The perimeter of a scene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2cm?

For the function f(x) = x + 2, the value of x when f(x) = 1, gives x = -1

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Given that:

f(x) = x + 2

When f(x) = 1, substituting:

1 = x + 2

x = -1

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The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Answer: 36 and 22 A=396

Step-by-step explanation:

half of 1 diagonal is 18, so the whole diagonal is 36

the other diagonal half is 11 so the whole is 22

put 36 and 22 into the boxes

then solve

\(A=\frac{1}{2} (36*22)\\A=396\)

Answer:

A = 99 in²

Step-by-step explanation:

Using the given formula with d₁ = 18 and d₂ = 11 , then

A = \(\frac{1}{2}\) × 18 × 11 = 9 × 11 = 99 in²

Answer:

9th min?

Step-by-step explanation:

lol sorry im set 4 maths

144π cm²/min is the surface area of the ball increasing when the radius is 9 cm.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given,

Radius of a spherical ball is increasing at a rate of 2 cm/min.

We need to find exactly what rate (in cm2/min) is the surface area of the ball increasing when the radius is 9 cm

S = surface area at time t,  and r = radius at time t

r=9cm

dr/dt = 2 cm/min

S = 4πr²

Differentiate with respect to t

ds/dt=2.4πrdr/dt

=8πr(2)

=16πr

=16π(9cm)

=144π cm²/min

Hence 144π cm²/min is the surface area of the ball increasing when the radius is 9 cm.

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Answer:

-141 is the answer.

Answer:

120

10 12

2 5 2 6

2 3

150

10 15

2 5 3 5

Step-by-step explanation:

120= 2x2x2x3x5

150= 2x3x5x5

Multiply all the common prime factors.

2x3x5

HCF= 30

The answer of the above question is [0,30]

An absolute value inequality is one with an absolute value sign and a variable inside.

An important point to remember: | x |= {x if x ≥ 0 }

| x |= {x if x< 0}

taking the expression  |-2z+30| ≤ 30

Write the equivalent compound inequality.

-30≤ -2z+30 ≤ 30

= -30-30 ≤ -2z ≤ 30-30

= -60≤ -2z ≤ 0

= -60/2 ≤ -z  ≤ 0

= -30 ≤ -z  ≤ 0

Solve the compound inequality.

= 0 ≥ z ≥ 30 (reversing of signs)

Hence, the solution using interval notation  [0,30].The check is left to you.

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Answer:

a. \(Probability = 0.2496\)

b. No, it won't change

Step-by-step explanation:

Represent \(the\ head\) with H and \(Tail\ with\) T

Such that:

\(P(H) = 48\%\)

Solving (a): First head in second trial

First, we determine P(T) i.e. the probability of obtaining a tail

\(P(H)+P(T) = 100\%\)

\(P(T) = 100\% -P(H)\)

Substitute 48% for P(H)

\(P(T) = 100\% -48\%\)

\(P(T) = 52\%\)

If the first head is obtained in the second trial, the probability is:

\(Probability = P(T\ and\ H)\)

\(Probability = P(T)\ and\ P(H)\)

\(Probability = P(T)\ *\ P(H)\)

\(Probability = 48\%* 52\%\)

\(Probability = 0.2496\)

Solving (b): Will it change if tossed three or four times?

Irrespective of the number of times the coin is tossed, the probability of obtaining a head in the second toss will always be the same because the coin has to be tossed twice before the third and the fourth time.

I think its D I hope you do good on your test! Good luck!

The equation that models the situation is  y = -8t + 212

After 4 days, a bookstore has 140 copies of a new title still on hand. After 9 days, the bookstore has 50 copies still on hand.

