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1 year ago

Identify the vertex

Mathematics

1 answer:

Svetradugi [14.3K]1 year ago

6 0

Answer:

The vertex is (-2,10)

Step-by-step explanation:

The vertex is the maximum point on a downward facing parabola

The maximum is (-2,10)

The vertex is (-2,10)

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2 years ago

Fill in the [?]<br>2.43 m = [?] cm<br>Give your answer in standard form.

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243

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2 years ago

stephanie and jenny each improved their yards by planting rose bushes and geraniums. they bought their supplies from the same st

galina1969 [7]

Answer:

The cost of one rose is $11., and the cost of one geranium is $5.

Step-by-step explanation:

The cost of one rose bush and one geranium can be determined by the use of simultaneous equation. Let the cost of a rose bush be represented by x, and the cost of one geranium by y.

So that,

13x + y = 148 .............. 1

9x + 14 y = 169 ............... 2

From eqaution 1,

y = 148 - 13x ............... 3

substitute the value of y in equation 2

9x + 14(148 - 13x) = 169

9x + 2072 - 182x = 169

2072 - 169 = 182x - 9x

1903 = 173x

x = $\frac{1903}{173}$

= 11

x = 11

substitute the value of x in equation 3

y = 148 - 13x

= 148 - 13(11)

= 148 - 143

y = 5

x = 11, y = 5

Thus, the cost of one rose is $11., and the cost of one geranium is $5.

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2 years ago

Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)

Rom4ik [11]

Answer:

Step-by-step explanation:

Given : $p(x)=x^{3} +6x^{2} -7x-60$

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, $\text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Since constant term = -60

Leading coefficient = 1

$\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}$

$\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}$

Thus the possible roots are $\pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60$

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is $x^{2} +x-12$