the negative sigh and get -10.

The possible values of x, given the number of bets are $54,999, $14,999, and -$1.

The expected winnings would be -$0.97.

The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.

The possible values would therefore be:
$54,999, $14,999, and -$1.

These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.

The expected winnings would be:

= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )

= - $ 0.97

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Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

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

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The solution of x is x = 0, x =2 and x = -5

The equation is given as:

2x^3+6x^2-20x=0​

Factor out x

x(2x^2+6x-20)=0​

Split the equation

x = 0 or 2x^2+6x - 20=0​

Solve for x in 2x^2+6x - 20=0​

Expand the equation

2x^2 + 10x - 4x - 20 = 0

Factorize the equation

(2x - 4)(x +5) = 0

Split the equation

2x - 4 = 0 and x + 5 = 0

Solve for x

x =2 and x = -5

Hence, the solution of x is x = 0, x =2 and x = -5

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Answer:  \(\boldsymbol{f(t) = 6(0.88)^t}\) which is choice A

This is the same as writing f(t) = 6(0.88)^t

====================================================

Explanation:

Exponential equations can be written in the form \(y = a*b^x\)

The 'a' represents the starting amount which means a = 6.

The b value is tied to the growth or decay.

In this case, we have r = -0.12 representing a decay of 12%

So b = 1+r = 1 + (-0.12) = 0.88

Therefore, we go from \(y = a*b^x\) to \(y = 6(0.88)^x\)

Then replace x with t, and replace y with f(t) to end up with \(f(t) = 6(0.88)^t\)

Note: the 0.88 represents having 88% leftover when you lose 12% of the mass.

The equation that models the exponential function for this situation is \(f(t) = 6(0.88)^t.\)

Option A is the correct answer.

We have,

The correct equation that best models the exponential function for the given situation is:

\(f(t) = 6(0.88)^t\)

In this equation, "t" represents the time in seconds, and \((0.88)^t\) represents the exponential decay factor as the substance loses 12% of its mass every second.

i.e

100% - 12% = 88%

This can be written as,

88/100 = 0.88

Now,

The initial mass of 6 g is multiplied by the decay factor for each second passed.

Therefore,

The equation that models the exponential function for this situation is \(f(t) = 6(0.88)^t.\)

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The number 4.4 is between \(4 \frac{1}{3}$\) and \(4 \frac{3}{5}$\) on the number line, so the answer is (D) 4.4.

To solve this problem, we need to convert the mixed numbers 4 1/3 and 4 3/5 to improper fractions and then find a number between them on the number line.

\(4 \frac{1}{3}$\) can be written as \(\frac{13}{3}$\) and \(4 \frac{3}{5}$\) can be written as \(\frac{23}{5}$\).

To find a number between \(\frac{13}{3}$\) and \(\frac{23}{5}$\), we need to find a common denominator. The least common multiple of 3 and 5 is 15, so we can rewrite the fractions with a denominator of 15:

\($\frac{13}{3} = \frac{65}{15}$\)

and

\($\frac{23}{5} = \frac{69}{15}$\)

Now we can see that the number \(\frac{67}{15}$\) is between \(\frac{65}{15}$\) and \(\frac{69}{15}$\), and we can convert it back to a mixed number:

\($\frac{67}{15} = 4 \frac{7}{15}$\)

Therefore, the number 4.4 is between \(4 \frac{1}{3}$\) and \(4 \frac{3}{5}$\) on the number line, so the answer is (D) 4.4.

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Answer:

Step-by-step explanation:

Answer:3

Hope this helps

Answer:

Hi Suuuman  the answer for your deleted question is OP = 7.75

Step-by-step explanation:

– 2x + 23 and -8 + 2x = 23 - 2x and -8 + 2x = x= 31 /4 =7 3/4 =7.75 measure of OP = – 2 ( 7.75) + 23 = -15.5 + 23 = 7.75

Step-by-step explanation:

Answer for this question Sarah went on a 36 mile trip to a soccer game. On the way back, due to road construction she had to drive 18 miles per hour slower. This made the trip take 1 hour longer.   36 = 18 +18(a+1)How fast did she drive to the soccer game? let the returning speed be x mphgoing to game speed = x+18 Answer is 18 km/h while returning

Step-by-step explanation:    Distance = 36

1 hour more while returning

time return - time going = 1

36/x - 36/(x+18) = 1

LCD= x ( x + 18 )

multiply by LCD

36 ( x + 18 ) - 36 x = 1 x ( x + 18 )

36*18=

36 x + 648 - 18 x = 1x ^2 + 18 x

648 = 1 x^2 - 18 x

x^2 + 18 x -648 = 0

x^2 +36x-18x-648=0

x(x+36)-18(x+36)=0

(x-18)(x+36)=0

x=-36 or 18

x =18

18 km/h while returning

while going speed = 18+18 = 36 km/h

SuuuuMan deseres all the credits as someone deleted his first ever question in error and i was shocked to see as no diagram was needed there or here -see answer in this post instead- and have requested moderators get SuuuMan an appology ok as and while you both learn the any ways to interprete x and setting both amounts to 0 and or setting amounts to = each other to find the value of x