Verify the identity.

cos(x+pi/2) = -sinx

Answer:

perpendicular is the opposite, so -3

Answer:

FIRST OPTION: -3

Step-by-step explanation:

By definition, if two lines are perpendicular to each other, then their slopes are negative reciprocals.

In this case you can observe that that the slope of the line is [tex]\frac{1}{3}[/tex] and you know that the other line is perpendicular to this line. Therefore, their slopes are negative reciprocals.

This means that:

If [tex]slope_1=\frac{1}{3}[/tex] ,then  [tex]slope_2=-3[/tex]

This matches with the first option.

Answer:

3 3/7 hours.

Step-by-step explanation:

We work in  rates / hour:

Anita  does 1/8 of the pool in 1 hour and Chao does 1/6 in an hour.

Let x be the time they would clean the pool working together,  then we have:

1/8 + 1/6 = 1/x

3/24 + 4/24 = 1/x

7/24 = 1/x

7x= 24

x = 24/7 hours.

It will take 24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds) hours to clean a typical pool Anita and Chao working together.

The typical setup for these work problems is

                         [tex]\frac{t}{a}+\frac{t}{b} =1[/tex]

Here, a and b are how long they can do it by themselves, and t is how long they work together.

                      ⇒[tex]\frac{t}{8}+\frac{t}{6} =1[/tex]

Now, we will do LCM of 8 and 6 and we get 24;

                     ⇒[tex]\frac{3t+4t}{24} =1[/tex]

                     ⇒[tex]\frac{7t}{24}=1[/tex]

Now, we will multiply 24 on both sides, and we get;

                    ⇒[tex]7t=24[/tex]

Now, we will divide by 7 on both sides, we get:

                   ⇒[tex]t=\frac{24}7}[/tex]

Hence, the answer is [tex]\frac{24}7}[/tex] hours.

x=24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds)

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.

The lowest common multiple of 3 and 8? Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Multiples of 8 are 8, 16, 24, 32, 40... So the lowest common multiple of 3 and 8 is 24.

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17680 cm2

Using the formula V=W*H*L. The area can be divided by two since it is a right triangle. That gives you the height and length which is 85. 9.5*85*85

Answer:

80

Step-by-step explanation:

Answer:

C [tex]11+13+15+17+...[/tex]

Step-by-step explanation:

Consider the series

[tex]\sum\limits_{n=3}^{\infty}(2n+5)[/tex]

The nth term of series is [tex]a_n=2n+5[/tex]

The bottom index tells you that n starts changing from 3, so

[tex]a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...[/tex]

Thus, the sum of all terms is

[tex]11+13+15+17+...[/tex]

The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.

To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.

Given:

- Length of stained glass window = 4 feet

- Width of stained glass window = 2 feet

- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet

- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet

Let's denote the width of the border as x feet.

The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.

The area of the total window with the border is the product of its length and width:

(4 + 2x)(2 + 2x) = 15

Expanding this equation:

8 + 4x + 4x + 4x^2 = 15

8 + 8x + 4x^2 = 15

4x^2 + 8x - 7 = 0

Now, let's solve this quadratic equation using the quadratic formula:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

Where a = 4, b = 8, and c = -7.

[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]

[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]

Since the width cannot be negative, we take the positive root:

[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]

Therefore, the width of the border is approximately 1.15 feet.

The point which will lie in the solution set to the following system of inequalities is:

                          (2,5)

The system of inequality is given by:

       y>-3x+3--------(1)

and  y>x+2----------(2)

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.

a)

 (2,-5)

when x=2 and y= -5

then by first inequality we have:

-5>-3×2+3

i.e.

-5>-6+3

i.e.

-5>-3

which is a false identity.

This means that the point will not lie in the solution set.

b)

(-2,5)

when x= -2 and y=5

then  by first inequality we have:

5>-3×(-2)+3

i.e.

5>6+3

i.e.

5>9

which is a false identity.

Hence, option: b is incorrect.

c)

(2,5)

when x=2 and y=5

then by first inequality:

    5>-3×2+3

i.e.  5>-6+3

i.e.  5>-3

which is true

and by second identity:

      5>2+2

i.e.  5>4

which is again true.

Hence, (2,5) lie in the solution set.

d)

(-2,-5)

when x= -2 and y= -5

then by first inequality we have:

-5>-3×(-2)+3

i.e.

-5>6+3

i.e.

-5>9

which is a false identity.

Hence, the point (-2,-5) do not lie in the solution set.

To calculate the likelihood of drawing cards 5 and 6 in sequence from a shuffled deck of 8 cards, we multiply the individual probabilities of drawing each card. The result is a probability of 1/56.

The question asked is a probability question which involves finding the likelihood of drawing two specific cards in sequence from a shuffled deck. However, the detailed information provided relates to different scenarios involving card colors numbered cards, and rolling dice. It does not directly provide the information needed for calculating the specific probability of selecting cards 5 and 6 from a stack of 8 cards numbered 1-8. Nonetheless, if we base our calculation on a standard probabilistic approach without considering the provided scenarios:

The probability of selecting the card number 5 first from the stack of 8 is 1/8 since there is one card number 5 out of eight total cards. Once card number 5 has been selected, it is no longer in the stack, so there are now seven cards left. The probability of selecting card number 6 after that is 1/7. Therefore, the probability of selecting card 5 and then card 6 in the sequence is the product of the two probabilities: 1/8 * 1/7 = 1/56.

The expression that gives us the number of miles that Mr. Roberts drove on Tuesday is (42÷2) +5.

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

42 / 2  = 21

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

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Question

On Monday, Mr. Roberts drove 42 miles. On Tuesday, he drove 5 miles more than half the distance he drove on Monday. Which expression shows how you could find the distance, in miles, Mr. Roberts drove on Tuesday?( 42 ? 5 ) × 2 42 ? ( 5 × 2 ) ( 42 ÷ 2 ) ? 5 ( 42 ÷ 2 ) + 5

Answer:

[tex]3m =\frac{57}{5}=11.4=11\ \frac{2}{5}[/tex]

Step-by-step explanation:

We know that

[tex]m = 3\ \frac{4}{5}[/tex]

Therefore

[tex]m = 3+\frac{4}{5}\\\\m=\frac{19}{5}[/tex]

Now multiply the value of m by 3.

[tex]m=\frac{19}{5}\\\\3m=3*\frac{19}{5}\\\\3m =\frac{57}{5}=11.4[/tex]

The answer is 3m = 11.4

Answer:

C.14

Step-by-step explanation:

Answer:

Polygons are 2 dimensional figures and have NO volume.

Maybe you are thinking of polyhedrons?

If 2 polyhedrons have the same volume, they are probably NOT congruent.

Step-by-step explanation:

Final answer:

Polygons are considered congruent if they can be superimposed with matching corresponding segments and angles. Polygons with equal area or equal content are not necessarily congruent; they may have the same size but their shapes can differ.

Explanation:

When referring to two polygons, the term "congruent" is used to describe figures where not only the corresponding angles are equal but also the lengths of corresponding sides are equal. In contrast, polygons having the same volume, which applies to three-dimensional solids or having the same area, which applies to two-dimensional figures, do not necessarily need to be congruent. According to our established theorems in geometry, two polygons are considered congruent if they can be superimposed on one another such that every corresponding segment and angle matches. In the case of polygons, this means that the lengths of sides and angles are exactly the same in both figures.

The concept of equal area differs from congruence. Polygons of equal area have the same total size in terms of square units, but their shapes can be vastly different. Therefore, polygons with equal area or equal content aren't necessarily congruent because congruence requires the polygons to have identical size and shape, with all corresponding sides and angles being equal. Equal content refers to the possibility of adding other polygons of equal area to two non-congruent polygons to achieve two resulting polygons with equal area. It's important to note that while congruent figures will always have equal content and area, figures with equal content and area may not be congruent.

