What is the length of the long leg in the right triangle shown below? O A. 6 B. 3 C. 643 D. 6√2 30* N 60°​

The real root of the number √0.49 is given by 0.7.

We are given the expression:

√0.49

We need to find the root of the number.
For this, we will make the factors of the number and then solve the expression accordingly.

First, we know that 0.49 can also be written as 49 / 100

Now, we also know that:

49 = 7 × 7 and 100 = 10 × 10

So, the square root of 49 will be 7 and 100 will be 10.

So, we get the root of the number as:

√0.49 = 7 / 10

√0.49 = 0.7

Therefore, the real root of the number √0.49 is given by 0.7.

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Answer:

8x^2 + 13.

Step-by-step explanation:

(f o g)(x) is found by replacing the x in f(x) by g(x).

= 4(2x^2 + 3) + 1

= 8x^2 + 12 + 1

= 8x^2 + 13.

The numbers are 88, 90 and 92. So the first number in this sequence is 88.

Given that

The sum of 3 consecutive even numbers is 270 .

What is consecutive numbers?

      Let the numbers be n, n+2, and n+4.

      n+(n+2)+(n+4) = 270

      3n+6 = 270

      3n = 264

      n = 264/3

      n=88

First number = x = 88

Second number = x + 2 = 88 + 2 = 90

Third number = x + 4 = 88 + 4 = 92

Therefore, the first number is 88.

Hence, the numbers are 88, 90 and 92.

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The value of x for the equation is 8 to roundoff the nearest ten-thousand  = 8.0000.

A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). For instance, the base ten logarithms of 100 equals 2, because ten raised towards the power of two equals 100: log 100 = 2.

Solving for x  the equation  log₂4 x=5.

log₂4 x=5

witting this as :

4x = 2⁵

4x  = 32

x = 32/4

x = 8

The value of x for the equation is 8 to roundoff the nearest ten-thousand  = 8.0000

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Answer:

-429

Step-by-step explanation:

Answer:

2751

Step-by-step explanation:

2+5 times 12 times 54 minus 10 minus 475 minus 6

2+3240-10-475-6=2751

Answer:

8x+8

Step-by-step explanation:

perimeter = lengths of all sides added up

we want all sides to add up to 6x + 4

so far, we have 2x-7 and -4x + 3

side 1 + side 2 + side 3 = perimeter = 6x + 4

2x - 7 + (-4x + 3) + side 3 = 6x + 4

-2x -4 + side 3 = 6x + 4

add (2x+4) to both sides to isolate side 3

side 3 = 8x + 8

Answer:

3/8 is a proper fraction which means it can't be written as a mixed number

Step-by-step explanation:

If the numerator is bigger than the denominator then you can convert it to a mixed number.

Answer:

3/8 is equal to 0.375

i dont think this can be turned into a mixed number becuase the fraction isn't over 8

example: 18/8 can be changed into the mixed number 2 3/8

Step-by-step explanation:

The average weekly change in your running time bases on the information will be 4 seconds.

It should be noted that the mean simply means the average of the numbers that are given.

It should be noted that in this case, the person approve your time running a course by 5 seconds in week one, by three seconds in week two in by four seconds in week three.

Therefore, the average weekly change in your running time will be:

= Total seconds / Number of weeks

= (5 + 3 + 4) / 3

= 12 / 3.

= 4 seconds

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If the equation of the parent graph, shown in the reference picture attached hereby, is [f(x) = |x|], then the equation of the translated graph will be [f(x) = (|x-2| + 1)].

Along with the question statement, we are provided with a reference attachment, which is a grid, consisting of two graphs, and the equation of the parent graph is [f(x) = |x|].

We are required to calculate the equation of the other graph, which is a translated version of the parent graph.

From the reference grid, we can clearly see that, the vertex of the parent graph is at the origin (0, 0) while that of the translated graph is at (-2, 1), i.e., the vertex translated by 2 units to the left along the x-axis and then, 1 unit upwards along the y-axis. And this translation will be followed by every point of the daughter graph.

Hence, the equation of the translated graph will be [f(x) = (|x-2| + 1)].

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Solve for x by factoring. Obtain the roots of the expression. Solve the quadratic form and obtain the complex solutions. Equate the expression to zero and divide by the common factor 4, and factor out x.

4x^3-8x^2+16x

4x^3-8x^2+16x = 0

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

x =0

x^2-2x+4 = 0

by quadratic formula,

x =  (-b±√(b²-4ac))/(2a)

x= (--2±√((-2)²-4(1x4))/(2)

x =  (2±√(4-16))/(2)

x =  (2±√-12)/(2)

Let √-12 = i , a complex root

x =   (2±i)/(2)

x =  (2+i)/(2)

x =  (2-i)/(2)

Thus,

x = 0

x =  (2+i)/(2)

x =  (2-i)/(2)

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The value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10

The equation is given as:

4 x 3 7/10 = 12 7/10

Remove the result

So, we have

4 x 3 7/10

Express 3 7/10 as an improper fraction

So, we have

4 x 37/10 = 4 x 37/10

Evaluate the product of 4 and 37

So, we have

4 x 37/10 = 148/10

Evaluate the quotient of 148 and 10

So, we have

4 x 37/10 = 14 8/10

Hence, the value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10

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The values of the missing sides of the similar shapes are:

x = 7

y = 10

z = 20

Similar shapes have side lengths whose ratios are the same, or have proportional side lengths.

Use the following ratios to find the missing lengths of the two similar shapes in the given diagram:

35/14 = 17.5/x

Cross multiply

(35)(x) = (17.5)(14)

35x = 245

Divide both sides by 35

35x/35 = 245/35

x = 7

35/14 = 25/y

Cross multiply

(35)(y) = (25)(14)

35y = 350

35y/35 = 350/35

y = 10

35/14 = z/8

(35)(8) = 14z

280 = 14z

z = 280/14

z = 20

Therefore, the values of the missing sides of the similar shapes are:

x = 7

y = 10

z = 20

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Answer:

(-∞, 4]

Step-by-step explanation:

Domain: x-axis

(-∞, 4]

Graph type: √-x

I hope this helps!

The given expression can be written in its simplest form by using the rule of negative exponent.

As the negative exponent is applied to the second term, which also has a power, we will first multiply the powers. As we know that (x^n)^m=x^nm, hence,

(x^2/3)^-1=x^2/3*-1=x^-2/3

Now the expression will become 5x^-2/3

Now solving the second term for the negative exponent, the rule of negative exponent states that when a base term has a negative exponent, the negative sign can be solved by inversing the base term. We know that x^-a=1/x^a, therefore

5x^-2/3=5/x^2/3

The simplest form of the expression is 5(x²/₃)⁻¹=5/x^2/3

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Answer:

45 feet

Step-by-step explanation:

Set up Ratios

1/2 in/5 ft = 4 1/2 in/x

Solve for x by cross-multiplying:

[tex]\frac{1/2}{5}[/tex] times [tex]\frac{4 1/2}{x}[/tex]

4 1/2 times 5 = 22 1/2

1/2 times x = 1/2x

22 1/2 = 1/2x

45 = X

Therefore the actual length of the bus is 45 feet.

Hope it helps :)

The equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

A bisector divides segments or angles into two equal halves.

Given the data in the question;

Since AC is bisected at point E and we know that a bisector divides segments or angles into two equal halves.

AC = 2 × AE

Hence

40 = 2( 4x + 2 )

Rewrite the equation such that x will be at the left side.

2( 4x + 2 ) = 40

To solve for x, remove the parenthesis using distributive property.

2( 4x + 2 ) = 40

2×4x + 2×2 = 40

Rewrite the equation such that x will be at the left side.

8x + 4 = 40

Subtract 4 from both sides.

8x + 4 - 4 = 40 - 4

8x = 36

Divide both sides by 8

8x/8 = 36/8

x = 36/8

x = 4.5

Therefore, the equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

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The profit for 33 sales is $145

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

f(x) = 5x is the  revenue (in dollars) for selling x hamburgers.

profit = $20 less than revenue

So, the equation for the profit is

profit = 5x - 20

Now, if sales is 33 i.e., x=33 then profit will be

profit = 5(33) - 20

profit = 165-20

profit = $145

Hence, the profit is $145

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Answer:

1. -8/11

2. -1 3/7

Step-by-step explanation(Q1):

Using order of operations, start with parentheses and work with exponents second. Then, M/D/A/S.

