find the length of AD

Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

[tex]f(x) = 5x - 12[/tex]

[tex]f(2) = 5(2)- 12[/tex]

[tex]f(2) = 10 - 12[/tex]

[tex]\boxed{f(2) = - 2}[/tex]

Hence,f(2) is equal to -2.

Answer:

36.2

Step-by-step explanation:

Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2

33^2+15^2=c^2

1089+225=c^2

1314=c^2

Square root of 1314 = square root of c^2

36.2 aapproximately c

Answer:

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Step-by-step explanation:

Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.

The given algebraic equation is [tex]x^{2} -\frac{4}{x^{2} } +2x[/tex]

now for simplifying it

First of all take L.C.M of [tex]x^{2}[/tex]

= [tex]\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }[/tex]

We get [tex]\frac{x^{2} -4+2x^{3}}{x^{2} }[/tex]

Further we can write it as  [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

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Answer:

Step-by-step explanation:

AFR = VFN (opposite angle rule)

7x + 33 = 9x + 7

33 - 7 = 9x - 7x

26 = 2x

x = 26 : 2

x = 13°

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

check

7 * 13 + 33 = 9 * 13 + 7   (remember PEMDAS)

91 + 33 = 117 + 7

124 = 124

the answer is good

ΔDGC is right because Line E G is perpendicular-to CC', Option D is the correct answer.

Reflection along a line is plotting a new object as a mirror image of the original object .

It is given that the there are two Triangles , ABC and A'B'C' as an image.

The figure is attached with the answer.

D is the mid point of the line joining BB'

As the line of reflection is always perpendicular to the object and the image.

And as it is given that C G F is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

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Answer:

D

Step-by-step explanation:

The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]

The products can be simplified as follows;

Multiplying fraction,

[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]

Hence,

Let's reduce the fraction by dividing

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]

Hence,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]

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Answer:

A, b+3/2

Step-by-step explanation:

The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.

The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.

Hence, it follows that the attached image represents the transformation.

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Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

7/8 <> 0.875

0.875 * 6 = 5.25

5.25 <> 42/8

(<> is used to show decimal to fraction and vice versa [the other way around])

Answer:

B. Exactly One Solution

Step-by-step explanation:

Given:

[tex]7(y+3)=5y+8[/tex]

Expand the brackets:

[tex]\implies 7y + 21 = 5y + 8[/tex]

Subtract 21 from both sides:

[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]

[tex]\implies 7y=5y-13[/tex]

Subtract 5y from both sides:

[tex]\implies 7y-5y=5y-13-5y[/tex]

[tex]\implies 2y=-13[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]

[tex]\implies y=-\dfrac{13}{2}[/tex]

Therefore, the equation has exactly one solution.

The height of the tree will be 18.35 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Matt is trying to measure the height of a tree using trigonometry.

He is having trouble because of the terrain around the tree.

The horizontal distance from the tree to Matt's eyes is 120 feet.

The angle of depression from the horizontal is 30°.

Matt's angle of sight to the top of the tree is 23°.

The diagram is given below.

Let x be the height of tree and AM be h.

The value of (h + x) will be

tan 30° = (x + h) / 120

   x + h = 69.288

Then the value of h will be

tan 23° = h / 120

        h = 50.94 feet

Then the height of the tree will be

⇒ h + x – h

⇒ 69.29 - 50.94.

⇒ 18.35 feet

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Answer:

x = 5.00 cm

Step-by-step explanation:

• area of the rectangle = [tex]x[/tex]   x   [tex](x + 1)[/tex]

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

• area of the circle = π r²

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x + 2)^2[/tex]

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4)[/tex]

∴   [tex]x^2 + x[/tex]   +    [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4) = 184[/tex]  

⇒  [tex]x^2 + x[/tex]      +   [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]

⇒  [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]

• Using quadratic formula, where

a = [tex]\frac{29}{7}[/tex]

b = [tex]\frac{95}{7}[/tex]

c = [tex]\frac{-1200}{7}[/tex] ,

[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]

[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]

[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]

As length (x) cannot be a negative number,

x = 5.00 cm

A fraction is a way to describe a part of a whole. The correct option is C.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The choice that is equivalent to the fraction  can be found by rationalizing the denominator of the fraction. Therefore, we can write,

[tex]\dfrac{2}{2-\sqrt{6x}}\\\\\\=\dfrac{2}{2-\sqrt{6x}} \times \dfrac{2+\sqrt{6x}}{2+\sqrt{6x}}\\\\\\= \dfrac{4+2\sqrt{6x}}{4-6x}\\\\\\=\dfrac{2(2+\sqrt{6x})}{2(2-3x)}\\\\\\= \dfrac{2+\sqrt{6x}}{2-3x}[/tex]

Hence, the correct option is C.

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Using the given information, the smallest possible value of x - z is 12

From the question, we are to determine the smallest possible value of x - z

From the given information,

w and x are whole numbers

and

w > 60

x < 50

∴ w = 61, 62, 63, 63, 65, ...

x = 49, 48, 47, 46, 45, ...

Then,

The smallest possible value of x - z is

x - z = 61 - 49

x - z = 12

Hence, the smallest possible value of x - z is 12

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Answer:

 17.14

Step-by-step explanation:

You have the data values {3, 4, 5, 7, 10, 12, 15}

To find the mean, [tex]\frac{3+4+5+7+10+12+15}{7} =8[/tex], yay a whole number, my favorite.

