I need to know 3/8 + 1/6 in simplist form

Answer:

The measure of the third angle is a 90 degrees

Step-by-step explanation:

Let

A and B ----> two complementary angles in a triangle

C ---> the measure of the third angle in a triangle

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

[tex]A+B=90^o[/tex] ---> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]A+B+C=180^o[/tex] ----> equation B

substitute equation A in equation B

[tex](90^o)+C=180^o[/tex]

solve for C

subtract 90 degrees both sides

[tex]C=180^o-90^o[/tex]

[tex]C=90^o[/tex]

therefore

we have a right triangle

I am not sure if i understand that 3600 is the cost of all the bikes they have bought in total, but they would have to sell 31 bikes to break even.

Answer:

The slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel.

Step-by-step explanation:

The quadrilateral ABCD has vertices A(-5,1), B(-2,5), C(5,3) and D(2,-1).

Now, slope of line AB = [tex]\frac{5 - 1}{- 2 - ( - 5)} = \frac{4}{3}[/tex]

Slope of line BC = [tex]\frac{3 - 5}{5 - (- 2)} = - \frac{2}{7}[/tex]

Slope of line CD = [tex]\frac{- 1 - 3}{2 - 5} = \frac{4}{3}[/tex]

And slope of DA = [tex]\frac{1 - ( - 1)}{- 5 - 2} = -\frac{2}{7}[/tex]

Therefore, the slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel. (Answer)

Answer:

The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3, and the slope of AD is -2/7. Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.

Step-by-step explanation:

Answer:

see the prime factors

Step-by-step explanation:

24= 6*4=3*2*2*2

=2*3*4

Answer:

No

Step-by-step explanation:

First off, the number 4 is not a prime number and the prime factorization of a number has to consist of all prime numbers. 2*3*4 does result in 24 but 4 is not prime because a prime number is a whole number with exactly two factors, itself and 1. 4 has more than two factors; the factors of 4 are 1, 2, and 4 so 4 isn't prime.

2*2*2*3 is the prime factorization of 24 because when you break down 24 into prime numbers, the results are 2*2*2*3.

24=2*12(here, we broke the number 24 into two factors 2 and 12. it doesn't matter which factors you break the number into because you still get the same result.)

2*12=2*2*6(we broke the number 12 into 2*6 because 12 isn't prime. we have to break each number into prime numbers.)

2*2*6=2*2*2*3(finally, we broke down 6 because it is the only number left that is not prime. 2*3=6 and 2 and 3 are prime so we break down 6 into 2*3)

Now you have the prime factorization of 24!

24=2*2*2*3

Answer:

The equation of the line is 2 x +3 y = 15.

Step-by-step explanation:

Here the given points are ( -3, 7) & ( 3, 3) -

Equation of a line whose points are given such that

[tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-

 y - [tex]y_{1}[/tex]   =  [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex]   ( x - [tex]x_{1}[/tex]  )

i.e.  y - 7= [tex]\frac{3 - 7}{3 - (-3)}[/tex]  ( x- (-3))

      y - 7 =  [tex]\frac{-4}{3 + 3}[/tex] ( x + 3 )

      y - 7= [tex]- \frac{2}{3}[/tex]  ( x + 3 )

      3 ( y - 7)  =  - 2 ( x + 3)

      3 y -21 = -2 x - 6

      2 x + 3 y = 21 - 6

      2 x + 3 y = 15

Hence the equation of the required line whose passes trough the points ( - 3, 7) & ( 3, 3)  is 2 x + 3 y = 15.

We know that we can use y for "how much the job pays" and x for "hours of work."

Let's find how much the job pays in 1 hour by dividing.

25 / 2 = $12.5 per hour

We can mulitply x to 12.5 because this shows how much he earned.

An equation will look like 12.5x = y

Best of Luck!

The job pays $12.50 per hour. The equation to represent the pay, y, for x hours of work is 'y = 12.5x', which depicts direct proportionality.

To solve this question, you must first understand that the job pays $25 for every 2 hours worked. Therefore, to find out how much the job pays for x hours of work, you'd simply multiply the rate per hour ($12.50, since $25 divided by 2 is $12.50) by x hours.

The equation that represents how much the job pays, y, for x hours of work is: y = 12.5x.

