A 15 foot ladder leans against a house with the base of the ladder 4 feet from the house. How high, to the nearest foot, up the wall will the ladder reach? ​

For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}

The domain of a function are the independent variable of the function for which it exists,

For graphs, the domain exists on the x-axis of the curve or line on the xy plane.

For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}

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Answer:

[tex]2x - 3 + \frac{1}{x-1}[/tex]

Step-by-step explanation:

Attachment :)

We use long division

Answer:

-0.4 or [tex]\frac{-2}{ 5}[/tex]

Step-by-step explanation:

[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]

tan ( 2π-21.80)

but 2π = 360

Therefore our question becomes:

tan ( 360-21.80)=tan(338.2)= -0.4

Answer: 22.5

Step-by-step explanation:

[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]

Answer: 433.33 cm^3

Step-by-step explanation: Since the base is a square, volume = base area × height / 3

10*10 = 100,  100 * 13 = 1300, divided by 3 = 433.33 cm^3

Answer: 13.6

Step-by-step explanation: Use a theorem which exists s. then you use pythagoreom

The length of the segment indicated is 13.6

From the question, we have the following parameters that can be used in our computation:

The circle

Assuming that lines which appear to be tangent are tangent, we have

?² = (2 * 6)² + 6.4²

Evaluate

?² = 184.96

So, we have

? = 13.6

Hence, the length of the segment indicated is 13.6

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Answer:

42.8571

Step-by-step explanation:

We would need to divide 150 by 7 and multiply it by 2 to get the answer.

150/7 = 21.42857

21.42857*2 = 42.8571

The base is a square, so the area of the square is (10 cm)² = 100 cm²

To find the area of each triangle use the formula

base • height

10 cm • 9 cm = 90 cm²

now multiply by the number of triangles

90 cm • 4 = 360 cm²

Add the area of the square:

100 cm² + 360 cm² = 460 cm²

I hope it's correct

Answer:

SA = 280 cm²

Step-by-step explanation:

SA = area of base + area of 4 congruent triangles

     = 10² + (4 × [tex]\frac{1}{2}[/tex] × 10 × 9 )

     = 100 + (2 × 10 × 9)

     = 100 + 180

     = 280 cm²

The equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

Given the equation; 3[x + 3(4x – 5)] = 15x – 24

We expand and collect like terms

3[x + 3(4x – 5)] = 15x – 24

3( x + 12x - 15 ) = 15x - 24

3x + 36x - 45 = 15x - 24

We add the like terms on both sides

39x - 45 = 15x - 24

Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

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Answer: S=6√6 m².

Step-by-step explanation:

                                   Heron's formula

                            [tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],

a, b, c - sides of a triangle,

[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]

S - triangle area.

a=7 m,  b=5 m,  c=6 m.

[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]

Hence,

[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]

The perimeter of the trapezoid is 18 lines

Formula for perimeter of a trapezoid is given as;

Perimeter = a + b+ c + d

a = 1

b = 4

c = 4

d = 9

Perimeter = 1 + 4 + 4 + 9

Perimeter = 18

Thus, the perimeter of the trapezoid is 18 lines

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Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8

Step-by-step explanation:

There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.

We're given the centre and a point on the circumference: [tex](-2,1),(6,7)[/tex].

Find the distance between them using the distance equation:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the given points:

[tex]d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10[/tex]

Therefore, the radius of the circle is 10 units.

Multiply the radius by 2 to find the length of the diameter:

10 × 2

= 20

Therefore, the length of the diameter is 20 units.

20 units

The money paid to the secretary is $14000 and the money paid to mathematician is $22000.

A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.

Total money available for hiring = $36000

Let the money given to secretary = X

Money given to the mathematician = X + 8000

X + (X + 8000) = 36000

2X = 28000

X = 14000

Money given to secretary is $14000.

Money given to the mathematician is $22000.

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The ratio of the number of female attendants to the number of male attendants is 21/17

let

900 = 1200x + 800y / (x + y)

900x + 900y = 1200x + 800y

900x + 1200x = 800y + 900y

2100x = 1700y

x : y = 2100 / 1700

x : y = 21 ; 17

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Answer: The answer is (x+2)(x-4)(x-4)
Or as a short form you can write it as [tex](x+2) (x-4)^{2}[/tex]

Step-by-step explanation:

Answer is very lengthy but I am 100% sure that's the correct answer

Answer:

(x³ - 6x² + 32) = (x - 4)²(x + 2)

Step-by-step explanation:

