3 sin2(θ) + 16 sin(θ) − 35 = 0

[tex]\\ \text{Given that the base salary of Vanessa is }\$400.00 \text{ every week}\\ \\ \text{And she gets an additional }5\% \text{ commission on everything she sells}.\\ \\ \text{Given that last week Vanessa sold }\$1650.00 \text{ worth of items,}\\ \text{so her commission last week was}\\ \\ =5\% \text{ of 1650}\\ \\ =0.05\times 1650\\ \\ =\$ 82.5\\ \\ \text{hence the total salary of Vanessa for last week}=400+82.5=\$482.5[/tex]

Hence the total salary of Vanessa last week was $482.5

Answer:  The correct option is (C) 3 cm, 4 cm, 5 cm.

Step-by-step explanation:  We are given to select the correct side lengths that could form a triangle.

We know that

the sum of the lengths of any two sides of a triangle is always greater than the third side.

That is, if a, b and c represents the lengths of three sides of a triangle, then we must have

[tex]a+b>c,~~b+c>a,~~c+a>b.[/tex]

Option (A) is

a = 2 cm, b = 2 cm, c = 4 cm.

We have

[tex]a+b=2+2=4=c~~~\Rightarrow a+b=c.[/tex]

Hence, this option is NOT correct.

Option (B) is

a = 3 cm, b = 5 cm, c = 10 cm.

We have

[tex]a+b=3+5=8<10=c~~~\Rightarrow a+b<c.[/tex]

So, this option is NOT correct.

Option (C) is

a = 3 cm, b = 4 cm, c = 5 cm.

We have

[tex]a+b=3+4=7>5=c~~~\Rightarrow a+b>c,\\\\b+c=4+5=9>3=a~~~\Rightarrow b+c>a,\\\\c+a=5+3=8>4=b~~~\Rightarrow c+a>b.[/tex]

So, this option is CORRECT.

Option (D) is

a = 4 cm, b = 8 cm, c = 15 cm.

We have

[tex]a+b=4+8=12<15=c~~~\Rightarrow a+b<c.[/tex]

So, this option is NOT correct.

Thus, (C) is the correct option.

Answer:

Option C.

Step-by-step explanation:

To form a triangle we should always remember that a triangle is possible when sum of two smaller sides of the triangle is greater than the largest side.

If smaller sides are a, b and largest side is c

Then a + b > c

Now we take each option given

Option A) 2 cm, 2 cm, 4 cm

2 + 2 = 4 which equal to the largest side so to form a triangle is not possible.

Option B) 3 cm, 5 cm, 10 cm

3 + 5 = 8 < 10 cm

Here sum of smaller sides is less than to the largest side so triangle will not be formed.

Option C. 3 cm, 4 cm, 5 cm

3 + 4 = 7 > 5 cm

Therefore triangle can be formed.

Option D) 4 cm, 8 cm, 15 cm

4 + 8 = 12 < 15 cm

so triangle can not be formed.

Option C is the correct option.

Answer:

She needs  to pay $4.38

Step-by-step explanation:

Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off.

The original price is $4.73. 35 cents off

35 cents can be converted into dollars when we divide by 100

35 divide by 100=0.35

to find the amount she need to pay, we subtract 0.35 from original price

Amount to pay=[tex]4.73-0.35=4.38[/tex]

Answer is B. -2√3+2√15

By using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given

12 × (-1 + [tex]\sqrt{5}[/tex])

Apply distributive property

= 12 × (-1) + 12 × [tex]\sqrt{5}[/tex]

= -12 + 12[tex]\sqrt{5}[/tex]

≅ 14.832

Hence by using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

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No, Oswaldo did not meet his goal. He needed at least 66 grams of whole grains for his 220 grams of carbohydrates, but he only ate 55 grams, 11 grams less than required.

Let's check if Oswaldo met his goal of getting at least 30% of his carbohydrates from whole grains.

Calculate the percentage of whole grains :

  Given:

  - Total carbohydrates = 220 grams

  - Whole grains = 55 grams

The percentage of carbohydrates from whole grains is calculated by:

[tex]\[ \text{Percentage} = \left( \frac{{\text{grams of whole grains}}}{{\text{total grams of carbohydrates}}} \right) \times 100. \][/tex]

Plugging in the values, we get:

 [tex]\[ \left( \frac{{55}}{{220}} \right) \times 100 = 25\%. \][/tex]

Since the goal is at least 30%, but his actual percentage is only 25%, he did not meet his goal.

Calculate how much more whole grains he needed to meet his goal :

  To get 30% of 220 grams, we need to calculate 30% of 220:

  [tex]\[ 0.30 \times 220 = 66 \text{ grams}. \][/tex]

This means Oswaldo needed 66 grams of whole grains, but he only ate 55 grams.

The difference between what he needed and what he ate is:

 [tex]\[ 66 - 55 = 11 \text{ grams}. \][/tex]

Thus, Oswaldo did not meet his goal, and he ate 11 grams less of whole grains than he needed to meet the goal.

The complete question is : Oswaldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains. Did Oswaldo meet his goal? Why? Yes No Oswaldo ate grams of whole grains more less than his goal.

Answer:

y = -5x + 12

Step-by-step explanation:

Slope intercept form of a line is,

y = mx + c

Where, m is the slope of the line,

Here, the given equation of line,

10x+2y=-2,

2y = - 10x - 2

y = -5x - 1,

By comparing,

m = -5,

So, the slope of line 10x+2y=-2 is -5,

We know that the two parallel line have same slope,

Let the equation of the parallel line of the 10x+2y=-2  is,

y = -5x + c

According to the question,

It passes through the point (0,12),

That is (0, 12) must satisfy this line,

12 = -5(0) + c ⇒ c = 12,

Hence, the equation of the parallel line is,

y = -5x + 12

Answer: The answer is x= 52°

Step-by-step explanation: These are vertical angles so that means both sides would equal the same. One side is 52° So the other side would also be 52°.

To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations and solve them using substitution or elimination.

To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations. Let's assume the two numbers are x and y. From the given information, we have the following equations:

x - y = 2828

xy = 39003900

We can solve this system of equations by substitution or elimination. Let's use the substitution method:

From the first equation, we can express x as y + 2828. Substituting this into the second equation, we get (y + 2828)y = 39003900. Simplifying, we get y^2 + 2828y - 39003900 = 0.

Now we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula. Once we find the value of y, we can substitute it back into the first equation to solve for x. This will give us the two positive numbers.

Answer:

A= 40 B=50 c=60

Step-by-step explanation:

The sum of the interior angle measures of an 18-gon is calculated using the formula (n-2)  imes 180 degrees, which equals 2880 degrees.

The sum of the interior angles of an n-gon (a polygon with n sides) can be found using the formula (n-2)  imes 180 degrees. For an 18-gon, we can substitute 18 for n in the formula to calculate the sum of interior angles.

Sum of interior angles = (18-2)  imes 180
Sum of interior angles = 16  imes 180
Sum of interior angles = 2880 degrees

Therefore, the sum of the interior angle measures of an 18-gon is 2880 degrees.

A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables. (a) Mrs. Roberts simplified this ratio to 2:6. Explain/show how you know she is incorrect. Can you tell where she might have made a mistake while simplifying?

Solution:

So, A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables.

Ratio of dressing:vegetables=2:12.

Let us divide 2 and 12 by 2

Ratio of dressing: vegetables= [tex] \frac{2}{2} [/tex] : [tex] \frac{12}{2} [/tex]

So, finally we get ratio=1:6 and not 2:6. The mistake is in this step while simplifying.

So, Simplified Ratio of dressing:vegetables=1:6.

The amount we deposited in the month of october is $151, option A is correct.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

We need to find the total amount deposited in 10 months, starting with $16 in January and increasing by $15 each month.

The first term is $16 and the common difference is $15.

The nth term can be found using the formula for the nth term of an arithmetic sequence:

an=a+(n-1)d

a=16, d=15

Now plug in n as 10, (10th month is october)

a₁₀=16+(10-1)15

=16+9(15)

=151

Hence, the amount we deposited in the month of october is $151, option A is correct.

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Answer:

20 minutes

Step-by-step explanation:

5/6 x 2/5= 10/30

10/30 x 60 minutes = 600/30

simplify

600/30 = 20 minutes

Final answer:

To determine the decimal value of a signed binary number in sign-magnitude form, consider the sign and magnitude separately. (a) -102 (b) +116 (c) -64.

Explanation:

To determine the decimal value of a signed binary number in sign-magnitude form, you need to consider the sign and the magnitude separately.

(a) 10011001:

This number is negative in sign-magnitude form because the leftmost bit is 1. To find its magnitude, you invert the remaining bits (01100110) and convert it to decimal (102).

The final decimal value is -102.

(b) 01110100:

This number is positive in sign-magnitude form because the leftmost bit is 0. The magnitude is obtained by converting the bits (01110100) to decimal (116).

The final decimal value is +116.

(c) 10111111:

This number is negative in sign-magnitude form because the leftmost bit is 1. The magnitude is obtained by inverting the remaining bits (01000000) and converting it to decimal (64).

The final decimal value is -64.

(a) -25, (b) 116, (c) -63; sign bit denotes sign, remaining bits represent magnitude converted to decimal.

Let's go through each signed binary number in sign-magnitude form:

(a) 10011001:

Step 1: Determine the sign bit:

The leftmost bit, or the most significant bit (MSB), is the sign bit. In sign-magnitude representation, 1 denotes a negative number and 0 denotes a positive number. So, the sign bit here is 1, indicating a negative number.

Step 2: Convert the magnitude:

To find the magnitude, we ignore the sign bit and treat the remaining bits as a magnitude in binary form. So, the magnitude here is 0011001.

Step 3: Convert the magnitude to decimal:

The magnitude 0011001 in binary is equivalent to:

(1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 16 + 8 + 1 = 25

Step 4: Apply the sign:

Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10011001 in sign-magnitude form is -25.

(b) 01110100:

Step 1: Determine the sign bit:

The leftmost bit is 0, indicating a positive number.

Step 2: Convert the magnitude:

The magnitude here is 1110100.

Step 3: Convert the magnitude to decimal:

The magnitude 1110100 in binary is equivalent to:

(1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 64 + 32 + 16 + 4 = 116

Step 4: Apply the sign:

Since the sign bit is 0, indicating a positive number, the decimal value remains positive. Therefore, the decimal value of 01110100 in sign-magnitude form is 116.

(c) 10111111:

Step 1: Determine the sign bit:

The leftmost bit is 1, indicating a negative number.

Step 2: Convert the magnitude:

The magnitude here is 0111111.

Step 3: Convert the magnitude to decimal:

The magnitude 0111111 in binary is equivalent to:

(0 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) = 32 + 16 + 8 + 4 + 2 + 1 = 63

Step 4: Apply the sign:

Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10111111 in sign-magnitude form is -63.

So, the decimal values for each signed binary number in sign-magnitude form are:

(a) -25

(b) 116

(c) -63

6√2 ≈ 8.485 inches

The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.

_____

Comment on isosceles right triangle

It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:

... c² = a² + b²

... c² = 1² + 1² = 2 . . . . for legs of length 1

... c = √2 . . . . . . . . . . take the square root.

Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.