There were 75 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 2/5 of the remaining runners dropped out. How many runners finished the race?

Answer:

[tex]x=0,\;x=\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{x}=\sqrt{3}x[/tex]

Square both sides:

[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]

[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]

[tex]\implies x=3x^2[/tex]

Subtract x from both sides:

[tex]\implies x-x=3x^2-x[/tex]

[tex]\implies 0=3x^2-x[/tex]

[tex]\implies 3x^2-x=0[/tex]

Factor out the common term x:

[tex]\implies x(3x-1)=0[/tex]

Apply the zero-product property:

[tex]\implies x=0[/tex]

[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]

Answer:

[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]

Step-by-step explanation:

The equation given is,

→ √x = √3x

Now the value of x will be,

→ √x = √3x

→ x = (√3x)²

→ x = 3x²

→ 3x² = x

→ 3x² - x = 0

→ (3x - 1)(x) = 0

→ 3x - 1 = 0 || → x = 0

→ 3x = 0 + 1 || → [ x = 0 ]

→ 3x = 1 ||

→ [ x = 1/3 ] ||

These are the values of x.

The reflection of (-3, 2) over the y-axis is (-3, -2).

The reflection of a point (x, y) over the y-axis is (x, -y).

Therefore, the reflection of (-3, 2) over the y-axis is (-3, -2).

To calculate the reflection of (-3, 2) over the y-axis, we first use the formula (x, -y).

In this case, x = -3 and y = 2, so the reflection of (-3, 2) over the y-axis is (-3, -2).

We can also calculate the reflection of (-3, 2) over the y-axis using the distance formula.

The distance formula  is d = √(x2-x1)2 + (y2-y1)2

In this case, x1 = -3, x2 = 0, y1 = 2, and y2 = 0.

Therefore, the distance d = √(02-(-3)2 + (02-2)2 = √(9 + 4) = √13

The reflection of (-3, 2) over the y-axis is (-3, -2). This can be verified using the distance formula.

d = √(x2-x1)2 + (y2-y1)2 = √(-3-0)2 + (-2-0)2 = √(9+4) = √13

The distance d is equal to the distance between (-3, 2) and (-3, -2). Hence, the reflection of (-3, 2) over the y-axis is (-3, -2).

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The box has 18 glazed donut hole that Chad bought.

The percentage of glazed donut holes = 60%

The percentage of powdered sugar donut hole = (100 - 60) % = 40%

Let us consider the total number of donut hole in the box bought by Chad to be 'x'

Number of powdered sugar donut hole = 12

Hence, we can say that the number of powdered sugar donut hole in the box Chad bought is:

(40% of x) = 12

Therefore, x = (12 x 100) / 40 = 30

Since the total number of donut hole in the box = 30

The number of glazed donut hole = 30 - 12 = 18

Thus, the box that Chad bought had 18 glazed donut hole.

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An equation of the line that passes through the point (6, 0) and had a slope of -5/6 is y = -5x/6 + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line is given by;

y - y₁ = m(x - x₁)

y - 0 = -5/6(x - 6)

y = -5x/6 + 5

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The correct graph is the third one: graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2.

News grapher using a function with inputs and outputs to depict a function. A function is a connection between two variables in which the input determines the output. In a graph, the y-axis shows the output, while the x-axis shows the input.

An unweighted, undirected graph with no graph loops or numerous edges is referred to as a simple graph (also known as a strict graph; Tutte 1998, p. 2; West 2000, p.

The line that connects the coordinates (x, y) = (-2, -3) and (y = 1/2x + 2) on this graph expresses the equation y = 1/2x + 2. (0, -2). When we enter those coordinates into the equation, we get the points on the graph, y = 1/2(-2) + 2 = -3 and y = 1/2(0) + 2 = 2.

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On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines

A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.

1) For this case, we have to define perpendicular lines:

Angle y = angle H

10x-27 - 2x + 29

x = 32

they are perpendicular

2) they are perpendicular

3)  they are intersecting lines

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Answer:

3x of 180=8x of 90

Use this equation

Answer:

x=6 z=73

Step-by-step explanation:

9x+53=6x+71

3x+53=71

3x=18

x=6

9(6)+53

54+53

107

107+z=180

z=73

Answer:

y = 120.8

Step-by-step explanation:

y − 58.8 = 62

Add 58.8 to both sides

y = 120.8

Let's check

120.8 - 58.8 = 62

62 = 62

So, y = 120.8 is the correct answer.

Answer:y= 120.8 I hope this helps

Step-by-step explanation:

y-58.8=62

Move the constant to the right-hand side and change its sign

Like this

Y=62+58.8

Then Add the numbers 62 and 58.8

Which will give you

Plus bring down your y

Your answer is y=120.8

The mirrors image of points (2, 3) under the origin is (-2, -3)

What is a mirror image?

A mirror image is a reflected duplicate of a seemingly identical item that is turned the other way in the plane perpendicular to the mirror surface. It manifests as an optical effect as a result of reflection off of materials like a mirror or water.

Here,

We have to find the mirror image of points (2, 3) under the origin.

We concluded that the mirror image of a point(2,3) is (-2,-3).

The coordinates of the origin are denoted by (0, 0). It means that at origin, x=0 and y=0.

Hence, the mirrors image of points (2, 3) under the origin is (-2, -3)

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Andrew would need to invest $61,300 for the account to reach $93,000.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

The equation to find final amount in compound interest is,

A = P (1 + r/n)^(n t)

Here A is the final amount, P is the initial amount, r is the rate of interest, n is the number of times compounding is done in a year, t is the time in years.

Given, A = $93,000

t = 19 years

r = 2.2% = 0.022

n = 4 (since compounding is quarterly)

93,000 = P [1 + (0.022/4)]^(4×19)

93,000 = P [1.0055]^(76)

93,000 = P (1.517)

P = 61,297.8516

To the nearest hundred dollars, P = $61,300

Hence the principal amount Andrew need to invest is $61,300.

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Angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts.

Given that lines AB and BC are parallel. Angles ABD and CBD are bisected by the dashed rays. Angle EBF is measured at 45 degrees because angle ABC is 90 degrees, line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

As a result, the angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

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To solve the equation (3.4)(6.7) using the standard algorithm, first multiply 3.4 and 6.7. Then, the result is 22.78.

The standard algorithm for multiplication is a step-by-step process that involves breaking down the numbers being multiplied into simpler parts, and then multiplying those parts together.

First, you would need to multiply the ones place of the first number (4) by the ones place of the second number (7), which would give you 28.

Next, you would need to multiply the ones place of the first number (4) by the tens place of the second number (6), which would give you 24.

Then, you would add the two products from steps 1 and 2 to get the result: 28 + 24 = 52.

Alternatively, you can use the distributive property of multiplication to simplify the problem.

(3.4)(6.7) = 3.46 + 3.40.7 = 22.8

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18-12=6, peter now has 6 dimes left after buying a drink. Since the number he has left is ONE HALF of the number of pennies he has. 6x2=12.

peter has 12 pennies. hoped that helped

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=5x[/tex]

To complete the function table, substitute each given value of x into the given function:

[tex]x=-4 \implies f(-4)=5(-4)=-20[/tex]

[tex]x=1 \implies f(1)=5(1)=5[/tex]

[tex]x=2 \implies f(2)=5(2)=10[/tex]

[tex]x=3 \implies f(3)=5(3)=15[/tex]

[tex]x=6 \implies f(6)=5(6)=30[/tex]

Completed table:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.

The value of 0 to the 0 exponents is undefined or indeterminate. The reason for this is that the mathematical definition of exponentiation states that any number to the power of 0 is equal to 1, except for 0, which is undefined. However, when we try to apply this rule to 0 to the power of 0, it creates a paradox.

If we assume that 0 to the 0 exponents is 1, then any number raised to the power of 0 would be equal to 1, which is not true. For example, 2 to the power of 0 is not equal to 1, but 2, so this assumption doesn't hold true.

