In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=5, a=3

Answer:  blue water: 00

               Yellow water: 000

Step-by-step explanation:

just show how many parts

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

77 degrees

Step-by-step explanation:

The interior angles of a triangle always add up to 180 degrees, so you can form an equation:

\(x + 71 + 32 = 180\)

\(x + 103 = 180\\x = 77\)

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

-7+4=-3

(-7+4)=-3

3(3)=9

Sec A is solved to be \(\frac{8}{\sqrt{55} }\)

Solving  cosx / secx - cotx / tan x gives  cos^2 x - cot^2 x

This is division of circle into 4 parts. each part is termed a quadrant

sine θ = opposite / hypotenuse

In the third quadrant:

The opposite = -3

hypotenuse = 8

sec θ = 1 / cos θ

cosθ = adjacent / hypotenuse

From Pythagoras theorem

hypotenuse² = adjacent² + opposite²

adjacent = √64 - 9

= √55

cos θ = √55/8

sec ∅ = 1 / cos ∅ = 8/√55

from trigonometry we know that:

secx = 1 / cosx and cotx = 1 / tanx

plugging the trigonometry values to the given expression gives

cosx / secx - cotx / tan x = cosx / 1/cosx - 1/tanx / tanx

= cosx / 1/cosx - 1/tanx / tanx

= cosx * cosx - cotx * cotx

= cos^2 x - cot^2 x

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Answer:

25

Step-by-step explanation:

because I go it wrong and the quiz told me the answer was 25. Pog. I am just as confused.

We have that Linda's net and expression incorrect

With the Expression of the surface area of attic

45 (40 + 25 + 25) + 1/2 (40 x 15)

Hence, Surface area is,

X = 4050 + 600

X = 4650 feet²

Hence, The answer is No, Because Her expression for the triangles are incorrect;

1/2(40 x 15)

Instead of,

1/2 x 40 x 15

Hence, Linda's net and expression incorrect,

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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.

She needs to find the approximate surface area of the attic, including the walls, floor, and

ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes

the expression below to represent the surface area of the attic. Are Linda's net and

expression correct?

The coordinate of the midpoint of the line segment is (-1.5, -5.5)

The coordinate of the midpoint of a line is the half x values and y values. Thus:

Xm = (X1 + X2)/2 and Ym = (Y1 + Y2)/2

where m is the midpoint

Given:  (−1, −1) and (−2,−10)

X1 = -1, Y1 = -1 and X2 = -2, Y2 = -10

Xm = (-1 +(-2))/2  = -1-2/2 = -3/2 = -1.5

Ym = (-10 + (-1)) = -10-1/2 = -11/2 = - 5.5

Therefore, the coordinates of the midpoint are x = -1.5 and y = -5.5 or (-1.5, -5.5)

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To answer this question we will use the formula for simple interest:

where F is the final amount, I is the initial amount, r is the interest rate in decimal form, and t is the time in years.

Substituting r=0.03, I=1200, and t=3 in the above formula we get:

Therefore, after 3 years you will have a total of $1308, which means you have a gain of:

dollars.

Answer: $108.

Answer:

4112

Step-by-step explanation:

Answer:

By applying law of conservation of mass.

Explanation:

Every balanced chemical equation follows law of conservation of mass.

This law states that mass can neither be created nor can be destroyed but it can only be transformed from one form to another form.

This law also states that the total number of individual atoms on the reactant side must be equal to the total number of individual atoms on the product side.

For the given reaction, the balanced chemical equation follows:

4Na1+Pb(SO4)__Pb14+2Na2SO4

On reactant side:

Number of sodium atoms = 4

Number of iodine atoms = 4

Number of lead atoms = 1

Number of sulfur atoms = 2

Number of oxygen atoms = 8

On product side:

Number of sodium atoms = 4

Number of iodine atoms = 4

Number of lead atoms = 1

Number of sulfur atoms = 2

Number of oxygen atoms = 8

Hence, the balanced chemical equation is written above.

Step-by-step explanation:

Answer:

11x^2+x-1

Step-by-step explanation:

To solve this problem follow these steps:

1. Substract the number of pages she has already read to the number of pages of the book:

2. Divide this number by the number of days she has to finish the book, it means, 2 days:

She needs to read 67 pages each day.

Answer:

Step-by-step explanation:

First, the data set is:

  Gender     Race        Salary   WorkTimeStatus   Education   Tenure

1. Female  Caucasian  32196     Full Time                     14yrs          2 yrs

2. Male      Black          62385    Full Time                     16yrs         10yrs

Now to the questions:

(A) This data set contains 2 cases; 1 for the first employee (the female caucasian) and 2 for the second employee (the male black).

(B) This data set contains 6 variables;

1. Gender  2. Race  3. Salary  4. Work time status  5. Years of education

6. Number of years in/with the company

(C) Out of these 6 variables, the quantitative ones (those that can be measured or weighted numerically) are:

3. Salary   5. Years of education   6. Years with the company

Altogether, 3 in number

(D) The qualitative variables are:

1. Gender   2. Race   4. Work Time Status

Altogether that's 3 variables

Answer:

Then the area of the triangle is 240 m²

Step-by-step explanation:

Area of a triangle:

The area of a triangle is given by the multiplication of its height and altitude, divided by 2.

In this question:

Base = 24m, altitude = 20m. So

\(A = \frac{24*20}{2} = 24*10 = 240\)

Then the area of the triangle is 240 m²

Answer:42.55

Step-by-step explanation:

Les get the big boi out of the way first. We see that it is 3.5 by 9 and if we multiply we get 31.5. Next left triangle 2 by 2 so four but divided by 2 is 2. God so many  2's. So total is 33.5 so far. Next triangle is 2 by 5 soo  10 divided by 2 is 5. total is 38.5. Last dude in the middle. We know one side is two so we have to subtract here from the triangles which gets u the other side of 2 so 4. Total is 42.5

The Area of the Shape Shown is 42.5 square units.

The area of Rectangle is length times of width.

The area of the rectangle in the given figure is

Area of rectangle=3.5×9

=31.5 square units.

The area of left side triangle is

Area of triangle=1/2×2×2

=2 square units

The area of right side triangle 1/2×5×2

=5 square units

Now the area of square =2²

=4 square units.

Now total area of figure is 31.5+2+5+4 is 42.5 square units.

Hence, the Area of the shape Shown is 42.5 square units.

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Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Step-by-step explanation:

1 week = 7 days of 24 hours each = 7×24 = 168 hours.

the first team can do 1/700 of the total work per hour.

the second team can do 1/600 if the total work per hour.

if they work together, then 1/700 + 1/600 of the total work can be done per hour.

to add these 2 fractions we need to bring them to the same denominator. and that would be 4200 (LCM of 700 and 600).

1/700 + 1/600 = 6/4200 + 7/4200 = 13/4200

so, together, they can do 13/4200 if the total job in 1 hour.

how many hours will they need together to finish the job ?

well, how often does 13 fit into 4200 (as 4200/4200 is the complete job) ?

4200 / 13 = 323.0769231... hours

so, it will still take a little bit over 323 hours to clean all the streets.

but there are only 168 hours until the film crew starts.

so, no, there is not enough time.

Answer:

well I have this question too if you are doing amplify math so I got the soulutions x+3=14 and x=14-3.

Step-by-step explanation:

And for the x= part its x=11

Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.

A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.

A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.

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Full Question:

Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.

A) No. You would need to know that LK ⊥ MK

B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK

Answer:

31 and 13

Step-by-step explanation:

let the 2 numbers be x and y , with x > y , then

x + y = 44 → (1)

y = x - 18 → (2)

Substitute y = x - 18 into (1)

x + x - 18 = 44

2x - 18 = 44 ( add 18 to both sides )

2x = 62 ( divide both sides by 2 )

x = 31

and

y = 31 - 18 = 13

The 2 numbers are 31 and 13

Answer:

Step-by-step explanation:

The commutative, associative, and distributive properties help you rewrite a complicated algebraic expression into one that is easier to deal with. When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied.

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Step-by-step explanation:

h(x) = f(x) - g(x) = 15(7x) - (100x + 5) =

= 105x - 100x - 5 = 5x - 5

if h(x) < 0, then g(x) (company B) is more expensive.

if h(x) > 0, then f(x) (company A) is more expensive.

if h(x) = 0, then both companies charge the same.

2 weeks :

h(2) = 5×2 - 5 = 10 - 5 = 5

company A is more expensive, so, it costs her less to rent from company B.

1 week :

h(1) = 5×1 - 5 = 5 - 5 = 0

it will cost her the same with either company.

Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.

If Marguerite rents for 1 week, it will cost her the same at either company

h(x) = 5x - 5

Step-by-step explanation:

Given information:

Let x = number of weeks

Company A rate structure:

\(f(x)=15(7x)\)

Company B rate structure:

\(g(x)=100x+5\)

2 week rental

\(\textsf{Company A}:\quad f(2)=15(7\cdot 2)=210\)

\(\textsf{Company B}:\quad g(2)=100(2)+5=205\)

Therefore, it will cost less renting from Company B.

1 week rental

\(\textsf{Company A}:\quad f(1)=15(7\cdot 1)=105\)

\(\textsf{Company B}:\quad g(1)=100(1)+5=105\)

Therefore, it will cost the same at either company.

Difference between two rate structures

\(\begin{aligned}\textsf{If }h(x) & = f(x)-g(x)\\\\\implies h(x) & = 15(7x)-(100x+5)\\& = 105x-100x-5\\& = 5x-5\end{aligned}\)

True Statements

Answer:

72, 96

Step-by-step explanation:

You list down all the multiples like so:

8: 56, 64, 72, 80, 88, 96

3: 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

12: 60, 72, 84, 96

Then find the common ones like so:

8: 56, 64, (72), 80, 88, (96)

3: 57, 60, 63, 66, 69, (72), 75, 78, 81, 84, 87, 90, 93, (96), 99

12: 60, (72), 84, (96)

Then list them. That is how you do it.

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer: 96 books

If 6 shelves have 48 books on them, this is one half of 12 shelves, because 6 is one half of 12 shelves.

There are 12 shelves. So, multiply 48 by 2.

48 x 2 = 96.

Answer to the question = 96

Answer:

Area of Training field is 6076m^2

Step-by-step explanation:

Solution:

Here,

Length of the training field(l) = 98m

Breadth of the training field(b) = 62m

We know,

Area of the training field = l*b = 98m * 62m = 6076m^2

The measure of angle O is 56 and the value of m and n are 8.1 in and 14.5 in respectively.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The longest side is hypotenuse and it is the side facing the right angle. The other two sides are opposite and adjascent.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan,(tetha) = opp/adj

angle O = 180-(90+34)

= 180- 124

= 56°

To find m,

Tan 34 = m/12

m = Tan34 × 12

m = 8.1 in

using Pythagoras theorem to find n,

n= √8.1²+12²

n = √65.61+144

n = √209.61

= 14.5 in

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Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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