Suppose h(t)= -0.2 + 2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds

Answers

Answer 1

The maximum height of the ball is found at 64 feet

Explanation:

Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:

[tex]f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64[/tex]

Finally, the maximum height of the ball is found at 64 feet

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Related Questions

Joe's annual income has been increasing in the same dollar amount. The first year his income was $15,200, and the 4th year his income was $17,900. In which year was his income $19,700?​

Answers

Answer:

Therefore 6th year his income was $19,700.

Step-by-step explanation:

Given, Joe's annual income has been increasing in some dollar amount . The first year his income was $15,200 and 4th  year his income was $17,900.

A=$17900, P= $15,200 and n = 3 year

[tex]A= P(1+\frac{r}{100} )^n[/tex]

[tex]\Leftrightarrow 17900=15200(1+\frac{r}{100})^3[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})^3=\frac{17900}{15200}[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})=(\frac{17900}{15200})^{\frac{1}{3} }[/tex]

[tex]\Leftrightarrow \frac{r}{100}=(\frac{17900}{15200})^{\frac{1}{3} }-1[/tex]

[tex]\Leftrightarrow r=5.60[/tex]

Let  [tex]t^{th}[/tex] year Joe's income was $19,700.

[tex]\therefore 19700=15,200(1+\frac{5.60}{100} )^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1+0.056)^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1.056)^{t-1}[/tex]

[tex]\Leftrightarrow log(1.296)= (t-1)log(1.056)[/tex]

[tex]\Leftrightarrow \frac{log(1.296)}{log(1.056)}= (t-1)[/tex]

[tex]\Leftrightarrow t-1= 4.75[/tex]

[tex]\Leftrightarrow t= 4.75+1[/tex]

[tex]\Leftrightarrow t = 5.75[/tex] ≈6

Therefore 6th year his income was $19,700.

If the number of professors in a college is P and the number of students is S, and there are 19 times as many students as professors,write an algebraic equation that shows the

Answers

Answer:

[tex]S =19P\\S-19P = 0[/tex]                              

Step-by-step explanation:

We are given the following in the question:

Let P be the number of professor and S be the student in a college.

According to the question:

There are 19 times as many students as professors.

We have to write an equation to show the given relationship between professors and students.

[tex]S =19P\\S-19P = 0[/tex]

The above situation is the situation that represents the given relationship.

What is the degree of the polynomial below?
2х^2 + 3x +1​

Answers

Answer:

the degree for the polynomial is 2

Questiul 4 15 points)
Laurie and Maya sold at most $50 worth of get-well and friendship cards. The
friendship cards, x, were sold for $2 each and the get-well cards, y, were sold for
$1.50 each. Which point represents a reasonable number of cards sold?

Answers

Answer:

2 dollars cuz ur poor

Step-by-step explanation:

Find the value of x and explain please
ANSWER ASAP!!!!!!!!!!!!!!!!!

Answers

Answer:

y = - 4

Step-by-step explanation:

Given

y = 2 - 9x ← substitute x = [tex]\frac{2}{3}[/tex]

y = 2 - ( 9 × [tex]\frac{2}{3}[/tex] ) ← cancel the 9 and 3 by 3

  = 2 - (3 × 2 )

  = 2 - 6

  = - 4

Plz help now for 30 points k

Answers

Find total of non blue socks:

7 + 8 + 4 = 19

There are 9 blue socks.

Ratio is blue / non blue = 9/19

Does the bowling ball have more potential energy or kinetic energy as it sit on top of the building? Why?

Answers

Answer:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Step-by-step explanation:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Answer:

Before the ball hits the ground it has more potential energy but when is going down it looses potential energy and creates kinetic energy so when the ball hits the floor it would have more kinetic energy.

Step-by-step explanation:


Solve this equation 3x4x4x15-14+1= ?

Answers

Answer:

my answer is 707

Step-by-step explanation:

i used a calculator lol

Answer:

707

Step-by-step explanation:

How do you divide a decimal by a whole fraction

Answers

Answer

wherever the decimal is, put it directly on top of the dividing line thing. Now that the decimal looks like a regular whole number you can divide like you usually would. Whenever you do regular long division, your answer is always going to be on the top of the line. Your answer should have a decimal in it ... and that should be your answer.

Sidneys made $38 more than 3 times Casey’s weekly salary. If x represents Casey’s weekly salary , write an expression for sidneys weekly salary

Answers

y=3x+38 is the expression for Sidney's weekly salary.

Step-by-step explanation:

Given,

Casey's weekly salary = x

Let,

y be the weekly salary of Sidney's.

According to given statement;

Sidney makes $38 more than 3 times Casey's weekly salary.

Sidney's weekly salary = 3 times Casey's weekly salary + $38

[tex]y=3x+38[/tex]

y=3x+38 is the expression for Sidney's weekly salary.

