Which of the following is a trigonometric identity?
A. cot theta + tan theta = 1
B. sec^2theta + csc^2theta = 1
C. tan^2theta = sin^2theta × sec^2theta
D. cos^2theta = sec^2theta × tan^2theta

Answer:

46¢

Step-by-step explanation:

Note that there are 12 cola's in all. The total cost is $5.46. Divide the total cost with the amount of cola's there is:

5.46/12 = 0.455

Round: 0.455 rounded to the nearest hundredths is $0.46 (You round to the nearest hundredths, for the smallest amount for US currency is a penny, which is 1/100 of a dollar bill).

Each cola costs $0.46

~

Answer:

Option B

Part a) The focus is [tex](1/28,0)[/tex]

Part b) The directrix is [tex]x=-1/28[/tex]

Part c) The equation is  [tex]y^{2}= (1/7)x[/tex]

Step-by-step explanation:

step 1

Find the equation of the parabola

we know that

The parabola in the graph has a horizontal axis.

The standard form of the equation of the horizontal parabola is

[tex](y - k)^{2}= 4p(x - h)[/tex]

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h + p, k).

The directrix is the line x= h- p.

The axis is the line y = k.

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left

In this problem we have that the vertex is the origin

so

(h,k)=(0,0)

substitute in the equation

[tex](y - 0)^{2}= 4p(x - 0)[/tex]

[tex]y^{2}= 4p(x)[/tex]

The points (7,1) and (7,-1) lies on the parabola-----> see the graph

substitute the value of x and the value of y in the equation and solve for p

[tex](1)^{2}= 4p(7)[/tex]

[tex]1= 28p[/tex]

[tex]p=1/28[/tex]

The equation of the horizontal parabola is

[tex]y^{2}= 4(1/28)(x)[/tex]

[tex]y^{2}= (1/7)x[/tex]

step 2

Find the focus

we know that

The focus is at (h + p, k)

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex](0+1/28,0)[/tex]

therefore

The focus is at

[tex]F (1/28,0)[/tex]

step 3

Find the directrix

The directrix is the line x = h- p

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex]x=0-1/28[/tex]

[tex]x=-1/28[/tex]

Answer:

B

Step-by-step explanation:

Confirmed on E D G 2021

Answer:

domain:   (-∞, ∞) ; range: [-5, 0]

Step-by-step explanation:

Let's begin with the basics:

The domain of cos x is (-∞, ∞); the range is [-1, 1].

The domain of cos²x is still (-∞, ∞).

Likewise, the domain of -5 cos²x is(-∞, ∞).

The range of cos²x differs: it is [0, 1] because squaring a negative number results in a positive output.

Multiplying cos²x by 5 expands the range to [0, 5].

Finally, multiplying 5 cos²x by -1 changes the range to [-5, 0].

Answer:

C

Step-by-step explanation:

Cuz edge

Remember to be mindful of signs when adding and subtracting. 2c^2+5c+4

Answer:

B

Step-by-step explanation:

First

Get totals for food items:

Pizza $14.95 ×2=$29.90

Salad=$4.35

Drinks $2.49 ×4=$9.76

Total Bill

$29.90

$ 4.35

+$ 9.76

$44.21 Food Bill

Second Step

Find Tip Amount Before Tax

Total Bill $44.21 × .15=$6.63 Tip

Third Step

Find Tax on Total Food Bill

$44.21 × .07675=$3.39

Fourth Step

Find amount left from paying bill with tax.

Total Bill including tax:

$44.21 (bill) +$3.39 tax=$47.60

Cash $ 50.00

Total Bill - $47.60

$ 2.40 Change left over

Fifth Step

Find amount needed to give $6.63 tip from above.

We have $2.40 we need $6.63

Subtract $6.33 -$2.40=$4.23 more money needed for tip

The correct option is B. $ 4.23. Mr. Wright needs an additional $4.23 to leave a 15% tip.

First, we need to calculate the total cost of the meal before tax and tip. The Wright family ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. So, the cost of the pizzas is [tex]2 \times $14.95[/tex], the salad is $4.35, and the drinks are 4 \times $2.49.

Cost of pizzas: [tex]2 \times $14.95 = $29.90[/tex]

Cost of salad: $4.35

Cost of drinks: [tex]4 \times $2.49 = $9.96[/tex]

Total cost before tax: [tex]\$29.90 +\$\4.35 + \$\9.96 = \$\44.[/tex]21

Next, we calculate the sales tax, which is 7.675% of the total cost before tax.

Sales tax: [tex]\$\44.21 \times 7.675% = \$\44.21 \times 0.07675 = \$\3.39[/tex]

Now, we add the sales tax to the total cost before tax to get the total cost including tax.

Total cost with tax: [tex]\$\44.21 + \$\3.39 = \$\47.60[/tex]

Mr. Wright wants to leave a 15% tip on the total bill before tax. So, we calculate 15% of the total cost before tax.

Tip: [tex]\$\44.21 \times 15% = \$\44.21 \times \$\0.15 \times \$\ 6.63[/tex]

Mr. Wright paid with a $50 bill, so we subtract the total cost with tax from $50 to find out how much change he should receive.

Change from [tex]\$50: $50 - $47.60 = $2.40\[/tex]

To find out how much more money Mr. Wright needs to leave a 15% tip, we subtract the change he receives from the tip amount.

Additional money needed: [tex]\$6.63 - $2.40 = $4.23\[/tex]

Therefore, Mr. Wright needs an additional $4.23 to leave a 15% tip.

Answer:

A

Step-by-step explanation:

The formula for the Perimeter of a rectangle is P = 2W + 2L.

Let's equate this to 60 units and substitute 11 for W and 24 units for L:

2(11 units) + 2(24 units) = 22 units + 48 units = 70 units.  NO (Answer A)

For this case we have to, by definition:

[tex]cos (F) = \frac {h} {26.4}[/tex]

This means that, the cosine of the angle F, will be equal to the leg adjacent to the angle on the hypotenuse of the triangle.

So, by clearing h we have:

[tex]h = 26.4 * cos (35)\\h = 26.4 * 0.81915204\\h = 21.6256[/tex]

Rounding out the value of h we have:

[tex]h = 21.6[/tex]

Answer:

Option B

Answer:

The correct answer is option b.   21.6

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Cos θ = adjacent side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of h

It is given that, g=26.4 and F= 35°

Cos F =  adjacent side/Hypotenuse

Cos 35 =  adjacent side/Hypotenuse

     = FG/FH = h/g

h = g * Cos F = 26.4 * Cos 54 = 26.4 * 0.8191 = 21.62 ≈ 21.6  

Therefore the correct answer is option b.  21.6

Answer:

g, f, h

Step-by-step explanation:

By definition, the average rate of change of a function f over an interval [a,b] is given by

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

So, in your case, we want to compute the quantity

[tex]\dfrac{f(3)-f(0)}{3}[/tex]

for all the three function

Average rate of change of f:

We will simply use the table to check the values for f(3) and f(0):

[tex]\dfrac{f(3)-f(0)}{3}=\dfrac{10-1}{3} = 3[/tex]

Average rate of change of g:

We will use the graph to to check the values for g(3) and g(0):

[tex]\dfrac{g(3)-g(0)}{3}=\dfrac{8-1}{3} = \dfrac{7}{3}[/tex]

Average rate of change of h:

We can plug the values in the equation to get h(3) and h(0):

[tex]h(3)=3^2+3-6=9+3-6=6,\quad h(0)=0^2+0-6=-6[/tex]

And so the average rate of change is

[tex]\dfrac{h(3)-h(0)}{3}=\dfrac{6-(-6)}{3} = 4[/tex]

Answer:

g,f,h

I just took the test and was right

Step-by-step explanation:

Answer:

0.04746

Step-by-step explanation:

To answer this one needs to find the area under the standard normal curve to the left of 5 minutes when the mean is 4 minutes and the std. dev. is 0.6 minutes.  Either use a table of z-scores or a calculator with probability distribution functions.

In this case I will use my old Texas Instruments TI-83 calculator.  I select the normalcdf( function and type in the following arguments:  :

normalcdf(-100, 5, 4, 0.6).  The result is 0.952.  This is the area under the curve to the left of x = 5.  But we are interested in finding the probability that a conversation lasts longer than 5 minutes.  To find this, subtract 0.952 from 1.000:   0.048.  This is the area under the curve to the RIGHT of x = 5.

This 0.048 is closest to the first answer choice:  0.04746.

Answer:

Kylie could have a $5 bill and seven quarters while Ethan could have two $1 bills and forty pennies.

Step-by-step explanation:

Since Kylie has seven quarters, that is seven multiplied by the value of the quarter, a quarter is 25 cents. So 7 x 25 = 125 OR $1 and 25 cents. Leaving Kylie with a total of $7 and 25 cents with the addition of the $5 bill.

Ethan has two $1 bills and forty pennies, forty multiplied by the value of the penny, a penny is 1 cent. So 40 x 1 = 40 OR 40 cents. Leaving Ethan with $2 and 40 cents with the addition of the two $1 bills from earlier.

Ethan has more bills and coins than Kylie and yet still has less money than Kylie.

Answer:

Final answer is [tex]P(B/A)=0.5[/tex]

Step-by-step explanation:

Given that P(A) =0.20

P(B) = 0.25

P(A and B) = 0.10.

Now we need to find about what is the value of P(B/A).

P(A and B) = P(A) * P(B/A)

Plug the given values into above formula:

[tex]0.10=0.20\cdot P(B/A)[/tex]

[tex]\frac{0.10}{0.20}=P(B/A)[/tex]

[tex]0.5=P(B/A)[/tex]

[tex]P(B/A)=0.5[/tex]

Hence final answer is [tex]P(B/A)=0.5[/tex]

Answer:

c is the answer

Step-by-step explanation:

Answer:

a) 180

b) CJ= 5.83095189485

CK= 9.89949493661

CL= 8.0622577483

c) All angles formed by a point and its image, with the vertex at the center of rotation, are congruent. Each point on the original figure is the same distance from the center of rotation as its image.

Step-by-step explanation:

Answer:

D) π/2 and 3π/2

Step-by-step explanation:

The equation can be factored:

(1 -sin(x))(1 +sin(x)) = 0

The factors will be zero when ...

sin(x) = 1 ⇒ x = π/2

sin(x) = -1 ⇒ x = 3π/2

Answer:

See below.

Step-by-step explanation:

This inequality is < 0 for all real values of x. We see this by solving  -x^2 - 6 = 0 for x:

-x^2  - 6 = 0

-x^2 = 6

x^2 = -6   for which there are no real solutions of x. So the graph does not pass through the x axis.

At x = 0. f(x) < -6 so that is the one critical value - all values of f(x) are below this value.

Answer:

0 critical points

Step-by-step explanation:

Just did it and got it right

===================================================

Explanation:

"given that the first die rolled is a 2" means we know 100% that the first die shows a 2. Either we can see the die or a friend is telling us the status. Since we know the first die is a 2, this means we can effectively ignore it. Everything will hinge on the second die. If the second die shows an odd number, something like 1, then 2+1 = 3 is the result which is also odd.

The general rule is odd+even = odd and even+even = even.

Therefore, the two dice must together be even for the sum to be even.

Of the six possible ways to roll a die {1,2,3,4,5,6}, there are 3 even values {2,4,6} so the chances of rolling an even number on the second die is 3/6 = 1/2. Again we dont need to consider the first die at all since everything practically hinges on this second die.

Answer:

50%

Step-by-step explanation:

For the total to be even, when the first number is even, the second number also has to be even.

2, 4, and 6 are even, out of 6 numbers. That is 3 numbers out of 6, which gives us that the probability is 1 out of 2, or 50%.

Answer:

h=1    K =2    a =6    b=2

Step-by-step explanation:

look this solution :

Answer:

h = 1, k = 2, a = 6 and b = 2.

Step-by-step explanation:

Start by grouping the terms in x and y together:

4x^2 - 8x  + 36y^2 - 144y = -4

Factor out the coefficient:

4(x^2 - 2x) + 36(y^2 - 4y) = -4

Complete the squares:

4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4

4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4

4(x - 1)^2 + 36(y - 2)^2 =  144

Divide through by 144:

(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1

(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1  (answer).

Answer:

Length = 13

x = 80

Step-by-step explanation:

Question One

Let the width = x

Let the length = x + 5

Area = 104

Equation

Area = L * W

Area = (x+5)*x

Solution

x ( x + 5) = 104                  Remove the brackets

x^2 + 5x = 104                  Subtract 104 from both sides.

x^2 + 5x - 104 = 104 - 104

x^2 + 5x - 104 =  0            Factor the equation    

(x + 13)(x - 8) = 0

Only x - 8 = 0 works

x = 8

The width = 8

The Length = 8 + 5 = 13

Question Two

Draw AP

<BAP = 20o                     The triangle (APB) is isosceles: 2 sides are radii

<BPA = 180 - 20 - 20      The three angles of a triangle = 180

<BPA = 140                      Combine

Similarly <CAP = 140       Go through exactly the same steps.

<BPA + <CAP + X = 360  The total of the 3 angles in the center = 360

140 + 140 + X = 360         Combine

280 + X = 360                 Subtract 280 from both sides.

x = 80

Answer:

[tex]\large\boxed{\sum\limits_{k=3}^5(-2k+5)=-9}[/tex]

Step-by-step explanation:

[tex]\sum\limits_{k=3}^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_{k=3}^5(-2k+5)=-1+(-3)+(-5)=-9[/tex]

The answer is C. (5,3)

Explanation:

(X,Y) is how ordered pairs should be set up.

Answer:

C (5,3)

Step-by-step explanation:

The first point in an ordered pair is the x coordinate.

We move 5 units to the right, so it is +5

The second coordinate is the y coordinate.

We move 3 units up, so it is +3

(5,3)

35%

First, we need to find the amount of money that is being spent. Add all of the amounts together.

$350 + $100 + $120 + $80

$450 + $120 + 80

$570 + $80

$650

So, Ian spends $650 of his budget each month. How much does that leave for savings? Just subtract $650 from $1,000 to find that he saves $350 each month.

Now, you just need to find the percentage. The percentage is the same as the numerator in a fraction with a denominator of 100, so x% = x/100. For example, 1% = 1/100. $350 / $1000 = x / 100

How do we turn 1,000 into 100? Divide it by 10. And if you do something to the denominator of a fraction, you have to do it to the numerator as well. So, divide $350 by 10 and divide $1000 by 10, leaving you with $35 / $100 = x / 100

Multiply both sides by 100 to get x by itself. This leaves you with 35 = x, so 35% of Ian’s budget with go towards saving.

The answer is (-4x-1)(2x^2+3) when factoring this expression by grouping

Answer:

The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]-8x^3-2x^2-12x-3[/tex]

The above expression can be written as:

[tex](-8x^3-2x^2)+(-12x-3)[/tex]

Take out the greatest common factor from each group.

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

Further solve the above expression.

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

Hence, the required expression is

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

The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]

BC also has length 12 because arcs DC and CE add up to 117 degrees in measure, so that arc DE is congruent to arc BC, and the chords DE and BC that respectively intercept these arcs must also be congruent.

Answer:

A

Step-by-step explanation:

y bar basically means the average of the y-values.

To get the average, we add up all the y-values in the table and divide by the total number of values (here we have 5 values). Hence,

y bar = [tex]\frac{5+7+10+15+18}{5}=11[/tex]

correct answer is A

Answer:

225

Step-by-step explanation:

15(1+15/2) *2= 240-15=225

The sum of the arithmetic series given by the terms (2n - 1) for n=1 to 5 is 25, computed using the formula for the sum of an arithmetic series.

The series in question is an arithmetic series with a difference of 2 and the sum of the first n terms can be represented by the formula for the sum of an arithmetic series, Sn = n/2[2a + (n-1)d], where 'a' is the first term and 'd' is the common difference between the terms.

In the provided series, each term is of the form (2n - 1) starting with n=1 and going till n=5. So the first term, a = 2(1) - 1 = 1, and the common difference, d = 2 since each subsequent term increases by 2.

We can compute this sum directly by evaluating S5, using the formula for an arithmetic series: S5 = 5/2[2(1) + (5-1)(2)] = 5/2[2 + 8] = 5/2[10] = 25. So, the sum of the series is 25.

Answer:

72

Step-by-step explanation:

The two acute angles add up to 90 degrees. That's because the given triangle is a right triangle.

So x + 4x + 90 = 180           All triangles = 180°. Combine left side terms.

5x + 90 = 180                      Subtract 90°

5x + 90 - 90 = 180 - 90      Combine

5x = 90                                Divide by 5

5x/5 = 90/5                         Combine

x = 18

The larger angle is 4x so

The larger angle = 4*18 = 72

[tex]g\circ f(-9)=g(f(-9))[/tex]

By definition of [tex]f[/tex],

[tex]f(-9)=3\cdot9-8=19[/tex]

and by definition of [tex]g[/tex],

[tex]g\circ f(-9)=g(f(-9))=g(19)=\sqrt{14-19}-10=\sqrt{-5}-10[/tex]

which is undefined if [tex]f,g[/tex] are supposed to be real-valued functions. If they're complex-valued, then [tex]\sqrt{-5}=i\sqrt 5[/tex] and [tex]g\circ f(-9)=-10+i\sqrt 5[/tex].

Add 8 to both sides of the equation.

You need to get x by itself. The only way to do that here is to do the opposite of subtracting 8, which is adding 8.

Also, when you do something to one side of the equation, you have to also do it to the other side to keep the equation equal.

Answer: Add 8 to both sides of the equation

Step-by-step explanation:

d - 8 = 9

in this equation you need to solve for d. To do that you have to get d by itself.

By adding 8 to both sides of the equation you cancel out the -8 and add 8 to 9 which solves for d.

Answer:

[tex]\$14.18[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$10\\ r=0.035\\n=12[/tex]  

substitute in the formula above  

[tex]A=P(1+\frac{0.035}{12})^{12*10}=\$14.18[/tex]  

Answer:

The median price of a new home

Step-by-step explanation: