ABC is a straight line. The length of AB is four times the length of BC. AC = 75cm
Work out the length of AB. Thanks, I'm so bad at math :)

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer:

8.5

Step-by-step explanation:

First we need to get BC using the pythagoras theorem

BC² = AC² + AB²

BC² = 8² + 15²

BC² = 64+225

BC² = 289

BC = √289

BC = 17

DB = 1/2BC

DB = 1/2 * 17

DB = 8.5

Hence the length of DB is 8.5

Answer:

x=12°

Step-by-step explanation:

(7x-16)°=(x+8)°=4x

first, take everything out of the parenthesis

7x-16=x+8=4x

now combine like terms

7x-x-4x=16+8

2x=24

divide both sides by 2

x=12

Answer: 5.175

Step-by-step explanation: 18 - 9.7 - 3 1/8 = 5.175

Answer:

20%

Step-by-step explanation:

There is a 20% chance you get selected for researching China because 5 out of 25 spaces are ones for researching China.

\(\frac{5}{25} =\frac{20}{100}\)

Answer:

34 5/8 inches

Step-by-step explanation:

Let the two strips be fabric A and fabric B

Fabric A= 14 3/4 inches

Fabric B = 20 7/8 inches

To form one length, the strips are sown together using 1/2 inch

Length after sewing=

Fabric A - 1/2 inch

= 14 3/4 inches - 1/2 inch

= 59/4 - 1/2

= 59-2 /4

= 57/4 inches

Length after sewing=

Fabric B - 1/2 inch

= 20 7/8 inches - 1/2 inch

= 167/8 - 1/2

= 167-4 /8

= 163/8 inches

Final length of the fabric after two strips are sewn together

= 57/4 inches + 163/8 inches

= 114+163 /8

= 277/8

= 34 5/8 inches

Final length of the fabric after two strips are sewn together= 34 5/8 inches

Answer:

1/3

Step-by-step explanation:

I assume that 2/5 and -7/5 are exponents.

3^(2/5) × 3^(-7/5) = 3^(2/5 + (-7/5)) = 3^(-5/5) = 3^(-1) = 1/3

Answer: 136/5

Step-by-step explanation: First simplify the fraction

1) 3 2/5 = 17/5

3 multiply by 5 and add 5 into it.

2) 3(-7/5) = 8/5

3 multiply by 5 and add _7 in it.

By multiplication of 2 fractions,

17/5 multiply 8/5 = 136/5

=136/5

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The accounting equation is a fundamental principle in accounting that states that assets equal liabilities plus equity. Using this equation, missing amounts can be determined in various situations.

The accounting equation is expressed as Assets = Liabilities + Equity. It serves as the foundation for double-entry bookkeeping and ensures that the financial statements are balanced. By rearranging the equation, missing amounts can be determined.

For example, if the assets and equity are given, the missing amount of liabilities can be calculated by subtracting equity from assets. Conversely, if the liabilities and equity are known, the missing amount of assets can be calculated by adding liabilities to equity.

Similarly, if the assets and liabilities are provided, the missing amount of equity can be calculated by subtracting liabilities from assets. Alternatively, if the assets and equity are known, the missing amount of liabilities can be calculated by subtracting equity from assets.

In each situation, the missing amount can be determined by applying the accounting equation and rearranging it to solve for the missing variable. This equation provides a framework for ensuring that all financial transactions are properly recorded and that the financial statements accurately reflect the financial position of a business.

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The more consistent the results given by repeated measurements, the higher the precision of the measurement procedure.

Precision refers to the degree of agreement or reproducibility among multiple measurements of the same quantity. When repeated measurements yield similar results with little variation, it indicates a high precision. This suggests that the measurement procedure has a low level of random error or uncertainty.

Precise measurements are valuable because they provide reliable and consistent information about the quantity being measured, allowing for more accurate comparisons, analyses, and conclusions. Precision is an important characteristic of any measurement procedure to ensure the reliability and validity of the obtained data.

Therefore, the more consistent the results given by repeated measurements, the higher the precision of the measurement procedure.

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The graph shows the relationship between the number of students who attend a homecoming dance and the amount of money raised. The graph is a straight line with a slope of $10, passing through the point (0, $80) and another point on the line. The fixed cost for decorations is $80, which is a constant cost that does not depend on the number of students attending the dance. For each additional student that attends the dance, the amount of money raised will increase by $10.

Answer:

y = 10x - 80

Therefore your answer is B, hope this helps! :)

The overall shape of the distribution is normal.

If the overall shape of the combined distribution for both the class samples and the simulation samples was normal, then it suggests that the individual distributions of the samples were either normally distributed or approximately normally distributed.

A normal distribution, also known as a Gaussian distribution or a bell curve, is a probability distribution that is symmetric and bell-shaped. The normal distribution is commonly used in statistical analysis and modeling because it is often observed in real-world data and has some desirable properties.

When the individual distributions of the samples are combined, their values are added up or averaged, resulting in a larger sample size and a more representative estimate of the underlying distribution. If the individual distributions are normally distributed, then the central limit theorem states that the combined distribution will tend towards normality as the sample size increases. This can explain why the overall shape of the combined distribution for both the class samples and the simulation samples was normal.

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40

First you multiply 50 and 0.30 to get 15 then you add 25 and 15 to get 40.

A. Emma; Bob. Emma has a comparative advantage in milkshakes, while Bob does not have a comparative advantage in either milkshakes or ice cream sundaes. Emma also has an absolute advantage in both goods.

Comparative advantage refers to the ability to produce a good or service at a lower opportunity cost compared to another producer. In this case, Emma can produce 17 milkshakes in the same time it takes her to produce 102 ice cream sundaes. On the other hand, Bob can only produce 6 milkshakes in the same time it takes him to produce 30 ice cream sundaes. Emma's opportunity cost of producing milkshakes is lower than Bob's, indicating that she has a comparative advantage in milkshakes.

