Three pieces of wood are cut from a plank 1 metre long.
Each piece is 30 cm long.
How long is the piece left over

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{1}) \\\\\\ y-5=2x-2\implies {\Large \begin{array}{llll} y=2x+3 \end{array}}[/tex]

The value of x in the equation x - 3(x - 3 + x + 1) = 6(6 + 15) is -24

From the question, we have the following parameters that can be used in our computation:

x-3(x-3+x+1)=6(6+15)

Express properly

So, we have

x - 3(x - 3 + x + 1) = 6(6 + 15)

Evaluate tje like terms

This gives

x - 3(2x - 2) = 126

Open the brackets

x - 6x + 6 = 126

So, we have

-5x = 120

Divide

x = -24

Hence the value of x is -24

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Answer:

6 + 13i – (7 – 15i)

= 6 + 13i - 7 + 15i (distribute the negative sign)

= -1 + 28i (combine like terms)

Therefore, the answer is -1 + 28i in the form of a + bi.

Step-by-step explanation:

The Volume of a cone is,

⇒ V = 50π units³

We have to given that;

In a cone,

Diameter = 10 feet

Height = 6 feet

Hence, Radius of cone,

r = 10/2 = 5 feet

Since, Volume of cone is,

V = 1/3 (πr²h)

V = 1/3 (π × 5² × 6)

V = 50π units³

Thus, The Volume of a cone is,

⇒ V = 50π units³

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Since the graph of F(x), has the same shape as the graph of G(x) = x³ - x², but it is shifted to the left 1 unit, its equation is: B. F(x) = (x + 1)³ - (x + 1)²

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have the following transformation:

(x, y)                               →                  (x - 1, y)

G(x) = x³ - x²                  →        F(x) = (x + 1)³ - (x + 1)²

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Complete Question:

The graph of F(x), shown below, has the same shape as the graph of G(x) = x³ - x², but it is shifted to the left 1 unit. What is its equation?

F(x) =

OA. F(x) = (x-1)3³ -(x-1)²

B. F(x) = (x + 1)³ - (x + 1)²

C. F(x)=x²-x²-1

O D. F(x)=x²-x²+1

The solution is, the angles of the right triangle are approximately:

A = 12° 33'

B ≈ 1.03°

C ≈ 76° 27'

We are given angle A = 12° 33' and side c = 283 ft. Let's first find angle C using the sine ratio:

sin C = opposite / hypotenuse

sin C = a / c

a = c * sin C

Using a calculator:

sin C = sin(90° - A) ≈ 0.996

a ≈ 282.95 ft

Therefore, we have side a ≈ 282.95 ft. To find the remaining side b, we can use the Pythagorean theorem:

b² = c² - a²

b² = (283 ft)² - (282.95 ft)²

b ≈ 0.79 ft

(Note that we may have some rounding error in the last digit due to using approximate values for a and c, but it should be insignificant.)

Now let's find the angles:

Angle B = 90° - A ≈ 77° 27'

Using the sine ratio again:

sin B = opposite / hypotenuse

sin B = b / c

B ≈ 1.03°

(Note that we may have some rounding error here due to using an approximate value for b, but it should be insignificant compared to the precision of the given angles.)

Therefore, the angles of the right triangle are approximately:

A = 12° 33'

B ≈ 1.03°

C ≈ 76° 27'

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A variable with equal distances between score units and a true meaningful zero is called a ratio variable.

Ratio variables have the properties of interval variables, meaning that the distances between consecutive values are consistent, and they also have an absolute zero point. The true zero allows for meaningful ratios to be calculated between values. For example, if we have a variable representing weight, a value of 0 indicates the absence of weight, and we can make meaningful statements such as "one object is twice as heavy as another."

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When x = 8, 26 is the right answer.

We have to given that;

A team in a group trivia game receives 5 points for a right response and -2 points for an incorrect one.

In addition, the game has 15 questions.

Since, We know that;

According to the definition of a mathematical expression, it is a grouping of variables and functions that are created using addition, subtraction, multiplication, and division.

Now, We have find the expression as;

For a team, the correct answer is worth 5 points, and the incorrect response is worth -2 points.

In addition, the game has 15 questions.

Hence, We get;

⇒ 5x - 2 (15 - x)

At x = 8;

⇒ 5 × 8 - 2 (15 - 8)

⇒ 40 - 2 × 7

⇒ 40 - 14

⇒ 26

Thus, The correct solution when x = 8 is,

⇒ 26

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The sum of the given expression from n = 3 to 7 is 241.

The given expression is to be evaluated from n = 3 to 7.  The given expression is,begin{align*}\sum_{n=3}^{7} (n^2 + 2n)\end{align*}Now, we can substitute the values of n and add them up to evaluate the expression. So, the sum of the expression is, \begin{align*}\sum_{n=3}^{7} (n^2 + 2n) &= (3^2 + 2 \cdot 3) + (4^2 + 2 \cdot 4) + (5^2 + 2 \cdot 5) \\&\qquad+ (6^2 + 2 \cdot 6) + (7^2 + 2 \cdot 7)\\&= 9 + 20 + 35 + 72 + 105\\&= \boxed{241}.\end{align*}.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

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The value of the original price is, $1,029

We have to given that;

At a sale this week a desk is being sold for $247 this is a 24% discount from the original price.

Let us assume that, the original price is x

Hence, we can formulate;

24% of x = 247

Solve for x;

24/100 × x = 247

24x = 24700

x = 24700/24

x = 1,029

Thus, The value of the original price is, $1,029

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Answer:

an=a1rn−1 a n = a 1 r n - 1

Step-by-step explanation:

multiplying the previous term in the sequence by 2 gives the next term

I hope this helps...

Have a nice day<3

In a time-series graph, the horizontal axis is marked off in units of time, such as days, months, quarters, or years. The time intervals between the marks on the horizontal axis are usually equal, which allows the graph to show changes in the variable being measured over time.

The vertical axis of the graph shows the values of the variable being measured, and the line or curve connecting the points on the graph represents the trend of the data over time. Time-series graphs are often used to visualize patterns and trends in economic, financial, and other types of data that vary over time.

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[tex]A(x)=4x^2-5x-3x^3+6[/tex]    and   [tex]B(x)=3x^3-5x-4+6x^2[/tex]. Sort the polynomial A(x), B(x) according to the decreasing power of the variable. The final solution for N(x) is;

  [tex]N(x)=10x^2-10x+2[/tex]

To type the polynomials A(x) and B(x) in line with the lowering energy of the variable, we want to arrange the phrases in order that the highest diploma term comes first, observed with the aid of the next maximum diploma time period, and so forth. We also want to mix any like phrases which have identical diplomas. For example, A(x) has two terms with degree 2, so we will upload them collectively. Here is how we kind A(x) and B(x):

[tex]A(x) = -3x^3 + 4x^2 - 5x + 6[/tex]

[tex]B(x)=3x^3+6x^2-5x-4[/tex]

To calculate N(x) = A(x) + B(x), we want to feature the corresponding phrases of A(x) and B(x) which have an equal degree. For example, to locate the coefficient of [tex]x^3[/tex] in N(x), we want to add the coefficients of x^three in A(x) and B(x), which might be -3 and +3 respectively. Here is how we calculate N(x):

[tex]N(x)=(-3+3)x^3+(4+6)x^2+(-5-5)x+(6-4)[/tex]

[tex]N(x)=10x^2-10x+2[/tex]

This is the final solution for N(x).

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∠FGK and ∠FGH are the pairs of non-overlapping angles that share a ray to make a right angle. option C

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

In the given figure, we need to find the pairs of non-overlapping angles that share a ray to make a right angle.

We can see that ∠EGF and ∠HGF make a right angle but line FG is overlapping or common in both the angles.

∠FGK and ∠FGH make a right angle and pairs of non-overlapping angles.

So, this is the correct pair for the condition.

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Answer:

A

Step-by-step explanation:

Range = Highest value - Lowest value

At Park Zoo:

R = 44 - 38

= 6

At Countryside Zoo;

R = 45 - 38

= 7

So, it cannot be D, because the ranges are not the same and it cannot be B because the range is greater at countryside zoo

The mode is the value that appears the moat frequently.

At Park zoo, the mode is 41 since it has the most dots.

At Countryside zoo, the mode is 40, since it has the most dots

So, it cannot be C because Park zoo has a greater Mode.

so, the only answer is A

Answer:

90 square feet

Step-by-step explanation:

area of rectangle = 12 X 30 = 360 square feet

look at the green triangle in top left. it has area 0.5 X (12 - 3) X (30)

= 0.5 X 9 X 30 = 135

area of other green triangle is equal (they are congruent)

so, the area of the path is 360 - 2 (135) = 360 - 270 = 90 square feet

A clockwise rotation about the origin preserves distance, a dilation of 3/5 Preserves angle measures, a reflection in the y-axis and dilation of 3  angle measures and a translation down 2 units and right 4 units Preserves distance and angle measures.

A clockwise rotation about the origin:

Preserves distance, but not angle measures.

A dilation of 3/5:

Preserves angle measures, but not distance.

A reflection in the y-axis and dilation of 3:

Preserves angle measures, but not distance.

A translation down 2 units and right 4 units:

Preserves distance and angle measures.

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Answer: System

Step-by-step explanation:

The question defined a system.