The answer is 150 degrees.

The sum of angle in a triangle is 180 degrees.. The measure of <1 from thediagram is 150 degrees

The sum of angle in a triangle is 180 degrees. From the given disgaram, the sum of the angles of the right triangle is 180 degrees.

Using the expression to find the measure of the acute angle

90 + 60+x = 180

150 + x = 180

x = 180 - 150

x = 30

Determne the value of <1

<1 + 30 = 180

<1 = 180 - 30

<1 = 150degrees

Hence the measure of <1 from thediagram is 150 degrees

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Answer:

$4,723.21​

Step-by-step explanation:

Formula for COMPOUND INTEREST:

A = P ( 1 + r/n) ^ nt

Where A = principal money + interest earned,

P = Principal Money

r = interest rate in decmial

n = no. of times i.rate is compounded

nt = time

Since the qns asked to be compounded /monthly', you have the following formula:

A = 3250 ( 1 + 7.5%/12) ^ 60

7.5% is a yearly rate so divide it by 12 (as in 12 months)

60 = 5 years x 12 months

so use a calculator and you'll get $4723.206, round off and it's $4723.21

To find out how much Connie's investment in a savings account with a 7.5% annual interest rate compounded monthly will be worth in five years, use the compound interest formula. After calculations, her investment will be worth $4,723.21 in five years.

The student asks about the future value of an investment made in a savings account with compound interest. To calculate the amount Connie's investment will be worth in five years, we can use the compound interest formula, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($3,250), r is the annual interest rate (7.5% or 0.075 as a decimal), n is the number of times the interest is compounded per year (12, since it's monthly), and t is the number of years (5).

Using these values, we calculate the future value (A) as follows:

Convert the percent interest to a decimal: 7.5% = 0.075.

Divide the annual rate by the number of compounding periods: 0.075/12.

Add 1 to the interest rate per period: 1 + (0.075/12).

Calculate (1 + (0.075/12)) raised to the power of the total number of compounding periods: (1 + (0.075/12))^(12*5).

Multiply the principal by this amount: $3,250 × (1 + (0.075/12))^(12*5).

Connie's investment will grow to $$4,723.21 after five years, using compound interest.

[tex]

A=3(4b^2+2b+6) \\

A=\boxed{12b^2+6b+18}

[/tex]

Answer:

D. [tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We can use a process of elimination in order to easily solve this.

The shape of [tex]g(x)=-|x|[/tex] will be two diagonal lines that meet at (0,0)

[tex]g(x)=-x^2[/tex] Will be an upside down parabola

[tex]g(x)=-x[/tex] Will be a line with a slope of -1.

This means that the answer must be D

Answer:

The correct option is D.

Step-by-step explanation:

From the given graph it is clear that the y-intercept of the function is -1. It means the graph passes through (0,-1).

Check each function, whether the function passes through the point (0,-1) or not. Substitute x=0 it each function to find the y-intercept.

In option A,

[tex]g(x)=|x|[/tex]

[tex]g(0)=|0|=0[/tex]

The y-intercept of the function is at (0,0).

In option B,

[tex]g(x)=x^2[/tex]

[tex]g(0)=0^2=0[/tex]

The y-intercept of the function is at (0,0).

In option C,

[tex]g(x)=x[/tex]

[tex]g(0)=0[/tex]

The y-intercept of the function is at (0,0).

In option D,

[tex]g(x)=-2^x[/tex]

[tex]g(0)=-1[/tex]

The y-intercept of the function is at (0,-1).

The graph of [tex]g(x)=-2^x[/tex] passes through the point (0,-1).

Therefore the correct option is D.