Additionally, Emma has an absolute advantage in both milkshakes and ice cream sundaes. She can produce more milkshakes (17) than Bob (6) in the same time period. Similarly, she can produce more ice cream sundaes (102) than Bob (30) in an hour. Absolute advantage refers to the ability to produce more of a good or service using the same amount of resources or the ability to produce the same amount using fewer resources. Therefore, based on the given information, the correct answer is A. Emma; Bob.

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Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Answer: the slope=0

Step-by-step explanation:

\(\displaystyle\\(-6,4)\ \ \ \ \ (-15,4)\\\\\boxed {The\ slope=\frac{y_2-y_1}{x_2-y_1} }\\\\The\ slope=\frac{4-4}{-15-(-6)} \\The\ slope=\frac{0}{-15+6} \\\\The\ slope=0\)

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

\(\sf\longrightarrow 5^{x -2}= 8 \)

Take log on both sides with base as " 10" . We have ,

\(\sf\longrightarrow log_{10} 5^{x-2}= log_{10}\ 8\)

Simplify using the property of log , \(\sf log a^m = m log a \) , we have ,

\(\sf\longrightarrow ( x -2) log_{10} 5 = log_{10} 8 \)

Simplify ,

\(\sf\longrightarrow ( x -2 ) log_{10}5 = log_{10} 2^3\)

Again simplify using the property of log ,

\(\sf\longrightarrow (x-2) log 5 = 3 log 2\)

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

\(\sf\longrightarrow ( x - 2 ) = \dfrac{ 3\times 0.301}{0.69}\)

Simplify the RHS ,

\(\sf\longrightarrow x - 2 = 1.30 \)

Add 2 both sides ,

\(\sf\longrightarrow \boxed{\blue{\sf x = 3.30}}\)

Hence the Value of x is 3.30 .

Answer:

its actually 3.292 because we round to the nearest thousandth and thats not even the equation you use above

Step-by-step explanation:

For this equation we use the formula log a^m=m (log a) so the equation will be written as log 5 (5^x-2) = log 5 (8). You use the base, which is 5, and use log to base 5 on both sides of the equation. Then you take the exponent " x-2" and write( x-2) log 5 (5) = log 5(8). Since log a =1, you multiply that 1 by x-2, which keeps it x-2. Making the equation x-2 = log 5 (8). Next, we use the change of the base properties with the formula log b^y= log y/ log b. The equation will be written as x-2 = log 8/ log 5, since 5 is the base it stays in the bottom or basement. We then add +2 to both sides of x-2 and log 8/ log 5. To solve this equation, you can find out what log 8 and log 5 are and divide those and add +2 to solve. So log 8 = 0.903 and log 5 = 0.698970 and divide those to get 1.29190 +2 and you get the answer rounded as 3.292. 

Step-by-step explanation:

what can go in

both numbers

2,4,8

let use 8 since u said to the simplest form

48÷8=6

16÷8=2

therefore, 6:2

According to the information we can infer that the greater area is the striped region.

To calculate what is the greater area we have to calculate the area of each segment of the target. Fist we can calculate the area of the striped region.

Then we have to calculate the area of the shaded region with the following procedure:

According to the above, the striped area has the greater area.

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The equation for the polynomial graphed is:

y = (x + 1)*(x + 1)*(x - 1)*(x - 2)

Remember that for a polynomial whose zeros are at the values (x₁, x₂, ...) and the leading coefficient is a, the equation will be:

f(x) = a*(x - x₁)*(x - x₂)*...

Here we can see that the leading coefficient is a = 1, and we can see that the zeros of the function are at:

x = -1   (with a multiplicity of 2, because it is a vertex)

x = 1

x = 2

Then the zeros are {-1, -1, 1, 2}

And the polynomial is:

y = (x + 1)*(x + 1)*(x - 1)*(x - 2)

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Gender is the independent variable (IV) and Galvanic Skin Response (GSR) is the dependent variable (DV). This means that you are investigating how differences in gender might affect the GSR.

So, the correct is A. Gender: GSR

Gender, as the IV, refers to the classification of individuals as male, female, or other, while GSR, as the DV, is a physiological measure of emotional arousal, often used in psychological research.

By examining the relationship between these two variables, you aim to determine whether variations in gender have any impact on GSR levels.

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Answer:

Easy

Step-by-step explanation:

-19-9=-28

-28/-4=7

thus x=7

Answer:

your answer would be a whole number, so your answer would be 1,000 i think.

this should be the answer because if you multiply

9*1000 you get  9000

if you multiply

25 * 1000 you get 25000

so on and so on

Step-by-step explanation:

hope this helps :)

Answer:

x=3/4

Step-by-step explanation:

Look at the picture so you understand how To solve it.

The data set in discuss which contains three points and two of the residuals are 7 and -3 would have its third residual as; -4.

According.tinthe task content, the data set in discuss has three points and consequently should have three residuals.

Additionally, two of the three residuals have been given and on this note, it follows that the third residual must have a value such that the algebraic sum of all residuals is 0.

Hence, we have; -3 + 7 +x = 0;

x = 3-7 = 4.

Ultimately, the third residual is; -4.

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Avani sold 190 pencils in the given period.

Let's anticipate that Avani sold x pencils within the given duration.

Now we can form an linear equation based on the given facts:

Right here, 2(45) represents the total earnings earned through selling 45 pens. solving this equation for x, we get:

Consequently, Avani sold 190 pencils in the given period.

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The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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Answer:

i think its 1/16

Step-by-step explanation: