A man is walking away from a lamppost with a light source h = 4 m above the ground. The man is m = 2 m tall. How long is the man's shadow when he is d = 15 m from the lamppost? [Hint: Use similar triangles.]

Answer:

x=11

Step-by-step explanation:

4x + 17 = 5x + 6

Solve for x

Subtract 4x from each side

4x-4x + 17 = 5x-4x + 6

17 = x+6

Subtract 6 from each side

17-6 = x+6-6

11 =x

Answer:

[tex] \sf \: x = 11[/tex]

Step-by-step explanation:

[tex] \sf \: 4x + 17 = 5x + 6[/tex]

Subtract both sides by 4x to remove 4x.

[tex] \sf4x + 17 - 4x = 5x - 4x + 6 \\ \sf 17 = x + 6[/tex]

Subtract both sides by 6 to remove 6 .

[tex] \sf17 - 6 = x + 6 - 6 \\ \sf11 = x[/tex]

The transformed equation is:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

We know that the graph of F(x) has the same shape of G(x) = x^2, but shifted to the left 2 units.

Remember that for a random function f(x), a shift of 2 units to the left is written as:

h(x) = f(x + 2).

Then, in this case, we can write:

F(x) = G(x + 2)

Replacing G(x), we can get the transformed equation:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

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Answer:

The [tex]y[/tex]-coordinate of this midpoint is [tex]5[/tex].

Step-by-step explanation:

Let [tex]{\sf A}[/tex] and [tex]{\sf B}[/tex] denote two points in the cartesian plane.

If point [tex]{\sf A}[/tex] is at [tex](x_{a},\, y_{a})[/tex] while point [tex]{\sf B}[/tex] is at [tex](x_{b},\, y_{b})[/tex], the midpoint of [tex]{\sf AB}[/tex] would be at:

[tex]\begin{aligned}\left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2} \right)\end{aligned}[/tex].

In other words, the [tex]y[/tex]-coordinate of the midpoint of [tex]{\sf AB}[/tex] would be the average of the [tex]y\![/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex].

In this question, the [tex]y[/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex] are [tex]3[/tex] and [tex]7[/tex], respectively. The [tex]y\![/tex]-coordinate of the midpoint of [tex]{\sf A}\![/tex] and [tex]{\sf B}[/tex] would be the mean [tex](3 + 7) / (2) = 5[/tex].

Answer:

nothing there

Step-by-step explanation:

Answer:

Step-by-step explanation:

perimeter of rectangular: 2(a+b)

we know from the graph, assume that a = 2x b = x+ 3

so the perimeter (C) in terms of x is C = 2(2x + x +3) = 6x + 6

The negative rational numbers are -9/ 4, -20/ 3 . Option A and B

A rational number can be defined as a number that is expressed as a fraction where both the numerator and the denominator are integers.

Examples of rational numbers are;

-1/ 2, 3/ 5, 9/ 2 -3/ 5

Given the expressions;

The rational numbers are -9/4 , -20/ 3 , 5/4

Thus, the negative rational numbers are -9/ 4, -20/ 3 . Option A and B

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a. The formula solved for t is t = I/Pr

b. The value of t in the table is 3 years

From the question, we are to solve for t in the given formula

The given formula is the formula for simple interest

I = Prt

To solve for t, we will divide both sides of the equation by Pr

That is,

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

The formula solved for t is t = I/Pr

b. We are to find the value of t when

I = $75

P = $500

r = 5% = 0.05

From

t = I/Pr

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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Answer:

There are no values of x that make this equation true.

Step-by-step explanation:

We know h(x)=[tex]\sqrt{x-3} +5[/tex]

So lets substitute h(x) for 3

3=[tex]\sqrt{x-3}+5[/tex]

We are going to then subtract 5 from each side leaving us with

-2=[tex]\sqrt{x-3}[/tex]

We then need to get rid of the square root, so we will square both sides. which gives us

4=x-3

We then need to subtract 3 from both sides which leaves us with

x=1

However, when you substitute 1 for x into the original equation, you get

h(x)=[tex]\sqrt{-2}+5[/tex]

Which is not equal to 3

Therefore, there are no values of x that make this equation true.

(2x6)^3/2  in it's simplest form is equal to 41.56. See the computation below.

Using BODMAS, we say

(2 x 6) = 12

12^(3/2)

= 41.5692

[tex]$\approx$[/tex] 41.56

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Answer: 2 2/3

Step-by-step explanation:

2/3 x 4/1 multiply the numerators together and the denominators together

2 time 4/ 3 times 1= 8over 3

then simplfy it

so your answer will be 2 and 2/3

The expression that is equivalent to the given expression is 3⁶/7¹⁵

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]

Simplifying

[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]

[tex]\left(\frac{7^{-3 \times 3} }{3^{-2 \times 3} \times 7^{2 \times 3}} \right)[/tex]

[tex]\left(\frac{7^{-9} }{3^{-6} \times 7^{6}} \right)[/tex]

= [tex]\left( 7^{-9} \times \frac{1}{3^{-6}} \times \frac{1 }{7^{6}} \right)[/tex]

= [tex]\left( \frac{1}{7^{9} } \times 3^{6} \times \frac{1 }{7^{6}} \right)[/tex]

= [tex]\left(\frac{3^{6} }{7^{9} \times 7^{6}} \right)[/tex]

= [tex]\frac{3^{6} }{7^{9+6}}[/tex]

= [tex]\frac{3^{6} }{7^{15}}[/tex]

Hence, the expression that is equivalent to the given expression is 3⁶/7¹⁵

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The equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is:

Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?

n = (1/2)(1/5)

n = (1/2)(5/1)

n = (1/2)(5)

n = (1/2)

From the data given in the question:

Let n be the fraction of a quart of grape juice n that is in each glass:

n = (1/2)(1/5)

Thus, the equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.

