84,600,600 Write each number in scientific notation

4) Mandy has a flower garden that is 30

Softa [21]

Answer:

using quaderatic expression solving problems of algebraic expressions.

Step-by-step explanation:

no1.

take the smallest side to be x

and the longest side to be x-1/3

then expand the expression equating to 30.

then solve for x value

6 0

2 years ago

What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

Serggg [28]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-2\\
n=6\\
S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
\\\\\\
-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
\\\\\\
\cfrac{-105}{-21}=a_1\implies 5=a_1$

7 0

3 years ago

You are hiking on a trail that leads to the top of a mountain. At 1 P.M. you reach an elevation of 4400 feet. At 4 P.M. you reac

shusha [124]

Let
t = time, hours
h = height, feet

At 1 PM, the time and height are respectively
t₁ = 1 hour
h₁ = 4400 feet

At 4 PM, the time and height are respectively
t₂ = 4 hours
h₂ = 5600 feet

By definition, the mean hourly change in elevation is
$\frac{h_{2} - h_{1}}{t_{2} - t_{1}} = \frac{5600-4400}{4-1} = \frac{1200}{3} =400$

Answer: 400 feet per hour

5 0

3 years ago

Read 2 more answers

Multiplying a measure<br> by a scale to produce a<br> reduced or enlarged<br> measure

svetoff [14.1K]

Answer:

we conclude that:

If the scale factor > 1, the image is stretched

If the scale factor < 1, the image is reduced

If the scale factor = 1, the image and object will be congruent

Step-by-step explanation:

A dilation is a transformation which generates an image that is the same shape as the original object but in a different size.

The image can be obtained by multiplying the measure of the original object by a scale factor.

If the scale factor > 1, the image is stretched

If the scale factor < 1, the image is reduced

If the scale factor = 1, the image and object will be congruent

For example, if we multiply the measure of the coordinates of the vertex A(2, 2) of a triangle by a scale factor of 2, the image A' is stretched as the scale factor > 1.

Dilation with scale factor 2, multiply by 2.

(x, y) → (2x, 2y)

A(2, 2) → (2(2), 2(2)) = A'(4, 4)

So, the image point A'(4, 4) is enlarged.

Dilation with scale factor ½, multiply by ½.

(x, y) → (½x, ½y )

A(2, 2) → (2(1/2), 2(1/2)) = A'(1, 1)

So, the image point A'(1, 1) is reduced.

Therefore, we conclude that:

If the scale factor > 1, the image is stretched

If the scale factor < 1, the image is reduced

If the scale factor = 1, the image and object will be congruent

5 0

3 years ago

5th grade "tony had an equal number of cranberry bars and walnut bars. he gave away 66 cranberry bars. he then had 4 times as ma

dimulka [17.4K]

He had 528 bars all together

7 0

4 years ago