The foot of a ladder is placed 7 meters from a wall. If the top of the ladder rests 9 meters up on the wall, how long is the ladder?

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

Answer:

x = 19

Step-by-step explanation:

3(x - 9) = 30

Divide both sides by 3 to isolate the binomial.

x - 9 = 10

Add 9 to both sides to isolate x.

x = 19

Check your answer by plugging x = 19 back into the equation.

3(x - 9) = 30

3(19 - 9) = 30

Subtract.

3(10) = 30

Multiply.

30 = 30

Your answer is correct.

Hope this helps!

Answer:

x = 19

Step-by-step explanation:

First, we must distribute 3(x-9) = 30

[tex]3x - 27 = 30[/tex]

Now, that we've distributed this equation, we can proceed.

Secondly, since there is a subtraction sign in front of 27, we must do the opposite, addition.

Add 27 to 27 and 30:

[tex]3x - 27 = 30[/tex]

[tex]-27 + 27 = 0[/tex]

[tex]30 + 27 = 57[/tex]

Furthermore, -27 + 27 is 0, so it cancels itself out. Also, since we added 30 and 27 and got 57, replace 30 with 57.

[tex]3x = 57[/tex]

Lastly, divide 57 by the number in front of coefficient, 3.

[tex]57/3=19[/tex]

Therefore, [tex]x=19.[/tex]

**TO MAKE THIS MORE UNDERSTANDING, THIS IS HOW YOUR EQUATION SHOULD LOOK WHILE SOLVING**

Answer:

is it 21 or 2 whole?

Step-by-step explanation:

plz clarify the question first i am discombobulated

Answer:

18

Step-by-step explanation:

20-2=18

please brainiest

its 18

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bye! <3

when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.

As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.

Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.

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identification of the expression 4x- 2y + 6 = 2x is

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, a linear expression 4x-2y + 6 = 2x

Coefficient:

Coefficients are the numbers by which the variables in an equation are multiplied

Thus, the Coefficient terms for this equation = 4x, -2y, 2x

Constants:

the constant is the part of the expression that does not vary with the value of x and y.

Thus, constant terms for this equation = 6

variable terms:

These are the terms that vary at the different values of x and y.

Thus, variable terms for this equation = 4x, -2y

Like terms:

Terms that have identical variable parts (same variable(s) and same exponent(s))

thus, Like terms for this expression = 4x, 2x

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The time that it will take for the spaceships to meet is given as follows:

3 hours.

Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The positive direction is considered from the first spaceship towards the second spaceship.

The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:

710,000 - 110,000 = 600,000 km.

Then the functions are given as follows:

They will meet when:

x1(t) = x2(t).

Hence:

110t = 600 - 90t

200t = 600

t = 600/200

t = 3 hours.

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The time that it will take for the spaceships to meet is given as follows:

3 hours.

How to model the situation?

Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The slope m represents the velocity.

The intercept b represents the initial position.

The positive direction is considered from the first spaceship towards the second spaceship.

The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:

710,000 - 110,000 = 600,000 km.

Then the functions are given as follows:

x1(t) = 110t.

x2(t) = 600 - 90t. (negative as they travel in opposite direction).

They will meet when:

x1(t) = x2(t).

Hence:

110t = 600 - 90t

200t = 600

t = 600/200

t = 3 hours.

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Answer:

C

Step-by-step explanation:

hopes it helps you!

Answer:

Flipping a coin

Step-by-step explanation:

It is the best answer, because the other choices do not represent a 50% chance. Rolling a 6-sided number cube would be good if you had 6 things, spinning a spinner would be ideal for 3, and using a number generator would be good for 9 things.

Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.

The amount of federal income tax deducted from the weekly cheque is:

6.2% from Social Security plus 1.45% from Medicare.

= 7.5 percent of the weekly gross salary.

The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:

= 0.0765 × 683

= $52.25

Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.

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Answer:

A

Step-by-step explanation:

When you distribute what is in the parentheses you get 2.5m + 7m=9.5m, and then you add that to m aka 1m, which is 10.5m and they both end with -2.

Answer:

f(x)=11

g(x)=8

Step-by-step explanation:

f(x)=(2)+9=11

g(x)=4(2)=8

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Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

given

Rewrite the above expression as:

[tex]2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }[/tex]

Evaluate the cube roots

[tex]2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }[/tex]

Evaluate the differences

-7ab(2√3ab²)

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

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The gross monthly earnings for February will be $1012.2

It should be noted that gross monthly earnings simply means the earnings that an individual makes for a particular month.

