How do you prove 4 (cos^4A + sin^4A) / (3+cos4A) = (cos^4A-sin^4A) sec2A?​

Answer:

The first term is 28.

Step-by-step explanation:

Given: 8th term of Geometric sequence , [tex]a_8=-3584[/tex]

and 3rd term of Geometric Sequence, [tex]a_3=112[/tex]

We have to find First term of given geometric Sequence.

Let a be the first term of geometric sequence.

We know that,

[tex]a_n=ar^{n-1}[/tex]

So,

[tex]\frac{a_8}{a_3}=\frac{ar^{8-1}}{ar^{3-1}}=\frac{-3584}{112}[/tex]

[tex]\frac{r^{7}}{r^{2}}=-32[/tex]

[tex]r^5=-32[/tex]

[tex]r=-2[/tex]

So, 3rd term = 112

a × (-2)² = 112

a = 112 / 4

a = 28

Therefore, The first term is 28.

Answer:

1 and a8 =16,384

Step-by-step explanation:

Answer:

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

Step-by-step explanation:

[tex]8x^2+4x+1=0[/tex]

Using Quadratic formula to solve this equation:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a = 8 \,\, b = 4\,\, c = -1\\Putting \,\, values \,\, in \,\, the\,\, equation\\x= \frac{-4\pm\sqrt{(4)^2-4(8)(-1)}}{2(8)}\\x= \frac{-4\pm\sqrt{16+32}}{16}\\x= \frac{-4\pm\sqrt{48}}{16}\\x= \frac{-4+ \sqrt{48}}{16} \,\, and \,\, x= \frac{-4- \sqrt{48}}{16}\\x= \frac{-1+ \sqrt{3}}{4} \,\, and \,\, x= \frac{-1- \sqrt{3}}{4}[/tex]

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

____________________________________________________

Answer:

Your answer would be 1,385.44 ft²

____________________________________________________

Step-by-step explanation:

To find the area of a circle, we would use the equation [tex]\pi r^2[/tex]

In this case we have the diameter, and that's 42.

The radius of a circle is half of the diameter, therefore the radius would be 21.

Now we know the radius,we can plug that in to our equation.

Your equation should look like this:

[tex]\pi (21)^2[/tex]

Pi would be 3.14159

Now, you can solve.

[tex]3.14159(21)^2\\\\3.14159*441\\\\=1,385.44[/tex]

When you'r edone solving, you should get 1,385.44

1,385.44 ft² would be your FINAL answer.

____________________________________________________

Answer:

1384.74

Step-by-step explanation:

diameter = 42

radius = 42/2 = 21

area of a circle = πr2 (pie r square)

= 3.14 X 21 X 21

=1384.74 sq.ft

Options 1, 2, and 3 are valid based on the given information and calculations.

1. When added, the sum of the y-intercepts must be 8:

  - If the y-intercepts are denoted as b₁ and b₂ for f(x) and g(x) respectively, then . [tex]b_1 \times b_2 = 8[/tex].

2. When multiplied, the product of the y-intercepts must be 8:

  - This translates to [tex]b_1 \times b_2 = 8[/tex].

3. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change:

  - This implies that the slopes of the lines have opposite signs.

Checking the given U-turn points (-2, 8) and (8, 2). The slope (rate of change) between these points can be calculated as:

[tex]\[ m = \frac{change\:in\:y}{change\:in\:x} \][/tex]

[tex]\[ m = \frac{2 - 8}{8 - (-2)} = \frac{-6}{10} = -\frac{3}{5} \][/tex]

4. f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3:

  - This statement is inconsistent with the calculated slope.

5. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1:

  - This statement is also inconsistent with the calculated slope.

Therefore, options 1, 2, and 3 are valid based on the given information and calculations.

Answer:

1 When multiplied the product of the y intercepts must be 8

2 Either f(x) or g (x) has a positive rate of change and the other has a negative rate of change

3 f (x) could have a rate of change equal to 2 and g (x) could have a rate change of -1

Answer:

-26

Step-by-step explanation:

Plug in 12 for n.

-4-2(12-1)

-4-2(11)

-4-22

-26

-26 !!!!!!!!!!!!!!!!!!!!!

Answer:

The first part is A then the second part is B 1/19

Step-by-step explanation:

If you add all together you get 20 then you get a green marble since you removed one that would make the odds into 1 out of 19 that's how you get the next answer. Hope this Helped! ʢ◉ᴥ◉ʡ

Answer:

the correct option is C.

Step-by-step explanation:

The x-intercept of both functions g(x) and f(x) occur at point (1, 0).

Now, we need to find where g(x) > f(x) and f(x) > g(x)

We know that the greater the base of a logaritmic function is, the faster it will grow/decay.

For that reason, we can say that g(x) > f(x)  on (1, +inf).

Now, when x<1 then y<0. So on the interval (0, 1) the function g(x) will decay much faster than the function f(x), so we can say that f(x) > g(x) on (0, 1). So the correct option is C.

Check the graph, to verify all this.

Answer:

B

Step-by-step explanation:

The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 109, 111, and Z or unknown. The mean of them is 100. Solve for Z.

100 =(109+111+Z)/3

300=220+Z

80=Z

The speed of Car Z is less than 100.

The correct answer is B. The speed of Car Z is less than 100 miles per hour.

To estimate the speed of Car Z, we can use the given mean speed of the three cars. The mean speed is given as 100 miles per hour. Since Car X is driving at 109 miles per hour and Car Y is driving at 111 miles per hour, both of these speeds are above the mean. To maintain an average of 100 miles per hour, Car Z must be driving at a speed less than 100 miles per hour to balance the speeds of Car X and Car Y, which are pulling the average up.

To find the actual speed of Car Z, we can use the formula for the mean speed of the three cars:

[tex]\[ \text{Mean speed} = \frac{\text{Speed of Car X} + \text{Speed of Car Y} + \text{Speed of Car Z}}{3} \][/tex]

Given that the mean speed is 100 miles per hour, we can plug in the known values and solve for the speed of Car Z:

[tex]\[ 100 = \frac{109 + 111 + \text{Speed of Car Z}}{3} \][/tex]

Multiplying both sides by 3 to clear the denominator:

[tex]\[ 300 = 109 + 111 + \text{Speed of Car Z} \][/tex]

Adding the speeds of Car X and Car Y:

[tex]\[ 300 = 220 + \text{Speed of Car Z} \][/tex]

Subtracting 220 from both sides to isolate the speed of Car Z:

[tex]\[ \text{Speed of Car Z} = 300 - 220 \] \[ \text{Speed of Car Z} = 80 \text{ miles per hour} \][/tex]

Thus, the actual speed of Car Z is 80 miles per hour, which confirms our initial estimation that it is less than 100 miles per hour.

First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.

Rearrange equations

[tex]4x + y = 19[/tex]

[tex] - 2x + y = 1[/tex]

To cancel y, we must do equation 1 minus equation 2. Similarly:

[tex]4x - - 2x = 4x + 2x = 6x[/tex]

[tex]19 - 1 = 18[/tex]

[tex]6x = 18[/tex]

[tex]x = 18 \div 6 = 3[/tex]

So the x coordinate is 3.

The y coordinate can be found with substitution of x into one of the equations:

[tex]y = 2x + 1 = 2(3) + 1 = 7[/tex]

So where the two lines intersect is at the point (3, 7), which is the solution to the equations.

Answer:

The correct option is 2.

Step-by-step explanation:

The given system of equations is

[tex]y=-4x+19[/tex]           ..... (1)

[tex]y=2x+1[/tex]               ..... (2)

The slope intercept form of a line is

[tex]y=mx+b[/tex]             .... (3)

where, m is slope and b is y-intercept.

From (1) and (3), we get

[tex]m=-4,b=19[/tex]

The slope of first line is -4 and the y-intercept is 19. It means it is a decreasing line and intersect the y-axis at (0,19).

From (2) and (3), we get

[tex]m=2,b=1[/tex]

The slope of first line is 2 and the y-intercept is 1. It means it is an increasing line and intersect the y-axis at (0,1).

Put y=0, to find the x-intercepts.

[tex]0=-4x+19\Rightarrow x=\frac{19}{4}=4.75[/tex]

[tex]0=2x+1\Rightarrow x=\frac{-1}{2}=-0.5[/tex]

Therefore the x-intercept of first line is 4.75 and the x-intercept of the second line is -0.5.

Only the second graph satisfy all the above condition.

One solving the given equation we get

[tex]-4x+19=2x+1[/tex]

[tex]19-1=2x+4x[/tex]

[tex]18=6x[/tex]

Divide both sides by 6.

[tex]3=x[/tex]

Put this value in equation (1).

[tex]y=-4(3)+19=-12+19=7[/tex]

Therefore the solution of the given system of equation is (3,7).

Hence the correct option is 2.

B

12 is equal to 4y, or 4(3)

you can multiply 4 by x to get 9 since they’re inversely proportionate.

Answer:

A) 1.

Step-by-step explanation:

y is inversely proporcional to x so the equation has the form:

y = c/x

With c been any constant, to find the value of c we use y=4 and x=3:

4 = c/3

c=4*3

c=12

So the equation is

y=12/x

Using y=12 to find x:

12=12/x

(12/12)=x

x=1

The area of the circle with [tex]\(r = 1\)[/tex] is [tex]\(\pi\)[/tex].

The area ([tex]\(A\)[/tex]) of a circle is given by the formula:

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

Where [tex]\(r\)[/tex] is the radius of the circle.

Given that [tex]\(r = 1\)[/tex], we can substitute this value into the formula:

[tex]\[A = \pi \times (1)^2\][/tex]

[tex]\[A = \pi \times 1\][/tex]

[tex]\[A = \pi\][/tex]

Therefore, the area of the circle with [tex]\(r = 1\)[/tex] is [tex]\(\pi\)[/tex].

Answer:

X= O.8 or 10 over 12.5

Step-by-step explanation: Hope this helps darling

The correct answer to the question is option (2): [tex]\( h\left(\frac{x}{3}\right) \).[/tex]

To address the question about the horizontal stretching of the graph of a function [tex]\( f(x) \)[/tex] by a factor of 3, we need to understand how transformations affect the graph of a function. Here are the steps to determine the correct transformation:

1. Identify the Base Function: Recognize that the graph in question is of some function [tex]\( f(x) \)[/tex]. We don't need to know the form of \( f(x) \) to understand how it will be transformed.

2. Understand Horizontal Stretching: A horizontal stretch by a factor of [tex]\( a \)[/tex] is achieved by replacing every [tex]\( x \)[/tex] in the function with [tex]\( \frac{x}{a} \)[/tex]. In this case, [tex]\( a = 3 \).[/tex]

3. Apply the Stretch to the Function: Replace [tex]\( x \)[/tex] with [tex]\( \frac{x}{3} \)[/tex]in the function [tex]\( f(x) \).[/tex]

4. **Write Down the Transformed Function**: The new function after the horizontal stretch will be [tex]\( f\left(\frac{x}{3}\right) \).[/tex]

5. **Choose the Correct Answer**: Look for the choice that represents the transformation [tex]\( f\left(\frac{x}{3}\right) \).[/tex]

The correct transformation that indicates a horizontal stretch by a factor of 3 is:

[tex]\[ f\left(\frac{x}{3}\right) \][/tex]

This means that for any given value of [tex]\( x \)[/tex] in the original function, its corresponding point on the graph will now be three times further away from the y-axis, thus stretching the graph horizontally. If the original function had a point at [tex]\( (x, y) \)[/tex], the new function after the stretch will have a corresponding point at [tex]\( (3x, y) \)[/tex], which means the x-values have been stretched out.

Now, from the options given in the image:

1. [tex]\( h(3x) \)[/tex] represents a horizontal compression by a factor of 3, not a stretch.

2. [tex]\( h\left(\frac{x}{3}\right) \)[/tex] is the correct representation of a horizontal stretch by a factor of 3.

3. [tex]\( h(x) + 3 \)[/tex] represents a vertical shift upwards by 3 units.

4. [tex]\( 3h(x) \)[/tex] represents a vertical stretch by a factor of 3.

Therefore, the correct answer to the question is option (2): [tex]\( h\left(\frac{x}{3}\right) \).[/tex]

Answer:

Step-by-step explanation:

y=mx+b

8=-7m+b

2=0m+b

subtract

6=-7m

-6/7=m

2=0m+b

2=b

y=-6/7x+2

change to standard from

y+6/7x=2

The simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

= 70 -7.7

The expression can be defined as the combination of constants and variables with mathematical operators.

Using the rule of BODMAS

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.

On simplification

= 62.3 [after subtracting 7.7 from 70]

Thus, the simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.

Learn more about the arithmetic operation here:

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Final answer:

To subtract 7.7 from 70, align the decimal points and subtract to find the result is 62.3.

Explanation:

The problem at hand requires us to subtract a decimal number from a whole number. Here's the step-by-step calculation for 70 - 7.7:

Therefore, the subtraction of 7.7 from 70 gives us 62.3.

Answer:

Step-by-step explanation:

The graph of y= -4x² is that of a parabola with vertex at (0, 0) that opens down.

The graph of y= -4x² - 5 is the same, except that it's the result of translating the entire graph of y= -4x² down by 5 units.

Answer:

Step-by-step explanation:

To find how many gallons of seawater contain 2.5 pounds of salt, convert the salt to ounces (40 ounces) and divide by the salinity concentration (1.2 ounces per liter) to get 33.33 liters. Then convert liters to gallons, resulting in approximately 8.8 gallons of seawater.

To solve this problem, we need to convert all units to be compatible and calculate the amount of seawater needed to obtain 2.5 pounds of salt based on the salinity given.

First, we convert 2.5 pounds of salt to ounces because the salinity is given as 1.2 ounces per liter. Since 1 pound is equal to 16 ounces, we have 2.5 pounds * 16 ounces/pound = 40 ounces of salt.

Next, we divide the total ounces of salt by the salinity concentration to find out how many liters of seawater we need:

40 ounces of salt / 1.2 ounces of salt per liter = 33.33 liters of seawater.

Then, we convert liters of seawater to gallons. There are approximately 3.785 liters in a gallon, so:

33.33 liters / 3.785 liters per gallon = 8.8 gallons

Therefore, to the nearest tenth of a gallon, it would take 8.8 gallons of seawater to contain 2.5 pounds of salt.

Answer:

8(3 + 8)

Step-by-step explanation:

Note that 8 is a factor common to both 24 and 64.

Thus, 8(3 + 8) is equivalent to 24 + 64.

Answer is number a

First you find the common factor between 24 and 64 and you factor it out and divide both numbers by it

8(3+8)

Answer:

$451.5

Step-by-step explanation:

For saturdays, Edward will earn 1.5 times the normal (10.50). So saturday hourly pay is 1.5 * 10.5 = $15.75

For sundays, Edward will earn twice the normal (10.50). So sunday hourly pay is 2 * 10.5 = $21

Edward's hours:

Regular 25 hours: 25 * 10.5 = $262.5

Saturday 4 hours: 4 * 15.75 = $63

Sunday 6 hours: 6 * 21 = $126

Total Pay = 262.5 + 63 + 126 = $451.5

Final answer:

Lisa Edwards' total pay for the week is $451.50, which is the sum of her regular pay for 25 hours, time-and-a-half pay for 4 hours on Saturday, and double-time pay for 6 hours on Sunday.

Explanation:

Lisa Edwards' total pay for the week can be calculated by considering her regular hourly wage, her time-and-a-half pay for Saturday, and her double-time pay for Sunday. Her regular hourly rate is $10.50 per hour. For her regular 25 hours of work, she would earn $10.50 x 25 = $262.50.

On Saturday, Lisa earns time-and-a-half. This means she gets $10.50 x 1.5 = $15.75 per hour for 4 hours, which totals to $15.75 x 4 = $63.00.

On Sunday, Lisa earns double-time pay, which amounts to $10.50 x 2 = $21.00 per hour. For 6 hours of work on Sunday, she will earn $21.00 x 6 = $126.00.

To find out Lisa's total weekly pay, add her earnings from all the days: $262.50 (regular hours) + $63.00 (Saturday) + $126.00 (Sunday) = $451.50.

Answer:

109.38

Step-by-step explanation:

Recall the formula for compound interest is as follows:

         A  =  P·(1  +  r/n)nt ,   where

    P = principal amount (initial amount deposited)

     r = annual rate of interest (in decimal form)

     t = # of years amount is deposited for

    n = # of times interest is compounded per year

    A = amount accumulated after t years, including interest

The problem asks how much money Heather will have in the bank by her 16th birthday when she deposited $100 on her 13th birthday in a bank with 3% interest compounded quarterly. From this, we have the following information:

    P = $100

    r = 0.03     ==>     3%/100% = 0.03

    t = 3 years     ==>     16 - 13 = 3

    n = 4     ==>     since there are 12 months per year and 12/4 = 3 months,

                then interest is compounded  every 3 months which is a total of 4 times per year

Therefore,

         A = P(1 + r/n)nt

            = 100(1 + 0.03/4)4·3

            = 100(1 + 0.0075)12

            = 100(1.0075)12

            = 109.38069

            ≈ 109.38

Thus, Heather will have $109.38 in the bank by her 16th birthda

Answer:

[tex]1,715\ in^{2}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> surface area of the enlarged figure

y----> surface area of the original figure

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=7[/tex]

[tex]y=35\ in^{2}[/tex]

substitute

[tex]7^{2}=\frac{x}{35}[/tex]

[tex]x=7^{2}(35)=1,715\ in^{2}[/tex]

Answer:

C. 1/9

Step-by-step explanation:

Blue/Fish

White/Fish

Green/Fish (SELECTED CARD)

Blue/Insect

White/Insect

Green/Insect

Blue/Bird

White/Bird

Green/Bird

There are 9 so the chances of getting one is 1/9.

Answer:

The answer is c

Step-by-step explanation:

Answer:

4/45

Step-by-step explanation:

When you convert 2/10 to 1/5, you get 1/5*4/9. If you multiply the numerator and the denominator, you get 1*4/5*9, which simplifies to 4/45.

Answer:

your answer should be 4/45, if I'm correct.

ANSWER

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

EXPLANATION

[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]

[tex]\sin(x) = \frac{3}{4} [/tex]

This means the opposite side is 3 units and the hypotenuse is 4 units.

We use Pythagoras Theorem to find

[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]

[tex]{ |ZX| }^{2} +9=16[/tex]

[tex]{ |ZX| }^{2} =16 - 9[/tex]

[tex]{ |ZX| }^{2} = 7[/tex]

[tex]{ |ZX| } = \sqrt{7} [/tex]

[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

Final answer:

Given sin(X) = 3/4 in a right-angled triangle XYZ, by using trigonometric identities and the Pythagorean theorem, we find that tan(Y) is 1/3.

Explanation:

In triangle XYZ with angle Z being a right angle (90 degrees or π/2 radians), if we are given that sin(X) = 3/4, we can use trigonometric identities to find tan(Y). Since sin(X) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, we have a side opposite angle X which is 3 units long and a hypotenuse that is 4 units long. From this, we can deduce that the side adjacent to angle X, which is also the side opposite to angle Y, is 1 unit long (using the Pythagorean theorem, as the square of the hypotenuse is equal to the sum of the squares of the other two sides: 3² + 1² = 4²).

Now, to find tan(Y), which is the ratio of the side opposite to Y to the side adjacent to Y, we just take the length of the side opposite to X (which is the same as the side adjacent to Y) and the length of the hypotenuse. Therefore, tan(Y) = opposite side / adjacent side, which in this case is 1/3.

Answer:

I would say the second car.

Step-by-step explanation:

372/15.2 = 24 miles per gallon

198/7.2 = 27.5 miles per gallon

So the answer is the second car is better on gas mileage!

Answer:

Alternate Exterior

Step-by-step explanation:

Answer: A- 6 inches

Step-by-step explanation:

since the triangle has an area of 36in you would reverse the formula of finding the area of a triangle which is bh divided by 2 so i divided 36 by 2 to get 18 then 18 divided by 3= 6

Answer:

B: 12inches

Step-by-step explanation:

Answer:

The perimeter of a shape is the sum of the measurements of all sides. Since a rectangle have equal lengths and widths, you can just add the numbers twice.

So, 15 + 15 + 8 + 8. So the perimeter is 46 cm.

Answer:

E. 46

Step-by-step explanation:

The perimeter of a square or rectangle can be found by using the following formula:

(length + legnth) + (width + width) = perimeter

Our length here is 15 and the width is 8, so substitute the values into the equation.

(15 + 15) + (8 + 8) = perimeter

Now solve

(15 + 15) + (8 + 8)

(30) + (8 + 8)

(30) + (16)

=46

Therefore, the perimeter (and answer) is E. 46

I hope this helps!

Answer: b. borrow $840 for 1 week at an APR 550%, since jimmie will owe less interest this way than with the fee of $90. APEX

The "better" deal is borrowing borrow $840 for 1 week at an APR of 550%

What is APR 550% mean?

The interest on the borrowing amount for one year on the credit card.

Jimmie has a borrowing APR is 550%

One month interest 5.50÷12

                                   ⇒0.4583

For one day =0.4583/30

                      =0.01527

for one week=0.01527*7

                        =0.107

APR for borrowing $840 for 1 week is charged on  purchased amount        =$840*0.107

=$89.8

Borrowing the $840 for 1 week with a fee of $90.

Learn more about APR here:-https://brainly.com/question/24703884

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Answer:

the answer is true im pretty sure i really hope this helps

Step-by-step explanation: