Graph ​ y+6=45(x+3) ​ using the point and slope given in the equation

[tex]\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\text{Therefore}\\\\\sqrt3=3^\frac{1}{2}\\\\\sqrt[5]{3}=3^\frac{1}{5}\\\\\text{We have}\\\\(\sqrt3)(\sqrt[5]3)=3^\frac{1}{2}\cdot3^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=3^{\frac{1}{2}+\frac{1}{5}}=3^{\frac{5}{10}+\frac{2}{10}}=3^{\frac{7}{10}}\\\\Answer:\ \boxed{D.\ 3^{\frac{7}{10}}}[/tex]

[tex]Use:\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^n)^m=a^{nm}\\\\\left(5^{\frac{3}{4}}\right)^{\frac{2}{3}}=5^{\frac{3}{4}\cdot\frac{2}{3}}=5^{\frac{1}{2}\cdot\frac{1}{1}}=5^{\frac{1}{2}}=\sqrt[2]{5}=\boxed{\sqrt5}[/tex]

Hi There!

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Problem #1:

At the dealership where she works, Sade fulfilled 3/10 of her quarterly sales goal in January and another 1/10 of her sales goal in February. What fraction of her quarterly sales goal had Sade reached by the end of February?

3/10 + 1/10 = 4/10

4/10 of her goal.

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Problem #2:

Shane has been monitoring his mileage. According to last week's driving log, he drove 1/10 of a mile in his car and 9/10 of a mile in his truck. How far did Shane drive last week in all?

1/10 + 9/10 = 10/10 = 1

Shane drove 1 mile.

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Problem #3:

For a class experiment, Vina's class weighed a log before and after subjecting it to termites. Before subjecting it to termites, the log weighed 7/10 of a pound. After the termites, the log weighed 3/10 of a pound. How much weight did the termites take from the log?

7/10 - 3/10 = 4/10

The termites took 4/10 pound away from the log.

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Hope This Helps :)

Answer:

Statement                                            Reason

1. <R=<Q, AS=AT                                  Given

2. <5=<6                                               Base <'s of isosceles triangles are =

3. <4, <5 are supplementary               Exterior sides in opposite rays

   and <6, <7 are supplementary

4. <4=<7                                                Two <'s supplementary to equal <'s are =

5. Triangle RAS congruent to              AAS

   Triangle QAT

6. RS=QT                                              CPCTE

Step-by-step explanation:

Statement

1. <R=<Q, AS=AT. This is given.

2. <5=<6, because base angles of isosceles triangles are congruent.

3. <4, <5 are supplementary and <6, <7 are supplementary, because they have exterior sides in opposite rays.

4. <4=<7, because two angles supplementary to equal angles are congruent

5. Triangle RAS congruent to Triangle QAT because Angle Angle Side (AAS)    

6. RS=QT, because Congruent Parts in Congruent Triangles are equal (CPCTE)

Answer: [tex]36 cm^2[/tex]

Explanation:

Since here ABCD is the parallelogram.

Where E is the mid point of the line segment BC.

And, F is the intersection point of the segments AE and BD,

Also,  Area of △BEF is 3 [tex]cm^2[/tex].

We have to find Area of parallelogram ABCD.

Since,In  ΔBEF  and ΔACD,

∠ADF=∠EBF ( because AD ║ BE )

∠DFA = ∠BFE (vertically opposite angle)

Thus, By AA similarity postulate,

[tex]\triangle BEF \sim \triangle ACD[/tex],

Thus, [tex]\frac{area of \triangle ADF }{area of \triangle BFE} =(\frac{AD}{BE})^2[/tex]

But, AD = 2 BE,

Therefore,  [tex]\frac{area of \triangle ADF }{area of \triangle BFE} =(\frac{2BE}{BE})^2[/tex] = 4/1

Thus, area of Δ ADF = [tex]12 cm^2[/tex]

Similarly, [tex]\triangle ADB \sim \triangle BAE[/tex]

Now, let the area of the triangle AFB = x [tex]cm^2[/tex]

Thus, x + 12 = 2(x+3) ( because the area of the ΔADB = 2(area of ΔBAE) )

⇒ x = 6 [tex]cm^2[/tex]

Therefore, area of ΔAFB= 6 [tex]cm^2[/tex]

⇒ area of ΔABD = 12 + 6 = 18 [tex]cm^2[/tex]

By the definition of diagonal of parallelogram,

Area of parallelogram ABCD = 2× area of Δ ABD= 2 × 18 = 36 [tex]cm^2[/tex]

Answer:

A and B.

Step-by-step explanation:

where m is the slope and c is the the y-intercept.

A. y = x + 6

For this equation m = 1

B. y = -x - 9  

For equation B, m = -1

C. y = 2x + 1  

In this equation, m = 2  

D. y = -7x - 2

In equation D, m = -7

The equation with the highest slope is D while the one with the least slope/steep is A and B.

Answer:

Area = 2x^2 -5x-12

Step-by-step explanation:

Area = length * width

Area = (2x+3) * (x-4)

We will use the FOIL technique  to multiply the terms.

First:  2x*x = 2x^2

Outer:  2x* -4 = -8x

Inner:  3*x = 3x

Last = 3* -4  = -12

Add the 4 terms together:  2x^2 -8x+3x -12   = 2x^2 -5x-12

Area = 2x^2 -5x-12

Answer: 2x^2 - 5x - 12

Step-by-step explanation: The correct answer is 2x^2 - 5x - 12. To find the area of a rectangle you multiply the length by the width. So you multiply (2x + 3)(x - 4) using the FOIL method.

Answer:

1. 1:2

2. 2:2

3. 2:5

4. 2:10

5. 4:10

Step-by-step explanation:

Answer:

The cost of the bench is 425 dollars.

Step-by-step explanation:

Let x represent the garden table.

Let y represent the bench.

x + y = 804

x = y - 46

Use the substitution method.

y - 46 + y = 804

2y - 46 = 804

Add 46 to both sides.

2y = 850

Divide both sides by 2.

y = 425

Answer:

The cost of the bench is 425 dollars.

Answers

First train's speed is 363 mph

Second train's speed is 356.1 mph

=====================================

Explanation:

x = speed of first train, y = speed of second train

x+y = 719.1 because the two speeds add to this value (sum means result of addition)

x = y+6.9 due to the fact that the first train (x) is faster than the second train (y) by 6.9 mph

Use substitution to find that...

x+y = 719.1

y+6.9+y = 719.1 <--- replace x with y+6.9

2y+6.9 = 719.1

2y = 719.1-6.9 <--- subtract 6.9 from both sides

2y = 712.2

y = 712.2/2 <--- divide both sides by 2

y = 356.1

now use this y value to find x

x = y+6.9

x = 356.1+6.9

x = 363

The speed of the first train is 363 mph and the speed of the second train is 356.1 mph. To find these, we solved the equation 2x + 6.9 = 719.1, where x represents the speed of the slower train.

To solve this problem, we will use algebra to set up equations based on the information given. Let's denote the speed of the second train as x miles per hour. Accordingly, the speed of the first train is described as x + 6.9 miles per hour, since we are told it is 6.9 mph faster than the second train. The sum of their speeds is given to be 719.1 mph. Therefore, we can write the following equation to find the speeds of each train:

Hence, the speed of the second train is 356.1 mph. Now to find the speed of the first train we add 6.9 mph to the speed of the second train:

So the speed of the first train is 363 mph, and the speed of the second train is 356.1 mph.

Answer:

2000>= 637+ x

1363>= x

He can spend no more than $1363 on everything else

Step-by-step explanation:

If he has 2000 dollars to spend in total, that will go on one side of the inequality.  Everything he spends goes on the other.  2000 is the maximum he can spend.  He is going to sped 637 on an airline ticket plus x on other expenses.

2000>= 637+ x

Subtract 637 from each side

2000-637 >= 637-637 +x

1363>= x

To find out how much your brother can spend for everything else, subtract the cost of the airplane ticket from his total savings. Your brother can spend up to $1,363 for everything else.

To find out how much your brother can spend for everything else, we need to subtract the cost of the airplane ticket from his total savings. Let's say his total savings is $2,000 and the cost of the airplane ticket is $637. We can write the inequality as:

2000 - 637 ≤ x

Simplifying the inequality, we have:

1363 ≤ x

Therefore, your brother can spend up to $1,363 for everything else.

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Answer:

a.  He started with $50 in the the account.

b.  The account grow by $10 dollars each week

c see graph

Step-by-step explanation:

y = 50 + 10x

We can rewrite this as

y = 10x+50

This is in the form y = mx+b

where m = 10 which is the slope and b =50 which is the y intercept

The y intercept = 50 is the starting value or the value when x = 0

a.  He started with $50 in the the account.

The slope is how much it grows by as x grows.  As x increase by 1 , y will grow by the slope or 10, so  the account will grow by 10 each week.

b.  The account grow by $10 dollars each week

c see graph

Answer: 59,000

Step-by-step explanation:

(2.5 * 10^4) + (3.4 * 10^4)

(2.5 * 10,000) + (3.4 * 10,000)

25,000 + 34,000

59,000

10 • 10 • 10 • 10 = 10,000

(2.5 • 10,000) + (3.4 • 10,000)

    25,000             34000

25,000 + 34,000 = 59,000

Answer:

C. about 17 feet

Step-by-step explanation:

Since, we know that,

The area of a square is,

[tex]A=s^2[/tex]

Where,

s = side length,

If A = 290 square feet,

[tex]\implies 290 = s^2[/tex]

[tex]\implies s = \sqrt{290}=17.0294\approx 17[/tex]

Hence, the side length of the patio would be about 17 ft,

OPTION C is correct.

Answer:

Answer is: 5^ -8  *  5^4 =  5^-4

Step-by-step explanation:

To simplify : 5^ -8  *  5^4

This can also be written as :

5^ -8  *  5^4 = 1/5^8 * 5^4

or 5^ -8  *  5^4 = 5^4 / 5^8

or 5^ -8  *  5^4 = 5^(4 - 8)

or 5^ -8  *  5^4 = 5^-4

Hence we got 5^ -8  *  5^4 =  5^-4

Answer:

5v

Step-by-step explanation:

First you convert all the subtraction to addition: 2v+8v+(-5v)

Then you combine like terms: 2v+3v:

5v

2v + 8v - 5v    combine like terms

= (2 + 8 - 5)v

= (10 - 5)v

= 5v

Answer:

The solution of the system is the point where the graphs intersect, or have the same x and y values. This means that the company's cost to produce 400 caps is the same as the income made from selling 400 caps. Therefore, the company will not make a profit.

The cost to produce 400 caps is the same as the income made from selling 400 caps.

The company will break even when it sells 400 caps; it will not make a profit.

Step-by-step explanation:

Answer: Your response may vary. Sample answer below is the correct response.

Step-by-step explanation:  Sample response: The solution of the system is the point where the graphs intersect, or have the same x and y values. This means that the company's cost to produce 400 caps is the same as the income made from selling 400 caps. Therefore, the company will not make a profit.

Make sure to include in your answer:

Good Luck! :)

Answer:

f = 0.30(x)

Step-by-step explanation:

Let x = # of dollars

Let f = final amount

Note that 30% is the same as 30/100, which in decimal form is 0.30

Set the equation.

Each pair of shoes costs x amount, in which it is decreased by 30%, which leads to the cost in f amount.

~

Answer:

slope is easy it is rise over run

Step-by-step explanation:

rise/run

rise means up

run means move sideways

Answer:

Slope = rise/run

Step-by-step explanation:

Example: (6,3) (2, 2)

Add the x's and divide by two and then add the y's and divide by two.

6 + 2 = 8

8/2 = 4

3 + 2 = 5

5/2 = 2.5

So, the slope would be 4/2.5

Answer:

well you would need to look at how much he gets a weekend, and then worry anout the tips.

Step-by-step explanation:

He gets paid $80 each weekend, and a 15% with tips.

you would need to figure out the tips, by taking the $725 and timesing it by .15 for the percent.

which would be 108.75

you would now take 108.75 and add 80 to get what he made that weekend.

108.75+80 = 188.75 dollars

Answer:

I am pretty sure your answer is n because of the font i think.

Answer:

I believe the correct answer would be A. N.

Step-by-step explanation:

For two reasons. Reason 1, it's in a different font than everything else which indicates that it stands for something more than just the letter N. Reason two is, letters are usually used to indicate names of points on graphs, and in equations.

Answer:

m = [tex]\frac{3n}{4}[/tex]

Step-by-step explanation:

given 4m + 2n = 5n ( subtract 2n from both sides )

4m = 3n ( divide both sides by 4 )

m = [tex]\frac{3n}{4}[/tex]

Answer:

m = 3/4 n

Step-by-step explanation:

4m+2n=5n

Subtract 2n from each side

4m +2n-2n = 5n-2n

4m = 3n

Divide by 4

4m/4 = 3n/4

m = 3/4 n

Answer:

It would be -3/5, -0.4, |-1/2|, 0.6, 4/5.

