If a/b = 2, what is the value of 4b/a?
A) 0
B) 1
C) 2
D) 4

We have two right triangles and three different rectangles.

The formula of an area of a right triangle:

[tex]A_T=\dfrac{1}{2}l_1l_2[/tex]

l₁, l₂ - legs

We have l₁ = 20cm and l₂ = 21cm. Substitute:

[tex]A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2[/tex]

The formula of an area of a rectangle:

[tex]A_R=lw[/tex]

l - length

w - width

We have:

rectangle #1: l = 22cm, w = 29cm

[tex]A_{R1}=(22)(29)=638\ cm^2[/tex]

rectangle #2: l = 22cm, w = 21cm

[tex]A_{R2}=(22)(21)=462\ cm^2[/tex]

rectangle #3: l = 22cm, w = 20cm

[tex]A_{R3}=(22)(20)=440\ cm^2[/tex]

The total Surface Area of the triangular prism:

[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2[/tex]

Answer:

the answer is D because both are to the power of 8

Step-by-step explanation:

Answer:

Option D is correct

[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]

Step-by-step explanation:

[tex]\text{Given the fraction }(\frac{5}{9})^8[/tex]

we have to choose the correct option which is equivalent to above.

As we know

[tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]

Put a=5, b=9, x=8

[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]

Therefore, option D is correct

Answer: A

Step-by-step explanation: sin45(9 radical 2)

Answer:

$0.75  

Step-by-step explanation:

We have been given that a proportional relationship between the number of pounds of carrots (x) and the price in dollars (y).

We can represent this information as: [tex]y=kx[/tex].

We are also told that the ordered pair (8, 6) is on the graphed line. Let us substitute x= 8 and y= 6 in our proportional equation to find the constant of proportionality.

[tex]6=k*8[/tex]

[tex]k=\frac{6}{8}[/tex]

[tex]k=\frac{3}{4}[/tex]

Now let us substitute k=3/4 and x=1 in our proportionality equation.

[tex]y=\frac{3}{4}*1[/tex]

[tex]y=\frac{3}{4}[/tex]

[tex]y=0.75[/tex]

Therefore, the price of 1 pound of carrots will be $0.75.

Answer: 6

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

Explanation:

The triangles are similar triangles (we can use the AA similarity theorem to prove this). So the vertical sides pair up, and the horizontal sides pair up, to form the proportion below

x/4.5 = 8/6

Note the order of the terms. I'm dividing the upper triangle's sides by the corresponding lower triangle's sides. Cross multiply and solve for x

x/4.5 = 8/6

6x = 4.5*8

6x = 36

x = 36/6

x = 6

Answer:

Wrong Answer 176.8

Step-by-step explanation:

Multiply 3.4 * 52 = 176.8

Answer: 2000 v-bucks

Step-by-step explanation: The bright bomber costs 1,200 and the glider costs 800

The value of (-14°)-2 is the reciprocal of 196 since the negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent. The correct answer is 1/196.

The question asks for the value of (-14°)-2, which represents a mathematical expression that requires simplification using exponent rules. The notation a-n means that you should take the reciprocal of an, which in this case is the reciprocal of (-14°) squared. When squaring a negative degree value, the square of a negative number is positive, so (-14°)2 = 196°. Therefore, taking the reciprocal of 196° gives us 1/196.

The value of (-14°)-2 is 1/196.

Answer:

$3.92  per gallon

10 gallons of gas at $3.49 a gallon will cost $34.90

Step-by-step explanation:

To find the price per gallon, we take the total cost, and divide by the number of gallons.  I will change 16 1/2 to a decimal for ease of math calculations.  

16 1/2 = 16.5

cost/gallons

$62.70/16.5

3.91875

Since we are working with money, we round to the nearest cent

$3.92  per gallon

To find the  total cost, we multiply the cost per gallon times the number of gallons.  We have a cost per gallon of $3.49.  If we multiply by 10 gallons

cost = $3.49 * 10

        $34.90

10 gallons of gas at $3.49 a gallon will cost $34.90

Answer:

There are 14 halves in seven.

Step-by-step explanation:

7(1/2)=14

7(2)=14

OR, you could just count by halves until you reach 7, but that takes a while. (;

Answer:  

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:  

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.  

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

i believe the answer is 30

Step-by-step explanation:

Answer:

2.  No it is not direction variation

3. This is direct variation with the constant being 2

Step-by-step explanation:

The equation for direct variation is y=kx

2.  8y = 3x+1

Divide each side by 8

8y/8 = 3x/8 + 1/8

y = 3/8 x + 1/8

We are adding 1/8 to each time so it is not direct variation

3.  12y = 24x

Divide each side by 12

12y/12 = 24x/12

y = 2x

This matches y= kx, where k=2

This is direct variation with the constant being 2

9.95 / 5 = 1.99

4 x 1.99 = 7.96

$7.96

Answer:

80 gal

Step-by-step explanation:

20 gal takes her 400 mi

Vol. of gas = 1600 ×20/400

Vol. of gas = 1600 ×1/20

Vol. of gas = 80 gal

Betty will use 80 gal of gas.

Answer:

The answer is A.

Step-by-step explanation:

Answer:

(1,2) is the solution to both lines a and b

Step-by-step explanation:

You find the slope using 2 point and do y2-y1/x2-x1 . To create the equations for the two lines you do y=mx+b where m=slope and b=y-intercept.

f(5) means that x=5

Now, we solve 5x-3 because we know what x is.

5(5)-3

25-3

22

F(5)=22

Answer:

F (5)= 22

Step-by-step explanation:

Answer:  The​ traveler's speed off the​ walkway= 3 ft/s

The speed of the moving​ walkway= 2 ft/s

Step-by-step explanation:

Given: A traveler is walking on a moving walkway in an airport.

Let 't' be the​ traveler's speed off the​ walkway and 'w' be the speed of walkway.

Then the​ traveler's ground speed against the walkway (t-w)= 1 ​ft/s

And the​ traveler's ground speed  with the walkway (t+w)= 5 ft/s

thus we get the following equations [tex]t-w=1..........(1)\\t+w=5.............(2)[/tex]

Adding (1) and (2), we get

[tex]2t=6\\\Rightarrow\ t=3[/tex]

Subtract (2) from (1), we get

[tex]2w=4\\\Rightarrow\ w=2[/tex]

Therefore, the​ traveler's speed off the​ walkway= 3 ft/s

The speed of the moving​ walkway= 2 ft/s

Answer:

-18x+ 27

Step-by-step explanation:

Answer:

3 Bookmarks

Step-by-step explanation:

1) Find the remaining money which is 0.96

2)Divide 0.96 evenly into 3 people, you should get O.32

3) If each bookmark costs 0.10, and each person gets 0,32 the greatest number of bookmarks they can get is 3.

Answer:

No.

Step-by-step explanation:

42 has the following prime factors: 2, 3, 7

105 has prime factors: 3, 5, 7

Both prime factors 3 and 7 divide 42 and 105. If 42 and 105 were relatively prime (co-prime), the set of prime factors that divide both would be empty.  

Answer:

What options are there

Step-by-step explanation:

Answer:

Step-by-step explanation:

Between the third and fourth months, the size of K's collection grew by 3.  This is the steepest slope / greatest rate of change.

Final answer:

The inequality representing all possible values of b, the number of bottles of water Jamie can buy, is b ≤ 13, as Jamie has $16.45 left to spend after buying nine candy bars and each bottle costs $1.25.

Explanation:

The student must buy nine candy bars, which cost $0.95 each. The total cost for the candy bars is 9 * $0.95 = $8.55. Jamie has $25.00 to spend, so after buying the candy bars, she will have $25.00 - $8.55 = $16.45 left for bottles of water. Each bottle of water costs $1.25, so the number of bottles she can buy is represented by the inequality $1.25b ≤ $16.45, where b is the number of bottles of water Jamie can purchase.

Now, let's solve this inequality for b. Dividing both sides of the inequality by $1.25 gives us b ≤ 13.16. Since Jamie can't buy a fraction of a bottle, she must buy at most 13 bottles of water.

Therefore, the inequality representing all possible values of b (i.e., the number of bottles of water Jamie can buy) is b ≤ 13.

Answer:

1% of 4000 + 4% of B = 2% of (4000 + B)

40 + 0.04*B = 0.02( 4000 + B)

40 + 0.04* B = 80 + 0.02*B

40 + 0.04*B - 80 - 0.02B = 0

0.02*B - 40 = 0

0.02*B = 40

2B = 4000

B = 2000

Step-by-step explanation:

Plant B produced 1000 panels.

The total number of defective panels from Plant A is 7% of 6000,

= (7/100) x 6000

= 420 panels.

and, total number of defective panels from Plant B is 2% of x,

= (2/100) x

= (1/50) x.

The overall number of defective panels from both plants is 4% of the total number of panels

= (4/100)(6000 + x)

= (1/25) (6000 + x).

Now, set up the equation:

420 + (1/50)  x = (1/25) (6000 + x)

To solve for x, we can multiply both sides of the equation by 50 * 25 to eliminate the fractions:

50 . 25 . 420 + 50 x = 25 (6000 + x)

125000 + 50x = 150000 + 25x

50x - 25x = 150000 - 125000

25x = 25000

x = 25000 / 25

x = 1000

Therefore, Plant B produced 1000 panels.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ6

Answer:

3:2

Step-by-step explanation:

Triangle:circle

3 triangle:2 circle

Answer: X < -3

Step-by-step explanation:

-15x - 3 > 42

-15x - 3 + 3 > 42 + 3

-15x > 45

-15x/-15 > 45/-15

Since we are dividing by a negative, we flip the >

x < -3

So, let's check

-4 < -3

-15*-4 - 3 > 42

60 - 3 > 42

57 > 42

Now, let's see if -3 will work.

-15*-3 - 3 > 42

45 - 3 > 42

42 > 42 (False)

Okay, now let's try 4

-15*4 - 3 > 42

-60 - 3 > 42

-63 > 42

This is false, so it is x < -3

The correct answer is x < -3

Explanation:

To solve our equation we first need to set out our equation, -15x – 3 > 42. Next, we add 3 to both sides of our equation, -15x - 3 + 3 > 42 + 3 = -15x > 45. Then, we multiply both sides by -1(Or in other words, reverse the inequality), -15x * -1 > 45 * -1 = 15x < -45. And then, we divide both sides by 15, 15x/15 < -45/15 = x < -3. Finally, we have our answer of x < -3.

Hope This Helps!!!

-AnimeDabGirl

recall that the slope, namely the average unit rate of change, is rise/run.

so, what's the slope for the function in the table?  well, we can simply pick any two points and get it, or just use the first point rise of 8 and a run of 7, gives us a slope of 8/7 or 1⅐.

now, let's take a peek at the lines, they all have a "rise" of 6, notice they're all lying on the y = 6 line horizontally.

1)

rise = 6, run = 2, slope 6/2 = 3.

well, 3 is more than 2, so no that one.

2)

rise = 6, run = 3, slope = 6/3 = 2.

well 2 = 2, so no that one either.

3)

rise = 6, run = 4, slope 6/4 = 3/2.

3/2 is actually larger than 8/7 and less than 2, you can check. so ✔

4)

rise = 6, run = 5, slope = 6/5.

6/5 or 1⅕ is more than 8/7, and is clearly less than 2, so ✔

5)

rise = 6, run = 6, slope = 6/6 = 1.

well, needless to say 1 is less than 2 but is less than 8/7, recall 8/7 is actually 1⅐.

Answer:

View the picture for your answer!

Have a wonderful day:))

y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.

Select any two x values and calculate y values:

[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=0\to(0,\ 2)\\\\for\ x=-4\to y=\dfrac{1}{2}(-4)=-2+2=0\to(-4,\ 0)[/tex]

[tex]y=x+5\\\\for\ x=0\to y=0+5=5\to(0,\ 5)\\\\for\ x=-5\to y=-5+5=0\to(-5,\ 0)[/tex]

Look at the picture.

The solution of the system of equations is the intersection point of the line.