Difference of squares. Pls help algebra factoring polynomials 10 points

Answer:

Step-by-step explanation:

12

Answer:

a) 12

b) 11

c) 8

Step-by-step explanation:

Using the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

a is the shorter side,

b is the longer side,

c is the hypotenuse.

a) [tex]a^2 + b^2 = c^2\\5^2+b^2=13^2\\25+b^2=169^2\\b^2=169-25\\b^2=144\\b=\sqrt{144}=12\\ b=12[/tex]

b)[tex]a^2 + b^2 = c^2\\a^2+60^2=61^2\\a^2+3600=3721\\a^2=3721-3600\\a^2=121\\a=\sqrt{121}=11\\ a=11[/tex]

c)[tex]a^2 + b^2 = c^2\\a^2+15^2=17^2\\a^2+225=289\\a^2=289-225\\a^2=64\\a=\sqrt{64}=11\\ a=8[/tex]

260

Step-by-step explanation:

11y + 6 =139

-6

11y. = 133

÷11

y. = 133/11

22y - 6

22 x 133/11 - 6

=260

Hope this helps!

Step-by-step explanation:

[tex]11y + 6 = 139 \\ 11y = 133 \\ y = 12.0909[/tex]

so,

[tex]22y - 6 \\ 22(12.1) - 6 \\ = 260[/tex]

The cost of each pizza is $12.50 while the cost of each drink is $1.99.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the cost of each pizza and y the cost of each drink. Hence:

3x + 5y = 47.45  (1)

Also:

4x + 8y = 65.92  (2)

From both equations:

x = 12.5, y = 1.99

The cost of each pizza is $12.50 while the cost of each drink is $1.99.

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Using the z-distribution, it is found that there is enough evidence to conclude that taking a low-dose aspirin each day reduces the chance of developing cancer.

At the null hypotheses, it is tested if there is no difference among the proportions, that is:

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternative hypotheses, it is tested if the aspirir proportion is lower, that is:

[tex]H_0: p_1 - p_2 < 0[/tex]

For each sample, they are given by:

[tex]p_1 = \frac{15}{500} = 0.03, s_1 = \sqrt{\frac{0.03(0.97)}{500}} = 0.0076[/tex]

[tex]p_2 = \frac{26}{500} = 0.052, s_2 = \sqrt{\frac{0.052(0.948)}{500}} = 0.0099[/tex]

Hence, for the distribution of differences, they are given by:

[tex]\overline{p} = p_1 - p_2 = 0.03 - 0.052 = -0.022[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0076^2 + 0.0099^2} = 0.0125[/tex]

It is given by:

[tex]z = \frac{\overline{p} - p}{s}[/tex]

In which p = 0 is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{p} - p}{s}[/tex]

[tex]z = \frac{-0.022 - 0}{0.0125}[/tex]

z = -1.76.

Considering a left-tailed test, as we are testing if the proportion is less than a value, the critical value is [tex]z^{\ast} = -1.645[/tex]

Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that taking a low-dose aspirin each day reduces the chance of developing cancer.

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The total time it takes the soccer ball to hit the ground, which bounces up at a velocity of 20 feet per second, is 1.535 seconds.

Vertical motion model is the model which is used to find the height of the object which is thrown vertically upward. It can be given as,

[tex]h(t)=-16t^2+v+t[/tex]

Here, t is time and v is velocity.

Soccer player jumps up and heads the ball while it is 7 feet above It bounces up at a velocity of 20 feet ground. per second.  Thus, the vertical motion model for this situation is,

[tex]h(t)=-16t^2+20t+7[/tex]

When the ball hit the ground, the value of height (h) become zero. Thus,

[tex]0=-16t^2+20t+7\\16t^2-20t-7=0[/tex]

On solving this quadratic, the value of x we get,

[tex]x=1.535,x=-0.285[/tex]

Taking positive side x=1.535 second. Thus, the total time it take the soccer ball to hit the ground which bounces up at a velocity of 20 feet per second, is 1.535 seconds.

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Answer: 16

Step-by-step explanation:

Answer:

96 degress letter G

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To evaluate the expression for a= 3, replace (or 'substitute') every 'a' you see with a '3' in the expression.

Given expression: 32 -4a

When a= 3,

32 -4a

= 32 -4(3)

= 32 -12

= 20

Answer:

Step-by-step explanation:

In the question we're given with an expression that is 32 - 4a , value of a is 3 . And we are asked to evaluate the expression for a = 3 .

Solution : -

[tex] \longmapsto \: 32 - 4a[/tex]

Step 1 : Substituting value of a in given expression :

[tex] \longmapsto \:32 - 4(3)[/tex]

Step 2 : Multiplying 4 with 3 :

[tex] \longmapsto \:32 - 12[/tex]

Step 3 : Subtracting 12 from 32 :

[tex] \longmapsto \: \red{\boxed{ \frak{20}}}[/tex]

Answer:

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

Step-by-step explanation:

Looking at the graph its obviously a circle as it said.

We have to find (h,k) and the radius of that circle.

(h, k)  = (3,2)

Origin to the edge of the A.

radius = 4

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

The scatter plot shows the association between the ordered pairs

The two ordered pairs that can be joined to best draw the line of best fit for this scatter plot are (0, 13) and (10, 0)

To draw the line of best fit, the line must pass through at least two points such that the number of points on either sides of the line must be equal

See attachment for illustration

From the attached image of the graph, we can see that the line passes through the points (0, 13) and (10, 0), and there are 4 points on either sides

Hence, the two ordered pairs are (0, 13) and (10, 0)

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Answer: (0,13) and (10,0)

Step-by-step explanation:

I took the test on flvs.net

Answer:

π 36 m^2

Step-by-step explanation:

C = 2π R = 12π m --> R = 6m

A = π R^2 = π 36 m^2

Answer:

Step-by-step explanation:

In the question we are given that circumference of circle is 12π m . And we are asked to find the area of circle in term of π .

Solution : -

For finding area of circle we need to find the radius of circle . In the question circumference of circle is given . So we can find radius of circle using it . We know that ,

[tex] \qquad \quad \pink{\underline{\pink{\boxed{\frak{Circumference_ {(Circle) }= 2\pi r}}}}}[/tex]

Where ,

But as in the question , it is given that we have to find the area in term of π. So we aren't using π as 3.14 or 22/7 .

Now, Radius :

[tex] \longrightarrow \qquad \: 12 \cancel{\pi }= 2 \cancel{\pi} r[/tex]

Step 1 : Cancelling π and we get :

[tex] \longrightarrow \qquad \:12 = 2r[/tex]

Step 2 : Dividing both sides by 2 :

[tex] \longrightarrow \qquad \: \cancel{\dfrac{12}{2} } = \dfrac{ \cancel{2}r}{ \cancel2} [/tex]

On further calculations we get :

[tex] \longrightarrow \qquad \: \boxed{ \bf{r = 6 \: m}}[/tex]

Finding Area :

As we have find the radius of circle above so we can find its area easily . We know that ,

[tex] \qquad \: \qquad \pink{\underline{\pink{ \boxed{{\frak{ Area_{(Circle)} = \: \pi r {}^{2} }}}}}}[/tex]

Now substituting value of radius :

[tex] \longmapsto \: \qquad \quad\pi (6) {}^{2} [/tex]

[tex] \longmapsto \: \qquad \quad \pi \times \: 6 \times 6[/tex]

[tex] \longmapsto \: \qquad \quad \pi \times 36[/tex]

We get :

[tex] \longmapsto \: \qquad \quad \blue{\underline{\blue{\boxed{\frak{ \bf{36 \pi \: m {}^{2} }}}}}}[/tex]

Answer:

number of passengers is an independent variable, average speed depends on the number of passengers so its a dependent variable, liters of fuel used depends on average speed so its a dependent variable

Step-by-step explanation:

Answer:

  3/8

Step-by-step explanation:

A ratio is expressed in lowest terms by removing common factors from numerator and denominator.

  [tex]\dfrac{2.7\text{ hr}}{7.2\text{ hr}}=\dfrac{3\cdot0.9\text{ hr}}{8\cdot0.9\text{ hr}}=\boxed{\dfrac{3}{8}}[/tex]

Answer:

$91.66

Step-by-step explanation:

We need to calculate how much they've saved so far. So we multiply 12 * 14 to get 168 months (14 years). Then we can multiply 350 by 168 to get $58,800.

We then subtract 58,800 from 80,000 to get 21,200 left to cover over 4 years. In 4 years, there are 48 months so we just divide 21,200 by 48 to get 441.66.

Subtract 350 from 441.66 to get 91.66.

We can check this by doing (350*168) + (441.66 * 48).

Hope this helps,

As always, correct me if I'm wrong

Answer:

Given :-

Money saved by her parents each month = $350

Time = 14 years = 14 × 12 = 168 months

To find :-

How much money ger parents have to save in next 4 years to achieve the goal of $80,000

Total money saved in 14 years = 350 × 168 = $58,800

Total money left to achieve goal = 80,000 - 58,800

= $21,200

Money they have saved next 4 years in each month to achieve the goal

[tex] = \frac{21200}{4 \times 12} \\ = \frac{21200}{48} \\ = 441.69 [/tex]

They need $441.69 each month to complete $80,000 for her college.

Answer:

C

Step-by-step explanation:

If that is wrong tell me. I am sure it is right tho

Answer:

See below

Step-by-step explanation:

Decreasing 10% means the car retains 90 % of its value

Value of car = 5000 ( .90)^x      where x = number of years

Answer:

[tex]1 \2 (7 + 12)6 \\ 1 \2(19)6 \\ 114 \times 1 \2 = 72[/tex]

so therefore area is 72cm²

The expression that represents the volume of the cone, in cubic units is ¹/₃πr²h.

The volume of a cone is given by the following formula presented below;

V = ¹/₃πr²h

where;

The volume of a cone can be determined by multiplying the square of the radius and height of the cone.

Thus, the expression that represents the volume of the cone, in cubic units is ¹/₃πr²h.

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Answer:

[tex]\frac{2}{3}[/tex] π x³

Step-by-step explanation:

Answer:

697

Step-by-step explanation:

A product is an answer to a multiplication question

Answer:

Computer Science is more harder so I would go with Precalculus.

25 minutes long

Hope this helps!

Ok so we know that the movie starts at 7:15 PM. The duration of the movie is 1.5 hours long. She begins eating her snack after the movie which, sense 7:15 plus 1.5 hours is 8:45, is 8:45. She finishes her snack at 9:10. What is the difference between 9:10 and 8:45?

For me, the easiest thing to do we would be to add a half hour (30 minutes) to the 8:45. This gets 9:15. Since 9:15 is past 9:10, I subtract the difference to get 5 minutes. I then take the 30 minutes I added to the 8:45 and subtract the 5 minutes that it went over to get 25 minutes. This is the easiest way to get the answer in my opinion. Sorry if this could not be of help to you!

Diagram to better understand maybe? (I did the best I could with this lol)

                                              x (the 25 minutes you found once you solved it)

                                                                                      ^

7:15 PM ----------------------------- 1.5 hours later----------------------------------- 9:10 PM

^                                                          ^                                                            ^

Time the movie started          Movie length             When she finished eating

Answer:

sphere have a same diameter of cone so

the sphere have a diameter of 40 then the diameter is 40÷2=20

that's mean than the radios is 20

Answer:

1cm=20km

multiply both sides by 9

you get

9cm=20x9km

9cm=180km

The length of arc PS from the information given in the task content is; 31.5 ft.

It follows from the task content that;

On this note, the length of arc PS is;

arc PS = (164/360) × 2 × 3.14 × 11.

arc PS = 31.5ft.

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The maximum height of the egg with an equation of h(t) = -16t² + 96t - 120.35 is 23.65 feet at 3 seconds

An equation is an expression used to show the relationship between two or more numbers and variables.

Let us assume the height of the egg (h) at time t is given by:

h(t) = -16t² + 96t - 120.35

The maximum height is at h' = 0, hence:

h' = -32t + 96 = 0

-32t + 96 = 0

t = 3 sec

h(3) = -16(3)² + 96(3) - 120.35 = 23.65

The maximum height of the egg with an equation of h(t) = -16t² + 96t - 120.35 is 23.65 feet at 3 seconds

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