Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)

Answer:

the greatest age is 8

Step-by-step explanation:

i took the test

The length of the picture frame is 17 inches, which is found by substituting the given width and perimeter into the perimeter formula and solving for the length.

The question asks to calculate the length of a picture frame using the perimeter formula P = 2l + 2w, where P stands for the perimeter, l is the length, and w is the width. Given that the width (w) is 19 inches and the perimeter (P) is 72 inches, we can substitute these values into the formula:

P = 2l + 2w

72 = 2l + 2(19)

72 = 2l + 38

2l = 72 - 38

2l = 34

l = 34 / 2

l = 17 inches

So, the length (l) of the frame is 17 inches.

The regular price of the table is $650.

The student has asked to find the regular price of a table that is currently on sale for $403, which is 38% less than the regular price. To find the regular price, we can consider the sale price to be 62% (100% - 38%) of the regular price. Let's denote the regular price as R. Thus, we can set up the equation 0.62 * R = $403. Solving for R, we divide both sides by 0.62 to find the regular price:

R = $403 / 0.62

R = $650

Therefore, to find the regular price of a table on sale for $403 at 38% off, we determine that the sale price is 62% of the regular price. By dividing the sale price by 0.62, we discover that the regular price is $650.

The value of kj is 15.

It is required to find the value of kj.

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given that:

k is the midpoint of hj and hk.

hk=x+6

hj=4x-6

We know that midpoint cuts the segment hj in 2 equal parts that means hk=kj and hk+kj=hj

hk+hk=hj

2hk=hj

2hk=hj

2 (x+6)=(4x-6)

2x+12=4x-6

12+6=4x-2x

18=2x

Divide 2 on both sides, we get

18/2=2x/2

9=x

hk=kj=x+6=(9)+6=15

kj=15

Therefore, the value of kj is 15.

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Chris bought  [tex]8[/tex]  Oranges.

Reasoning is the process of using existing knowledge to draw conclusions, make predictions, or construct explanations.

We have,

Chris and Pat bought [tex]48[/tex] oranges.

Let,

Oranges bought by Pat [tex]= x[/tex]

Oranges bought by Chris [tex]= y[/tex]

Now,

According to the question;

As  Pat bought five times as many as bought by Chris.

i.e.

[tex]x=5y[/tex]     [tex]........(i)[/tex]

And,

Chris and Pat bought [tex]48[/tex] oranges.

i.e.

[tex]x+y=48[/tex]     [tex]........(ii)[/tex]

Now,

Substituting value of [tex]x[/tex] from equation [tex](i)[/tex] in equation [tex](ii)[/tex];

We get,

[tex]5y+y=48[/tex]

[tex]6y=48[/tex]

[tex]y=8[/tex]

Now,

Substituting value of [tex]y[/tex]  in equation [tex](i)[/tex];

[tex]x=5y[/tex]

[tex]x=5*8[/tex]

[tex]x=40[/tex]

Hence, we can say that Chris bought  [tex]8[/tex]  Oranges and Pat bought [tex]40[/tex] Oranges.

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Answer: 6 rows - tomatoes

Step-by-step explanation:

Answer:

(–2.1)(3) + (–2.1)(0.4)

Step-by-step explanation

It's D

Answer:

[tex]3+\frac{3}{4}x\geq 12[/tex]

Step-by-step explanation:

Given,

The number of hour he already practiced in this week = 3,

Also, she practices for three fourth of an hour each session,

If x be the number of remaining session,

So, the additional number of hours he practiced in this week = [tex]\frac{3x}{4}[/tex]

Thus, the total number of hours he practiced in this week = [tex]3+\frac{3x}{4}[/tex]

According to the question,

Total number of hours ≥ 12 hours

[tex]\implies 3+\frac{3x}{4}\geq 12[/tex]

Which is the required inequality.

Answer:

h = 2A/a+b  

or 1st answer

Step-by-step explanation:

The solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.

"It is a finite set of equations for which we find the solution."

For given question,

We have been given a system of equations.

4x +2y = -2                     ................(i)

x - 3y = 24                      ................(ii)

From equation (ii),

x = 24 + 3y                .............(iii)

Substitute this value of x in equation (i)

⇒ 4(24 + 3y) +2y = -2

⇒ 96 + 12y + 2y = -2

⇒ 14y = -98

⇒ y = -7

Substitute this value of y in equation (iii)

⇒ x = 24 + 3(-7)

⇒ x = 24 - 21

⇒ x = 3

Therefore, the solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.

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Option (C) √3 + 8.486 is an irrational number.

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. Those real numbers that are not rational numbers are known as irrational numbers.

For the given situation,

We need to check the options, that is irrational.

Option A: 7.51... x -4

⇒ [tex](7.51 ) (-4)[/tex]

We can express this as fraction. So it is not an irrational number.

Option B: root 16 + 3/4

⇒ [tex]\sqrt{16} +\frac{3}{4}[/tex]

⇒ [tex]4+\frac{3}{4}[/tex]

We can express this as fraction. So it is not an irrational number.

Option C: root 3 + 8.486

⇒ [tex]\sqrt{3} +8.486[/tex]

⇒ [tex]\sqrt{3}[/tex]  is an irrational number, so the sum is also an irrational number.

Option D: 8 2/3 × 17.75

⇒ [tex](8\frac{2}{3})(17.75)[/tex]

We can express this as fraction. So it is not an irrational number.

Hence we can conclude that option (C) √3 + 8.486 an irrational number.

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Answer:

2^(6-3) = 2^3 = 8

Step-by-step explanation:

To simplify radical 64/8

We will express 64 and 8 in powers of 2

64 = 2×2×2×2×2×2= 2^6

8 = 2×2×2=2^3

From the law of indices,

a^5 / a^3 = a^ (5-3) = a^2

Applying this law of indices to the given radical,

64/8 = 2^6/ 2^3

= 2^(6-3)

= 2^3 = 8

Also, we can try another way. since

64 = 2×2×2×2×2×2= 2^6

8 = 2×2×2=2^3

64/8 = 2×2×2×2×2×2 / 2×2×2

2×2×2 cancels out 2×2×2 and

It remains 2×2×2 = 8

So which ever way we do it,

radical 64/8 simplified is 2^3 = 8

Answer: The total cost of the dinner is found by adding the two prices together. Then this sum is multiplied by 1.05, which is 100% + 5%, to get a cost of $11.72.

Step-by-step explanation:

This is the sample answer.

To calculate the total cost including sales tax, convert the percent tax rate to a decimal, multiply it by the meal's cost, and add it to the original cost. In this case, a 5 percent tax on a $3.99 salad and a $7.17 fettuccini alfredo results in a final total cost of $11.72.

First, to find the sales tax for Abelita's Italian salad and Franco's fettuccini alfredo, you convert the tax rate from a percent to a decimal. The tax rate is 5 percent, which as a decimal is 0.05. Next, add the cost of the Italian salad ($3.99) and fettuccini alfredo ($7.17) to get the total cost before tax, which is $11.16. Multiply this total by the tax rate to find the amount of sales tax: $11.16 × 0.05 = $0.558. Round this to the nearest cent, which gives us $0.56.

The next step is to add the sales tax to the total cost before tax to find the final total cost. Thus, $11.16 (meal cost) + $0.56 (sales tax) = $11.72. Therefore, the total cost for their dinner, including the 5 percent sales tax, is $11.72.

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To calculate the number of gallons Peter needs, multiply the surface area of one side of the wall (225 ft2) by 2 for both sides, and then by 2 again for two coats, totaling 900 ft2. Then divide 900 ft2 by the coverage per gallon x to get the expression 900 / x.

To determine the number of gallons of paint Peter needs, we must first calculate the total paintable surface for both the inside and outside of the walls and then factor in the two coats of paint. Peter has 5 walls, with each side having 45 ft2 of paintable surface, so the total paintable surface for one side is 5 walls  imes 45 ft2/wall = 225 ft2. Since he wants to paint both sides, we double this to get 450 ft2. For two coats, we need to double this again, resulting in 900 ft2. Now, if a gallon of paint covers x ft2, the number of gallons needed is total square footage divided by coverage per gallon, which is 900 ft2 / x ft2/gallon.

Therefore, the expression to represent the number of gallons Peter needs is 900 / x.

In the right angle triangle ABC  [tex]\rm a^2+b^2=c^2[/tex] because (e + f = c) and this can be determined by using the Pythagorean theorem.

Given :

Right △ABC is shown where CD is an altitude of the triangle.

The following steps can be used in order to prove that [tex]a^2+b^2=c^2[/tex]:

Step 1 - According to the Pythagorean theorem, the sum of the square of the shorter side is equal to the square of the longer side.

Step 2 - The Pythagorean theorem is given below:

[tex]\rm H^2=B^2+P^2[/tex]   --- (1)

where H is the hypotenuse, B is the base, and P is the perpendicular.

Step 3 - So, according to the given diagram:

H = e + f

B = a

P = b

Step 4 - Substitute the values of the known terms in the expression (1).

[tex]\rm a^2+b^2=(e+f)^2[/tex]

Step 5 - According to the diagram, (e + f = c). So, the above expression becomes:

[tex]\rm a^2+b^2=c^2[/tex]

Therefore, the correct option is C).

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