If you want to increase the length of the side of a square by 30%, what fraction can be used as the
multiplier to find the length of the new side?​

Answer:

323 ft^2

Step-by-step explanation:

Separate the figure on the left into two figures, a trapezoid and a square

The area of a trapezoid is

A = 1/2 (b1+b2)h

A = 1/2 (12+15)*7

  = 1/2 (28)7

     98 ft^2

The area of a square is

A = s^2

   = 15^2

   = 225 ft^2

Add the areas together

A total = 98+225 =323 ft^2

Answer:

2:3

Step-by-step explanation:

We know that there are 24 red and black cards in the 48 pack because their ratio is 1:1. When 8 red cards are removed we have 16 red and 24 black cards. The ratio of this is 16:24 which simplifies to 2:3.

The ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

The total amount of cards (red or black) in the pack is = 48

The ratio of the number of red cards to the number of black cards is = 1:1

The number of cards removed from the pack = 8

Therefore the total number of cards( red or black = 48 -8

= 40 cards

But to calculate the number of red card

= 1+1 = 2

40/2 = 20 red cards

The number of black cards

1+1 = 2

40/2 = 20 black cards

The ratio of red is to black cards = 20:20 or 20/20 = 1:1 or 1/1

Therefore the ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

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Answer:

Probability = 0.2603

Step-by-step explanation:

Consider the steps below;

[tex]Probability of Experiment Involving Cats - 5 / 7,\\Probability That 4 Chosen Experiments Are All Involving Cats - ( 5 / 7 )^4,\\\\5 / 7 * 5 / 7 * 5 / 7 * 5 / 7 =\\\\Conclusion; Probability - 625 / 2401[/tex]

Solution; Probability = ( About ) 0.2603

Answer:

∠1 = 90°

Step-by-step explanation:

The angle inscribed in a semicircle is always 90°

∠1 = 90°

Answer:

[tex] - \frac{1}{12} \\ [/tex]

Step-by-step explanation:

[tex] - \frac{1}{3} \times \frac{1}{4} \\ \\ = - \frac{1}{12} [/tex]

Answer:

slope = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 3) ← 2 points on the line

m = [tex]\frac{3-2}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

30°=15° 52°=26° 172°=86° 171'30°=85.75°

Step-by-step explanation:

okay so re-reading over the question, and analyzing what the question wants us to answer, you will then realize that the way to get the answer is to divide x by 2.

our x examples, in this case, would be 30°,52°,172°, and 171'30°.

and that's how you find the answer to this type of question. :)))

Answer:

a. 9

Step-by-step explanation:

[tex]k = \frac{9}{-3} = -3\\y = -3x\\-27 = -3x\\\frac{-27}{-3} = \frac{-3x}{-3} \\9 = x[/tex]

Answer:

a. 9

Step-by-step explanation:

because the orginal number was 9 and the newer one is -27 we can determine that y was multiplied by -3 so you would apply the same rule to -3 or x and you would get a product of 9 because two negatives equals a postive

Answer:

no whole number

Step-by-step explanation:

263 is a prime number, so it can be divided only by 1 and 263. So, no whole number will be square root for 263.

Answer: 24 m^3

Step-by-step explanation:

Given that you have a base with an area of 6 square meters, it has already calculated the product of length and width. In the Volume Formula Length x Width x Height, you're pretty much multiplying that given area by a height of 4, since you already have that length and width in the form of 6 square meters. The result you'll have is 24 Meters Cubed.

Answer:

The measurement of ∠3 is 135°

Step-by-step explanation:

In the problem, we are given a measurement. The measurement of ∠1 is 135°. We are asked to find the measurement of ∠3.

∠1 and ∠3 are corresponding angles. This means that they will have the same measurements.

So, if m∠1 is 135° then the m∠3 is also 135°

Answer:

m∠=135°

Step-by-step explanation:

These lines are parallel lines, which is indicated by the two arrows towards the right of the lines.

Since these lines are parallel, corresponding angles, such as ∠1 and ∠3 can exist.

Corresponding angles are congruent, which means they have the same measure.

∠1 and ∠3 are corresponding angles, therefore

∠1=∠3

We know that the measure of ∠1 is 135 degrees. Therefore, ∠3 will also have a measure of 135 degrees.

135=∠3

The measure of ∠3 is 135 degrees.

Answer:

D

Step-by-step explanation:

[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]

Therefore, the correct answer is choice D. Hope this helps!

Answer:

$3,745

Step-by-step explanation:

First, you have to calculate the price after the discount is applied:

Price of the car: $25,000

Discount: 18%

$25,000*18%= $4,500

$25,000-$4,500= $20,500

Second, you have to calculate the total amount she has to pay including the 7% tax:

$25,000*7%= $1,750

$25,000+$1,750= $26,750

Third, as the statement indicates that Ms. Eve had to put  14% of what she had to pay as down payment, you have to calculate the 14% of $26,750:

$26,750*14%= $3,745

According to this, Ms. Eve has to pay $3,745 for the down payment.

Answer:

[tex]f(n)=\frac{1}{3}n[/tex]

Step-by-step explanation:

To convert from feet to yards, divide by the value 3.

Answer:

Option (D).

Step-by-step explanation:

Initial population of the deer [tex]P_{0}[/tex] = 4800

Decrease in the population of the deer after every 8 years = [tex]\frac{1}{2}\times (\text{Initial population})[/tex]

Decrease in population is an exponential process, so the expression representing population will be,

[tex]P_{t}=P_{0}(1-r)^x[/tex]

Where [tex]P_{t}[/tex] is the population after 'x' slots of 8 years.

r = fraction of decrease in the population

x = [tex]\frac{\text{Number of years}}{8}[/tex]

By substituting the values of r and x in the expression,

[tex]P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}[/tex]

[tex]P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}[/tex]

Therefore, Sylvia should do few corrections in her expression.

(8) should be replaced by ([tex]\frac{1}{2}[/tex]) and [tex]\frac{t}{2}[/tex] should be replaced by [tex]\frac{t}{8}[/tex].

Option D. will be the answer.

Answer:

D

Step-by-step explanation:

The range means the possible values of the y coordinate which is y ≥ 1 in this function

Answer:

16

Step-by-step explanation:

1/2*1/2*1/2 = 1/8 cubic units

2/(1/8) = 16

Answer:

16

Step-by-step explanation:

[tex](\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\\\frac{2}{\frac{1}{8}} = 2 \cdot 8 = 16[/tex]

Answer:

The Solution Set

Step-by-step explanation:

Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.

[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\S=\{3,4\}[/tex]

Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.

[tex](3)^{2}-7(3)+12=0\\-12+12=0\\0=0[/tex]

The output or possible values you could get as a result from an expression or equation is the solution set of the equation

Take for instance, we have the following equation

[tex]x^2 = 4[/tex]

When solved, the equation becomes

[tex]x = \pm 2[/tex]

This can be rewritten as:

[tex]x = \{-2,2\}[/tex]

This means that -2 and are the solution set of the equation [tex]x^2 = 4[/tex]

Hence, the output or possible values are called solution set

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Answer:

If you know two number a and b and need find, b is what percentage of a, P=b

- 100%

a

Answer:

124

Step-by-step explanation:

A circle is a curve sketched out by a point moving in a plane. The measure of the arc mFD is 124°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As we know that the angle made at the center of the circle is 360°. And it is mentioned that the measure of mFE is 146°, while mED is 90°. Therefore, the sum of all angles can be written as,

[tex]\angle FOE + \angle EOD + \angle FOD = 360^o\\\\146^o + 90^o + \angle FOD = 360^o\\\\236^o +\angle FOD =360^o\\\\\angle FOD = 124^o[/tex]

Thus, the measure of the arc mFD is 124°.

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Answer:

if its 8 to 5 then 16 is 10

answer: 10 miles

Answer:

10 miles

Step-by-step explanation:

8 km = 5 miles

So, Let's use the unitary method

1 km = [tex]\frac{5}{8}[/tex] miles

Multiplying both sides by 16, we get

16 km = [tex]\frac{5}{8} * 16[/tex] miles

16 km = 5 × 2 miles

16 km = 10 miles

Answer:

3 hours

Step-by-step explanation:

 Jasmine's hourly distance covered (her rate of travel) is 45 mi / hr.