Here, 'y' denotes the total payment received and 'x' is the number of hours worked. This format is commonly used in equations representing direct proportionality, where one variable (in this case, pay) changes directly as the other (hours worked).

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Answer:

C : 40%

Step-by-step explanation:

20 ÷ 50 = 0.40 also to solve just divide the smaller number from the greater number in order to be able to get the correct percentage.

Answer:

Step-by-step explanation

is / of = % / 100.....proportion formula

20 is what percent of 50...

20 / 50 = x / 100

cross multiply

50x = 2000

x = 2000/50

x = 40.......so 20 is 40% of 50

Answer:

4.0

Step-by-step explanation:

AB / AC = AE / AD

1 / 4.5 = AE / 18

4.5 AE = 18

AE = 4.0

Since BE and CD are parallel, triangles ABE and ACD are similar, meaning their side lengths are proportional.

AC = AB + BC = 1 + 3.5 = 4.5

The proportion of AB to AC (corresponding sides of two similar triangles) is 1 / 4.5

Let x be the variable that represents the unknown length of AE

The proportion of AE to AD (another set of corresponding sides of two similar triangles) is x / 18

Since the triangles are similar, these two proportions must be equal.

1 / 4.5 = x / 18

Cross multiply

4.5x = 18

Divide both side by 4.5

x = 4

The length of AE is 4, no need to round since the answer is already a whole number.

Let me know if you need any clarifications, thanks!

Answer:The reasonable time for the base ball to land on the ground is 5 seconds

Step-by-step explanation:

To get the time we will differentiate

h(t) = -16t2 + 80t + 224, w.r.t t

dh(t)/dt= 0

-32t +80=0

32t=80

t=80/32

t= 2.5 seconds This is the time the base ball has been in the air

The reasonable time for it to take the baseball to land on the ground is T= 2×t

T= 2×2.5

T=5 seconds

The rate at which the vehicle can travel is 6 miles per gallon

Solution:

Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water

To find: Rate at which the vehicle can travel, in miles per gallon of water

distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]

gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]

Miles per gallon is given as:

[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]

Substituting the given value we get,

[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]

So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon

Answer:

12.87%

Step-by-step explanation:

To identify the % of their monthly income is spent on entertainment we use following formula

Total Budget of Entertainment / Total Net Income

$399/$3,100*100

12.87%

Well, when your rounding by ones, if the ones place is lower than 5,  round lower. Like for example, 4 is lower than 5. So if you have 5,784, you have to round that 4 down to a 0. So it would be 5,780.

if it's higher that 5, like 7, you round up. Like for example, 507, you round it to 10, so 510.

Rounding up numbers involves looking at the digit to be dropped: if it's 5 or above, round up the last retained digit. Several examples like 31.57 up to 32 and 8.1649 down to 8.16 illustrate this process.

Rounding up a number involves several steps. Let's take a few examples:

(a) The number 31.57 rounds up to 32. Here, the dropped digit is 5, and the digit we keep or retain is even. Since our dropped digit is 5 or higher, we add one to the retained digit, thus getting 32.

(b) The number 8.1649 rounds down to 8.16. The dropped digit is 4, which is less than 5, so we do not add any to our retained number, getting 8.16.

These examples demonstrate that we are rounding to the nearest whole number or to certain decimal places depending on the precision needed in the problem. When the digit we are dropping is 5 or above, we round up the previous digit. If it is less than 5, we leave the previous digit as it is.

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Answer: 54678 years

Step-by-step explanation:

This can be solved by the following equation:

[tex]N_{t}=N_{o}e^{-\lambda t}[/tex] (1)

Where:

[tex]N_{t}=54\%=0.54[/tex] is the quantity of atoms of carbon-14 left after time [tex]t[/tex]

[tex]N_{o}=1[/tex] is the initial quantity of atoms of C-14 in the mammal hide

[tex]\lambda[/tex] is the rate constant for carbon-14 radioactive decay

[tex]t[/tex] is the time elapsed

On the other hand, [tex]\lambda[/tex] has a relation with the half life [tex]h[/tex] of the C-14, which is [tex]5730 years[/tex]:

[tex]\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}[/tex] (2)

Substituting (2) in (1):

[tex]0.54=1e^{-(0.000121 years^{-1}) t}[/tex] (3)

Applying natural logarithm on both sides of the equation:

[tex]ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})[/tex] (4)

[tex]-0.616=-(0.000121 years^{-1}) t[/tex] (5)

Isolating [tex]t[/tex]:

[tex]t=\frac{-0.616}{-0.000121 years^{-1}}[/tex] (6)

[tex]t=54677.68 years \approx 54678 years[/tex] (7)  This is the age of the mammal hide

The age of the mammal hide to the nearest year is approximately 11,239 years.