(x³ - 6x² + 32)/(x - 4) =

           x² - 2x - 8

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

x - 4    |  x³ - 6x² + 0x + 32

             x³ - 4x²

            ----------

                  -2x² + 0x

                  -2x² + 8x

                 ----------------

                            -8x + 32

                            -8x + 32

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

                                       0

(x³ - 6x² + 32) = (x - 4)(x² - 2x - 8) = (x - 4)(x - 4)(x + 2) =

= (x - 4)²(x + 2)

Answer:

slope = - 1 , y- intercept = 2

Step-by-step explanation:

calculate the slope m using the slope formula

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

with ( x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

the y- intercept is the point on the y- axis where the line crosses , so

y- intercept = 2

Answer:

Slope: -1

Y-intercept: 2

Step-by-step explanation:

The line crosses the y-axis at 2. and the slope would be -1 since going down by one unit, and the line going down would mean that it is negative.

I hope it helps! Have a great day!

bren~

Answer:

8.9mm

Step-by-step explanation:

To solve for x, we use the Pythagoras theorem.

Pythagoras theorem states that in a right angled triangle, the square of the Hypotenus is equal to the sum of the square of the other two sides.

The Hypotenus is the longest side, or the side facing the right angle.

From the question above,

[tex]12.4 {}^{2} = \: 8.6 {}^{2} + x {}^{2} \\ \\ 153.76 \: = 73.96 \: + x {}^{2} \\ \\ collecting \: liketerms \\ \\ x { \: }^{2} = 153.76 - 73.93 \\ = 79.83 \\ \\ squareroot \: bothsides \\ \\ \sqrt{x {}^{2} } = \sqrt{79.83} \\ \\ x = 8.9[/tex]

The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.

The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.

Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.

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Answer:

Step-by-step explanation:

Obtuse, greater than 90 degrees

Answer:

It should be an obtuse angle

Step-by-step explanation:

Well, it just is

Answer:

Step-by-step explanation:

The value of w from the given equation is w=(x-3y+1)/3.

Given  an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.

The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.

x=3y+3w-1

Now take w at one end and all other variables in other end.

3w=x-3y+1

Now divide both sides by 3.

3w/3=(x-3y+1)/3

Now cancel 3 from numerator and denominator in left side.

w=(x-3y+1)/3

Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.

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44% is the answer

6 Article price at buying =5 Rs

1 Article price at buying = 5/6...(i)

5 Articles sold at Rs. 6

1 Articles cost at sold = 6/5 ....(ii)

% Gain=((6/5 - 5/6)/ 5/6) * 100

= 11/25 * 100 = 44%

Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.

The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.

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The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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Answer:

B, C and E

Step-by-step explanation:

Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

Given that NL and MK are diameters of circle J.  

 Size of arc MP is 62+90=152°, since MP is smaller than MLN

             then it is a minor arc. Hence the correct statement is:  

             M P is a minor arc and measures 152°.

Size of M L N is 360-62=298°, thus it is a major arc. Hence the

             correct statement is:

             MLN is  major arc and measures 298°.

Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

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Answer:

Complete the statements about circle J.

Arc M P is a

✔ minor arc

and measures

✔ 152

degrees.

Arc M L N is a

✔ major arc

and measures

✔ 298

degrees.

Step-by-step explanation:

edge 2022

Answer:

4

Step-by-step explanation:

Slope=rise/run

there is a increase of 4 in y for every increase of 1 in x

Step-by-step explanation:

Solution

verified

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Correct option is A)

In an isosceles right angled triangle, the two sides on the right angle are equal.

Let the equal sides be a.

Hence, hypotenuse of the isosceles right angled triangle =

a

2

+a

2

=

2

a

Given, perimeter of the triangle =(6+3

2

)m

⇒a+a+

2

a=(6+3

2

)m

⇒a(2+

2

)=3(2+

2

)m

⇒a=3m

In the isosceles right triangle, the base and height =a

Hence, area of the triangle =

2

1

×base×height =

2

1

×3×3=4.5m

2

The value of equation 4-2(x+7)=3(x+5) is that x=-5/7.

Given equation 4-2(x+7)=3(x+5)

We are required to  solve the equation for the value of variable x.

Equation is relationship between two or more variables expressed in equal to form.Equation of two variables looks like ax+by=c. It can be a linear equation,quadratic equation, cubic equation. It can be solved for finding the value of variables.

The given equation is 4-2(9x+2)=3(x+5)

It is a linear equation.

We have to first remove the brackets by multiplying the numbers to inside numbers.

4-18x-4=3x+15

Now collect variable x at one end and constant at other end.

-18x-3x=15-4+4

-21x=15

x=-15/21

x=-5/7

Hence the solution of equation 4-2(x+2)=3(x+5) is that x=-5/7.

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