The situation can be modelled in a linear form, c(t) = mt + b as follows:

where

Therefore, using (4, 140)(9, 50)

m = slope = 50 - 140 / 9 - 4

m = - 90 / 5

slope = - 18

Hence,

c(t) = mt + b

where

Therefore, let's find c using (9, 50)

c(t) = - 18t + c

50 = -18(9) + c

50 + 162 = c

c = 212

Therefore, the equation is y = -18t + 212

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The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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Answer:

False ;

False ;

False

Step-by-step explanation:

In a perfectly symmetric distribution, the mean and Median values are the same. But for skewed distributon, the median is greater than the mean (negatively skewed or left skewed data). Hence, the assertion is false.

The sign of the correlation Coefficient does not give information about how good a line fits. The sign attached to the correlation Coefficient gives information about the slope and hence, the type of relationship between the variables.

Positive (+) sign = positive relationship between variables ; negative (-) sign = negative relationship between variables.

C.)

The value of the range is not always higher Than the value of the interquartile range. The IQR might have the same value as the value of the range.

For instance :

Given the data :

1, 1, 1, 2, 2, 3, 4, 4, 4

Range = maximum - minimum

Range = 4 - 1 = 3

Interquartile range (IQR) :

IQR = Q3 - Q1

Q3 = 3/4(n+1)th term

Q3 = 3/4(10) = 7.5th term

Q3 = (7th + 8th) / 2 = (4+4)/2 = 4

Q1 = 1/4(10) = 2.5th term

Q1 = (2nd + 3rd) / 2

Q1 = (1 + 1) /2 = 1

Q3 - Q1 = 4 - 1 = 3

Hello!

The distance, d, is less than 200 miles.

B. d > 200

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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Answer:

You gained 2.14lbs

Step-by-step explanation:

My opinion

the total lbs you gained is 107 lbs + (107 lbs x 2%) = 109.14 lbs

then you subtract the total for the initial lbs

it will be 109.14 lbs - 107 lbs = 2.14 lbs

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The best way for us to identify which function type would each data set corresponds is to plot the given points. Let's plot the points given to us and identify what type of function does the plot corresponds to.

A. The plot for the set A is

Based on the shown plot, we can see a linear plot, hence, set A is a linear function.

B. The plot for the set B is

Based on the shown plot, there is a sudden increase in value of y per increasing value of x, hence, set B can be classified as an exponential function.

C. The plot for the set C is

The plot shows a curve behavior going up, which means that set C can be classified as a quadratic function.

D. The plot for the set D is

Based on the shown plot, there is a sudden increase in value of y per increasing value of x, hence, set D can be classified as an exponential function.

Answer:

24

Step-by-step explanation:

The the triangles are similar, the lengths of corresponding sides are in proportion.

15/20 = 18/n

3/4 = 18/n

1/4 = 6/n

n = 4 × 6

n = 24

Answer:

n = 24

Step-by-step explanation:

In similar triangles, corresponding sides are in same ratio.

\(\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24\)

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Step-by-step explanation:

See image below

Answer: 37cm²

Step-by-step explanation:

1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

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

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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The probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

f = 100 stamps in the collection

A = stamps in the 20th century

B = British stamps

We can make a linear equation to solve for x as the total stamps are 100 in the collection.

\(\rm x(x-6)+x+2x+32= 100\\\\\rm x^2-6x+x+2x+32 = 100\\\\\rm x^2-3x-68 = 0\)

After solving x = 9.88, or x = -6.88

Probability can't be negative so neglecting the negative ones

x = 9.88

The probability that it is British:

\(=\rm \frac{x +2x + 32}{100}\)  

\(=\rm \frac{9.88 +2(9.88) + 32}{100}\)

= 61.64/100

= 0.6164

Thus, the probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

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The given function for peanuts is continuous function.

A continuous function, as the name implies, refers to one for whom the graph is continuous without a breaks or jumps.

For the given expression in the question;

The relation between the cost 'c' and wight 'p' in pounds for the peanuts is given as;

c = 1.5p

As, you can see that the expression is a polynomial having two variables with the highest degree 1.

And, as we know that the every polynomial is a continuous function.

The given function forms a straight line on as for every different real value of p there s single value of c, which varies linearly.

Therefore, the function c = 1.5p is a continuous function forming a straight line.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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