[tex]5-3\\=2\\=2^{3}\\=\boxed{8}\\3^2\\=9\\=1+9-21\\1+9\\=10\\=10-21\\=\boxed{-11}\\=\frac{8}{-11}[/tex]

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

Step-by-step explanation(Q2):

Given x = 3, y = -2

[tex]4\left(3\right)\\=12\\=12+\left(-2\right)\\12+\left(-2\right)\\=12-2\\=10\\\downarrow\\2\left(-2\right)\\=-4\\=-4-3\\=\left(-4\right)-3\\=-7\\=\frac{10}{-7}\\=-\frac{10}{7}\\\\\bold{Long~Division}\\7 \div 10 = 1\\1 \times 7 = 7\\7 - 10 = 3\\= 1,R3\\\\\frac{10}{7}\\=1\frac{3}{7}\\=-1\frac{3}{7}[/tex]

Answer:

(a + b) = 9

Step-by-step explanation:

The a² - b² formula is also known as "the difference of squares formula"

It can be decomposed as follows:
a² - b²  = (a - b)(a + b)

Since we are given a + b = 5 and a² - b² = 45

we have

45 = 5 (a + b)

Dividing by 5 both sides
45/5 = (a + b)

9 = (a + b)

or,

(a + b) = 9

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit. If Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. Then the original investment is $1500.

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

Percent to decimal 4%=4/100=0.04

A=P(1+rt)

where A is the final amount

P is initial principle balance, t is time and r rate of interest.

1560=P(1+0.04)

1560=1.04P

P=1560/1.04

P=1500

Therefore $1500 is originally invested.

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The statement employs that Because b > 1, the function shows  exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.

Exponential growth is the process by which quantity rises over time. It happens when the instantaneous rate of alteration of a quantity with regard to time is proportionate to the amount itself.

As a result, the exponential growth formula is: x(t) = 10,000 * (1 + 0.05)t = 10,000 * 1.05t. Here is the amount of years that have gone since 2019. In our situation, t = 11 should be used for the year 2030 because that is the lot of years between 2030 as well as the initial year 2019.

y=0.1(10)ˣ

y = 0.1(10)⁰

y = 0.1(1)

y = 0.1

Because b > 1, the function shows exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.

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Answer:

7 = b.

8 = a.

Answer:

x=42

y=12

Step-by-step explanation:

If three integers have a mean of 9, a median of 12, and a range of 13, then the three integers are 1, 12, and 14.

As the median is the value that's exactly in the center of a set of values, one of the three integers is 12.

Considering the first and third integers to be x and y, the range can be given as

x - y = 13

x = 13 + y

As mean can be given as,

x + 12 + y / 3 = 9

Putting x = 13 + y in this equation,

13 + y + 12 + y / 3 = 9

25 + 2y = 9 × 3

25 + 2y = 27

2y = 27 - 25

2y = 2

y = 2/2

y = 1

As,

x = 13 + y

x = 13 + 1

x = 14

Hence the three integers are calculated to be 1, 12, and 14.

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Just by adding the second row to the first one in the matrix, we can see that the solution of the system of equations is x = 0.5 and y = 20.

Here we have the system of equations:

300x - y = 130

200x + y = 120

And we want to solve it using a matrix equation. Remember that we could add the two rows, subtract them, etc to remove one of the variables.

Here is really simple to see that if we add the two rows (or the two equations, depending on how you see the system) the variable y will be removed.

Then we can add the second row to the first one to get.

(300x + 200x) + (-y + y) = (130 + 120)

Now our matrix will look like:

500x + 0y = 250

200x + y = 120

With the first row we can find the value of x, it just is:

x = 250/500 = 0.5

And with taht we can find the value of y:

200*0.5 + y = 120

100 + y = 120

y = 120 - 100 = 20

Just by adding two rows, we can see that the solution of the system of equations is x = 0.5 and y = 20.

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The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.

A fraction is a non- whole number that consists of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.

When Kyle finishes building the shed, he would have finished building 1 of the shed. In order to determine the amount of shed Kyle needs to build in order to build one shed, divide 1 by 5/8.

1 ÷ 5/8

= 1 x 8/5 = 8/5

The amount of shed that Jack will have built when Kyle finishes the shed is:

8/5 x 1/5 = 8/25

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Answer: 21

Step-by-step explanation: