Solve the following systems of equations. To unlock puzzle three
find the product of each solution (ordered pair -x and y value)
and then find the mean of all five products.

The GCF is 4

The polynomial factors to [tex]4(3x^2+x+5)[/tex]

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Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

[tex]12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)[/tex]

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

Answer: 110

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary, so [tex]70+x=180 \longrightarrow x=110[/tex]

Answer:

Step-by-step explanation:

since this answer wants an approximation,  we can round the  cost up

Ham- 6                                 1/2 of 6 = 3

Turkey- 5                             1 pound of turkey= 5

Roast Beef- 7                       1/4 of 7= 1.75

Salami- 3                              2 x 3= 6   1/2 of 3= 1.5 = 7.5

bologna- 4                            No bologna was purchased.

3+5+1.75+ 7.5= 17.25 which is approximately 17.  

Answer:

7.6

Step-by-step explanation:

We want to find the distance between (0,6) and (-3,-1)

We can find the distance between any two points using the distance formula

Distance between two points =

[tex] \sqrt{(x2 - x1)^{2} +(y2 - y1) {}^{2} } [/tex]

Where the values of x and y are derived from the the two points. (x1,y1) and (x2,y2)

Here the two points are (0,6) and (-3,-1)

So we have (x1,y1) = (0,6) so x1 = 0 and y1 = 6

And we have (x2,y2) = (-3,1) so x2 = -3 and y2 = -1

Now we plug in the values of x and y into the formula and evaluate to get the distance.

Again recall distance = √(x2-x1)²+(y2-y1)²

==> plug in x2 = -3 , x1 = 0, y2 = -1 and y1 = 6

Distance = √(-3-0)²+(-1-6)

==> evaluate operations inside of parenthesis

Distance = √(-3)²+(-7)²

==> evaluate all exponents

Distance = √9+49

==> and 9 and 49

Distance = √58 = 7.6 (rounded)

Answer:

False

Step-by-step explanation:

Range can be calculated by taking the difference of the lower limit and upper limit of the data
The Upper limit here is 8.5 (considering) and lower limit is 4
So,
R= 8.5-4
R=4.5
The given says it is 2.5 so it is false.

Answer:

I'm pretty sure it is (c)

Step-by-step explanation:

bc the angle is not read in the right order

Answer:

1, 6, 11, and 16 in that order

Step-by-step explanation:

every time the x value increases by 1, the f(x) value increased by 5

Based on the height of the pyramid and the dimensions of the square base, the space that Maria has inside the pop-up net is 1,280 in³.

This can be found as the volume of a pyramid which is:

= (Length x Width x Height) / 3

Solving gives:

= (16 x 16 x 15) / 3

= 3,840 / 3

= 1,280 in³

Find out more on the volume of a pyramid at https://brainly.com/question/3722054.

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Answer:

to find z

Step-by-step explanation:

8=z/6

z=6 x 8
z= 48

Answer:

No and the density changes along with the weight.

Answer:

  (a) No. The weight is more than 150 lb.

  (b) No. Density is not a function of volume.

Step-by-step explanation:

The weight of the aquarium is the product of the volume and the density of the contents.

The volume of the aquarium is the product of its dimensions:

  V = LWH = (1.75 ft)(1.75 ft)(1.75 ft) = 1.75³ ft³ = 5.359375 ft³

The weight of its contents, at 72 lb/ft³ will be ...

  (72 lb/ft³)(5.359375 ft³) = 385.875 lb

The aquarium should not be placed on the table. The weight of the aquarium is too great for the load limit of the table.

__

The density of water is the ratio of its mass to its volume. Density does not change with depth or volume. It is essentially constant. (Water is considered to be virtually incompressible. Its density changes slightly with temperature,)

No, the density of the water would not change.

_____

Additional comments

The half-full aquarium would weigh about 385.875/2 lb ≈ 194 lb. This is still too heavy for the table.

The density of water is actually about 62.4 lb/ft³. We assume the extra 10 lb/ft³ might take into account the weight of the aquarium and any gravel or other non-water content.

Answer:

Step-by-step explanation:

Answer:

The area of triangle ABC is 60 mm^2

Step-by-step explanation:

x = the area of triangle ABC

15/6 * x/24

x=60

Answer:

  (d)  150 mm²

Step-by-step explanation:

The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.

__

ΔABC is larger than ΔPRT by the factor ...

  AC/PT = 15/6 = 5/2

The area of ΔABC is the square of this factor times the area of ΔPRT:

  area ABC = (5/2)²×area PRT

  area ABC = (25/4)×(24 mm²)

  area ABC = 150 mm²

Triangle ABC and triangle DEF are congruent by the SAS Congruence Postulate

Two triangles are said to be congruent if they have the same shape and their corresponding sides are also congruent.

We can say that two triangles are congruent using these 5 rules:

1: SSS or the side, side, side rule, that means that we have two triangles with all three sides equal.

2. SAS or side, angle, side states that in the two triangles, two sides and the included angle are equal.

3. ASA or angle, side, angle states that in two triangles, the two angles and the included side are equal.

4. AAS or angle, angle, side states that we have two triangles where two angles and the non-included side are equal.

5. HL or the Hypotenuse Leg rule states that, if the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, then the two triangles are congruent.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are also congruent.

Example:-From the diagram, given that:

AB = DE, BC = EF and ∠B = ∠E

Triangle ABC and triangle DEF are congruent by the SAS Congruence Postulate

Find out more on congruent triangles at:

brainly.com/question/2644832

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Answer:

-5

Step-by-step explanation:

3 - 9 + 1 = -6 + 1 = -5

Hope this helped! I would appreciate a Brainliest!

(BTW, if you can, can you please answer my question? It's due today!)

Answer:

Step-by-step explanation:

Answer:

ok this is pretty simble you just have to subtract the bottom exponents from the top so

3-2=1

2-2=0

a^1=a

a

Hope This Helps!!!

Answer:

Min max median and q3 is correct, q2 should be 8.5

Answer:

7.04, 7.134 ,7.2, 7.413

Step-by-step explanation:

Answer:

Volumer of cylinder

=(πd²/4)×h

=(36π/4)11

99π yd³

Answer:

23

Step-by-step explanation:

let the number = X

subtracting 13 from X = X -13

multiplying the difference by -4= (X -13)×-4

the result is -40 means (X-13)×-4=-40

(X- 13)×-4 = -40

-4 X +52 = -40

collect like term

-4 X = -40-52

- 4X = -92

dividing bothsides by -4

-4 X /-4 = -92/-4

X = 23

Answer:

false

Step-by-step explanation:

Using proportions, the amount that Sally can expect to receive from social security annually is given by:

c. $19,153.26.

A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.

She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:

A = 0.42 x 45603 = $19,153.26.

Which means that option C is correct.

More can be learned about proportions at https://brainly.com/question/24372153

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Answer:

11

Step-by-step explanation:

volume of a prism = area of base × height

plug in what we are given

275 = 25 × height

==> divide both sides by 25

11 = height

Answer:

60π

Step-by-step explanation:

Formula for surface area of a cylinder is 2πrh + 2r²π

2πrh: this is the formula to find the area of the cylinder itself (circumference of the base times the height of the cylinder)

2r²π: this is the formula to find the area of the 2 circles at the end of the cylinder (area of a circle times 2)

We can substitute h with 7 and r with 3 to solve:

2πrh + 2r²π

2(3)(7)π + 2π(3²)

42π + 18π

60π

That is your answer

- Kan Academy Advance

Answer: Let's put the chart into ordered pairs:

(x, y)

(2,1)

(3,4)

(3,3)

(4,2)

(5,5)

In bold, we see that there are two y-values at x=3. This means that this relation fails the vertical line test (two points on the same verticle line). This is not a function.

The answer options may be mis-written.

The answer is no, because one x value corresponds to more than one y-value.

Have a great day!

and night..

;).

Step-by-step explanation:

Answer:

60 ft³

Step-by-step explanation:

Concepts

The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.

Application

In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.

Solution