Solve (x-2)^2-3=1 graphically then use algebraic strategies to solve the equation and verify that your graphical solutions are correct.

Answer:

3.6 m

Step-by-step explanation:

[tex] \frac{3}{15} = \frac{h}{18} [/tex]

[tex]15h = 54[/tex]

[tex]h = \frac{18}{5} = 3.6[/tex]

Answer:

3.6 meters.

Step-by-step explanation:

We can use the concept of similar triangles to solve this problem. The ratio of the height of the first tree to its shadow length is the same as the ratio of the height of the second tree to its shadow length.

Let h1 be the height of the first tree, s1 be its shadow length, h2 be the height of the second tree, and s2 be its shadow length.

For the first tree: h1/s1 = 3/15

For the second tree: h2/18 = 3/15

Solving for h2:

h2 = (18 * 3) / 15 = 3.6 meters

Therefore, the height of the second tree is 3.6 meters.

Using curves, we can find that the value of y at the indicated point on the curve is √3.

What is the definition of curves?

A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.

Here in the question,

Given equation:

x = y² - 2

As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:

1 = y² - 2.

Adding 2 on both sides:

1 + 2 = y² - 2 + 2

⇒ 3 = y²

⇒ y = √3.

Therefore, the value of y at the indicated point on the curve is √3.

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The slope of the equation is 1/2 and the y-intercept is -5.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

Step 1:

The relationship between x and y can be expressed as:

y = (1/2)x - 5

This equation says that y is equal to half of x, with 5 subtracted from that value.

Step 2:

To graph this equation using the slope-intercept form (y = mx + b), we can identify the slope and y-intercept.

The slope of the equation is 1/2, which means that for every increase of 1 unit in x, y increases by 1/2 unit.

The y-intercept is -5, which is the point where the line crosses the y-axis.

To graph the equation, we can start by plotting the y-intercept, which is the point (0, -5).

Next, we can use the slope to find another point on the line. Since the slope is 1/2, we can move up 1 unit and right 2 units (since the slope is rise over run, or change in y over change in x). This gives us the point (2, -4).

We can now draw a line that connects these two points, which represents the relationship between x and y.

The two points are:

(0, -5)

(2, -4)

The graph of the equation is in the attached image.

Hence, The slope of the equation is 1/2 and the y-intercept is -5.

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Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd

The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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1. The value of x and y are 16 and 8√3 respectively.

2. The value of x and y are 8 and 8√2 respectively.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

1. therefore;

tan 30 = 8/y

1/√3 = 8/y

y = 8√3

sin 30 = opp/hyp

1/2 = 8/x

x = 8×2 = 16

2. x = 8( isosceles triangle)

cos 45 = 8/y

1/√2 = 8/y

y = 8√2

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The company should charge $227.50 for the 2 year extended warranty to break even.

What is expected cost?

Expected cost is a statistical measure that represents the average cost that is expected to be incurred over a period of time, taking into account the probability of different outcomes and their associated costs.

Let's call the price the company should charge for the 2 year extended warranty "x". To break even, the expected value of the extended warranty should be equal to the expected cost of replacing failed products.

The probability of a product failing within the 2 year extended warranty period is (1 - 0.09) = 0.91 (since 9% are expected to fail after the original warranty period). If a product fails within the 2 year period, the replacement cost is $250.

So the expected cost of replacing a failed product is:

0.91 * $250 = $227.50

To break even, the expected value of the extended warranty should be equal to the expected cost of replacing failed products:

x * 1.0 = $227.50

Therefore, the company should charge $227.50 for the 2 year extended warranty to break even.

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Answer:The diagram shows the market demand and supply curves for the bread market. You know that there are 250 identical bakeries operating in the market

Step-by-step explanation:

Answer:

1. (a-1)(a-2)

2. (b+1)(b+3)

3. (c+1)(c+5)

4. (x+1)(x+7)

5. (y+1)(y+9)

6. (r+1)(r+11)

7. (m+1)(m+4)

8. (a-1)(a-7)

9. (x-1)(x-11)

10. (x+1)(x+10)

11. (t-6)(t-12)

12. (r-6)(r-10)

13. (z-10)^2

14. (y+5)(y-1)

15. (b-4)(b+2)

16. (x-8)(x+5)

17.  (2x-1)(x-2)

18. (3x+1)(x+3)

19. (2x+1)(x+5)

20. (2x+3)(x+2)

The number of packs of peanut m&m's did they sell that day is 378 packs.

The distance traveled by the plane is 1,008 miles.

The time taken by the plane is 7.78 hours.

Let

Number of peanut sold = x

Ratio of peanut to plain

7 : 10 = x : 540

7/10 = x/540

7 × 540 = x × 10

3,780 = 10x

divide both sides by 10

x = 3,780 / 10

x = 378

When t = 2.8 hours

d = 360t

d = 360(2.8)

d = 1,008 miles

Therefore, the time taken for the plane to fly 2800 miles is;

d = 360t

2800 = 360t

divide both sides by 360

t = 2,800/360

t = 7.78 hours

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Answer:

circumference of a circle is

[tex]2\pi\:r[/tex]

And the area of the circle is

[tex]\pi \: r {}^{2} [/tex]

The proof that AE is tangent to circle C is given below:

The angle addition postulate is a fundamental concept in geometry that states that the measure of an angle formed by two adjacent angles can be obtained by adding the measures of the two angles.

More specifically, given two adjacent angles with measures A and B, the measure of the angle formed by the two adjacent angles (denoted as AOB) can be found by adding the measures of the two angles:

A + B = AOB

This postulate is often used in geometric proofs and can be applied to any adjacent angles, including those formed by intersecting lines, parallel lines, or polygons.

