Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

Therefore, we can write,

PQ = 2(RQ)

8 = 2(RQ)

RQ = 4

PR = (RQ)√3

PR = 4√3

Hence, the length of the side PR in ΔPQR is 4√3 units.

The complete question is mentioned in the image below.

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Answer:

D) f(x) 3 cos 4x-4 (I just took it)

It is given in the question that

You will be charged 12.5% interest on a loan of $678.

So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125

So we have to find the value of 0.125 of 678.

[tex]0.125*678 = 84.75[/tex]

Therefore the interest that you will have to pay on loan is $84.75 .

Final answer:

The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.

Explanation:

The area of a rectangle can be found by multiplying its length and width.

In this case, the length is 15 feet and the width is 9 feet.

To find the area, multiply 15 feet by 9 feet:

Area = 15 feet x 9 feet = 135 square feet

Therefore, the area of the rectangle is 135 square feet.

The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.

Arithmetic Sequence: 100, 102, 104, 106,...

Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.

Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.

Answer:

Option C is correct .i.e., ∠3 and ∠7

Step-by-step explanation:

Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.

From Given Figure,

Following are pairs of corresponding angles,

∠1 and ∠5

∠2 and ∠6

∠4 and ∠8

∠3 and ∠7

Therefore, Option C is correct .i.e., ∠3 and ∠7

Answer:

f(-7)=0 that is option 4th is correct.

Step-by-step explanation:

If we have given any polynomial  then its factor means that value is giving zero of that polynomial

And opposite sign of factor is the zero of the polynomial

For example:

x+a is factor of any polynomial f(x) then f(-a)=0

Similarly, If x+7 is a factor of any polynomial then f(-7)=0

Hence, option 4th is correct.

Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].

[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]

[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]

[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]

[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]

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

[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]

[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]

[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]

car 1 = x

 car 2 = y

x+y =40 gallons

x=40-y

15x +20y = 675

15(40-y) +20y = 675

600-15y +20y =675

600+5y = 675

5y=75

y=75/5 = 15 gallons

x=40-15 =25 gallons

 Car 1 used 25 gallons

 Car 2 used 15 gallons

y-6 = -4(x+1)

y-6 = -4x-4

add 6 to each side

y=-4x+2

A is the correct answer

558.16 x 12 = 6697.92 every year

6697.92 x 30 = 200937.60 total

200937.60-150000 = $50,937.60 total interest paid

[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]

Hello!

The number of pairs of shoes each man can repair is its speed times the time.

Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.

Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.

Thus, we can equate:

[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]

That is the speed of the assistant. Then, the speed of the repairman is:

[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]

That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)

To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.

To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.

Let's denote the time it takes the repairman to repair one pair of shoes by x hours.

Since the assistant takes twice as long, their time would be 2x hours for one pair.

Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.

Now, we express their combined work rate as the sum of their individual work rates.

The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.

Together, this should equal their combined rate of 2 pairs per hour:

1/x + 1/(2x) = 2

Solving this equation for x, we first find a common denominator and get:

2/2x + 1/2x = 2

3/2x = 2

3 = 4x

x = 3/4

Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.

We can solve this problem by using the formula:

s = σ / sqrt(n)

where,

s = standard deviation of the sample

σ = standard deviation of the population = 3 years

n = number of samples = 100

Substituting:

s = 3 years / sqrt (100)

s = 0.3 years                       (ANSWER)

Assuming a regularly shaped rectangle, the formula for the area is given as:

A = L * W

where L and W are the length and width respectively

A = 3.6 x 10^2 miles * 2.8 x 10^2 miles

A = 100,800 square miles

or

A = 10.08 x 10^2 miles

Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Step-by-step explanation:

The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]

and height , [tex]H=2.8\times 10^{2}\, miles[/tex]

Area of rectangle , [tex]A=L\times W[/tex]

=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]

=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Final answer:

The magnitude of 6 + 2i is 2√10.

Explanation:

To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:

|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10

Therefore, the magnitude of 6 + 2i is 2√10.

Answer:

Option C. is the correct option.

Step-by-step explanation:

Equation of line is represented as y = mx + c

where m = slope of the line

c = y - intercept

Since line is passing through origin (0, 0) and a point (6, 2)

Therefore y intercept of the line will be 0.

c = 0

Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]

[tex]m=\frac{2-0}{6-0}[/tex]

[tex]m=\frac{2}{3}[/tex]

So the equation will be

[tex]y=\frac{1}{3}x[/tex]

Therefore, option C. is the answer.