Show how you could set up and find the exact value of cos(5π/4) in two different ways.

B

the equation of a line in standard form is

Ax + By = C

where A is a positive integer and B, C are integers

3x + 5y = - 15 is in standard form → B

Answer:

Equation of line in Standard form is

[tex]ax \pm by \pm c=0,[/tex]

Among the two options given,

A. -2 x = 13

Here, coefficient of x= -2

Coefficient of y=0

But we can say that this is a point in one dimensional form.

So, it is not equation of line in standard form.

B. 3 x +5 y= -15

3 x + 5 y +15=0

Comparing with, a x + b y + c=0

a=3, b=5, c=15

Neither the coefficient of x ,nor the coefficient of y is equal to 0.

So, Option B: 3 x + 5 y = -15 →3 x+ 5 y+15=0

is equation of line in standard form.

Answer: y = 1/7(x) or y = x/7

Step-by-step explanation:

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In order to vertically compress the equation y = x by 1/7, we would simply need to multiply x by 1/7. Therefore, this gives us the equation y=1/7(x) or y=x/7.

Hope this helps!! :)

A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x where each y-value of the original function is 1/7 of its original height.

A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x. In vertical compression, each y-value of the original function is multiplied by the factor of compression, in this case, 1/7. Thus y=x becomes y=1/7x. This means for any x value in the original function, the corresponding y value in the new function is 1/7 of its original height. For example, where x was 1, y was also 1 for the original equation. In the new equation, when x is 1, y is now 1/7.

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Answer:

The total price depends on the number of crates.

Step-by-step explanation:

Without seeing the graph, we can't provide a definitive answer. Generally, in such situations, total price would likely depend on the quantity of goods (pumpkins or crates) purchased (Options D and B).

To answer this question, we'd need to closely examine the given graph. However, generally, in a graph showcasing a transaction, the total price depends on the quantity of goods, such as pumpkins or crates, purchased. Hence without explicit information from the graph at hand, option D. 'The total price depends on the number of pumpkins', and option B. 'The total price depends on the number of crates' could potentially be accurate. But we cannot determine definitively without further information.

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the answer is 53 bags

the other number is 50 - p

Consider a numeric example

2 numbers sum to 5 , one of the numbers is 3 what is the other ?

Obviously 2 , that is 5 - 3 = 2 gives the number

In the same way the number here is p and 50 - p is the other number

Answer:

d. 11.4

Step-by-step explanation:

point r is half the line qs. qr is 5.7 so to get the whole line multiply it by two to get 11.4

To solve the equation, multiply both sides by 2 and simplify. The value of Qburgers is 5.

The question involves solving an equation for the variable Qburgers.

The value of Qburgers is 5.

∠B = 52°

Since the triangles are similar then

∠C = ∠S = 56°

∠B = 180° - (72 + 56)° = 52°

Area = length * width

width = w

length = 2w+7

A = (2w+7) * w

250 =2w^2+7w

0 = 2w^2 +7w-250

w is the width, hence length is 2w + 7 ( 7 more than twice the width )

area = length × width = w( 2w + 7 ) = 250

2w² + 7w - 250  = 0 ← in standard form

Christine has $20, Manuel has $60 and Henry has $29

let x be the amount Christine has then

Manuel has 3x and Henry x + 9

summing the amounts gives the equation

x + 3x + x + 9 = 109

5x + 9 = 109 ( subtract 9 from both sides )

5x = 100 ( divide both sides by 5 )

x = 20

thus Christine has $29, Manuel has (3 × 20 ) =$60 and

Henry has 20 + 9 = $29

check : 20 + 60 + 29 = 109

The "meter" is a larger unit than the "centimeter." Every time you need to convert a larger metric unit to a smaller one, you must multiply to find a greater value.

there are 100 cm in a meter so the fraction would be 8/100 or simplified 2/25

diameter = 5

the diameter is twice the radius

diameter = 2.5 × 2 = 5

We have to add the polynomials [tex](4x^2-4x-3)[/tex] and [tex](3x^2-3x-5)[/tex]

To add the polynomials we need to add the like terms, by like terms we understand that the terms with the same exponent of the variables.

So in this case,

[tex](4x^2-4x-3)+(3x^2-3x-5)[/tex]

We will add the coefficients of [tex]x^2, x[/tex], and constants separately, we get:

[tex](4+3)x^2+(-4-3)x+(-3-5)=7x^2+(-7)x+(-8)=7x^2-7x-8[/tex]

Similarly, for the polynomials [tex](4x^2-4x-3)-(3x^2-3x-5)[/tex]

We will subtract the coefficients of like terms, we get:

[tex](4-3)x^2-(4-3)x-(3-5)=x^2-x+2[/tex]

We need to simplify the expression:

[tex]12x^{-6}y^{10} \times (3x^{7}y)[/tex]

Now, we know that we can resolve the exponents of the variables with the like terms only and we can multiply the coefficients independently:

Now,  

[tex]12x^{-6}y^{10} \times 3x^{7}y=(12 \times 3)\times (x^{-6}\times x^{7})\times (y^{10}\times y)[/tex]

On simplifying the above expression we get:

[tex]36\times x^{(-6+7)}\times y^{(10+1)}[/tex]

[tex]=36 \times x^{1}\times y^{11}[/tex]

[tex]=36 \times x \times y^{11}[/tex]

[tex]=36xy^{11}[/tex]

So the simplified form of the expression [tex]12x^{-6}y^{10} \times 3x^{7}y=36xy^{11}[/tex].

calculating each of the products

noting that i² = (√- 1 )² = - 1

(1 + 2i)(8i) ( distribute by 8i )

= 8i + 16i² = - 16 + 8i ← complex number

(1 + 2i)(2 - 5i) ( expand using FOIL )

= 2 - 5i + 4i - 10i²

= 2 - i + 10 = 12 - i ← complex number

(1 + 2i)(1 - 2i) ( expand using FOIL )

= 1 - 2i + 2i - 4i²

= 1 + 4 = 5 ← real number

(1 + 2i)(4i) ( distribute by 4i )

= 4i +8i² = - 8 + 4i ← complex number

(1 + 2i)(1 - 2i) is the only product which results in a real number

The digit _ that will make 2.4_1 be more than 2.463 must be 7, 8, or 9.

If the first number in your sequence is 2.48 (not 2.84), then the unknown digit must be 7.

2.48 > 2.471 > 2.463

[tex](x+y)^2 =x^2+2xy+y^2\not=x^2+y^2[/tex]

Answer:

d

Step-by-step explanation:

-6 + 4x < x +3       : Distributive property

-6 + 3x < 3           : Subtraction property of inequality

3x < 9                  : Addition property of inequality

x  <3                    : Division property of inequality

Answer:

[tex]-2(3-2x)<x+3[/tex] Given,

[tex]-6+4x<x+3[/tex]: Distributive property,

[tex]-6+3x<3[/tex]: Subtraction property of order,

[tex]3x<9[/tex]: Addition property of order,

[tex]x<3[/tex]: Division property of order.

Step-by-step explanation:

We have been given an inequality. We are asked to match each step for solving the equation with reason.  

[tex]-2(3-2x)<x+3[/tex]

Using distributive property, we will get:

[tex]-2\cdot3-(-2)\cdot2x<x+3[/tex]

[tex]-6+4x<x+3[/tex]

Subtract x from both sides:

[tex]-6+4x-x<x-x+3[/tex]

[tex]-6+3x<3[/tex]

Add 6 on both sides:

[tex]-6+6+3x<3+6[/tex]

[tex]3x<9[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}<\frac{9}{3}[/tex]

[tex]x<3[/tex]

False.  That is a cubic equation.

To answer the question, you need to determine the amount Mr. Traeger has left to spend, then find the maximum number of outfits that will cost less than that remaining amount.

Spent so far:

... 273.98 + 3×7.23 +42.36 = 338.03

Remaining available funds:

... 500.00 -338.03 = 161.97

The cycling outfits are about $80 (slightly less), and this amount is about $160 (slightly more), which is 2 × $80.

Mr. Traeger can buy two (2) cycling outfits with the remaining money.

_____

The remaining money is 161.97/78.12 = 2.0733 times the cost of a cycling outfit. We're sure he has no interest in purchasing a fraction of an outfit, so he can afford to buy 2 outfits.

Answer:

20a. 143 deg

20b. 37 deg

20c. corresponding angles, congruent

20 d. same-side interior angles, supplementary

Step-by-step explanation:

20a.

m<7 = 34

m<5 + m<7 = 180       (linear pair)

m<5 = 180 - 37 = 143

m<4 = m<5 = 143      (alt int angles)

20b.

m<2 = m<7 = 37     (alt ext angles)

20c. corresponding angles, congruent

20d. same-side interior angles, supplementary

(a)

∠7 = 37° = ∠6 ( vertical angles )

∠4 = 180° - 37° = 143° ( 4 and 6 are supplementary interior angles )

(b)

∠2 = 37° (2 and 4 form a straight angle )

(c)

∠4 and ∠8 are corresponding congruent angles

(d)

∠3 and ∠5 are supplementary interior angles

Answer:

Step-by-step explanation:

(−5y+1) - (3y+2) = −9

(-5y-3y) + (1-2) = -9

-8y - 1 = -9

-8y = -8

y = 1

the difference between the 2 expressions is

- 5y + 1 - (3y + 2 ) = - 9

- 5y + 1 - 3y - 2 = - 9

- 8y - 1 = - 9 ( add 1 to both sides )

- 8y = - 8 ( divide both sides by - 8 )

y = 1

In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.

Answer:

1152 hours - 42 days =)

Step-by-step explanation:

B

the spread of the graph of a parabola is determined by the multiplier k

the standard comparison is against k = 1

• If k > 1 then the graph narrows towards the y-axis

• If 0 < k < 1 then graph widens towards the x- axis

Answer: 15.5 is a rational number.

Step-by-step explanation:  We are given to check whether the number 15.5 is a rational or irrational.

We know that

a real number is said to be

(i) rational, if the digits after the decimal are either repeating or terminating.

(ii) irrational, if the digits after the decimal are non-repeating and non-repeating.

The given number is 15.5.

Here, the digits after the decimal are terminating.

So, the given number is a rational number.

Thus, 15.5 is a rational number.

r =√ ( A / 4π )

given A = 4πr² ( isolate r² by dividing both sides by 4π )

A / 4π = r² ( take the square root of both sides )

r =√( A / 4π )

Answer:

The expression of r in terms of A is:

[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

Step-by-step explanation:

We are given the surface area, A, of a sphere in terms of its radius, r, as:

A(r) = 4πr²

[tex]A=4\pi\ r^2[/tex]

⇒ [tex]r^2=\dfrac{A}{4\pi}[/tex]

⇒ [tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

Hence, the expression of r in terms of A is:

[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]

To find out how much an angelfish has grown in feet, divide the number of inches by 12, since there are 12 inches in a foot. As an example, if an angelfish has grown 6 inches, it would be 6 inches / 12, equaling 0.5 feet.

To convert a measurement from inches to feet, we use the fact that one foot is equal to 12 inches. For example, if an angelfish has grown 6 inches, we divide the number of inches by 12 to find the growth in feet:

The angelfish has grown 0.5 feet.

Similarly, let’s convert 374 inches to feet as another example of going from a smaller unit to a larger unit:

the probability is a ratio of number of relevant outcomes and total number of possible cases.

In this scenario, the relevant outcomes are

4, 5, 10    (and their count is 3)

and the total number of possible outcomes:

12

so the probability is

3/12 = 1/4

the answer is 3/12 cause when you divied 12 by 4 you will get 3 and we know that there is 12 faces on the cube so that gives you the ratio 3/12.