To find the age of the mammal hide with 37% of its original amount of C-14 remaining, we can use the decay formula for a substance undergoing exponential decay, which is described by the equation N(t) = N0(1/2)t/T, where N(t) is the remaining amount of substance, N0 is the original amount of substance, t is the time that has elapsed, and T is the half-life of the substance.

In this case, the half-life of C-14 is 5,730 years. Since we know the remaining amount of C-14 is 37% of the original amount, we can set up the equation 0.37 = (1/2)t/5730. To solve for t, we take the natural logarithm of both sides:

ln(0.37) = ln((1/2)t/5730)

ln(0.37) = (t/5730) * ln(1/2)

t = (ln(0.37)/ln(1/2)) * 5730

When we compute the value for t, we get the age of the mammal hide. By performing this calculation, we find that t is approximately 11,239 years. This is the estimated age of the mammal hide to the nearest year.

The fir trees are 9 meters tall and the pine trees are 12 meters tall

Solution:

Let f be the height of one fir tree

Let p be the height of one pine tree

Given that combined height of one fir tree and one pine tree is 21 meters

So we get,

height of one fir tree + height of one pine tree = 21

f + p = 21 ----- eqn 1

Also given that height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree

height of 4 fir trees stacked on top of each other  = 24 + height of one pine tree

4f = 24 + p ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "f and "p"

From eqn 1,

f = 21 - p ----- eqn 3

Substitute eqn 3 in eqn 2

4(21 - p) = 24 + p

84 - 4p = 24 + p

-4p - p = 24 - 84

-5p = - 60

Substitute p = 12 in eqn 3

f = 21 - 12 = 9

Summarizing the results:

height of one fir tree = 9 meters

height of one pine tree = 12 meters

Answer:

The wingspan of 26 atlas moths are 286 inches.

Step-by-step explanation:

Given:

An Atlas moth has a wingspan of 11 inches.

Now, to find the wingspan of 26 atlas moths.

So, we use unitary method:

As given an atlas wingspan has 11 inches.

Then for wingspan of 26 atlas we multiply it by 11 inches:

⇒  [tex]26\times 11\ inches[/tex]

[tex]=286\ inches.[/tex]

Therefore, the wingspan of 26 atlas moths are 286 inches.

Final answer:

To find the total wingspan of 26 Atlas moths, multiply the wingspan of one moth, 11 inches, by 26, resulting in a total of 286 inches.

Explanation:

The question involves simple multiplication to determine the total wingspan of 26 Atlas moths. If one Atlas moth has a wingspan of 11 inches, then the wingspan of 26 Atlas moths can be found by multiplying 11 inches by 26.

Step-by-step calculation:

Determine the wingspan of one Atlas moth, which is already given as 11 inches.

Multiply the wingspan of one moth by the total number of moths: 11 inches * 26 = 286 inches.

Therefore, the total wingspan of 26 Atlas moths is 286 inches.

Answer:

I think its 500 each or its Love seat=500. Sofa=1000

Step-by-step explanation:

For 500 you would do 1500/3 because sofa is double+love seat. So each would cost 500 if you divide it by 3. So the sofa would be 1000. The love seat would be 500. 1000+500=1500.

Hope this helps!!

Final answer:

To determine the cost of the sofa and love seat, we create an equation from the given information. Solving for x, we find that the love seat costs $500 and the sofa, costing double, is $1000.

Explanation:

To solve the problem in question, let's call the cost of the love seat x. According to the information given, the sofa costs double the love seat, so the sofa's cost will be 2x. Together, the sofa and love seat cost $1500, which gives us the equation:

x + 2x = $1500

Combining like terms, we get:

3x = $1500

To find the value of x, we divide both sides of the equation by 3:

x = $1500 / 3

x = $500

This means the love seat costs $500. To find the cost of the sofa, we multiply the cost of the love seat by 2:

2x = 2 * $500

2x = $1000

Therefore, the sofa costs $1000, and the love seat costs $500.

Answer:

You're not giving enough details about the figure

When a triangle is translated, the resulting triangle will be congruent to the original triangle.

The congruency statement is ABCD = ZYXW

From the complete question, corresponding points are:

This means that:

Hence, the congruency statement is ABCD = ZYXW

Read more about congruency at:

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Answer: The answer is 5.2 (rounded to the nearest tenth)

Actual Answer: 5.19615242

Hope this helps!

Answer:

its the square root of 27 to the power of 2

Step-by-step explanation: hope this helps

Answer:

Area of Trapezoid is 39 unit²

Step-by-step explanation:

Given as :

For A Trapezoid

The measure of base side 1 = [tex]b_1[/tex] = 10 unit

The measure of base side 2 = [tex]b_2[/tex] = 16 unit

The height of the Trapezoid = h = 3 unit

Let  The Area of Trapezoid = A square unit

Now, From Formula

Area of Trapezoid = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height

I.e A =  [tex]\dfrac{1}{2}[/tex] × ([tex]b_1[/tex] + [tex]b_2[/tex]) × h

Or, A =  [tex]\dfrac{1}{2}[/tex] × (10 unit + 16 unit) × 3 unit

Or, A =  [tex]\dfrac{1}{2}[/tex] × (26 unit) × 3 unit

Or, A =  [tex]\dfrac{1}{2}[/tex] × 78 unit²

Or, A = [tex]\dfrac{78}{2}[/tex] unit²

I.e A = 39 unit²

So, The Area of Trapezoid = A = 39 unit²

Hence, The Area of Trapezoid is 39 unit² . Answer

Answer:

1/36

Step-by-step explanation:

3(1/3)=3/3=1

2*3=6

(1/6)^2=(1/6)(1/6)=1/36

Answer:

Carrie read at a rate of 21 2/3 pages per hour

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time Ms. Graves gave her class to read = 18 minutes

Number of pages Carrie read in 18 minutes = 6 1/2 pages

2. At what rate, in pages per hour, did Carrie read?

Rate = Number of pages/Time given

For getting the exact rate per hour, we should use the Rule of Three Simple, this way:

Number of pages in 60 minutes * 18 = 6 1/2 * 60

Number of pages in 60 minutes = (6.5 * 60)/18

Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3

Carrie read at a rate of 21 2/3 pages per hour

Answer:

Step-by-step explanation:

1 - 25 (a+b)^2 = 1 - 5² (a+b)²

= 1 - (5*[a + b) ]²                    { [tex]a^{m} *a^{n}  = a^{m+n}[/tex] }

= 1 - (5a +5b)²

= (1 + 5a +5b) (1 - [5a + 5b])      { a² - b² = (a + b)(a - b)   }

=(1 + 5a +5b) (1- 5a - 5b)

Answer:

linear

Step-by-step explanation:

This graph is linear

Final answer:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. Plug in the given values of the lengths of the legs EF and EG, and solve the equation to find the length of GF.

Explanation:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is line segment GF. Let's label the length of EF as x, and the length of EG as y.

Using the Pythagorean theorem, we can set up the following equation: x^2 + y^2 = GF^2.

Plugging in the given values, x = 9.4 and y = 6.8, we get: 9.4^2 + 6.8^2 = GF^2. Solving this equation will give us the length of line segment GF.

Answer:

all work is shown and pictured

155-45=110

3850÷110=385 bicycles

Answer:

35

Step-by-step explanation:

3850/(155-45)

3850/110

35

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Answer:

y+1=5(x+2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=5(x-(-2))

y+1=5(x+2)

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

How I got that answer:

The vertex is the lowest point of parabolas that open upward.

(h,k) = vertex

(h,k) = (-3,-1)

h = -3

k = -1

For each of the answer choices, a = 1.

The general template of a quadratic in vertex form is

y = a(x-h)^2 + k

Plug a = 1, h = -3, k = -1 into that equation. Simplify.

y = a(x-h)^2 + k

y = 1(x-(-3))^2 + (-1)

y = (x+3)^2 - 1

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola. The provided equations have vertices at different points. You must match the vertex of your graph with the correct equation.

In order to find the equation of the graph in vertex form, we need to locate the vertex on the graph. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.

Considering the options provided:

However, without a graph or specific vertex provided, we won't be able to define the equation of the graph precisely in vertex form. You need to match the vertex of your graph to one of the above options.

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