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The correct answer will be option D. Y intercept will be greater and X will be less.

A "coordinate system" is a mathematical framework that uses a set of coordinates to identify points in space or on a surface. It describes the location of a point in relation to a reference point or origin, often using numerical values. A coordinate system is made up of one or more axes, which are imaginary lines that cross at the origin, and units of measurement that run along each axis.

When the trucking firm starts paying a driver 0.25 cents per mile, it raises their operational expenditures, which has a direct influence on their profit (Y-axis). As a result, the Y-intercept (the point at which the profit crosses the Y-axis) will be larger since the company's costs will be bigger.

The X-axis, on the other side, displays the distance travelled by the vehicle. Because the corporation is now paying for a driver, it may decide to decrease the amount of kilometres the truck goes to save money. This indicates that the X-axis will be shorter, suggesting that the truck will drive fewer miles than previously.

As a result of the modification, the Y-intercept will be higher (showing higher costs) and the X-axis will be lower (meaning less kilometres travelled).

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The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

Two ratios are said to be equal when a proportion is stated. Ratios, which can be written as a fraction or a colon, are used to compare two objects or values. For instance, a class might have a boy to girl ratio of 2:3 or 2/3. A percentage is an equation proving the equality of two ratios. The formula is a/b = c/d, where a, b, c, and d are all numerical values or variables. Numerous branches of mathematics, science, and daily life, including banking, engineering, and cookery, require proportions.

Given that, it takes the principal 30 seconds to sign 4 diplomas.

Setting the proportion we have:

30 seconds / 4 diplomas = x seconds / y diplomas

x = 7.5y

Substituting the values of x and y from the table we have:

For y = 12

x = 7.5(2) = 90

Similarly, for y = 20:

x = 7.5(20) = 150

For x = 210:

210 = 7.5y

y = 28

The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

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The complete question is:

Answer:

thats 4th grade math... 0_0               but the answer is 414 ft².

Step-by-step explanation:

So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo

Answer:

-4 + 8 = 4

-2 + 6 = 4

-1 + 5 = 4

So the three pairs are -4 and 8; -2 and 6; and -1 and 5.

Hence, the cylinder segment's longest side measures about 2.5 inches as the other two sides are the segment's height .

The width of a circle in geometry is the separation between any two or more points on the ring that pass through the centre. It is the longest chord that may divide a circle to two equal half, which are referred to as semicircles. The radius of a circle, which corresponds to the distance between any two points on its circumference, and the diameter, which is sometimes symbolised by the letter "d," are connected by the following formula: d = 2r where r denotes the circle's radius. In many mathematics, such as geometry, trigonometry, and calculus, the diameter is a significant measurement scale.

given

We can first create a diagram of the cylinder portion to help us tackle this issue. We are aware that the cylinder has a 4 inch diameter, which indicates that its radius is 2 inches.

The diagonal "d" in this instance serves as the hypotenuse, while the other two sides are the segment's height (which is equal to the cylinder's radius, or 2 inches), and half of its length (which is 3/2 inches).

Hence, we can construct the equation:

D2 is equal to (2 inches) + (3/2 inches).

If we simplify, we get:

[tex]d^2 = 4 + 2.25\\d^2 = 6.25[/tex]

When we square the two sides, we obtain:

2.5 inches for d

Hence, the cylinder segment's longest side measures about 2.5 inches as the other two sides are the segment's height .

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Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

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Answer:

125cm^2

Step-by-step explanation:

the area of a triangle is b*h/2 and area of a square is side*side so since the area of the square is 25 the side length must be 5 because 5*5=25

that being said we use 5 as base for the triangles and 10 as height

area of a triangle= 5*10/2=25 since there are 4 triangles 25*4=100cm^2 +square base (25 cm^2)=125cm^2

Answer:

1  17/30.

Step-by-step explanation:

you can find this out by seeing how many 30s go into 47 which is 1.

Then subtract to find how much is leftover still over 30.

47 - 30 = 17

So 1 and 17/30

Answer: c. 9

Step-by-step explanation:

The cost of pizza with no toppings is $6. So correct option is C.

A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.

There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.

Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.

Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.

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The complete question is:

To find the constant k for this type of bacteria, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.

We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:

N(25) = 2 * N0

Substituting this into the formula, we get:

2 * N0 = N0 * e^(k*25)

Dividing both sides by N0 and simplifying, we get:

2 = e^(25k)

Taking the natural logarithm of both sides, we get:

ln(2) = 25k

Solving for k, we get:

k = ln(2)/25 ≈ 0.0278

Therefore, the equation for modeling the exponential growth of this type of bacteria is:

N(t) = N0 * e^(0.0278t)

*IG:whis.sama_ent

a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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Answer:   2(b - 6) = 7

Step-by-step explanation:

"b" represents the unknown number.

6" means (b - 6), and "twice the difference of a number and 6" means 2(b - 6). "Is" translates to the equals sign (=) in the equation, and "7" represents the value that the expression on the left side of the equation is equal to.

The expression represented by the model is 4. 6/13 - 2/7.

Expression in math is a combination of numbers, symbols, and operators, such as variables and constants, used to represent a mathematical relationship. It can be used to represent the solution of a problem or the evaluation of a function. Expressions are used in algebra, calculus, and other branches of mathematics to describe the relationships between different elements.

This expression can be seen by looking at the model; the shaded portion represents the fraction 6/13 and the portion that was subtracted from it is 2/7. Thus, the expression represented by the model is 6/13 - 2/7.

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