Answer:

a)zw  = 44.295 cos(1.924) +isin(1.924))

b) z/w= 4.921 cos(-0.936) + isin(-0.936)

Step-by-step explanation:

Given:

z=13+7i

w=3(cos(1.43)+isin(1.43)  

a. convert zw using De Moivre's theorem  

First coverting z into  polar form:

13^2 + 7^2  = 14.765

[tex]\sqrt{14.765}[/tex] =r

θ= arctan (7/13)

 = 0.49394                            (28.301 in degrees)

z= 14.765(cos(0.49394)+isin(0.49394)  )

Now finding zw

zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be multiplied

14.765 x 3=44.295

whereas the angles will be added

.494+1.43=1.924

Thus:

zw  = 44.295 cos(1.924) +isin(1.924))

b)

finding z/w

z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be divided

14.765 / 3 = 4.921

whereas the angles will be subtracted:

.494-1.43=-0.936

Thus:

z/w= 4.921 cos(-0.936) + isin(-0.936) !

Answer:

The answer is 195

Step-by-step explanation:

The formula is V= 1/2 of the height times the two bases

V=1/2*h*b*b

V=1/2*13*6*5

V=195 meters squared.

Hoped this helped!

Answer: 390

Step-by-step explanation:

Length x Width x Height = Volume

Answer:

I'm pretty sure it's the one you chose, which means the 2nd pic.

Answer:

I think It is the first one, that is a cone flipped and there is a hole in it.

Well it depends. If your radical is wrapped around the entire expression, then your answer would be 3xy²z²√10xz, but if your radical is ONLY wrapped around 90, then your answer would be 3√10x³y⁴z⁵ [radical wrapped ONLY around 10]. So, with the way this is written, although it is simple to figure this out, it is difficult to find the answer you are looking for.

6(7-4)+10

First distribute 6 into the parentheses

42-24+10= 28

So your answer is A. 28

Final answer:

To evaluate 6(x - 4) + 10 when x = 7, after substituting and simplifying, the result is 28 (option A).

Explanation:

Step-by-Step Solution

To evaluate the expression 6(x - 4) + 10 when x = 7, follow these steps:

Therefore, the expression 6(x - 4) + 10 when x = 7 equals to option A. 28.

Answer:

P(gummy bear) = [tex]\frac{4}{11}[/tex]

Explanation:

Probability of a certain outcome can be calculated as follows:

[tex]P(certain-outcome)=\frac{number-of-occurrences-of-this-outcome}{total-number-of-possible-outcomes}[/tex]

In the given problem we have:

20 gummy bears and 35 orange slices

We want to find P(gummy bear)

This means that:

number of occurrences of desired outcome = number of gummy bears = 20

Total number of possible outcomes = gummy bears + orange slices

Total number of possible outcomes = 20 + 35 = 55

Substitute with the givens in the above formula, we get:

[tex]P(gummy-bears)=\frac{20}{55}=\frac{4}{11}[/tex]

Hope this helps :)

Final answer:

The probability of selecting a gummy bear from a bag containing 20 gummy bears and 35 orange slices is approximately 36.36%.

Explanation:

The student's question is about finding the probability of selecting a gummy bear from a bag of sweets. Given that there are 20 gummy bears and 35 orange slices in the bag, to find the probability of selecting a gummy bear, we use the formula P(gummy bear) = (number of gummy bears) / (total number of sweets). Therefore, P(gummy bear) = 20 / (20 + 35) = 20 / 55. Simplifying this, we get approximately 0.3636, which can also be expressed as a percentage, 36.36%.

[tex]\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(75^o)}{17}=\cfrac{sin(D)}{10}\implies \cfrac{10sin(75^o)}{17}=sin(D) \\\\\\ sin^{-1}\left[ \cfrac{10sin(75^o)}{17} \right]=D\implies 34.6\approx D[/tex]

since all interior angles in a triangle must be 180°, that means that C = 180 - 75 - 34.6 = 70.4.  Let's find AD, which is the other sides pair length.

[tex]\bf \cfrac{sin(75^o)}{17}=\cfrac{sin(70.4^o)}{AD}\implies ADsin(75^o)=17sin(70.4^o) \\\\\\ AD=\cfrac{17sin(70.4^o)}{sin(75^o)}\implies AD\approx 16.58[/tex]

now, check the picture below, let's find the altitude of the parallelogram.

[tex]\bf sin(34.6^o)=\cfrac{\stackrel{opposite}{h}}{\stackrel{hypotenuse}{16.58}}\implies 16.58sin(34.6^o)=h\implies 9.4\approx h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=9.4 \end{cases}\implies A=(17)(9.4)\implies A=159.8[/tex]

2(x-50)

2(x+3)

7(2-x)

Find the greatest common factors and then put them outside the parentheses

Answer:

False

Step-by-step explanation:

The number of degrees of freedom associated with the t-test, when the data are gathered from a paired samples experiment with 12 pairs, is;

12 - 1 = 11

The paired samples t-test is equivalent to a one sample t-test for the mean. The degrees of freedom are obtained by subtracting one from the number of pairs;

Answer:

B. g(x) = |x + 3|

Step-by-step explanation:

The answer is:

The dimensions of the paper for Gift C, are: 25" x 12"

and its area is:

[tex]GiftCArea=300inch^{2}[/tex]

To solve the problem, we need to calculate the total area of the remaining paper, and then, subtract it from the paper used for the gift A and B.

We know that:

[tex]GiftA=TotalPaperArea*\frac{2}{5}\\\\GiftB=TotalPaperArea*\frac{1}{3}[/tex]

Now, the paper for Gift C will be:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

From the statement we know that the dimenstions of the remaining paper are 25" x 45", so calculating the area we have:

[tex]TotalArea=25inch*45inch=1125inch^{2}[/tex]

Now, calculating the area of the paper for Gift A and B, we have:

[tex]GiftA=1125inch^{2}*\frac{2}{5}=450inch^{2}\\\\GiftB=1125inch^{2}*\frac{1}{3}=375inch^{2}[/tex]

Then, calculating the paper for Gift C, we have:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

[tex]GiftCArea=1125inch^{2}-(450inch^{2}+375inch^{2}+)[/tex]

[tex]GiftCArea=1125inch^{2}-825inch^{2}=300inch^{2}[/tex]

[tex]GiftCArea=300inch^{2}[/tex]

Therefore, calculating the dimensions of the paper for Gift C, knowing the height of the paper (25inches), we have::

[tex]GiftCArea=Height*Width\\\\Width=\frac{GiftCArea}{25inches}=\frac{300inches^{2} }{25inches}=12inches[/tex]

Hence, the dimensions of the paper for Gift C, are: 25" x 12".

Have a nice day!

The answer is A) 1 centiliter

Answer:

D. (2, 6)

Step-by-step explanation:

Look at the picture.

Check:

(2, 6) → x = 2, y = 6

Put the coordinates of the point to the inequalities:

y < x² + 6

6 < 2² + 6

6 < 4 + 6

6 < 10    TRUE

y > x² - 4

6 > 2² - 4

6 > 4 - 4

6 > 0   TRUE

Final answer:

The correct solution to the system of inequalities is point D (2,6), as it satisfies both inequalities y < x^2 +6 and y > x^2 -4 when x=2 and y=6 are substituted into them.

Explanation:

The student is asked to select the point that is a solution to the system of inequalities.

The two inequalities given are:

< x^2 +6

y > x^2 -4

To solve this, we need to check which point(s) satisfy both inequalities. Let's evaluate the options given:

A. (0,8): Substituting x=0 into both inequalities gives 8 < 6 (false) and 8 > -4 (true), so point A does not satisfy both inequalities.

B. (-2,-4): Substituting x=-2 into both inequalities gives -4 < 10 (true) and -4 > 0 (false), so point B does not satisfy both inequalities.

C. (4,2): Substituting x=4 into both inequalities gives 2 < 22 (true) and 2 > 12 (false), so point C does not satisfy both inequalities.

D. (2,6): Substituting x=2 into both inequalities gives 6 < 10 (true) and 6 > 0 (true), so point D satisfies both inequalities and is the correct solution.

Therefore, the solution to the system of inequalities is point D (2,6).