Andy is a landscaper, Yesterday, he planned a 2- foot- tall elm tree and a 14- foot tall maple tree. The elm tree is expected to grow 5 feet taller each year. The maple tree is expected to grow 2 feet taller each year. At those rates, in how many years will the tree be the same height?

Answer: -6i

Step-by-step explanation:

When the rectangle is dilated, the new and the old rectangles will have a different area

The area of the image of the rectangle is 12k^2

The area of the rectangle is given as:

A = 12

The scale of dilation is given as k.

So, the area of the image of the dilation is:

[tex]A_2 = A * k^2[/tex]

This gives

[tex]A_2 = 12 * k^2[/tex]

Evaluate the product

[tex]A_2 = 12k^2[/tex]

Hence, the area of the image of the rectangle is 12k^2

Read more about dilation at:

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Answer:

1 Is In The Thousands Place

Step-by-step explanation:

Uhm You Should Know This But Heres The Answer

900,000

80,000

1,000

400

40

3

Answer:

-2

Step-by-step explanation:

make 'n' subject of formula

n= 5 -7

n= -2

Answer:

n = -2

Step-by-step explanation:

7 + n = 5

prove that the value of n is -2

proven

Answer:

x=15

y=25

Step-by-step explanation:

first number x

second number y

x+y=40

y=2x-5

x+(2x-5)=40

x+2x-5=40

3x=45

x=45/3=15

y=(2*15)-5=25

Answer:

186.5663

Step-by-step explanation:

12*9=108

11*6=66

pi4^2=50.26548/4=12.5663

add all together

186.5663

(a) The claim is made for all positive integers n, so we start at n = 1. We have

[tex]\displaystyle \sin(x) \sum_{k=1}^1 \sin(2kx) = \sin(x) \sin(2x) = \sin(1x) \sin((1+1)x)[/tex]

so the claim is true for the base case.

Suppose the claim is true for n = m, so that

[tex]\displaystyle \sin(x) \sum_{k=1}^m \sin(2kx) = \sin(mx) \sin((m+1)x)[/tex]

We want to use this to establish the identity for n = m + 1. That is, we want to prove that

[tex]\displaystyle \sin(x) \sum_{k=1}^{m+1} \sin(2kx) = \sin((m+1)x) \sin((m+2)x)[/tex]

Working with the left side, we remove the last term from the sum and we have

[tex]\displaystyle \sin(x) \sum_{k=1}^{m+1} \sin(2kx) = \sin(x) \sum_{k=1}^m \sin(2kx) + \sin(x) \sin(2(m+1)x) \\\\\\ = \sin(mx) \sin((m+1)x) + \sin(x) \sin(2(m+1))x[/tex]

Recall the angle sum identities:

[tex]\sin(x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)[/tex]

[tex]\sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y)[/tex]

[tex]\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)[/tex]

[tex]\cos(x - y) = \cos(x) \cos(y) + \sin(x) \sin(y)[/tex]

Then

[tex]\sin(2(m+1)x) = 2 \sin((m+1)x) \cos((m+1)x)[/tex]

so we can remove a factor of sin((m + 1) x) :

[tex]\displaystyle \sin(x) \sum_{k=1}^{m+1} \sin(2kx) = \sin((m+1)x) \bigg(\sin(mx) + 2 \sin(x) \cos((m+1)x)\bigg)[/tex]

and we also have

[tex]2 \sin(x) \cos((m+1)x) = \sin(x+(m+1)x) + \sin(x - (m+1)x) \\\\ = \sin((m+2)x) + \sin(-mx) \\\\ = \sin((m+2)x) - \sin(mx)[/tex]

Then the sin(mx) terms cancel, and we're left with what we wanted:

[tex]\displaystyle \sin(x) \sum_{k=1}^{m+1} \sin(2kx) = \sin((m+1)x) \sin((m+2)x)[/tex]

and the induction proof is complete.

(b) From the identities mentioned earlier, one has

[tex]\sin\left(x - \dfrac\pi4\right) = \sin(x) \cos\left(\dfrac\pi4\right) - \cos(x) \sin\left(\dfrac\pi4\right) \\\\ = \dfrac{\sin(x) - \cos(x)}{\sqrt2}[/tex]

Then

[tex]\sin^2\left(x - \dfrac\pi4\right) = \dfrac{(\sin(x) - \cos(x))^2}2 \\\\ = \dfrac{\sin^2(x) - 2 \sin(x) \cos(x) + \cos^2(x)}2 \\\\ = \dfrac{1 - \sin(2x)}2[/tex]

We can then rewrite the sum as

[tex]\displaystyle \sum_{k=1}^{369} \sin^2\left(\dfrac{k\pi}5 - \dfrac\pi4\right) = \frac12 \sum_{k=1}^{369} \left(1 - \sin\left(\frac{2k\pi}5\right)\right) \\\\ = \frac12 \sum_{k=1}^{369} 1 - \frac12 \sum_{k=1}^{369} \sin\left(\frac{2k\pi}5\right)[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 1 + \cdots + 1 = n[/tex]

For the sum involving sine, let x = π/5. Then using the result from part (a),

[tex]\displaystyle \sin\left(\frac\pi5\right) \sum_{k=1}^{369} \sin\left(\dfrac{2k\pi}5\right) = \sin\left(\dfrac{369\pi}5\right) \sin\left(\dfrac{370\pi}5\right)[/tex]

and this sum vanishes, since sin(370π/5) = sin(74π) = 0.

It follows that

[tex]\displaystyle \sum_{k=1}^{369} \sin^2\left(\dfrac{k\pi}5 - \dfrac\pi4\right) = \frac12 \sum_{k=1}^{369} 1 = \boxed{\frac{369}2}[/tex]

Answer: Win $0.33

Step-by-step explanation:

Answers win 0.33

Step-by-step explanation:

I got you

Answer:

can u please tell what is 158° here

Answer:

x = 11

Step-by-step explanation:

the inscribed angle CDE is half the measure of its intercepted arc CE , so

8x - 9 = [tex]\frac{1}{2}[/tex] × 158 = 79 ( add 9 to both sides )

8x = 88 ( divide both sides by 8 )

x = 11

Answer:

[tex]8\frac{4}{7}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

5) Volume  = Volume of rectangular prism 1  + volume of rectangular prism2

 =  10* 6 * 4 +  (7*4*2)

 = 240 + 56

 = 296 cm³

6) Volume = (5*6*8) + (9*6*2)

                  = 240 + 108

                   = 348 ft³

7) Volume = (11*12*4) + (5*5*12)

                 = 528 + 300

                 = 828 m³

Answer:

25%

Step-by-step explanation:

3 bears increase is a fourth of 12. So a fourth of 100 is 25 percent increase.

Answer:

37in.^2

Step-by-step explanation:

So if the triangles at the top have a hypotenuse of 5, and a length of 4, then doing reverse Pythagorean theorem, you find out that the width is 3.[tex]a^{2} +b^{2} =c^{2}[/tex]. so reverse of that for this problem would be [tex]c^{2} -b^{2} =a^{2}[/tex] and if we plug it in, we get 25 -16=9 and the square root of 9 is 3. so if we find the are of the triangle, 3*4*1/2=6 and there are 2 triangles so 12 for both triangles. The square is 5*4=20. and the smaller triangles on the side are 1*5*1/2=2.5, and there are 2 traingles so 2.5*2= 5. So 5+20+12=37. You can do this on most calculators, and please put my answer as the brainliest.✌

Answer:

+act of kindness and its We are given with the expression sin 52° cos 13° - cos 52° sin 13° The expression can be patterned from the trigonometric identity sin (a - b) = sin a cos B - cos A sin B. In this case, the expression is equal to sin (52-13) or equal to a simplified term sin 39

Step-by-step explanation:

Answer:

The expression for length of the rectangle is x-2 meters.

Step-by-step explanation:

Given the area of the rectangle as : x²- 7x+10 square meters

The width of the rectangle is : x-5 meters

Area of a rectangle is given by the product of its length and width.

Dividing the expression for area with the expression for width will give the expression for length.

Here, perform the long division of the polynomial; where the numerator is  x²- 7x+10 and the denominator is x-5

First divide  x²- 7x+10 by x-5 to get x

Multiply x by x-5 to get x²-5x

Subtract x²-5x from x²-7x+10 to get  -2x+10

Then divide -2x+10 by x-5 to get -2

Multiply x-5 by -2 to get -2x+10

Perform subtraction to remain with zero.

The expression for length will now be x-2 meters

Answer:

B/ 5/6

Step-by-step explanation:

5/6 represents a part of a whole while the others represent a part of a whole AND a whole.

Answer:

2/3 = 8/12

1/4 = 3/12

Step-by-step explanation:

2/3

12/3 = 4, so for the fraction 2/3, we multiply the numerator and denominator by 4.

2/3 = 8/12

1/4

12/4 = 3, so for the fraction 1/4, we multiply the numerator and denominator by 3.

1/4 = 3/12

Answer:

[tex]\frac{8}{12}[/tex] and  [tex]\frac{3}{12}[/tex]

Step-by-step explanation:

To do this, you must multiple the numerator and denominator of each fraction by whatever number gives you 12 on bottom.

for [tex]\frac{2}{3}[/tex] , you would multiply it by 4 since 4×3=12. You would also need to multiply the top by 4, making that fraction [tex]\frac{8}{12}[/tex]

For [tex]\frac{1}{4}[/tex] , multiply it by 3, which would equal [tex]\frac{3}{12}[/tex]

Answer:

$512.67 (surplus)

Step-by-step explanation:

Monthly fixed expenses = $3,900

Monthly living expenses = $676

Monthly annual expenses = $561

⇒ Total monthly expenses = 3900 + 676 + 561 = $5,137

Annual net income = $67,796

⇒ Monthly net income = $67,796 ÷ 12 = $5,649.67

Monthly budget = Monthly net income - Total monthly expenses

                           = $5,649.67 - $5,137

                           = $512.67 (surplus)

Answer:

Yes

Step-by-step explanation:

Answer:

The answer is Yes. Hope this helps :)

Step-by-step explanation:

Answer:

g(9) = 48

Step-by-step explanation:

g(x)= – x2–5x + 12

I'll assume this is

g(x)= – x^2–5x + 12

find g(9)

find g(9)

g(9)= – 9^2–5(9) + 12

g(9)= 81–45 + 12

g(9) = 48

Answer:

y+4=3(x+2)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(8-(-4))/(2-(-2))

m=(8+4)/(2+2)

m=12/4

m=3

y-y1=m(x-x1)

y-(-4)=3(x-(-2))

y+4=3(x+2)

Answer:$1.5

$30*5/100=15/10=3/2=$1.5

Step-by-step explanation:

Part A: what tool can help Jada find possible dimensions for the base of the block? Explain.

     I am not sure what a "tool" is by their wording, but we can use the formula for volume to solve for the base.

-> B is the base, length times width, and H is the height

V = B * H

350 in³ = B * 5 in

70 in² = B

  Answer: The base will be 70 in²

Part B: Give one pair of possible whole-number dimensions for the base.

     Since we know the base will be 70 in², we can find a possible pair of whole-number dimensions for the base.

B = L * W

70 in² = L * W

     Now we just need to find pairs of whole numbers that multiply to 70:

70 / 2 = 35

  Answer: A possible pair of whole-number dimensions for the base is 2 and 35.

Answer:

Fifty six thousand and seventy eight

Step-by-step explanation:

Fifty six thousand and seventy eight

Part (a)

The domain is the set of allowed x inputs of a function.

The graph shows that x = 0 is not allowed because of the vertical asymptote located here. It seems like any other x value is fine though.

To write this in interval notation, we can say [tex](-\infty, 0) \cup (0, \infty)[/tex] which is the result of poking a hole at 0 on the real number line.

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

The range deals with the y values. The graph makes it seem like it stretches on forever in both up and down directions. If this is the case, then the range is the set of all real numbers.

In interval notation, we would say [tex](-\infty, \infty)[/tex] which is almost identical to the interval notation of the domain, except this time of course we aren't poking at hole at 0.

=======================================================

Part (b)

We can compact that to the notation [tex]x = \pm 4[/tex]

These are the locations where the blue hyperbolic curve crosses the x axis.

=======================================================

Part (c)

Reason: The presence of an oblique asymptote cancels out any potential for a horizontal asymptote.

=======================================================

Part (d)

The vertical asymptote is located at x = 0, so the equation of the vertical asymptote is naturally x = 0. Every point on the vertical dashed line has an x coordinate of zero. The y coordinate can be anything you want.

=======================================================

Part (e)

The oblique or slant asymptote is the diagonal dashed line.

It goes through (0,0) and (2,6)

The equation of the line through those points is y = 3x

If you were to zoom out on the graph (if possible), then you should notice the branches of the hyperbola stretch forever upward but they slowly should approach the "fencing" that is y = 3x. The same goes for the vertical asymptote as well of course.

Answer:

1.68 seconds.

Step-by-step explanation:

The question, is, essentially asking for time, t, at position 325 feet.

So:

Set h(t) equal to 325.

325 = 16t^2 + 168t + 5

Subtract 325 over, to get the quadratic:

0 = 16t^2 + 168t - 320

Factor out an eight, simply to make the equation easier:

0 = 2t^2 + 21t - 41

Now, use the quadratic formula to find the "zeros", or solutions:

{-21 + (21^2 - [(4)(2)(-41)]^.5}/(2)(2); {-21 - (21^2 - [(4)(2)(-41)]^.5}/(2)(2)

Simplify:

(-21 + [441 + 328]^.5)/4; (-21 - [441 + 328]^.5)/4

(-21 + [769]^.5)/4; (-21 - [769]^.5)/4

(-21 + 27.73)/4; (-21 - 27.73)/4

(6.73)/4; (-48.73/4)

t = 1.68, -12.18

It makes no sense for t to be negative, since t represents time.

Therefore, the potato is 325 feet in the air after 1.68 seconds.

I hope this helped! :)

The potato is 325 feet in the air after 1.68 seconds on the way back down.

The quadratic function is defined as a function containing the highest power of a variable is two.

The question is effectively inquiring about time, t, at 325 feet.

Set h(t) equal to 325.

325 = 16t² + 168t + 5

Subtract 325 over, to get the quadratic:

0 = 16t² + 168t - 320

Factor out an eight, simply to make the equation easier:

0 = 2t² + 21t - 41

2t² + 21t - 41 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -12

Now, use the quadratic formula to find the "zeros", or solutions:

[tex]\quad x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\dfrac{-21\pm \sqrt{21^2-4\cdot \:2\left(-41\right)}}{2\cdot \:2}[/tex]

[tex]\sqrt{21^2-4\cdot \:2\left(-41\right)}[/tex]

[tex]=\sqrt{21^2+328}[/tex]

t = (-21 + 27.73)/4; (-21 - 27.73)/4

t = (6.73)/4; (-48.73/4)

t = 1.68, -12.18

Because t symbolizes time, it makes no sense for it to be negative.

As a result, after 1.68 seconds, the potato is 325 feet in the air.

Learn more about quadratic function here:

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Answer:

Solving steps:

Explanation:

The first bit of information is about amount, and the second part is about cost. We will make an equation for each one. Just so you know, I'm going to abbreviate "children" to c and "adults" to a .

The first equation is about amount. So since the total amount of people that came was

283

, this is the equation:

c + a = 283

The second is about cost. Children cost

$5.50 and adults cost $15.00, so we can make this equation:

=> 5.50c + 15.00a = 2,649.00

Now rearrange the first equation so that we can solve for one of the variables:

c + a = 283 → c = 283 − a

Substitute it into the second equation:

5.5c +15a = 2,649

5.5(283 − a) + 15a = 2,649

1,556.5 − 5.5a + 15a = 2,649

1,556.5 + 9.5a = 2,649

9.5a = 1,092.5

a = 115

115 adults came.

Now substitute the value of into this equation and solve for c

.c = 283 - a

c = 283 - 115

c = 168

168 children came.

Answer: SAS

Step-by-step explanation:

It is given that DN is congruent to ML.

It is also given that angle DNL is congruent to angle MLN

We can figure out that NL is congruent to LN by the reflexive property.

Therefore, these triangles are congruent by Side-Angle-Side