In this case, Dave earns $200 per week plus 4.1 commission. He sold $5175.50 in the month of February. His gross monthly earnings for February will be:

= ($200 × 4) + (4.1% × $5175.50)

= $1012.2

Therefore, $1012.2 will be the earnings.

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Answer:

3

Step-by-step explanation:

It equal .4, which is rational because it doesn't repeat.

Answer:

3

Step-by-step explanation:

Answer:

2/9 or 22.22% and 4/9 or 44.44%

Step-by-step explanation:

6+4+8=18   4/18=2/9   8/18=4/9

Answer:

1 1/2

Step-by-step explanation:

7-5 1/2 is 1 1/2 so 1 1/2+5 1/2 -7

Answer:

(a)

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]

(b)

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {0} &{0.1}&{0.03} & {0.01} & {0.14} & {1} &{0.08}&{0.20} & {0.06} &{0.34}& {2} &{0.05}&{0.14} & {0.33} &{0.52 } \ \end{array}[/tex]

Solving (a): Find PMF of y if x = 1

This implies that, we consider the dataset of the row where x = 1 i.e.

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {1} &{0.08}&{0.20} & {0.06} &{0.34} \ \end{array}[/tex]

The PMF of y given x is calculated using:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{P(x)}[/tex]

When x = 1

[tex]P(x) = 0.34[/tex] --- the sum of the rows

So, we have:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.34}[/tex]

For i = 0 to 2, we have:

[tex]i = 0[/tex]

[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=0|x)=\frac{0.08}{0.34}[/tex]

[tex]P(y=0|x)=0.2353[/tex]

[tex]i =1[/tex]

[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=1|x)=\frac{0.20}{0.34}[/tex]

[tex]P(y=1|x)=0.5882[/tex]

[tex]i = 2[/tex]

[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=2|x)=\frac{0.06}{0.34}[/tex]

[tex]P(y=2|x)=0.1765[/tex]

So, the PMF of y given that x = 1 is:

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]

Solving (b): The interpretation of (b) is to find the PMF of y if x = 2

This implies that, we consider the dataset of the row where x = 2 i.e.

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {2} &{0.05}&{0.14} & {0.33} &{0.52 }\ \end{array}[/tex]

When [tex]x = 2[/tex]

[tex]P(x) = 0.52[/tex]

So, we have:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.52}[/tex]

For i = 0 to 2, we have:

[tex]i = 0[/tex]

[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=0|x)=\frac{0.05}{0.52}[/tex]

[tex]P(y=0|x)=0.0962\\[/tex]

[tex]i =1[/tex]

[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=1|x)=\frac{0.14}{0.52}[/tex]

[tex]P(y=1|x)=0.2692[/tex]

[tex]i = 2[/tex]

[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=2|x)=\frac{0.33}{0.52}[/tex]

[tex]P(y=2|x)=0.6346[/tex]

[tex]P(y=0|x)=0.0962\\[/tex]

[tex]P(y=1|x)=0.2692[/tex]

[tex]P(y=2|x)=0.6346[/tex]

So, the PMF of y given that x = 1 is:

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]

Answer:

x = 5.9

Step-by-step explanation:

Reference angle = 26°

Opposite = x

Adjacent = 12

Apply TO A:

Tan 26 = Opp/Adj

Substitute

Tan 26 = x/12

Multiply both sides by 12

12*Tan 26 = x

5.85279107 = x

x = 5.9 (nearest tenth)

Answer:

7 Can I have brainliest

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Frequency means the number of times the number appears.

2 appears the most since its frequency is the largest. 2 appeared 5 times.

Answer:

To find the mode, you have to find the number that appears the most.

Here, I see that 2 appears the most.

2 is the mode.

Step-by-step explanation:

There are a lot of lazy students.

I hope you are not one of them!

Answer:

3500 = 20x + 60y

Step-by-step explanation:

Its just the answer

Answer:

b = 4

Step-by-step explanation:

[tex]2(-2b) + 2b = -8[/tex]

[tex]=> -4b + 2b = -8[/tex]

[tex]=> -2b = -8[/tex]

[tex]=> \frac{-2b}{-2} = \frac{-8}{-2}[/tex]

[tex]=> b = 4[/tex]

Answer:

Why is there no general symmetry?

Does it always take  six points or six pieces of information to describe a quintic function?

Why are the roots not solvable by radicals?

I really don't know the "why", I just steer away from them when I can.