On the other hand, if we assume that 0 to the 0 exponents is 0, then any number multiplied by 0 would be 0, which is not true either. For example, 2 multiplied by 0 is not equal to 2.

Therefore, 0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.

It's important to note that in some fields of mathematics such as limit, the value of 0 to the 0 exponent is defined as 1, but this is limited to the context of limit and not in general math.

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The exponential form of 8x8x8x8 is 2^(4*3) = 2^12.

Answer:

Step-by-step explanation:

Sara will win a medal if she keeps practicing gymnastics.

As per the given equation, the first plant is produce 2x+21 more items than second plant.

The term equation is known as a mathematical statement that shows that two mathematical expressions are equal.

Here we have given that the first plant produces 5x+14 items daily

And the second plant produces 3x-7 items daily

In order to find the number of items produced on first plant, then we have to calculate the differences between number of items by the two plants daily, then it can be written as by using the equations,

=> (5x+14) - (3x-7)

Now, we have to expand the equations, then we get

=> 5x+14 - 3x+7

=> 2x+21

Therefore, first plant produces 2x+21 more items daily than the second plant.

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Answer: There are 520 pounds of dog and cat food

Step-by-step explanation:

1. 14+12= 26

2. 26x20=520

Answer:

A) f(2) = 120, g(2) = 4.

B) f'(x) = 5x + 20

C) R - {-2}.

Step-by-step explanation:

A) Just apply given value and resolve:

[tex]f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4[/tex]

B) g(2) is 4, so just divide f(x) by 4:

[tex] \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20[/tex]

C)

[tex] \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} [/tex]

Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.

1. The value of F(2) = 120 and g(2) = 4.

2. The division is 5(x+4)

3. The domain is real number except -2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours.

1. F(2)= 20(2)+ 80= 40+ 80= 120

and, g(2)= 2 + 2 = 4

2. The division is

= F(x) / g(2)

= (20x + 80)/ (2+2)

= 20 (x+4) / 4

= 5 (x+4)

3. The domain of F(x) / g(x) is all real number except -2.

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4Answer:

Step-by-step explanation:

24 divided by 4 = 6

The maximum number of mangos that she could buy = 9

Let x represents the number of apples and y represents the number of mangos.

Given that:

the cost of each apple = $0.50

and the cost of each mango = $0.75

Camila has $7. 75 to spend.

This means, the total cost of apples and mangos together must be less than or equal to 7.75

So, we get an inequality,

0.50x + 0.75y ≤ 7.75

And she must buy no less than 11 apples and mangos altogether.

x + y ≥ 11

consider a system of equations.

0.50x + 0.75y = 7.75

x + y = 11

If we solve this system of equations we get x = 2 and y = 9

So, she can buy at most 9 mangos.

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Based on the questions, 13 guests are attending her best friend’s baby shower.

Firstly, we need to write down the numbers that are already stated in the question.

43 + 9 × х = 160

Secondly, move the x to continue counting.

9x = 160 – 43

Thirdly, calculate the numbers above.

9x = 117

Then, move the X to get the answer.

X = [tex]\frac{117}{9}[/tex]

Lastly, try to finish the division.

X = 13

In conclusion, the result shows that 13 guests attend Mrs. Wright’s best friend's baby shower.

The above question is about the algebraic word problem.

A word problem is a math question written in a short story scenario. Usually, it is a simple short story that is easy to understand.

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Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Here,

Given:

thus . We do factorization of given expression and

we come on a result

=>  3x - 9x²

=> 3x (1 -3x)

x=0 and x=1/3

Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

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The equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

What is percentage?

A number or ratio expressed as a fraction of 100 is known as a percentage in mathematics. Though the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. An amount that is a percentage is dimensionless and has no assigned measurement.

Given:

The current box holds 85 ounces, 25% less rice.

We have to find the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.

Let, y be the original amount of ounces of rice in a box.

The current box holds 85 ounces.

The 25% less than 85 ounces are 85*0.25.

So, the equation becomes y = 0.25*85.

Hence, the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

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Answer: 5x − 4 > 2x + 3

Step-by-step explanation:

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.