Confusing question pls help

Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.

Interpretation is Pedro collected 29 football cards and 68 baseball cards.

As given,

Total number of cards=97

Let y=football cards

    x=baseball cards

System of equations are

x + y=97  __(1)

x=y +39    __(2)

Substitute (2) in (1)

y+ 39 +y=97

⇒2y=58

⇒y=29

Substitute y=29 in (2),

x=29 +39

 =68

Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.

Interpretation is Pedro collected 29 football cards and 68 baseball cards.

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The derivative of the function \(f(x) = (f(x) - f(a))/(x - a) is f'(a) = 3/2.\)

The derivative of the function \(f(x) = (f(x) - f(a))/(x - a)\) can be found using the limit definition of the derivative. Let's calculate it using two different formulas:

a) Using the formula f'(a) = lim(x→a) [(f(x) - f(a))/(x - a)], we can evaluate the limit as x approaches a:

f'(a) = lim(x→a) [(f(x) - f(a))/(x - a)]

      = lim(x→a) [3x/(x - 3)]    (since f(x) = 3x)

      = 3a/(a - 3).

Therefore, f'(a) = 3a/(a - 3).

b) Using the formula f'(a) = lim(h→0) [(f(a + h) - f(a))/(2h)], we can calculate the limit as h approaches 0:

f'(a) = lim(h→0) [(f(a + h) - f(a))/(2h)]

      = lim(h→0) [(3(a + h) - 3a)/(2h)]  (since f(x) = 3x)

      = lim(h→0) [3h/(2h)]

      = lim(h→0) (3/2)

      = 3/2.

Therefore, f'(a) = 3/2.

In summary, using the given formulas, we find that f'(a) = 3a/(a - 3) and f'(a) = 3/2. These formulas provide the derivative of the function f(x) at the point a, where a ≠ 3, using two different approaches: directly evaluating the limit as x approaches a, and evaluating the limit as h approaches 0.

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Answer: 170 cm

Step-by-step explanation: 5x12=60. 60+8=68. 68x2.5=170.

The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

Answer:

See Below.

Step-by-step explanation:

We want to verify that:

\(\displaystyle \sec^6 A + \tan ^6 A = (2 \sec^2 A - 1)( \sec ^4 A - \sec^2 A + 1)\)

Recall that:

\(\displaystyle (a^3 + b^3) = (a+b)(a^2 - ab + b^2)\)

Let a = sec²(A) and b = tan²(A). This yields:

\(\displaystyle \sec^6 A + \tan ^6 A = (\sec ^2 A + \tan^2 A)(\sec^4 A - \sec^2 A \tan^2 A + \tan^4 A)\)

Recall that from the Pythagorean Identity, tan²(θ) + 1 = sec²(θ). Hence:

\(\displaystyle \begin{aligned}\displaystyle \sec^6 A + \tan ^6 A &= (\sec ^2 A + \tan^2 A)(\sec^4 A - \sec^2 A \tan^2 A + \tan^4 A) \\ \\ &=(\sec ^2 A + (\sec^2 A -1))(\sec^4 A - \sec^2 A \tan^2 A + \tan^4 A) \\ \\ &= (2\sec^2 A - 1)(\sec^4 A - \sec^2 A \tan^2 A + \tan^4 A) \end{aligned}\)

Likewise:

\(\displaystyle \begin{aligned}\sec^4 A - & \sec^2 A \tan^2 A + \tan^4 A = \sec^4 A - \sec^2 A (\sec^2 A - 1)+ (\sec^2 A -1)^2\\ \\ &=\sec^4 A - \sec^4 A + \sec^2 A + (\sec^4 A - 2\sec^2 A + 1) \\ \\ &= \sec^4 A -\sec^2 A + 1\end{aligned}\)

Hence:

\(\displaystyle \begin{aligned}\displaystyle \sec^6 A + \tan ^6 A &= (2\sec^2 A - 1)(\sec^4 A - \sec^2 A \tan^2 A + \tan^4 A) \\ \\ &= (2\sec^2 A -1)(\sec^4 A - \sec^2 A + 1)\\ \\ &\stackrel{\checkmark}{=} (2\sec^2 A -1)(\sec^4 A - \sec^2 A + 1)\end{aligned}\)

Hence verified.

The required shortest distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

The slope is defined as the ratio measure of rise to measure of the run.

Here,
The shortest possible distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

This is because, if the doorway is 1.3 feet above the parking lot, the ramp will need to rise 1.3 feet in order for a person or vehicle to be able to enter the building. The length of the ramp will be equal to the rise, so in this case, the shortest possible distance between the building and the end of the ramp would be 1.3 feet.

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Answer: 16

Step-by-step explanation:

you have to make an aquesion

15/6=40/x

then you cross multiply and you will get the answer

x=16

Answer:

100 toys

Step-by-step explanation:

15 toys-->6 hours

x toys-->40 hours

we can do a cross multiplication problem now.

15*40=6*x

6x=600

x=100

Answer:

its D

Step-by-step explanation:

The money left will be $20

The slope is used to measure the inclination of a straight line regarding abscissa axis ( x axis) .

Given : x=0 ( no pack is bought)

to find : y = ? ( money left )

slope of a straight line = y2-y1 / x2-x1

Let us take two coordinates from the given ones (1,16) and (5,0)

slope = 0 -16 / 5-1 = -16 /4 = -4

since , slope is same for any coordinate for the whole line

to find y , using coordinate (1,16) and (0,y)

-4 = y-16 / 0-1

4 =  y- 16

y = 20

answer is option d) $20 will be left if she doesn't buy any pack

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

1.) y = 2x -2

2.) y = 1/3x + 1

3.) y = 1x - 1

4.) y = -3x - 4

Remember that

97 1/2 % is the same that 97.5%

Let

x ----> the number

so

97.5%=97.5/100=0.975

0.975*x=117

solve for x

x=117/0.975

x=120

The logical expression to determine if the sum of variables 'a' and 'b' is greater than 3 or if variable 'b' multiplied by 2 is less than 300 is equals to the a + b > 3 || a + 2b < 300.

Logical expressions are the statements that either true or false and it show the values, comparisons, and equality of the variables. Variable types: Variable type is used to show the type of variable. In logical expressions,

X< Y.

'||'.

We have, two variables 'a' and 'b'. Also, sum of variables is greater than 3 and in logical expression form, a + b > 3 .

And if variable 'b' multiplied by 2 is less than 300, in logical expression form, a + 2b < 300. Now, the logical expression form for if the sum of variables 'a' and 'b' is greater than 3 or if variable 'b' multiplied by 2 is less than 300 is represented by a + b > 3 || a + 2b < 300.

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Answer:

1/3

Step-by-step explanation:

13/39 = 1/3

Answer:

It is 1/3

Step-by-step explanation:

because 13/39=1/3

Answer:

Step-by-step explanation:

Given:

n= Total number of random sample of people taken=400

x= Number of people who provided yes responses= 124

P= The point of estimate of the sample of the population portion taken=?

Now,

P=x/n

P=124/400

P= 124/4×100

P= 32/100

P= 0.32 or 32%

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0.31 or 31% is the point estimate of the proportion of the population that would provide yes responses

Estimate of Proportion: If we divide the random variable, the mean, and the standard deviation by n, we get a normal distribution of proportions with P′, called the estimated proportion, as the random variable. (Recall that a proportion as the number of successes divided by n.)

a simple random sample of 400 individuals provides 124 yes responses

The point estimate of individuals that would provide yes responses is the sample proportion.

n= Total number of random sample of people taken=400

x= Number of people who provided yes responses= 124

P= The point of estimate of the sample of the population portion taken

The sample proportion is calculated by dividing number of yes responses by sample size

p = x/n = 124/400= 0.31 or 31%

0.31 or 31% is the point estimate of the proportion of the population that would provide yes responses

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sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1].

Using the power-reducing formula for cosine:

cos(2x) = cos²(x) - sin²(x)

We can write:

cos²(x) = 1/2 [cos(2x) + 1]

sin²(x) = 1/2 [1 - cos(2x)]

Using these formulas, we can rewrite the expression:

sin^2(4x) cos^2(4x) = [sin²(2(2x))] [cos²(2(2x))]

= [1/2 (1 - cos(4x))] [1/2 (cos(4x) + 1)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + cos^2(0)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

Therefore, sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

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To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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Answer:

$486 (Paul)

$243(Brian)

$81(Colin)

Solving steps:

let Paul Be x, Brian be x,Colin be x

since Paul got twice as much as Brian which shows that brian and got three times

So Paul,= 3×2 so he got six times as much as the two others

while Brian got three times

and colins got once

so let's make an equation for this problem

=> 6x + 3x + x = $810

add 6 x + 3 x + x which give you 10 x

=> 10x = $810

divide both side by the coefficient of x

=> \( \frac{10x}{10} = \frac{810}{10} \)

=> \(x = \frac{810}{10} \)

=> x = 81

since you we have find what the value of x

insert into the previous equation which is

=> 6x + 3x + x

=> 6(81) = $486-----(for Paul)

3(81) = $243-------(for Brian)

(81) = $81 ---------(for Collin)

Answer:

Last choice

Step-by-step explanation:

The basic definition of inverse function is both domain and range are swapped.

The domain is defined as set of all x-values while range is defined as set of all y-values.

If we have set of function h = {(1,2), (3,4), (5,6)} then the inverse will be {(2,1), (4,3), (6,5)}. Thus, if set of (x,y) is original function then set of (y,x) will be inverse of set of (x,y).

Henceforth, the inverse of f(x) will be g(x) = {(3,8), (1,4), (-1,0), (-3,-4)}.

Answer:

D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Step-by-step explanation:

hope this helps:)

Answer:

Step-by-step explanation:

find a number that can go into 30 and go and then what ever you get multiply it with five and X will be your answer

Answer:

MP=(6,8)

Step-by-step explanation:

\(MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )\\MP= (\frac{9+3}{2} )(\frac{7+9}{2})\\MP= (\frac{12}{2} )(\frac{16}{2} )\\MP= (6,8)\)

Answer:

m∠B ≈ 28.05°

Step-by-step explanation:

Because we don't know whether this is a right triangle, we'll need to use the Law of Sines to find the measure of angle B (aka m∠B).  

The Law of Sines relates a triangle's side lengths and the sines of its angles and is given by the following:

\(\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}\).

Thus, we can plug in 36 for C, 15 for c, and 12 for b to find the measure of angle B:

Step 1:  Plug in values and simplify:

sin(36) / 15 = sin(B) / 12

0.0391856835 = sin(B) / 12

Step 2:  Multiply both sides by 12:

(0.0391856835) = sin(B) / 12) * 12

0.4702282018 = sin(B)

Step 3:  Take the inverse sine of 0.4702282018 to find the measure of angle B:

sin^-1 (0.4702282018) = B

28.04911063

28.05 = B

Thus, the measure of is approximately 28.05° (if you want or need to round more or less, feel free to).

Answer: In decimal form, it's 12.8, or improper fraction 64/5, or mixed number 12 4/5

Step-by-step explanation:

(2 2/3)*(4 4/5)

convert the improper fraction into a mixed number: 2*3+2/3* 4 4/5

calculate the product: 6+2/3*4 4/5

convert 4 4/5

64/5= 12 4/5

Hope this helps!

Answer:

ans:88.18cm

Step-by-step explanation:

In the given right-angled triangle, the sine, cosine, and tan of the angle A are: sin A =0.88, cos A = 0.4705, tan A= 1.875

We have a right angles triangle ABC with AC as the hypotenuse and AB and AC as the other two sides.

Given, hypotenuse AC=34, side BC = 30, side AB = 16

∴From the formulae for evaluating sin, cos, and tan of an angle

sin A\(=\frac{opposite}{hypotenuse}= \frac{BC}{AC}=\frac{30}{34}=\frac{15}{17}=0.88\)     (1)

cos A\(= \frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{8}{17}=0.4705\)          (2)

tan A\(=\frac{OppositeSide}{AdjacentSide}=\frac{30}{16}=\frac{15}{8}=1.875\)           (3)

Thus sin A= 0.88, cos A= 0.4705, tan A= 1.875

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the rule for division is:

Then:

you will substract the exponents

Answer:

D.

Step-by-step explanation:

D is the correct answer

The answer is D. there is exactly one solution at (3, 1)

Answer:

(-1, -4.5)

(-1.5, -2.5)

Step-by-step explanation:

To find the midpoint add the coordinates and divide by 2

19.( -8,-2) (6,-7)

((-8+6)/2, (-2+-7)/2) = (-2/2, -9/2) = (-1, -4.5)

20. ( 6,5) (-8,-10)

(( 6+-8)/2 , (5-10)/2) = (-3/2,-5/2) = (-1.5, -2.5)

Answer:

19. (-1, -4.5)

20. (-1, -2.5)

Step-by-step explanation:

19.

Use the midpoint formula.

\(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\)

Substitute the values.

\(\frac{-8+6}{2},\frac{-2-7}{2}\)

Add/Subtract the numerators.

\(\frac{-2}{2},\frac{-9}{2}\)

Divide.

-1, -4.5

20.

Use the midpoint formula.

\(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\)

Substitute the values.

\(\frac{6-8}{2},\frac{5-10}{2}\)

Add/Subtract the numerators.

\(\frac{-2}{2},\frac{-5}{2}\)

Divide.

-1, -2.5

The perimeter of triangle ABC is 40 cm and the area is 84.85 cm^2.

To get the length of AB in triangle ABC, we can use the Pythagorean theorem since we are given the lengths of sides BC and AC. Using the theorem, we get:
AB^2 = BC^2 + AC^2
AB^2 = 15^2 + 8^2
AB^2 = 225 + 64
AB^2 = 289
AB = √289
AB = 17 cm
Therefore, the length of AB is 17 cm.
To find the perimeter of triangle ABC, we need to add up the lengths of all three sides:
Perimeter = AB + BC + AC
Perimeter = 17 + 15 + 8
Perimeter = 40 cm
To get the area of triangle ABC, we can use the formula: Area = (1/2) x base x height
Since we do not know the height of triangle ABC, we can use the length of side AB as the base and draw a perpendicular line from point C to AB, creating a right triangle. This right triangle has base AB and height h, which we can solve for using the Pythagorean theorem:
h^2 = AC^2 - (AB/2)^2
h^2 = 8^2 - (17/2)^2
h^2 = 64 - 144.5
h^2 = -80.5 (not a possible value)
However, we can see that the height of triangle ABC is outside the triangle, meaning that the triangle is obtuse and the height extends beyond the opposite side. Therefore, we cannot use the formula for the area of a triangle with a right triangle base.
Instead, we can use Heron's formula, which is:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter (half of the perimeter), and a, b, and c are the lengths of the sides. In this case, we have:
s = (a + b + c)/2 = (17 + 15 + 8)/2 = 20
a = AB = 17
b = BC = 15
c = AC = 8
Plugging these values into the formula, we get: Area = √(20(20-17)(20-15)(20-8))
Area = √(20(3)(5)(12))
Area = √(7200)
Area = 84.85 cm^2
Therefore, the perimeter of triangle ABC is 40 cm and the area is 84.85 cm^2.

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