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2 years ago

In the expression 14b what is the coefficient? *

Mathematics

1 answer:

Pachacha [2.7K]2 years ago

4 0

Answer:

Step-by-step explanation:

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Consider the equation below.

Korvikt [17]

Answer:

Equation in square form:

$y=3(x+5)^2-4$

Extreme value:

$(h,k)=(-5,-4)$

Step-by-step explanation:

We are given

$y=3x^2+30x+71$

we can complete square

$y=3(x^2+10x)+71$

we can use formula

$a^2+2ab+b^2=(a+b)^2$

$y=3(x^2+2\times x\times 5)+71$

now, we can add and subtract 5^2

$y=3(x^2+2\times x\times 5+5^2-5^2)+71$

$y=3(x^2+2\times x\times 5+5^2)-3\times 5^2+71$

$y=3(x+5)^2-75+71$

So, we get equation as

$y=3(x+5)^2-4$

Extreme values:

we know that this parabola

and vertex of parabola always at extreme values

so, we can compare it with

$y=a(x-h)^2+k$

where

vertex=(h,k)

now, we can compare and find h and k

$y=3(x+5)^2-4$

we get

h=-5

k=-4

so, extreme value of this equation is

$(h,k)=(-5,-4)$

6 0

3 years ago

Read 2 more answers

Rectangle ABCD is similar to rectangle RSTU .

Alenkasestr [34]

Answer:

The scale factor of a dilation from ABCD to RSTU is $\frac{1}{2}$

Step-by-step explanation:

We know that the rectangle ABCD is similar to rectangle RSTU.

Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS

Working with the lengths of the sides :

DC.(Scale factor) = UT

AB.(Scale factor) = RS

Replacing with the values of the lengths (Scale factor : SF) :

$DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

$AB.SF=RS\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

Notice that the scale factor is dimensionless.

We can verify this result with the sides AD and BC :

$AD.SF=UR\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

$BC.SF=TS\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

The scale factor (SF) is $\frac{1}{2}$

7 0

2 years ago

Read 2 more answers

Which cross-sectional shapes do you find the most surprising? Explain why.

Zanzabum

By critically observing the cross-sections of the three-dimensional object I used, a cone is the cross-sectional shape I find most surprising.

<h3>The cross-section of a three-dimensional object?</h3>

In this exercise, you're required to use an online tool to investigate and determine the cross-sections of three-dimensional objects such as pyramids, cylinders, cones, etc., by passing different planes through them.

By critically observing the cross-sections of the three-dimensional object I used, a cone is the cross-sectional shape I find most surprising because rotating the slice around Y produced a circular curve that transitioned into a parabolic curve.

Read more on cross-sections here: brainly.com/question/1924342

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