Then, [tex](3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2=120[/tex].

Since n=7, σ^2≈[tex]17.14[/tex]

Step-by-step explanation:

Hi There! Let me help you :)

To answer this question, we have to know about the way to simplify it. First, you find the factor of 48.

[tex] = {48}^{ \frac{1}{2} } [/tex]

[tex] = {(16 \times 3)}^{ \frac{1}{2} } [/tex]

[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]

[tex] \: [/tex]

—Use the general formula of the exponential, where a^m/n = ^n√a^m.

[tex] \: [/tex]

[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]

[tex] = \sqrt[2]{16} \times {3}^{ \frac{1}{2} } [/tex]

[tex] = 4 \times {3}^{ \frac{1}{2} } [/tex]

The answer is C.

Sum of triangle angles = 180

smallest angle = x

second angle = 3x

third angle = x +35

180 = x + 3x + x + 35

145 = 5x

x = 29 is the smallest

the second is 87

the third is 64

Answer:

slope = 3

y-intercept: -4

explanation on how to graph given in step-by-step explanation

Step-by-step explanation:

y=3x-4 is given in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept (when x = 0)

So the first coordinate that is easy to graph is the y-intercept since it's just (0, b) or in this case (0, -4). So that's the first point you graph. Now from here you can use the slope to graph all the other points. The slope is 3, which essentially means every time x increases by 1, the y-value increases by 3. So from the y-intercept (0, -4) you're going to go one unit to the right and three units up which should give you the coordinates (1, -1). Then from that coordinate go one unit to the right and three units up which should get you (2, 2) then from that coordinate go one unit to the right and three units up which should get you to (3, 5). Now go back the y-intercept (0, -4) and instead of going to the right 1 and up 3 you're going to do the inverse and instead go left 1 and down 3. So from (0, -4) go to the left one unit and down 3 units which should get you to (-1, -7). And now with all these points plotted draw a line through all of them

Answer:

Value of x is 20.

Step-by-step explanation:

The angle opposite to 4x is also 4x.

Similarly, the angle opposite to 5x is also 5x.

So, 4x+4x+5x+5x=360

18x=360

x=360/18

x=20

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The intercept is 3 and 5

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

To find x- intercept, y=0

x² + 2x -15=0

x² -5x + 3x -15=0

x(x-5) - 3(x-5) = 0

(x-5)(x-3)=0

Hence, the x- intercept is 3 and 5.

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The value of the function f(x)=6/-2+2[tex]e^{-0.3x}[/tex] at x=4 after rounded to the nearest tenth is -2.4.

Given Function of x : f(x)=6/-2+2[tex]e^{-0.3x}[/tex]

The given function showing the relationship between x and f(x) is f(x)=6/-2+2[tex]e^{-0.3x}[/tex] where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.

f(4)=6/-2+2[tex]e^{-0.3*4}[/tex]   ( The value of e is 2.7812)

f(4)=-3+2[tex]e^{-1.2}[/tex]                    

f(4)=-3+2*0.30119   (The value of [tex]e^{-1.2}[/tex] is 0.30119)          

f(4)=-3+0.60238

f(4)=-2.3972

Round -2.3972 to tenth is -2.4.

Hence the value of function of at x=4 is -2.4.

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The value of f(4) is -4.3.

The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.

For example: f(x)=3x+9

To get the value of the function at any point of x, we have to put the number in the function to get its function value.

For example the value of f(x) in above function at x=a will be f(a)=3a+9

Similarly given function in the question

[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]

to get the value of f(x) at x=4 put the value of x in the function,

[tex]f(x)=\frac{6}{-2+2e^{-0.3*4}}[/tex]

⇒[tex]f(x)=\frac{6}{-2+2e^{-1.2}}[/tex]

⇒f(x)=-4.3

Therefore the value of f(4) is -4.3.

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Answer:

overlapping congruent triangles:

ΔACE ≅ ΔBCD

Proof:

given: AC ≅ BC, angle A ≅ angle B

angle ACB ≅ angle BCA by the reflexive property

ΔACE ≅ ΔBCD by the ASA triangle congruence property

The number of gallons of paint needed to paint the entire fence is 26.4 gallons.

Area = length × width

= 33 m × 2 m

= 66 square meter.

Number of gallons of paint needed = 66 square meter / 2.5 m²

= 26.4 gallons

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Answer:

Step-by-step explanation:

Comment

This is an arithmetic series. It has the following givens.

a = 27     The first term

d = - 2       The difference between one term and the one behind it.

n = quite small

Tn = a + (n - 1)*d

tn = 27 - 2n  + 2

tn = 29 - 2n

Answer:

After solving this question I got and 120 tokens

Answer:

y=(-5x)+(-7)

Step-by-step explanation:

The equation for slope is y=mx+b

so you would say -5x as the mx in the equation and -7 as the u intercept.

Hii!

_________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

y=-5x-7

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.

The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.

Since we have both m and b, we can stick them into the formula. Upon doing this we obtain

[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf y=-5x-7[/tex]

[tex]\bullet[/tex] Great job! We found the equation

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

4020 grams

Step-by-step explanation:

4kg=4000g

2 dag= 20g

Total: 4000g + 20g = 4020g

Answer:

4020 grams

Step-by-step explanation:

1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20

Answer:

the sum of all exterior angle is 360 degree

Answer:

Pythagoras was the Greek geometer .

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