For future reference

Temperature is a measure of the average kinetic energy of molecules

Potential Energy is a measure of how much energy can be turned into kinetic energy (think a ball about to be dropped)

Matter is a term for stuff, everything is made of matter, atoms and molecules

Kinetic energy is energy in motion (think a falling object)

States are the position or form things are in, this is probably going to be used as "states of matter" (solids, liquids, gasses)

Conduction is the transfer of heat or electricity through two objects touching

Energy is "the ability to do work" think of energy like a general term for potential and kinetic energy, undefined if you ill

Hope this helps

The area of the figure E in terms of x  is x² + 2xy + y²

The figure is added as an attachment

The dimensions of the figures are

A = x by x

B = x by y

C = y by y

D = x by y

So, we have

Area of A = x²

Area of B = xy

Area of C = y²

Area of D = xy

This means that the area of E is

E = x² + 2xy + y²

From the above, we can see that the expression has 3 terms

Also, we have the coefficient of x² to be 1 and the coefficient of x to be 2y

The degree of the expression is 2

This is because the highest power is 2

The name of the algebraic expression is a sum of squares

Lastly, we have

x = 3 and y = 2

This means that

Area = 3² + 2 * 3 * 2 + 2²

Evaluate

Area = 25

Hence, the value of the expression is 25

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Answer: B. Food

Step-by-step explanation:

Hello,

kᵃ x kᵇ = kᵃ⁺ᵇ

kᵃ ÷ kᵇ = kᵃ⁻ᵇ

7⁹/7² x 7⁹

= 7⁹⁻² x 7⁹

= 7⁷ x 7⁹

= 7⁷⁺⁹

= 7¹⁶

Answer: D

Step-by-step explanation:

If u know that the total is 423, u can narrow the options down. They mention the variables with each food. Substitute and find the answer. Hope it helps!

Answer:

3/10

Their favourite is pizza

Step-by-step explanation:

30% = 30/100

simplified is 3/10

Answer:

3/10

Step-by-step explanation:

1. 30%=3/10

2. The schools favorite lunch is pizza

The distance between you and your friend is 61.8 feet.

You let 52 feet of string on your kite. Your friend is standing in an unknown distance from you, with the kite flying on air somewhere between you two. From your friend the angle of elevation is 70 degrees. The angle formed at the kite is 64 degrees.

Therefore, the distance between you and your friend can be calculated as follows:

The situation forms a triangle. The distance between them can be found using sine law.

Hence,

a / sin A = b / sin B = c / sin C

Therefore,

52 / sin 70 = b / sin 64

where

Therefore,

52 / sin 70 = b / sin 64

cross multiply

52 sin 64 = b sin 70

b = 52 sin 64 / sin 70

b = 47.8413539862 / 0.77389068155

b = 61.8175709726

b = 61.8 feet

Therefore,

distance between them = 61.8 feet

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Answer:

Step-by-step explanation:

You want the solutions to various problems involving ratios, proportions, and scale factors.

The ratio of 15 apples ot 25 oranges can be written several ways, with and without units:

  15 apples to 25 oranges, or 15 to 25.

  Reduced to 3 apples to 25 oranges, or 3 to 5

  15 apples : 25 oranges, or 15 : 25

  Reduced to 3 apples : 5 oranges, or 3 : 5

  15 apples / 25 oranges, or 15/25

  Reduced to 3 apples / (5 oranges), or 3/5

You can solve the proportion ...

  x/9 = 10/12

by multiplying both sides by 9:

  x = 9·10/12 = 90/12

  x = 15/2 = 7.5

If each inch represents 12 ft, then 8 inches represents 8·12 ft = 96 ft.

The actual length of the back wall is 96 feet.

#95141404393

The most appropriate answer would be option a) "Confounding is likely to be a problem in the interpretation of these results."

Now, let's consider the 95% confidence interval (CI) provided as (0.8, 3.8). A confidence interval is a range of values within which the true population parameter (in this case, the risk ratio) is likely to fall. The lower and upper bounds of the confidence interval in this case are 0.8 and 3.8, respectively.

Confounding refers to the presence of an extraneous factor that is associated with both the exposure and the outcome and can distort the observed association.

In this situation, since the confidence interval includes the null value of 1 (i.e., 1 is within the range), it suggests that the observed association may not be statistically significant.

A statistically significant result means that the observed association is unlikely to have occurred due to chance alone.

Therefore, option a) "Confounding is likely to be a problem in the interpretation of these results" is a reasonable conclusion.

Hence the correct option is (a).

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Complete Question:

What can be said about the situation in a cohort study reporting an adjusted risk ratio of 2.5, with a 95% confidence interval of (0.8, 3.8)

a) Confounding is likely to be a problem in the interpretation of these results,

b) This estimate had a P value that was at or below 0.05.

c) There is a clear and strong association between the exposure and the health outcome understudy.

d) None of the above.

Answer:

Step-by-step explanation:

Evaluating the expression gives:

Therefore, the value of the expression is 1536.

1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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Answer:

gradient = - 2 , y- intercept = 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope (gradient) and c the y- intercept )

given

2x + y = 1 ( subtract 2x from both sides )

y = - 2x + 1 ← in slope- intercept form

with gradient m = - 2 and y- intercept c = 1

Answer:

23

Also correct 7.32pi

Step-by-step explanation: