select one card at random from the deck let A be the event that the randomly select a card is a club and let B be the event that the card is a five

Answer:

since ABC and ADE are similar,they have equal areas.

(AC)^2/(AE)^2=area ABC/ADE

areaABC=ACE=1

so substitute it in the afformentioned equation

u will get,AC=AE

The length of side CA in triangle ABC is c * (a² + ab + ac) / (a * (a + b + c)).

To find the length of side CA in triangle ABC, we need to use the concept of similarity and corresponding sides. Let's denote the lengths of sides in each triangle:

Triangle ABC:

Length of side AB: a

Length of side BC: b

Length of side CA: c

Triangle ADE:

Length of side AD: x (corresponding to side AB in ABC)

Length of side DE: y (corresponding to side BC in ABC)

Length of side EA: z (corresponding to side CA in ABC)

Since triangles ABC and ADE are similar, their corresponding sides are in proportion:

AD/AB = DE/BC = EA/CA

We know that AD corresponds to AB, and DE corresponds to BC, so we can set up the following proportions:

x/a = y/b

Solving for y, we get:

y = (b * x) / a

Next, we can set up the proportion for EA/CA:

z/c = x/a

Solving for z, we get:

z = (c * x) / a

Now, we have expressions for y and z in terms of x, a, and b. Since the sum of the lengths of the sides of a triangle is always constant, we can write the equation:

x + y + z = a + b + c

Substituting the expressions for y and z:

x + (b * x) / a + (c * x) / a = a + b + c

To find the value of x, we can multiply the entire equation by a to eliminate the denominator:

a * x + b * x + c * x = a² + ab + ac

Combining the x terms:

x * (a + b + c) = a² + ab + ac

Dividing both sides by (a + b + c):

x = (a² + ab + ac) / (a + b + c)

Now that we have found the value of x, we can substitute it back into the expression for z:

z = (c * x) / a

z = (c * (a² + ab + ac) / (a + b + c)) / a

Simplifying:

z = c * (a² + ab + ac) / (a * (a + b + c))

Thus, we have found the length of side CA in triangle ABC:

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[tex]\\ \rm\Rrightarrow tan^2135-cosec^260=-xcos45.sin45.cot60[/tex]

[tex]\\ \rm\Rrightarrow (-1)^2-(\dfrac{2}{\sqrt{3}})^2=-\dfrac{x}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow 1-\dfrac{4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3-4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{-1}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{\sqrt{3}}=\dfrac{x}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2}{\sqrt{3}}[/tex]

Answer:

B, 34 degrees

Step-by-step explanation:

Since all triangles equal to 180 degrees, you have to add together the angles you already know and subtract from 180.

123+23=146  180-146=34

Hopefully this helps, have a nice day/night!

Answer:

It is a trapezoid! because you can tell that that is the shape of the entire model

Answer:

If your money is in a savings account earning 3% a year, it will take around 24 years.

Answer: Approximately 24.53%

Explanation:

I could be misreading what you posted, but it appears there are 39 female Democrats out of 39+27+57+36 = 159 total people surveyed.

This leads to the percentage 39/159 = 0.2453 = 24.53% which is approximate.

Answer:

Step-by-step explanation:

6/9 x 45 = 2/3 x 45 = 30

[tex] \frac{2}{3} \times 45 = 30[/tex]

Answer:

Step-by-step explanation: height h =

slant height s =

side length a =

perimeter of base P =

lateral edge length e =

1/2 side length r =

volume V =

lateral surface area L =

base surface area B =

total surface area A =

Get a Widget for this Calculator

Square Pyramid Shape

Pyramid Diagram with h = height, l = length and w = width and s = slant height

h = height

s = slant height

a = side length

P = perimeter of base

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Calculator Use

This online calculator will calculate the various properties of a square pyramid given 2 known variables. The square pyramid is a special case of a pyramid where the base is square. It is a regular pyramid with a square base.

Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm3, L in mm2, B in mm2 and A in mm2.

NAN: means not a number. This will show as a result if you are using

Answer:

x = 0

I hope this helps!

Solution:

Given ratio: [tex]0.45:1.35[/tex]

Multiply both sides by 100:

[tex]0.45:1.35[/tex]

[tex]\rightarrow 0.45 \times 100:1.35 \times 100[/tex]

[tex]\rightarrow 45:135[/tex]

Convert the ratio into a fraction:

[tex]\rightarrow 45:135 = \dfrac{45}{135}[/tex]

Simplify the fraction:

[tex]\rightarrow \dfrac{45}{135} = \dfrac{45 \div5}{135 \div 5} =\dfrac{9}{27} = \dfrac{9 \div 9}{27 \div 9} = \dfrac{1}{3}[/tex]

The simplified fraction representing the ratio 0.45 to 1.35 is 1/3.

To express the ratio 0.45 to 1.35 as a simplified fraction, we can divide both numbers by their greatest common divisor (GCD) to simplify the ratio. In this case, the GCD of 45 and 135 is 45.

So, divide both numbers by 45:

0.45 ÷ 45 = 0.01

1.35 ÷ 45 = 0.03

The simplified ratio is 0.01 to 0.03. To make it an integer ratio, we can multiply both parts by 100:

0.01 * 100 = 1

0.03 * 100 = 3

So, the simplified fraction representing the ratio 0.45 to 1.35 is 1/3.

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Answer:

7.61 gallons.

Step-by-step explanation:

you take the 46, and you divide on both sides. 350÷46= approximately 7.61 gallons.

Answer:

Step-by-step explanation:

The triangles are similar because they have two sides and the angle between them (EFG) respectively equals, and it’s evident the factor between the two triangles is 2. So EG=2CB=2*8=16

Answer:

the value of EG is 20.

Step-by-step explanation:

3×4 = 12, AB and EF is similar but the value of AB is multiplied by 4 to become 12 for EF.

similarly, 4×4 = 16, BC and FG is similar but the value of BC is multiplied by 4 to become 16 for FG..

In this way, AC and EG are also similar so 5×4 = 20.

All the values are multiplied by 4 ...

The area of the triangle is the amount of space on it.

The area of the triangle is 85.5 square yard

The given parameters are:

a = 12 yd

b = 16 yd

c = 15 yd

Start by calculating the semi-perimeter (s)

s = 0.5 * (a + b + c)

This gives

s = 0.5 * (12 + 16 + 15)

s = 21.5

The area of the triangle is then calculated as:

[tex]A = \sqrt{s * (s - a) * (s - b) * (s - c)[/tex]

This gives

[tex]A = \sqrt{21.5 * (21.5 - 12) * (21.5 - 16) * (21.5 - 15)[/tex]

Evaluate the product

[tex]A = \sqrt{7301.9375[/tex]

Evaluate the square root

A = 85.5

Hence, the area of the triangle is 85.5 square yard

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Answer:

Jayla's expenses are: $245.00

Jayla's revenue from the sales are: $479.00

Total profit: $234.00

------------------------------------------

Hope this helps! This should be correct !

Answer:

- $245

+ $479

+ $234

Step-by-step explanation:

expenses : (25 x 2) + (15 x 3) + (30 x 5) = 50 + 45 + 150 = 95 + 150 = $245

revenue : (38 x 2) + (26 x 3) + (65 x 5) =  76 + 78 + 325 = 154 + 325 = $479

total profit : 479 - 245 = $234

Answer:  n = -2; i = 1

Step-by-step explanation:

i + 2n = -3

        i = -3 - 2n

Plug in i in 2i - 3n = 8, we get:

2i - 3n = 8

2(-3 - 2n) - 3n = 8

-6 - 4n - 3n = 8

-6 - 7n = 8

     -7n = 14

        n = -2

substitute n = -2 into i = -3 - 2n

i = -3 - 2n

i = -3 - 2(-2)

i = -3 + 4

i = 1

Answer:

3 dollars 3 years

Step-by-step explanation:

don't ask

don't ask

Answer:

a) most students got a better grade on the second page than the first. which makes it positive

b) the pupil could've gotten a 61% score

Step-by-step explanation:

Answer:

200%

Step-by-step ex

Answer:

200%

Step-by-step explanation:

x% of 20 = 40

x/100 × 20 = 40

x/10 × 2 = 40

x/5 = 40

x = 40×5

x = 200

Answer:

please give the complete question. cannot find answer with only half of the question

Answer:

Step-by-step explanation:

Use slope formula:

1) Points (1, 2) and (5, 4)

2) Points (1, -5) and (3, 5)

3) Points (2, 3) and (-1, 6)

4) Points (4, 2) and (-2, 2)

Answer:

1/5, 1, decreasing, 0

Step-by-step explanation:

Total amount after 4 years will be $63. If he invest principle amount of $42 for rate of interest of 12.5%.

Simply multiply the principal amount by the interest rate and the time to calculate simple interest. "Simple Interest = Principal x Interest Rate x Time," the formula says. You must multiply the borrowed principal amount by 1 plus the interest rate.

The simple interest rate is the rate at which you borrow or lend money. When a borrower borrows money from a lender, the lender receives an additional sum of money. The principal is the borrowed money that is given for a specific period of time. The interest is the extra amount paid back to the lender for using the money.

First, converting R percent to r a decimal

r = R/100 = 12.5%/100 = 0.125 per year.

To find the total amount  A = P (1+rt).

= 42(1 + 0.125 *6)

=  $63

The total amount is $63

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Answer:

x=2

Hope this helps! :)

3x+5x=8x

23-7=16

16÷8

Answer:

x = 2

Step-by-step explanation:

3x + 7 = 23 - 5x

3x + 5x = 23 - 7

8x = 16

x = 2

Answer:

C)

Step-by-step explanation:

[tex]\sqrt{x}[/tex] : original function

[tex]\sqrt{-x}[/tex] : reflect across the y-axis

[tex]\sqrt{-\dfrac13x}[/tex] : horizontal stretch by a scale factor of 3

[tex]\sqrt{-\dfrac13(x-3)}[/tex]: translate right 3 units

f(x) : original function

f(-x) : reflection over y-axis

f(ax) : horizontal stretch of the graph by a scale factor of 1/a

f(x - a) : horizontal translation right a units

Answer:

  5 ft

Step-by-step explanation:

You can find the missing dimension by using the area formula and solving it for the missing dimension.

__

  A = 1/2(b1 +b2)h . . . . . . . . . . . . formula for the area of a trapezoid

  25.5 ft² = 1/2(7 ft +3.2 ft)h . . . . with the given numbers filled in

  (25.5/5.1) ft = h = 5 ft . . . . . . . . . divide by the coefficient of h

The height of the trapezoid is 5 ft.

Answer:

1.) 75

2.) 75

3.) 2

Step-by-step explanation:

120n-150=45n

add 150 to both sides

120n=45n+150

subtract 45n from both sides

75n=150

divide by common number, since 75 is half of 150, use 75.

n=2

Step-by-step explanation:

area : 180+130 cm2 = 310cm2

perimeter = 76cm

hope this helps you.

Answer:

P=76 cm / A=310 cm²

Step-by-step explanation:

The perimeter is the sum of all sides in a polygon;

P=20+18+10+5+10+13= 76 cm

The area which i will divide into 2 parts and add them;

The rectangle of length 20 cm and width 13 cm;

A=lw=20×13=260 cm²

The rectangle of length 5 cm and width 10 cm;

A=lw=5×10=50 cm²

A(Total)=260+50= 310 cm²

Answer:

they have a difference of 4 cups.

Step-by-step explanation:

container one: 1 gallon = 16 cups. 2 gallons = 32 cups.

container Two: 1 quart = 4 cups. 9 quarts = 36 cups.

36 cups - 32 cups = 4 cups

Answer:

x^5+2x^3+6x+1/5

Step-by-step explanation:

our given equation is already written in standard form.

Answer:

It is already in standard form

Step-by-step explanation:

The standard equation should be arranged from high order to low order

   So x^5+2x^3+6x+1/5 = x^5+2x^3+6x+1/5

It is already in standard form

Answer:

[tex]\displaystyle y = 4x + 12[/tex]

Step-by-step explanation:

−4x + y = 12

+ 4x + 4x

_________

[tex]\displaystyle \boxed{y = 4x + 12}[/tex]

I am joyous to assist you at any time.