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3 years ago

10

The graph models the projected populations, in thousands, of two towns after x years. Both towns experience a 1.9% annual growth

rate.

1 answer:

spin [16.1K]3 years ago

3 0

whats the question

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The rectangle below has an area of x^2-7x+10square meters and a width of x - 5 meters. What expression represents the length of

jolli1 [7]

Answer:

L = (x - 2) meters

Step-by-step explanation:

The area of the rectangle = (x² - 7x + 10) m²

The width = (x - 5) m

length = ?

Area of a rectangle = length × width

x² - 7x + 10 = L(x -5)

note L = length

divide both sides by (x-5)

(x² - 7x + 10)/(x - 5) = L

L = x² - 7x + 10 / (x -5)

Factorize x² - 7x + 10

find the numbers you can multiply to give you 10 and also add to give you -7

The numbers are -2 and -5. Therefore,

x² - 2x - 5x + 10 = 0

x(x - 2) - 5(x - 2) = 0

(x-5)(x-2) = 0

Let us go back to our division

L = x² - 7x + 10 / (x -5)

x² - 7x + 10 = (x-5)(x-2)

L = (x-5)(x-2) / (x -5)

L = (x - 2) meters

7 0

3 years ago

Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?

Feliz [49]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see

$\bf h(x)=-x+5\implies h(x)=\stackrel{A}{-1}(\stackrel{B}{1}x\stackrel{C}{+0})\stackrel{D}{+5}$

a shift down by 3 units, means a vertical shift downwards, so D needs to drop by 3 units.

$\bf h(x)=\stackrel{A}{-1}(\stackrel{B}{1}x\stackrel{C}{+0})\boxed{\stackrel{D}{+5-3}}\implies h(x)=-1(1x+0)+2
\\\\\\
h(x)=-x+2$

4 0

3 years ago

8. An Isosceles triangle HIJ has sides HI and HJ as 19 meters each. If angle I and angle J are 67 degrees, what is the distance

PtichkaEL [24]

Answer:

$IJ=14.8$

Step-by-step explanation:

In a triangle the sum of all angle measures is always 180 degrees

$A+B+C=180$

$2(67)+C=180$

$C=46$ degrees

By splitting the isosceles triangle down the middle we can calculate the base

So ∠H = 23°, ∠K = 90°, ∠J = 67°, HJ = 19

With this we can solve for half of the base. the trig function will need to use is sin, since the side opposite of ∠H will be part of the base. $sin=\frac{opposite}{hypotenuse}$

now we need to rearrange the formula for what we have.

$hypotenuse(sin)=opposite$

$19sin(23)=7.423$

This value is only half of the base, so we need to double it

$IJ=2(7.423)=14.8$

8 0

3 years ago

Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through c

GenaCL600 [577]

Reading the question carefully, "<span>He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle." - that implies that Mateo is still in the process of drawing the circle by which the equilateral is inscribed to.

The next steps should be:
*He should draw the upper and lower arcs using the compass opened to a width equivalent to the radius of the sircle.
*Make a vertical diameter using centroid P as basis.
*Draw two right triangles facing the opposite directions using the top most point by which the vertical diameter of the circle touches the top most circumference of the circle.

Doing these steps, Mateo will be able to draw an equilateral triangle inscribed in a circle.
</span>

7 0

3 years ago

How many cubic ft in a cylendar 12 inches wide and 24 inches tall

Pavel [41]

1130.97^3 im pretty sure (: That may not be the exact answer but there should be an answer choice similar to that

5 0

3 years ago