Keywords: variable, addition

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How many times can 27 go into 224

Answers

27 can go into 224 8 times, it has a remainder of 8
8.29 times if you want to be exact

9. A relation contains the points ( -5,-10),( -2,-4)(-1,-2),(4,8) and (5,10) . Is this a function? Explain. (2 points)

Answers

Answer:

Yes it is a function given by f(x) = 2x

Step-by-step explanation:

Any function can approximated as series or a polynomial. For example,

[tex]e^{x} = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} ...[/tex]    (exponential function)

(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ;  3! = 3.2.1 = 6)

and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.

General form of a polynomial/series: [tex]f(x) = a + bx +cx^{2} + ...[/tex]

For the given set of points, we can start with the straight line equation:

[tex]f(x) = y = a + bx[/tex]    ........(1)

Let us take two points from the given relation: (-5, -10), (-1, -2)

and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of [tex]a[/tex] and [tex]b[/tex]:

[tex]-10=a-5b[/tex]    ........(2)

[tex]-2=a-b[/tex]    ..........(3)

Now (3) - (2) gives us: [tex]b=2[/tex] and putting the value of [tex]b[/tex] in any of the above equation gives us [tex]a=0[/tex]

Hence, we get the equation, [tex]f(x)=y=2x[/tex]

It can be seen that all the given points satisfies this relation and since we get a unique [tex]y[/tex] for every [tex]x[/tex], we can call this a function.

Final answer:

The provided relation is a function because each x-value is unique and maps to exactly one y-value, fulfilling the criterion that every element of the domain is associated with exactly one element of the range.

Explanation:

The question asks if a relation containing the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10) is a function. To determine if this relation is a function, we need to examine if any x-value (the first number in each pair) repeats with a different y-value (the second number in each pair). Upon inspection, we see that each x-value is unique to a single y-value, which means that each element of the domain maps to a unique value in the range. Therefore, we can conclude that this relation is indeed a function.

In general, a function is defined as a relation in which every element of the domain (set of all first elements) is associated with exactly one element of the range (set of all second elements). This criterion is met in the relation provided as each x-value is unique and paired with only one y-value.

How to divide 704 by 3 using long division

Answers

Answer:

Step 1: D for Divide. How many times will 5 go into 65? ...

Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5. ...

Step 3: S for Subtract. Next you subtract. ...

Step 4: B for Bring down. ...

Step 1: D for Divide. ...

Step 2: M for Multiply. ...

Step 3: S for Subtract.

Step-by-step explanation:

Expand to write an equivalent expression: -1/4(8x+12y)

Answers

Answer:

-2x-3y

Step-by-step explanation:

-1/4(8x+12y)

-8/4x-12/4y

-2x-3y

Final answer:

The expression -1/4(8x+12y) is expanded by distributing -1/4 to both 8x and 12y, resulting in the equivalent expression -2x - 3y.

Explanation:

To expand the expression -1/4(8x+12y), you need to distribute the term outside the parenthesis (-1/4) to each term inside the parenthesis. This process is known as the distributive property of multiplication over addition. Here's the step-by-step process:

Multiply -1/4 by 8x to get -2x.Multiply -1/4 by 12y to get -3y.Combine these two products to get the expanded expression: -2x - 3y.

In conclusion, the equivalent expression after expanding -1/4(8x+12y) is -2x - 3y.

Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?

Answers

Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5

Step-by-step explanation:

PLEASE HELP ME THIS IS DUE TODAY! TYSM IF YOU CAN. a.) Lines AD and BE intersect at point C, as shown. Create an expression that represents the measure of angle DCE in terms of X. b.) Using your expression, solve for the missing value of X if DCE was 120 degrees.

Answers

Answer:

1)  ∠DCE = (180  - x)°

2)   x  = 60°

Step-by-step explanation:

Here, given :  Lines AD and BE intersect at point C

(a)  Now, as we know, c BE is a straight line.

⇒∠BCD + ∠DCE = 180 °  (LINEAR PAIR)

⇒x °  + ∠DCE = 180 °

or, ∠DCE = (180  - x)° ....... (1)

(b) ∠DCE  = 120°

Putting the value in the equation (1), we get:

120°  = (180  - x)°

or, x =  180 - 120° = 60°

or, x  = 60°

A figure is dilated by a factor of 3. which statement about the mesurements of the image is true

Answers

A Dilation factor of 3 means that all dimensions of the figure are three times larger than those of the original figure. This applies to every dimension of the figure including height, width, and depth (if applicable). An example is a rectangle with original measurements 2 cm by 4 cm becoming 6 cm by 12 cm after dilation.

When a figure undergoes a dilation, all its dimensions are altered by the dilation factor.

In this case, the dilation factor is 3, which means that each dimension of the figure is three times larger than before.

It is important to note that this applies to all dimensions: height, width, and depth (if applicable).

For instance, suppose you have a rectangle with a height of 2 cm and width of 4 cm.

If the rectangle is dilated by a factor of 3, the new dimensions would be 6 cm (2 cm * 3) for height and 12 cm (4 cm * 3) for width.

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The question probable may be:

Explain the concept of dilation and provide an example illustrating how the dimensions of a figure change when subjected to a dilation factor. In particular, discuss the scenario where a rectangle with a height of 2 cm and width of 4 cm undergoes a dilation by a factor of 3. What are the new dimensions, and how does this align with the general principle of dilation?

How many times can 27 go into 224

Answers

Answer:

27 can go into 224 8 times by dividing 224 by 27 .

8.29 times is how much it can go

4√6 •√3 how do I show work for this because the answer is 2√12​

Answers

Answer:

[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]

Step-by-step explanation:

We want to simplify the radical expression:

[tex]4 \sqrt{6} \times \sqrt{3} [/tex]

We write √6 as √(2*3).

This implies that:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2 \times 3} \times \sqrt{3} [/tex]

We now split the radical for √(2*3) to get:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times \sqrt{3} \times \sqrt{3} [/tex]

We obtain a perfect square at the far right.

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times (\sqrt{3} )^{2} [/tex]

This simplifies to

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times 3[/tex]

This gives us:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \times 3 \sqrt{2} [/tex]

and finally, we have:

[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]

WILL GIVE BRAINLIEST!?!?!!?!?!? WHATS 9+10?????

Answers

the answer to 9 + 10 is 19
9 + 10 is equal to 21

SHOW ALL WORK: Graph each lineby plotting its intercepts or by using the y intercept and slope. {2x-y=4 {3y-3x=6

Answers

Answer:

x-y=-2

Step-by-step explanation:

Divide both sides if the equations by 3.

(3y-3x)÷3=6÷3

y-3x÷3=2

calculate the quotient

y-x=2

multiply both sides of the equation bub -1

-1x(-x)-1y=-1x2

any expression multiplied by -1

x-1y=-1x2

any expression multiplied by 1 remains the same.

x--y=-1x2

x-y=-2

What is the answer to this equation
3 3/7 + 4 5/7=

Answers

Conversion a mixed number 3 3
7
to a improper fraction: 3 3/7 = 3 3
7
= 3 · 7 + 3
7
= 21 + 3
7
= 24
7


To find new numerator:
a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7
7
= 21
7

b) Add the answer from previous step 21 to the numerator 3. New numerator is 21 + 3 = 24
c) Write previous answer (new numerator 24) over the denominator 7.

Three and three sevenths is twenty-four sevenths
Conversion a mixed number 4 5
7
to a improper fraction: 4 5/7 = 4 5
7
= 4 · 7 + 5
7
= 28 + 5
7
= 33
7


To find new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7
7
= 28
7

b) Add the answer from previous step 28 to the numerator 5. New numerator is 28 + 5 = 33
c) Write previous answer (new numerator 33) over the denominator 7.

Four and five sevenths is thirty-three sevenths
Add: 24
7
+ 33
7
= 24 + 33
7
= 57
7

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(7, 7) = 7. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 7 = 49. In the next intermediate step the fraction result cannot be further simplified by cancelling.
In words - twenty-four sevenths plus thirty-three sevenths = fifty-seven sevenths.

Answer:

8  1/7

Step-by-step explanation:

First,you take 3 and 3/7 and line it up with 4 and 5/7 and first you add your whole numbers which come before the fractions and get 7.Next,you add the fractions and get 8/7. Now you know it needs symplified because its an improper fraction. To symplify you have to × or ÷ and whatever one you do you have to do it to both the numerator and denominator. If you divide 8÷7=1 R1  7÷7=1.  Last add 7+1+1/7=8 1/7.

Jeannie needs 2 cups of milk to make her homemade brownies. How many fluid ounces does Jeannie need?

Answers

Answer:

16 fluid ounces=2 cups

Hope this helps!

Step-by-step explanation:

Answer:

16 fluid ounces

Step-by-step explanation:

1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.

Nara multiplied two whole numbers together to equal a product of 90.
Then she accidentally spilled ketchup on her work.

Select the three responses below that could be one of the numbers Nara multiplied.

Answers

Answer:

30×3=90 10×9=90 45×2=90 . .

Answer: 5, 10, 18

Step-by-step explanation:

does anyone know the answer ?

Answers

Answer:

15.7cm

Step-by-step explanation:

2 + 1.4 + 1.3 + 1.2 + 4.1 + 1.3 + 1.4 + 3

can someone help me one the questions I have not answered?

Answers

                             Q # 1

Answer:

[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime Number

Explanation:

391

[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]

[tex]=17\cdot \:23[/tex]

17, 23 are all prime number. So no further factorization possible

[tex]=17\cdot \:23[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime Number                                                 Q # 3

Answer:

[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime Number

Explanation:

291

[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]

[tex]=3\cdot \:97[/tex]

3, 97 are all prime number. So no further factorization possible

[tex]=3\cdot \:97[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime Number                            Q # 4

Answer:

[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime Number  

Explanation:

37

37 is a prime number. So no further factorization possible

[tex]=37[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime Number                                                                                                Q # 6

Answer:

[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime Number

Explanation:

411

[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]

[tex]=3\cdot \:137[/tex]

3, 137 are all prime number. So no further factorization possible

[tex]=3\cdot \:137[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime Number                                Q # 7

Answer:

[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime Number

Explanation:

387

[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]

[tex]=3\cdot \:129[/tex]

[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]

3, 43 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:43[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime Number                                           Q # 9

Answer:

[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime Number

Explanation:

113

113 is a prime number. So no further factorization possible

[tex]=113[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime Number                                               Q # 16

Answer:

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime Number

Explanation:

293

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]

[tex]=293[/tex]

[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]

[tex]=293[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime Number                             Q # 17

Answer:

[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime Number

Explanation:

451

[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]

[tex]=11\cdot \:41[/tex]

11, 41 are all prime number. So no further factorization possible

[tex]=11\cdot \:41[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime Number                       Q # 18

Answer:

[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime Number

Explanation:

459

[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]

[tex]=3\cdot \:153[/tex]

[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:51[/tex]

[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

3, 17 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime Number                       Q # 19

Answer:

[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime Number

Explanation:

385

[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]

[tex]=5\cdot \:77[/tex]

[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]

[tex]=5\cdot \:7\cdot \:11[/tex]

5, 7, 11 are all prime number. So no further factorization possible

[tex]=5\cdot \:7\cdot \:11[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime Number                    Q # 20

Answer:

[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime Number

Explanation:

162[tex]162\:\mathrm{divides\:by}\:2\quad \:162=81\cdot \:2[/tex][tex]=2\cdot \:81[/tex][tex]81\:\mathrm{divides\:by}\:3\quad \:81=27\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:27[/tex][tex]27\:\mathrm{divides\:by}\:3\quad \:27=9\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:9[/tex][tex]9\:\mathrm{divides\:by}\:3\quad \:9=3\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex][tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex]

So,

[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime Number

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Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
5x + 3y = 9
-10x – 6y = -18

Answers

Answer:

The system has infinitely many solutions

Step-by-step explanation:

we have

[tex]5x+3y=9[/tex] ----> equation A

[tex]-10x-6y=-18[/tex] ----> equation B

Multiply by -2 both sides equation A

[tex]-2(5x+3y)=-2(9)[/tex]

[tex]-10x-6y=-18[/tex] ----> equation C

Compare equation B and equation C

The equations are identical (is the same line)

therefore

The system has infinitely many solutions

Is a consistent dependent system

She gave 1/3 of cookies for her husband 1/4 of the cookies to her son and 1/6 of a cookies to her neighbor she ate the remaining six cookies how many cookies did she make

Answers

She made 15 cookies

Solution:

Let "x" be the number of cookies she made

She gave 1/3 of cookies for her husband

Therefore,

[tex]Husband = \frac{1}{3}x[/tex]

Find the remaining

[tex]Remaining = x - \frac{x}{3} = \frac{3x-x}{3} = \frac{2x}{3}[/tex]

1/4 of the cookies to her son

Therefore,

[tex]son = \frac{1}{4} \times \frac{2x}{3} = \frac{x}{6}[/tex]

Now again find the remaining

[tex]Remaining = \frac{2x}{3} - \frac{x}{6} = \frac{x}{2}[/tex]

1/6 of a cookies to her neighbor

[tex]Neighbor = \frac{1}{6} \times \frac{x}{2} = \frac{x}{12}[/tex]

Now again find the remaining

[tex]Remaining = \frac{x}{2} - \frac{x}{12} = \frac{5x}{12}[/tex]

She ate the remaining six cookies

Therefore,

[tex]\frac{5x}{12} = 6\\\\5x = 72\\\\x = 14.4[/tex]

Thus she made approximately 15 cookies

What is the radius of a
cylinder with a diameter of
36?

Answers

Answer:

radius=diameter÷2=36÷2=13

Yo sup??

diameter=2*radius

36=2 r

r=18

therefore the radius is 18 units

Hope this helps

In a triangle, one angle measures 68° and another
angle measures 38°. What is the measure of the third
angle?​

Answers

Answer:

74°

Step-by-step explanation:

all angles of a triangle will always end up equal to 180°

68 + 38 = 106

180 - 106 = 74

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