Step-by-step explanation:

Answer:

-3/5 , -0.4 , -1/2 , 0.6 , 4/5

Step-by-step explanation:

-0.6, -0.4 , 0.5 , 0.6 , 0.8

In decimal form

Answer:

120√6

Step-by-step explanation:

Simplify the 5√8 to 2√2

simplify the √18 to 3√2

so it would be √3 * 2√2 * 5 * 2√2 * 3√2

when a square root of an expression is multiplied by itself:

√3 * 2 * 2* 5 * 2 * 3√2

so as we calculate it, 2 * 2* 5 * 2 * 3 = 120 and √2 * √3 = 6

[tex]\sqrt3\\2\sqrt2\\5\sqrt8=5\sqrt{4\cdot2}=5\sqrt4\cdot\sqrt2=5(2)\sqrt2=10\sqrt2\\\sqrt{18}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=3\sqrt2\\\\\sqrt3\cdot2\sqrt2\cdot5\sqrt8\cdot\sqrt{18}=\sqrt3\cdot2\sqrt2\cdot10\sqrt2\cdot3\sqrt2\\\\=(2\cdot10\cdot3)(\sqrt3\cdot\sqrt2\cdot\sqrt2\cdot\sqrt2)=60\sqrt{3\cdot2}\cdot\sqrt{2\cdot2}\\\\=60\sqrt6\cdot\sqrt4=60\sqrt6\cdot2=(60\cdot2)(\sqrt6)\\\\=\boxed{120\sqrt6}[/tex]

Answer:

u ≤ 4

Step-by-step explanation:

The given inequality

15 ≤ 39 - 6u

Subtract 39 from both sides, we get

15 - 39 ≤ 39 - 6u - 39

-24 ≤ -6u

Dividing both sides by -6, we get

4 ≥ u                      [Remember, when we divide by negative, the direction of    

                              the inequality changes]

Which is u ≤ 4.

Thank you.

Answer:

U is greater than or equal to 4

Step-by-step explanation:

(pretend theres a line under the <)

15 < 39 - 6u

subtract both sides by 39 to get -6u by itself

-24 < -6u

divide both sides by -6 and get u completely by itself

4 < u

u is greater than or equal to 4.

Answer:

$800 is the answer because you subtract 7200 from 8000 and you get 800

Final answer:

To earn an $8,000 commission at a rate of 4%, the car dealer needs to increase his total sales by $20,000, from $180,000 last month to $200,000 this month.

Explanation:

The car dealer wishes to increase his commission from $7,200 to $8,000. Since he earns a 4% commission on all cars sold, we first need to determine how much his sales were last month. To do this, we divide his commission for the last month by the commission rate:

Last month's sales = Commission / Commission rate = $7,200 / 0.04 = $180,000

To earn $8,000 this month, we need to find the total sales required:

This month's sales = Desired commission / Commission rate = $8,000 / 0.04 = $200,000

To find the increase in total sales needed, we subtract last month's sales from this month's sales target:

Required increase in sales = This month's sales - Last month's sales = $200,000 - $180,000 = $20,000

Answer: x = 5

Step-by-step explanation:

NOTE: 343 = 3 * 3 * 3 * 3 * 3

3ˣ = 3⁵

Since the bases are the same, we can eliminate the base and set the exponents equal to each other:

x = 5

Answer:

[tex]3^{5}[/tex]

Step-by-step explanation:

3 × 3 × 3 × 3 × 3 = 243

Answer:

402.88mm³

Step-by-step explanation:

To find the answer to this, we need to find the total area of the coin and then the size of the inner coin.

As this is a cylinder, the formula is:

[tex]\pi r^{2} h[/tex]

So lets find the area of the whole coin.

The radius is 11.5 and height is 2.2

[tex]\pi * 11.5^{2} * 2.2 = 914.05[/tex]

Now, the area of the inner circle:

Radius is 8.6 and height is 2.2:

[tex]\pi * 8.6^{2} * 2.2 = 511.17[/tex]

Now to find the area of the silver ring in the coin, you subtract the inner circle measurement from the whole coin measurement:

914.05 - 511.17 = 402.88

So the volume of the outer ring is 402.88mm³

Answer:

b = 26.97 or b = 0.03

Step-by-step explanation:

[tex]\frac{\frac{4}{5} }{b} +b=27[/tex]

[tex]\frac{4}{5b} +b=27[/tex]

[tex]\frac{4+5b^{2} }{5b} =27[/tex]

[tex]4+5b^{2} =135b[/tex]

[tex]5b^{2} -135b+4=0[/tex]

[tex]b=\frac{135+\sqrt{18225-80} }{10}[/tex] or

[tex]b=\frac{135-\sqrt{18225-80} }{10}[/tex]

b = 26.97 or b = 0.03