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svet-max [94.6K]

2 years ago

11

Jasmine needs to reduce the height of a picture from 5 inches to 2 inches so it will fit in the yearbook. What percentage of the

original height is the new height

1 answer:

Usimov [2.4K]2 years ago

6 0

Jasmine is reducing the height of the yearbook picture from 5 inches to 2 inches and we are trying to find the percentage of the original height that is the new height.

The original height was 5 inches and the new height is 2 inches.

new/original = 2/5

2÷5 = 0.4

0.4 = 40%

Thus, the new height is 40% of the original height.

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What is the equation of the following line written in slope-intercept form -2/3 and -1/-4? y = -11x - 7 y = -7x + 11 y = -7x - 1

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Answer:

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Step-by-step explanation:

Given:

The two points on the line are $(-2,3)$ and $(-1,-4)$ .

The slope of the line joining two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here, $x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4$

∴ $m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7$

Equation of line with a point $(x_{1},y_{1})$ and slope $m$ is given as:

$y-y_{1}=m(x-x_{1})$

Plug in -2 for $x_{1}$ , 3 for $y_{1}$ and -7 for $m$ . This gives,

$y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11$

Therefore, the equation of the line in vertex form is $y=-7x-11$ .

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Applying properties of Exponents In Exercise, use the properties of exponents to simplify the expression.

Nastasia [14]

Answer:

(a) $4^7$

(b) $7^6$

(c) $\dfrac{1}{16}$

(d) $3^{4}$

Step-by-step explanation:

We need to simplify the given expressions.

(a)

Consider the given expression is

$(4^5)(4^2)$

Using the property of exponent, we get

$=4^{5+2}$ $[\because a^ma^n=a^{m+n}]$

$=4^7$

(b)

Consider the given expression is

$(7^2)^3$

Using the property of exponent, we get

$=7^{2\times 3}$ $[\because (a^m)^n=a^{mn}]$

$=7^6$

(c)

Consider the given expression is

$2^{-4}$

Using the property of exponent, we get

$=\dfrac{1}{2^{4}}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

$=\dfrac{1}{16}$

(d)

Consider the given expression is

$\dfrac{3^8}{3^4}$

Using the property of exponent, we get

$=3^{8-4}$ $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$=3^{4}$

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3 years ago