In ΔQRS, the measure of ∠S=90°, SR = 45, QS = 28, and RQ = 53. What is the value of the tangent of ∠Q to the nearest hundredth?

Answer:

[tex]x=6+3\sqrt{2}[/tex] is the size of the square

Step-by-step explanation:

Let the side of the square cut from the cardboard be “x”

Size of the square base = [tex]12 -2x[/tex], height of the box = x

Volume of square box = Area * height = [tex](12-2x)^2 * x[/tex]

Differentiating the above equation and equating it to zero, we get –  

d/dx [tex]((12-2x)^2 * x)[/tex]

d/dx[tex]{(144 + 4x^2 -48x)*x}[/tex]= d/dx [tex](144x + 4x^3 -48x^2)[/tex]

d/dx [tex](144x + 4x^3 -48x^2) = 0[/tex]

[tex]144+8x^2-96X= 0\\18 +X^2-12X = 0[/tex]

On solving above equation, we get –  

[tex]x=6+3\sqrt{2} \\ x=6-3\sqrt{2}[/tex]

Answer:

The substance half-life is of 4.98 days.

Step-by-step explanation:

Equation for an amount of a decaying substance:

The equation for the amount of a substance that decay exponentially has the following format:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which k is the decay rate, as a decimal.

k-value of 0.1392.

This means that:

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

Find the substance's half life, in days.

This is t for which [tex]A(t) = 0.5A(0)[/tex]. So

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

[tex]0.5A(0) = A(0)e^{-0.1392t}[/tex]

[tex]e^{-0.1392t} = 0.5[/tex]

[tex]\ln{e^{-0.1392t}} = \ln{0.5}[/tex]

[tex]-0.1392t = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.1392}[/tex]

[tex]t = 4.98[/tex]

The substance half-life is of 4.98 days.

Answer:

add and subtract

Question:

Based on the same question options as found an online resource, we have;

Statement

G. The customer would pay $24,073 for car R

Answer:

The true statement

G. The customer would pay $24,073 for car R

Step-by-step explanation:

Discounts are deductions from the original price of a commodity or service

A rebate is a partial refund after payment is made

The discount offered by the car dealership are;

Discount 1;

5% reduction off a car built last year's original price, + $3,500 rebate

Discount 2;

10% reduction off a car built this year's original price + $1,250 rebate

The year car R was built = Last year

The original price for car R = $25,340

Let 'A' represent the amount the customer would pay, let, 'p' represent the price of the car, let 'd' represent the discount offered, and let 'r' represent the rebate

Given that the payment is made before the rebate, we have;

The amount the customer will pay, A = p - (p×d)

Therefore;

The amount the customer would pay for car R = $25,340 - (0.05 × $25,340) = $24,073

The amount the customer would pay for car S = $22,960 - (0.1 × $22,960) = $20,644

Therefore, the true statement, is the customer would pay $24,073

Answer:

$24,073

Step-by-step explanation:

Answer:

D 5

Step-by-step explanation:

the same scaling factor s applies to all sides when transforming from the small to the large triangle.

x×s = x + 5

(x-2)×s = x +1

=> s = (x+5)/x

=> (x-2)×(x+5)/x = x + 1

=> x² + 3x - 10 = x² + x

=> 3x - 10 = x

=> 2x = 10

=> x = 5

Respuesta:

a = 82; b 164

Explicación paso a paso:

a = 1 / 2b - - - (1)

a gana 66 = a + 66

b = b - 90

a = 2b

a + 66 = 2 (segundo - 90) - - - (2)

Ponga a = 1 / 2b en (2)

1 / 2b + 66 = 2 (b-90)

0.5b + 66 = 2b - 180

0.5b - 2b = - 180 - 66

-1,5b = - 246

b = 164

a = 1 / 2b

a = 1/2 * 164

a = 82

Answer:

40x - 15y

Step-by-step explanation:

Multiply the brackets together

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Have a good day :)

Answer:

40x - 15y

Step-by-step explanation:

Use the distributive property:

5(8x) - 5(3y) =

40x - 15y

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Explanation:

1 yard = 3 feet

We'll divide by 3 to convert from feet to yards

The basement is 9*6 = 54 square yards in floor area.

At $32 per square yard, the total cost to carpet the floor is 32*54 = 1728 dollars.

Answer:

45 and 225degrees

Step-by-step explanation:

Given the expression

tan⁻¹1

Using the calculator

tan⁻¹1

tan⁻¹1  = 45degrees

Since tan is positive in the third quadrant

theta=  180 + theta

theta = 180 + 45

theta = 225degrees

Hence the values of theta are 45 and 225degrees

Answer:

1)  6 feet

2) 38 feet

3)  at 1.5 seconds

4) 42 feet

5) in 3.12 seconds

Step-by-step explanation:

Answer:

$3,204.6

Step-by-step explanation:

$ 4,200              represents       100% of his salary

x amount  of $   represents      16.05 % in federal withholding

after you line up $ with $ and % with % think cross multiplication

x = 4,200* 16.05/ 100 = $674.1 is the amount in federal withholding

Net pay = 4,200 -674.1 -321.30 =  $3,204.6

Answer:

0.75 hours

Step-by-step explanation:

Time taken by my pump = 6 hours

Time taken by friend's pump = x

Combined time = 1.5 hours

Rate :

my pump = 1/6

Combined rate = 1/1.5

Combinwd rate = 1/6 + 1/x

Hence :

1/6 + 1/x = 1/1.5

(x + 6) / 6x = 1.5

x + 6 = 9x

x - 9x = - 6

-8x = - 6

x = - 6 / - 8

x = 0.75 hours

Answer:

1072.58feet

Step-by-step explanation:

Given the following

Angle of elevation = 40degrees

Height of helicopter above the water = 900feet

Required

Horizontal distance H

Using the SOH CAH TOA identity

tan theta = opposite/adjacent

tan 40 = 900/H

H = 900/tan40

H = 900/0.8391

H = 1,072.58feet

Hence the horizontal distance from the boat to the helicopter is 1072.58feet

Answer:

Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156.

Find the value of the bond when Tyler's mom purchased it. Explain your reasoning.

Step-by-step explanation:

Answer:

slope = 20

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, 0) and (x₂, y₂ ) = (10, 200) ← 2 points on the line

m = [tex]\frac{200-0}{10-0}[/tex] = [tex]\frac{200}{10}[/tex] = 20

Given:

The figure of two triangles.

To find:

The similarity statement for the given triangles.

Solution:

The corresponding sides of similar triangles are proportional.

In the given triangles,

[tex]\dfrac{XY}{AB}=\dfrac{6}{12}[/tex]

[tex]\dfrac{XY}{AB}=0.5[/tex]

Similarly,

[tex]\dfrac{YZ}{BC}=\dfrac{3}{6}[/tex]

[tex]\dfrac{YZ}{BC}=0.5[/tex]

And,

[tex]\dfrac{XZ}{AC}=\dfrac{7}{14}[/tex]

[tex]\dfrac{XZ}{AC}=0.5[/tex]

Since [tex]\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}[/tex], therefore

[tex]\Delta XYZ\sim \Delta ABC[/tex]

It can be written as:

[tex]\Delta ZYX\sim \Delta CBA[/tex]

Therefore, the correct option is A.

Answer:

Addituve Inverse

Step-by-step explanation:

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0. 

Answer:

additive Inverse or absolute value

Step-by-step explanation:

Answer:

2400 inches cubed

Step-by-step explanation:

The formula for the volume of a rectangular prism is:

V=whl

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So the formula is telling us to multiply the width, height, and length together. So in that case:

10 × 12 × 20 = 2400

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Have a good day :)

Answer:

$ 17 off

Step-by-step explanation:

20% is one fifth of the price

So divide 85 by 5  you get 17

Since you only get one 1/5 of the price off you save $17

Just to check and make sure you can do 17 * 5 = 85

Answer:

The answer is B

Step-by-step explanation:

The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.

Answer:

6

Step-by-step explanation:

4 – (3 – 5) =

PEMDAS says parentheses first

4 – (-2) =

Subtracting a negative is like adding

4 +2

6

Answer:

2-

Step-by-step explanation:

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Answer:

It would be 17 feet.

Step-by-step explanation:

So to do this, there is a right triangle being made with the height of the water slide and its base (length). With this, the Pythagorean Theorem can be used to find the hypotenuse of these lengths by the equation:

a^2 + b^2 = c^2

So by plugging in the given legs of the triangle, the answer can be found.

15^2 + 8^2 = c^2

225 + 64 = c^2

289 = c^2

c = 17

Answer:

D 3/4

Step-by-step explanation:

imagine a circle with its center in point A and going through point C.

the radius of that circle is 50 (AC).

remember, tan of an angle is sin/cos of that angle.

now rotate in our imagination that triangle to the right around point A, so that the side AB becomes the bottom base line.

now you see that 30 = sin(A)×radius = sin(A)×50

and 40 = cos(A)×radius = cos(A)×50

so, tan(A) = (sin(A)×50)/(cos(A)×50) = sin(A)/cos(A) = 30/40

= 3/4

Answer:

a) He can find the answer in one way

b) We make use of Addition property of mathematics

c) Total number of blocks = 12 blocks

Step-by-step explanation:

a) He can find the answer in one way

b) We make used of addition property of mathematics

c) The total number of blocks he is having is calculated as:

Blue blocks + Pink blocks + Green blocks

Where

Blue blocks = 5

Pink blocks = 3

Green blocks = 4

Hence:

Total number of blocks = 5 + 3 + 4 = 12 block

Answer:

30625

Step-by-step explanation:

Answer:

175²

Step-by-step explanation:

7 × 7 × 5 × 5 × 5 × 5

= (7 × 7) × (5 × 5 × 5 × 5)

= 7² × 5⁴

= 49 × 625

= 30.625

[tex] \sf = \sqrt{30.625} [/tex]

[tex] \sf = \sqrt{175 \times 175} [/tex]

[tex] \sf = 175[/tex]

[tex] \sf = {175}^{2} [/tex]

Conclusion:

Exponential Form of 7 × 7 × 5 × 5 × 5 × 5 adalah 175².