   45 miles       135 miles

   -------------- = ----------------

       1 hour               x

Cross-multiplying, we get 45x = 135, or x = 3 hours

Answer:

w=12 ft

l= 20 ft

A.

P= 2(12+20)= 64 ft

A= 12*20= 240 ft²

B.

P=2(12*1.2+20*1.2)= 76.8 ft

A= 12*1.2*20*1.2= 345.6 ft²

C.

(76.8-64)/64*100%= 20%

(345.6- 240)/240*100%= 44%

D.

perimeter increase is linear function of one dimension increase

area increase is function of 2 dimensions increase

Answer:

[tex]\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}[/tex]

Step-by-step explanation:

A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)

According to the trigonometric properties:

[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]

[tex]cos(theta) = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan(theta) = \frac{opposite}{adjacent}[/tex]

[tex](adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}[/tex]

[tex](adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}[/tex]

[tex](opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}[/tex]

Use the above formulas with corresponding sides:

[tex]13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83[/tex]

[tex]14) sin(theta) = \frac{\sqrt{5^{2}-3^{2} } }{5} = \frac{4}{5} = 0.8[/tex]

[tex]15) sin(theta) = \frac{9}{\sqrt{(8\sqrt{7}) ^{2} + 9^{2} } } = 0.391[/tex]

[tex]16) tan(theta) = \frac{3}{4} = 0.75[/tex]

Hope this helps!

:)

Answer:

10 5/8

Step-by-step explanation:

Answer:

Solve the rational equation by combining expressions and isolating the variable  

Answer:

Step-by-step explanation:

I assume that the equation is

[tex]e^x+\frac{e^{-x}}{e^x} -e^{-x}=t \\[/tex]

[tex]e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t[/tex]

[tex]e^{3x}+1-e^x=e^{2x}t[/tex]

[tex]e^{3x}-te^{2x}-e^x=-1[/tex]

Let u = e^x

[tex]u^3-tu^2-u=-1[/tex]

[tex]u(u^2-tu-1) = -1[/tex]

if u=1, then [tex]u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0[/tex]

then u = 0 (reject) or u = t

So far, we have u = 1 and u = t

if u =1, e^x =1 , then x = 0

if u = t, then e^x = t or x = lnt

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\sqrt{\frac{4x^2}{3y} }[/tex]

= [tex]\frac{\sqrt{4x^2} }{\sqrt{3y} }[/tex]

= [tex]\frac{2x}{\sqrt{3y} }[/tex]

Rationalise the denominator by multiplying the numerator/ denominator by [tex]\sqrt{3y}[/tex]

Note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a

= [tex]\frac{2x}{\sqrt{3y} }[/tex] × [tex]\frac{\sqrt{3y} }{\sqrt{3y} }[/tex]

= [tex]\frac{2x\sqrt{3y} }{3y}[/tex]

Answer:

C : Measure using the distance formula

Step-by-step explanation:

A Venn diagram is a diagram which shows the relation of all different sets

Just like it is given in the attachment there is a relation between the perimeter and the area.

The distance formula is

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]

where,

[tex](x_1, y_1)[/tex] is the first point coordinates

[tex](x_2, y_2)[/tex]  is the first point coordinates

By using the distance formula as discussed above shows the intersection of the Venn diagram

Hence, the correct option is C.

Answer: 17.9

Step-by-step explanation:

Using Heron's formula:

Area of a triangle is given by:

√s(s-a)(s-b)(s-c)

Where a, b and c ara sides of the triangle and

S = (a+b+c) / 2

In the question above sides are :

XY=XZ= 20 and YZ=18

S = (20 + 20 + 18) / 2 = 58/2 = 29

Area = √29(29-20)(29-20)(29-18)

Area = √29(9)(9)(11)

Area = √25839

Area = 160.74513

Altitude = height(h)

Area = 0.5 × base × height

Base = yz = 18

160.74513 = 0.5 × 18 × h

160.74513 = 9 × h

h = 160.74513 / 9

h = 17.9 (3 s.f)