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The equation of the function after translation: [tex]$y=\frac{|x|}{4}$[/tex]

The y values advance toward the x-axis as they are multiplied by a value between 0 and 1. This is known as a vertical shrink and tends to flatten the graph.

When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.

The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.

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The relation 1 is not a function, while the relation 2 is a function

For a relation to be a function, the following must be true:

Each y value in the function must have a unique x value

i.e. Each y value must have exactly one x value

Using the above as a guide, we have

Relation 1: This relation is not a function, because the x value 5 has two y values 2 and 4

Relation 2: This relation is a function, because each y value must have exactly one x value

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1. x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2. 3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. (x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

1. (x+4)(x+7)=0

We have that;

Zero product property;

x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2.  (3x-7)(2x+5)=0

We have that;

Zero product property ;

3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x² -3x - 40=0

x² -8x + 5x - 40 = 0

factorize the common multipliers

x(x - 8) + 5(x - 8) = 0

Zero product property;

x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. 3x² - 11x - 42=0

3x² +7x - 18x - 42 = 0

Factorize further

x(3x + 7) - 6(3x + 7) = 0

Zero product property;

(x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 10x² + 9x + 2 = 0

10x² + 5x + 4x + 2 = 0

Factorize

5x( 2x + 1) + 2 (2x + 1) = 0

Zero product property;

5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

Thus, the zero product property states that the product of two non-zero elements is not zero

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Answer: 14

207+14 = 221

221/17 = 13 (so the sum of 207 and 14 is divisible by 17)

Answer:

25,09

Step-by-step explanation:

So, you've converted 2000 Indian Rupee to 25.145200 US Dollar. We used 79.538043 International Currency Exchange Rate. We added the most popular Currencies and CryptoCurrencies for our Calculator. You can convert Indian Rupee to other currencies from the drop down list. Selling 2000 Indian Rupee you get 25.145200 US Dollar

Answer:

$ 26

Step-by-step explanation:

Current exchange rate :  1 ruppee / .013 dollar

2000 r   /   (1 r / .013 dollar) = 26 dollars

Step-by-step explanation:

Take Reference of Z-angle forward and backward and X-Angle if none are  in this category then write none.

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Answer:

Smallest integer=14

Step-by-step explanation:

(x+x+2+x+4+x+6)/4=17

(4x+12)/4=17

4x+12=68

4x=68-12

4x=56

x=56/4

x=14

numbers are: 14, 16, 18, 20

Answer

1.2 + 0.68 should have equaled 0.80

Step-by-step explanation:

jason solved this problem by changing 6/4 to 1.2. He then added 1.2 to 0.68 and got 1.88.

This answer is incorrect. What did he do wrong?

If Jason solved this problem by changing 6/4 to 1.2, The wrong thing he did is ; 6/4 should have been changed to 1.5. Option C is correct

To find the correct answer, let's first evaluate the expression step by step:

1. 6/4 is equal to 1.5, not 1.2.

2. 1.5 + 0.68 equals 2.18, this is not 1.88.

So, the correct answer is: Jason made a mistake in the first step. He changed 6/4 to 1.2, but it should have been 1.5.

Therefore, the correct calculation is 1.5 + 0.68 = 2.18.

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Answer:

1400x

Step-by-step explanation:

10^3 in scientific notation means to move the decimal 3 places to the right.

We can express this as:

x + 2x = £3.45

We can solve for x with no additional work.

x + 2x = £3.45
3x = £3.45
3x/3 = £3.45/3
x = £1.15

Im guessing you're British by the use of the £ symbol, and I don't understand what "dearer" means as in America we don't use that term. I'll just give you both values.

x = £1.15 (this is the first book)
2x = £2.30 (this is the second book, which costs twice as much as the first.)

The total distance covered is 6,000 m.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object had also covered regardless of its starting as well as ending point.

Now, as per the question;

The distance around track is 400 m.

14 more laps has been covered along with the initial one.

Thus the total distance will be;

Total distance  = 400 + 400×14

                         = 400 + 5,600

Total distance  = 6,000

Therefore, the total distance covered is 6,000 m.

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Answer:64y^2 −80y+25

Step-by-step explanation:

Answer:

0.00000057652

Step-by-step explanation:

5.764 × 10^-7 = 0.0000005764 (move the decimal place 7 steps forward)

0.00000057652>0.0000005764 (65>64)

Therefore 0.00000057652 is greater.

Hope this helped! ^^

Answer:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

Step-by-step explanation:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

Answer:

True

Step-by-step explanation:

dividing both sides by M you are left with L=P