Show that the points (6,1), (5,6), (-4,3), (-3,2) are the vertices of a parallelogram

Answer:

12

Step-by-step explanation:

We can use the property of exponents  [tex]\frac{a^b}{a^c}=a^{b-c}[/tex]  over here.

Let's use this property to write:

[tex]\frac{a^n}{a^3}\\=a^{n-3}[/tex]

This is equal to a^9, hence, n - 3 = 9. Let's solve for n:

[tex]n-3=9\\n=9+3\\n=12[/tex]

n = 12

Answer:

option C

12

Step-by-step explanation:

Given in the question an expression

[tex]\frac{a^{n} }{a^{3} }=a^{9}[/tex]

To solve for n we will use rules of exponent

cross multiply

[tex]a^{n}=a^{9}a^{3}[/tex]

apply product rule

[tex]a^{n}=a^{9+3}[/tex]

[tex]a^{n}=a^{12}[/tex]

Apply logarithm on both sides of equation

[tex]lna^{n}=lna^{12}[/tex]

apply power rule of logarithm

nln(a) = 12ln(a)

ln(a) will cancel out on each side so we are left with

n= 12

x = 899xy + 63

29x31xy + 29x^2+5

29(31y+2)+85

=29

63-58=5

The remainder will be 5.

Answer:

Your answer would be C. 5

Step-by-step explanation:

-44>-2x-8

Add 8 on both sides

-36>-2x

Divide by -2 dice your x can't be negative

18<x

The sign flips when you divide by a negative. Therefore if the question is a true or false question, the answer would be false

Answer:  18 ≤ x < 0

Step-by-step explanation:

-44 > -2x - 8 ≥ -8

-36 > -2x ≥ 0          added 8 to all three sides

18 < x ≤ 0    divided all three sides by -2 (which flips the inequality signs)

Answer:

Step-by-step explanation: the pattern is going positive to negative and going further away from zero so the next term would be -3

Answer:  in 12 years (2017)

               23,000 students enrolled

Step-by-step explanation:

Let x represent the number of years since 2005.

Let y represent the number of students enrolled.

College A: y = 14,000 + 750x

College B: y = 35,000 - 1000x

Solve the system using the Substitution Method:

14,000 + 750x = 35,000 - 1000x

           +1000x               +1000x

14,000  + 1750x = 35,000

-14,000                 -14,000

                1750x = 21,000

                        x = 12

Input x = 12 into one of the equations to solve for y.

y = 35,000 - 1000x

  = 35,000 - 1000(12)

  = 35,000 - 12,000

  = 23,000

Explanation on when two colleges will have the same enrollment and what the enrollment will be at that time.

Step 1: Set up equations for the enrollment at each college over time. Let x be the number of years since 2005:

College A enrollment = 14000 + 750x

College B enrollment = 35000 - 1000x

Step 2: Set the two equations equal to each other:

14000 + 750x = 35000 - 1000x

Step 3: Solve for x to find when the colleges will have the same enrollment:

x = 10 years

Step 4: Substitute x back into the equations to find the enrollment at each college after 10 years:

College A enrollment = 14000 + 750(10) = 21500 students

College B enrollment = 35000 - 1000(10) = 25000 students

Answer:

10 - 3x

Step-by-step explanation:

given

12 - [tex]\frac{6x+4}{2}[/tex]

= 12 - [tex]\frac{6x}{2}[/tex] - [tex]\frac{4}{2}[/tex]

= 12 - 3x - 2 ← collect like terms

= 10 - 3x

Answer:

14

Step-by-step explanation:

Using the law of cosines on ΔRST, then

s² = 9² + 8² - (2 × 9 × 8 × cos111° )

   = 81 + 64 - ( 144 × cos111° )

   = 145 - (- 51.6)

   = 145 + 51 . 6 = 196.6 ( take the square root of both sides )

s = [tex]\sqrt{196.6}[/tex] ≈ 14

The answer is: 14

Using the law of cosines and the given information, we can find the value of s.

Law of cosines is:

[tex]a^{2}=b^{2}+c^{2}-2abcos(A)[/tex]

Where,

[tex]a=s\\b=9\\c=8\\A=111(degrees)[/tex]

By substituting we have:

[tex]s=\sqrt{9^{2}+8^{2}-2*9*8*cos(111)}\\\\s=\sqrt{81+64-(144)*(-0.35)}=\sqrt{145+50.4}=\sqrt{195.4}=13.98=14[/tex]

So, the correct answer is:

[tex]s=14[/tex]

Have a nice day!

Answer: The real number is 8540

Step-by-step explanation: 85.4  1000

Answer:

$291,016.80

A is correct.

Step-by-step explanation:

You are applying for an 80/20 mortgage to buy a house costing $145,000.

Loan Formula:

[tex]EMI=\dfrac{P\cdot r}{1-(1+r)^{-n}}[/tex]

Case 1:

Loan amount, P = 80% of 145000 = $ 116,000

Rate of interest, r = 4.75% = 0.0475

Time of loan, n = 30 years = 360 months

Substitute the values into formula.

[tex]EMI=\dfrac{116000\cdot \frac{0.0475}{12}}{1-(1+\frac{0.0475}{12})^{-360}}[/tex]

[tex]EMI=605.11[/tex]

Total payment for case 1: 605.11 x 360 = $217,839.60

Case 2:

Loan amount, P = 20% of 145000 = $ 29,000

Rate of interest, r = 4.75% = 0.07525

Time of loan, n = 30 years = 360 months

Substitute the values into formula.

[tex]EMI=\dfrac{29000\cdot \frac{0.07525}{12}}{1-(1+\frac{0.07525}{12})^{-360}}[/tex]

[tex]EMI=203.27[/tex]

Total payment for case 1: 203.27 x 360 = $73,177.20

Total amount of the mortgage = $217,839.60 + $73,177.20

                                                    = $291,016.80

Hence, The total amount of the mortgage is $291,016.80

Answer:

A=75 cm

Step-by-step explanation:

The formula of the area of a triangle is A=bh/2.

A=(15)(10)/2.

A=150/2

A=75 cm is your answer.

Answer:

A=75 cm

Step-by-step explanation:

A=bh/2 is the formula for the area of a triangle

1) Multiply 15 the base and the height 10 first

A=(15)(10)

A= 150 cm

2) divide 150cm by 2

A=150/2

A=75 cm is your answer.

Hopes this helps My friend!

Answer:

64 ft

Step-by-step explanation:

if a projectile is fired straight upward from the ground with an initial speed of 64 feet per second, then its height in feet after seconds is given by the function h(t)=-16t^2 + 64t. find the maximum height of the projectile.

***

h(t)=-16t^2 + 64t

complete the square

h(t)=-16(t^2 -4t+4)+64

h(t)=-16(t-2)^2+64

This is an equation of a parabola that opens upward with vertex at (2,64)

maximum height of the projectile=64 ft (2 sec after it is fired)

Both Spencer and Jeremiah are correct

The given equation;

6x - 2 = -4x + 2

The first step is obtaining the solution to the given equation is to collect similar terms together.

Add 4x to both sides of the equation;

6x + 4x - 2 = -4x + 4x + 2

10x - 2 = 2

Or

Subtract 6x from both sides of the equation;

6x - 6x - 2 = -4x - 6x

-2 = -10x + 2

Thus, both Spencer and Jeremiah are correct.

Learn more about algebraic equation here: https://brainly.com/question/2164351

Answer:

36 and 32

Step-by-step explanation:

So what you do is look at the radius which is 18. The radius is half the distance. So all you have to do is do 18*2=36.

Same with the other one 16*2=32.

Those are your answers.

To determine how many apples you can buy for $168.00, you first calculate the cost per pound to be $3.50. Then, calculate that you can buy 48 pounds of apples, and since there are about 3.2 apples per pound, you can purchase approximately 153 apples for $168.00.

To determine how many apples you can buy for $168.00, let's start by calculating the cost per pound of the apples on sale, which is $28.00 for 8 pounds. This yields a cost per pound of $3.50.

Next, we'll find out how many pounds of apples you can buy for $168.00. By dividing $168.00 by the cost per pound ($3.50), we get 48 pounds of apples.

Since 1 pound equals 16 ounces, and each apple is approximately 5 ounces, we can calculate how many apples are in each pound by dividing 16 by 5, which gives us about 3.2 apples per pound.

Lastly, to find out the total number of apples you can buy for $168.00, we multiply the total pounds of apples (48) by the number of apples per pound (3.2), resulting in a total of approximately 153.6, which we can round down to 153 apples.

Answer:

B. Jacobs monthly bill shall be $48.75

Step-by-step explanation:

On this specific mont, Jacob used 124.8 minutes.

Considering that every fraction of a minute is rounded off to the next minute,

Jacob used 125 minutes.

Each minute goes for $0.35

Now multiply total nomber of minutes by $0.35 rate

0.35 * 125 = 43.75

This is bill for the minutes used.

The bill for service is $5 per month.

To get the total bill, we add $5 to $43.75

Which gives us $48.75

Answer:

Equations are composed for many expressions.

Expressions can indicate variables, constants, etc.

Best regards

Answer:

Step-by-step explanation:

Expressions generally contain literals and may be "evaluated" by subbing the given values of the literal into them.  Expressions may be simplified, including being rewritten in alternative forms.

Equations, on the other hand, involve the " = " symbol.  If a literal, such as x or y, is included in the equation, we can usually solve the equation for that literal, thereby creating a function.

Answer: $654.72

Step-by-step explanation:

11 percent of $704 is $77.44  -  (11*704/100)

You do $704-$77.44 because it is on sale.

Equalling $626.56

4 percent of $704 is $28.16 - (4*704/100)

Add $28.16 to 626.56 because your being taxed.

Equalling $654.72 your answer

The total cost of the $704 tablet computer, after an 11% discount and 4% sales tax, is $651.62.

To find the total cost of the $704 tablet computer, we first need to calculate the sale price after the 11% discount. The discount amount can be found by multiplying the original price by 11% (or 0.11). So, the discount amount is $704 * 0.11 = $77.44. The sale price is then $704 - $77.44 = $626.56.

Next, we need to calculate the sales tax amount. The sales tax rate is 4%, so the tax amount is $626.56 * 0.04 = $25.06.

Finally, to find the total cost, we need to add the sale price and the sales tax amount together. Therefore, the total cost of the $704 tablet computer, including the discount and sales tax, is $626.56 + $25.06 = $651.62.

https://brainly.com/question/36678254

#SPJ2

Answer:

I don't know either. I'd help if i knew the answer.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

its 3

Step-by-step explanation:

Answer:

Which U.S. political parties would likely approve of a plan to help unemployed workers?

Step-by-step explanation:

1. Communists

2. Democrats

3. Libertarians

4. Republicans

5. Socialists

the answer is 5,3,1

Final answer:

The Libertarian Party wants little to no government interference. The Democratic and Republican parties have different stances on helping unemployed workers, taxing businesses for environmental cleanup, and providing cheaper healthcare.

Explanation:

In the United States, the Libertarian Party is a third-party that wants little to no government interference. They advocate for limited government intervention in both social and economic areas. For example, they support lower taxes, less regulation, and individual freedom.

The Democratic and Republican parties would likely approve of a plan to help unemployed workers. The Democrats often propose policies such as extending unemployment benefits and increasing job training programs, while the Republicans tend to support tax cuts and reducing government regulations to stimulate job growth.

The Democratic party is more likely to approve of a tax on businesses to clean up the environment. They generally advocate for stricter environmental regulations and support policies aimed at reducing pollution. The Republican party, on the other hand, often opposes new taxes and regulations on businesses.

The Democratic party and the Progressive wing of the Democratic party would likely approve of a plan to provide cheaper healthcare. They have been pushing for measures such as expanding Medicaid, implementing a public health insurance option, and decreasing prescription drug prices. The Republican party, however, tends to advocate for free-market solutions and reducing government involvement in healthcare.

Answer:

The answer is A.

Step-by-step explanation:

Because the square root of 42 is about 6 and those two numbers are close to 6.

Hope this helps!

Please mark brainliest!! thanks!

A) 4 feet and 5 feet

The space occupied by a square is called area of the square.

Let, length of each side of the square = a unit

Then, Area of the square = [tex]a^{2}[/tex] sq.unit

Given, area of a small square patio = 42 sq. feet

Also the length of each side of the patio = [tex]\sqrt{42}[/tex] feet

The value of [tex]\sqrt{42}[/tex] = 6.48 (approx)

The required value is 6.48 feet, which is close to 4feet & 5feet.

Learn more about area of square here :

https://brainly.com/question/13389992

#SPJ2

Answer:

Smaller x   -10

Larger x     -2

Step-by-step explanation:

f(x) = (x+6) ^2 - 16

To find the zero's, we set the function equal to zero

0 =  (x+6) ^2 - 16

Add 16 to each side

16 =  (x+6) ^2 - 16 + 16

16 = (x+6)^2

Take the square root of each side

±sqrt(16) = sqrt((x+6)^2))

±4 = x+6

Subtract 6 from each side

-6±4 = x+6-6

-6±4 = x

-6 -4 = x        -6+4 =x

-10 =x                 -2 =x

Smaller x   -10

Larger x     -2

Answer:

Smaller x: -10

Larger x: -2

Step-by-step explanation:

You are looking for where the function equals 0. So, you can set f(x) equal to 0:

f(x) = [tex]0=(x+6)^{2} -16[/tex]

Now add 16 to both sides:

[tex]16=(x+6)^{2}[/tex]

Now that you have a perfect square on both sides, you can take the square root of both sides. On the right, this would simply remove the exponent. On the left, you have the square root of 16, or 4. It is important to remember that this can be positive or negative (since -4 squared also equals 16).

±4 = x + 6

To find your two solutions, you have to then evaluate the equation for 4 and -4. First, with -4:

-4 = x + 6       subtract 6 from both sides

-10 = x

Now, with 4:

4 = x + 6        subtract 6 from both sides

-2 = x

And there are your two solutions. Since -10 < -2, -10 is the smaller x and -2 is the larger one.

Answer:

a. y÷x=5 , b. y=60 because x is increased by 2 times  so y should be increased by 2 times

Step-by-step explanation:

Im pretty sure that the answer would be 3 cm, answer letter A

Answer:

75 degrees

Step-by-step explanation:

both the angles must add up to 18.

180 - 105 = 75

105 + 75 = 180

Answer:

105

Step-by-step explanation:

alternate angles are equal

Answer:

Step-by-step explanation:

3a-4=a(a-3)

3a-4=a²-3a

3a=a²-3a+4

0=a²-6a+4

a=(6±√[36-4(1)(4)])/2(1)

a=(6±√(36-16))/2

=(6±√20)/2

=3±(2√5)/2

=3±√5

a=3+√5

a=3-√5

Answer:   3 ± √5

Step-by-step explanation:

[tex]3a-4=a(a-3)\\\\3a-4=a^2-3a\qquad distributed\ "a"\ on\ the\ right\ side\\\\0=a^2-6a+4\qquad subtracted\ 3a-4\ from\ both\ sides\\\\a=1,\ b=-6,\ c=4\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4(1)(4)}}{2(1)}\\\\\\.\ =\dfrac{6\pm \sqrt{36-16}}{2}\\\\\\.\ =\dfrac{6\pm \sqrt{20}}{2}\\\\\\,\ =\dfrac{6\pm 2\sqrt5}{2}\\\\\\.\ =3\pm\sqrt5[/tex]

B.) 66

arc PN is 114 degrees bc it’s congruent to the central angle. therefore, the rest of the circle is 246 degrees bc 360-114=246. divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents. (246-114)/2=66

If Point O is the center of the circle then value of x is 66 degrees

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Point O is the center of the circle

We have to find the value of x

arc PN is 114 degrees because it’s congruent to the central angle.

We know that the total measure of triangle is 360 degrees

By removing arc PN  the remaining circle has 246 degrees of measure

Divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents.

(246-114)/2

=66 degrees

Hence, if Point O is the center of the circle then value of x is 66 degrees

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ2

Step-by-step explanation:

Area of a trapezoid is 1/2h(b1+b2)

So let's substitute.

1/2*17*(15+27)

1/2*17*42

Answer is 357 cm squared