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3 years ago

10

Which number line shows all the values of a that make the inequality - 3x +1 < 7 true?

1 answer:

GrogVix [38]3 years ago

5 0

Answer:

Third option

Step-by-step explanation:

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Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). Write the equati

Nutka1998 [239]

the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.

it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.

check the picture below.

so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9$

$\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill$

7 0

3 years ago

Darla has four buckets shaped like cylinders she is filling the buckets with water by using a scoop shaped like a cone if the co

padilas [110]

Answer:

12 Scoops

Step-by-step explanation:

Darla has 4 Cylinder Shaped Buckets

Volume of the Cylinders $=4*\pi r^2h$

The scoop is cone shaped and:

Volume of the Cone Scoop $=\frac{1}{3} \pi r^2h$

Since the radius and height of the cone scoop and cylindrical buckets are the same,

The number of Cone Scoops it will take to fill the buckets is:

Total Volume of Buckets/Volume of Cone Scoops

$=\dfrac{4*\pi r^2h}{\frac{1}{3} \pi r^2h} \\=4 \div \frac{1}{3}\\=12$

It will take 12 Scoops to fill the 4 buckets.

5 0

3 years ago

All of the following are irrational except _____.

a_sh-v [17]

The number that is not irrational is $1.\overline{45}$ . The correct option is the second option $1.\overline{45}$

<h3>Irrational numbers </h3>

From the question, we are to determine which of the given options is not irrational

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.

$1.\overline{45}$ is a repeating decimal and it can be expressed as a fraction

$1.\overline{45} = \frac{144}{99}$

∴ $1.\overline{45}$ is not an irrational number. It is a rational number

The other options cannot the expressed as a fraction.

Hence, the number that is not irrational is $1.\overline{45}$ . The correct option is the second option $1.\overline{45}$

Learn more on Irrational numbers here: brainly.com/question/11919233

#SPJ1

5 0

2 years ago

4/-7 + -6/5 <br><br>In simplest form

nlexa [21]

See attachment for math work and answer.

6 0

3 years ago

What is the value of x?<br><br> 27(x+4)=−6<br><br><br> −35<br><br> −25<br><br> 25<br><br> 35

Oksanka [162]

x = -38/9 !!!

27(x+4)=−6

Step 1: Simplify both sides of the equation.

27(x+4)=−6

(27)(x)+(27)(4)=−6 (Distribute)

27x+108=−6

Step 2: Subtract 108 from both sides.

27x+108−108=−6−108

27x=−114

Step 3: Divide both sides by 27.

27x/27=−114/27

x=−389

6 0

3 years ago