Explain how to evaluate a + b ÷ c, when a = 1 2/5, b = 2 2/5, and c = 3/4. You do not have to compute the values.

Answer:

x=6

Step-by-step explanation:

Let the number be x

Then 4 times a number divided by 3 is 5 more than that number divided by 2 gives the equation:

[tex] \frac{4x}{3} = \frac{x}{2} + 5[/tex]

Multiply through by the LCD, which is 6.

[tex] 6 \times \frac{4x}{3} = 6 \times \frac{x}{2} + 5 \times 6[/tex]

Cancel out to obtain:

[tex] 2 \times 4x =3 \times x + 30[/tex]

[tex]8x = 3x + 30[/tex]

Group similar terms

[tex]8x - 3x = 30[/tex]

Simplify the LHS

[tex]5x = 30[/tex]

Divide both sides by 5 to get:

[tex]x = 6[/tex]

Answer:

f(x) = 1/2x^2 – 4x + 5  (the third option)

Step-by-step explanation:

I looked it up on a graphing calculator.

The quadratic function that has a minimum located at (4, -3) is:

[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]

All the options are quadratic functions, so we need to find the one with a leading coefficient positive, which also has a vertex at (4, -3).

The 3 ones with positive leading coefficients are:

[tex]f(x) = (1/2)*x^2 + 4x -11[/tex]

[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]

[tex]f(x) = 2x^2 - 16x + 35[/tex]

The vertex of the first one is at:

[tex]x = -4/(2*1/2) = -4[/tex]

The x-value of the vertex must be x = 4, so we can discard this.

For the second quadratic function the x-value of the vertex is:

[tex]x = -(-4)/(2*1/2) = 4[/tex]

Then the y-value of the vertex is:

[tex]f(4) = (1/2)*4^2 - 4*4 + 5 = -3[/tex]

Then the vertex is at (4, -3), so this is the correct option.

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The area of a triangle is 1/2*base*height

So make your equation: 1/2*b*12=42

6*b=42

b=7

So the base is 7 inches long

Hope that helped!

3^15 = 14,348,907

Which means...

x^5 = 14,348,907

If we execute [tex]\sqrt[5]{14348907}[/tex] and do the same with x^5 we get...

x = 27

So the 5th power of 27 is equal to 3^15.

⭐ Answered by Hyperrspace (Ace) ⭐

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The fifth power of the number 27 is equal to 3¹⁵.

To find the fifth power of a number that is equal to 3¹⁵, we need to determine what number raised to the power of 5 gives us 3¹⁵.

Let's call the number we are looking for "x." So, we need to solve the equation:

x⁵ = 3¹⁵

To find x, we can take the fifth root of both sides of the equation:

x = (3¹⁵[tex])^{(1/5)[/tex]

x = 3³

x = 27

This means that if we raise 27 to the power of 5 (27⁵), we will get 3¹⁵ (3 raised to the power of 15).

In conclusion, the number we are looking for is 27, as 27^5 is equal to 3¹⁵.

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Answer:

[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]

Step-by-step explanation:

First we need to compute the side length as a function of h

So x be the side length of the right isosceles triangle, in Pythagorean formula we have

[tex]x^2 + x^2 = h^2[/tex]

[tex]2x^2 = h^2[/tex]

[tex]x = \frac{h}{\sqrt{2}}[/tex]

The cost for the legs is

[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]

The cost for the hypotenuse is

[tex]C_h = 16h[/tex]

So the total cost in term of h is

[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]

The total cost C of construction as a function of h is C =  16 / h +  8√2 / h

The pen is in the shape of an isosceles right angle. This means one of the

angle is 90 degrees and 2 sides of the triangle are equal and the base angles

are equal too.

Using pythagora's theorem

Therefore,

x² + x² = h²

2x² = h²

x² = h² / 2

x = √h²/ √2 = h/√2

cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h

cost of the hypotenuse = 16 / h

Total cost = 16 / h +  8√2 / h

C =  16 / h +  8√2 / h

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Answer:

L = B + 4

Step-by-step explanation:

Let the breadth be B

Let the length be L

But from the question, we were told that the length is 4 more than the breadth. This is expressed as

L = B + 4

Answer:

C.

Step-by-step explanation:

2 times 2 times 2 times 5 = 40

The prime factorization of 40 is 2 times 2 times 2 times 5, which can be written as 2^3 * 5. So, option C, "2 times 2 times 2 times 5," is the correct prime factorization of 40.

The prime factorization of the number 40 is 2^3 * 5. To arrive at this factorization, we break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, 2. Since 40 is even, it can be divided by 2 evenly, resulting in 20. We continue this process until we can no longer divide by 2, which leaves us with 20. Now, we try to divide 20 by the next smallest prime, which is also 2. This division gives us 10. Once again, we divide by 2, and we are left with 5. Since 5 is a prime number, we cannot further divide it. Therefore, we have prime factorized 40 as 2 * 2 * 2 * 5, which can be expressed as 2^3 * 5, where the exponent 3 indicates that we have three 2s multiplied together, and the 5 is the prime factor on its own.

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Make an x and y table, and pick any values to plug in for x in the equation.

I will use the numbers from -2 to 2

Now plug in the values you picked for x into the equation to find its y-value

x = -2

y = 3x - 1   Plug in -2 for x

y = 3(-2) - 1

y = -6 - 1

y = -7

x = -1

y = 3x - 1

y = 3(-1) - 1

y = -3 - 1

y = -4                

Do the same for the rest of the numbers, and graph each point and draw a line connecting them.

Answer:

2x + 13 = 3x - 2

Step-by-step explanation:

This should be the answer

Answer:

its 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

72% of the students in math 6 = 324

let x represent the students in math 6

turn ur percent to a decimal

0.72x = 324

x = 324 / 0.72

x = 450 students <===

Answer:

its 233.28

Step-by-step explanation:

cuz i took a test and this was the right answer

Answer:

10%

Step-by-step explanation:

The original price of the ticket was $85 and she had a discount of 20%. Since the website applied a 10% service fee to her discount price, then Lisa'a ticket would be 10% less than the original price.

Answer:

A - 110

Step-by-step explanation:

So if it is 6% increase you would times the number by 1.06. So you would do this like 5 times:

1,625 x 1.06 = 1722.5

1722.5 x 1.06 = 1825.85

1825.85 x 1.06 = 1935,401

1935.401 x 1.06 = 2051,52506

2051.52506 x 1.06 = 2174,6165636

Now you have the total number of bottles after 5 years, you would find the increase which is 2174.6165636 - 1,625 ≈ 550. 550 / 5 = 110

A

⭐ Answered by Foxzy0⭐

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The average increase in bottles purchased per year over that time is c) 110 bottles.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is generally denoted using the percent sign ''%''.

Now it is given that,

Number of bottles purchased per year, a = 1,625

Percentage increase per year, r = 6% = 0.06

Total time period, n = 5 years

Since, the equation of a exponential growth function is given as,

y = a(1 +r)ⁿ

⇒ y = 1625(1 +0.06)⁵

⇒ y = 1625(1.06)⁵

⇒ y = 1625*1.338

⇒ y = 2,175

Therefore, average increase in bottles purchased per year over that time   = (2175 - 1625) / 5

= 550 / 5

= 110 bottles

Thus, the average increase in bottles purchased per year over that time is c) 110 bottles.

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The x-Intercepts of the line 2x - 4y = -12 is -6 and the y-intercept is 3.

To identify the x and y intercepts of the line, we set one variable to zero and solve the equation for the other variable.

For the x-intercept, we set y=0 and solve for x in the equation: 2x - 4(0) = -12, hence x = -6.

For the y-intercept, set x=0 and solve for y in the equation: 2(0) - 4y = -12, hence y = 3.

Therefore, the x-intercept is -6 and the y-intercept is 3

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Answer:

The value of the expression is 4.

Step-by-step explanation:

Consider the provided information.

We have given that:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]

Now we need to find the value of:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =?[/tex]

Consider the provided fact:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]

Multiply [tex]\frac{1}{5}[/tex] both sides.

[tex]\dfrac{1}{5}\times \dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]

[tex]\dfrac{1\times2\dfrac{1}{2} }{5\times\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =4[/tex]

Hence, the value of the expression is 4.

Answer:

v = 13

b = 23

Step-by-step explanation:

To solve this system of equations, we can negate one equation and add it to other to cancel out one variable.

Looking at v and b, the coefficients are 6, 4 and 13, 9, respectively.

It would be easier to use the LCM of 6 and 4

[tex]E_1 : 6v + 13b = 377\\E_2: 4v + 9b = 259\\\\4E_1 + (- 6)E_2:\\24v + 52b = 1508\\-24v - 54b=-1554\\\\0v -2b = -46\\-2b = -46\\b = 23\\\\4v + 9(23) = 259\\4v + 207 = 259\\4v = 52\\v = 13\\\\6(13) + 13(23)\\78 + 299\\377[/tex]

Step-by-step explanation:

Given,

The zeros of the polynomial are - 4, - 2, 1 and 4

To find, the polynomial equation = ?

We know that,

The polynomial equation = (x - A)(x - B)(x - C)(x - D)

= (x + 4)(x + 2)(x - 1)(x - 4)

= [(x + 4)(x - 4)] [(x + 2)(x - 1)]

= ([tex]x^{2}-16[/tex])([tex]x^2-x+2x-2[/tex])

=  ([tex]x^{2}-16[/tex])([tex]x^2+x-2[/tex])

= [tex]x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32[/tex]

= [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex]

Thus, the required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].

The output y is [tex]y=22[/tex]

Explanation:

The expression is [tex]y=5 x-3[/tex]

We need to determine the output y, when the value of input is x is 5.

That is, substituting [tex]x=5[/tex] in [tex]y=5 x-3[/tex], we get,

[tex]y=5(5)-3[/tex]

Multiplying the value within the bracket, we have,

[tex]y=25-3[/tex]

Subtracting the terms, we get,

[tex]y=22[/tex]

Thus, the value of output y is [tex]y=22[/tex]

Answer:

60

Step-by-step explanation:

15*4=60

The 15x when x = 5 will be 60.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

x = 4

Now,

15x is nothing but we need to multiply 15 with x

So,

15x = 15 × 4

15x = 60

Hence,The 15x when x = 5 will be 60.

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The answer is in the graph picture

The zeros of the function f(x) = (x - 1)(x - 7) are 1 and 7

The function is given as:

f(x) = (x - 1)(x - 7)

Set the function to 0.

So, we have:

f(x) = (x - 1)(x - 7) = 0

This gives

(x - 1)(x - 7) = 0

Split

(x - 1) = 0 or (x - 7) = 0

Remove brackets

x - 1 = 0 or x - 7 = 0

Solve for x

x = 1 or x = 7

Hence, the zeros of the function are 1 and 7

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Answer:    ✔ 281.25

Step-by-step explanation:

Answer:

281.25

Step-by-step explanation:

It is correct E d g e n u i t y

Answer: C 25/9

Step-by-step explanation:

Add in Morse code is :

.—..-..

There are 8 total symbols, 5 of them are dots.

The fraction would be 5/8 are dots.

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The Morse Code for Add is:

.__.._..

There are 5 dots and 3 dashes, so there are 8 figures in total. The fraction is 5 divided by the total number of symbols, which is 8. So the answer is [tex]\frac{5}{8}[/tex]

Answer:

Result = 12

Step-by-step explanation:

Fractions

Fractions are the general expression for rational numbers, defined as

[tex]\displaystyle \frac{a}{b}, \ b\neq 0[/tex]

Where a and b are integer numbers. Some operations with fractions have special rules than those with integers. The product of two or more fractions is

[tex]\displaystyle \frac{x}{y}\cdot \frac{w}{z}\cdot \frac{r}{s}=\frac{xwr}{yzs}[/tex]

We'll use that rule to operate the numbers given in the question:

[tex]\displaystyle 56\cdot \frac{9}{14}\cdot \frac{1}{3}=\frac{504}{42}[/tex]

The fraction can be simplified to an integer by dividing it

[tex]\displaystyle \frac{504}{42}=12[/tex]

Answer:The Answer is 12.

Step-by-step explanation:

When going through a step by step problem you always  wanna go from the left to right.(Unless you have parentheses)

56*9=504

504/14=36

36*1/3=12

There for, you answer is 12.

Hope this helped you. Remember Stay Positive!

Answer:

X-Intercept is -45. (Answer would be (-45,0))

Step-by-step explanation:

You can use Desmos which is a graphing calculator to figure out the answer. Plug the equation into Desmos and it will show you a line and where the x-intercept is. And boom, you got your answer.

Answer:

C. 11

Step-by-step explanation:

First, find the value of "x" by solving the first equation. You need to move every other number to the other side of "x". When you move a number, you have to do the opposite operation to both sides.

5x + 6 = 10     The opposite of +6 is -6.

5x + 6 - 6 = 10 - 6     Subtract 6 from both sides

5x = 10 - 6       The "6" on the left cancelled out. Simplify the right side

5x = 4          The opposite of multiply by 5 is divide by 5

5x/5 = 4/5           Divide both sides by 5

x = 4/5           Value of "x"

Substitute the value of "x", which is 4/5, in the "x" for the second equation.

10x + 3

= 10(4/5) + 3             Multiply 10 and 4/5

= [tex]\frac{10*4}{5}[/tex] + 3        Combine into the numerator

= [tex]\frac{40}{5}[/tex] + 3         Divide the top by the bottom

= 8 + 3             Add

= 11                  Value of second equation

Therefore the value of 10x + 3 is 11.

Answer: 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

4x4 is 4 groups of four.

You can visibly show this by doing four lines of four dots.

••••

••••

••••

••••

count those dots, you get 16

Answer:

Step-by-step explanation:

First, start off by solving for the slope using this formula:

[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Then, plug in the values: [tex]\frac{0-(-3)}{7.5-0}[/tex]

Solve the equation: [tex]\frac{3}{7.5}[/tex]

That's your slope.

Then plug in one of the coordinates given in the problem for x and y and solve this equation:

y=[tex]\frac{3}{7.5}[/tex]x+b

Hope that helped!!! :)