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3 years ago

Elise babysat her cousins during her parents' holiday party. The table shows the total earned for each cousin she babysat.

Mathematics

2 answers:

Jet001 [13]3 years ago

5 0

Answer:

C. $49

Step-by-step explanation:

It is going up by $7 each cousin

Sedbober [7]3 years ago

4 0

The correct answer is C. The slope (rate of change) for this table is given by the equation (14-7)/(2-1) which comes out to be 7/1 or 7 meaning that every time x increases by 1, y increases by 7. In other words, Elise earns $7 for each child she baby sits. So 7 children times $7 per child gives you $49.

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Which of the following strategies is appropriate for factoring polynomials with 4 terms?

labwork [276]

I would say D, determine if it can be factored by grouping (sorry, I forgot to put in the answer here).

5 0

3 years ago

In a GP the second and fourth terms are 0.04 and I respectively find the common ratio and the first term

Reptile [31]

Answer:

common ratio=0.5, a1= 0.08

Step-by-step explanation:

r=a3/a2

r=a4/a3

compare both we get:

a3/a2=a4/a3

subtitute a2=0.04 and a4=1

a3/0.04=1/a3

(a3)^2=0.04*1

(a3)^2=0.04

taking square root in both sides

a3=0.02

For r, r=a3/a2

subtitute a3 and a2 above

r=0.02/0.04

r=0.5 common ratio

For a1

r=a2/a1

0.5=0.04/a1

a1=0.04/0.5

a1=0.08

4 0

3 years ago

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use

Naddik [55]

Question has missing figure, the figure is in the attachment.

Answer:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

Step-by-step explanation:

Given,

We have an isosceles triangle which we can named it as ΔABC.

In which Length of AB is equal to length of BC.

And also m∠B is equal to m∠C.

ext.m∠C= 115°(Here ext. stands for exterior)

We have to find the measure of angles angles 1 through 5.

Solution,

For ∠1.

∠1 and ext.∠C makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle1+ext.\angle C=180\°$

On putting the values, we get;

$\angle 1+115\°=180\°\\\\\angle1=180\[tex]\therefore m\angle2=65\°$ -115\°=65\°[/tex]

Thus the measure of ∠1 is 65°.

For ∠2.

Since the given triangle is an isosceles triangle.

So, $m\angle1=m\angle2$

Thus the measure of ∠2 is 65°.

For ∠3.

Here ∠1, ∠2 and ∠3 are the three angles of the triangle.

So we use the angle sum property of triangle, which states that;

"The sum of all the angles of a triangle is equal to 180°".

$\therefore \angle1+\angle2+\angle3=180\°$

Now we put the values and get;

$65\°+65\°+\angle3=180\°\\\\130\°+\angle3=180\°\\\\\angle3=180\°-130\°=50\°$

Thus the measure of ∠3 is 50°.

For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle2 +\angle 4 =180\°$

Substituting the values of of angle 2 to find angle 4 we get;

$65\°+ \angle 4 = 180\°\\\\ \angle 4 = 180\°-65\°\\\\\angle 4= 115\°$

Thus the measure of ∠4 is 115°.

For ∠5.

∠4 and ∠5 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle4 +\angle 5 =180\°$

Substituting the values of of angle 4 to find angle 5 we get;

$115\°+ \angle 5 = 180\°\\\\ \angle 5 = 180\°-115\°\\\\\angle 5= 65\°$

Thus the measure of ∠5 is 65°.

Hence:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

6 0

3 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

ON YOUR OWN

vichka [17]

5 units because your starting from (-2,-2) so the last -2 will stay and the first number(-2) will go up until you hit the (,3) which will be 5 units away

6 0

2 years ago

Read 2 more answers