1.2 Prove the identity 1
\(\frac{1}{1 - \sin( \alpha ) } - \frac{1}{1 + \sin( \alpha ) } = \frac{2 \tan( \alpha ) }{ \cos( \alpha ) } \)
​

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

3x - 9 ===> A

x + 13 ===> C

5y ====> B

Step 02:

We must apply the properties of triangles.

x + 13 = 5y eq.1

3x - 9 = x + 13 eq.2

eq .2

3x - 9 = x + 13

3x + x = 13 + 9

4x = 22

x = 22/4 = 11 / 2

eq. 1

x + 13 = 5 y

The answer is:

x = 11 / 2

y = 37 / 10

Answer:

I hope this helps:)

Step-by-step explanation:

Answer:

First line

Step-by-step explanation:

It's an X-intercept line so you're plugging in the number that the dot is on in place of the X in the formula

If the demand for bananas at $2 per pound is 10 pounds, then the suppliers will supply 10 pounds of bananas.

The question is about determining the number of pounds of bananas suppliers will supply at a given price of $2 a pound.

To determine the number of pounds of bananas suppliers will supply, we need more information than just the price of bananas.

Supply is affected by many factors like cost of production, demand, and the price of substitutes.

Suppliers will supply bananas to the market until the price they get equals the cost of production plus a margin.

If the price is higher than the cost of production plus a margin, then they will continue to supply to maximize their profits.

In the given question, we don't have enough information about the cost of production, demand, and substitutes. Therefore, we cannot accurately predict the amount of pounds of bananas that will be supplied.

However, if we assume that the cost of production is constant and there are no substitutes, then the suppliers will supply bananas at a price of $2 per pound until the market reaches equilibrium.

At equilibrium, the quantity supplied equals the quantity demanded.

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Vertex , focus , and directrix of the given equation of parabola

12y = x² -6x +45 are as follow:

Vertex = ( 3, 3)

Focus = ( 3, 6)

Directrix is y =0.

As given in the question,

Given equation of the parabola is:

12y = x² -6x +45

Simplify the equation of parabola to get standard form:

12y = x² - 6x + 9 - 9 + 45

⇒ 12 y = ( x - 3 )² + 36

⇒ 12y - 36 = ( x - 3 )²

⇒ 12( y - 3 ) =  ( x - 3 )²

⇒ ( x - 3 )² = 4(3)(y - 3)

Standard form is :

( x - h )² = 4a ( y - k)

Here h = 3, k = 3 and a = 3

Vertex are ( h , k ) =  ( 3, 3 )

Focus is ( h, k + a) =  ( 3, 6)

Directrix is

   y = k -p

⇒y = 3 - 3

⇒y = 0

Therefore, for the given parabola the vertex is (3,3) , focus is (3,6) and directrix is y = 0.

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1. To convert -21 to 2's complement binary using 6 bits:

- First, convert the absolute value of the number (21) to binary: 10101.

- Then, invert all the bits: 01010.

- Finally, add 1 to the inverted value: 01011.

So, the 6-bit 2's complement binary representation of -21 is 01011.

2. To represent -4 in excess-16 using 5 bits:

- Add the excess value (16) to the absolute value of the number (4): 20.

- Convert 20 to binary: 10100.

So, the 5-bit excess-16 representation of -4 is 10100.

3. To represent -26 in sign-magnitude using 6 bits:

- Convert the absolute value of the number (26) to binary: 11010.

- Set the leftmost bit as the sign bit (1 for negative).

- So, the 6-bit sign-magnitude representation of -26 is 111010.

4. To convert the 6-bit excess-26 binary number (101101) to decimal:

- Subtract the excess value (26) from the binary value: 101101 - 26 = 101075.

- The resulting decimal value is 75.

So, the decimal equivalent of the 6-bit excess-26 binary number 101101 is 75.

5. In IEEE-754 floating-point representation, the exponent is expressed in binary, excess-k. The value of k is determined by the number of bits used for the exponent. Since 7 bits are used for the exponent in this case, the value of k would be 2^(7-1) - 1 = 63. So, an appropriate value for k is 63.

6. In IEEE-754 floating-point representation, the largest positive value that can be represented depends on the number of bits used for the exponent and the fractional mantissa.

Since 3 bits are used for the fractional mantissa and 4 bits are used for the exponent in this case, the largest positive value that can be represented is determined by the maximum exponent value of 2^(4-1) - 1 = 7. Therefore, the largest positive value that can be represented is 2^7 = 128 in decimal (base 10).

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Answer:

$33.75

Step-by-step explanation:

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 13.5%/100 = 0.135 per year,

Put time into years for simplicity,

6 months ÷ 12 months/year = 0.5 years,

then, solving our equation

I = Prt

I = 500 × 0.135 × 0.5 = 33.75

I = $ 33.75

The simple interest accumulated

on a principal of $ 500.00

at a rate of 13.5% per year

for 0.5 years (6 months) is $ 33.75

When a cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, the resulting cross section is an elliptical shape.

To visualize this, imagine a cylinder with circular bases. When a plane intersects the cylinder in a slanted direction, it cuts through the curved surface of the cylinder, creating an elliptical cross section.

The exact shape and size of the elliptical cross section will depend on the angle at which the plane intersects the cylinder and the specific orientation of the cylinder. The major axis of the resulting ellipse will be parallel to the slanted direction of the plane, while the minor axis will be perpendicular to it.

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Answer:

\(\frac{3x^2}{y}\)

Answer:

-5.66 + 4.1

Step-by-step explanation:

Whenever you subtract a negative number, it will change it to adding a positive number.

-5.66 - (-4.1) -> -5.66 + 4.1

Best of Luck!

Answer: -5.66 + 4.1

Step-by-step explanation:

Answer:

AB  = 8

Step-by-step explanation:

Using the similarity theorem of a triangle;

AC/AD = AB/AE

AC = AB + BC and AD = AE + ED

AB + BC/AE + ED = AB/AE

Substitute the given values

AB+12/15 = AB/6

Cross multiply

6(AB+12) = 15AB

6AB + 72 = 15AB

15AB - 6AB = 72

9AB = 72

AB = 72/9

AB = 8

The standard equation of a hyperbola centered at the origin and a vertical tranaverse axis is y²/64 - x²/81 = 1

A hyperbola is a locus of points in such a way that the distance to each focus is a constant greater than one.

The standard equation of a hyperbola centered at the origin and a vertical tranaverse axis is given by

y²/a² - x²/b² = 1

Now, for the given hyperbola, we have that

So, substituting the values of the variables into the equation, we have that

y²/a² - x²/b² = 1

y²/8² - x²/9² = 1

y²/64 - x²/81 = 1

So, the standard equation is y²/64 - x²/81 = 1

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To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).

A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:

So the quadratic function whose zeros are -2 and 9 is:

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The three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means both the A main effect and the B main effect.

What is meant by f-test?

In math, f-test refers to carry out the test for the equality of the two population variances.

Here we need to find in which of the three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means.

As per the definition of f-test, here we know that a two-way ANOVA do you collapse across the levels of the other factor has only two options that is main effect and interaction effect.

As we know that ANOVA separates the within group variance from the between group variance and the F-test is the ratio of the mean squared error between these two groups.

Therefore, in this one, both A and be has the main effect on each other.

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Answer: 840.  it won’t let me add my answer there has to be 20 letters so yea I’m just typing this but the answer 840.

Answer:840

Step-by-step explanation: trust me :)

Answer:

x=4.5

y=5.75

Step-by-step explanation:

since you dont have much time to wait, i wont put an explanation here

Answer:

1/2 =0.5

1/2+0i=io+1/2

1/2i=1/2i

1+2i

=1+2i

Step-by-step explanation:

The option 1/2+0i is the correct answer.

"Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called iota".

For the given situation,

The real number is 1/2.

The complex number is of the form, a + ib

On setting b = 0, we can write the real number as a complex number.

Thus the real number \(\frac{1}{2}\) becomes as a complex number

\(a+ib=\)  \(\frac{1}{2} + 0i\)

Hence we can conclude that the option 1/2+0i is the correct answer.

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The given question is incomplete as it does not provide the measurements for the time it takes to complete 5 rotations.

In order to provide a meaningful answer, we need the actual measurements for the time it takes to complete 5 rotations. Without the measurements, it is not possible to analyze the data or draw any conclusions regarding the time taken.

Once the measurements are available, they can be used to calculate the average time taken for 5 rotations. This can be done by summing up the individual measurements and dividing by the number of measurements taken. The average will provide an estimate of the typical time taken for 5 rotations.

Additionally, other statistical measures such as the standard deviation can be calculated to assess the variability or consistency of the measurements. A smaller standard deviation indicates less variability and a higher level of consistency in the time taken for 5 rotations.

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Answer:

a) 5² × 2³ × 3

b) 150

Step-by-step explanation:

HCF of 600 and 1050 = 150

5×5×2×3

The two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

We are given that a study of a very large number of pregnant women in Arkansas reports that the women gained, on average, 14 pounds during their pregnancy and that 18% of the women smoked.

Now, we need to tell the two variables of the study.

Now, we can see that the independent variable is pregnant women.

Also, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

Therefore, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

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Answer:

The answer is 6

Step-by-step explanation:

Why is it 6? because surface means like the total faces it has.

The log equation, log(x+1) (4x) = 67, written as an exponential equation is (x + 1)(4x) = 10⁶⁷

From the question, we are to write the given logarithmic equation as an exponential equation.

The given log equation is:

log(x+1) (4x) = 67

To convert this to an exponential equation, we can use the definition of logarithms, which states that:

log(base b) (y) = x is equivalent to y = b^x

That is,

log (x)(y) = n  ⇒ (x)(y) = 10ⁿ

Applying this definition to the given equation, we get:

(x + 1)(4x) = 10⁶⁷

This is the exponential equation equivalent to the given logarithmic equation.

Hence, the exponential equation is (x + 1)(4x) = 10⁶⁷

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Answer:

There are no questions attached.

Step-by-step explanation:

The triangle congruence theorem that proves triangle KLM and XYZ are congruent is the AAS Congruence Theorem.

The AAS (Angle-Angle-Side) Congruence Theorem states that if two triangles have two corresponding angles and a corresponding side that are congruent, then the triangles are congruent.

By observation, the angle L corresponds to the angle Y, and the angle M corresponds to the angle Z, Also the side KM corresponds to the side XM.

In conclusion, the congruence theorem that proves triangle KLM and XYZ are congruent is the AAS Congruence Theorem.

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Answer:

$225

Step-by-step explanation:

Given that:

Principal = $6,000

Interest rate = 5%

Time = 1 year

Taxes paid = 25% on the interest earned

To find:

Money earned after paying taxes ?

Solution:

First of all, let us calculate the total interest earned:

Formula for Simple Interest is given as:

\(SI =\dfrac{PRT}{100}\)

Where P is the principal

R is the rate of interest

T is the time taken

Putting the given values:

\(SI =\dfrac{6000 \times 5\times 1}{100} =\$300\)

Now, it is given that 25% of the interest earned is given as taxes.

Taxes paid = 25% of $300

\(\Rightarrow \dfrac{25}{100} \times 300 =\$75\)

Therefore, the money earned = Interest earned - Taxes paid

The money earned = $300 - $75 = $225

Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

Step-by-step explanation:

5. x <= -1/4 or x > 3

6. x <= -6 or x > 1

7. -5y <= 10-x

y > = 1/5x -2 (you reverse inequality when dividing by a negative number)